Important Math Question

Cyrien · #1 November 2nd, 2003, 05:40 AM

Once again I am going to step in and say that we are making very big statements about EVERYTHING THAT EXISTS when we personally have observed about... less than .00001% of .000001% of .000001% (I am being generous tonight!(also assuming that it is finite and can have a percent value for it)) of everything in the Universe and then stating that we know that ALL OF THE UNIVERSE is cooling so it can't be infinite.

Let's say the Universe is infinite. Then couldn't it quite possible have very small sections of it, oh say 10^999 square light year sections, that are in fact cooling due to their rapid expansion while others are absorbing tons of this radiation and heating up until *BOOM* they make their own big bang in a far far far distant not corner (infinite doesn't have corners) of the universe.

If you can neither create nor destroy matter and energy (and I'm not saying that is correct either but you have to have something to base stuff on) then in an infinite universe you have an infinite amount of energy and matter spread out over an infinite amount of space. But nothing says it has to be evenly spread. Some parts can be heating absorbing the energy until they reach a critical point then they release it while others are cooling off, then they switch off.

Infinity is not inherently linear it isn't nice and orderly. There is an infinity of numbers between any two numbers that can be named.

Quite simply the possibilities stagger the mind and we have no way and probably never will of knowing. So it makes for great arguments in forums all across the infinte space.

Oh... and just because something is infinite doesn't mean it has to include all sets and possibilites. The set of all real rational whole numbers is infinite but excludes things such as Pi, or fractions, etc. Yet it is still an infinite set. You can even make an infinite set with a beginning but no end.

Just because the universe is infinite does not mean that all possibilites are inherently capable of existing within it.

[ November 02, 2003, 04:00: Message edited by: Cyrien ]

Graeme Dice · #2 November 2nd, 2003, 09:58 AM

Quote:

Originally posted by Grandpa Kim:
[QB] Can't agree with you Phoenix-D. You are still underestimating infinity. In an infinite universe, there will be a star in every direction you care to point, in fact, an infinite number of them. Therefore, you are being bombarded by an infinite number of photons. True, each photon puts out an immeasurable amount of heat but that tiny amount is still there.

You need to seriously rethink your entire argument. Even if there is an infinite amount of energy in the universe, it still propagates at a finite speed. It will take an infinitely long time to travel from a source that is an infinite distance away, so we will never see that energy.

DavidG · #3 November 2nd, 2003, 01:21 PM

Quote:

Originally posted by Phoenix-D:

quote:
Originally posted by DavidG:

quote:
Originally posted by narf poit chez BOOM:
if the universe is infinite in size, the distance between us and any galaxy will still not be infinite.

If the distance between us and any galaxy is not infinite then clearly the universe is not infinite in size.
Err, not exactly. A universe being infinite in size doesn't preclude two things from being next to each other.

Yea like IF said. If the distance between us and every other galaxy is a finite measurable distance like the original quote said then the universe is not infinite.

deccan · #4 November 2nd, 2003, 01:25 PM

Quote:

Originally posted by Cyrien:
Once again I am going to step in and say that we are making very big statements about EVERYTHING THAT EXISTS when we personally have observed about... less than .00001% of .000001% of .000001% (I am being generous tonight!(also assuming that it is finite and can have a percent value for it)) of everything in the Universe and then stating that we know that ALL OF THE UNIVERSE is cooling so it can't be infinite.

I don't disagree with logic of your statement, but I do disagree with the sentiment behind your statement. Certainly, all of our theories on the subject of cosmology (and much else besides) should always come attached with the caveat "so far as we can tell". But just because we cannot know for certain is no excuse for saying that we can never know and that we shouldn't speculate, build theories and try our best to extend our knowledge, imperfect as our methods are.

XenoTheMorph · #5 November 3rd, 2003, 02:07 AM

Quote:

Originally posted by Grandpa Kim:

quote:
Originally posted by atari_eric:

Since we're on the subject of math, does anyone know the formula for finding the area of a 4-dimensional sphere? Assuming an equal radius for all 4 axes...

Sorry can't help you there but how about an additional question:

the formula for the 3D volume of a 4 dimensional sphere? This would be analogous to the area of a 3D sphere.

Well in anwser to these little questions:
wwwDOTbright.net/~mrf/hierarchy(1).html
(Yikes can't use links with brackets!!!! DOT is a ".")

1. A hypersphere (4D sphere) has a 4D "Area" of
V⁴ = π²r⁴/2

2. A hypersphere (4D sphere) has a 3D "Surface" of
S³ = 2π²r³

XenoTheMorph · #6 November 3rd, 2003, 02:43 AM

O.K. now onto the subject of infinite energy in an infinite universe.

Well Space is expanding due to the cosmological constant (vacuum energy, quintessance, so on whatever you call it or think it is, it all makes up the value of Lambda. If you followed that tell me how!

). This means that there is an edge to even an infinite universe, at least from our viewpoint, it is where the 'speed' of the expansion between the viewer and another point in space (whatever it happens to be) exceeds the speed of light.

This means that even though the both viewer and the other point are 'stationary' light cannot travel from one to the other (even over infinite time). The fact that nothing can travel faster than the speed of light (don't even say Tachyons

)is not a problem since nothing is, only the distance between the two points itself is changing.

Therefore even in an infinite universe you only get to see a finite volume of space. So only the Photons from objects in this volume can reach you, so no superheating problem! This also means that the cooling of space does not mean energy is being 'lost' only that the density of the energy is decreasing, same amount of energy larger volume.

Now i'm sure you are all wondering why I wrote all this, I don't know, no idea whatsoever.
Good Luck I hope you can follow this guys I'm not sure I can

[Edited for some clarity

]

[ November 02, 2003, 12:48: Message edited by: XenoTheMorph ]

Renegade 13 · #7 November 2nd, 2003, 04:24 PM

Quote:

Originally posted by XenoTheMorph:
Well Space is expanding due to the cosmological constant

Space is also expanding due to the mysterious force astronomers call "dark energy". It's an anti-gravitational form of energy that is accelerating the expansion of the universe. According to what I know of the theory, within several billion years, we will only be able to see stellar objects that are located in the Local Group, whose gravitational effects would overcome the anti-gravitational effects of dark energy.

This dark energy is believed to make up approximately 66% of the entire universe. Yet we know almost nothing about it. To say either that the universe is finite or infinite is pure guesswork. We know so little about the universe as a whole. For instance, only about 1% of the universe is made up of "normal" baryonic matter. The rest is dark matter and dark energy, which we know virtually nothing about. We need to find out more about these things before we can start formulating some hard theories about whether the universe is finite or not.

Don't get me wrong, I'm not discouraging debate and stuff like that. I'm just saying that even educated guesses are just that; guesses.

Renegade 13