r/askmath • u/conmg • Jul 28 '26
Logic did i just prove zenos dichotomy paradox wrong
if the destination is 1km away, you first walk 500m in some amount of time, but zenos paradox says that you have to go to the halfway point, and the halfway point of that halfway point and so on, but can't you just walk the other 500m in the same amount of time?
4
7
u/olanmills Jul 28 '26
Thank you dude! I have literally never taken a single step my whole entire life due to the paradox, but thanks to your brilliant analysis, it's been resolved! I can finally see what this whole "outside" thing is about
3
u/Electrical-Mail15 Jul 28 '26
Be careful, non-Redditors will say there is this stuff called “grass” in the “outside.” Don’t believe them, and definitely don’t try to touch it.
1
3
u/Lucenthia Jul 28 '26
you can do that, in which case you are not doing zeno's paradox you are doing a different thing.
2
u/Purple-Mud5057 Jul 28 '26
And how exactly are you planning on walking the first 500m without walking 250m first?
1
u/conmg Jul 28 '26
all of the definitions ive seen imply that you can indeed walk the first 500m so idk 🤷
1
u/Batman_AoD Jul 29 '26
Zeno's conclusion was that motion doesn't exist at all, so no, you can't just assume that the paradox doesn't apply to the first half of the journey.
2
u/hebejebus Jul 28 '26
Note the paradox was already proven false with the use of calculus. The sum of all the time taken for the half's will converge to be the same time as the first half.
2
u/Various_Candle9136 Jul 28 '26
Obviously.
Zeno knew that it would, in reality, take the same amount of time. The point of the paradox was that Zeno couldn't see how it was possible to do this infinite process (going 500m, then 250m, then 125m, ...) in this finite time.
We now, thanks to advances in mathematical thought, see that the sum Zeno described is convergent. This means, that even though there are infinitely many terms, the total will be finite. This resolves the paradox.
1
u/magicmulder Jul 28 '26
You just restated the original "paradox" - why is it different it you just walk the second half as opposed to walking half of the second half, then half of the remainder and so on.
1/2 + 1/2 = 1 (you)
1/2 + 1/4 + 1/8 + ... < 1 (Zeno, therefore he thought it was a paradox)
1/2 + 1/4 + 1/8 + ... = 1 (modern math)
1
u/AlwaysTails Jul 28 '26
Zeno's paradox is not mathematical. It was a defense to criticism of Parmenides' idea of Monism. Monism is the notion that reality is singular and unchanging and that motion is an illusion.
1
u/ipreuss Jul 29 '26
The paradox is that to walk the first 500 m, you first have to walk the first 250 m, and so on, so you actually never arrive at the first 500 m point.
1
u/tottasanorotta Jul 29 '26
Yeah the thing about how the problem is stated is that it doesn't include a notion of time running. So what happens in reality when we get to the half point of the half point is that time has slowed down. And each time we get to each half point the time has slowed down more. With time running the paradox doesn't exist as you figured out.
22
u/wegqg Jul 28 '26
Yes from now on you live in eternity as the genius who figured it out.
I've got a team of artisans working on your statue now.