Zeno

[xellos88330]

Ok, so I was in philosophy class today and this guy, Zeno, was the topic. He said that motion is false. He uses this to prove it...

If a man shoots an arrow at a target, the arrow will never hit the target. It is a mathematical impossiblity.

For example, the target is 100 yards away. To travel halfway to the target, it must move 50 yards. To travel halfway to the halfway point, it would have to travel 25 yards. Keep dividing the halfway point in half, and you will ALWAYS have distance between the target and the arrow. Talk about a fun paradox.

In short, I was never at class today because mathematically speaking, there is no possible way I could have arrived. Thus, motion is false or an illusion.


This probably wasn't thread worthy, but it blew my mind. I never took the time to actually think about something like that.

[silverblk mystix]

...take two steps back....


and drop...





The CHALUPA!

[BlackSwordsMan]

Zeno then stood out side a 100 yards away and got shot in the chest with an arrrow.

[BlackSwordsMan]

Romo for the past three years hasn't seen a 100 yard days either. lololromo

[baseline bum]

Zeno's argument is based on the incorrect belief that summing an infinite set of positive numbers gives infinity. His specific argument is that

1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512 + 1/1024 + ...

is infinite. It's not; that sum of infinitely many positive terms is 1 (see the geometric series).

[baseline bum]

Now if you want to see something that truly is strange involving infinite series, read the section entitled Rearrangements in Chapter 3 of Baby Rudin:

http://img64.imageshack.us/img64/2676/babyrudin.jpg (http://www.amazon.com/Principles-Mathematical-Analysis-Third-Walter/dp/007054235X/ref=sr_1_1?ie=UTF8&qid=1315435815&sr=8-1)

[MannyIsGod]

You can not halve into infinity. At some point you can no longer split something in half.

[baseline bum]

You can not halve into infinity. At some point you can no longer split something in half.

Even in an idealized situation where you can keep cutting the distance in half forever, the arrow still travels 100 yards:

50 yards + 25 yards + 12.5 yards + 6.25 yards + 3.125 yards + 1.5625 yards + ...

is the same as

100 yards * (1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + ...) = 100 yards * 1 = 100 yards

[silverblk mystix]

Ok, so I was in philosophy class today and this guy, Zeno, was the topic. He said that motion is false. He uses this to prove it...

If a man shoots an arrow at a target, the arrow will never hit the target. It is a mathematical impossiblity.

For example, the target is 100 yards away. To travel halfway to the target, it must move 50 yards. To travel halfway to the halfway point, it would have to travel 25 yards. Keep dividing the halfway point in half, and you will ALWAYS have distance between the target and the arrow. Talk about a fun paradox.

In short, I was never at class today because mathematically speaking, there is no possible way I could have arrived. Thus, motion is false or an illusion.


This probably wasn't thread worthy, but it blew my mind. I never took the time to actually think about something like that.

He didn't prove shit.

If an archer...or any idiot...pulls back on the bow...lets loose and hits the target...

ZERO's theory goes to shit.

[xellos88330]

Zeno's argument is based on the incorrect belief that summing an infinite set of positive numbers gives infinity. His specific argument is that

1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512 + 1/1024 + ...

is infinite. It's not; that sum of infinitely many positive terms is 1 (see the geometric series).

I understand that he is wrong in terms of addition, however, what if the formula subtracts using points in time/distance. Isn't it said that a point is infinitely small? If the world and/or time is divided into points, how can you actually get from point A to point B if the points you have to cross to get there are infinitely small?

This is what is driving me crazy. Is there some math that solves this? Calculus, physics? Whatever it is, I am kinda thinking about studying it just for shits and giggles.

[xellos88330]

He didn't prove shit.

If an archer...or any idiot...pulls back on the bow...lets loose and hits the target...

ZERO's theory goes to shit.

Well, the universe is made up mostly of empty space. There is mostly empty space inside atoms. The only reason why it would appear to hit and cause harm is due to electromagnetism. That is why people cannot walk through walls and stuff. Perhaps it doesn't ever reach the target because electromagnetic force of the target doesn't allow it to touch it, only sever the links to other portions of the atomic makeup of the target?

[MannyIsGod]

Well yeah, there are a lot of functions that will lead you to infinity. F(x) = 1/x represents what you're talking about the graph for the function never reaches zero but rather goes to positive infinity. Thats not how the real world works, though. You can't go smaller than the particle level, as far as I know.

[thispego]

lol, yeah military minds aint the smartest thats for sure

[Viva Las Espuelas]

You can not halve into infinity. At some point you can no longer split something in half.

?????? Really? How can you split nothing?

[MannyIsGod]

?????? Really? How can you split nothing?

I have no idea what you're talking about but nothing divided by anything is still nothing. No idea how you got there from what I said, though.

[Viva Las Espuelas]

How can you divide something into nothing?

"at some point you can no longer split something in half"
If you can't split "something", that means there's nothing, correct?

[MannyIsGod]

No you're misunderstanding what I'm saying. When you break something, you're splitting the it into two groups of atoms. Fairly huge groups, but groups none the less. Eventually if you keep splitting that you come down to two atoms. You then split it into atomic particles (protons neutrons electrons). You can then split those into particles (quarks etc) but that is as far as it goes. At some point you reach the smallest particle upon which the universe is built upon and can split no further. I'm not completely versed in modern physics theory but I don't think any of it accounts for an infinite ability to be able to go smaller.

[xellos88330]

lol, yeah military minds aint the smartest thats for sure

And your contribution would be?

[DeadlyDynasty]

lol, yeah military minds aint the smartest thats for sure

:rollin

[Oh, Gee!!]

A second is a minute, every hour’s infinite

[Viva Las Espuelas]

No you're misunderstanding what I'm saying. When you break something, you're splitting the it into two groups of atoms. Fairly huge groups, but groups none the less. Eventually if you keep splitting that you come down to two atoms. You then split it into atomic particles (protons neutrons electrons). You can then split those into particles (quarks etc) but that is as far as it goes. At some point you reach the smallest particle upon which the universe is built upon and can split no further. I'm not completely versed in modern physics theory but I don't think any of it accounts for an infinite ability to be able to go smaller.

Nah, I know what you're saying. I just don't think that's a true statement. I mean, on paper, you can halve something into infinity. I'm thinking the same applies to the physical. I could be wrong. Maybe.

[Spurminator]

No you're misunderstanding what I'm saying. When you break something, you're splitting the it into two groups of atoms. Fairly huge groups, but groups none the less. Eventually if you keep splitting that you come down to two atoms. You then split it into atomic particles (protons neutrons electrons). You can then split those into particles (quarks etc) but that is as far as it goes. At some point you reach the smallest particle upon which the universe is built upon and can split no further. I'm not completely versed in modern physics theory but I don't think any of it accounts for an infinite ability to be able to go smaller.

Even if you can't physically split that particle, wouldn't you still be able to "theoretically" split it into sections? For example, does that particle have a left side and a right side? And does its left side have a left side and a right side? Etc.?

(None of this is to say I agree with the Zeno idea)

[Viva Las Espuelas]

Exactly. That's what I mean by how get you get nothing by splitting/halfing/dividing something. Who cares that nothing below particles have been discovered or properly named. It's still a part that's being halved/split/divided into two from something. Mind you, I'm not completely versed in modern physics theory either.

[MannyIsGod]

Even if you can't physically split that particle, wouldn't you still be able to "theoretically" split it into sections? For example, does that particle have a left side and a right side? And does its left side have a left side and a right side? Etc.?

(None of this is to say I agree with the Zeno idea)

I don't think so. Not unless you believe you can infinitely go smaller.

[baseline bum]

Manny's got no love whatsoever for Cantor Sets tbh.

http://upload.wikimedia.org/wikipedia/commons/thumb/5/56/Cantor_set_in_seven_iterations.svg/729px-Cantor_set_in_seven_iterations.svg.png

[MannyIsGod]

Never heard of him or them, tbh. Considering he helped developed topology I'll have to read up on it though! Thanks!