This is why mathematics makes my head hurt... - by catbarf
catbarf on 28/9/2007 at 21:01
Okay, the other day a few friends and I were talking about the possibility of life on other planets, when one brought up the following argument:
1. Space is infinite, therefore there is an infinite number of planets.
2. Not all of those support life, so there is a finite number (less than infinite) that support life.
3. If there is a finite number of planets supporting life, there is a finite number of organisms.
4. To find the average number of organisms pr planet, we divide that number by the number of planets- which is infinity.
5. Divide by infinity, you get 0. Therefore there are no organisms, intelligent or otherwise, in the universe.
I also recall reading about a physicist who proved that gravity is impossible. Does anyone have a link?
So, my point is this: What other apparent absurdities are there? What is your favorite?
Chimpy Chompy on 28/9/2007 at 21:06
Quote Posted by catbarf
1. Space is infinite, therefore there is an infinite number of planets.
Wait it's not infinite in terms of infinite volume. Given that it started at a size of zero, and has expanded at a finite rate, in a finite time, it can't be infinite.
I think it might be infinite like the surface of sphere - pick any direction and you can travel forever, but you'll keep returning to the same spot.
CyberFish on 28/9/2007 at 21:10
This is bollocks. Firstly:
1. Space is not infinite. Current theories suggest that the volume of space is a sphere with a radius equal to the speed of light multiplied by the age of the universe (plus a bit to account for early inflation)
2. Even if space is infinite, this does not imply an infinite number of planets. There could quite easily be a finite number of planets in infinite space.
3. If there <b>is</b> an infinite number of planets, then there is also an infinite number of inhabited planets - any fraction of infinity is still infinity.
4. "Less than infinite" and "finite" are not the same thing. You can have different sizes of infinity. No, really.
mopgoblin on 28/9/2007 at 22:34
Quote Posted by CyberFish
3. If there <b>is</b> an infinite number of planets, then there is also an infinite number of inhabited planets - any fraction of infinity is still infinity.
There's nothing stopping a subset of an infinite set from being finite. The set of integers is infinite, but only a finite subset of them divide 6, for example. If you divide an infinite set into a finite set of equivalence classes, at least one of those equivalence classes must be infinite (and the same size as the original set) - it's possible that all are infinite, but not guaranteed.
CyberFish on 28/9/2007 at 23:04
True. However, I was working on the principle that there's a certain probability of life appearing on any given planet (which must be greater than zero, since we have observed life on one planet), in which case the subset is also infinite since it's simply a fraction of the infinite set.
DaveW on 28/9/2007 at 23:11
There can't be an infinte amount of planets because the universe was created by a certain amount of gasses. Those could not have been infinite, so the resultant rock formations after cannot be either :)
Spaztick on 28/9/2007 at 23:20
Also keep in mind that the universe couldn't have infinite planets even if the universe was finite, simply because that would mean there would have to be an infinite amount of energy at the big bang which would mean that the universe would still be expanding at the rate that it was when the big bang initially began (as fast as the speed of light), which it actually seems to have slowed down. Of course it's entirely possible that it's all relative and it only looks like we've slowed down when everything else outside our visible range is moving a whole lot faster.
dvrabel on 28/9/2007 at 23:29
Quote Posted by CyberFish
This is bollocks. Firstly:
4. "Less than infinite" and "finite" are not the same thing. You can have different sizes of infinity. No, really.
You can get different sizes of infinite but with sets of objects like planets, infinite sets are all the same size.
As an example, consider the two infinite sets:
A = { 0, 1, 2, 3, ... }
B = { 0, 2, 4, 6, ... }
i.e., the nth element of B, b(n) = a(2*n)
There's a one-to-one mapping between the objects in set A and B, therefore they're the same size.
AxTng1 on 28/9/2007 at 23:39
I think this was in the Hitch-Hiker's Guide to the Galaxy.
Also, the fact that we are here sort of defeats such reasoning before it can begin. Please don't go reasoning us all out of existence. I haven't played Bioshock yet.
37637598 on 28/9/2007 at 23:58
Quote Posted by catbarf
1. Space is infinite, therefore there is an infinite number of planets.
2. Not all of those support life, so there is a finite number (less than infinite) that support life.
There can be an infinite number of planets and an infinite number of planets with organisms on them, even though not all planets have organism on them. Infinite is not an amount but rather an ongoing image. Think of it like this.
Planets with organisms = X
Planets without organisms = 0
0--0--0--0--0--0--0--0--0--0--0--0--0--0--0--0
X-X--X---X----X-----X------X-------X--------X
Both lines can be infinite, they could continue on for an eternity, even though they do not have the same amount of planets.
EDIT: sorry dvrabel, looks like you already said pretty much what I did.
