JL Appendix 2

In this appendix, I want to put forward some suggestions concerning the Creation narrative, as presented in Genesis I and II and traditional Jewish commentaries thereto, and current scientific theories on the subject. (I wrote most of the text below some years ago; however, some more recent thoughts have been added in the last lines.)

A common preconception is the belief that Science and Religion are somehow in radical conflict. Many scientists wrongly presume that their discoveries exclude the existence of a spiritual dimension to the world, or even the existence of Gd. As a consequence, religious people, taking these natural scientists at their word, become suspicious towards the whole enterprise of science, its methods and results. But a bit of reflection shows that there is no inherent antipathy between these fields. There is no single discovery of science which in fact, in strict logic, implies an atheistic or anti-spiritual conclusion.

Consider evolution of species or of the universe. All science does is try to describe the process. Viewed from above, the process of evolution is simply a larger movement, than say the movement of your baby across the floor; it takes longer and affects more things, but it is still just a movement.

When scientists tell us the 'causes' of some phenomenon, all they are doing is describing some parts of it, or describing some other phenomena which seem to be repeatedly conjoined with it. Explanation is nothing more than further description, whether in the form of categorical propositions or in the form of some type of conditioning. There is no logical reason why this movement or process, which is a miniature thing in the hand of Gd, could not have been intended and willed by Him, as a natural outcrop of Creation. Thus, evolutionism and creationism have no inherent conceptual contradiction to each other.

Now, we confront this reconciliation with the literal interpretation of sacred texts - Genesis. How can a process, like evolution of species, or the unfolding of the universe, take millions or billions of years, and yet be claimed to have taken a week, some 5750 years ago?

I don't know the answer, but I can suggest some - enough to show that the compatibility of those propositions is quite conceivable, and therefore that there is no logical basis for regarding them as mutually exclusive. Remember that logical possibility is inferable from the absence of logical impossibility, according to the Law of the Excluded Middle (in an expanded, modal form: if not seemingly impossible, then seemingly possible).

Traces of the Past. For a start, the world could have made its appearance yesterday, or a minute ago - the world with all its memories and material traces of past existence and activity - and we would not know the difference. There is no way for us to infer with utter certainty, from the existence in the present of memories and material traces, the actual existence of the past as it appears to us by virtue of these memories and material traces.

The existence of the Past (or for that matter, the Future), is one of those ongoing hidden assumptions. It is only an assumption, whose counter-assumptions have not been considered or eliminated. (Notwithstanding, it is a pretty powerful appearance, and is worthy of belief. It is a rather radical solution to simply write it off.)

Time with Variable Geometry. Secondly, we can speculate concerning Time, and show that a universe in which a week is also a few billion years is quite conceivable. The number of moments in the Creation week is, say, n; the number of moments in the apparent eons of world-evolution is also n; each has the same number of discrete segments of time, only the segments are of different sizes.

Stars come and go, dinosaurs come and go, at accelerated rates, like a speeded up movie. They cannot tell the difference. The processes involved may be descriptively exactly identical, yet have different speeds than they seem to, from our perspective.

The Creator, who alone is beyond Time, is able to compare the segments of time of that bygone era, and the segments of time in the last few thousand years of human history, and can truthfully tell us: one moment of that past time was equal in size to, say, m moments of your time. Perhaps this was what the Psalmist meant, who said (Ps. 90):

The notion that space and time are continuous is a prejudicial assumption. Most people take it for granted, and are not aware of the possibility of an alternative viewpoint: the notion of space or time as discrete (or 'quantized', in modern parlance). An early Greek philosopher, Zeno of Elea, described several paradoxes in the concept of motion. One of these, was his paradox of Achilles and the Tortoise, which went something like this:

If, upon seeing a tortoise in the distance, the great runner Achilles tried to catch it, he would never succeed. For by the time he got to where the tortoise had been when he first spotted it, the slow-paced tortoise would not be there but a bit further on. Then again, by the time he got to its second station, it would already be at its third. And so on, ad infinitum. He could therefore never overtake it, however fast he ran.

The Newtonian reply to Zeno would be that the infinite subdivision of space by a moving body does not have to take an infinite duration of time, and that the different rates of this subdivision allow for the faster object to converge on and pass the slower one. This is the philosophical background of differential and integral calculus, and it is in agreement with experience and common sense.

However, the paradox could, seemingly equally well, have been resolved by another assumption. We could regard space and/or time as composed of discrete segments, extremely but not infinitely minuscule, within which bodies are invariably stationary (though not locked).

A moving body would pass from one station to another, by instantly disappearing from the first, and instantly reappearing in the second, without any of its parts having at all traveled within either station. The instantaneous change of place takes no time, only the static existence at each place has an extension in time.

Think of a stroboscopic light in a disco. Every time it flashes on the dancers are deployed slightly differently. You only assume that they 'moved' through intervening spaces, while the light was off. Suppose, instead, that they ceased to exist during intervening time; there would be no way for you to know it.

If that intervening time span is of zero duration (a point of time, an 'instant'), they cannot even be strictly said to have ceased to exist. If the time spans during which the light was on (the stationary 'moments'), were so small that change within them was invisible to the naked eye or any technological contraption, you would have no empirical basis for claiming that change was in fact occurring.

A valuable analogy is that of cinema. The film consists of a series of 'stills', yet moved rapidly enough through a projector, the image on the screen gives no hint of discontinuity, but appears smoothly ongoing. Even on a static level, Impressionist painters, like Van Gogh, Renoir or Milne, have well demonstrated how a mass of dots may from a distance seem quite integrated.

It is therefore quite conceivable that motion is not as continuous as it appears, but a series of momentary stops, separated by instantaneous 'disappearance here and reappearance there' of the phenomenon. This concept is, incidentally, suggested by the belief that Gd is constantly recreating, sustaining, the universe.

In that case, the speed (distance over time) of a movement would be defined as the sum of the diameters of the segments of space covered, divided by the sum of the diameters of the segments of time taken. Space and time need not both be discrete; it is also conceivable that only one of them is discrete, and the other continuous. These are further complications, which have to be addressed.

Note that the discreteness viewpoint implies that the Present is a moment, whereas the continuity idea implies it to be only an instant.

Now, my concern here is not the ultimate viability of this alternative hypothesis, which is for Physicists to consider. The point is that, so far as I know, no great effort if any has been put into formulating and testing this alternative, at least not by laypersons.

We accepted the first viable theory that came to mind, the continuum concept, and did not demonstrate the failure of other conceptions to accord with experience and be internally consistent. Even though our theory seems logically coherent and to go on fitting the facts, we still have some obligation to consider and hopefully eliminate any alternatives.

It may turn out that the non-continuous space-time idea solves some previously perplexing problems, like the particle-wave paradox. It treats space and time so differently that it is virtually bound to produce new concepts for us.

It may open new gates for us, like allowing for space or time segments of non-uniform sizes; or like allowing for instant travel from one minuscule of space to another station, a non-contiguous, distant one, without passing through intervening places.

Then again, we may find out that some tightly implied prediction by the maverick postulate is self-contradictory or contrary to experience; but in that case, we have succeeded in more firmly establishing the commonplace assumption.

Sometimes our tacit assumptions are eventually unmasked. An example of this is the Euclidean idea of space-time as straight (so that parallels never meet), which was not so long ago rejected by Einstein in his General Relativity theory, in an effort to solve the paradox of the constancy of the velocity of light, if I remember rightly.[1]

Luckily, recent geometricians (such as Gauss, as I recall) had already prepared the mathematical equipment for the notion that 'parallels' may meet. For instance, like the great circles of an enormous sphere, which seem parallel in a small locality, but ultimately at light-year distances do intersect.

Once we accept space and time as capable of being curved in reality, even though we have always represented them in our mind's eye and on paper as straight lines, it is quite easy to also imagine space or time as more severely irregular in shape. The lines may be warped and twisted in all sorts of different ways, even with kinks and loops, and there might even be holes in the fabric.

Such irregularities (which may in reality not be as extreme as here suggested) would simply signify that there are certain inherent possibilities and impossibilities in space-time, physical pathways and inhibitions which any passing body is locked into. There would be no way for us to know these infinitesimal restrictions, if the body's transition appeared quite smooth on an accessible level.

(For all we know, bodies may be nothing more than peculiar knots in the fabric of being. Moving, like a ripple of water; tracing a scar across time. I am just speculating.)

Thus, our preconception of space-time as necessarily evenly spaced, in accordance with the Cartesian image given by graph-paper, is not indubitably established. There are alternative conceptions, which seem in principle equally tenable (so far, to me, at least).

It is therefore quite conceivable, additionally, that space or time consists of discrete segments of varying size. One can carry an object like a ruler or clock from one place to another for measurement purposes. But if the ruler expands or contracts to fill an equal number of segments of space of different shapes and sizes, there would be no way for us to compare the dimensions of different segments of space. Likewise, if the clock (which is just a physical process) changed speed from time to time, in accordance with the varying durations of moments, time would still seem constant to an observer.

It may even be that time, instead of being universal, varies with place, so that they are more inextricably tied. In any case, the variations in size may be regular, perhaps ordered from the longest to the shortest or vice versa, or perhaps in cyclical arrangements, or they may be without any pattern whatever.

We would be unable to answer such questions, unless we could somehow see space itself or straddle more than one moment of time. It may be that some technology can be devised. Perhaps we can already experience the diverse sizes of time: perhaps a day which has seemed to pass more quickly than usual literally did so.

Variable time simply implies that all the processes in the universe vary in speed, but in unison or in concert. So long as their relative speeds remain the same, their common overall speed may vary wildly without affecting a thing. All physical equations remain identical; nothing is detected by measurement. There does not seem to be any physical way to distinguish this situation of 'variable geometry' from that in a universe of continuous and constant time.

It follows that many postulates are equally compatible with the given data. We may be able to construct distinctive testable predictions, or there may be no way for us to choose between them. The important thing is to keep in mind that even our most cherished beliefs may have alternative viewpoints. The object is not to destabilize, but to remain lucid.

Some may argue that these speculations diverge from the so-called Principle of the Uniformity of Indistinguishables. According to this principle, for instance, space and time are exactly the same everywhere and at all times - because, since there is no conceivable way to physically measure and compare different manifestations of these phenomena, they must be assumed uniform throughout.

But it is clear that this principle has no formal value, because we can conceive of logical reasons to justify an opposite belief - namely, that space or time may consist of discrete and somewhat distinct phenomena. If the principle of the uniformity of indistinguishables was regarded as formal, it would have to apply to all abstractions, so that there could only be one abstraction (since abstractions as such are not sensibly different). Yet we are all agreed that we may conceive of differences between various abstractions, like say the difference between an electron and a positron (or between the various concepts in any sentence we claim as true).

We can often distinguish between 'indistinguishables', at least with reference to their perceivable effects. We may well assume an identity to exist, so long as we have no logical reasons, in a broader context, to do otherwise. The principle in question is only an inductive instrument, and not a deductively compulsory generality.

Indeed, it is only since Newton's time that the infinite divisibility of space and time has been taken for granted. Prior to that, the issue was considered open, as discussions of Zeno's ideas by Aristotle well show. More recently, this principle has been considerably weakened by Albert Einstein's theory of the physical universe as the surface of a four dimensional sphere, instead of a Euclidean extension.

Einstein's intervention opens the door to an fundamental review of the principle of the identity of indistinguishables. For, once we understand that space and time need not fit the perfectly square conception of Euclidean geometry, then anything goes. A breach has been made between the geometry imposed by our limited imagination and the geometry of the wider, external world; that is, more precisely, our imagination has been freed from its Cartesian graph-paper with straight lines mentality, and we can now imagine graph-papers with lines of all sorts of shape.

The Swiss graphical artist M. S. Escher, you may recall, used to draw worlds in which water could go uphill, or stairs could return to the same level while always heading up (or down). If we look on such geometrical perspectives seriously, we might for instance understand the law of gravity, with reference to new definitions as to what constitutes a 'straight' line. We might then, like Escher, view a spiral as a straight line in real-world geometry; in which case there would be no up or down motion to account for.

In other words, Newton's definition of the Law of Inertia might simply be extended to invisible 'forces' like gravity, or electricity and magnetism, or subatomic fields, by redefining what we understand by a 'straight' line. If Newtonian momentum seems acceptable to us without further explanation, why not the mechanism of more curved movements? It is, ultimately, only with reference to volition that the concept of inertia becomes philosophically insufficient.

These are, of course, speculations - which might or might not be useful to Unified Field Theory, or even maybe to biology. But the point being made is that we are, especially since Einstein, more able to visualize alternative geometries - not only a real-world in which space and time are curved at astronomical intervals, but also similarly, a real-world in which there are localized geometries, which differ from each other. In this way, the principle of the identity of indistinguishables, becomes a very arbitrary assumption, which does not make an absolute philosophical claim on our loyalty.

There may be still other, better, explanations. I do not know, and it may well be that we are in principle not even able to confirm or discredit such speculations. What matters and is clear, in any event, is that scientific dating does not necessarily stand in logical contradiction to Biblical claims.

So long as conclusive tests are not available, neither position refutes or is refuted by the other. They are logically disconnected from each other, shown to be harmonious.

Thus, biologists and paleontologists, and likewise astronomers, have no logical justification, in any of their actual findings, for regarding the world as exclusively material and natural. Any process they describe would look exactly the same whether it was spontaneous or caused by Providence, so how can they claim an atheistic conclusion?

Conversely, believers can rest assured that scientific findings have no direct bearing on their beliefs. We know so little about time as such, that any statement concerning it is pure guess-work, anyway.

In conclusion, I would like to make here some comments concerning the exegesis of the Bereshit text about Creation. There has always been an ambiguity in Genesis 2:2 with regard to the Seventh Day. Was it a historic Sabbath, which took place at the beginning of the Time of the material world, or is it the Final Sabbath, which will happen towards the end of history? Are our weekly Sabbaths a celebration of the first Sabbath or a symbolic anticipation of the last? Commentators have tended to interpret it both ways, unsure of what to make of it.

We could say that the six days of Creation include all of natural and human 'history', to its end; whereas the seventh day is a futuristic, 'post-historical' event. That is, we may view our (past and future) history as interspersed into the textual space between Genesis 1:31 and 2:1, and consider Genesis 2:2 as referring to the 'rest' of Gd after the disappearance of the material world of diversity, when He will (supposedly) return to His solitary Oneness and relax.

Such a viewpoint is confirmed by the tradition that Gd did not really finish His work in the first six days, but continues to mold it (through miracles like those in the liberation from Egypt story or through hidden providential interference as in the story of Esther), working towards its Messianic perfection.

Implied in this viewpoint is that the word 'day' (yom, Moy) need not be taken literally as a day under the Earth's Sun, which notion is in any case doubtful in view of Einstein's ideas concerning the relativity of time[2]. This is confirmed within the text itself, where the very same word is used to refer equivocally to a longer period: "in the day that the Lrd Gd made earth and heaven" (Gen. 1:4) - from which it follows that 'day' can equally mean 'six days' or even (why not, therefore) 'an eon'.

In this case, it is not necessary to consider the Biblical text as insisting that the world was Created literally in one of our weeks - it could have taken any amount of time; and furthermore, we need not view the various first six days as being periods of equal length - they may each be a long period of time of any length (of whatever length scientific measurement shows them to be), without even needing to call upon a variable geometry concept of time.

There still remains a problem concerning the order of appearance of material bodies. Thus, the Earth and vegetable matter make their appearance on the third day; the Sun, Moon and Stars appear on the fourth day; the animals on the fifth and sixth days (interestingly, aquatic creatures and birds precede land creatures); and humans on the sixth. Science would not agree to this sequence of things. But medieval Jewish commentators have also previously suggested a revised order, claiming that the Divine decision concerning this or that event preceded its actualization, so that the physical sequence need not be taken literally as written. We may accept this argument, here.

Ultimately, if religion is to be free of the criticism leveled against it, with much justification, by Karl Popper, that unlike science it refuses to accept the methodological imperative of 'falsifiability', it must submit to change in the light of new data and give up on dogmatism. As far as I can see, the above suggestions are not hard-to-swallow changes.

[1] The reader is here referred to books on space-time Physics, such as that of Taylor and Wheeler. It is years since I personally studied the subject, so my memory of details is often sketchy, though I hopefully retained the main essentials.

[2] To some commentators, the claim of Genesis that the Earth was created a 'day' before the Sun is a problem, in that 'days' (of 24 hours) are counted only once both Earth and Sun are in existence. However, this objection does not seem weighty to me, since we are able to conceive of time and time-intervals more abstractly, starting from any manifestation of changing matter, or indeed of changing mind-stuff.

JUDAIC LOGIC