1. ## conceptualizing infinity

What a perfect forum to share a concept that has been amazing my mind for the past month. Im sure some will find this as intriguing as I do and of course others will not give a patsy.
Im taking this course at school on Physics Theory, and obviously no course on physics theory is thorough without profound class discussion on general relativity.
During a lecture concerned with the topology and size of the universe we got into the contents of finite variance and infinity. Everyone knows what infinity is - neverending and possibly boundless - but like myself previous to this class I think that most people fail to grasp the actual concept of NEVERending. For those like myself who haven't really appreciated the concept of infinity objectively, mull this over in your minds for a bit:

In an infinite universe of finite variance (countable number of particles and atoms) there is no other option but that everything has an exact copy or doppelganger of itself. So there is not only one other exact copy of Franco (me) in the universe but an infinite number of them traversing the cosmos, habitating on an exact replica of this planet, sitting on exactly the same couch, punching keys on the exact same laptop. We may be just copies of the originals, ourselves.

That this is a necessary truth, as long as the two concepts of an infinite universe and finite variance hold true, is quite awe-inspiring.

That a countable number of items can only be put together in so many combinations before the same combinations have to start repeating themselves and that in an infinite medium these combos would be repeated an infinite number of times, really bangs home just how intense a word infinity really is.

Its great to have the perfect forum to vent minded concepts, lol

2. Well Franco,

The problem as I see it is the concept of "finite variance"..............why should it even be countable, and, even if it were, why does that preclude the possibility of everything being different?

OK we know that at atomic and sub-atomic levels there is a fair degree of replication, but as soon as you get to meso and macro levels, this must be far less probable?.....................basically there are far more combinations and permutations of the lower level "building blocks".

Also, the Universe may be infinite, but it isn't full, and there is no reason that I can think of why it should be? You would only get the first true replication as you seem to be describing it, if all the possible combinations and permutations had been exhausted and the system was continuing to grow.

Similarly, there is no particular reason why exact replicas should not exist anyway, by chance? After all we know that they exist at the lower levels.

I guess I am arguing that it is more to do with the laws of probability than the concept and mathematics of infinity

3. ## ...

I notice that I didn't explicitly state that we have to assume both finite variance and spatial infinity have to be true for this to be a result.

Fair comment you made on whether space is fill or not - I want to respond to it further but its a friday house and my night has guests, lol

there's an interesting article in the April '99 issue of Scientific America titled 'Is Space Finite?' - I'd upload it but Im not sure of the legal issues since Iv paid for it.

You can try here but im not sure if it will work -
http://www.sciamdigital.com/index.cf...9C-94564BA4BE9

It sort of addresses questions of bounded or unbounded infinity . . .

most def the laws of probability apply - pi, the quantification of infinity - microcosmically, if written out to about 1500 places, one would be able, by the laws of prob, find any and all combinations of 3 digit combinations. So if pi were written out infinitely then any combination of any amount of digits could be located within pi an infinite amount of times.

if your interested in that article IM me ...

4. The thing that I always consider when trying to think of infinity, is how large the insides of infinity are: i.e. the number of sub-atomic molecules, to make and atom, to make an element, compounds and so on. (Approximately) if you think of every letter of every book in basically all the world, you are thinking of the same number of letters as cells in a human body... it makes you think.

5. Hi Franco, have a good week-end

I think We need to define some terms a bit here? me being from the UK and all?

By "Universe" I mean the whole thing, or "Space", which is supposedly infinite. I would be inclined to use the expression "Cosmos" for the part of the Universe that is occupied, or partially occupied at least.

Now, we would assume (in theory at least) that the Cosmos is measurable and finite, but the environment it is operating in is not. For all we know there could be numerous "Cosmoses" which we would be totally incapable of detecting?

"Bounded Infinity"....................that sort of reminds me of Euler (spelling) and his "Aleph zero"???????????????

I personally think that a "bounded infinity" is a contradiction in terms. It is rather "lawerish" but it puts me in mind of our property laws here. I own my house freehold, which means permanently (infinitely?). In the past I had a place with a 999 year lease.............. a "virtual freehold" so to speak. the first title is infinite but the second is finite but irrelevant, as it is effectively infinite.

I don't agree with your comment on Pi though, as if you wrote it out "infinitely" (assuming it is infinite) you would never finish, so you can never be sure as to how many combinations there were.

I am inclined to take the view that the laws of probability do not work well on a population that is infinite, or at least become highly questionable. The reliability of statistics declines with the size of the sample population being small and the total population being large? Well, infinity is a pretty large population

Johnno

6. I am trying to get my head around something which I have been thinking about (and it may sound silly, but I am 15 give me a chance ):
if we take the universe being of an infinite size to be true, and if the universe is always expanding, then isn't infinity become greater than infinity, therefore infinity is increasing... but it isn't... if you understand that.

7. -Chris-, I am not a great expert here, but It might help if you sort of mentally separated spatial infinity (astronomy or whatever) from mathematical infinity (number theory?).

Multiply 500 by infinity and the result is infinity. Multiply infinity by infinity and the result is infinity. Divide anything other than zero by zero and the result is infinity ( the famous divide by zero error in programming)

Space, or the Universe as I call it, is not expanding............the cosmos (the occupied bit) is expanding. Another way of trying to rationalise it is that if something has no end, it doesn't have a starting point to expand from?

Perhaps my posts should have some sort of government (mental) health warning?

8. Haya Nihil, Chris - thanx and weekend tidings to you both

Ive been coming back and forth trying to stay with the thread so my posts are getting shorter, lol

an example of bounded infinity would be the type of universe (or cosmos - I love that word) in which segments of time space are juxtoposed consecutively in all dimensions and an 'asteroid game' like medium - or one in which a space traveller flying to the right would exit to the right and immediately reappear from the left.

there are other examples of bounded infinitys as well ...

9. Hmmmm, "donut theory"?................and then we have "dimension X" ?

10. the paradox of an expanding infinity is a good point - there are postulates - and Im not specifically speaking for myself here - that the galaxies or any cosmic matter are not actually moving farther apart, but rather space is accumulating between them - that may help conceptualize expanding infinity - its not so much journeying outward from its edges, in this theory, but being shoved outwards by its infrastructure.

Theres another flabbergasting concept along these lines - that all points are at the center of infinity ...

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