This Is How Physics, Not Math, Finally Resolves Zeno’s Famous Paradox

The fastest human in the world, according to the Ancient Greek legend, was the heroine Atalanta. Although she was a famous huntress who even joined Jason and the Argonauts in the search for the golden fleece, she was renowned for her speed, as no one could defeat her in a fair footrace.

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Angela Merkel might be rolling her eyes

forbes.com on cutting edge science literacy

“aaaand v = dx/dt thanks see you later”

no wonder we have coronavirus pandemic

Tau.Neutrino said:

This Is How Physics, Not Math, Finally Resolves Zeno’s Famous Paradox

The fastest human in the world, according to the Ancient Greek legend, was the heroine Atalanta. Although she was a famous huntress who even joined Jason and the Argonauts in the search for the golden fleece, she was renowned for her speed, as no one could defeat her in a fair footrace.

more…

I can’t read it because I’m not turning my ad blacker off. What does it say? Oh, OK, I can bypass that block by using Google’s cached version.

Hold on! The article in Forbes isn’t about Zeno’s Paradox (ie. of the arrow) at all. It’s really about a simplified version of Achilles and the Tortoise. That’s easy to resolve in mathematics. Infinity exists, and a convergent infinite sum exists.

If you really want to see how physics handles Zeno’s Paradox, read https://en.wikipedia.org/wiki/Quantum_Zeno_effect

In the quantum Zeno effect, observing an arrow in flight often enough stops the motion of that arrow. Sometimes this effect is interpreted as “a system can’t change while you are watching it”. One can freeze the evolution of the system by measuring it frequently enough.

• To go from her starting point to her destination, Atalanta must first travel half of the total distance. To travel the remaining distance, she must first travel half of what’s left over. No matter how small a distance is still left, she must travel half of it, and then half of what’s still remaining, and so on, ad infinitum.

High school math teacher tried to use a similar example to introduce the idea of limits but I thought it was stupid then and I still think it is stupid. Because, for it to be true, for each half distance the velocity would also need to halve. No doubt someone will tell me I am wrong, much like the aforementioned math teacher, but I don’t care. Without accepting his example I still had no trouble learning the concept of limits…

If nothing else, you have to admire the way they simultaneously over-complicate things and over-simplify them.

The resolution of the traditional Zeno Paradox doesn’t require maths of physics, you just need to view the problem in a way that doesn’t require summing an infinite series.

I’d have to read up on the quantum Zeno paradox to make any sensible comment, and I suspect that is not possible within a finite time.

My favourite version of Zeno was in a New Scientist puzzle a few months ago:

4 snails sit on the corners of a square of side length 2, and simultaneously start to move towards each other in a clockwise direction at 2units/hour.

How long before the snails meet?

There is a very simple solution, but if you try and work it out by dividing it up into small steps you find they are each on a spiral path with an infinite number of cycles, so as their path approaches the centre angular velocity approaches infinity.

So how does that work?