Tuesday, October 29, 2013
Drunk and disorderly:
the rise (and fall) of entropy
Revised version of an Angelfire page published ca. 2010
Tip: use "control f" to quickly access footnotes other significant items
Consider using a service such as ChangeDetection.com to keep track of revisions to this page.
Please let me know about errors or points in need of clarifying at krypto78 attt gmaaail dottt commm.
Please see The many worlds of probability, reality and cognition; Part V focuses on the topic of entropy.
http://randompaulr.blogspot.com/2013/11/the-many-worlds-of-probability-reality.html
My thoughts on probability in the current paper should be taken as provisional.
0. Taken from a Wikipedia article: The dimension of thermodynamic entropy is energy divided by temperature, and its SI unit is joules per kelvin. In information theory, entropy is a measure of the uncertainty associated with a random variable. In this context, the term usually refers to the Shannon entropy, which quantifies the expected value of the information contained in a message, usually in units such as bits. Equivalently, the Shannon entropy is a measure of the average information content one is missing when one does not know the value of the random variable. The concept was introduced by Claude E. Shannon in his 1948 paper "A Mathematical Theory of Communication."
1. We should caution that the runs test, which works for n1 > 7 and n2 > 7, fails for the pattern HH TT HH TT... This failure seems to be an artifact of the runs test assumption that a usual number of runs is about n/2. I suggest that we simply say that the probability of that pattern is less than or equal to H T H T H T..., a pattern whose z score rises rapidly with n. Other patterns such as HHH TTT HHH... also climb away from the randomness area slowly with n. With these cautions, however, the runs test gives striking results.
2. Taken from Wikipedia: In information theory, entropy is a measure of the uncertainty associated with a random variable. In this context, the term usually refers to the Shannon entropy, which quantifies the expected value of the information contained in a message, usually in units such as bits. Equivalently, the Shannon entropy is a measure of the average information content one is missing when one does not know the value of the random variable. The concept was introduced by Claude E. Shannon in his 1948 paper "A Mathematical Theory of Communication." Shannon's entropy represents an absolute limit on the best possible lossless compression of any communication, under certain constraints: treating messages to be encoded as a sequence of independent and identically-distributed random variables, Shannon's source coding theorem shows that, in the limit, the average length of the shortest possible representation to encode the messages in a given alphabet is their entropy divided by the logarithm of the number of symbols in the target alphabet. A fair coin has an entropy of one bit. However, if the coin is not fair, then the uncertainty is lower (if asked to bet on the next outcome, we would bet preferentially on the most frequent result), and thus the Shannon entropy is lower. Mathematically, a coin flip is an example of a Bernoulli trial, and its entropy is given by the binary entropy function. A long string of repeating characters has an entropy rate of zero, since every character is predictable. The entropy rate of English text is between 1.0 and 1.5 bits per letter, or as low as 0.6 to 1.3 bits per letter, according to estimates by Shannon based on human experiments.
3. John Allen Paulos on Ramsey theory: 'A more profound version of this line of thought can be traced back to British mathematician Frank Ramsey, who proved a strange theorem. It stated that if you have a sufficiently large set of geometric points and every pair of them is connected by either a red line or a green line (but not by both), then no matter how you color the lines, there will always be a large subset of the original set with a special property. Either every pair of the subset's members will be connected by a red line or every pair of the subset's members will be connected by a green line. If, for example, you want to be certain of having at least three points all connected by red lines or at least three points all connected by green lines, you will need at least six points. (The answer is not as obvious as it may seem, but the proof isn't difficult.) For you to be certain that you will have four points, every pair of which is connected by a red line, or four points, every pair of which is connected by a green line, you will need 18 points, and for you to be certain that there will be five points with this property, you will need -- it's not known exactly - between 43 and 55. With enough points, you will inevitably find unicolored islands of order as big as you want, no matter how you color the lines.'
Revised Oct. 29, 2013
the rise (and fall) of entropy
Revised version of an Angelfire page published ca. 2010
Tip: use "control f" to quickly access footnotes other significant items
Consider using a service such as ChangeDetection.com to keep track of revisions to this page.
Please let me know about errors or points in need of clarifying at krypto78 attt gmaaail dottt commm.
Please see The many worlds of probability, reality and cognition; Part V focuses on the topic of entropy.
http://randompaulr.blogspot.com/2013/11/the-many-worlds-of-probability-reality.html
My thoughts on probability in the current paper should be taken as provisional.
By PAUL CONANT
One might describe the increase of the entropy (FN 0) of a gas to mean that the net vector -- sum of vectors of all particles -- at between time t0 and tn tends toward some constant, such as 0, and that once this equilibrium is reached at tn, the net vector stays near 0 at any subsequent time.
One would expect a nearly 0 net vector if the individual particle vectors are random. This randomness is exactly what one would find in an asymmetrical n-body scenario, where the bodies are close together and about the same size. The difference is that gravity isn't the determinant, but rather collisional kinetic energy. It has been demonstrated that n-body problems can yield orbits that become extraordinarily tangled. The randomness is then of the Chaitin-Kolmogorov variety: determining future position of a particular particle becomes computationally very difficult. And usually, over some time interval, the calculation errors increase to the point that all predictability for a specific particle is lost.
But there is also quantum randomness at work. The direction that an excited photon exits an atom is probabilistic only, meaning that the recoil is random. This recoil vector must be added to the other electric charge recoil vector associated with particle collision -- though its effect is very slight and usually ignored. Further, if one were to observe one or more of the particles, the observation would affect the knowledge of the momentum or position of the observed particles. Now supposing we keep the gas at a single temperature in a closed container attached via a closed valve to another evacuated container, when we open the valve, the gas expands to fill both containers. This expansion is a consequence of the effectively random behavior of the particles, which on average "find less resistance" in the direction of the vacuum.
In general, gases tend to expand by inverse square, or that is spherically (or really, as a ball), which implies randomization of the molecules.
The drunkard's walk
Consider a computerized random walk (aka "drunkard's walk") in a plane. As n increases, the area covered by the walk tends toward that of a circle. In the infinite limit, there is probability 1 that a perfect circle has been covered (though probability 1 in such cases does not exclude exceptions).
So the real question is: what about the n-body problem yields pi-randomness? It is really a statistical question. When enough collisions occur in a sufficiently small volume (or area), the particle vectors tend to cancel each other out.
Let's go down to the pool hall and break a few racks of balls. It is possible to shoot the cue ball in such a way that the rack of balls scatters symmetrically. But in most situations, the cue ball strikes the triangular array at a point that yields an asymmetrical scattering. This is the sensitive dependence on initial conditions associated with mathematical chaos. We also see Chaitin-Kolmogorov complexity enter the picture, because the asymmetry means that for most balls predicting where one will be after a few ricochets is computationally very difficult.
Now suppose we have perfectly inelastic, perfectly spherical pool balls that encounter idealized banks. We also neglect friction. After a few minutes, the asymmetrically scattered balls are "all over the place" in effectively random motion. Now such discrete systems eventually return to their original state: the balls coalesce back into a triangle and then repeat the whole cycle over again, which implies that in fact such a closed system, left to its own devices, requires that entropy to decrease, a seeming contradiction of the second law of thermodynamics. But the time scales required mean we needn't hold our breaths waiting. Also, in nature, there are darned few closed systems (and as soon as we see one, it's no longer closed at the quantum level), allowing us to conclude that in the ideal of zero friction, the pool ball system may become aperiodic, implying the second law in this case holds.
Maxwell's demon
And now, let us exorcize Maxwell's demon, which, though meant to elucidate, to this day bedevils discussions of entropy with outlandish "solutions" to the alleged "problem." Maxwell gave us a thought experiment whereby he posited a little being controlling the valve between canisters. If (in this version of his thought experiment) the gremlin opened the valve to let speedy particles past in one direction only, the little imp could divide the gas into a hot cloud in one canister and a cold cloud in the other. Obviously the energy the gremlin adds is equivalent to adding energy via a heating/cooling system, but Maxwell's point was about the very, very minute possibility that such a bizarre division could occur randomly (or, some would say, pseudo-randomly).
This possibility exists. In fact, as said, in certain idealized closed systems, entropy decrease MUST happen. Such a spontaneous division into hot and cold clouds would also probably happen quite often at the nano-nano-second level. That is, when time intervals are short enough, quantum physics tells us the usual rules go out the window. However, observation of such actions won't occur for such quantum intervals (so there is no change in information or entropy), and as for the "random" chance of observing an extremely high-ordering of gas molecules, even if someone witnessed such an occurrence, not only does the event not conform to a repeatable experiment, no one is likely to believe the report, even if true.
Truly universal?
Can we apply the principle of entropy to the closed system of the universe? A couple of points: We're not absolutely sure the cosmos is a closed system (perhaps, for example, "steady state" creation supplements "big bang" creation). If there is a "big crunch," then, some have speculated, we might expect complete devolution to original states (people would reverse grow from death to birth, for example). If space curvature implies otherwise, the system remains forever open or asymptotically forever open.
However, quantum fuzziness probably rules out such an idealization. Are quantum systems precisely reversible? Yes and no. When one observes a particle collision in an accelerator, one can calculate the reverse paths. However, in line with the Heisenberg uncertainty principle one can never be sure of observing a collision with precisely identical initial conditions. And if we can only rarely, very rarely, replicate the exact initial conditions of the collision, then the same holds for its inverse.
Then there is the question of whether perhaps a many worlds (aka parallel universes) or many histories interpretation of quantum weirdness holds. In the event of a collapse back toward a big crunch, would the cosmos tend toward the exact quantum fluctuations that are thought to have introduced irregularities in the early universe that grew into star and galactic clustering? Or would a different set of fluctuations serve as the attractor, on grounds both sets were and are superposed and one fluctuation is as probable as the other? And, do these fluctuations require a conscious observer, as in John von Neumann's interpretation?
Thinking in terms of computer-like algorithms, Stephen Wolfram writes in A New Kind of Science that it is unclear whether the "basic rules of the universe are really reversible," arguing that it could be that apparent reversibility arises due to effects of an attractor (he does not specify gravitational). He writes that "if pieces of the universe can break off but not reconnect, then there will be inevitably loss of information," thus increasing entropy. Of course, we face such difficulties when trying to apply physical or mathematical concepts to the entire cosmos. It seems plausible that any system of relations we devise to examine properties of space and time may act like a lens that increases focus in one area while losing precision in another. I.e., a cosmic uncertainty principle.
Conservation of information?
A cosmic uncertainty principle would make information fuzzy. As the Heisenberg uncertainty principle shows, information about a particle's momentum is gained at the expense of information about its position. But, you may respond, the total information is conserved.
But wait! Is there a law about the conservation of information? In fact, information cannot be conserved -- in fact can't exist -- without memory, which in the end requires the mind of an observer. In fact, the "law" of increase of entropy says that memories fade and available information decreases. In terms of pure Shannon information, entropy expresses the probability of what we know or don't know.2 Thus entropy is introduced by noise entering the signal. In realistic systems, supposing enough time elapses, noise eventually overwhelms the intended signal. For example, what would you say is the likelihood that this essay will be accessible two centuries from now? (I've already lost a group of articles I had posted on the now defunct Yahoo Geocities site.) Or consider Shakespeare's plays. We cannot say with certainty exactly how the original scripts read.
In fact, can we agree with some physicists that a specified volume of space contains a specific quantity of information? I wonder. A Shannon transducer is said to contain a specific quantity of information, but no one can be sure of that, prior to someone reading the message and measuring the signal-to-noise ratio. And quantum uncertainty qualifies as a form of noise, not only insofar as random jiggles in the signal, but also insofar as what signal was sent. If two signals are "transmitted" in quantum superposition, observation randomly determines which signal is read.
So one may set up a quantum measurement experiment and say that for a specific volume, the prior information describes the experiment. But quantum uncertainty still says that the experiment cannot be exactly described in a scientifically sensible way. So if we try to extrapolate information about a greater volume from the experiment volume, we begin to lose accuracy until the uncertainty reaches maximum. We see that quantum uncertainty can progressively change the signal-to-noise ratio, meaning entropy increases until the equilibrium level of no knowledge.
This of course would suggest that, from a human vantage point, there can be no exact information quantity for the cosmos.
So this brings us to the argument about whether black holes decrease the entropy of the universe by making it more orderly (i.e., simpler). My take is that a human observer in principle can never see anything enter a black hole. If one were to detect, at a safe distance, an object approaching a black hole, one would observe that its time pulses (its Doppler shift) would get slower and slower. In fact, the time pulses slow down asymptotic to eternity. So the information represented by the in-falling object is, from this perspective, never lost.
But suppose we agree to an abstraction that eliminates the human observer -- as opposed to a vastly more gifted intelligence. In that case, perhaps the cosmos has an exact quantity of information at ta. It then makes sense to talk about whether a black hole affects that quantity.
Consider a particle that falls into a black hole. It is said that all the information available about a black hole is comprised of the quantities for its mass and its surface area. Everything this super-intelligence knew about the particle, or ever could know, seemingly, is gone. Information is lost and the cosmos is a simpler, more orderly place, higher in information and in violation of the second law... maybe.
But suppose the particle is a twin of an entangled pair. One particle stays loose while the other is swallowed by the black hole. If we measure, say, the spin of one such particle we would ordinarily automatically know the spin of the other. But who's to tell what the spin is of a particle headed for the gravitational singularity at the black hole's core? So the information about the particle vanishes and entropy increases. This same event however means the orderliness of the universe increases and the entropy decreases. So, which is it? Or is it both. Have no fear, this issue is addressed in the next section.
Oh, and of course we mustn't forget Hawking radiation, whereby a rotating black hole slowly leaks radiation as particles every now and then "tunnel" through the gravitational energy barrier and escape into the remainder cosmos. The mass decreases over eons and eons until -- having previously swallowed everything available -- it eventually evaporates, Hawking conjectures. Actually, we needn't invoke tunneling; the condition that the object is rotating means that it has kinetic energy; some quanta of energy associated with rotational acceleration are at the event horizon and are energetic enough to escape the gravity field, assuming they are vectored appropriately.
Hawking's updated black hole view
http://www.nature.com/news/2004/040712/full/news040712-12.html
In 2005, Hawking revived a long-simmering argument about black holes and entropy.
"I'm sorry to disappoint science fiction fans, but if information is preserved, there is no possibility of using black holes to travel to other universes. If you jump into a black hole, your mass energy will be returned to our universe but in a mangled form which contains the information about what you were like but in a state where it can not be easily recognized. It is like burning an encyclopedia. Information is not lost, if one keeps the smoke and the ashes. But it is difficult to read. In practice, it would be too difficult to re-build a macroscopic object like an encyclopedia that fell inside a black hole from information in the radiation, but the information preserving result is important for microscopic processes involving virtual black holes."
Information loss in black holes
http://arxiv.org/pdf/hepth/0507171.pdf
A question: suppose an entangled particle escapes the black hole? Is the cosmic information balance sheet rectified? Perhaps, supposing it never reached the singularity. But, what of particles down near the singularity? They perhaps morph as the fields transform into something that existed close to the cosmic big bang. So it seems implausible that the spin information is retained. But, who knows?
Where's that ace?
There is a strong connection between thermodynamic entropy and Shannon information entropy (FN 0). Consider the randomization of the pool break on the frictionless table after a few minutes. This is the equivalent of shuffling a deck of cards. Suppose we have an especially sharp-eyed observer who watches where the ace of spades is placed in the deck as shuffling starts. We then have a few relatively simple shuffles. After the first shuffle, he knows to within three cards how far down in the deck the ace is. On the next shuffle he knows where it is with less accuracy. Let's say to a precision of (1/3)(1/3) = 1/9. After some more shuffles his potential error has reached 1/52, meaning he has no knowledge of the ace's whereabouts.
The increase in entropy occurs from one shuffle to the next. But at the last shuffle, equilibrium has been reached. Further shuffling can never increase his knowledge of where the ace is, meaning the entropy won't decrease. The runs test gives a measure of randomness (FN 1) based on the normal distribution of numbers of runs, with the mean at n/2, "Too many" runs are found in one tail and "too few" in another. That is, a high z score implies that the sequence is suspected of being non-random or "highly ordered."
What however is meant by order? (This is where we tackle the conundrum of a decrease in one sort of cosmic information versus an increase in another sort.)
Entropy is often defined as the tendency toward decrease of order, and the related idea of information is sometimes thought of as the surprisal value of a digit string. Sometimes a pattern such as HHHH... is considered to have low information because we can easily calculate the nth value (assuming we are using some algorithm to obtain the string). So the Chaitin-Kolmogorov complexity is low, or that is, the information is low. On the other hand a string that by some measure is effectively random is considered here to be highly informative because the observer has almost no chance of knowing the string in detail in advance.
However, we can also take the opposite tack. Using runs testing, most digit strings (multi-value strings can often be transformed, for test purposes, to bi-value strings) are found under the bulge in the runs test bell curve and represent probable randomness. So it is unsurprising to encounter such a string. It is far more surprising to come across a string with far "too few" or far "too many" runs. These highly ordered strings would then be considered to have high information value.
So, once the deck has been sufficiently shuffled the entropy has reached its maximum (equilibrium). What is the probability of drawing four royal flushes? If we aren't considering entropy, we might say it is the same as that for any other 20-card deal. But, a runs test would give a z score of infinity (probability 1 that the deal is non-random) because drawing all high cards is equivalent to tossing a fair coin and getting 20 heads and no tails. If we don't like the infinitude we can posit 21 cards containing 20 high cards and 1 low card. The z score still implies non-randomness with a high degree of confidence.
Negative entropy?
Our discussion should not ignore the impact of Ramsey theory, an important subdiscipline of network theory. "Self-organizing" possibilities are inevitable with sufficient number of nodes in a network. In fact, one might argue that Ramsey theory implies negative entropy. Suppose we had n poker players. The probability that among them there is a royal flush skyrockets quite rapidly. So as n increases, the probability of a specific set of cards increases and the information surprisal value decreases (FN 3).
0. Taken from a Wikipedia article: The dimension of thermodynamic entropy is energy divided by temperature, and its SI unit is joules per kelvin. In information theory, entropy is a measure of the uncertainty associated with a random variable. In this context, the term usually refers to the Shannon entropy, which quantifies the expected value of the information contained in a message, usually in units such as bits. Equivalently, the Shannon entropy is a measure of the average information content one is missing when one does not know the value of the random variable. The concept was introduced by Claude E. Shannon in his 1948 paper "A Mathematical Theory of Communication."
1. We should caution that the runs test, which works for n1 > 7 and n2 > 7, fails for the pattern HH TT HH TT... This failure seems to be an artifact of the runs test assumption that a usual number of runs is about n/2. I suggest that we simply say that the probability of that pattern is less than or equal to H T H T H T..., a pattern whose z score rises rapidly with n. Other patterns such as HHH TTT HHH... also climb away from the randomness area slowly with n. With these cautions, however, the runs test gives striking results.
2. Taken from Wikipedia: In information theory, entropy is a measure of the uncertainty associated with a random variable. In this context, the term usually refers to the Shannon entropy, which quantifies the expected value of the information contained in a message, usually in units such as bits. Equivalently, the Shannon entropy is a measure of the average information content one is missing when one does not know the value of the random variable. The concept was introduced by Claude E. Shannon in his 1948 paper "A Mathematical Theory of Communication." Shannon's entropy represents an absolute limit on the best possible lossless compression of any communication, under certain constraints: treating messages to be encoded as a sequence of independent and identically-distributed random variables, Shannon's source coding theorem shows that, in the limit, the average length of the shortest possible representation to encode the messages in a given alphabet is their entropy divided by the logarithm of the number of symbols in the target alphabet. A fair coin has an entropy of one bit. However, if the coin is not fair, then the uncertainty is lower (if asked to bet on the next outcome, we would bet preferentially on the most frequent result), and thus the Shannon entropy is lower. Mathematically, a coin flip is an example of a Bernoulli trial, and its entropy is given by the binary entropy function. A long string of repeating characters has an entropy rate of zero, since every character is predictable. The entropy rate of English text is between 1.0 and 1.5 bits per letter, or as low as 0.6 to 1.3 bits per letter, according to estimates by Shannon based on human experiments.
3. John Allen Paulos on Ramsey theory: 'A more profound version of this line of thought can be traced back to British mathematician Frank Ramsey, who proved a strange theorem. It stated that if you have a sufficiently large set of geometric points and every pair of them is connected by either a red line or a green line (but not by both), then no matter how you color the lines, there will always be a large subset of the original set with a special property. Either every pair of the subset's members will be connected by a red line or every pair of the subset's members will be connected by a green line. If, for example, you want to be certain of having at least three points all connected by red lines or at least three points all connected by green lines, you will need at least six points. (The answer is not as obvious as it may seem, but the proof isn't difficult.) For you to be certain that you will have four points, every pair of which is connected by a red line, or four points, every pair of which is connected by a green line, you will need 18 points, and for you to be certain that there will be five points with this property, you will need -- it's not known exactly - between 43 and 55. With enough points, you will inevitably find unicolored islands of order as big as you want, no matter how you color the lines.'
Revised Oct. 29, 2013
Monday, October 28, 2013
Einstein, Sommerfeld and the twin paradox
Please notify me of errors at Krypto78 attt gmaaail dottt commm
Topologist Jeff Weeks on the twin paradox
http://www.math.uic.edu/undergraduate/mathclub/talks/Weeks_AMM2001.pdf
Michel Janssen's paper
https://netfiles.umn.edu/users/janss011/home%20page/rel-of-grav-field.pdf
The paradox
Einstein's groundbreaking 1905 relativity paper, "On the electrodynamics of moving bodies," contained a fundamental inconsistency which was not addressed until 10 years later, with the publication of his paper on gravitation.
Many have written on this inconsistency, known as the "twin paradox" or the "clock paradox" and more than a few have not understood that the "paradox" does not refer to the strangeness of time dilation but to a logical inconsistency in what is now known as the special (for "special case") theory of relativity.
Among those missing the point: Max Born in his book on special relativity (1), George Gamow in an essay and Roger Penrose in Road to Reality (2), and, most recently, Leonard Susskind in The Black Hole War (3).
Among those who have correctly understood the paradox are topologist Jeff Weeks (see link above) and science writer Stan Gibilisco (4), who noted that the general theory of relativity resolves the problem.
As far back as the 1960s, the British physicist Herbert Dingle (5) called the inconsistency a "regrettable error" and was deluged with "disproofs" of his assertion from the physics community. (It should be noted that Dingle's 1949 attempt at relativistic physics left Einstein bemused (6). Yet every "disproof" of the paradox that I have seen uses acceleration, an issue not addressed by Einstein until the general theory of relativity. It was Einstein who set himself up for the paradox by favoring the idea that only purely relative motions are meaningful, writing that various examples "suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest." [Electrodynamics translated by Perett and Jeffery and appearing in a Dover (1952) reprint.] In that paper, he also takes pains to note that the term "stationary system" is a verbal convenience only (7).
But later in Elect., Einstein offered the scenario of two initially synchronized clocks at rest with respect to each other. One clock then travels around a closed loop, and its time is dilated with respect to the at-rest clock when they meet again. In Einstein's words: "If we assume that the result proved for a polygonal line is also valid for a continuously curved line, we arrive at this result: If one of two synchronous clocks at A is moved in a journey lasting t seconds, then by the clock which has remained at rest the traveled clock on its arrival at A will be 1/2tv2/c2 slow."
Clearly, if there is no preferred frame of reference, a contradiction arises: when the clocks meet again, which clock has recorded fewer ticks?
Both in the closed loop scenario and in the polygon-path scenario, Einstein avoids the issue of acceleration. Hence, he does not explain that there is a property of "real" acceleration that is not symmetrical or purely relative and that that consequently a preferred frame of reference is implied, at least locally.
The paradox stems from the fact that one cannot say which velocity is higher without a "background" reference frame. In Newtonian terms, the same issue arises: if one body is accelerating away from the other, how do we know which body experiences the "real" force? No answer is possible without more information, implying a background frame.
In comments published in 1910, the physicist Arnold Sommerfeld, a proponent of relativity theory, "covers" for the new paradigm by noting that Einstein didn't really mean that time dilation was associated with purely relative motion, but rather with accelerated motion; and that hence relativity was in that case not contradictory. Sommerfeld wrote: "On this [a time integral and inequality] depends the retardation of the moving clock compared with the clock at rest. The assertion is based, as Einstein has pointed out, on the unprovable assumption that the clock in motion actually indicates its own proper time; i.e. that it always gives the time corresponding to the state of velocity, regarded as constant, at any instant. The moving clock must naturally have been moved with acceleration (with changes of speed or direction) in order to be compared with the stationary clock at world-point P. The retardation of the moving clock does not therefore actually indicate 'motion,' but 'accelerated motion.' Hence this does not contradict the principle of relativity." [Notes appended to Space and Time, a 1908 address by Herman Minkowski, Dover 1952, Note 4.]
However, Einstein's 1905 paper does not tackle the issue of acceleration and more to the point, does not explain why purely relative acceleration would be insufficient to meet the facts. The principle of relativity applies only to "uniform translatory motion" (Elect. 1905).
Neither does Sommerfeld's note address the issue of purely relative acceleration versus "true" acceleration, perhaps implicitly accepting Newton's view (below). And, a review of various papers by Einstein seems to indicate that he did not deal with this inconsistency head-on, though in a lecture-hall discussion ca. 1912, Einstein said that the [special] theory of relativity is silent on how a clock behaves if forced to change direction but argues that if a polygonal path is large enough, accelerative effects diminish and (linear) time dilation still holds.
On the other hand, of course, he was not oblivious to the issue of acceleration. In 1910, he wrote that the principle of relativity meant that the laws of physics are independent of the state of motion, but that the motion is non-accelerated. "We assume that the motion of acceleration has an objective meaning," he said. [The Principle of Relativity and its Consequences in Modern Physics, a 1910 paper reproduced in Collected Papers of Albert Einstein, Hebrew University, Princeton University Press.]
In that same paper Einstein emphasizes that the principle of relativity does not cover acceleration. "The laws governing natural phenomena are independent of the state of motion of the coordinate system to which the phenomena are observed, provided this system is not in accelerated motion." Clearly, however, he is somewhat ambiguous about small accelerations and radial acceleration, as we see from the lecture-hall remark and from a remark in Foundation of the General Theory of Relativity (1915) about a "familiar result" of special relativity whereby a clock on a rotating disk's rim ticks slower than a clock at the origin.
General relativity's partial solution
Finally, in his 1915 paper on general relativity, Einstein addressed the issue of acceleration, citing what he called "the principle of equivalence." That principle (actually, introduced prior to 1915) said that there was no real difference between kinematic acceleration and gravitational acceleration. Scientifically, they should be treated as if they are the same.
So then, Einstein notes in Foundation, if we have system K and another system K' accelerating with respect to K, clearly, from a "Galilean" perspective, we could say that K was accelerating with respect to K'. But, is this really so?
Einstein argues that if K is at rest relative to K', which is accelerated, the oberserver on K cannot claim that he is being accelerated -- even though, in purely relative terms, such a claim is valid. The reason for this rejection of Galilean relativity: We may equally well interpret K' to be kinematically unaccelerated though the "space-time territory in question is under the sway of a gravitational field, which generates the accelerated motion of the bodies" in the K' system. This claim is based on the principle of equivalence which might be considered a modification of his previously posited principle of relativity. By the relativity principle, Einstein meant that the laws of physics can be cast in invariant form so that they apply equivalently in any unformly moving frame of reference. (For example, |vb - va| is the invariant quantity that describes an equivalence class of linear velocities.)
By the phrase "equivalence," Einstein is relating impulsive acceleration (for example, a projectile's x vector) to its gravitational acceleration (its y vector). Of course, Newton's mechanics already said that the equation F = mg is a special case of F = ma but Einstein meant something more: that local spacetime curvature is specific for "real" accelerations -- whether impulsive or gravitational.
Einstein's "equivalence" insight was his recognition that one could express acceleration, whether gravitational or impulsive, as a curvature in the spacetime continuum (a concept introduced by Minkowski). This means, he said, that the Newtonian superposition of separate vectors was not valid and was to be replaced by a unitary curvature. (Though the calculus of spacetime requires specific tools, the concept isn't so hard to grasp. Think of a Mercator map: the projection of a sphere onto a plane. Analogously, general relativity projects a 4-dimensional spacetime onto a Euclidean three-dimensional space.)
However, is this "world-line" answer the end of the problem of the asymmetry of accelerated motion?
The Einstein of 1915 implies that if two objects have two different velocities, we must regard one as having an absolutely higher velocity than the other because one object has been "really" accelerated.
Yet one might conjecture that if two objects move with different velocities wherein neither has a prior acceleration, then the spacetime curvature would be identical for each object and the objects' clocks would not get out of step. But such a conjecture would violate the limiting case of special relativity (and hence general relativity); specifically, such a conjecture would be inconsistent with the constancy of the vacuum velocity of light in any reference frame.
So then, general relativity requires that velocity differences are, in a sense, absolute. Yet in his original static and eternal cosmic model of 1917, there was no reason to assume that two velocities of two objects necessarily implied the acceleration of one object. Einstein introduced the model, with the cosmological constant appended in order to contend with the fact that his 1915 formulation of GR apparently failed to account for the observed mass distribution of the cosmos. Despite the popularity of the Big Bang model, a number of cosmic models hold the option that some velocity differences needn't imply an acceleration, strictly relative or "real."
Einstein's appeal to spacetime curvature to address the frame of reference issue is similar to Newton's assertion that an accelerated body requires either an impulse imputed to it or the gravitational force. There is an inherent local physical asymmetry. Purely relative motion will not do.
Frank Close points out that in the quantum arena, unlike in SR, superconductivity shows that there is an absolute state of rest, That is, he writes, the superconductor is at rest relative to the electron but not the converse (9).
Einstein also brings up the problem of absolute relative motion in the sense of Newton's bucket. Einstein uses two fluid bodies in space, one spherical, S1 and another an ellipsoid of revolution, S2. From the perspective of "Galilean relativity," one can as easily say that either body is at rest with respect to the other. But, the radial acceleration of S2 results in a noticeable difference: an equatorial bulge. Hence, says Einstein, it follows that the difference in motion must have a cause outside the system of the two bodies.
Of course Newton in Principia Mathematica first raised this point, noting that the surface of water in a rapidly spinning bucket becomes concave. This, he said, demonstrated that force must be impressed on a body in order for there to be a change in acceleration. Newton also mentioned the issue of the fixed stars as possibly of use for a background reference frame, though he does not seem to have insisted on that point. He did however find that absolute space would serve as a background reference frame.
It is noteworthy that Einstein's limit c can be used as an alternative to the equatorial bulge argument. If we suppose that a particular star is sufficiently distant, then the x component of its radial velocity (which is uniform and linear) will exceed the velocity of light. Such a circumstance being forbidden, we are forced to conclude that the earth is spinning, rather than the star revolving around the earth. We see that, in this sense, the limit c can be used to imply a specific frame of reference. At this point, however, I cannot say that such a circumstance suffices to resolve the clock paradox of special relativity.
Interestingly, the problem of Newton's bucket is quite similar to the clock paradox of special relativity. In both scenarios, we note that if two motions are strictly relative, what accounts for a property associated with one motion and not the other? In both cases, we are urged to focus on the "real" acceleration.
Newton's need for a background frame to cope with "real" acceleration predates the 19th century refinement of the concept of energy as an ineffable, essentially abstract "substance" which passes from one event to the next. That concept was implicit in Newton's Principia but not explicit and hence Newton did not appeal to the "energy" of the object in motion to deal with the problem. That is, we can say that we can distinguish between two systems by examining their parts. A system accelerated to a non-relativistic speed nevertheless discloses its motion by the fact that the parts change speed at different times as a set of "energy transactions" occur. For example, when you step on the accelerator, the car seat moves forward before you do; you catch up to the car "because" the car set imparts "kinetic energy" to you.
But if you are too far away to distinguish individual parts or a change in the object's shape, such as from equatorial bulge, your only hope for determining "true" acceleration is by knowing which object received energy prior to the two showing a relative change in velocity. Has the clock paradox gone away?
Now does GR resolve the clock paradox?
GR resolves the paradox non-globally, in that Einstein now holds that some accelerations are not strictly relative, but functions of a set of curvatures. Hence one can posit the loop scenario given inElectrodynamics and say that only one body can have a higher absolute angular velocity with respect to the other because only one must have experienced an acceleration that distorts spacetime differently from the other.
To be consistent, GR must reflect this asymmetry. That is, suppose we have two spaceships separating along a straight line whereby the distance between them increases as a constant velocity. If ship A's TV monitor says B's clock is ticking slower than A's and ship B's TV monitor says A's clock is ticking slower than B's, there must be an objective difference, nevertheless.
The above scenario is incomplete because the "real" acceleration prior to the opening of the scene is not given. Yet, GR does not tell us why a "real" acceleration must have occurred if two bodies are moving at different velocities.
So yes, GR partly resolves the clock paradox and, by viewing the 1905 equations for uniform motion as a special case of the 1915 equations, retroactively removes the paradox from SR, although it appears that Einstein avoided pointing this out in 1915 or thereafter.
However, GR does not specify a global topology (cosmic model) of spacetime, though Einstein struggled with this issue. The various solutions to GR's field equations showed that no specific cosmic model followed from GR. The clock paradox shows up in the Weeks model of the cosmos, with local space being euclidean (or rather Minkowskian). As far as this writer knows, such closed space geodesics cannot be ruled out on GR grounds alone.
Jeff Weeks, in his book The Shape of Space, points out that though physicists commonly think of three cosmic models as suitable for GR, in fact there are three classes of 3-manifolds that are both homogenous and isotropic (cosmic information is evenly mixed and looks about the same in any direction). Whether spacetime is mathematically elliptic, hyperbolic or euclidean, there are many possible global topologies for the cosmos, Weeks says.
One model, described by Weeks in the article linked above, permits a traveler to continue straight in a closed universe until she arrives at the point of origin. Again, to avoid contradiction, we are required to accept a priori that an acceleration that alters a world line has occurred.
Other models have the cosmic time axis following hyperbolic or elliptical geometry. Originally, one suspects, Einstein may have been skeptical of such an axis, in that Einstein's abolishment of simultaneity effectively abolished the Newtonian fiction of absolute time. But physicist Paul Davies, in his book About Time, argued that there is a Big Bang oriented cosmic time that can be approximated quite closely.
Kurt Goedel's rotating universe model left room for closed time loops, such that an astronaut who continued on a protracted space flight could fly into his past. This result prompted Godel to question the reality of time in general relativity. Having investigated various solutions of GR equations, Goedel argued that a median of proper times of moving objects, which James Jeans had thought to serve as a cosmic absolute time, was not guaranteed in all models and hence should be questioned in general.
Certainly we can agree that Goedel's result shows that relativity is incomplete in its analysis of time.
Mach's principles
Einstein was influenced by the philosophical writings of the German physicist Ernst Mach, whom he cites in Foundations.
According to Einstein (1915) Mach's "epistomological principle" says that observable facts must ultimately appear as causes and effects. Mach believed that the brain organizes sensory data into knowledge and that hence data of scientific value should stem from observable, measurable phenomena. This philosophical viewpoint was evident in 1905 when Einstein ruthlessly ejected the Maxwell-Lorentzian ether from physics.
Mach's "epistomological principle" led Mach to reject Newtonian absolute time and absolute space as unverifiable and made Einstein realize that the Newtonian edifice wasn't sacrosanct. However, in 1905 Einstein hadn't replaced the edifice with something called a "spacetime continuum." Curiously, later in his career Einstein impishly but honestly identified this entity as "the ether."
By rejecting absolute space and time, Mach also rejected the usual way of identifying acceleration in what is known as Mach's principle: Version A. Inertia of a ponderable object results from a relationship of that object with all other objects in the universe.
Version B. The earth's equatorial bulge is not a result of absolute rotation (radial acceleration) but is relative to the distant giant mass of the universe.
For a few years after publication of Foundations, Einstein favored Mach's principle, even using it as a basis of his "cosmological constant" paper, which was his first attempt to fit GR to a cosmic model, but was eventually convinced by the astronomer Wilem de Sitter (see Janssen above) to abandon the principle. In 1932 Einstein adopted the Einstein-de Sitter model that posits a cosmos with a global curvature that asymptotically zeroes out over eternity. The model also can be construed to imply a Big Bang, with its ordered set of accelerations.
A bit of fine-tuning
We can fine-tune the paradox by considering the velocity of the center of mass of the twin system. That velocity is m1v/m1 + m2. So the CM velocity is larger when the moving mass is the lesser and the converse. Letting x be a real greater than 1 we have two masses xm and m. The algebra reveals there is a factor (x/x+1) > 1/(x+1). The CM velocity for earth moving at 0.6c with respect to a 77kg astronaut is very close to 0.6c. For the converse, however, that velocity is about 2.3 meters per femto-second.
If we like, we can use the equation
E = mc2(1-v2/c2)1/2
to obtain the energies of each twin system.
If the earth is in motion and the astronaut at rest, my calculator won't handle the quantity for the energy. If the astronaut is in motion with the earth at rest, then E = 5.38*1041J.
But the paradox is restored as soon as we set m1 equal to m2.
Notes on the principle of equivalence
Now an aside on the principle of equivalence. Can it be said that gravitational acceleration is equivalent to kinematic acceleration? Gravitational accelerations are all associated with the gravitational constant G and of the form g = Gm/r2. Yet it is easy to write expressions for accelerations that cannot be members of the gravitational set. If a is not constant, we fulfill the criterion. If in rx, x =/= 2, there will be an infinity of accelerations that aren't members of the gravitational set.
At any rate, Einstein's principle of equivalence made a logical connection between a ponderable object's inertial mass and its gravitational mass. Newton had not shown a reason that they should be exactly equal, an assumption validated by acute experiments. (A minor technicality: Einstein and others have wondered why these masses should be exactly equal, but, properly they meant why should they be exactly proportional? Equality is guaranteed by Newton's choice of a gravitational constant. But certainly, min = kmgr, with k equaling one because of Newton's choice.)
Also, GR's field equations rest on the premise (Foundation) that for an infinitesimal region of spacetime, the Minkowskian coordinates of special relativity hold. However, this 1915 assumption is open to challenge on the basis of the Heisenberg uncertainty principle (ca. 1925), which sets a finite limit on the precision of a measurement of a particle's space coordinate given its time coordinate.
Einstein's Kaluza-Klein excursion
In Subtle is the Lord Pais tells of a period in which Einstein took Klein's idea for a five-dimensional spacetime and reworked it. After a great deal of effort, Einstein offered a paper which took Klein's ideas presented as his own, on the basis that he had found a way to rationalize obtaining the five-dimensional effect while sticking to the conventional perceptual view of space and time denoted 3D+T (making one wonder what he thought of his own four-dimensional spacetime scheme).
A perplexed Abraham Pais notes that a colleague dismissed Einstein's work as unoriginal, and Einstein then quickly dropped it (7). But reformulation of the ideas of others is exactly what Einstein did in 1905 with the special theory. He presented the mathematical and physical ideas of Lorenz, Fitzgerald and Poincare, whom he very likely read, and refashioned them in a manner that he thought coherent, most famously by rejecting the notion of ether as unnecessary.
Yet it took decades for Einstein to publicly acknowledge the contribution of Poincare, and even then, he let the priority matter remain fuzzy. Poincare's work was published in French in 1904, but went unnoticed by the powerful German-speaking scientific community. As a French-speaking resident of Switzerland, it seems rather plausible that the young patent attorney read Poincare's paper.
But, as Pais pointed out, it was Einstein's interpretation that made him the genius of relativity. And yet, that interpretation was either flawed, or incomplete, as we know from the twin paradox.
Footnotes
Apologies for footnotes being out of order. Haven't time to fix.
1. Einstein's Theory of Relativity by Max Born (Dover 1962).
2. Road to Reality by Roger Penrose (Random House 2006).
3. The Black Hole War by Leonard Susskind (Little Brown 2009).
4. Understanding Einstein's Theories of Relativity by Stan Gibilisco (Dover reprint of the 1983 edition).
7. In his biography of Einstein, Subtle is the Lord (Oxford 1983), physicist Abraham Pais mentions the "clock paradox" in the 1905 Electrodynamics paper but then summarily has Einstein resolve the contradiction in a paper presented to the Prussian Academy of Physics after the correct GR paper of 1915, with Einstein arguing that acceleration ends the paradox, which Pais calls a "misnomer." I don't recall the Prussian Academy paper, but it should be said that Einstein strongly implied the solution to the contradiction in his 1915 GR paper. Later in his book, Pais asserts that sometime after the GR paper, Einstein dispatched a paper on what Pais now calls the "twins paradox" but Pais uncharacteristically gives no citation.
5. Though Dingle seems to have done some astronomical work, he was not -- as a previous draft of this page said -- an astronomer, according to Harry H. Ricker III. Dingle was a professor of physics and natural philosophy at Imperial College before becoming a professor of history and the philosophy of science at City College, London, Ricker said. "Most properly he should be called a physicist and natural philosopher since his objections to relativity arose from his views and interpretations regarding the philosophy of science."
6. Dingle's paper Scientific and Philosophical Implications of the Special Theory of Relativityappeared in 1949 in Albert Einstein: Philosopher-Scientist, edited by Paul Arthur Schilpp. Dingle used this forum to propound a novel extension of special relativity which contained serious logical flaws. Einstein, in a note of response, said Dingle's paper made no sense to him.
8. See for example Max Von Laue's paper in Albert Einstein: Philosopher-Scientist edited by Paul Arthur Schilpp (1949).
9. The Infinity Puzzle: Quantum field theory and the hunt for an orderly universe by Frank Close basic books 2011
This paper updated Dec. 10, 2009, Oct. 28, 2013
Topologist Jeff Weeks on the twin paradox
http://www.math.uic.edu/undergraduate/mathclub/talks/Weeks_AMM2001.pdf
Michel Janssen's paper
https://netfiles.umn.edu/users/janss011/home%20page/rel-of-grav-field.pdf
The paradox
Einstein's groundbreaking 1905 relativity paper, "On the electrodynamics of moving bodies," contained a fundamental inconsistency which was not addressed until 10 years later, with the publication of his paper on gravitation.
Many have written on this inconsistency, known as the "twin paradox" or the "clock paradox" and more than a few have not understood that the "paradox" does not refer to the strangeness of time dilation but to a logical inconsistency in what is now known as the special (for "special case") theory of relativity.
Among those missing the point: Max Born in his book on special relativity (1), George Gamow in an essay and Roger Penrose in Road to Reality (2), and, most recently, Leonard Susskind in The Black Hole War (3).
Among those who have correctly understood the paradox are topologist Jeff Weeks (see link above) and science writer Stan Gibilisco (4), who noted that the general theory of relativity resolves the problem.
As far back as the 1960s, the British physicist Herbert Dingle (5) called the inconsistency a "regrettable error" and was deluged with "disproofs" of his assertion from the physics community. (It should be noted that Dingle's 1949 attempt at relativistic physics left Einstein bemused (6). Yet every "disproof" of the paradox that I have seen uses acceleration, an issue not addressed by Einstein until the general theory of relativity. It was Einstein who set himself up for the paradox by favoring the idea that only purely relative motions are meaningful, writing that various examples "suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest." [Electrodynamics translated by Perett and Jeffery and appearing in a Dover (1952) reprint.] In that paper, he also takes pains to note that the term "stationary system" is a verbal convenience only (7).
But later in Elect., Einstein offered the scenario of two initially synchronized clocks at rest with respect to each other. One clock then travels around a closed loop, and its time is dilated with respect to the at-rest clock when they meet again. In Einstein's words: "If we assume that the result proved for a polygonal line is also valid for a continuously curved line, we arrive at this result: If one of two synchronous clocks at A is moved in a journey lasting t seconds, then by the clock which has remained at rest the traveled clock on its arrival at A will be 1/2tv2/c2 slow."
Clearly, if there is no preferred frame of reference, a contradiction arises: when the clocks meet again, which clock has recorded fewer ticks?
Both in the closed loop scenario and in the polygon-path scenario, Einstein avoids the issue of acceleration. Hence, he does not explain that there is a property of "real" acceleration that is not symmetrical or purely relative and that that consequently a preferred frame of reference is implied, at least locally.
The paradox stems from the fact that one cannot say which velocity is higher without a "background" reference frame. In Newtonian terms, the same issue arises: if one body is accelerating away from the other, how do we know which body experiences the "real" force? No answer is possible without more information, implying a background frame.
In comments published in 1910, the physicist Arnold Sommerfeld, a proponent of relativity theory, "covers" for the new paradigm by noting that Einstein didn't really mean that time dilation was associated with purely relative motion, but rather with accelerated motion; and that hence relativity was in that case not contradictory. Sommerfeld wrote: "On this [a time integral and inequality] depends the retardation of the moving clock compared with the clock at rest. The assertion is based, as Einstein has pointed out, on the unprovable assumption that the clock in motion actually indicates its own proper time; i.e. that it always gives the time corresponding to the state of velocity, regarded as constant, at any instant. The moving clock must naturally have been moved with acceleration (with changes of speed or direction) in order to be compared with the stationary clock at world-point P. The retardation of the moving clock does not therefore actually indicate 'motion,' but 'accelerated motion.' Hence this does not contradict the principle of relativity." [Notes appended to Space and Time, a 1908 address by Herman Minkowski, Dover 1952, Note 4.]
However, Einstein's 1905 paper does not tackle the issue of acceleration and more to the point, does not explain why purely relative acceleration would be insufficient to meet the facts. The principle of relativity applies only to "uniform translatory motion" (Elect. 1905).
Neither does Sommerfeld's note address the issue of purely relative acceleration versus "true" acceleration, perhaps implicitly accepting Newton's view (below). And, a review of various papers by Einstein seems to indicate that he did not deal with this inconsistency head-on, though in a lecture-hall discussion ca. 1912, Einstein said that the [special] theory of relativity is silent on how a clock behaves if forced to change direction but argues that if a polygonal path is large enough, accelerative effects diminish and (linear) time dilation still holds.
On the other hand, of course, he was not oblivious to the issue of acceleration. In 1910, he wrote that the principle of relativity meant that the laws of physics are independent of the state of motion, but that the motion is non-accelerated. "We assume that the motion of acceleration has an objective meaning," he said. [The Principle of Relativity and its Consequences in Modern Physics, a 1910 paper reproduced in Collected Papers of Albert Einstein, Hebrew University, Princeton University Press.]
In that same paper Einstein emphasizes that the principle of relativity does not cover acceleration. "The laws governing natural phenomena are independent of the state of motion of the coordinate system to which the phenomena are observed, provided this system is not in accelerated motion." Clearly, however, he is somewhat ambiguous about small accelerations and radial acceleration, as we see from the lecture-hall remark and from a remark in Foundation of the General Theory of Relativity (1915) about a "familiar result" of special relativity whereby a clock on a rotating disk's rim ticks slower than a clock at the origin.
General relativity's partial solution
Finally, in his 1915 paper on general relativity, Einstein addressed the issue of acceleration, citing what he called "the principle of equivalence." That principle (actually, introduced prior to 1915) said that there was no real difference between kinematic acceleration and gravitational acceleration. Scientifically, they should be treated as if they are the same.
So then, Einstein notes in Foundation, if we have system K and another system K' accelerating with respect to K, clearly, from a "Galilean" perspective, we could say that K was accelerating with respect to K'. But, is this really so?
Einstein argues that if K is at rest relative to K', which is accelerated, the oberserver on K cannot claim that he is being accelerated -- even though, in purely relative terms, such a claim is valid. The reason for this rejection of Galilean relativity: We may equally well interpret K' to be kinematically unaccelerated though the "space-time territory in question is under the sway of a gravitational field, which generates the accelerated motion of the bodies" in the K' system. This claim is based on the principle of equivalence which might be considered a modification of his previously posited principle of relativity. By the relativity principle, Einstein meant that the laws of physics can be cast in invariant form so that they apply equivalently in any unformly moving frame of reference. (For example, |vb - va| is the invariant quantity that describes an equivalence class of linear velocities.)
By the phrase "equivalence," Einstein is relating impulsive acceleration (for example, a projectile's x vector) to its gravitational acceleration (its y vector). Of course, Newton's mechanics already said that the equation F = mg is a special case of F = ma but Einstein meant something more: that local spacetime curvature is specific for "real" accelerations -- whether impulsive or gravitational.
Einstein's "equivalence" insight was his recognition that one could express acceleration, whether gravitational or impulsive, as a curvature in the spacetime continuum (a concept introduced by Minkowski). This means, he said, that the Newtonian superposition of separate vectors was not valid and was to be replaced by a unitary curvature. (Though the calculus of spacetime requires specific tools, the concept isn't so hard to grasp. Think of a Mercator map: the projection of a sphere onto a plane. Analogously, general relativity projects a 4-dimensional spacetime onto a Euclidean three-dimensional space.)
However, is this "world-line" answer the end of the problem of the asymmetry of accelerated motion?
The Einstein of 1915 implies that if two objects have two different velocities, we must regard one as having an absolutely higher velocity than the other because one object has been "really" accelerated.
Yet one might conjecture that if two objects move with different velocities wherein neither has a prior acceleration, then the spacetime curvature would be identical for each object and the objects' clocks would not get out of step. But such a conjecture would violate the limiting case of special relativity (and hence general relativity); specifically, such a conjecture would be inconsistent with the constancy of the vacuum velocity of light in any reference frame.
So then, general relativity requires that velocity differences are, in a sense, absolute. Yet in his original static and eternal cosmic model of 1917, there was no reason to assume that two velocities of two objects necessarily implied the acceleration of one object. Einstein introduced the model, with the cosmological constant appended in order to contend with the fact that his 1915 formulation of GR apparently failed to account for the observed mass distribution of the cosmos. Despite the popularity of the Big Bang model, a number of cosmic models hold the option that some velocity differences needn't imply an acceleration, strictly relative or "real."
Einstein's appeal to spacetime curvature to address the frame of reference issue is similar to Newton's assertion that an accelerated body requires either an impulse imputed to it or the gravitational force. There is an inherent local physical asymmetry. Purely relative motion will not do.
Frank Close points out that in the quantum arena, unlike in SR, superconductivity shows that there is an absolute state of rest, That is, he writes, the superconductor is at rest relative to the electron but not the converse (9).
Einstein also brings up the problem of absolute relative motion in the sense of Newton's bucket. Einstein uses two fluid bodies in space, one spherical, S1 and another an ellipsoid of revolution, S2. From the perspective of "Galilean relativity," one can as easily say that either body is at rest with respect to the other. But, the radial acceleration of S2 results in a noticeable difference: an equatorial bulge. Hence, says Einstein, it follows that the difference in motion must have a cause outside the system of the two bodies.
Of course Newton in Principia Mathematica first raised this point, noting that the surface of water in a rapidly spinning bucket becomes concave. This, he said, demonstrated that force must be impressed on a body in order for there to be a change in acceleration. Newton also mentioned the issue of the fixed stars as possibly of use for a background reference frame, though he does not seem to have insisted on that point. He did however find that absolute space would serve as a background reference frame.
It is noteworthy that Einstein's limit c can be used as an alternative to the equatorial bulge argument. If we suppose that a particular star is sufficiently distant, then the x component of its radial velocity (which is uniform and linear) will exceed the velocity of light. Such a circumstance being forbidden, we are forced to conclude that the earth is spinning, rather than the star revolving around the earth. We see that, in this sense, the limit c can be used to imply a specific frame of reference. At this point, however, I cannot say that such a circumstance suffices to resolve the clock paradox of special relativity.
Interestingly, the problem of Newton's bucket is quite similar to the clock paradox of special relativity. In both scenarios, we note that if two motions are strictly relative, what accounts for a property associated with one motion and not the other? In both cases, we are urged to focus on the "real" acceleration.
Newton's need for a background frame to cope with "real" acceleration predates the 19th century refinement of the concept of energy as an ineffable, essentially abstract "substance" which passes from one event to the next. That concept was implicit in Newton's Principia but not explicit and hence Newton did not appeal to the "energy" of the object in motion to deal with the problem. That is, we can say that we can distinguish between two systems by examining their parts. A system accelerated to a non-relativistic speed nevertheless discloses its motion by the fact that the parts change speed at different times as a set of "energy transactions" occur. For example, when you step on the accelerator, the car seat moves forward before you do; you catch up to the car "because" the car set imparts "kinetic energy" to you.
But if you are too far away to distinguish individual parts or a change in the object's shape, such as from equatorial bulge, your only hope for determining "true" acceleration is by knowing which object received energy prior to the two showing a relative change in velocity. Has the clock paradox gone away?
Now does GR resolve the clock paradox?
GR resolves the paradox non-globally, in that Einstein now holds that some accelerations are not strictly relative, but functions of a set of curvatures. Hence one can posit the loop scenario given inElectrodynamics and say that only one body can have a higher absolute angular velocity with respect to the other because only one must have experienced an acceleration that distorts spacetime differently from the other.
To be consistent, GR must reflect this asymmetry. That is, suppose we have two spaceships separating along a straight line whereby the distance between them increases as a constant velocity. If ship A's TV monitor says B's clock is ticking slower than A's and ship B's TV monitor says A's clock is ticking slower than B's, there must be an objective difference, nevertheless.
The above scenario is incomplete because the "real" acceleration prior to the opening of the scene is not given. Yet, GR does not tell us why a "real" acceleration must have occurred if two bodies are moving at different velocities.
So yes, GR partly resolves the clock paradox and, by viewing the 1905 equations for uniform motion as a special case of the 1915 equations, retroactively removes the paradox from SR, although it appears that Einstein avoided pointing this out in 1915 or thereafter.
However, GR does not specify a global topology (cosmic model) of spacetime, though Einstein struggled with this issue. The various solutions to GR's field equations showed that no specific cosmic model followed from GR. The clock paradox shows up in the Weeks model of the cosmos, with local space being euclidean (or rather Minkowskian). As far as this writer knows, such closed space geodesics cannot be ruled out on GR grounds alone.
Jeff Weeks, in his book The Shape of Space, points out that though physicists commonly think of three cosmic models as suitable for GR, in fact there are three classes of 3-manifolds that are both homogenous and isotropic (cosmic information is evenly mixed and looks about the same in any direction). Whether spacetime is mathematically elliptic, hyperbolic or euclidean, there are many possible global topologies for the cosmos, Weeks says.
One model, described by Weeks in the article linked above, permits a traveler to continue straight in a closed universe until she arrives at the point of origin. Again, to avoid contradiction, we are required to accept a priori that an acceleration that alters a world line has occurred.
Other models have the cosmic time axis following hyperbolic or elliptical geometry. Originally, one suspects, Einstein may have been skeptical of such an axis, in that Einstein's abolishment of simultaneity effectively abolished the Newtonian fiction of absolute time. But physicist Paul Davies, in his book About Time, argued that there is a Big Bang oriented cosmic time that can be approximated quite closely.
Kurt Goedel's rotating universe model left room for closed time loops, such that an astronaut who continued on a protracted space flight could fly into his past. This result prompted Godel to question the reality of time in general relativity. Having investigated various solutions of GR equations, Goedel argued that a median of proper times of moving objects, which James Jeans had thought to serve as a cosmic absolute time, was not guaranteed in all models and hence should be questioned in general.
Certainly we can agree that Goedel's result shows that relativity is incomplete in its analysis of time.
Mach's principles
Einstein was influenced by the philosophical writings of the German physicist Ernst Mach, whom he cites in Foundations.
According to Einstein (1915) Mach's "epistomological principle" says that observable facts must ultimately appear as causes and effects. Mach believed that the brain organizes sensory data into knowledge and that hence data of scientific value should stem from observable, measurable phenomena. This philosophical viewpoint was evident in 1905 when Einstein ruthlessly ejected the Maxwell-Lorentzian ether from physics.
Mach's "epistomological principle" led Mach to reject Newtonian absolute time and absolute space as unverifiable and made Einstein realize that the Newtonian edifice wasn't sacrosanct. However, in 1905 Einstein hadn't replaced the edifice with something called a "spacetime continuum." Curiously, later in his career Einstein impishly but honestly identified this entity as "the ether."
By rejecting absolute space and time, Mach also rejected the usual way of identifying acceleration in what is known as Mach's principle: Version A. Inertia of a ponderable object results from a relationship of that object with all other objects in the universe.
Version B. The earth's equatorial bulge is not a result of absolute rotation (radial acceleration) but is relative to the distant giant mass of the universe.
For a few years after publication of Foundations, Einstein favored Mach's principle, even using it as a basis of his "cosmological constant" paper, which was his first attempt to fit GR to a cosmic model, but was eventually convinced by the astronomer Wilem de Sitter (see Janssen above) to abandon the principle. In 1932 Einstein adopted the Einstein-de Sitter model that posits a cosmos with a global curvature that asymptotically zeroes out over eternity. The model also can be construed to imply a Big Bang, with its ordered set of accelerations.
A bit of fine-tuning
We can fine-tune the paradox by considering the velocity of the center of mass of the twin system. That velocity is m1v/m1 + m2. So the CM velocity is larger when the moving mass is the lesser and the converse. Letting x be a real greater than 1 we have two masses xm and m. The algebra reveals there is a factor (x/x+1) > 1/(x+1). The CM velocity for earth moving at 0.6c with respect to a 77kg astronaut is very close to 0.6c. For the converse, however, that velocity is about 2.3 meters per femto-second.
If we like, we can use the equation
E = mc2(1-v2/c2)1/2
to obtain the energies of each twin system.
If the earth is in motion and the astronaut at rest, my calculator won't handle the quantity for the energy. If the astronaut is in motion with the earth at rest, then E = 5.38*1041J.
But the paradox is restored as soon as we set m1 equal to m2.
Notes on the principle of equivalence
Now an aside on the principle of equivalence. Can it be said that gravitational acceleration is equivalent to kinematic acceleration? Gravitational accelerations are all associated with the gravitational constant G and of the form g = Gm/r2. Yet it is easy to write expressions for accelerations that cannot be members of the gravitational set. If a is not constant, we fulfill the criterion. If in rx, x =/= 2, there will be an infinity of accelerations that aren't members of the gravitational set.
At any rate, Einstein's principle of equivalence made a logical connection between a ponderable object's inertial mass and its gravitational mass. Newton had not shown a reason that they should be exactly equal, an assumption validated by acute experiments. (A minor technicality: Einstein and others have wondered why these masses should be exactly equal, but, properly they meant why should they be exactly proportional? Equality is guaranteed by Newton's choice of a gravitational constant. But certainly, min = kmgr, with k equaling one because of Newton's choice.)
Also, GR's field equations rest on the premise (Foundation) that for an infinitesimal region of spacetime, the Minkowskian coordinates of special relativity hold. However, this 1915 assumption is open to challenge on the basis of the Heisenberg uncertainty principle (ca. 1925), which sets a finite limit on the precision of a measurement of a particle's space coordinate given its time coordinate.
Einstein's Kaluza-Klein excursion
In Subtle is the Lord Pais tells of a period in which Einstein took Klein's idea for a five-dimensional spacetime and reworked it. After a great deal of effort, Einstein offered a paper which took Klein's ideas presented as his own, on the basis that he had found a way to rationalize obtaining the five-dimensional effect while sticking to the conventional perceptual view of space and time denoted 3D+T (making one wonder what he thought of his own four-dimensional spacetime scheme).
A perplexed Abraham Pais notes that a colleague dismissed Einstein's work as unoriginal, and Einstein then quickly dropped it (7). But reformulation of the ideas of others is exactly what Einstein did in 1905 with the special theory. He presented the mathematical and physical ideas of Lorenz, Fitzgerald and Poincare, whom he very likely read, and refashioned them in a manner that he thought coherent, most famously by rejecting the notion of ether as unnecessary.
Yet it took decades for Einstein to publicly acknowledge the contribution of Poincare, and even then, he let the priority matter remain fuzzy. Poincare's work was published in French in 1904, but went unnoticed by the powerful German-speaking scientific community. As a French-speaking resident of Switzerland, it seems rather plausible that the young patent attorney read Poincare's paper.
But, as Pais pointed out, it was Einstein's interpretation that made him the genius of relativity. And yet, that interpretation was either flawed, or incomplete, as we know from the twin paradox.
Footnotes
Apologies for footnotes being out of order. Haven't time to fix.
1. Einstein's Theory of Relativity by Max Born (Dover 1962).
2. Road to Reality by Roger Penrose (Random House 2006).
3. The Black Hole War by Leonard Susskind (Little Brown 2009).
4. Understanding Einstein's Theories of Relativity by Stan Gibilisco (Dover reprint of the 1983 edition).
7. In his biography of Einstein, Subtle is the Lord (Oxford 1983), physicist Abraham Pais mentions the "clock paradox" in the 1905 Electrodynamics paper but then summarily has Einstein resolve the contradiction in a paper presented to the Prussian Academy of Physics after the correct GR paper of 1915, with Einstein arguing that acceleration ends the paradox, which Pais calls a "misnomer." I don't recall the Prussian Academy paper, but it should be said that Einstein strongly implied the solution to the contradiction in his 1915 GR paper. Later in his book, Pais asserts that sometime after the GR paper, Einstein dispatched a paper on what Pais now calls the "twins paradox" but Pais uncharacteristically gives no citation.
5. Though Dingle seems to have done some astronomical work, he was not -- as a previous draft of this page said -- an astronomer, according to Harry H. Ricker III. Dingle was a professor of physics and natural philosophy at Imperial College before becoming a professor of history and the philosophy of science at City College, London, Ricker said. "Most properly he should be called a physicist and natural philosopher since his objections to relativity arose from his views and interpretations regarding the philosophy of science."
6. Dingle's paper Scientific and Philosophical Implications of the Special Theory of Relativityappeared in 1949 in Albert Einstein: Philosopher-Scientist, edited by Paul Arthur Schilpp. Dingle used this forum to propound a novel extension of special relativity which contained serious logical flaws. Einstein, in a note of response, said Dingle's paper made no sense to him.
8. See for example Max Von Laue's paper in Albert Einstein: Philosopher-Scientist edited by Paul Arthur Schilpp (1949).
9. The Infinity Puzzle: Quantum field theory and the hunt for an orderly universe by Frank Close basic books 2011
This paper updated Dec. 10, 2009, Oct. 28, 2013
Monday, April 22, 2013
Appendix A: anecdotal accounts of synchronicity
Toward a signal model of perception
http://paulpages.blogspot.com/2013/03/toward-signal-model-of-perception.html
Synchronicity 'experiments'
http://paulpages.blogspot.com/2011/11/appendix-b-experiments-in-synchronicity.html
Please send corrections and comments to Krypto78@gmail.com
Presented here is a collection of anecdotal accounts of what some may believe are episodes of synchronicity, along with my comments. I have not sought to arrange these accounts in any particular order.
We must frankly admit that none of these incidents could be shown, using standard statistical tools, to result of non-random covert connections.
Pauli's pull
The physicist George Gamow gave a humorous example of the Pauli effect in his book Thirty Years that Shook Physics (Dover reprint 1985):
"It is well known that theoretical physicists cannot handle experimental equipment; it breaks whenever they touch it. Pauli was such a good theoretical physicist that something usually broke in the lab whenever he merely stepped across the threshold. A mysterious event that did not seem at first to be connected with Pauli's presence once occurred in Professor J. Franck's laboratory in Gottingen. Early one afternoon, without apparent cause, a complicated apparatus for the study of atomic phenomena collapsed. Franck wrote humorously about this to Pauli at his Zurich address and, after some delay, received an answer in an envelope with a Danish stamp. Pauli wrote that he had gone to visit Bohr and at the time of the mishap in Franck's laboratory his train was stopped for a few minutes at the Gottingen railroad station. You may believe this anecdote or not, but there are many other observations concerning the reality of the Pauli effect!"
Similarly, the physicist Abraham Pais relates in his book Niels Bohr's Times (Oxford 1991), that Pauli was very proud of the "Pauli effect" whereby, beginning in 1922, "something would go wrong whenever he entered a laboratory." Pauli "would tell with glee how his friend Otto Stern, experimentalist at Hamburg, would consult him only through the closed door leading to his working space."
Wolfgang Pauli, a founder of quantum mechanics, seems to have come to believe in a phenomenon that his former therapist and friend, Carl Jung, dubbed "synchronicity," though he was careful about his phrasing.
Another quantum physicist, Johnny Von Neumann, was, according to his wife Klari, intensely superstitious. "A drawer could not be opened unless it was pushed in and out seven times, the same with a light-switch, which had to be flipped seven times before you could let it stay." (Cited by George Dyson in Turing's Cathedral: the origins of the digital universe; Pantheon 21012.)
Von Neumann had a major role in development of the computer, which he, to Einstein's disgust, put to work on H bomb development.
His number came up
The novelist William S. Burroughs was fascinated by the number 23, recounts Robert Anton Wilson, a writer and mystic. "According to Burroughs, he had known a certain Captain Clark, around 1960 in Tangier, who once bragged that he had been sailing 23 years without an accident. That very day, Clark's ship had an accident that killed him and everybody else aboard. Furthermore, while Burroughs was thinking about this crude example of the irony of the gods that evening, a bulletin on the radio announced the crash of an airliner in Florida, USA. The pilot was another Captain Clark and the flight was Flight 23."
"Burroughs began collecting odd 23s after this gruesome synchronicity," Wilson wrote in the May 2007 issue of Fortean Times.
No scientist would consider Wilson, with his peculiar numerological theories, as a credible source, nor the Fortean Times as a reputable forum.
I have no interest in promoting any form of numerology, but I would say that such a scenario might reflect Burroughs' own mind. We don't know what he'd been thinking about or doing before this symmetrical coincidence set, but in our model reality signals at later times reflect interference of signals at an earlier time. The "meaningful coincidences" are similar subsignals triggered by a previous interference.
Traveling in Tennessee
One morning several years ago my son and I were driving from Knoxville in order to do some hiking in Tennessee mountain country. We had decided to take a scenic route and were barely aware that that route intersected a major interstate highway that linked to Knoxville. As we go to the intersection -- having slowed down after a wrong turn -- a man came down the embankment from the interstate. My son recognized him and we stopped to talk. The man, who my son had met with the day before, had had some difficulties and was hitch-hiking back to Ohio. My son was able to wish him well, say goodbye and give him some money for his journey.
I don't recall what the two of us had been discussing in the car, but I do recall thinking that that intersection of events was no random coincidence.
Safe conduct
A friend I have known for years recently confided this experience: He had gone with a group to go whitewater rafting in Pennsylvania. But there was no room for him on the raft and he rented a one-person kayak so he could accompany his friends.
When hitting some rapids, he capsized and spilled out of his vessel; his friends were nowhere in sight.
My friend is neurologically impaired and so was in quite a predicament, even though the water was not over his head.
At that point, a man appeared and from my friend's vantage point, "it looked like he was walking on water." The man helped my friend out of the stream and then took his leave. My friend was worried about the kayak, because ordinarily such an untended floatable shoots downstream. But, he turned and noticed it floating idly nearby.
My friend was clearly much taken with this experience.
My collage days
A few years ago I regularly indulged my artistic bent my artistic bent by composing collages in ways that I considered interesting and original.
On a number of occasions the "echoes" were quite strong, and occasionally gruesome. In fact, one collage was followed by an extraordinarily gruesome event that reflected the collage quite obviously (to me), and I have decided not to give details out of concern for the feelings of the survivors.
My thinking is that the juxtaposition of images that individually or collectively contain high E-values can have a profound impact on one's virtual world.
In fact, I became reluctant to make more of these and threw out almost all the ones I had made.
The collage technique underscores the interference effect. That is, the images form a superposed set, a collage, that influences the reality formulator, usually within 24 hours.
A cold day in hell
This could fit into the 'experiments' appendix, except that I was too irritable to consider what I was doing a detached experiment.
On the evening of January 23, 2009, I was in the San Diego Public Library glancing through a book on superconductivity, which occurs at extremes of cold. I noticed the word "transpire" used as a synonym for "occur" and was irritated at this unusual and unprofessional usage. In fact, I was so annoyed that I did "numerology" on the word and several anagrams of the word. But once the anger passed, I threw the paper with these scribblings in the trash bin.
The next morning, I encountered an internet story from the Independent about two young fishermen who survived shipwreck inside a floating icebox used for storing fish. They were enormously thirsty when rescued from the shark-infested South Pacific waters and had survived by drinking rainwater deposited by a typhoon that had failed to capsize their icebox.
Bad company
A year or two after the attacks of Sept. 11, 2001, I wrote a web page about the divisibility of numbers by a 9 or an 11.
The following summer afternoon I was enjoying a picnic put on by a spiritually inclined group. In the adjacent picnic grove was a gathering of members of the Pagans motorcycle gang, including women and children.
The Pagans are considered an outlaw gang and are known for their Nazi and occult symbolism.
They weren't raucous but rather subdued. They gave off "strange vibes."
My estimate is that the association that I and others have with the numbers 9 and 11 went into a reality projection of people who many, including myself, think of as engaging in evil.
I have noticed that when doing math, the projections, or "echoes," can be quite vivid.
Two Pied Pipers
When working on this page, I switched over to take a look at the news and noticed that Michael Jackson's heart had stopped and a short time later he was reported dead. I'm wondering if this sudden evil report is an echo of the "collage days" anecdote, which talks about the artist and gruesome happenings; in light of the singer's troubled public image, the Pagans anecdote might also have been a contributor.
After learning about Jackson's death, I stepped out of the library for a bite to eat and upon returning noticed a sign on the door advertising a rock performer who would sing for children that evening. The performer is a friend who is a member of the spiritually inclined group I was with at the picnic (though I don't recall that he was at the picnic). In fact, I later overheard some of his performance but did not attend.
The two singers who entertain children represent two spiritual paths offered in life, on the one hand represented by the hedonistic Pagans and on the other by the spiritually inclined group I was with (we like pleasure but strive against self-defeating pleasure).
Would all this mean that I think I caused a man's death? This type of thinking is akin to the questions that can and cannot properly be asked in quantum mechanics. The best that can be said is that the interference effects are followed by a possibly synchronistic report. The report very often is about an event that precedes the interference, just as would be expected in the discussion in my main article.
What do you know?
I had been studying differential equations the morning of April 23, 2009, and later jotted down a thought that impressed me taken from a book by Werner Heisenberg (Physics and beyond). He had written, according to my notes, that there were no determinants that could give the position of an emitted radium electron, that the quantum information gave all the knowledge there was.
Later, I visited a church where the speaker had the unusual first name, Knowledge.
I have many, many more personal anecdotes. But I don't have the notes of them and they are only randomly stored in my memory. So some of the more entertaining and perhaps compelling ones aren't here. If I happen to get around to it, I may add some more.
Time and tide
In the vicinty of noon, Wed., Sept. 25, 2013, on a whim, I posted the following on Facebook:
LUCKY 7?
So I have this hypothesis that the 7-days-of-creation story of Genesis is a poetic means of asserting the monotheistic idea, while incorporating pagan religious symbolism -- much in the manner of the church "christianizing" pagan holidays. The number 7 was important in the ancient near and middle East because there are 7 visible celestial objects, including planets, that wandered like gods, and were assumed to be gods.
(Note that not all ancient societies had a 7-day week. Egypt, for example, had an 8-day week.)
The early Hebrews thought of their god, El or Yahweh (meaning "He Is") as a god of gods (as in boss of bosses). But, that idea was later suppressed and the title changed to "Lord of Hosts." Similarly, when the 7-day account in Genesis was written, the author had in mind supplanting the 7 sky gods with seven powerful things that a single God had done. He was educating his hearers and readers to think monotheistically. Other parts of Genesis disclose the earlier idea that the god of the Hebrews was the most powerful of the gods, although these references were edited in order to conform to the new monotheism.
An interpretation: God was disclosing more about himself over time, but spoke to people in the language to which they were accustomed, as when Paul the apostle used Greek ideas to appeal to the people at Mars Hill.
First posted June 25, 2009
Modified April 2013
Modified Sept. 2013
Toward a signal model of perception
http://paulpages.blogspot.com/2013/03/toward-signal-model-of-perception.html
Synchronicity 'experiments'
http://paulpages.blogspot.com/2011/11/appendix-b-experiments-in-synchronicity.html
Please send corrections and comments to Krypto78@gmail.com
Presented here is a collection of anecdotal accounts of what some may believe are episodes of synchronicity, along with my comments. I have not sought to arrange these accounts in any particular order.
We must frankly admit that none of these incidents could be shown, using standard statistical tools, to result of non-random covert connections.
Pauli's pull
The physicist George Gamow gave a humorous example of the Pauli effect in his book Thirty Years that Shook Physics (Dover reprint 1985):
"It is well known that theoretical physicists cannot handle experimental equipment; it breaks whenever they touch it. Pauli was such a good theoretical physicist that something usually broke in the lab whenever he merely stepped across the threshold. A mysterious event that did not seem at first to be connected with Pauli's presence once occurred in Professor J. Franck's laboratory in Gottingen. Early one afternoon, without apparent cause, a complicated apparatus for the study of atomic phenomena collapsed. Franck wrote humorously about this to Pauli at his Zurich address and, after some delay, received an answer in an envelope with a Danish stamp. Pauli wrote that he had gone to visit Bohr and at the time of the mishap in Franck's laboratory his train was stopped for a few minutes at the Gottingen railroad station. You may believe this anecdote or not, but there are many other observations concerning the reality of the Pauli effect!"
Similarly, the physicist Abraham Pais relates in his book Niels Bohr's Times (Oxford 1991), that Pauli was very proud of the "Pauli effect" whereby, beginning in 1922, "something would go wrong whenever he entered a laboratory." Pauli "would tell with glee how his friend Otto Stern, experimentalist at Hamburg, would consult him only through the closed door leading to his working space."
Wolfgang Pauli, a founder of quantum mechanics, seems to have come to believe in a phenomenon that his former therapist and friend, Carl Jung, dubbed "synchronicity," though he was careful about his phrasing.
Another quantum physicist, Johnny Von Neumann, was, according to his wife Klari, intensely superstitious. "A drawer could not be opened unless it was pushed in and out seven times, the same with a light-switch, which had to be flipped seven times before you could let it stay." (Cited by George Dyson in Turing's Cathedral: the origins of the digital universe; Pantheon 21012.)
Von Neumann had a major role in development of the computer, which he, to Einstein's disgust, put to work on H bomb development.
His number came up
The novelist William S. Burroughs was fascinated by the number 23, recounts Robert Anton Wilson, a writer and mystic. "According to Burroughs, he had known a certain Captain Clark, around 1960 in Tangier, who once bragged that he had been sailing 23 years without an accident. That very day, Clark's ship had an accident that killed him and everybody else aboard. Furthermore, while Burroughs was thinking about this crude example of the irony of the gods that evening, a bulletin on the radio announced the crash of an airliner in Florida, USA. The pilot was another Captain Clark and the flight was Flight 23."
"Burroughs began collecting odd 23s after this gruesome synchronicity," Wilson wrote in the May 2007 issue of Fortean Times.
No scientist would consider Wilson, with his peculiar numerological theories, as a credible source, nor the Fortean Times as a reputable forum.
I have no interest in promoting any form of numerology, but I would say that such a scenario might reflect Burroughs' own mind. We don't know what he'd been thinking about or doing before this symmetrical coincidence set, but in our model reality signals at later times reflect interference of signals at an earlier time. The "meaningful coincidences" are similar subsignals triggered by a previous interference.
Traveling in Tennessee
One morning several years ago my son and I were driving from Knoxville in order to do some hiking in Tennessee mountain country. We had decided to take a scenic route and were barely aware that that route intersected a major interstate highway that linked to Knoxville. As we go to the intersection -- having slowed down after a wrong turn -- a man came down the embankment from the interstate. My son recognized him and we stopped to talk. The man, who my son had met with the day before, had had some difficulties and was hitch-hiking back to Ohio. My son was able to wish him well, say goodbye and give him some money for his journey.
I don't recall what the two of us had been discussing in the car, but I do recall thinking that that intersection of events was no random coincidence.
Safe conduct
A friend I have known for years recently confided this experience: He had gone with a group to go whitewater rafting in Pennsylvania. But there was no room for him on the raft and he rented a one-person kayak so he could accompany his friends.
When hitting some rapids, he capsized and spilled out of his vessel; his friends were nowhere in sight.
My friend is neurologically impaired and so was in quite a predicament, even though the water was not over his head.
At that point, a man appeared and from my friend's vantage point, "it looked like he was walking on water." The man helped my friend out of the stream and then took his leave. My friend was worried about the kayak, because ordinarily such an untended floatable shoots downstream. But, he turned and noticed it floating idly nearby.
My friend was clearly much taken with this experience.
My collage days
A few years ago I regularly indulged my artistic bent my artistic bent by composing collages in ways that I considered interesting and original.
On a number of occasions the "echoes" were quite strong, and occasionally gruesome. In fact, one collage was followed by an extraordinarily gruesome event that reflected the collage quite obviously (to me), and I have decided not to give details out of concern for the feelings of the survivors.
My thinking is that the juxtaposition of images that individually or collectively contain high E-values can have a profound impact on one's virtual world.
In fact, I became reluctant to make more of these and threw out almost all the ones I had made.
The collage technique underscores the interference effect. That is, the images form a superposed set, a collage, that influences the reality formulator, usually within 24 hours.
A cold day in hell
This could fit into the 'experiments' appendix, except that I was too irritable to consider what I was doing a detached experiment.
On the evening of January 23, 2009, I was in the San Diego Public Library glancing through a book on superconductivity, which occurs at extremes of cold. I noticed the word "transpire" used as a synonym for "occur" and was irritated at this unusual and unprofessional usage. In fact, I was so annoyed that I did "numerology" on the word and several anagrams of the word. But once the anger passed, I threw the paper with these scribblings in the trash bin.
The next morning, I encountered an internet story from the Independent about two young fishermen who survived shipwreck inside a floating icebox used for storing fish. They were enormously thirsty when rescued from the shark-infested South Pacific waters and had survived by drinking rainwater deposited by a typhoon that had failed to capsize their icebox.
Bad company
A year or two after the attacks of Sept. 11, 2001, I wrote a web page about the divisibility of numbers by a 9 or an 11.
The following summer afternoon I was enjoying a picnic put on by a spiritually inclined group. In the adjacent picnic grove was a gathering of members of the Pagans motorcycle gang, including women and children.
The Pagans are considered an outlaw gang and are known for their Nazi and occult symbolism.
They weren't raucous but rather subdued. They gave off "strange vibes."
My estimate is that the association that I and others have with the numbers 9 and 11 went into a reality projection of people who many, including myself, think of as engaging in evil.
I have noticed that when doing math, the projections, or "echoes," can be quite vivid.
Two Pied Pipers
When working on this page, I switched over to take a look at the news and noticed that Michael Jackson's heart had stopped and a short time later he was reported dead. I'm wondering if this sudden evil report is an echo of the "collage days" anecdote, which talks about the artist and gruesome happenings; in light of the singer's troubled public image, the Pagans anecdote might also have been a contributor.
After learning about Jackson's death, I stepped out of the library for a bite to eat and upon returning noticed a sign on the door advertising a rock performer who would sing for children that evening. The performer is a friend who is a member of the spiritually inclined group I was with at the picnic (though I don't recall that he was at the picnic). In fact, I later overheard some of his performance but did not attend.
The two singers who entertain children represent two spiritual paths offered in life, on the one hand represented by the hedonistic Pagans and on the other by the spiritually inclined group I was with (we like pleasure but strive against self-defeating pleasure).
Would all this mean that I think I caused a man's death? This type of thinking is akin to the questions that can and cannot properly be asked in quantum mechanics. The best that can be said is that the interference effects are followed by a possibly synchronistic report. The report very often is about an event that precedes the interference, just as would be expected in the discussion in my main article.
What do you know?
I had been studying differential equations the morning of April 23, 2009, and later jotted down a thought that impressed me taken from a book by Werner Heisenberg (Physics and beyond). He had written, according to my notes, that there were no determinants that could give the position of an emitted radium electron, that the quantum information gave all the knowledge there was.
Later, I visited a church where the speaker had the unusual first name, Knowledge.
I have many, many more personal anecdotes. But I don't have the notes of them and they are only randomly stored in my memory. So some of the more entertaining and perhaps compelling ones aren't here. If I happen to get around to it, I may add some more.
Time and tide
In the vicinty of noon, Wed., Sept. 25, 2013, on a whim, I posted the following on Facebook:
LUCKY 7?
So I have this hypothesis that the 7-days-of-creation story of Genesis is a poetic means of asserting the monotheistic idea, while incorporating pagan religious symbolism -- much in the manner of the church "christianizing" pagan holidays. The number 7 was important in the ancient near and middle East because there are 7 visible celestial objects, including planets, that wandered like gods, and were assumed to be gods.
(Note that not all ancient societies had a 7-day week. Egypt, for example, had an 8-day week.)
The early Hebrews thought of their god, El or Yahweh (meaning "He Is") as a god of gods (as in boss of bosses). But, that idea was later suppressed and the title changed to "Lord of Hosts." Similarly, when the 7-day account in Genesis was written, the author had in mind supplanting the 7 sky gods with seven powerful things that a single God had done. He was educating his hearers and readers to think monotheistically. Other parts of Genesis disclose the earlier idea that the god of the Hebrews was the most powerful of the gods, although these references were edited in order to conform to the new monotheism.
An interpretation: God was disclosing more about himself over time, but spoke to people in the language to which they were accustomed, as when Paul the apostle used Greek ideas to appeal to the people at Mars Hill.
About 2 p.m. that day, I left the Princeton Public Library for some strong coffee and on my way back, I glanced through the Labyrinth Bookstore's sidewalk sale racks and found, to my delight, a The Mystery of the Last Supper, a book by Colin J. Humphreys, whose The Miracles of Egypt had made a very favorable impression on me. Upon reading the beginning of the book, I reflected on on the "echoes" associated with my find. Firstly, I definitely considered the find to be happy fortune, or lucky. Secondly, Humphreys's book is highly focused on calendrical matters and associated celestial (astronomical) matters. Thirdly, Humphreys's book concerns historical interpretation of scripture. Fourthly, the book concerns the Creator, whom Christians believe authored the Creation described in Genesis. Fifthly, Humphreys's motive of applying modern critical analyses to discern the probable correct meaning scriptures, some of which seem contradictory, echoes what I was trying to do in my conjecture.
First posted June 25, 2009
Modified April 2013
Modified Sept. 2013
Monday, April 15, 2013
Where is Zion?
First published ca. 2005
Consider using a page monitor, such as Changedetection.com, to keep track of modifications of this page.
By PAUL CONANT
Many wonder about the emergence of the modern state of Israel. What is the divine purpose? Is this reconstituted Jewish state a sign of the end times? How should Christians deal with this situation?
The believer is admonished by scripture to beware false prophets, perhaps appearing as born again 'angels of light,' teaching demonic theories intended to hinder the work of the gospel of salvation through Jesus Christ [2 Cor 11.13]. Peter also warns that unspiritual people can falsely interpret the word of God. [2 Pet 1.20] Therefore, it is important that the believer, with the aid of the Spirit, examine the basis for various apocalyptic theories and timetables that are popular these days, rightly and diligently dividing scripture [2Tim 2.15]
An appendix (scroll down) contains interpretations of scriptures that contain the word 'Zion.'
Because many of those who adhere to such theories are known as Christian Zionists, it seems appropriate to examine the concept of Zionism from the point of view of gospel-centered, born-again Christianity, in accord with Christian precepts that anything can be tested against the Bible.
As Paul wrote: 'All scripture is inspired by God and profitable for teaching, for reproof, for correction, for training in righteousness; so that the man of God may be adequate, equipped for every good work.' [2 Tim 3.16,17]. However, when the flesh interprets scripture, the result is dead wrong, as we know from Satan's temptation of Jesus. Peter, in his struggle against false prophets, said that 'no prophecy of scripture is a matter of personal opinion,' not being an act of human will but rather of the Holy Spirit motivating the speaker [2 Pet 1.20,21].
EARLY IDEAS OF 'ZION'
The first biblical mention of 'Zion' is Deut. 4.48 and is another name for Mount Hermon in Lebanon. This 'Zion' derives from 'Sirion,' a name given to the mountain by the Sidonians. This Zion is referred to again in Psalm 133.3 when the poet compares brotherly love to 'the dew of Hermon coming down on the mountains of Zion.'
'Zion' is next cited in 2Sam 5.7, where it is reported that 'David took the stronghold of Zion (that is, the City of David).' This was a fortified enclave held by the Jebusites on a site later known as Jerusalem. David built his palaces in this fort and laid the groundwork for the first temple, which was built by his son Solomon, on a nearby hill. The term 'Zion' then came to refer to the entire palace and temple compound. It was often used specifically for the temple or the temple and its hill. Scholars think 'zion' was originally a word for 'hill.'
'Zion' was often extended in the Bible to mean the entire city of Jerusalem, where the general populace lived adjacent to the palace-temple compound. In fact, sometimes the Old Testament Bible extends the definition of 'Zion' to include the people of Israel or a remnant of that people.
THE CONCEPT OF TIME
Some Bible commentators seem to unconsciously believe that, when it comes to time, God is not as subtle as he is in other matters. They would have the anticipated fulfillments of prophecies fit nicely onto a 'railroad timetable.'
However, this illusion is refuted directly and indirectly by scripture.
Josh 10.13, describing the halting of the sun and moon, may be read literally or figuratively. The author may have meant that the victory was so astonishing that it was tantamount to the sun and moon standing still (and this may have been a jibe against a monarch whose authority supposedly included the sun and the moon).
Or, he may have been recounting that the sun, along with a pale daylight moon, stood still during the battle. If literally interpreted, then we see that God may extend a day's duration at will. If figuratively interpreted, then the author says that God is so powerful he could, if he wished, make the sun stand still, meaning in God's hands time is truly flexible, a point made by the prophet Daniel, who lauded God as one who 'changes times and the seasons' [Dan 2.21].
God's control of time is demonstrated in Is 38.8, when God told Hezekiah that the sun's shadow would go back ten steps on the stairway of Ahaz, which is what then happened. God showed that he erased a period of history that led up to the point in time of Hezekiah's death. He gave Hezekiah a new lease on life by bypassing a sin-laden time in this man's life.
The disciples found that their concepts of space gave way to the power of God when they were with Jesus in a boat in the middle of the Sea of Gallilee and suddenly found themselves at the shore. The time it takes to cross that space was voided. So, we can accept that God can and does compress time. Likewise, he can expand it, as we know from Hezekiah's experience.
Of a prophecy given to Habbakkuk, God said, 'For the vision is yet for the appointed time; it hastens toward the goal and will not fail. Though it tarries, wait for it; for it will certainly come, it will not delay'[Hab 2.3]. Note that the appointed time may seem, to human observers, to be close at hand or even overdue. So we can see that if the prophecy isn't fulfilled at an expected time, then it must be fulfilled in an unexpected way.
This point is driven home by the chronologically inconsistent narratives found in Genesis and elsewhere. For example, ages of Abraham and his family at key points don't jibe -- if we use modern western definitions. The number for age represented a benchmark, such as '40' representing the period of mature manhood, rather than a specific year.
But even if we 'solve' this difficulty, others remain: for example, when were the people of earth who married into the family of Adam and Eve born?
What happened to the giants (the nephilim or 'fallen') when the flood hit? These demon-people appear again after the flood. Could it be that time is not really representable as a real number line? Should we accept that perhaps the Bible contains serious errors (we certainly know that different versions contain minor errors that Bible scholars are continually attempting to correct), or might we conclude that there is simply much that we don't fully understand?
So then, if the Bible itself demonstrates the impossibility of drawing up a superficially logically consistent timeline of events of old, what makes us think we can use biblical references to map a 'logically consistent' history of the future?
Often in scripture, a time is said to arrive when the measure of something (such as sin or wrath) is full. The Greeks had two words for time: 'kronos' and 'kairos.' Kronos is the time of clocks and astronomical cycles. Kairos implies the propitous time. It is more spiritual in nature. A kairos time may be thought of as a balloon that fills up, perhaps quickly, perhaps slowly, with a gas until the point of bursting. That is when the consummation of the kairos time has arrived. We might consider the second coming as a the consummation of a kairos time.
Even atheists who seek the truth in modern physics have found that time is supple and relative, and not at all like the typical person's view of it. At extremely short intervals, time can be said not to exist. On larger scales, as Einstein proved, time is relative to the observer. Here's an idea of what that means: If you left earth on a starship traveling near the speed of light and traveled deep into space and then back, you would find that your twin brother was substantially older than you upon your return. In fact, you could conceivably return to an earth where centuries had elapsed, though for you only months had elapsed.
When Martha was grieving for Lazarus, dead for four days, she told Jesus she believed Jesus could get any favor from God. Jesus then told her that her brother would rise again. 'I know that he will rise again in the resurrection on the Last Day,' she answered. 'I am the resurrection and the life; he who believes in me will live even if he dies, and everyone who lives and believes in me will never perish. Do you believe this?'
You see, Martha had the traditional Jewish understanding of the Old Testament prophecies, but she was hoping Jesus would find a way to revive her brother anyway! Her faith was honored when Jesus said, in effect: Don't stand on tradition! Just BELIEVE! This is GOD talking! [John 11.22-26]
The great and awesome day of the Lord had arrived for Lazarus and was witnessed by Martha.
It wasn't the sidereal day that counted, but rather belief when the word came. The awesome day of the Lord is on a spiritual (which does not mean 'unreal') plane: 'SEE IT NOW! ETERNAL LIFE!'
In general, we may say that the launch of Jesus' salvation mission was indeed the dawn of the great day.
The malleability of time and the physical world is indicated in the variant accounts of the resurrection. Some skeptics see these seemingly irreconcilable versions as proof of biblical error. And, it is conceivable that God permits minor structural or form errors on the basis that it's the spirit that counts, just as when one hears a spirit-filled person give the word, even though he makes some grammatical or even factual slips. The slips are not important; it's the spirit, the word, that counts.
Even so, there is a serious school of thought among physicists known as the 'many worlds theory' -- reflecting Jesus' word, 'In my father's house are many mansions [possibilities]' [Jn 14.2] -- in which alternate realities can coexist. In some related areas of scientific conjecture, such alternate realities are thought to interact strongly rather than weakly.
Mathematicians are accustomed to dealing with 'projection,' in which a more complex form is projected as a set of simpler forms. For example, if you shine a flashlight above a globe, you will see an elliptical or circular shadow below.
Suppose we think of a unified event occurring in a purely spiritual dimension, such as heaven or hell, as being projected into the earthly dimension where man lives. It is quite reasonable to suppose that its projections, or reflections, will be fragmentary, meaning that, from a human perspective, the one 'higher dimension' event is seen in various ways at different times and places on the earthly plane.
You needn't believe that this idea is correct to see the point that the commonplace idea of linear time may not suffice for prophecy.
Earthbound people can be misled by a spirit of deception that puts falsehoods into the mouths of wicked prophets [1 Kings 22.22] and thus blinded by a 'strong delusion' [2 Thes 2.11]. While it is true that the born-again believer is fit to understand scripture, as illuminated by God's Spirit, it is still possible for the believer to be influenced by the delusive nature of this world.
DEAD LITERALISM
As Christians, we are strongly advised to study scripture [2 Tim 2.15]. We cannot however understand what we read without the help of the Holy Spirit. Though scripture is written in Hebrew and Greek, its origin is divine, and divine language is beyond human ken [Rom 8.26]. Scripture means what God says it means.
Who has plumbed the mind of God? Who has exhausted the deep well of the wisdom of God? [Rom 11.33,34]
God's thoughts are far above our thoughts [Is 55.9]. We must beware assuming that we can know the full meaning of a scriptural passage or group of scriptural passages.
Dead literalism is effectively refuted by Jesus in a number of places, such as when he healed on the sabbath day and when he upbraided the scribes and pharisees for focusing on technicalities rather than on the point of God's teachings: love of God and one another.
Jesus, obeying the Spirit, told his hearers that a scripture from Isaiah that he had just read had been 'fulfilled in your hearing.' [Luke 4.21] Jesus halted his reading at 'to proclaim the favorable year of the Lord,' leaving unread the other part of the couplet 'and the day of vengeance of our God.' [Is 61.1-2]
Does this mean the unquoted prophecy is untrue? No, but we can assume that the fulfillment of the entire passage from Isaiah does not necessarily follow a simple human schedule.
After the long-lost Book of the Law was recovered, it was read to the people and interpreted for them by the Levite priests [Neh 8.7]. Language and custom had evolved, so that strict literalism would have left the hearers perplexed. The Bible here shows that, without inspired interpretation, we have the dead letter of the law.
The word of God is 'alive and active and sharper than any two-edged sword, and piercing as far as the division of soul and spirit, of both joints and marrow, and able to judge the thoughts and intentions of the heart,' says the writer of Hebrews [Heb 4.12], after quoting several Old Testament passages.
So if a man is to understand the word, he cannot rely on human wisdom [1 Cor 1-9]. Just as the spirit within a man knows his thoughts, the Spirit of God knows God's thoughts [1 Cor 2.11]. In fact, the Spirit reveals scriptural meaning to believers 'for the Spirit searches all things, even the depths of God.' [1 Cor 2.10]
Or, as Paul wrote elsewhere, the new arrangement for Christians is 'not of the letter but of the spirit; for the letter kills, but the spirit gives life.' [2 Cor 3.6]. So the assertion that 'the Bible is literally true' should perhaps be changed to read that 'the Bible contains no error.' Since God 'makes all things work together for the good' for his chosen [Rom 8.28], he is able to make human missteps into truth. We know this from Caiaphas, who, as high priest, spoke a truth, though he had no idea of the divine profoundness of his words [Jn 18.14].
An example of literalness is the Mosaic command for Jews to put symbols of God's word on their foreheads and hands [Deut 6.8]. Some Jews to this day observe this custom. But, isn't it plain that the real point of this thought is that the Jews were to think about God's word and practice it? Why would God want people to honor this custom but not honor God's will in the more important area of behaving on the square with one's neighbors?
People who want to be excessively literal may not be aware that Jewish and Christian editors have over the centuries sifted ancient writings in efforts to obtain God's word at its purest. The fact that the Bible is such an authoritative source of truth and wisdom shows that many of these editors were, like Paul who rightly divided the word of truth [2 Tim 2.15], divinely inspired.
Many modern Bible texts identify words attributed to Jesus with red type or quotation marks. However, the Greek texts have no such graphical devices. This means that there are some passages sometimes attributed directly to Jesus that might actually be divinely inspired editorial comments. Also, there are variant literal versions of some of the words attributed to Jesus, though they are close in substance. With the aid of the Spirit, it is possible for the contemporary mind to understand the meaning of these words.
And the sayings of Jesus clearly were compiled early on and later woven into the synoptic gospel accounts. Does this make the gospel accounts wrong? Only if one insists on literally precise chronological narratives. Otherwise, they are rather like the modern newspaper report that lays out the relevant details in a way that 'tells a story.'
If a newspaper reporter extracts a couple of relevant sentences from some document and includes a one-sentence paraphrase in his story, he could not fairly be accused of improperly quoting the document. We should give Bible writers the same leeway. To wit, Paul, whose eyesight was poor and who probably relied on memory, in several places conflates scriptural passages in order to make a point. For example, Rom 9.33 apparently splices Is 28.16 and Is 8.14. This splice is easily defended as summarizing later prophetic fulfillments. So Paul is not in error, but we would be foolish to be excessively literal: there is no single such passage in the Septuagint (the Greek-language Bible in use at the time).
In Rom 11.26, Paul quotes scripture thus: 'The deliverer will come from Zion, he will remove ungodliness from Jacob. This is my covenant with them, when I take away their sins.'
The quotation is more a paraphrase than an exact quote. In fact, some might argue that the paraphrase misquotes Is 59.20,21 to give it a meaning it does not have. However, the import of the paraphrase is justified elsewhere, such as Psalm 14.7 and Psalm 15.
I sympathize with the apostle. I had in my mind that Jesus had, in assuring believers of his steadfastness, asked rhetorically whether a mother could forsake her child. It turns out that the relevant verse is Is 49.14, where I hear the voice of the Messiah.
Consider Mt. 21.5, which tells of Jesus' triumphal donkey ride into Jerusalem. Two old testament scriptures, Is 62.11 and Zech 9.9, are spliced together here, illustrating that different prophetic utterances can be fulfilled in one action.
Or consider John 12.15 which quotes Zech 9.9 but omits 'shout, O daughter of Jerusalem.' Yet, the omission is inconsequential. The meaning of Zech 9.9 is faithfully preserved. Writers of the period did not follow rules of quotation used today. So we cannot easily ascribe error here.
When we are told that 'the scripture cannot be broken' [Jn 10.35], the Old Testament was meant (specifically, Ps 82.6). So then, what do we make of Jude's citation from the Book of Enoch, which is regarded by Jewish and Christian scholars as largely a group of entertaining tall tales that on the whole lack divine inspiration?
Accepting that the Book of Jude is scripture, then is the scripture broken if Jude cites a non-scriptural source? [Jude 1.9]
Firstly, Jude was using an example from a book familiar to his contemporaries in order to make the moral point: If even Michael, in his dispute with Satan over Moses' body, wouldn't revile the devil himself, who are we to revile anyone at all? Now, regardless of the scriptural accuracy of this story, the moral point is substantiated by the words of Jesus, who occasionally alluded to the Book of Enoch.
And, we cannot rule out the possibility that the Book of Enoch contains fragments of real scripture and that Jude cites such a fragment.
New Testament writers cite numerous passages from the Old Testament in order to make their case about Jesus. However, if one were to apply the railroad timetable technique to the Old Testament writings, one would doubtless be able to argue that the writers were taking scripture out of context in order to justify their pet theories. But, the reality is the reverse: the Spirit illuminated the authors' minds as to how the written word was being fulfilled in their day. But the human wisdom -- railroad timetable analysis -- was to be scorned. As Paul said to the Corinthians, he decided to put Jesus first and then see what the Spirit revealed.
He always respected scripture, but insisted that the Spirit should lead in its interpretation.
So it is that sometimes a person apprehends a spiritual reality to such an extent that, for him, prophecy is being fulfilled. One wakes up to a truth, which was there all along, previously unnoticed. It's like suddenly seeing the solution to a math problem. The solution always existed, independently of the observer, but now that solution has become a potent part of the observer's reality.
Paul, when caught up to the third heaven, could not tell whether he was in the body or out of the body [2 Cor 12.2-4]. That is, the spirit world was so intense that the material world faded out, a non-issue. In paradise, Paul heard inexpressible words, which a man is not permitted to speak. That is, the language of heaven far exceeds the capacity of the earthly vessels. So we should be careful about trying to interpret spirit reality according to earthly standards.
Now Paul's experience here is echoed elsewhere in scripture: Sky (heaven) and earth had passed away! The sky was torn asunder and rolled up like a scroll! The stars fell from their places and sun and moon became nothing in comparison with God's glory [Is 34.4]! He was in paradise and his world was gone in the blink of an eye! Yet, we can expect that such scriptures will be fulfilled again in other ways.
Consider the believer content in Christ and filled with the Spirit not even noticing supposed bodily hardships. Sky and earth have begun to pass away, as with Stephen during his martyrdom. Or think of Jesus in the desert being comforted by angels following his victory over Satan. That desert was no desert! It was gushing with refreshing streams and blooming with beautiful flowers!
So we can see that fulfillment of scripture is not naively chronological but comes in surprising ways. Often a prophecy had already been in part fulfilled in the shadowy pre-gospel sense but awaited complete fulfillment in Jesus. Also, even when a prophecy is being fulfilled at the dawn of the Christian era, that does not mean there isn't more to come. For example, take Acts 2.17,18 when the spirit-filled Peter quotes Joel's prophecy that in the last days God will pour out his spirit on all flesh (1).
And indeed, since that time that prophecy has been fulfilled by God granting his Spirit to people of every race and background. And its fulfillment is not yet complete.
As Paul said, human wisdom is insufficient for understanding God. So we can appreciate that when God speaks to man through prophetic scripture, he is infusing man's tribal viewpoint and his local legends with the Spirit in order to lift the hearer into an expanded consciousness. He is using man's language and man's way of thinking to reflect God's thoughts.
Because of this, the word of God may seem to some to be ambiguous or inconsistent. Also, linear history seems to matter to modern humans far more than it does to God, who is focused on spiritual growth.
Our ability, even with the Spirit, to comprehend prophecy 'through a glass darkly' [1 Cor 13.12] (as a dim reflection) has a counterpart in modern astronomy. Before powerful telescopes made most of the physical cosmos observable, one could only make educated guesses as to most of what was out there, even though scientists had Einstein's highly accurate general theory of relativity as their 'bible.'
Though the theory's general predictions are repeatedly verified as astronomy progresses, no one in the early years of the 20th century anticipated the fantastic view of the cosmos that eventually unfolded.
Previously, scientists had the physical truth, and yet they still perceived the cosmos 'through a glass darkly' before having their consciousness expanded to a much bigger reality (and this reality is nothing in comparison to what God has in store).
The Book of Revelation can be thought of as the Big Picture of spiritual reality. It gives a panoramic sweep that includes events of the past and of the future. We can think of it as a completed picture of a jigsaw puzzle. But, try as we might, our human mental strength does not suffice to perfectly match puzzle pieces found elsewhere in scripture and in contemporary events to that Big Picture.
However, that does not mean we should ignore various 'end times' events unfolding about us. We should indeed use these events to toughen up in our Christian walk. Why are we being so worldly? Can't we see the Bible is right?
THE TRUE ZION
The issue of Judaism's primacy was addressed by Jesus and the apostles with such sayings as 'Salvation comes through the Jews' [Jn 4.22] 'to the Jew first, and then to the Gentile' [Rom 2.9,10], 'the first shall be last and the last shall be first' [Mt 20.16].
The Samaritan woman was puzzled by religious differences. 'Our fathers worshiped in this mountain,' she said, 'and your people say that in Jerusalem [on Mount Zion] is the place where men ought to worship.' Jesus replied, 'Woman, believe me, an hour is coming when neither in this mountain nor in Jerusalem will you worship the Father. You worship what you do not know; we worship what we know, for salvation is from the Jews. But an hour is coming, and now is, when the true worshipers will worship the Father in spirit and in truth.' [John 4.20-23].
In other words, God was creating a new world, or covenant, where the heart of the believer was the issue, as opposed to a particular geographic location.
In that same chapter, Jesus -- who was breaking the Middle Eastern taboo of conversing with a woman without her male folk present -- tells her that he would be happy to fill her up with 'living water' from a spring that won't run dry. 'Living water' (what in English is called 'running water') is a poetic description of the Holy Spirit. Jesus was bringing salvation to a hapless, roughly handled Palestinian woman.
The Lord was not terribly interested in geography or property rights [Luke 12.14]. His aim was and is to confer the gift of salvation and eternal life. Recall his assertions that 'the kingdom of heaven is within you' [Luke 17.21] and 'my kingdom is not of this world' [Jn 18.36].
The writer of Hebrews says that Jewish religious customs are a 'copy and a shadow of heavenly things.' [Heb 8.5]. Likewise, Paul wrote that the Jewish law, including the ten commandments, was intended to school the Jews as to the meaning of right and wrong so that they would become aware of how much they needed the unmerited favor of salvation [Gal 3.24].
A new order replaces the old order, as Heb. 8.8-13 says, quoting prophecy [Jer 31.31]:
'"Behold, days are coming, says the Lord, when I will effect a new covenant with the House of Israel and with the House of Judah; not like the covenant which I made with their fathers on the day when I took them by the hand to lead them out of the land of Egypt; for they did not continue in my covenant, and I did not care for them, says the Lord. For this is the covenant that I will make with the House of Israel after those days, says the Lord: I will put my laws into their minds, and I will write them on their hearts. And I will be their God. And they shall be my people..." When he said, "a new covenant," he has made the first obsolete.
But whatever is becoming obsolete and growing old is ready to disappear.'
And when does the new covenant appear? It is made evident at the Feast of Pentecost, when, as Peter said, quoting from Zechariah, Jerusalem became 'the city of truth.' That passage [Zech 8.2-17] also says that the Lord is 'exceedingly jealous for Zion.' The covenant dawned at Pentecost and is still in process of fulfillment.
Or, as Heb 12.22-24 points out, the terrifying experience of Mount Sinai is no more, but rather, 'you have come to Mount Zion and the City of the Living God, the heavenly Jerusalem, and to myriads of angels, to the general assembly and church of the firstborn who are enrolled in heaven, and to God, the judge of all, and to the spirits of the righteous made perfect, and to Jesus, the mediator of a new covenant...' Plainly, Zion here is a spiritual place, the realm of salvation. The old world of the old covenant will be shaken and only what is unshakable will remain, but 'we receive a kingdom which cannot be shaken' [Heb 12.27,28].
Paul says that eventually 'all Israel will be saved; just as it is written, "The deliverer will come from Zion, he will remove ungodliness from Jacob." "This is my covenant with them, when I take away their sins" [Rom 11.26,27]. Paul adds, 'From the standpoint of the gospel, they [the Jews] are enemies for your sake, but from the standpoint of God's choice they are beloved for the sake of the fathers; for the gifts and calling of God are irrevocable' [Rom 11.28,29].
He is explaining that the Jews have been partially hardened in order to permit the 'fulness of the Gentiles to be gathered into the body of Christ' (indicating that many who perished without seeing Jesus must still arise to meet him as their Savior).
A recurrent theme of Paul is the unity of Jews and Gentiles in Christ. In God's eyes, there is no distinction. 'For by one Spirit we were all baptized into one body, whether Jews or Greeks [Gentiles], whether slaves or free, and we were all made to drink of one spirit.' [1 Cor 12.13].
So then the new Zion is filled with the new Israel, the redeemed Jews and Gentiles. Under the new covenant, 'the virgin daughter of Zion' [2 Kings 19.21] has become the bride of Christ [2 Cor 11.2, Rev 21.9,24]. 'For out of Jerusalem will go forth a remnant, and out of Mount Zion, survivors' [2 Kings 19.31]. This prophecy was fulfilled by the fact that the Jewish identity survived Nebuchadnezzar's destruction of Jerusalem, but that prophecy is fulfilled in an expanded sense by the fact that born-gain Jewish Christians, the ultimate survivors, fanned out from Jerusalem.
A MAJOR SIGN
Though interpretation of end-times prophecies requires a special gift, there is one prophecy that stands out as a beacon in our time. Luke 21.24 quotes Jesus thus: 'and they will fall by the edge of the sword, and will be led captive into all nations; and Jerusalem will be trampled underfoot by the Gentiles until the times of the Gentiles are fulfilled.'
After the Romans led the Jews away captive, Jerusalem remained under Gentile domination for nearly 2,000 years. Upon Israel's founding in 1948, Jerusalem became the Jewish state's capital, though this status has long been a diplomatic sore point. After a fight, Jordan occupied east Jerusalem, but then lost that sector during the 1967 war.
So then, it is fair to say that the times of the Gentiles are about over. However, we might also note that Arabs predominate in East Jerusalem, possibly indicating that the Gentile era is not quite over. Certainly, the Israeli government cannot end the Gentile era by trying to complete this prophecy.
For one thing, the Gentile era is the period when the message of salvation is going out to the Gentiles. Once the full complement of Gentiles destined for salvation has been reached, then the Gentile era ends, according to Paul, writing in Romans 11.11-32 -- in particular Rom 11.25. Once this occurs, Paul says, Jews who had been unable to receive the gospel will be saved.
Of course, that implies that a powerful evangelical campaign must come in Israel, accompanied by great pressure to thwart the gospel.
Further light on the Gentile era is shed in the Book of Revelation (Rev 11.2) where John is told not to measure the outer court of the temple, which is given over to the Gentiles, who will tread Jerusalem underfoot for 42 months (three-and-a-half years).
Two witnesses will prophecy for 1,260 days (three-and-half years), clothed in sackcloth. They have tremendous power, and can kill with the fire of their mouths. (Rev 11.3-6)
In Rev 12.14, we are told that the woman flies from the serpent's presence to the wilderness to be nourished for three-and-a-half times.
This echoes Daniel 12.7, where it is prophesied that wonders would cease -- the world would end -- after three-and-a-half times. A general resurrection occurs after the holy ones are overcome, a theme found in Rev 11 and in Jesus' end-times discourse.
In scripture, a 'time' can be taken to be a solar year. And it is interesting that the Roman-Jewish war lasted about three-and-a-half years, culminating in the destruction of Jerusalem.
However, if we keep in mind the Greek idea of kairos, we might think of 'a time' as meaning a period in which certain trends accumulate until reaching the critical point, which ends that period. So then, we might interpret the three-and-a-half years of Revelation as three-and-a-half kairos times, meaning that the era of the Gentiles ends amidst some other era -- perhaps the age of grace, which must still be extended to the Jews.
Here we have another argument against eschatological timetables, since kairos eras can overlap. On the other hand, it should be acknowledged that some accept that Jeremiah's prophecy -- that Jerusalem would be resettled by the Jews after 70 years of desolations by Gentiles -- was fulfilled after about 70 solar years (Jer 25.11,12, Jer 29.10). However, Daniel, in Babylon, seems to have been perplexed that the 70 years was up and the prophecy in need of fulfillment, if solar years were meant. The angel Gabriel responded by giving Daniel a vision of the Messianic era to come, and explained that this era would begin after '70 weeks.'
Interpreting a week as seven years, the kronos time of 490 years seems to accord with the Jewish resettlement of Jerusalem in 538 BCE and the ascension of Jesus around 34 CE (about 496 years), though the Messiah was also supposed to be cut off after 62 weeks -- in kronos time, 434 years, which does not jibe.]
Realizing that the Spirit can cause believers to see a scripture or set of scriptures as being fulfilled in many ways, we offer this scenario as a possibility:
In Rev 11.2, the Gentiles are in the outer court of the temple. That is, these are the Gentiles being brought to salvation; meanwhile, the Gentiles are walking all over the holy city. Now, the 'holy city' may signify the kingdom of God -- which they, like the prostitutes, are storming into -- and-or it may signify earthly Jerusalem, which seems likely, since Jesus in Luke 21.24 certainly was talking about earthly Jerusalem. So then, we would assert that once earthly Jerusalem came under Jewish rule, the times of the Gentiles begin drawing to a close. Now which times are meant? One time evidently is the era for the gospel to the Gentiles; another time apparently is the era of Gentile rule over earthly affairs.
Now the two witnesses of Rev 11 may mean the Jewish Christian and the Gentile Christian components of the body of Christ. True Christians have tremendous power, as the gospel accounts and the Acts of the Apostles, show. But they are at their best when they are humble, eschewing earthly wealth. They are 'in sackcloth' during the age of witness, but eventually they will wear divine apparel. However, I am aware that such an interpretation might constitute a partial fulfillment of prophecy, with a complete fulfillment to come.
We are now in a position to suspect that the three-and-a-half times of Daniel may correspond with the three-and-a-half years of Rev 11. Similarly, we can interpret the woman of Rev 12 as the church -- the body of born-again believers -- who, harshly persecuted in Judea, escaped to the 'wilderness' of Gentile lands, where she has been nourished for three-and-a-half times.
However, I am uncertain as to what three eras are meant, though I would guess that the 'half-era' refers to the age of grace.
At various points, the Bible says that the coming of the last days is accompanied by birth pangs. Severe stress presages the birth of a new world era.
I suggest that the closing days of the age of the Gentiles mean great suffering on the part of the Gentiles. The plague of AIDS appears poised to sharply reduce the earth's population, possibly by 2028 (2). Poor nations are ill equipped to combat this disease, which has already devastated sub-Saharan Africa -- leaving 11 million AIDS orphans -- and which is on the verge of bringing about a similar catastophe across Eastern Europe, Russia and Asia. In addition, the rapid increase in global warming is likely to have numerous calamitous effects, including triggering devastating malarial and ebola epidemics.
We also cannot rule out the possibility that weapons of mass destruction may yet be unleashed on a genocidal scale. But, even if such arms are contained, pandemics and related famines are likely to promote civil disorder and war. The developed nations can no more escape the judgment than the Titanic could escape sinking. The great distress will cross borders, despite all efforts, and then spiral out of control in the supposedly safe areas.
We cannot say that the state of Israel will be unaffected. However, a remnant of Jews will remain, perhaps still in control of Jerusalem. Yet, the scepter of world rule will not be passed to earthly Israel. If so, why would the Bible repeatedly point to a Messianic era as the culmination of Jewish aspirations? My guess is that, while the distress of nations is under way, Israel will undergo a harsh internal fight as Christian Jews begin to make headway.
At some point, the Christian Jews will be eradicated. BUT, we cannot assume that this will occur at any particular time.
The scenario I have outlined is plausible, but I do not claim that I am correct in every jot and tittle.
A NOTE ON THE ABRAHAMIC BLESSING
An important topic of end-times discussions is the blessing given to Abraham, which was routed through the Jews.
'And I will bless those who bless you, and curse those who curse you: and in you shall all the families of the earth be blessed' [Gen 12.3].
Abraham's real descendents are those who heed God, not merely people with certain DNA characteristics who have been circumsized [Jn 8.39]. Obviously, the blessing points to Jesus, who blesses all the nations of the earth. Those who bless Abraham will be blessed and those who curse him will be cursed. This certainly applies to Abraham's spiritual progeny, the born-again Christian.
But supposing that God's pledge also applies to Abraham's descendents in the flesh, a question must be posed: does the pledge apply to the state of Israel, the Israeli government, Jewish residents of Israel, or Jews in general, wherever they live? I raise that question because some seem to equate any criticism of Israeli government policies as tantamount to invoking a curse against onself. I don't wish to attempt to neutralize the potency of that scripture, but I am concerned that some are deploying it for propaganda purposes.
THOUGHTS ON 'ELOHIM'
A verse in the Song of Moses, Deut. 32:8, reads:
'When the Most High apportioned the nations,
when he divided humankind,
he fixed the boundaries of the peoples
according to the number of the sons of God.'
The phrase 'sons of God' was rendered 'sons of Israel' in the traditional Jewish Bible, but a fragment from the Dead Sea scrolls attests to the former.
Who were these sons of God? Were they related to the sons of God who intermarried with earth women and spawned demonic offspring? What is known is that various non-canonical writings, along with some clues in the Bible, indicate that these were the 70 (probably a symbolic number) angels who led the nations surrounding ancient Israel. The highest of these divine beings, who came to be known as Elohim and also YHWH (roughly: 'Yahweh'), chose the nation of Israel for himself.
Scholars have found that, though 'Elohim' is used in the singular in the Hebrew scripture that we have now, the word itself is a plural form of 'El,' which was the name of the Canaanite's chief god. So 'Elohim' simply means 'the gods.'
But the Hebrews were forbidden to worship any God but Elohim -- which evolved into a a generic name for God -- who eventually revealed his special name to them as YHWH, just as he has revealed to Christians his special name of his son Jesus. Elohim brooked no competition from his 'sons.'
So it is apparent that the Hebrews knew of the Canaanite pantheon -- which is similar to other pantheons, in which one god is chief of the others.
However, as Hebrew religion and language evolved, we find that the Canaanite 'sons of El' -- which is equivalent to 'the gods' -- becomes 'sons of Elohim,' which is later rendered as 'angels,' which are directly created divine beings (note that this makes Jesus a hybrid of son of man -- because born of a woman -- and angel, or son of God, because directly created, which is also what born-again believers are). Angels could have god-like power but were not to be worshiped. The theological issue bothered the Pharisees, who took 'son of God' to mean a god who must not be worshiped.
Elsewhere we learn that Michael is Israel's special protecting angel (whose name means 'Who is like God?'). So then he is, possibly, identified as a projection (message) of Elohim. In addition, we learn in Daniel and Revelation (and in extra-biblical texts) that Michael is waging war with the devil and his angels. In particular, we find that the prince of Persia is a demonic angel. So we can guess that the angels that lead the nations are demonic, or at any rate inferior, angels, perhaps those who intermarried with earth girls.
We might think of the pantheon of the gods as a muddled (reprobate) intuition of a situation in which the human soul is a projection of a particular angel. So all those who are a projection of a particular angel are in the 'nation' ruled by this angel. But Jesus taught that those who are not ruled by the Father must be ruled by Satan, implying that the unregenerate are either reflections of fallen angels, or, are tares that have been planted by an enemy.
Be this as it may, clearly some will suspect that the Jewish religion is simply a variant of the older Canaanite religion with which it clearly has similarities. Scholars would add that as Jewish theology evolved, it took on some of the imagery and concepts of Zoroastrianism, a Persian religion of great antiquity. (A number of Zoroastrian concepts make sense in terms of Judaeo-Christian traditions. Take, for example, 'the Lie,' which can be thought of as a place where many are headed. It is also the pull to proceed into such a place. The Lie is the door opening to one of the 'many mansions' in God's universe, as well as the pull toward that door. The Lie is the pull toward Death, death itself being a lie.)
So my thinking is that God was using the imagery with which the Hebrew tribesmen were familiar in order to gradually unveil the higher things of God. Recall Paul on Mars Hill, when he preached to the Athenians on the 'unknown God.' The monument to which he referred was put there in the event that the polite and cosmopolitan Athenians had neglected to honor some visitor's god. Yet Paul used the concept of 'unknown God' as a jumping off point to preach the good news that the way to know God was via Jesus Christ. Similarly, we can see that God could have used old stories, imbuing them with his spirit, in order to reveal some of the depth and magnitude of the true God.
Think of the transfiguration:
Jesus had previously quoted a scripture that said 'you are gods' (or possibly 'you are as gods') and had held that if God IS the God of Abraham and Isaac, then God is the God of the living.
On the mountain, his disciples saw him with Moses and Elijah, all blazing with unearthly light, and then, after closing their eyes in fear, saw only Jesus.
That is, these divine beings were united by a single Spirit.
As Paul says, born-again believers are heirs with Jesus of the kingdom [Eph 3.6], sons of God that is. In fact, they are as gods, indeed they are gods. Nevertheless, they, who are junior partners of Christ, are certainly not to be worshiped.
The promise to the believer is that, as he becomes more Christ-like, he will become one with God -- though he actually is already one with God, just as Jesus is one with the Father.
In any event, we can see that the Hebrew word 'Elohim,' though it stemmed from a pagan theory, fits well with God's revelation to the Jews, who he did indeed choose as his special people, though their heory of God is past its prime.
APPENDIX: 'Zion' prophecies interpreted
Following are my interpretations of a number of scriptures concerning Zion:
Ps 9.11
'Sing praises to the Lord, who dwells in Zion.'
Under the old covenant, the invisible God dwelt in the ark of the covenant. Within that ark were the stone tablets on which God had personally inscribed the 10 commandments. The two stones can be viewed as a token of God's covenant with the children of Israel. But also we see that the Lord himself was the true covenant -- the word and the guarantor of that word.
Under the new covenant, the invisible God -- the Spirit of God -- dwells in the mind of the believer, making the believer's body, 'the temple of the Holy Spirit' [1 Cor 6.19]. So then, would God go back to the old covenant in order to take up residence in another stone temple?
Ps. 14.7
'O that the salvation of Israel would come out of Zion, when the Lord restores his captive people, Jacob will rejoice, Israel will be glad.'
Jesus rose to heaven out of Jerusalem, where he could then send the Spirit to the Jews -- and Gentiles -- who were to be set free. 'Whom the son sets free is free in deed'[John 8.36].
Ps. 65.1
'silence before you and praise in Zion'
Or, 'be still and know I AM' [Ps 46.10]. This intimacy with God requires the presence of Jesus in the believer, who then can enjoy God.
Ps. 69.35,36
'For God will save Zion and build the cities of Judah, that they may dwell there and possess it. The descendants of his servants will inherit it, and those who love his name will dwell in it.'
Zion and the cities of Judah are reserved for the descendants of his servants and those who love God's name. A true descendant of God's servant is also God's servant. Otherwise the devil is his father [Jn 8.44]. So is earthly Jerusalem filled with such people?
The 'cities of Judah' needn't refer to old Middle Eastern towns; instead what is indicated is a land where the redeemed, who love the name Jesus, can enjoy life.
Ps. 78.67,68,70
'He also rejected the tent of Joseph, and did not choose the tribe of Ephraim, but chose the tribe of Judah, Mount Zion which he loved.'... 'He also chose David his servant and took him from the sheepfolds.'
Though this refers to the preservation of David's tribe, Judah, after the destruction of the other 11 tribes, these words are fulfilled by Jesus, the good shepherd descendant of David, who established spiritual Zion by his conquest of evil at the cross.
Ps. 84.5,7
'How blessed is the man whose strength is in you, in whose heart are the highways (to Zion)... every one of them appears before God in Zion.'
Those who love God are approaching Zion.
Ps. 87.2
'The Lord loves the gates of Zion more than all the other dwelling places of Jacob.'
English-language translations of the Bible customarily italicize words not found in the Hebrew or Greek scriptures but that seemed necessary. In this case, if we omit 'other,' we can interpret this passage to say that 'Jacob' refers to the unregenerate Jew. He cannot enter Zion until he has been transformed, by the renewing of his mind [Rom 12.2] into 'Israel.' The name 'Israel' means 'wrestler with god' and the name 'Jacob' means 'he who grabs by the heel' or more generally 'trickster.'
Recall the encounter between Jesus and Nathanael, who knew salvation was to proceed from Jerusalem. Nathanael's question 'Can any good thing come out of Nazareth?' was followed by Jesus' retort: 'Look, a real Israeli, in whom there is no guile.' Or, that is: 'Look, a real contender with God, in whom there is no Jacob.'
Ps. 87.6
'The Lord will count when he registers the peoples, "This one was born there [in Zion]."
As Jesus said, the birth that counts is the spiritual birth. Those written in the Lamb's Book of Life [Rev 20.12] have been born of the Spirit, not of flesh and blood [Jn 3.5,6]. So there is no use having been born in Jerusalem if one hasn't been born again, saved by the intervention of Jesus Christ.
Ps. 97.7
'Let all those be ashamed who serve graven images, who boast themselves of idols ... Zion heard this and was glad.'
The real Zionists are glad when God shames the money-worshipers and their type.
Ps. 99.2
'The Lord is great in Zion'
Or, Zion is a place where the Lord's glory shines brightly. And isn't that in the hearts of those who worship God 'in spirit and in truth'?
Ps. 102.21
'that men may tell the name of the Lord in Zion'
Utterance of that name -- as represented in scripture by the Hebrew letters YHWH -- came to be forbidden to Jews of old and such utterance is still considered impious for Jewish residents of modern Jerusalem, assuming anyone could be sure of the pronunciation.
The name of the Lord, under the old covenant, is not, under the new covenant, fully revealed since the name of 'Jesus' suffices as the name of the Lord.
It has become possible to tell the name of the Lord openly, even if with difficulty.
'Jesus' or 'Yah shua' means 'Yaweh saves.' Knowing this name suffices just as seeing Jesus sufficed for seeing the Father [Jn 14.8].
Ps 110.1,2
'The LORD says to my Lord: sit at my right hand until I make your enemies a footstool for your feet. The LORD will stretch forth your strong scepter from Zion...'
Jesus cites this passage [Mt 22.44] to show that David calls his son, the messiah, his lord. So then we can be sure that Jesus is one with YHWH (the name of God using only consonants, as translated from Hebrew) whose great power over heaven and earth extends from the kingdom of God, which is Zion.
The fourth verse of this psalm says that God has determined that this savior is 'a priest forever according to the order of Melchizedek,' a passage that Heb. 7.21 says refers to Jesus, the consummate priest.
Ps. 129.5
'May all who hate Zion be put to shame and turned backward.'
Those who love their sin more than the light remain under judgment and are continually injured by their own wilfulness [Jn 3.18], since they reap what they sow [Gal 6.7].
A specific instance of this scripture being fulfilled occurred when an armed troop came to arrest Jesus. Jesus asked whom they sought. When told, he replied, 'I am he.' On hearing 'I am,' which is a name for God, the men stumbled backward in confusion and were then only able to proceed with God's permission [Jn 18.4-6].
Ps 135.21
'Blessed be the LORD from Zion, who dwells in Jerusalem.'
The writer was likely thinking of the Temple in Jerusalem. Yet, when Jesus died on the cross, the veil of the Temple was torn apart, indicating the departure of God's Spirit from the veiled ark of the covenant. Where does the Lord dwell today? Within those who put their trust in Jesus.
Is 1.27
'Zion will be redeemed with justice and her repentant ones with righteousness.'
Justice was served by the sacrifice of Jesus, the son of God, whose crucifixion paid in full the price of all sin.
Those who humbly turn to him will be made right with God.
Is 8.18
'Behold, I and the children whom the Lord has given me are for signs and wonders from the LORD of hosts, who dwells on Mount Zion.'
Heb 2.13 takes this passage to refer to Jesus.
Is 24.23
'The LORD of hosts will reign on Mount Zion and in Jerusalem.'
We know that Mount Zion is a spiritual place and the Book of Revelation tells us to expect a new, heavenly Jerusalem [Rev 3.12].
Is 28.16,18
'Behold, I am laying in Zion a stone, a tested stone, a costly cornerstone for the foundation, firmly placed. He who believes in it will not be disturbed [moved].'
'Your pact with Sheol will not stand.'
Paul in Rom 9.33 and Peter in 1 Pet 2.6 say Is 28.16 refers to Jesus. Now the old, earthly Zion was overthrown by the Romans in 70 A.D. So the new Zion is the kingdom of God that Jesus is yet bringing forth.
Jesus will cancel the sin-sick soul's contract with death.
Is 29.8
'It will be as when a hungry man dreams--and behold, he is eating; but when he awakens, his hunger is not satisfied, or when a thirsty man dreams--and behold, he is drinking, but when he awakens, behold, he is faint and his thirst is not quenched. Thus the multitude of all the nations will be who wage war against Mount Zion.'
Anybody who fights God is deluded. Any 'victory' over the LORD is hollow.
Though this passage specifically refers to Gentiles, certainly it also holds for Jews.
A nearby passage [Is 29.10] says that God 'has poured over you a spirit of deep sleep [or 'strong delusion']' blinding the prophets and the seers. Paul [Rom 11.8] says this scripture applies to the bulk of the Jews, who 'were hardened.'
That is, those who resist God, and his works, are turned away from his kingdom by a strong delusion, reminiscent of the angels guarding the gates of Eden.
Is 30.19-21
'O people in Zion, inhabitant in Jerusalem, you will weep no longer. He will surely be gracious to you at the sound of your cry; when he hears it, he will answer you. Although the Lord has given you bread of privation and water of oppression, your Teacher will no longer hide himself, but your eyes will behold your Teacher.
Your ears will hear a word behind you, "This is the way, walk in it," whenever you turn to the right or the left.'
God will comfort his people. Yet, who can see God? Yet his people will see the Teacher, who will guide their minds. Those who walk with Jesus recognize the Teacher's voice [Jn 10.27], which can only be heard via the Holy Spirit. He is the road and he makes sure that every follower will learn more and more about God.
Is 31.4,9
Like a lion with its prey unworried by the shepherds, so will 'the LORD of hosts come down to wage war on Mount Zion and on its hill.'
'whose fire is in Zion and whose furnace is in Jerusalem.'
Have you ever noticed that on occasion titanic contests occur with little recognition of what is going on -- hardly anyone is paying attention?
Jesus was sent by the Father to wage spiritual warfare against the devil and his hordes. A scene in that struggle occurred when he picked up a whip and drove the businessmen from the Temple.
Certainly Jesus could not be deterred from achieving his victory over hell.
That victory was exemplified when, during the feast of Pentecost, tongues of fire descended upon the apostles in Jerusalem to launch the true church.
Is 33.5
'He has filled Zion with justice and righteousness.'
Not much of that in wordly Jerusalem. However, Jesus embodies the phrase 'justice and righteousness.'
Is 33.20
'Look upon Zion... Your eyes shall see Jerusalem ... a tent which will not be folded; its stakes will never be pulled up. No oarboat or warship will pass on its great streams.'
What great streams? These must be streams flowing in the heavenly Jerusalem of Rev 3.12, where commerce and war are no more.
Is 35.5,6,10
'Then the eyes of the blind will be opened and the ears of the deaf will be unstopped. Then the lame will leap like a deer, and the tongue of the mute will shout for joy.'
'And the ransomed of the LORD will return and come with joyful shouting to Zion, with everlasting joy upon their heads.'
When John the Baptist queried Jesus as to whether he was the Messiah, Jesus replied: 'Go and report to John what you have seen and heard: the blind receive sight, the lame walk, the lepers are cleansed and the deaf hear, the dead are raised up, the poor have the good news preached to them.'
All of Isaiah 35 foretells, in rhapsodic imagery, Zion's wonderful future. From Jesus' response, we can see that he was a sign of the true Zion. And a person who has truly received Jesus as Lord has entered that Zion, the land of eternal bliss, and, despite hardships, will shout for joy at the wonder of this event.
Is 37.32
'For out of Jerusalem will go forth a remnant and out of Mount Zion, survivors.'
Those who have been born by the Spirit.
Is 40.9
'Get yourself up on a high mountain, O Zion, bearer of good news ... say to the cities of Judah "Here is your God."'
Jesus was lifted up on Mount Calvary with the inscription: 'King of the Jews.'
Is 49.14
'But Zion said, the LORD has forsaken me...'
Jesus cried out on the cross: 'My God, my God, why have you forsaken me?' [Mk 15.34]
Is 51.3
'Indeed, the LORD will comfort Zion...and her wilderness he will make like Eden.'
How sweet it is to follow Jesus.
Is 51.11
'So the ransomed of the LORD will return and come with joyful shouting to Zion.'
How wonderful to have your sins paid for by Jesus.
Is 52.3
Zion 'will be redeemed without money.'
Those destined for eternal life have had their sin paid for by the blood of Jesus.
Is 52.7
'How lovely on the mountains are the feet of him who brings good news, who announces peace and brings good news of happiness, who announces salvation, and says to Zion, "Your God reigns!"'
Jesus announced the good news of salvation, and so do his followers.
Is 52.8
'For they will see with their own eyes when the LORD restores Zion.'
Witnesses saw the works of Jesus, including his ascension into heaven. However, many of those suffering spiritual blindness were unable to see that Zion was being restored. Isaiah begins his description of the suffering servant with 'who has believed our report?' [Is 53.1]
Is 61.2,3
'...to comfort all who mourn, to grant all those who mourn in Zion...'
Jesus tells us to fear not, to be cheerful, because he has overcome the world [Jn 16.33].
Jesus told his hearers that Is 61.1,2 had been fulfilled in their hearing.
Is 62.1,2
'For Zion's sake will I not hold my peace, and for Jerusalem's sake, I will not rest' until the 'nations [Gentiles] will see your righteousness...and you will be called by a new name, which the mouth of the LORD will designate.'
The name of Jesus is lifted up among the Gentiles.
Is 66.8
'Can a land be born in one day? Can a nation be brought forth all at once? As soon as Zion travailed, she also brought forth her sons.'
The new Zion was brought forth by the sacrifice of Jesus and began in power on the day of the feast of Pentecost, when immediately thousands turned to Jesus for salvation [Acts 2.41].
Jer 3.14
'...return O faithless sons...and I will take you one from a city, and two from a family, and I will bring you to Zion.'
Many are called, but few are chosen for Christ's kingdom.
Joel 2.32
'And it will come about that whoever calls upon the name of the LORD will be delivered; for on Mount Zion and in Jerusalem there will be those who escape.'
Paul in Rom 10.13 applies this scripture to anyone who calls on Jesus, who will then escape hellfire. Joel 2.28 -- 'I will pour out my spirit on all mankind' -- is cited by Peter during the Pentecost speech.
Had Jesus' warning been remembered [Lk 21.20], those in Jerusalem during the Roman-Jewish war would have known it was time to flee when they saw the Temple profaned by Jewish rebels.
In the case of the prophecies of Joel and of Jesus, we can see that they may be specifically fulfilled and yet we cannot rule out their being fulfilled again. However, Paul is less interested in 'future history' than in getting people to see the main point: the salvation provided by Jesus more than fulfills scripture.
Obadiah 17
'...on Mount Zion will be those who escape...'
Those who escape the wrath to come [Mt 3.7] are those who put their trust in Jesus.
Mic 4.2
'Many nations will come and say, Come let us go up to the mountain of the LORD and to the house of the
God of Jacob, that he may teach us about his ways and that we may walk in his paths. For from Zion will go forth the law, even the word of the LORD from Jerusalem.'
Some may read this passage literally, but I see it as fulfilled by non-Jews who are able to get into the kingdom of God through the mercy of Jesus, who is the word of the LORD personified and who is the fulfillment of the law of the LORD. As Jesus taught at age 12, the House of God is the work of the Lord [Lk 2.49] and for humanity the greatest work is salvation.
Zeph 3.12-15
'But I will leave among you a humble and lowly people, and they will take refuge in the name of the LORD.
The remnant of Israel will do no wrong and tell no lies, nor will a deceitful tongue be found in their mouths; for they will feed and lie down with no one to make them tremble.
'Shout for joy, O daughter of Zion! Shout in triumph, O Israel!...The LORD has taken away his judgments against you, he has cleared away your enemies.'
Jesus told us to learn of him, who is humble and lowly [Mt 11.29]. Those who trust in Jesus, who paid for all crimes against God, no longer need fear anything at all, and as they are perfected, they become less and less prone to wrongdoing. And God does not look upon sin because the believer has been pardoned by Jesus. So those put right with God through Jesus have every reason to shout for joy.
Zec 9.9
'Rejoice greatly, O daughter of Zion...Behold your king is coming to you; he is just and endowed with salvation, humble and mounted on a donkey...'
Fulfilled by Jesus' triumphal entry into Jerusalem, where he was greeted as the son of David -- the Messiah.
Zec 9.10
'I will cut off the [war] chariot from Ephraim and the [war] horse from Jerusalem; and the war bow will be cut off. And he will speak peace to the nations; and his dominion will be from sea to sea, and from the River to the ends of the earth.'
Jesus, who has been granted all power in heaven and earth, gives his followers the 'peace of God, that passes understanding'[Phlp 4.7]. Once his kingdom has spread everywhere, warfare will cease.
(1) Colin J. Humphreys, a Cambridge scientist and Bible investigator, has analyzed Peter's interpretation of the prophecy of Joel as related to historical events that can be corroborated. His keen mind is revealed in his book The Mystery of the Last Supper: Reconstructing the Final Days of Jesus (Cambridge University Press, 2011). He is also the author of The Miracles of Exodus: a Scientist Reveals the Extraordinary Natural Causes Underlying the Biblical Miracles (Harper Collins, 2003).
His web site: http://www.csap.cam.ac.uk/network/colin-humphreys/
(2) When that was written, such a global catastrophe seemed plausible. However, education and distribution of anti-AIDS medicines seems to have blunted the threat, though we cannot be sure it won't return.
______________________________
Sept. 2013. This article has had minor editing on several occasions between 2005 and Sept. 2013.
Consider using a page monitor, such as Changedetection.com, to keep track of modifications of this page.
By PAUL CONANT
Many wonder about the emergence of the modern state of Israel. What is the divine purpose? Is this reconstituted Jewish state a sign of the end times? How should Christians deal with this situation?
The believer is admonished by scripture to beware false prophets, perhaps appearing as born again 'angels of light,' teaching demonic theories intended to hinder the work of the gospel of salvation through Jesus Christ [2 Cor 11.13]. Peter also warns that unspiritual people can falsely interpret the word of God. [2 Pet 1.20] Therefore, it is important that the believer, with the aid of the Spirit, examine the basis for various apocalyptic theories and timetables that are popular these days, rightly and diligently dividing scripture [2Tim 2.15]
An appendix (scroll down) contains interpretations of scriptures that contain the word 'Zion.'
Because many of those who adhere to such theories are known as Christian Zionists, it seems appropriate to examine the concept of Zionism from the point of view of gospel-centered, born-again Christianity, in accord with Christian precepts that anything can be tested against the Bible.
As Paul wrote: 'All scripture is inspired by God and profitable for teaching, for reproof, for correction, for training in righteousness; so that the man of God may be adequate, equipped for every good work.' [2 Tim 3.16,17]. However, when the flesh interprets scripture, the result is dead wrong, as we know from Satan's temptation of Jesus. Peter, in his struggle against false prophets, said that 'no prophecy of scripture is a matter of personal opinion,' not being an act of human will but rather of the Holy Spirit motivating the speaker [2 Pet 1.20,21].
EARLY IDEAS OF 'ZION'
The first biblical mention of 'Zion' is Deut. 4.48 and is another name for Mount Hermon in Lebanon. This 'Zion' derives from 'Sirion,' a name given to the mountain by the Sidonians. This Zion is referred to again in Psalm 133.3 when the poet compares brotherly love to 'the dew of Hermon coming down on the mountains of Zion.'
'Zion' is next cited in 2Sam 5.7, where it is reported that 'David took the stronghold of Zion (that is, the City of David).' This was a fortified enclave held by the Jebusites on a site later known as Jerusalem. David built his palaces in this fort and laid the groundwork for the first temple, which was built by his son Solomon, on a nearby hill. The term 'Zion' then came to refer to the entire palace and temple compound. It was often used specifically for the temple or the temple and its hill. Scholars think 'zion' was originally a word for 'hill.'
'Zion' was often extended in the Bible to mean the entire city of Jerusalem, where the general populace lived adjacent to the palace-temple compound. In fact, sometimes the Old Testament Bible extends the definition of 'Zion' to include the people of Israel or a remnant of that people.
THE CONCEPT OF TIME
Some Bible commentators seem to unconsciously believe that, when it comes to time, God is not as subtle as he is in other matters. They would have the anticipated fulfillments of prophecies fit nicely onto a 'railroad timetable.'
However, this illusion is refuted directly and indirectly by scripture.
Josh 10.13, describing the halting of the sun and moon, may be read literally or figuratively. The author may have meant that the victory was so astonishing that it was tantamount to the sun and moon standing still (and this may have been a jibe against a monarch whose authority supposedly included the sun and the moon).
Or, he may have been recounting that the sun, along with a pale daylight moon, stood still during the battle. If literally interpreted, then we see that God may extend a day's duration at will. If figuratively interpreted, then the author says that God is so powerful he could, if he wished, make the sun stand still, meaning in God's hands time is truly flexible, a point made by the prophet Daniel, who lauded God as one who 'changes times and the seasons' [Dan 2.21].
God's control of time is demonstrated in Is 38.8, when God told Hezekiah that the sun's shadow would go back ten steps on the stairway of Ahaz, which is what then happened. God showed that he erased a period of history that led up to the point in time of Hezekiah's death. He gave Hezekiah a new lease on life by bypassing a sin-laden time in this man's life.
The disciples found that their concepts of space gave way to the power of God when they were with Jesus in a boat in the middle of the Sea of Gallilee and suddenly found themselves at the shore. The time it takes to cross that space was voided. So, we can accept that God can and does compress time. Likewise, he can expand it, as we know from Hezekiah's experience.
Of a prophecy given to Habbakkuk, God said, 'For the vision is yet for the appointed time; it hastens toward the goal and will not fail. Though it tarries, wait for it; for it will certainly come, it will not delay'[Hab 2.3]. Note that the appointed time may seem, to human observers, to be close at hand or even overdue. So we can see that if the prophecy isn't fulfilled at an expected time, then it must be fulfilled in an unexpected way.
This point is driven home by the chronologically inconsistent narratives found in Genesis and elsewhere. For example, ages of Abraham and his family at key points don't jibe -- if we use modern western definitions. The number for age represented a benchmark, such as '40' representing the period of mature manhood, rather than a specific year.
But even if we 'solve' this difficulty, others remain: for example, when were the people of earth who married into the family of Adam and Eve born?
What happened to the giants (the nephilim or 'fallen') when the flood hit? These demon-people appear again after the flood. Could it be that time is not really representable as a real number line? Should we accept that perhaps the Bible contains serious errors (we certainly know that different versions contain minor errors that Bible scholars are continually attempting to correct), or might we conclude that there is simply much that we don't fully understand?
So then, if the Bible itself demonstrates the impossibility of drawing up a superficially logically consistent timeline of events of old, what makes us think we can use biblical references to map a 'logically consistent' history of the future?
Often in scripture, a time is said to arrive when the measure of something (such as sin or wrath) is full. The Greeks had two words for time: 'kronos' and 'kairos.' Kronos is the time of clocks and astronomical cycles. Kairos implies the propitous time. It is more spiritual in nature. A kairos time may be thought of as a balloon that fills up, perhaps quickly, perhaps slowly, with a gas until the point of bursting. That is when the consummation of the kairos time has arrived. We might consider the second coming as a the consummation of a kairos time.
Even atheists who seek the truth in modern physics have found that time is supple and relative, and not at all like the typical person's view of it. At extremely short intervals, time can be said not to exist. On larger scales, as Einstein proved, time is relative to the observer. Here's an idea of what that means: If you left earth on a starship traveling near the speed of light and traveled deep into space and then back, you would find that your twin brother was substantially older than you upon your return. In fact, you could conceivably return to an earth where centuries had elapsed, though for you only months had elapsed.
When Martha was grieving for Lazarus, dead for four days, she told Jesus she believed Jesus could get any favor from God. Jesus then told her that her brother would rise again. 'I know that he will rise again in the resurrection on the Last Day,' she answered. 'I am the resurrection and the life; he who believes in me will live even if he dies, and everyone who lives and believes in me will never perish. Do you believe this?'
You see, Martha had the traditional Jewish understanding of the Old Testament prophecies, but she was hoping Jesus would find a way to revive her brother anyway! Her faith was honored when Jesus said, in effect: Don't stand on tradition! Just BELIEVE! This is GOD talking! [John 11.22-26]
The great and awesome day of the Lord had arrived for Lazarus and was witnessed by Martha.
It wasn't the sidereal day that counted, but rather belief when the word came. The awesome day of the Lord is on a spiritual (which does not mean 'unreal') plane: 'SEE IT NOW! ETERNAL LIFE!'
In general, we may say that the launch of Jesus' salvation mission was indeed the dawn of the great day.
The malleability of time and the physical world is indicated in the variant accounts of the resurrection. Some skeptics see these seemingly irreconcilable versions as proof of biblical error. And, it is conceivable that God permits minor structural or form errors on the basis that it's the spirit that counts, just as when one hears a spirit-filled person give the word, even though he makes some grammatical or even factual slips. The slips are not important; it's the spirit, the word, that counts.
Even so, there is a serious school of thought among physicists known as the 'many worlds theory' -- reflecting Jesus' word, 'In my father's house are many mansions [possibilities]' [Jn 14.2] -- in which alternate realities can coexist. In some related areas of scientific conjecture, such alternate realities are thought to interact strongly rather than weakly.
Mathematicians are accustomed to dealing with 'projection,' in which a more complex form is projected as a set of simpler forms. For example, if you shine a flashlight above a globe, you will see an elliptical or circular shadow below.
Suppose we think of a unified event occurring in a purely spiritual dimension, such as heaven or hell, as being projected into the earthly dimension where man lives. It is quite reasonable to suppose that its projections, or reflections, will be fragmentary, meaning that, from a human perspective, the one 'higher dimension' event is seen in various ways at different times and places on the earthly plane.
You needn't believe that this idea is correct to see the point that the commonplace idea of linear time may not suffice for prophecy.
Earthbound people can be misled by a spirit of deception that puts falsehoods into the mouths of wicked prophets [1 Kings 22.22] and thus blinded by a 'strong delusion' [2 Thes 2.11]. While it is true that the born-again believer is fit to understand scripture, as illuminated by God's Spirit, it is still possible for the believer to be influenced by the delusive nature of this world.
DEAD LITERALISM
As Christians, we are strongly advised to study scripture [2 Tim 2.15]. We cannot however understand what we read without the help of the Holy Spirit. Though scripture is written in Hebrew and Greek, its origin is divine, and divine language is beyond human ken [Rom 8.26]. Scripture means what God says it means.
Who has plumbed the mind of God? Who has exhausted the deep well of the wisdom of God? [Rom 11.33,34]
God's thoughts are far above our thoughts [Is 55.9]. We must beware assuming that we can know the full meaning of a scriptural passage or group of scriptural passages.
Dead literalism is effectively refuted by Jesus in a number of places, such as when he healed on the sabbath day and when he upbraided the scribes and pharisees for focusing on technicalities rather than on the point of God's teachings: love of God and one another.
Jesus, obeying the Spirit, told his hearers that a scripture from Isaiah that he had just read had been 'fulfilled in your hearing.' [Luke 4.21] Jesus halted his reading at 'to proclaim the favorable year of the Lord,' leaving unread the other part of the couplet 'and the day of vengeance of our God.' [Is 61.1-2]
Does this mean the unquoted prophecy is untrue? No, but we can assume that the fulfillment of the entire passage from Isaiah does not necessarily follow a simple human schedule.
After the long-lost Book of the Law was recovered, it was read to the people and interpreted for them by the Levite priests [Neh 8.7]. Language and custom had evolved, so that strict literalism would have left the hearers perplexed. The Bible here shows that, without inspired interpretation, we have the dead letter of the law.
The word of God is 'alive and active and sharper than any two-edged sword, and piercing as far as the division of soul and spirit, of both joints and marrow, and able to judge the thoughts and intentions of the heart,' says the writer of Hebrews [Heb 4.12], after quoting several Old Testament passages.
So if a man is to understand the word, he cannot rely on human wisdom [1 Cor 1-9]. Just as the spirit within a man knows his thoughts, the Spirit of God knows God's thoughts [1 Cor 2.11]. In fact, the Spirit reveals scriptural meaning to believers 'for the Spirit searches all things, even the depths of God.' [1 Cor 2.10]
Or, as Paul wrote elsewhere, the new arrangement for Christians is 'not of the letter but of the spirit; for the letter kills, but the spirit gives life.' [2 Cor 3.6]. So the assertion that 'the Bible is literally true' should perhaps be changed to read that 'the Bible contains no error.' Since God 'makes all things work together for the good' for his chosen [Rom 8.28], he is able to make human missteps into truth. We know this from Caiaphas, who, as high priest, spoke a truth, though he had no idea of the divine profoundness of his words [Jn 18.14].
An example of literalness is the Mosaic command for Jews to put symbols of God's word on their foreheads and hands [Deut 6.8]. Some Jews to this day observe this custom. But, isn't it plain that the real point of this thought is that the Jews were to think about God's word and practice it? Why would God want people to honor this custom but not honor God's will in the more important area of behaving on the square with one's neighbors?
People who want to be excessively literal may not be aware that Jewish and Christian editors have over the centuries sifted ancient writings in efforts to obtain God's word at its purest. The fact that the Bible is such an authoritative source of truth and wisdom shows that many of these editors were, like Paul who rightly divided the word of truth [2 Tim 2.15], divinely inspired.
Many modern Bible texts identify words attributed to Jesus with red type or quotation marks. However, the Greek texts have no such graphical devices. This means that there are some passages sometimes attributed directly to Jesus that might actually be divinely inspired editorial comments. Also, there are variant literal versions of some of the words attributed to Jesus, though they are close in substance. With the aid of the Spirit, it is possible for the contemporary mind to understand the meaning of these words.
And the sayings of Jesus clearly were compiled early on and later woven into the synoptic gospel accounts. Does this make the gospel accounts wrong? Only if one insists on literally precise chronological narratives. Otherwise, they are rather like the modern newspaper report that lays out the relevant details in a way that 'tells a story.'
If a newspaper reporter extracts a couple of relevant sentences from some document and includes a one-sentence paraphrase in his story, he could not fairly be accused of improperly quoting the document. We should give Bible writers the same leeway. To wit, Paul, whose eyesight was poor and who probably relied on memory, in several places conflates scriptural passages in order to make a point. For example, Rom 9.33 apparently splices Is 28.16 and Is 8.14. This splice is easily defended as summarizing later prophetic fulfillments. So Paul is not in error, but we would be foolish to be excessively literal: there is no single such passage in the Septuagint (the Greek-language Bible in use at the time).
In Rom 11.26, Paul quotes scripture thus: 'The deliverer will come from Zion, he will remove ungodliness from Jacob. This is my covenant with them, when I take away their sins.'
The quotation is more a paraphrase than an exact quote. In fact, some might argue that the paraphrase misquotes Is 59.20,21 to give it a meaning it does not have. However, the import of the paraphrase is justified elsewhere, such as Psalm 14.7 and Psalm 15.
I sympathize with the apostle. I had in my mind that Jesus had, in assuring believers of his steadfastness, asked rhetorically whether a mother could forsake her child. It turns out that the relevant verse is Is 49.14, where I hear the voice of the Messiah.
Consider Mt. 21.5, which tells of Jesus' triumphal donkey ride into Jerusalem. Two old testament scriptures, Is 62.11 and Zech 9.9, are spliced together here, illustrating that different prophetic utterances can be fulfilled in one action.
Or consider John 12.15 which quotes Zech 9.9 but omits 'shout, O daughter of Jerusalem.' Yet, the omission is inconsequential. The meaning of Zech 9.9 is faithfully preserved. Writers of the period did not follow rules of quotation used today. So we cannot easily ascribe error here.
When we are told that 'the scripture cannot be broken' [Jn 10.35], the Old Testament was meant (specifically, Ps 82.6). So then, what do we make of Jude's citation from the Book of Enoch, which is regarded by Jewish and Christian scholars as largely a group of entertaining tall tales that on the whole lack divine inspiration?
Accepting that the Book of Jude is scripture, then is the scripture broken if Jude cites a non-scriptural source? [Jude 1.9]
Firstly, Jude was using an example from a book familiar to his contemporaries in order to make the moral point: If even Michael, in his dispute with Satan over Moses' body, wouldn't revile the devil himself, who are we to revile anyone at all? Now, regardless of the scriptural accuracy of this story, the moral point is substantiated by the words of Jesus, who occasionally alluded to the Book of Enoch.
And, we cannot rule out the possibility that the Book of Enoch contains fragments of real scripture and that Jude cites such a fragment.
New Testament writers cite numerous passages from the Old Testament in order to make their case about Jesus. However, if one were to apply the railroad timetable technique to the Old Testament writings, one would doubtless be able to argue that the writers were taking scripture out of context in order to justify their pet theories. But, the reality is the reverse: the Spirit illuminated the authors' minds as to how the written word was being fulfilled in their day. But the human wisdom -- railroad timetable analysis -- was to be scorned. As Paul said to the Corinthians, he decided to put Jesus first and then see what the Spirit revealed.
He always respected scripture, but insisted that the Spirit should lead in its interpretation.
So it is that sometimes a person apprehends a spiritual reality to such an extent that, for him, prophecy is being fulfilled. One wakes up to a truth, which was there all along, previously unnoticed. It's like suddenly seeing the solution to a math problem. The solution always existed, independently of the observer, but now that solution has become a potent part of the observer's reality.
Paul, when caught up to the third heaven, could not tell whether he was in the body or out of the body [2 Cor 12.2-4]. That is, the spirit world was so intense that the material world faded out, a non-issue. In paradise, Paul heard inexpressible words, which a man is not permitted to speak. That is, the language of heaven far exceeds the capacity of the earthly vessels. So we should be careful about trying to interpret spirit reality according to earthly standards.
Now Paul's experience here is echoed elsewhere in scripture: Sky (heaven) and earth had passed away! The sky was torn asunder and rolled up like a scroll! The stars fell from their places and sun and moon became nothing in comparison with God's glory [Is 34.4]! He was in paradise and his world was gone in the blink of an eye! Yet, we can expect that such scriptures will be fulfilled again in other ways.
Consider the believer content in Christ and filled with the Spirit not even noticing supposed bodily hardships. Sky and earth have begun to pass away, as with Stephen during his martyrdom. Or think of Jesus in the desert being comforted by angels following his victory over Satan. That desert was no desert! It was gushing with refreshing streams and blooming with beautiful flowers!
So we can see that fulfillment of scripture is not naively chronological but comes in surprising ways. Often a prophecy had already been in part fulfilled in the shadowy pre-gospel sense but awaited complete fulfillment in Jesus. Also, even when a prophecy is being fulfilled at the dawn of the Christian era, that does not mean there isn't more to come. For example, take Acts 2.17,18 when the spirit-filled Peter quotes Joel's prophecy that in the last days God will pour out his spirit on all flesh (1).
And indeed, since that time that prophecy has been fulfilled by God granting his Spirit to people of every race and background. And its fulfillment is not yet complete.
As Paul said, human wisdom is insufficient for understanding God. So we can appreciate that when God speaks to man through prophetic scripture, he is infusing man's tribal viewpoint and his local legends with the Spirit in order to lift the hearer into an expanded consciousness. He is using man's language and man's way of thinking to reflect God's thoughts.
Because of this, the word of God may seem to some to be ambiguous or inconsistent. Also, linear history seems to matter to modern humans far more than it does to God, who is focused on spiritual growth.
Our ability, even with the Spirit, to comprehend prophecy 'through a glass darkly' [1 Cor 13.12] (as a dim reflection) has a counterpart in modern astronomy. Before powerful telescopes made most of the physical cosmos observable, one could only make educated guesses as to most of what was out there, even though scientists had Einstein's highly accurate general theory of relativity as their 'bible.'
Though the theory's general predictions are repeatedly verified as astronomy progresses, no one in the early years of the 20th century anticipated the fantastic view of the cosmos that eventually unfolded.
Previously, scientists had the physical truth, and yet they still perceived the cosmos 'through a glass darkly' before having their consciousness expanded to a much bigger reality (and this reality is nothing in comparison to what God has in store).
The Book of Revelation can be thought of as the Big Picture of spiritual reality. It gives a panoramic sweep that includes events of the past and of the future. We can think of it as a completed picture of a jigsaw puzzle. But, try as we might, our human mental strength does not suffice to perfectly match puzzle pieces found elsewhere in scripture and in contemporary events to that Big Picture.
However, that does not mean we should ignore various 'end times' events unfolding about us. We should indeed use these events to toughen up in our Christian walk. Why are we being so worldly? Can't we see the Bible is right?
THE TRUE ZION
The issue of Judaism's primacy was addressed by Jesus and the apostles with such sayings as 'Salvation comes through the Jews' [Jn 4.22] 'to the Jew first, and then to the Gentile' [Rom 2.9,10], 'the first shall be last and the last shall be first' [Mt 20.16].
The Samaritan woman was puzzled by religious differences. 'Our fathers worshiped in this mountain,' she said, 'and your people say that in Jerusalem [on Mount Zion] is the place where men ought to worship.' Jesus replied, 'Woman, believe me, an hour is coming when neither in this mountain nor in Jerusalem will you worship the Father. You worship what you do not know; we worship what we know, for salvation is from the Jews. But an hour is coming, and now is, when the true worshipers will worship the Father in spirit and in truth.' [John 4.20-23].
In other words, God was creating a new world, or covenant, where the heart of the believer was the issue, as opposed to a particular geographic location.
In that same chapter, Jesus -- who was breaking the Middle Eastern taboo of conversing with a woman without her male folk present -- tells her that he would be happy to fill her up with 'living water' from a spring that won't run dry. 'Living water' (what in English is called 'running water') is a poetic description of the Holy Spirit. Jesus was bringing salvation to a hapless, roughly handled Palestinian woman.
The Lord was not terribly interested in geography or property rights [Luke 12.14]. His aim was and is to confer the gift of salvation and eternal life. Recall his assertions that 'the kingdom of heaven is within you' [Luke 17.21] and 'my kingdom is not of this world' [Jn 18.36].
The writer of Hebrews says that Jewish religious customs are a 'copy and a shadow of heavenly things.' [Heb 8.5]. Likewise, Paul wrote that the Jewish law, including the ten commandments, was intended to school the Jews as to the meaning of right and wrong so that they would become aware of how much they needed the unmerited favor of salvation [Gal 3.24].
A new order replaces the old order, as Heb. 8.8-13 says, quoting prophecy [Jer 31.31]:
'"Behold, days are coming, says the Lord, when I will effect a new covenant with the House of Israel and with the House of Judah; not like the covenant which I made with their fathers on the day when I took them by the hand to lead them out of the land of Egypt; for they did not continue in my covenant, and I did not care for them, says the Lord. For this is the covenant that I will make with the House of Israel after those days, says the Lord: I will put my laws into their minds, and I will write them on their hearts. And I will be their God. And they shall be my people..." When he said, "a new covenant," he has made the first obsolete.
But whatever is becoming obsolete and growing old is ready to disappear.'
And when does the new covenant appear? It is made evident at the Feast of Pentecost, when, as Peter said, quoting from Zechariah, Jerusalem became 'the city of truth.' That passage [Zech 8.2-17] also says that the Lord is 'exceedingly jealous for Zion.' The covenant dawned at Pentecost and is still in process of fulfillment.
Or, as Heb 12.22-24 points out, the terrifying experience of Mount Sinai is no more, but rather, 'you have come to Mount Zion and the City of the Living God, the heavenly Jerusalem, and to myriads of angels, to the general assembly and church of the firstborn who are enrolled in heaven, and to God, the judge of all, and to the spirits of the righteous made perfect, and to Jesus, the mediator of a new covenant...' Plainly, Zion here is a spiritual place, the realm of salvation. The old world of the old covenant will be shaken and only what is unshakable will remain, but 'we receive a kingdom which cannot be shaken' [Heb 12.27,28].
Paul says that eventually 'all Israel will be saved; just as it is written, "The deliverer will come from Zion, he will remove ungodliness from Jacob." "This is my covenant with them, when I take away their sins" [Rom 11.26,27]. Paul adds, 'From the standpoint of the gospel, they [the Jews] are enemies for your sake, but from the standpoint of God's choice they are beloved for the sake of the fathers; for the gifts and calling of God are irrevocable' [Rom 11.28,29].
He is explaining that the Jews have been partially hardened in order to permit the 'fulness of the Gentiles to be gathered into the body of Christ' (indicating that many who perished without seeing Jesus must still arise to meet him as their Savior).
A recurrent theme of Paul is the unity of Jews and Gentiles in Christ. In God's eyes, there is no distinction. 'For by one Spirit we were all baptized into one body, whether Jews or Greeks [Gentiles], whether slaves or free, and we were all made to drink of one spirit.' [1 Cor 12.13].
So then the new Zion is filled with the new Israel, the redeemed Jews and Gentiles. Under the new covenant, 'the virgin daughter of Zion' [2 Kings 19.21] has become the bride of Christ [2 Cor 11.2, Rev 21.9,24]. 'For out of Jerusalem will go forth a remnant, and out of Mount Zion, survivors' [2 Kings 19.31]. This prophecy was fulfilled by the fact that the Jewish identity survived Nebuchadnezzar's destruction of Jerusalem, but that prophecy is fulfilled in an expanded sense by the fact that born-gain Jewish Christians, the ultimate survivors, fanned out from Jerusalem.
A MAJOR SIGN
Though interpretation of end-times prophecies requires a special gift, there is one prophecy that stands out as a beacon in our time. Luke 21.24 quotes Jesus thus: 'and they will fall by the edge of the sword, and will be led captive into all nations; and Jerusalem will be trampled underfoot by the Gentiles until the times of the Gentiles are fulfilled.'
After the Romans led the Jews away captive, Jerusalem remained under Gentile domination for nearly 2,000 years. Upon Israel's founding in 1948, Jerusalem became the Jewish state's capital, though this status has long been a diplomatic sore point. After a fight, Jordan occupied east Jerusalem, but then lost that sector during the 1967 war.
So then, it is fair to say that the times of the Gentiles are about over. However, we might also note that Arabs predominate in East Jerusalem, possibly indicating that the Gentile era is not quite over. Certainly, the Israeli government cannot end the Gentile era by trying to complete this prophecy.
For one thing, the Gentile era is the period when the message of salvation is going out to the Gentiles. Once the full complement of Gentiles destined for salvation has been reached, then the Gentile era ends, according to Paul, writing in Romans 11.11-32 -- in particular Rom 11.25. Once this occurs, Paul says, Jews who had been unable to receive the gospel will be saved.
Of course, that implies that a powerful evangelical campaign must come in Israel, accompanied by great pressure to thwart the gospel.
Further light on the Gentile era is shed in the Book of Revelation (Rev 11.2) where John is told not to measure the outer court of the temple, which is given over to the Gentiles, who will tread Jerusalem underfoot for 42 months (three-and-a-half years).
Two witnesses will prophecy for 1,260 days (three-and-half years), clothed in sackcloth. They have tremendous power, and can kill with the fire of their mouths. (Rev 11.3-6)
In Rev 12.14, we are told that the woman flies from the serpent's presence to the wilderness to be nourished for three-and-a-half times.
This echoes Daniel 12.7, where it is prophesied that wonders would cease -- the world would end -- after three-and-a-half times. A general resurrection occurs after the holy ones are overcome, a theme found in Rev 11 and in Jesus' end-times discourse.
In scripture, a 'time' can be taken to be a solar year. And it is interesting that the Roman-Jewish war lasted about three-and-a-half years, culminating in the destruction of Jerusalem.
However, if we keep in mind the Greek idea of kairos, we might think of 'a time' as meaning a period in which certain trends accumulate until reaching the critical point, which ends that period. So then, we might interpret the three-and-a-half years of Revelation as three-and-a-half kairos times, meaning that the era of the Gentiles ends amidst some other era -- perhaps the age of grace, which must still be extended to the Jews.
Here we have another argument against eschatological timetables, since kairos eras can overlap. On the other hand, it should be acknowledged that some accept that Jeremiah's prophecy -- that Jerusalem would be resettled by the Jews after 70 years of desolations by Gentiles -- was fulfilled after about 70 solar years (Jer 25.11,12, Jer 29.10). However, Daniel, in Babylon, seems to have been perplexed that the 70 years was up and the prophecy in need of fulfillment, if solar years were meant. The angel Gabriel responded by giving Daniel a vision of the Messianic era to come, and explained that this era would begin after '70 weeks.'
Interpreting a week as seven years, the kronos time of 490 years seems to accord with the Jewish resettlement of Jerusalem in 538 BCE and the ascension of Jesus around 34 CE (about 496 years), though the Messiah was also supposed to be cut off after 62 weeks -- in kronos time, 434 years, which does not jibe.]
Realizing that the Spirit can cause believers to see a scripture or set of scriptures as being fulfilled in many ways, we offer this scenario as a possibility:
In Rev 11.2, the Gentiles are in the outer court of the temple. That is, these are the Gentiles being brought to salvation; meanwhile, the Gentiles are walking all over the holy city. Now, the 'holy city' may signify the kingdom of God -- which they, like the prostitutes, are storming into -- and-or it may signify earthly Jerusalem, which seems likely, since Jesus in Luke 21.24 certainly was talking about earthly Jerusalem. So then, we would assert that once earthly Jerusalem came under Jewish rule, the times of the Gentiles begin drawing to a close. Now which times are meant? One time evidently is the era for the gospel to the Gentiles; another time apparently is the era of Gentile rule over earthly affairs.
Now the two witnesses of Rev 11 may mean the Jewish Christian and the Gentile Christian components of the body of Christ. True Christians have tremendous power, as the gospel accounts and the Acts of the Apostles, show. But they are at their best when they are humble, eschewing earthly wealth. They are 'in sackcloth' during the age of witness, but eventually they will wear divine apparel. However, I am aware that such an interpretation might constitute a partial fulfillment of prophecy, with a complete fulfillment to come.
We are now in a position to suspect that the three-and-a-half times of Daniel may correspond with the three-and-a-half years of Rev 11. Similarly, we can interpret the woman of Rev 12 as the church -- the body of born-again believers -- who, harshly persecuted in Judea, escaped to the 'wilderness' of Gentile lands, where she has been nourished for three-and-a-half times.
However, I am uncertain as to what three eras are meant, though I would guess that the 'half-era' refers to the age of grace.
At various points, the Bible says that the coming of the last days is accompanied by birth pangs. Severe stress presages the birth of a new world era.
I suggest that the closing days of the age of the Gentiles mean great suffering on the part of the Gentiles. The plague of AIDS appears poised to sharply reduce the earth's population, possibly by 2028 (2). Poor nations are ill equipped to combat this disease, which has already devastated sub-Saharan Africa -- leaving 11 million AIDS orphans -- and which is on the verge of bringing about a similar catastophe across Eastern Europe, Russia and Asia. In addition, the rapid increase in global warming is likely to have numerous calamitous effects, including triggering devastating malarial and ebola epidemics.
We also cannot rule out the possibility that weapons of mass destruction may yet be unleashed on a genocidal scale. But, even if such arms are contained, pandemics and related famines are likely to promote civil disorder and war. The developed nations can no more escape the judgment than the Titanic could escape sinking. The great distress will cross borders, despite all efforts, and then spiral out of control in the supposedly safe areas.
We cannot say that the state of Israel will be unaffected. However, a remnant of Jews will remain, perhaps still in control of Jerusalem. Yet, the scepter of world rule will not be passed to earthly Israel. If so, why would the Bible repeatedly point to a Messianic era as the culmination of Jewish aspirations? My guess is that, while the distress of nations is under way, Israel will undergo a harsh internal fight as Christian Jews begin to make headway.
At some point, the Christian Jews will be eradicated. BUT, we cannot assume that this will occur at any particular time.
The scenario I have outlined is plausible, but I do not claim that I am correct in every jot and tittle.
A NOTE ON THE ABRAHAMIC BLESSING
An important topic of end-times discussions is the blessing given to Abraham, which was routed through the Jews.
'And I will bless those who bless you, and curse those who curse you: and in you shall all the families of the earth be blessed' [Gen 12.3].
Abraham's real descendents are those who heed God, not merely people with certain DNA characteristics who have been circumsized [Jn 8.39]. Obviously, the blessing points to Jesus, who blesses all the nations of the earth. Those who bless Abraham will be blessed and those who curse him will be cursed. This certainly applies to Abraham's spiritual progeny, the born-again Christian.
But supposing that God's pledge also applies to Abraham's descendents in the flesh, a question must be posed: does the pledge apply to the state of Israel, the Israeli government, Jewish residents of Israel, or Jews in general, wherever they live? I raise that question because some seem to equate any criticism of Israeli government policies as tantamount to invoking a curse against onself. I don't wish to attempt to neutralize the potency of that scripture, but I am concerned that some are deploying it for propaganda purposes.
THOUGHTS ON 'ELOHIM'
A verse in the Song of Moses, Deut. 32:8, reads:
'When the Most High apportioned the nations,
when he divided humankind,
he fixed the boundaries of the peoples
according to the number of the sons of God.'
The phrase 'sons of God' was rendered 'sons of Israel' in the traditional Jewish Bible, but a fragment from the Dead Sea scrolls attests to the former.
Who were these sons of God? Were they related to the sons of God who intermarried with earth women and spawned demonic offspring? What is known is that various non-canonical writings, along with some clues in the Bible, indicate that these were the 70 (probably a symbolic number) angels who led the nations surrounding ancient Israel. The highest of these divine beings, who came to be known as Elohim and also YHWH (roughly: 'Yahweh'), chose the nation of Israel for himself.
Scholars have found that, though 'Elohim' is used in the singular in the Hebrew scripture that we have now, the word itself is a plural form of 'El,' which was the name of the Canaanite's chief god. So 'Elohim' simply means 'the gods.'
But the Hebrews were forbidden to worship any God but Elohim -- which evolved into a a generic name for God -- who eventually revealed his special name to them as YHWH, just as he has revealed to Christians his special name of his son Jesus. Elohim brooked no competition from his 'sons.'
So it is apparent that the Hebrews knew of the Canaanite pantheon -- which is similar to other pantheons, in which one god is chief of the others.
However, as Hebrew religion and language evolved, we find that the Canaanite 'sons of El' -- which is equivalent to 'the gods' -- becomes 'sons of Elohim,' which is later rendered as 'angels,' which are directly created divine beings (note that this makes Jesus a hybrid of son of man -- because born of a woman -- and angel, or son of God, because directly created, which is also what born-again believers are). Angels could have god-like power but were not to be worshiped. The theological issue bothered the Pharisees, who took 'son of God' to mean a god who must not be worshiped.
Elsewhere we learn that Michael is Israel's special protecting angel (whose name means 'Who is like God?'). So then he is, possibly, identified as a projection (message) of Elohim. In addition, we learn in Daniel and Revelation (and in extra-biblical texts) that Michael is waging war with the devil and his angels. In particular, we find that the prince of Persia is a demonic angel. So we can guess that the angels that lead the nations are demonic, or at any rate inferior, angels, perhaps those who intermarried with earth girls.
We might think of the pantheon of the gods as a muddled (reprobate) intuition of a situation in which the human soul is a projection of a particular angel. So all those who are a projection of a particular angel are in the 'nation' ruled by this angel. But Jesus taught that those who are not ruled by the Father must be ruled by Satan, implying that the unregenerate are either reflections of fallen angels, or, are tares that have been planted by an enemy.
Be this as it may, clearly some will suspect that the Jewish religion is simply a variant of the older Canaanite religion with which it clearly has similarities. Scholars would add that as Jewish theology evolved, it took on some of the imagery and concepts of Zoroastrianism, a Persian religion of great antiquity. (A number of Zoroastrian concepts make sense in terms of Judaeo-Christian traditions. Take, for example, 'the Lie,' which can be thought of as a place where many are headed. It is also the pull to proceed into such a place. The Lie is the door opening to one of the 'many mansions' in God's universe, as well as the pull toward that door. The Lie is the pull toward Death, death itself being a lie.)
Think of the transfiguration:
Jesus had previously quoted a scripture that said 'you are gods' (or possibly 'you are as gods') and had held that if God IS the God of Abraham and Isaac, then God is the God of the living.
On the mountain, his disciples saw him with Moses and Elijah, all blazing with unearthly light, and then, after closing their eyes in fear, saw only Jesus.
That is, these divine beings were united by a single Spirit.
As Paul says, born-again believers are heirs with Jesus of the kingdom [Eph 3.6], sons of God that is. In fact, they are as gods, indeed they are gods. Nevertheless, they, who are junior partners of Christ, are certainly not to be worshiped.
The promise to the believer is that, as he becomes more Christ-like, he will become one with God -- though he actually is already one with God, just as Jesus is one with the Father.
In any event, we can see that the Hebrew word 'Elohim,' though it stemmed from a pagan theory, fits well with God's revelation to the Jews, who he did indeed choose as his special people, though their heory of God is past its prime.
APPENDIX: 'Zion' prophecies interpreted
Following are my interpretations of a number of scriptures concerning Zion:
Ps 9.11
'Sing praises to the Lord, who dwells in Zion.'
Under the old covenant, the invisible God dwelt in the ark of the covenant. Within that ark were the stone tablets on which God had personally inscribed the 10 commandments. The two stones can be viewed as a token of God's covenant with the children of Israel. But also we see that the Lord himself was the true covenant -- the word and the guarantor of that word.
Under the new covenant, the invisible God -- the Spirit of God -- dwells in the mind of the believer, making the believer's body, 'the temple of the Holy Spirit' [1 Cor 6.19]. So then, would God go back to the old covenant in order to take up residence in another stone temple?
Ps. 14.7
'O that the salvation of Israel would come out of Zion, when the Lord restores his captive people, Jacob will rejoice, Israel will be glad.'
Jesus rose to heaven out of Jerusalem, where he could then send the Spirit to the Jews -- and Gentiles -- who were to be set free. 'Whom the son sets free is free in deed'[John 8.36].
Ps. 65.1
'silence before you and praise in Zion'
Or, 'be still and know I AM' [Ps 46.10]. This intimacy with God requires the presence of Jesus in the believer, who then can enjoy God.
Ps. 69.35,36
'For God will save Zion and build the cities of Judah, that they may dwell there and possess it. The descendants of his servants will inherit it, and those who love his name will dwell in it.'
Zion and the cities of Judah are reserved for the descendants of his servants and those who love God's name. A true descendant of God's servant is also God's servant. Otherwise the devil is his father [Jn 8.44]. So is earthly Jerusalem filled with such people?
The 'cities of Judah' needn't refer to old Middle Eastern towns; instead what is indicated is a land where the redeemed, who love the name Jesus, can enjoy life.
Ps. 78.67,68,70
'He also rejected the tent of Joseph, and did not choose the tribe of Ephraim, but chose the tribe of Judah, Mount Zion which he loved.'... 'He also chose David his servant and took him from the sheepfolds.'
Though this refers to the preservation of David's tribe, Judah, after the destruction of the other 11 tribes, these words are fulfilled by Jesus, the good shepherd descendant of David, who established spiritual Zion by his conquest of evil at the cross.
Ps. 84.5,7
'How blessed is the man whose strength is in you, in whose heart are the highways (to Zion)... every one of them appears before God in Zion.'
Those who love God are approaching Zion.
Ps. 87.2
'The Lord loves the gates of Zion more than all the other dwelling places of Jacob.'
English-language translations of the Bible customarily italicize words not found in the Hebrew or Greek scriptures but that seemed necessary. In this case, if we omit 'other,' we can interpret this passage to say that 'Jacob' refers to the unregenerate Jew. He cannot enter Zion until he has been transformed, by the renewing of his mind [Rom 12.2] into 'Israel.' The name 'Israel' means 'wrestler with god' and the name 'Jacob' means 'he who grabs by the heel' or more generally 'trickster.'
Recall the encounter between Jesus and Nathanael, who knew salvation was to proceed from Jerusalem. Nathanael's question 'Can any good thing come out of Nazareth?' was followed by Jesus' retort: 'Look, a real Israeli, in whom there is no guile.' Or, that is: 'Look, a real contender with God, in whom there is no Jacob.'
Ps. 87.6
'The Lord will count when he registers the peoples, "This one was born there [in Zion]."
As Jesus said, the birth that counts is the spiritual birth. Those written in the Lamb's Book of Life [Rev 20.12] have been born of the Spirit, not of flesh and blood [Jn 3.5,6]. So there is no use having been born in Jerusalem if one hasn't been born again, saved by the intervention of Jesus Christ.
Ps. 97.7
'Let all those be ashamed who serve graven images, who boast themselves of idols ... Zion heard this and was glad.'
The real Zionists are glad when God shames the money-worshipers and their type.
Ps. 99.2
'The Lord is great in Zion'
Or, Zion is a place where the Lord's glory shines brightly. And isn't that in the hearts of those who worship God 'in spirit and in truth'?
Ps. 102.21
'that men may tell the name of the Lord in Zion'
Utterance of that name -- as represented in scripture by the Hebrew letters YHWH -- came to be forbidden to Jews of old and such utterance is still considered impious for Jewish residents of modern Jerusalem, assuming anyone could be sure of the pronunciation.
The name of the Lord, under the old covenant, is not, under the new covenant, fully revealed since the name of 'Jesus' suffices as the name of the Lord.
It has become possible to tell the name of the Lord openly, even if with difficulty.
'Jesus' or 'Yah shua' means 'Yaweh saves.' Knowing this name suffices just as seeing Jesus sufficed for seeing the Father [Jn 14.8].
Ps 110.1,2
'The LORD says to my Lord: sit at my right hand until I make your enemies a footstool for your feet. The LORD will stretch forth your strong scepter from Zion...'
Jesus cites this passage [Mt 22.44] to show that David calls his son, the messiah, his lord. So then we can be sure that Jesus is one with YHWH (the name of God using only consonants, as translated from Hebrew) whose great power over heaven and earth extends from the kingdom of God, which is Zion.
The fourth verse of this psalm says that God has determined that this savior is 'a priest forever according to the order of Melchizedek,' a passage that Heb. 7.21 says refers to Jesus, the consummate priest.
Ps. 129.5
'May all who hate Zion be put to shame and turned backward.'
Those who love their sin more than the light remain under judgment and are continually injured by their own wilfulness [Jn 3.18], since they reap what they sow [Gal 6.7].
A specific instance of this scripture being fulfilled occurred when an armed troop came to arrest Jesus. Jesus asked whom they sought. When told, he replied, 'I am he.' On hearing 'I am,' which is a name for God, the men stumbled backward in confusion and were then only able to proceed with God's permission [Jn 18.4-6].
Ps 135.21
'Blessed be the LORD from Zion, who dwells in Jerusalem.'
The writer was likely thinking of the Temple in Jerusalem. Yet, when Jesus died on the cross, the veil of the Temple was torn apart, indicating the departure of God's Spirit from the veiled ark of the covenant. Where does the Lord dwell today? Within those who put their trust in Jesus.
Is 1.27
'Zion will be redeemed with justice and her repentant ones with righteousness.'
Justice was served by the sacrifice of Jesus, the son of God, whose crucifixion paid in full the price of all sin.
Those who humbly turn to him will be made right with God.
Is 8.18
'Behold, I and the children whom the Lord has given me are for signs and wonders from the LORD of hosts, who dwells on Mount Zion.'
Heb 2.13 takes this passage to refer to Jesus.
Is 24.23
'The LORD of hosts will reign on Mount Zion and in Jerusalem.'
We know that Mount Zion is a spiritual place and the Book of Revelation tells us to expect a new, heavenly Jerusalem [Rev 3.12].
Is 28.16,18
'Behold, I am laying in Zion a stone, a tested stone, a costly cornerstone for the foundation, firmly placed. He who believes in it will not be disturbed [moved].'
'Your pact with Sheol will not stand.'
Paul in Rom 9.33 and Peter in 1 Pet 2.6 say Is 28.16 refers to Jesus. Now the old, earthly Zion was overthrown by the Romans in 70 A.D. So the new Zion is the kingdom of God that Jesus is yet bringing forth.
Jesus will cancel the sin-sick soul's contract with death.
Is 29.8
'It will be as when a hungry man dreams--and behold, he is eating; but when he awakens, his hunger is not satisfied, or when a thirsty man dreams--and behold, he is drinking, but when he awakens, behold, he is faint and his thirst is not quenched. Thus the multitude of all the nations will be who wage war against Mount Zion.'
Anybody who fights God is deluded. Any 'victory' over the LORD is hollow.
Though this passage specifically refers to Gentiles, certainly it also holds for Jews.
A nearby passage [Is 29.10] says that God 'has poured over you a spirit of deep sleep [or 'strong delusion']' blinding the prophets and the seers. Paul [Rom 11.8] says this scripture applies to the bulk of the Jews, who 'were hardened.'
That is, those who resist God, and his works, are turned away from his kingdom by a strong delusion, reminiscent of the angels guarding the gates of Eden.
Is 30.19-21
'O people in Zion, inhabitant in Jerusalem, you will weep no longer. He will surely be gracious to you at the sound of your cry; when he hears it, he will answer you. Although the Lord has given you bread of privation and water of oppression, your Teacher will no longer hide himself, but your eyes will behold your Teacher.
Your ears will hear a word behind you, "This is the way, walk in it," whenever you turn to the right or the left.'
God will comfort his people. Yet, who can see God? Yet his people will see the Teacher, who will guide their minds. Those who walk with Jesus recognize the Teacher's voice [Jn 10.27], which can only be heard via the Holy Spirit. He is the road and he makes sure that every follower will learn more and more about God.
Is 31.4,9
Like a lion with its prey unworried by the shepherds, so will 'the LORD of hosts come down to wage war on Mount Zion and on its hill.'
'whose fire is in Zion and whose furnace is in Jerusalem.'
Have you ever noticed that on occasion titanic contests occur with little recognition of what is going on -- hardly anyone is paying attention?
Jesus was sent by the Father to wage spiritual warfare against the devil and his hordes. A scene in that struggle occurred when he picked up a whip and drove the businessmen from the Temple.
Certainly Jesus could not be deterred from achieving his victory over hell.
That victory was exemplified when, during the feast of Pentecost, tongues of fire descended upon the apostles in Jerusalem to launch the true church.
Is 33.5
'He has filled Zion with justice and righteousness.'
Not much of that in wordly Jerusalem. However, Jesus embodies the phrase 'justice and righteousness.'
Is 33.20
'Look upon Zion... Your eyes shall see Jerusalem ... a tent which will not be folded; its stakes will never be pulled up. No oarboat or warship will pass on its great streams.'
What great streams? These must be streams flowing in the heavenly Jerusalem of Rev 3.12, where commerce and war are no more.
Is 35.5,6,10
'Then the eyes of the blind will be opened and the ears of the deaf will be unstopped. Then the lame will leap like a deer, and the tongue of the mute will shout for joy.'
'And the ransomed of the LORD will return and come with joyful shouting to Zion, with everlasting joy upon their heads.'
When John the Baptist queried Jesus as to whether he was the Messiah, Jesus replied: 'Go and report to John what you have seen and heard: the blind receive sight, the lame walk, the lepers are cleansed and the deaf hear, the dead are raised up, the poor have the good news preached to them.'
All of Isaiah 35 foretells, in rhapsodic imagery, Zion's wonderful future. From Jesus' response, we can see that he was a sign of the true Zion. And a person who has truly received Jesus as Lord has entered that Zion, the land of eternal bliss, and, despite hardships, will shout for joy at the wonder of this event.
Is 37.32
'For out of Jerusalem will go forth a remnant and out of Mount Zion, survivors.'
Those who have been born by the Spirit.
Is 40.9
'Get yourself up on a high mountain, O Zion, bearer of good news ... say to the cities of Judah "Here is your God."'
Jesus was lifted up on Mount Calvary with the inscription: 'King of the Jews.'
Is 49.14
'But Zion said, the LORD has forsaken me...'
Jesus cried out on the cross: 'My God, my God, why have you forsaken me?' [Mk 15.34]
Is 51.3
'Indeed, the LORD will comfort Zion...and her wilderness he will make like Eden.'
How sweet it is to follow Jesus.
Is 51.11
'So the ransomed of the LORD will return and come with joyful shouting to Zion.'
How wonderful to have your sins paid for by Jesus.
Is 52.3
Zion 'will be redeemed without money.'
Those destined for eternal life have had their sin paid for by the blood of Jesus.
Is 52.7
'How lovely on the mountains are the feet of him who brings good news, who announces peace and brings good news of happiness, who announces salvation, and says to Zion, "Your God reigns!"'
Jesus announced the good news of salvation, and so do his followers.
Is 52.8
'For they will see with their own eyes when the LORD restores Zion.'
Witnesses saw the works of Jesus, including his ascension into heaven. However, many of those suffering spiritual blindness were unable to see that Zion was being restored. Isaiah begins his description of the suffering servant with 'who has believed our report?' [Is 53.1]
Is 61.2,3
'...to comfort all who mourn, to grant all those who mourn in Zion...'
Jesus tells us to fear not, to be cheerful, because he has overcome the world [Jn 16.33].
Jesus told his hearers that Is 61.1,2 had been fulfilled in their hearing.
Is 62.1,2
'For Zion's sake will I not hold my peace, and for Jerusalem's sake, I will not rest' until the 'nations [Gentiles] will see your righteousness...and you will be called by a new name, which the mouth of the LORD will designate.'
The name of Jesus is lifted up among the Gentiles.
Is 66.8
'Can a land be born in one day? Can a nation be brought forth all at once? As soon as Zion travailed, she also brought forth her sons.'
The new Zion was brought forth by the sacrifice of Jesus and began in power on the day of the feast of Pentecost, when immediately thousands turned to Jesus for salvation [Acts 2.41].
Jer 3.14
'...return O faithless sons...and I will take you one from a city, and two from a family, and I will bring you to Zion.'
Many are called, but few are chosen for Christ's kingdom.
Joel 2.32
'And it will come about that whoever calls upon the name of the LORD will be delivered; for on Mount Zion and in Jerusalem there will be those who escape.'
Paul in Rom 10.13 applies this scripture to anyone who calls on Jesus, who will then escape hellfire. Joel 2.28 -- 'I will pour out my spirit on all mankind' -- is cited by Peter during the Pentecost speech.
Had Jesus' warning been remembered [Lk 21.20], those in Jerusalem during the Roman-Jewish war would have known it was time to flee when they saw the Temple profaned by Jewish rebels.
In the case of the prophecies of Joel and of Jesus, we can see that they may be specifically fulfilled and yet we cannot rule out their being fulfilled again. However, Paul is less interested in 'future history' than in getting people to see the main point: the salvation provided by Jesus more than fulfills scripture.
Obadiah 17
'...on Mount Zion will be those who escape...'
Those who escape the wrath to come [Mt 3.7] are those who put their trust in Jesus.
Mic 4.2
'Many nations will come and say, Come let us go up to the mountain of the LORD and to the house of the
God of Jacob, that he may teach us about his ways and that we may walk in his paths. For from Zion will go forth the law, even the word of the LORD from Jerusalem.'
Some may read this passage literally, but I see it as fulfilled by non-Jews who are able to get into the kingdom of God through the mercy of Jesus, who is the word of the LORD personified and who is the fulfillment of the law of the LORD. As Jesus taught at age 12, the House of God is the work of the Lord [Lk 2.49] and for humanity the greatest work is salvation.
Zeph 3.12-15
'But I will leave among you a humble and lowly people, and they will take refuge in the name of the LORD.
The remnant of Israel will do no wrong and tell no lies, nor will a deceitful tongue be found in their mouths; for they will feed and lie down with no one to make them tremble.
'Shout for joy, O daughter of Zion! Shout in triumph, O Israel!...The LORD has taken away his judgments against you, he has cleared away your enemies.'
Jesus told us to learn of him, who is humble and lowly [Mt 11.29]. Those who trust in Jesus, who paid for all crimes against God, no longer need fear anything at all, and as they are perfected, they become less and less prone to wrongdoing. And God does not look upon sin because the believer has been pardoned by Jesus. So those put right with God through Jesus have every reason to shout for joy.
Zec 9.9
'Rejoice greatly, O daughter of Zion...Behold your king is coming to you; he is just and endowed with salvation, humble and mounted on a donkey...'
Fulfilled by Jesus' triumphal entry into Jerusalem, where he was greeted as the son of David -- the Messiah.
Zec 9.10
'I will cut off the [war] chariot from Ephraim and the [war] horse from Jerusalem; and the war bow will be cut off. And he will speak peace to the nations; and his dominion will be from sea to sea, and from the River to the ends of the earth.'
Jesus, who has been granted all power in heaven and earth, gives his followers the 'peace of God, that passes understanding'[Phlp 4.7]. Once his kingdom has spread everywhere, warfare will cease.
(1) Colin J. Humphreys, a Cambridge scientist and Bible investigator, has analyzed Peter's interpretation of the prophecy of Joel as related to historical events that can be corroborated. His keen mind is revealed in his book The Mystery of the Last Supper: Reconstructing the Final Days of Jesus (Cambridge University Press, 2011). He is also the author of The Miracles of Exodus: a Scientist Reveals the Extraordinary Natural Causes Underlying the Biblical Miracles (Harper Collins, 2003).
His web site: http://www.csap.cam.ac.uk/network/colin-humphreys/
(2) When that was written, such a global catastrophe seemed plausible. However, education and distribution of anti-AIDS medicines seems to have blunted the threat, though we cannot be sure it won't return.
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Sept. 2013. This article has had minor editing on several occasions between 2005 and Sept. 2013.
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