Chris Peterson wrote:mst66186 wrote:If length is quantized then it follows there's an integer number of Planck lengths from one side of the observable universe to the other. Always have been and always will be. Likewise if time is quantized, which it is, then there have been an integer number of Planck times since the big bang.

If the Universe is of infinite size, or infinite duration, there will not be an integer number of Planck lengths or times defining it. It makes little sense to restrict this question to the observable Universe, which is nothing more than a subset of the entire Universe- which may well be infinite in size, and also in (ultimate) duration.

Finally, there is a finite amount of matter and energy in the observable universe. So the big question has to be where is this mysterious infinity anyway?

Outside the observable Universe. Just because we can't observe it doesn't mean it isn't there. And it doesn't mean that it isn't important to understand, since material currently outside the observable Universe played a role in defining what we

*can* observe.

...however, when you're dealing with the real world I don't see why you need to visualize anything larger than that - ever! Sorry if I sound like a wet blanket about infinity.

Visualization is a useful tool for most people to use in trying to understand physical concepts. It probably isn't a very good one- at least initially- for trying to grasp infinity. But it's a natural thing for people to try.

Wow. I hardly know what to say. When I first started reading what you had put, I thought I was skirting around the issue by only considering the contents of the observable universe. But then you went on to assert that infinity is 'Outside the observable Universe. Just because we can't observe it doesn't mean it isn't there.' (!!) I might accept what you're saying if it was accompanied by a proof - what do you /know/ about the extent of the universe to support that? I was also interested by the way you were able to throw away the facts about the observable universe that preclude the existence of infinity with the use of 'if' in this one: 'If the Universe is of infinite size, or infinite duration, there will not be an integer number of Planck lengths or times defining it'.

(the above is not supposed to be a flame)

Interestingly, you snipped out the part of the post that I thought was critically important.

OK. I'm a humble scientist of little brain, so I'll say this: I believe that in order to be able to say that something exists, you have to be able to find an instance of it in the real world. You can observe it directly, like an atom, or by looking at the effect it has on other things, like dark matter, or Santa Claus.

Now, my system of mathematics is based on set theory and I have a set-theoretical model of the world around me. When counting, I enumerate.

The number three definitely exists; I can put three beans in a jar and there's an instance of the number 3.

I dare say the number 10e80 exists because there are 10e80 atoms in the observable universe.

Not too sure about 10e102. I agree the system of notation we are using can be extended beyond the point it is practically useful, and arbitrarily far.

I challenge you to tell me where can I go to find an example of infinity. In fact I'll be happy if you can do 10e103 without limiting yourself to pure math.

Surely if something exists in the real world you can show us an instance of it without resorting to hypotheticals that push it outside the observable universe.

It is a symbol used to denote something that is practically too big to measure. The business about quantized length/time/energy above could be taken as a proof that you will never encounter infinity in the real world. -- ever!