# Comment on Feynman’s Discussion of Zeno’s Paradox

UPDATE

I got critical feedback on the example I came up with in this post and wrote this blog comment in response:

I think I got mixed up in the following way:

I used an everyday example that varied in some details from the Achilles-tortoise race to check my understanding of Feynman’s explanation of Zeno’s paradox. I imported some background assumptions about how bills work (like lots tend to be regularly repeating on say a monthly basis) but then made the bills deviate from how bills actually work (and also made income deviate from how it actually works) in order to try to fit the ratios of the Achilles-tortoise race. So I basically did a poor rewrite of the original Zeno’s paradox using some superficial elements from the paradox in a new hypothetical where they didn’t make a lot of sense.

original post below

From one of the Feynman lectures on physics:

8–2 Speed

So the error is reasoning from the infinite divisibility of a particular amount of time in the abstract to the conclusion that there is infinite time in reality. Is that right?

At this point I think I’m not really “solid” on this idea so I want to CHEW it some.

Using your mind you can conceptually cut up a length of time as many times as you want, but it’s still the same total length.

It’s kinda like if you had \$100, and you reasoned as follows:
When I get my next bill for \$100, I’ll also get another \$10 of income.
When I get a bill after that for \$10, I’ll also get \$1 of income.
When I get a bill after that for \$1, I’ll also get 10 cents of income.
And on and on.
THEREFORE,
I will never run out of money!
In reality, you won’t have infinite time to keep getting the smaller amount of income that lets you handle the smaller bills. At some point it’ll be next month, and the big bill will be do again, and you’ll be in trouble.

Likewise with the Zeno stuff. The tortoise doesn’t have infinite time to keep getting another increment ahead. Eventually he runs out, and Achilles laps him, and that’s that.

## 3 thoughts on “Comment on Feynman’s Discussion of Zeno’s Paradox”

1. x says:

extremely confusing. where are the bills coming from? what determines the amounts?

1. justinthemallone says:

fair questions, maybe it’s not a great example

1. justinthemallone says:

I think I got mixed up in the following way:

I used an everyday example that varied in some details from the Achilles-tortoise race to check my understanding of Feynman’s explanation of Zeno’s paradox. I imported some background assumptions about how bills work (like lots tend to be regularly repeating on say a monthly basis) but then made the bills deviate from how bills actually work (and also made income deviate from how it actually works) in order to try to fit the ratios of the Achilles-tortoise race. So I basically did a poor rewrite of the original Zeno’s paradox using some superficial elements from the paradox in a new hypothetical where they didn’t make a lot of sense.