“A problem can never be solved on the same level it was created”

I remember hearing of Zeno’s paradox and thinking it was stupid. A tortoise  with a 100 meter head start can never be overtaken by a runner? Because ‘that which is in locomotion must arrive at the half-way stage before it arrives at the goal’? That makes no sense. Time does not splice up endlessly, it flows! I still agree with my younger self but I believe there is more to it than my initial gut response.

Zeno’s paradox can be explained mathematically as an unsolved equation between X (time) and Y (distance). Aristotle’s ‘halfway’ rule sets up for the following ‘solution’:

The relative distance between the tortoise and runner is infinitely divided, therefore the runner is always behind. He nears the point of overtaking the tortoise infinitely close but he never reaches it, for that point is a mathematic asymptote.

In reality time does not work like that. Time flows. The reason you can’t initially solve Zeno’s paradox is because you relied on the reasoning Zeno gave you: that which is in locomotion must arrive at the half-way stage before it arrives at the goal. It’s a bs rule. Zeno tricked you into using his set of rules within the paradox to solve the paradox:

A problem can not be solved on the same level it was created. When we correct for Zeno’s crustacean definition of time we can suddenly see clearly that the runner indeed overtakes the tortoise:

Solved.

The thing about life is that not all its paradoxes are solvable. Or, as a brahmin would say: the thing about paradoxes is that they are per definition not solvable. Ergo Zeno’s paradox was never a paradox – it was a riddle. Zeno was the Greek version of the Riddler (or the Sfinx, whatever signaling you prefer) and we solved his riddle.

Yet some people will still insist it is a paradox. They will say: ‘you attach a similar crustacean definition to time as Zeno did! Time is not linear! Look at Einstein!’ Well I looked at Einstein and saw a man who spend the latter part of his life looking for God. But I get their skepticism, for they are right: time does not completely fit my definition either. It is more accurate than Zeno’s definition hence it is preferable, but there might very well be dimensions of perception in which the tortoise always stays ahead.

However, if we follow this line of reasoning there are an infinite amount of  time paradoxes possible. Back to the Future I II III, Donnie Darko, Terminator & The Butterfly Effect to name some random movies. Each one uses a different set of rules to create a different set of time paradoxes and all of them could be true. Were we to adhere the same level of respect to these movies as to Zeno’s paradox, we would call them Back to the Future’s paradox, Donnie Darko’s paradox, Arnie’s paradox & Ashton Kutcher’s paradox. Generally I don’t, so Zeno’s riddle it is.

Naturally the possibility of truths in these paradoxes remains, if it is but a glimmer. I will always concede this point, but I will argue that there is a quicker way to express this paradox:

It is at this point that I have nothing clever to say. This is nothing people before me have not thought of before. It’s not like I’ve given the irrefutable proof of God. It’s just a version of God: paradox as a synonym for God. So… Yeah.

1. That’s a mighty strange solution to Zeno’s Paradox. The solution is not that there is only a finite number of midpoints between any two points based on some interpretation of quantum mechanics, but that there are finite solutions to infinite sums, which is something no ancient AFAIK could have predicted.

E.g.,

&Sigmai=1∞ (1/2^i) = 1.

(Here’s to hoping that html code rendered…)

1. Ack that should read Sum from i=1 to infinity of (1/2^i). Obviously it adds up to one.

1. You’ve made me rethink the whole tobacco thing but on this I maintain ground.

Most importantly: a finite solutions for an infinite equation does not make sense. When mathematics employs the ‘∞’ sign it does not make infinity finite, it just expresses the idea of infinity.

Hypothetically, a computer given infinite time could solve the equation. But then we give a con answer to a con question. We might as well explain mathematically how many angels dance on a pinhead.