31. Time and Space

     Time is the means by which we first have our cake and then eat it. Space allows things not to be themselves. A physical world is a system in which the logically impossible is permissible in fact. And what accommodates the difference between a physical system and a logical system is time and space.

     An example of a logically impossible statement is "If X then not X". This says that if X is true then X is false. As a proposition in a logical system, it contradicts itself. A logical system cannot be consistent if it contradicts itself, and so there can be no reliable order in it. If X is a physical object, rather than an assertion, X cannot both exist and not exist-- that is, not at the same time. But it is entirely possible for X to exist and then not exist at a later time-- either because it is destroyed (transformed) or because it no longer exists in the same location (it has moved).

     Time is a device with which contradiction can be lived out in an orderly way. Contradiction becomes oscillation when considered in time. "Day implies not day" expresses the diurnal cycle. "If up then down" describes a bouncing ball. A logical contradiction is endlessly recursive but timeless: "If X then not X, then not (not X), then not (not (not X))..."etc. There is a static, timeless stand-off between X and its opposite. They are two equal opponents in an eternal stalemate. A physical system accommodates self-contradiction by allowing one force and then the other to have its moment on the stage sequentially. Instead of cancelling each other out, one transforms into the other. Implication-- the then of logic-- becomes cause, the then of time.

     Indeed, time is measured by regular oscillation-- the ticking of clocks, the planet orbiting the sun, atoms vibrating in crystals. How do we know how long the cycle of an oscillation is, or that a clock is regular? Solely by comparing it with other oscillators believed to be reliable. And what about them ? The problem is similar with space. How do we know how long a foot is, or that all the inches in a foot are equal? By comparing with other rulers or measures of space. Intuitively, we judge an interval of time or space by what other processes transpire during that interval of time, or what other distances fill up that interval of space. The interval has no intrinsic size apart from such references. Without them we can determine neither the length nor even the nature of the interval (whether it is space or time).

     Just as time is the physical counterpart of logical implication, space is the physical counterpart of logical separability. If two things are logically or "numerically" distinct, then by definition they are two and not one. (Two things are one when there are simply two references to the same item). It must be assumed that any thing is identical to itself. Certainly there could not be any more blatant contradiction than the assertion "X is not X"-- that something is not itself. If it cannot be assumed that an element of a logical system is identical to itself, there can be no order in that system. But in a physical system, two elements can be identical in every way except their spatial location. We are used to thinking that apparently identical objects are nevertheless subtly different, if examined closely enough. But it seems that on the subatomic level two particles may indeed be qualitatively identical, while numerically distinct because of their separation in space. It is therefore space that allows for the multiplicity of particles, while in every qualitative respect there may be only one such particle. Like the answer to a riddle, X is not X when it is somewhere else.

     It is said that at the beginning of time and space there was but one "particle", a singularity infinitely dense (and apparently unstable). Something "happened", at which event its inner contradictions ceased to be potential (logical) and became actual (physical). The singularity became a multiplicity, and the logically distinct elements of the cosmos became physically distinct, requiring spatial separation and the mutual distances which their properties required. Or perhaps it was the other way around-- space itself exploded under the pressure of logical contradiction, and "particles" precipitated as fallout in the sudden expansion. Either way, it went from a very tense and chaotic oneness, where everything was timelessly present together, to a more unwound and orderly world in which incompatible possibilities could be systematically developed in time. The Big Bang heralds our separation in distinct physical bodies, and also points back to our primordial spiritual unity. After all, before the Big Bang, we all literally were each other, since every bit of matter and energy in the universe was together at the same point! Because the universe did not expand into a preexisting space, like a conventional explosion, the whole cosmos is in some sense still together at one point. In other words, space, time and multiplicity are merely appearances.