Time and Motion: A Thought Experiment

I wanted to share an interesting thought experiment concerning the nature of time. I’ve known about this for many years, but can’t for the life of me remember the name of the philosopher who came up with it—I’m 99% sure it was a woman, but beyond that I have no clue. If any one knows the origin, please let me know. [UPDATE: Not a woman. It was Sydney Shoemaker, who proposed this thought experiment as a counter to J. M. E. McTaggert’s proposition “There could be no time if nothing changed” — a view held by Aristotle, among others, and a view that I’m more sympathetic too than not—interesting as I find Shoemaker’s thought experiment.]

Anyhow, our unknown philosopher [Sydney Shoemaker] asks us to imagine a universe with some unusual properties.  This universe is very much like our own, except that it is divided into three distinct regions, call them A, B, and C.

And each region has a strange property with respect to motion. Every so often, at regular intervals, all motion in a given region stops completely, leaving everything and everyone inside the region completely “frozen” or “suspended.” Anyone in a non-suspended region can easily observe that everyone and everything in a suspended region is completely motionless.  Each motion freeze lasts for exactly one year.  Those inside the motion frozen region do not experience the freeze subjectively at all.  From their perspective, it appears as if the other non-frozen region(s) change totally in an instant (a year’s worth of change).

Region A motion freezes 1 year out of every 3.

Region B motion freezes 1 year out of every 4.

Region C motion  freezes 1 year out of every 5.

So it looks like this:

So let’s consider what this would look like as the years pass.  I have arbitrarily decided to start in a cycle where B and C are both motion-frozen in year 1 and A was frozen in year 0 and so on this chart freezes again in year 3:

It isn’t hard to work out that regions A and B will freeze together once every 12 years (3 x 4), that regions A and C will freeze together once every 15 years (3 x 5) and that regions B and C will freeze together once every 20 years (4 x 5).  And it further isn’t hard to work out that all three regions A, B, and C, will freeze together once every 60 years (3 x 4 x 5)—something that happens to happen in the 21st year as I’ve set it up (I can’t be bothered to type out 120+ years—you can see the patterns well enough).

Now, everyone agrees that time in very closely related to motion or change.  And indeed, we usually imagine a timestop in fantasy or science fiction as a “freeze” or “suspension” of all motion, just as actually occurs in this universe.  And indeed, from the subjective point of view of those in a motion-frozen region in this universe, no time will have been experienced as passing, either subjectively or by external objective phenomena within the region (e.g. no one will have aged in the frozen “year”).

So, here is the question: is time independent of motion, or not?

From the point of view of anyone within a non-frozen region looking at a frozen region in universe ABC, it is clear that “that region is frozen for one year,” so that time passes despite the lack of motion. So they have good reason to think time is independent of motion, at least the motion of the frozen regions.

From the point of view of those in a frozen region, although they experience no passage of time during their “frozen year” they do see that the other regions freeze for one year, and they see that on a regular basis, the other regions they expect to be non-frozen while they are frozen do indeed “leap ahead” by one year.  So they have good reason to think time is independent of motion.

What about year 21? Or more generally, the year that occurs every 60 years when regions A, B, and C all freeze? No one at all will experience this freeze, or be able to see it “from outside” since it affects all three regions. There will be absolutely no detectable evidence that it occurred at all.

However, my philosopher whose name I can’t recall [but I now know to be Shoemaker] asks: isn’t the most rational conclusion to hold that all three regions of the universe did, in fact, “freeze for one year” in which time did, in fact, pass—even though with motion suspended this had no effect on anything or anyone?  Wouldn’t it be more rational to believe that “one year passed in which nothing happened because everything was frozen” than to believe that otherwise entirely regular and predictable time freeze simply did not occur (when what we would expect is for it to occur in all three regions, and thus expect it to be undetectable)?

One consequence of this would be to hold that year 21 DID NOT HAPPEN, but it this is so, then it would not be true that A freezes every 3 years, B every 4, and C every 5, but that this happens except that, every 60 years, when the freeze would include A, B, and C, no year happens, and A waits 6 years to freeze, B 8, and C 10 years.  The principle of parsimony suggests that an ad hoc adjustment require by saying that the “unexperienced by all year” simply did not happen is less rational than simply accepting that there really was a “year experienced by no one,” which is both in line with the rules of this universe and also what we would expect of the 60th year—namely, that it really did happen, but since everyone happened to be frozen, no one experienced it.

But if this is the case, must it not be the case that time—however much we experience by means of and through motion—is yet not motion, but something that can also, theoretically, measure rest or non-motion?

What do you think? Leave some comments. I’m interested if you find this thought experiment enough to motivate an intuition that time really is logically and really distinction from motion or change, however closely connected the two are either ontologically or phenomenologically.