Thanks God, we have James to help us with this math problems.

Hi Miguel

I gave the real solution. Though modern mathematicians will disagree with me.

Although I gave their solution too, it's just that their solution is incorrect.

I am good, there are some big changes in my life that are happening as we speak... a temporary stay with my parents while I look for a more permanent place to move. My house legally changes hands in the middle of June, so I just got a head start. Should be completely out of this house by Mon. or Tues., physically at least...

Pursuing employment opportunities in other states, just because I no longer wish to live in Ohio. Hawaii and Florida have employers which have expressed the most interest. The trips are already planned to visit or are being so done.

I really want Hawaii, of course... I so hope...


KonA... KonA... KonA...


Oooops... wrong thread... good thing I know the OP!


James is good for helping...


I am glad to hear that you are well, I know that you work hard at your goals. I always wish you all the best, my friend.

I stayed out of your Oral Tradition thread out of respect, besides, we already know the other thinks, for the most part... and the respect is shared...

In this paradox, he(Zeno) assumes that distance is infinitely divisible but time is not, thus the correction with exponential notation(s) of Marley, according to calculus?

I'm sorry James for being such an ignorant, but i have a question.
if time is a mathmatical quantity why it can't be divided infinitely as any other quantity?

first of all, thank you.
second of all, this quantum physics breaks down too many concepts. it's very hard for me to get the concepts yet.
the other day i was trying to read "a brief story of time" and i realize that i'm not ready yet.
At least not in english. I need to learn a lot more, and expand my horizons to understand that at some point what i understand as truth it's going to break down.

uhhhh creative one ... aren't you supposed to be packing?

Maybe he's only going to fly half-way.

Then stop and call you.

Then fly half of that remaining distance.

Then stop and call you.

Then half of the remaining distance.

Then stop and call you.

And so on,... forever and ever.

Always getting half-way closer to your heart.

uh oh ... does that mean he will always be half way?

That depends on your belief.

If you believe in modern calculus he's eventually make it all the way. But he might be totally exhausted after having completed an infinite number of tasks to get there. (he would have had to get half-way to close to you an infinite number of times).

Each time being half-way closer to you than he was before. But he'll do this quicker and quicker as he approaches you to finally collapse in your arms with infinite exhaustion.

Or,…

If you believe in quantum physics, he'll just make a quantum leap and be right over all bright-eyed and bushy-tailed.

It’s all in what you believe (but you might need to proselytize that belief onto him too so you’re both on the same wavelength)

Hey, if I were in Michael’s shoes I would have quantum leaped over to you a long time ago.

That’s precisely where the solution lies. The premise is indeed incorrect. The universe is not a continuum. At least not for this problem.

Although, you’ll find that even modern day mathematicians have not solved this problem correctly even though they believe they have solved it with calculus. They have not.

The solution actually comes from physics, and the work of Max Planck (i.e. Quantum Physics)

Before I being (this will probably be a lengthy post), let me say that Zeno of Elea and Leucippus of Miletus were two of my most revered childhood idols (at least from ancient Greece).

Let me begin by stating the real problem.

The real problem was the idea of the continuum. The idea that everything can be divided up continuously forever and ever with out end. Leucippus was the first to propose that this is not the case. That the world is actually made up of atoms (individual discrete parts). Of course he wasn’t taking about the atoms we know of today, he was speaking on a purely philosophical level.

Well, the mainstream Greek philosophers of the time didn’t believe like Leucippus, they believed that everything is continuous.

Zeno knew about the work of Leucippus, and Zeno had a wonderful epiphany. He realize that if the world was truly continuous then motion would be impossible (for the very argument you gave in the OP). Although I he actually gave a dozen or so arguments for this. They all were based on the same idea. The idea that it would be impossible to complete an infinite number of tasks. That’s his basic premise – it would be impossible to complete an infinite number of tasks, therefore if the world is truly continuous then motion would be impossible.

He was actually giving support to Leucippus’ idea that realty must be discrete. Obviously he wasn’t trying to argue that things can’t move, he clearly knew that things can move!!! What he was arguing is that if the world it a continuum motion would be impossible.

Well, the mainstream philosophers weren’t prepared to accept that the world is discrete so they saw this as a ‘paradox’ that must be solved within the framework of the continuum. But they could not resolve the paradox so it become known as Zeno’s Paradox of Motion.

In fact, no one could solve this so-called paradox until Isaac Newton and Gottfrid Leibniz invented Calculus. Then it was proclaimed that the paradox had been solved. But they really didn’t solve it! However it is still believed today that Calculus solves the paradox whilst preserving a continuum. This is false, so I won’t spend a lot of time on this,….

First off Marley is correct. He has given you the modern calculus solution. And that solution has to do with derivatives. For example dx/dt is the velocity dx²/dt is acceleration and so on where x is position, t is time, and d means to take the derivative. (just as you learned in high school calculus)

The idea here is that it can be shown mathematically that rates of change between time and distance are sufficient to complete motions required. And they give (feeble) arguments that even though it appears that you need to keep cutting things in half, you don’t really need to because the time it takes to move is also heading toward zero. They claim that the time it takes to move is heading to zero faster than the distance is heading to zero, thus solving the apparent paradox.

Actually their full of baloney.

This doesn’t solve the problem. The problem that Zeno actually proposed it that it would required an infinite number of tasks to complete the move. In other words, you’d have to close that halfway mark an infinite number of times if the world is a continuum!!!

Zeno is right and the modern day calculus solution is wrong. Yet this is still accepted as the correct solution by modern day mathematicians.

However, there is nothing in calculus that states than an infinite number of tasks can actually be completed. On the contrary if you look at the formal definition for the calculus limit (I can type it in here without symbols but it probably wouldn’t mean anything to you anyway, even most mathematician truly don’t understand it!)

You will see, that it does not even imply that an infinite number of task can be completed. In fact any mathematician worthy his salt will tell you that to prove that a limit exists all one must do is prove that it is bounded, and has a certain trend toward a given number. Then you can say the limit exists. However, even when you can prove a limit exists that doesn’t even mean that the actual quantity exists! In other words you can prove that some equation that is approaching zero in it’s denominator will have a limit at that zero. However, that doesn’t mean that the a actual limit can be reached at that zero mark. It only means that this is the quantity it is heading toward as the denominator approaches zero!

In other words, the calculus limit (formally defined by Karl Weierstrass) doesn’t prove anything. It’s just means of calculating trends with great precision. So the calculus limit can’t even be used to disprove Zeno anyway.

Ok, so what’s the real solution?

The real solution is that Zeno was right all along!

If the world truly is a continuum then motion would be impossible! But the world isn’t a continuum! We know this know from Quantum Theory. On the quantum level you can either be here, or there but not in-between.

There is a smallest distance that can be traveled. A smallest amount of energy that can be expended, and even a smallest tick of time that can tick. At some point as you are cutting those distances in half you’re eventually going to make a quantum leap and pass the tortoise.

Quantum Physics has confirmed that Zeno was indeed correct. Our universe is not a continuum. At least not with respect to the motion of the physical things within it. It still has a oneness about it, that the Greeks refused to give up. What they didn’t realize is that they can have both, a universe that is physically discrete and still has a nature of oneness. In fact, this is the modern day paradox of Quantum Mechanics. We solved Zeno’s paradox, only to discover a newer and deeper paradox.

So Zeno was right. Can we send a Nobel Prize back in time????