Print

Please login or register.
1 Hour 1 Day 1 Week 1 Month Forever
Login with username, password and session length

[Neruz]

There are several possible explanations for the paradox, but the simplest one that fits all of the data, and therefore the one chosen by occam's razor, is that it is possible to complete an infinite number of tasks.

To which the next question becomes "How?"

Zeno's conclusion is essentially that nothing we sense is real, which, while possible, is needlessly overcomplicated. Besides, if time and distance are illusions then there is no point in thinking about it, as the very process of thought is, therefore, an illusion.

Since this conclusion is unacceptable, another must be used, even if Zeno was correct science is devoted to producing more accurate, useful models of the universe, not "correctness".

Or, perhaps, the conclusion one could come to is that we're still missing some pieces of the puzzle? Simply because we have concluded that we do not have the answer here does not mean we do have it somewhere else.

[Baughn]

Enough, already!

If you insist on solving Zeno's paradox, the appropriate solution is to look at physics and point out that space is discrete.

In other words, the first assumption - that, to go somewhere, you first need to go to the halfway point - is incorrect. Once you get down to the planck scale, there is no halfway point.

[Neruz]

Which would be what i said way back when i first started this conversation.


Also in theory there could be a halfway point between planck points, it's just (in theory) impossible to ever measure such a point, ergo for all practical purposes space is discrete at the planck scale.

[Baughn]

Well.. in some theories. Not, as it turns out, the most interesting ones.

Though even in those, you can't measure a space that small, and no particles that small can exist, so it's pretty much a moot point.

[Neruz]

Like i said, for all practical purposes.

[winner]

There are several possible explanations for the paradox, but the simplest one that fits all of the data, and therefore the one chosen by occam's razor, is that it is possible to complete an infinite number of tasks.

To which the next question becomes "How?"

calculus

[darius]

Answer to any question in life: CALCULUS
How to use: Needs a degree in math (or at least studying it for a year). Then everything is very simple (bash the question with calculus till it bleeds to death)

[Granite26]

Answer to any question in life: CALCULUS
How to use: Needs a degree in math (or at least studying it for a year). textbook. Then everything is very simple (bash the question with calculus textbook until it bleeds to death)

Fix'd

[dragnar]

That sounds like a very... dwarven approach to calculus.
Where we see a textbook, they see a blunt weapon.

Or, perhaps, the conclusion one could come to is that we're still missing some pieces of the puzzle? Simply because we have concluded that we do not have the answer here does not mean we do have it somewhere else.

Right, what I mean is that while we might not be correct, calculus is still our best bet for now. Calculus solves Zeno's paradox by allowing infinitesimals, eventually other solutions may be created, altering different pieces of his logic.

Calculus may not be "correct", but unlike Zeno's paradox, it fits our observation of the world around us.

[Granite26]

isn't it a priori?

[Eidalac]

Basically stating that before you can go from one point to another, you must first reach the half-way stage between those two points. And before you can get to the half-way stage you need to reach the point half-way betwen your current point and the half-way point and so on, ad infinitum.

The problem with this line of thought, to my mind at least, is that while it is true you have to cross half the distance before all the distance, space is not discrete at a human scale - so you don't -have- to move in half-steps, which is presumed (but not stated) in the problem. 

Another way to look at it:  In classic math, a given distance can be divided into an infinite number of halves, since you can always divide a non-zero number by 2.  This does not mean there is an infinite number of measurable units, it just means you can always divide by 2, because there is no limit on the number of ... numbers.  This is, however, not the same as saying there is no limit on the number of motions needed to cross a distance.

In a way, it's a good show of the issue of quantum level events compared to macro-scale events - if you try to apply quanta to something like taking a 2 foot step, you get weirdness like this problem, because quanta don't apply on this scale.  This, in it self, means we don't have a perfect mathematical understanding of reality.

[zchris13]

Yeah.  Wrestling gets very very confusing, what with so many different options.  (grab his upper left leg with your lower right arm, Y/N?)

Close quarters combat is much simpler. Simply walk towards your target repeatedly!

[Neruz]

Ok, seriously, is it just me or has this entire discussion just gone around a loop and started again?

[zchris13]

I started reading all 8 pages of heavy physics, but balked, and just posted like I only read the OP.

[Neruz]

Actually i was referring to the Zeno's paradoxes discussion. We appear to have started all over again.