Zeno's dichotomy paradox and its solution.

What is Zeno's Dichotomy Paradox? How can it be solved? Is motion an illusion? All answers and details are in the video.

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[BiswajitBanerjeeAuthor]

In my humble opinion, the mathematical solution offered here doesn't quite solve Zeno's paradoxes. It is not enough to say infinite terms sum up to finite quantities. The question is how? When we assume a variable to be approaching a number and say something such as 'x' tends to 'n' where n could be any finite number, we are approximating, and thus the underlying process we are trying to explain mathematically is at best explained approximately. No approximation can claim to be absolutism, and thus, the mere statement that infinite series converges to finite quantity doesn't quite satisfy a thinker's intuitive faculties. This solution is as good as ignoring or overstepping the puzzle without offering a true solution! To imagine that Zeno did not understand the apparent convergence of infinity to finiteness is an insult to the great mind!

[SuperEliasc]

To some, this paradox still stands today even against the view of modern set theorist in mathematics. This video fails to answer any of the assumption of Zeno, the most important of them being: 1. that there are infinite points between two points and 2. an infinite series cannot be completed

[bledarkodra_alb]

As n approaches infinity 1/2n approaches zero, key word approaches but it’s never zero.

[lawrence]

The solution is simple:

By means of the same reasoning as the 'paradox', in order to get to the end of the journey one has to go 1/2 of twice the length of the journey.

Boom boom.

[PaulIshak]

You aren’t traveling to the park, but rather traveling in divided distances found along the path to the park. You are purposely and infinitely setting destinations before the parks final destination, never choosing to travel 100% of the remaining distance. This should be the theory of procrastination. I have a similar theory that I haven’t been able to put to words yet.

[thecarman]

Why couldn't Zeno think of the original distance he wanted to cover as simply being 1/2 the distance to a location twice as far as he wished to travel? He already conceded that traveling 1/2 of some distance was doable, therefore his ability to travel to his original location is accepted by default. No infinite series math required.

[survivordragon]

The actual problem is that Zeno's Paradox is NOT a paradox. It's a logical error. Essentially, it turns velocity into a function of distance traveled. In other words, Zeno's Paradox assumes that velocity equals the distance traveled times the amount time moving. In yet other words, the paradox is assuming that you are slowing down more and more as you approach point B because the time intervals are shorter and shorter.

This is NOT how motion works.

In reality, your speed remains constant as you move forward so long as no other forces are acting to change that speed. The halfway point time intervals, however, are actually getting shorter and shorter as you approach a destination. Essentially, there are an infinite number of shorter and shorter time intervals between you and your destination BUT, your speed is CONSTANT. Therefore, because the time intervals are halving, the proportion of your speed to the amount of distance remaining is growing exponentially. Math kicks in and the limit is reached and your speed compared to the distance remaining is infinite and you pass the point.

Again, its not a paradox. It's a logical error.

[AsianTheDomination]

That picture is actually Zeno of Citium, the first stoic

[PaulIshak]

I discovered this theory because I was curious how much you would have to slow time down to observe the grid snapping which I hypothesize would be seen in the observation of motion. Because of the dichotomy paradox, how could something smoothly move from point a to point b without a snap???

[RF-fipt]

This argument of one convergent series to proof movement why is more powerful than a counterexample with other series (also with succession lim n->inf=0), wich cannot explain movement? If Zeno ask for 1/2+1/3+1/4+...+1/n wich we know is divergent series. The winer is if we have more convergent than divergent so is proof of movement, or if we find only one case against all the others cannot be used as absolutely proof?

[bertrc]

I'm not a mathematician, but here is a proof that this is a purely theoretical math issue. Instead of arbitrarily selecting 1/2, select a 1/4. You wont get halfway! Select 1/8 and you won't get a 1/4 way. Follow this reasoning far enough and you won't be able to start your journey!

[robertwilsoniii]

Why do you think it's possible to infinitely divide reality?

[mikheilloladze]

Why does it become 1/2n zero??? Please explain. This is not possible.

[iallalli]

Hi.
Zeno's paradox will be solved only when you are yourself.
He is only talking about Parmenides' the one real being, not any time space thoughts.
When you have solved Zeno's then you have already solved Parmenides Socrates and Jesus.
If you are brave enough then challenge to digest Thomas Gospel, not following other's deluded opinions.
For tip, This one put Thomas gospel's 114
Simon Peter said, Let Mary leave us. For women are not worthy of life.
Jesus said, I myself shall lead her in order to make her male to be the one and same so that she become living spirit resembling you male who become the one and same.
For every woman who will take her male in herself to be the one and same will enter the kingdom of heaven.

Have happy life.
!!!

[bertrc]

So, 'Near enough is good enough' is the new mathematical rule! All this video proves is that math fails to describe reality.