You Can't Move #shorts

How many times have you heard that the shortest distance between two points is a straight line? What if it's actually... the longest distance? What if it's an infinite distance? What if it's impossible to move at all?!

That's the theory behind Zeno's thought experiment on movement. If every distance can be divided up into smaller parts, and traversing every part takes a non-zero amount of time, then how can we make any progress at all in a finite amount of time?

This is obviously wrong, since you can walk to the mailbox and back every day without facing an existential or physics-based crisis. The tale of Achilles and the Tortoise has a certain logic to it that took thousands of years to unravel -- but once we understood the power of the convergent series, the paradox disappeared.

#maths #education #mathematics

[kewillia]

There once was a fellow named Zeno
And some would say "Hey, what did he know?"
He held a strange notion
That there was no motion
But if that's true, then where did he go?

[TristanJCumpole]

It's simply a premise built upon a faulty assumption. A line between two points whose fixed length is divided into infinitely small divisions would require an inversely proportional amount of time to traverse between two infinitely-close points. Conflating fractional measurements with discrete ones is a huge error.

[awareqwx]

An infinitesimal distance requires an infinitesimal amount of time to cross. Therefore, a finite distance requires a finite time.

This is an excellent example of spotting a flaw in a model when relating it to reality.

[k-techpl]

Hi, I wanted to correct a mistake in your video. Zeno's paradoxes are named after Zeno of Elea (in modern day italy), what you have shown is a bust of Zeno of Citium (in modern day Cyprus) who was the founder of Stoicism and NOT the same guy.

[EebstertheGreat]

Interestingly, Antiphon may have used the method of exhaustion to effectively find the sums of convergent series within Zeno's lifetime. The two were apparently contemporaries, and in the latter half of Antiphon's life, he allegedly developed the method of exhaustion for computing areas and volumes. In some forms, this method resembles Riemann integration, and in others, it can involve the sum of an infinite series, both of which could be used to directly confront Zeno's line of reasoning here. Antiphon's method was known to Eudoxus and presumably to Aristotle who wrote of Zeno's paradoxes. To my knowledge, he never connected the two.

[PaulGrayUK]

You can apply zoomed-in data from a zoomed-out perspective and blow your own mind. Perspective is relative and with that, don't mix perspectives without the right scaling is the thinking you want.

[BrotherAlpha]

"There's no limit to how small these..." Planck length.

[Juan-gu]

U do realize that that a human foot is bigger than the infinitely small points, that is how we get through the line

[hugoclarke]

If you define two connected points, it's no longer infinite. Infinite just means only one point has been defined, in which state you have a loop.

[camerongray]

This exact problem troubled me for ages as a small child. Then I learnt about Planck length and then everything makes sense

[skyswinger]

But the thing about the real world is that we have a smallest distance:
The plank length

[sanfordgfogg]

The quantum effect of the Plank Length disproves the basis of this thought experiment. At some level, the lengths can no longer be divided, thus, there cannot be infinite quantity. And associated with this is: The Plank Second, which is the minimum amount of time that has meaning.

[clad]

Even if it's theorically possible to imagine an infinite small distances (which isn't true in reality) the thing is that you traverse these infinite small distances in an infinitely small time period. There is no end of points but there is no end of how fast you are to cross them.

[davidlohcc]

"A straight line is ACTUALLY the longest distance"?! Hey you got to stop misleading young audiences who don't think about what they watch. Do your variational principle calculus please

[OC]

Your fractional distance correlates with fractional time. Can't reduce one measurement without reducing the other.

[jeffb]

Dude. That's awesome that you bring this up, this is the way I find new areas to explore when I am tripping.

[nateu]

Nobody:

One piece series: One huge line

[casperghost]

So how does this relate to you initial hypothesis? Are curved lines somehow immune to this effect or was it just a completely irrelevent way to bring up the topic?

[Skav]

planck length: "Im boutta end this mans whole career"

[zenko_m]

In geometry, a point is a location represented by a dot. A point does not have any length, width, shape or size, it only has a position. Basically a point cannot be defined in terms of previously defined objects. A point becomes the basic concept.