Important Math Question

[Jack Simth]

Geo - perhaps instead of fraction you should have used "finite portion of" - which is doable without having infinities in the portion. E.g., the set of whole numbers is an infinite set, while the set of whole numbers between 0 and 10 inclusive is a finite portion of the set of whole numbers.

[geoschmo]

Yes, finite portion might have been more correct. However, you still have problems trying to calculate the possible number of photons at any one point in space at any particular point in time.

The whole issue of infinity is probbably beyond our reach as a species anyway, except in a very theoretical discussion. Calculations involving infinity tend to break down into paradoxes. Perhaps the question shouldn't be whether the universe is infinite, but whether infinity even exsists.

[Jack Simth]

Originally posted by geoschmo:
Yes, finite portion might have been more correct. However, you still have problems trying to calculate the possible number of photons at any one point in space at any particular point in time.

Once you have it limited to a finite volume, the task becomes much easier; the energy of a single photon is hv, where h is a particular constant (and depends on units) and v is the frequency of the photon. With the energy density of the light in that volume, and the freqency distribution in that volume (both measureable), the total number of photons can be calculated fairly readily.

If you are talking about an absolute point, rather than a volume, then the answer is trivial: 0. Photons don't seem to exist as points; they seem to exist as waves and particles.

[Ran-Taro]

Originally posted by geoschmo:
Hmmmm, I seem to have hit a problem here. My previous post started out as a statement showing why Phoenix-D was right, that an infinite universe would not be infinitly hot.

However, in my post I stated that any particular point in in infinite universe would contain not an infinite number of photons, but very small and finite fraction of the total number of photons in the universe. However, according to those that are supposed to know about this stuff, any fraction of infinity is still infinity. Of course mathematics also tells us that any number divided by itself is 1. Therefore infinity divided by infinity is simultaneously equal to infinity, and 1. (By the way, if noone has thought of that before I am going to name it the Geoschmo paradox. )

So I guess Phoenix-D and Grandpa Kim are both right. Glad we cleared that up.

Infinity is not a number. It is a concept.

Dividing Infinity by Infinity is like dividing an apple by an apple.

[edit] However dividing infinity in half is not like dividing an apple in half. You would get two infinities, not two halves of infinity (because you cannot reduce something that is limitlessly big in size by dividing it, since the half would still, by definition, be limitlessly big).

Imagine trying to halve all the possible idea's in the world - both halves would still be limitlessly big, hence infinite.

My head hurts.

[ November 04, 2003, 20:59: Message edited by: Ran-Taro ]

[Suicide Junkie]

When you have an infinity over infinity, try L'hopital's rule from calculus

[PvK]

An infinite quantity divided by two gives two infinite quantities. Example: the number of points in any volume is infinite. Divide a sphere in two, and you have two hemispheres, and both contain an infinite number of points.

An infinite number of something is not the same as every instance of a thing, in mathematics.

PvK

[EvilGenius4ABetterTomorro]

Sorry but I think the universe is finite. The Last I heard is that the universe is expanding and when it is done expanding, it will contract upon itself because of the pull of dark matter.
Eventually probably leading to another big bang.

The only other theory has the universe expanding until the time when even electrons will decay and matter falls apart and dissapates (heat death) although it's really the lack of heat. This end makes me sad. Boo hoo!

Now I ask you, If/when the universe starts contracting, will time run backwards?
Yeah I really didn't want to get in the middle of the infinite terminology photon debate thingy but really the Last I heard was the universe is finite.
Oh and I saw from space.com that the "average" color of the universe is Biege?
oh well "To infinity and beyond!"