Zeno’s Motion Paradoxes.

Zeno of Elea (Ancient Greek Philosopher) is often noted for his paradoxes involving motion which he thought a rather impossible concept.

Here’s a modern variation on a Zeno paradox of motion: You can’t fly from New York City to L.A. because you first have to travel half-way towards that distance to L.A. [that’s Point A] and then again half-way between that point [A] and L.A. [that’s Point B] and yet again half-way between that point [B] and L.A. [that’s Point C], and yet again half-way between that point [C] and L.A. [that’s Point D] and so on and so on. You keep getting closer and closer but by shorter and shorter intervals which never decrease to zero. So before you ever reach L.A. – which you can’t actually do – your plane runs out of fuel because it can never actually reach L.A. and thus it crashes and you die! Now that in itself is a paradox since you have arrived (crash landed) somewhere short of L.A. Yet if where you crash landed had actually been your destination (instead of L.A.) all along, then you would have the same set of circumstances that prevented you from reaching L.A. Taken to a logical extreme, the conclusion is when you boarded the plane in New York City, you couldn’t go and actually arrive anywhere – including to L.A.

Examples of actual Zeno motion paradoxes include the ‘fact’ that a shot arrow actually stands still (since a shot whole arrow can’t be in two places at the same time it has to be either here or there and hence the arrow is not moving); Achilles can’t beat a tortoise in a race where the tortoise has a head start (since every time Achilles reaches the point where the tortoise was the tortoise has moved further ahead); and you can’t cross a room from one side to the other (just like you can’t fly from New York City to L.A.).

So where’s the fallacy? I think that Zeno puts the cart before the horse. He assigns imaginary spatial or temporal divisions / intervals (the cart) and then imposes motion upon them (the horse). Rather, motion isn’t imaginary and is way, way, way more fundamental than dividing time and space up into segments like one-half, one-quarter, one-eighth, one-sixteenth, one thirty-second, one sixty-fourth,, etc. If you start with motion (and motion existed way before there was anyone around to impose imaginary dividing spatial and temporal lines on what was going to be moving) then after-the-fact you can draw any number of temporal or spatial divisions on what moved without affecting the outcome whatsoever.

There is a modern version of this called the Quantum Zeno Effect. Just like your aircraft can’t even leave New York City and expect to arrive anywhere, far less L.A., an instable atomic nucleus can’t ever decay and go ‘poof’. Say from the time you start the clock, T = 0, a radioactive nucleus has a 50% chance of going ‘poof’ in one hour. But say after five seconds has elapsed you peek and note that the nucleus has not (yet) gone ‘poof’. That resets the clock back to T = 0 and you start again. Five seconds later, peek! That resets the clock again back to T = 0. Repeat again and again and again. That unstable nucleus just isn’t ever going to decay unless it does so in the first five seconds. But then you could up the ante and peek every second or half a second. You’ve stopped radioactivity in its tracks. Of course this all has to be pseudoscientific nonsense since there can’t be any such thing as The Observer Effect (of which the Quantum Zeno Effect is supposed to be an example of). As before, arbitrary manmade units of time are being imposed on motion (and radioactive decay and going ‘poof’ is motion) when in reality motion is independent of your concept of units of time.