Zeno's Paradox: Achilles and Tortoise Race

The paradoxes of the philosopher Zeno, born approximately 490 BC in southern Italy have puzzled mathematicians, scientists, and philosophers for millennia. Although none of his work survives today, over 40 paradoxes are attributed to him which appeared in a book he wrote as a defense of the philosophies of his teacher, Parmenides. The most famous of Zenos arguments is Achilles and Tortoise race paradox.

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[strawdolluserrichy]

Here to learn about Satoru Gojo's technique, don't mind me

[TheIanderthal]

I woke up from a nightmare, got onto Instagram. I had seen a tumbler post about zenos. Now I'm here

[uncaboat]

Since it looks to be hundreds of videos about Zeno's Paradox, I'll share my joke again.
There's an old joke back in Engineering School about the difference between Engineers and Mathematicians.
The high school dance starts off in the gym with all the girls on one wall and all the boys on the opposite wall. The Mathematicians reason that, in order to get to the other side to ask a girl to dance, they have to first cross half the distance across the gym. Then cross half the distance of what remains. Then half again, half again, on to infinity. Since it is impossible to ever cross the gym a full 100% to reach the girls, they give up and go home.
The Engineers reason that, yes, it is impossible to cross the gym a full 100% -- but we can get close enough!!

[jsoren]

The paradox doesn't incorporate velocity, just dividing the distance traveled by a half each time.

[connordavey]

Might use this for when I’m late for work…

[AegisRick]

I see people saying they've solved this paradox by claiming that space and time cannot be divided infinitely, due to the plank length and plank time. However, doing this you are incorrectly applying the limits of the geometric series and will not have an answer that converges to that 12.5 meters. Trying to inject physics to this paradox will lead you to the wrong mathematical conclusion. One that we very clearly know is right. The geometric series is a perfect way to analyze this physical problem but we must work in infinites. When we do integrals in calculus are we constrained by the plank length to solve physical problems? No, because if you were, you would reach the wrong conclusion.

[Platin_]

You are just describing the point where he passes the turtle with an infinite precision. Lets take an easier example: The man runs 10 times as fast as the turtle and the turtle is 10 meters away from him. Now when he reaches 10 meters, the turtle would be at 11 meters. When the man reaches 11 meters, the turtle reaches 11, 1 meters. Now if we keep doing this forever, We will get to the point and so on. And this is the exact point, where the man passes the turtle.

[joeanom]

In his Achilles and tortoise race "paradox", Zeno starts off by saying that both time and distance are finite (Achilles and the tortoise both have a specific velocity, in other words, specific distance over specific time) so Achilles will catch the tortoise at a specific point. Pretending that movement over a finite distance for a finite time can be divided up infinitely is just a word game.

[tejailla]

Zeno:When you can't convey them confuse them!!!

[atharvaphadtare]

The fault in our stars brought me here.

[davidschrecengost]

Zeno forgot to define the distance of the race. Assuming the race was a race to infinity, did Zeno believe the tortoise would still be ahead of Achilleses after 10, 000 years?

[squeaky]

That’s because Zeno’s Paradox is infinitely approaching a certain value; in this case, it’s logarithmic. If he had instead accounted for the actual distance traveled per unit of time, 10 m/s, Achilles would’ve surpassed the tortoise at 12.5 seconds. It’s like biting pieces of cheese off of a cube. If you bite half of the cheese off each time, at a rate of .2 bites per second, theoretically, you would never completely finish the cheese because you will always be able to split it in half (until you reach atomic scale which then would be impossible because the thickness of the tips of your teeth is an uncountable number of atoms.

[gorgono]

Well you can also think about it that way. If we take that the smallest thing is Planck Length.(1.6 10^-35) then there is no such thing as infinity. You can't divide infinitely. You can calculate how many Planck Lengths there are in 10m and calculate how many times you need to divide before you reach the end. But to calculate it you need to start at 10m + 1xPlanck Length. Space, Time and Numbers(made by human) are connected.

[IHatoHandels]

I just came to figure out what gojo meant, now I know if we met my stupid would show

[John-oylt]

10 meters per sec so 20 meters should have happened by now

[jeromemalenfant]

2:46 "Zeno's assumption is that you can infinitely divide space and time, which is wrong" 
No. Zeno's assumption is that the sum of an infinite number of terms, (time intervals in this case), is infinite. That assumption is wrong if the terms get smaller at a fast enough rate (which they do in this case) so that the sum converges.

[muhammedshanushan]

What does relativity theory has to do with wave particle duality?
Time id discrete, finite number of indivisible particles, how is that wrong?

[CreepyBio]

Philosophy is literally the modern art of ancient times: everyone who has no talent wants in on it.

[MANIMARAN-dbgl]

Can’t we use the concept of Relative velocity?

[lordfritzropero]

This is no paradox to me (I don't get it). I mean, it is already flawed. After all, it's called a "race" but Achilles isn't trying to make the tortoise eat dust, but only covers the same distance the tortoise does after the tortoise does it. In an actual race (with a finish line perhaps) Achilles would win. So how is this a paradox pls help