What is the significance of googolplex in mathematics and science?

[ElliotSmith]

Googolplex is a number so large that is greatly exceeds the total number of atoms that there are in the universe.

I've got two questions.

Are there any actual applicatons for this number in any branch of science/physics/mathematics, and does the scientific community have any use for googolplex?

https://en.wikipedia.org/wiki/Googolplex

 

[Mark44]

The first I heard about a googol (not to be confused with Google) was in a physics class back in the early 70s. At $10^{100}$, a googol was larger than the hypothesized number of particles in the universe, which if memory serves, was around $10^{98}$. A googolplex is so much larger in size that I can't imagine any practical use for it for counting anything.

My 2¢

 

[Mentallic]

Googolplex is a number so large that is greatly exceeds the total number of atoms that there are in the universe.

I've got two questions.

Are there any actual applicatons for this number in any branch of science/physics/mathematics, and does the scientific community have any use for googolplex?

https://en.wikipedia.org/wiki/Googolplex

If we assume there are a googol number of atoms in the observable Universe (it's less, but let's just pretend), and I am given 10 colours to choose from, then in how many different ways can I colour the Universe if I coloured each atom in any of these colours? A googolplex ways.

 

[Bystander]

If one wishes to consider the number of possible hundred unit polypeptides that can be made from the "twenty essential" amino acids, or the number of possible DNA sequences in billion base pair strands, it's a useful number, arguably, even a bit undersized.

 

[jbriggs444]

The number of possible DNA sequences in a billion base pair strands would be on roughly $4^{1000000000}$, right? While that's way more than a googol, it is woefully under-sized compared to a googolplex.

If you wanted to sit all of these possible strands around a circular table and calculate the number of possible seating arrangements, $(4^{1000000000}-1)!$ if I've not blundered, the googolplex would be the under-sized number.

 

[micromass]

I have not seen any uses for the googolplex. That said, mathematics sometimes does need very large numbers (massively larger than the googolplex). For example, the largest number ever to be used in a serious proof is called Graham's number http://en.wikipedia.org/wiki/Graham's_number It is mind boggling how absolutely massive this number is!

A nice read: http://www.scottaaronson.com/writings/bignumbers.html

 

[ElliotSmith]

I've heard of Graham's number, apparently it is the largest number ever even thought of..

 

[Mentallic]

I've heard of Graham's number, apparently it is the largest number ever even thought of..

Ever thought of? I just thought of Graham's number + 1, praise me!

But no, it's the largest number used in a serious mathematical proof.

 

[DaveC426913]

Graham's Number fascinates me.

Every once in a while I go back and try to get my head around the math notation required merely to represent it. I fail every time.

 

[Hercuflea]

Whenever you make a statement about every member of R you are making a statement about the number googolplex. Mathematicians make statements about every member of R all the time. Therefore...mathematicians make statements about the number googolplex all the time.