Koyaanisqatsi

There's an awful lot of linear thinking here, which I consider dangerous when discussing infinity.

So here's one to hit around: infinity (all possible events) occurs simultaneously; it is only the subjective observation that gives the illusion of linearity, which in turn means that "infinity" is unbounded, unfixed and instantaneous.

'ere...*sucks in smoke*...

CardinalMan

I was just walking through the library when I noticed the book "Zermelo's Axiom of Choice: Its Origins, Development, and Influence" by Gregory H. Moore. For those who are interested and can get their hands on a copy, it seems to contain an extensive discussion of the relation between infinite sets and Dedekind-infinite sets, and how the different points of view (and the desire for the definitions to be equivalent) had an influence on the adoption of the Axiom of Choice within set theory.

CardinalMan

Theophage

Quoted material by Draygomb will be in bold:

If there is a finite amount of energy then there is a finite amount of matter

Yes.

and space

No, not necessarily.

and a finite number of possible combinations of matter in space.

Yes.

I wouldn't count pattern X, which is exactly the same as pattern Y but two feet to the left, as a separate and distinct pattern from Y. Thus even in an infinte space, there would only be a finite number of possible configurations of a finite amount of matter.

Tf each combination is a unique moment in time and time must continue then eventually some combination must be repeated.

No, this is a non-sequitur.

It is quite possible to reach a particular combination such that ceratin other combinations simply could never arise thereafter due to cause and effect. Perhaps if the combinations were shuffled around randomly, then you'd be right.

This means that if energy is finite then time looops around and starts its self.

Not at all.

[ January 30, 2002: Message edited by: Theophage ]

[ January 30, 2002: Message edited by: Theophage ]</p>

Theophage

double post, disregard

[ January 30, 2002: Message edited by: Theophage ]</p>

Clutch

Cardinalman, thanks for the tip.

Franc, which definition of infinity you use makes a huge functional difference. For instance, if you use countable infinities, you are limited to (speaking quite roughly) using the rational numbers. If you wish to characterize some phenomenon in terms of irrational numbers, you will invoke the Real numbers, which are uncountably infinite. Since our best physical theories require characterizations in terms of the Reals... which definition you settle on in a given context is rather important. Hope that answers your question.

Francois Tremblay

Not really, no. I am asking you how any possible functional difference has any influence on whenever actualities can be infinite or not, and if you could give us some examples.

Clutch

Ah, well then you asked it rather unclearly in the first place, viz:

I thought this was two questions, given your use of the plural term "questions", and that the position attributed to me ("that position") concerned the first of them -- what functional difference it makes which of several conceptions of infinity one works with. I answered it. Since I've said absolutely nothing about actual infinities, it did not occur to me that I should explain them, nor give examples. (And who's "us"? You recently become royalty?)

Re-read my posts. If you find anything that makes it seem like I have some sort of explanatory commitment here, do let me (or us) know.

Francois Tremblay

Well, part of the initial question was about infinities being actual, so I thought your answer was related to that also, that you were making some kind of statement that the functional differences you hypothesized made some infinities actual. I'm sorry if this was some kind of misunderstanding.

Draygomb

Theo

True, but if change continues to occur then eventually some possible combinations must be repeated.

Draygomb

Koy

If all possible moments exist and no others can be added then there is a finite number of moments.