Community votes are collected from you and other visitors to Ask500People. Independent votes are collected from visitors to hundreds of other websites around the world.
Sign Up or Login
Sorry, this data is only available to users with an account.
It is very arguable :). In fact, there is an entire branch of mathematics (called _analysis_) dedicated to problems which reduce to this (for sufficiently large values of epsilon[1]).
In fairness to Zeno, we didn't figure it out until the late 1800s.
So, you know why venomous snakes 'doing it' on a table made out of unplaned tree limbs always have offpring?
Because any adder can multiply on a log table!
An engineer and a mathematician are on one side of a room, and a beautiful naked woman on the other. Which one gets the woman?
The Engineer!
The Mathematician knows Zeno's Paradoxes and realizes that he can never reach her. The engineer knows he can get close enough for all practical purposes.
"In order to leave a room, you first have to cross half the distance to the door. Right?Then you must cross half the remaining distance. Right?" Uhh... no. If you only do this, then you'll only be halfway.
You must cross the entire remaining distance. Right?
You pretty much got it. Your distance 'd' is divided by 2 each time. So you get the equation: dNew = dOld / ( 2^n ), where n is the number of steps you take. As n approaches infinity the equation becomes undefined by "regular" mathematics. However, analysis gives us the concept of the limit. The limit of that equation as n approaches infinity is 0.
P.S. That is pretty much the definition of the fundamental theory of calculus :). Pretty sexy, huh?
[1 point]3 years ago by chaleurReplyEdited 3 years ago by chaleur
You can always argue the fundamental premises of any logical (or mathematical) system. Every system is based on some assumptions.
For example, there is an assumption in most "common sense" logical systems that it is not possible for (A) and (NOT A) to be true at the same time.
There's no good reason to make this assumption from a system-level perspective. We make it because we observe it being true in our experience. In fact, it's notably not true at the quantum level.
A similar example in geometry is the assumption that parallel lines never intersect. There's no good reason to make this assumption. Throwing it away, we get non-euclidian geometry, which gives us some awesome and very useful results.
Whose logic system? This is especially important when you're arguing about ideas like "God". Most logical systems fail utterly at the concept of infinity. It is reasonable to suppose that a logical system that cannot deal with the infinite cannot be used to consider "God".
This doesn't mean I believe in "God" :P. I'm just saying it's pointless to try and argue about "God" one way or the other, because "God" is deliberately defined in such a way that logic does not apply.
[1 point]3 years ago by chaleurReplyEdited 3 years ago by chaleur
United Kingdom
Logic isn't arguable, that's why it's logic. But some people on this site seem to disagree.
In order to leave a room, you first have to cross half the distance to the door. Right?
Then you must cross half the remaining distance. Right?
Then you must cross half the remaining distance. Right?
Continue forever.
Using this logic, you will NEVER reach the door, as you must continually cross half the remaining distance first.
It's logical. It's unarguable. However, it turns out to be quite incorrect.
One Zeno's Paradoxes
I always found these interesting
It is very arguable :). In fact, there is an entire branch of mathematics (called _analysis_) dedicated to problems which reduce to this (for sufficiently large values of epsilon[1]).
In fairness to Zeno, we didn't figure it out until the late 1800s.
[1] Math joke :P. It's funny. Trust me.
So, you know why venomous snakes 'doing it' on a table made out of unplaned tree limbs always have offpring?
Because any adder can multiply on a log table!
An engineer and a mathematician are on one side of a room, and a beautiful naked woman on the other. Which one gets the woman?
The Engineer!
The Mathematician knows Zeno's Paradoxes and realizes that he can never reach her. The engineer knows he can get close enough for all practical purposes.
Either that or the Mathematician is a homosexual.
Awesome :).
"In order to leave a room, you first have to cross half the distance to the door. Right?Then you must cross half the remaining distance. Right?" Uhh... no. If you only do this, then you'll only be halfway.
You must cross the entire remaining distance. Right?
You pretty much got it. Your distance 'd' is divided by 2 each time. So you get the equation: dNew = dOld / ( 2^n ), where n is the number of steps you take. As n approaches infinity the equation becomes undefined by "regular" mathematics. However, analysis gives us the concept of the limit. The limit of that equation as n approaches infinity is 0.
P.S. That is pretty much the definition of the fundamental theory of calculus :). Pretty sexy, huh?
I think I'll stick to regular porn.
You can always argue the fundamental premises of any logical (or mathematical) system. Every system is based on some assumptions.
For example, there is an assumption in most "common sense" logical systems that it is not possible for (A) and (NOT A) to be true at the same time.
There's no good reason to make this assumption from a system-level perspective. We make it because we observe it being true in our experience. In fact, it's notably not true at the quantum level.
A similar example in geometry is the assumption that parallel lines never intersect. There's no good reason to make this assumption. Throwing it away, we get non-euclidian geometry, which gives us some awesome and very useful results.
You got it backwards, Fly. Logic is a set of rules for arguing by.
But to argue against logic itself. That won't get you anyway, would it?
Whose logic system? This is especially important when you're arguing about ideas like "God". Most logical systems fail utterly at the concept of infinity. It is reasonable to suppose that a logical system that cannot deal with the infinite cannot be used to consider "God".
This doesn't mean I believe in "God" :P. I'm just saying it's pointless to try and argue about "God" one way or the other, because "God" is deliberately defined in such a way that logic does not apply.
I dont really...know...so I've voted for "undecided"...