# What Type of Finite or Infinite Universe?

Following is an entry from Q is for Quantum by John Gribbin.

infinity There is more (sometimes less) to infinity for a mathematician than to the person in the street. Science-fiction fans and amateur philosophers may be familiar with the idea that, if the Universe is infinite, then not only must anything that is possible happen somewhere in the Universe, but anything that is possible will happen an infinite number of times, in an infinite number of places. In that case, all the weirdness of the quantum world could be explained as just one huge statistical interference fluke affecting our corner of an infinite Universe. But the catch (apart from the mind-boggling nature of such a statistical fluke) is that this requires a special kind of infinity, called an exhaustively random infinity. It is quite possible to have an infinity that does not include everything - a trivial example is the set of all the even numbers. It is certainly infinite, but it is not exhaustive (or random) because it does not contain any of the odd numbers. Nobody knows whether or not the Universe is infinite, let alone whether or not it is an exhaustively random infinity. -Q is for Quantum-

Are there other plausible infinities and finitudes for the universe? As example, what we've learned about quarks suggest the universe, finite or infinite, is not exhaustively random but a special set. -CeeAnne-

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Chronos
Gold Member
The universe, according to modern physics, is not randomly ordered. It appears to obey many rules that have been confirmed with great accuracy [re: GR and QM]. It makes sense to demand compelling evidence before abandoning those models.

I've not heard of the idea of an exhaustively random infinity, but I have wondered about applying Cantor's ideas to the universe. Some people don't like the idea of a universe with a finite age, as you can always ask 'what came before'. However, even if you take the universe to be a countable number ($$\omega$$) of days old, you can always ask, "what happened $$\omega +1$$ days ago?"

turbo
Gold Member
There are degrees of infinitude. For instance, between the integers 0 and 1, there are an infinite number of intermediate values. You can continue to divide that space finer and finer forever. The Mandelbrot set (nice self-similar fractals that make gorgeous pictures) is at the intersection of real and imaginary numbers, and again, depending how long you can wait for your computer to grind out the results, you can delve deeper and deeper into that set forever. As physicists, we expect to see some limits on infinite divisibility of time and space at the Planck scale, if not larger scales. Mathemeticians work in fields where such limits aren't always expected.

as Sir martin Rees often points out- we probably live in a universe that is transinfinite with infinities within infinities within infinities- there are infinite types of universes with the infinite/eternal multiverse- an infinite number of these universe are spatially infinite- and each type of universe has an infinite population- and each individual universe is essentially a bundle of infinite branching parallel quantum states-

given this infinite hierarchy of infinities within infinites it is almost unavoidable that any plausible finite form exists transinfinitely-

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Infinity

John Worrell Keely Our World is a Musical Universe, almost everything we do involves waves. (Satelite,computers,cable,doppler,light,) frequencies that over time we discover and harness to produce smaller or larger waves.

To me Infinity means there is no beginning and no end only change. Everything has a rate of decay and atomic numbers on the elemental tree cubed will give you the frequency of that brief part of infinity. Just because you can see something doesnt mean it exists or doesnt exist, it only means that even we as humans can only comprehend a brief amount of universal information within our senses. Are there particles smaller than quarks or muons ? Yes infinitely. One day we will break a quark into even smaller particles etc. Who knows maybe the more we learn the less infinite everything becomes. Its one step closer to what is already there.