Numbers, scale, and the relationship to reality

I've been tossing around some thoughts, and I'll try to make some meaning out of my questions.

It is possible to create a number that is larger than the total number of particles in the universe... and then raise that number by a power of itself.

I'm not referring to infinity here; I'm talking about numbers that are outside the realm of normal usefulness in calculations, in theoretical discussions, that sort of thing. They aren't going to be involved in engineering and manufacturing, or in physics, or really anywhere. But, since numbers are ideas, and we can think of them, they nevertheless exist.

Although they must conform to the rules that allowed them to be created, do they also perform the same way as more useful numbers? (I hesitate to say "common"; no number is any more or less common than another.) Is it meaningful to even think of them like that? Are we inclined to think of all those numbers as all the same number? After all, when a number has some incredibly huge amount of places to the left of the decimal, of what importance could the numbers near the decimal point have, even if they would be the most countable by a being in the real world?

Once a number has no meaning as an analog of reality, is it really a number?

I came up with -1 .

Quote: Mosca

It is possible to create a number that is larger than the total number of particles in the universe... and then raise that number by a power of itself.

Yes.

First count all the particles in the Universe, then add one. Write down the number, then raise it to that power. It's that easy, but it could take some eons to do it.

Quote:

Once a number has no meaning as an analog of reality, is it really a number?

Yes.

Exhibit A: SQR (-n) where n is an integer.

deleted

Yes, I read about Graham's Number. I really enjoyed the knowledge. I retract my question, but retain my wonder!

I still stand by -1 until I am proven wrong.

Quote: sodawater

Graham's Number is so big that even if every single atom in the universe were devoted to writing it out, you could not do it

Huh ?

Graham formulated his number on a few sheets of paper, didn't he ? So he already wrote down his number.

There is a difference between a mathematical "number" and it's representation.
The representation is something you can write down with the aim; whenever two representations are the same, so are the numbers they represent.

The number PI is an existing number as the number of fingers on my right hand, and both can be represented with a "finite amount of atoms". Either by a writing
the digit "5", by writing a (convergent) series expression, or even an algorithm calculating that number. Graham's Number is no different from that.


However, there must be numbers which cannot be represented with a "finite amount of atoms". Simply because there are only a finite number of possible representation. Identical representations must give identical numbers, so there is only a finite number of numbers who can be represented by a finite amount of atoms.
Hence there exists numbers which cannot be represented by a finite representation. But Graham's Number certainly does not fall into this class (since he already stated a representation).