Author Topic: Infinities  (Read 217 times)

0 Members and 1 Guest are viewing this topic.

Offline jaimehlers

  • Fellow
  • *******
  • Posts: 4837
  • Darwins +557/-17
  • Gender: Male
  • WWGHA Member
Infinities
« on: December 03, 2013, 11:54:49 AM »
I was reading an interesting discussion in another thread regarding whether infinity could exist or not.  Unfortunately, the discussion was more than a month old, and I didn't want to revive it in the topic itself since it had moved on since.

Basically, it was an argument between One Above All and Deus ex Machina about the nature of infinities and the universe as a whole.  As I was reading the discussion, one thing stuck out for me:  If infinities are impossible, then the Big Bang cannot have come from an infinitely-dense singularity, as that would violate the premise.  So either infinities are possible, in which case the premise is simply wrong, or they are not and thus one of the major premises behind the Big Bang Theory is wrong or at least incomplete.

My personal opinion is that infinities are not possible.  They break the laws of physics, and while it is possible that there are places in the universe where the laws of physics do not hold, it is impossible to accept that they could be so much different as to allow something that is impossible under the laws of physics that we do know.

Offline wheels5894

  • Reader
  • ******
  • Posts: 2443
  • Darwins +106/-1
  • Gender: Male
Re: Infinities
« Reply #1 on: December 03, 2013, 01:35:55 PM »
As far as I know, the description of 'infinitely small' in relation to the Big Bang juts means very small. Otherwise it would mean that there was no matter at all since the smallest one can get in nothing! This is if, of course, the Big Bang was a singularity before expanding and not one of the various other ideas that attempt to explain the exploding start to our universe.

As to infinities themselves, I suppose it depends what one means. After all, the real numbers between 0 and 1 are, in a sense infinite because whatever number I chose - say 0.987645362, adding one extra decimal place and we have another number and so on. I imagine we could, in principle count them but they are effectively and infinity.

Likewise, the universe is expanding and accelerating while doing so. How far can it expand? In what is it expanding? It appears that the universe is expanding time and space as it expands so if it continues to do that  is the dimension of the universe so expanding an infinity?

Clearly the use of Infinities in such models as Hilbert's Hotel would appear to be mind games rather than represent reality (though wouldn't it be fun to stay at such an hotel?) but I can't see how we can rule out infinities in the sense of things like the size of the ever expanding universe.

Of course William Lane Craig like to tell us we can't have infinities of gods so the god he proposes must have always existed (infinite life perhaps) but I'm not sure a philosopher is the best person to ask about such things.
No testimony is sufficient to establish a miracle, unless the testimony be of such that its falshood would be more miraculous than the facts it endeavours to establish. (David Hume)

Offline jaimehlers

  • Fellow
  • *******
  • Posts: 4837
  • Darwins +557/-17
  • Gender: Male
  • WWGHA Member
Re: Infinities
« Reply #2 on: December 03, 2013, 01:57:24 PM »
The problem is, those are not actually infinities.  They are boundlessly finite.

For example, how many times could a person go around the Earth?  To say that it's an infinite number of times is wrong - because the Earth did not always exist, and it will at some point in the future cease to exist.  That means that the number of times it's possible to go around the Earth is boundlessly finite.  There is no upward bound on the number of times you can go around the Earth, but at the same time it will always be a finite number.

The number of positive integers?  Boundless but finite.

The number of real numbers between 0 and 1?  Boundless but finite.

The size of the universe?  Boundless but finite.

I have no problems with boundless quantities.  They are still finite, after all.

Offline wheels5894

  • Reader
  • ******
  • Posts: 2443
  • Darwins +106/-1
  • Gender: Male
Re: Infinities
« Reply #3 on: December 03, 2013, 02:00:08 PM »
back to the drawing board then....
No testimony is sufficient to establish a miracle, unless the testimony be of such that its falshood would be more miraculous than the facts it endeavours to establish. (David Hume)

Offline Graybeard

  • Global Moderator
  • ******
  • Posts: 6611
  • Darwins +523/-19
  • Gender: Male
  • Is this going somewhere?
Re: Infinities
« Reply #4 on: December 04, 2013, 07:08:18 PM »
Infinities are not impossible but they have no real existence. Infinity is not a number (which are infinite) but a concept.

Here is the 60 second version of Hilbert's Hotel


However, it gets more complex. If the infinite number of guests who arrived in the bus all leave, then you still have an infinite number of guests (the first set of guests)

Nobody says “There are many things that we thought were natural processes, but now know that a god did them.”

Offline Graybeard

  • Global Moderator
  • ******
  • Posts: 6611
  • Darwins +523/-19
  • Gender: Male
  • Is this going somewhere?
Re: Infinities
« Reply #5 on: December 04, 2013, 07:18:24 PM »
And this is why infinity is a concept: Graham's NumberWiki:


It's big, but nowhere near as much as infinity (Graham's Number)2 doesn't even come close...
Nobody says “There are many things that we thought were natural processes, but now know that a god did them.”