What is the significance of googolplex in mathematics and science?

  • Thread starter Thread starter ElliotSmith
  • Start date Start date
Click For Summary
SUMMARY

Googolplex, defined as 10 raised to the power of a googol (10100), is a number significantly larger than the estimated total number of atoms in the universe, which is around 1098. While its practical applications in science, physics, or mathematics are limited, it serves as a conceptual tool for understanding vast quantities, such as the number of ways to color atoms or the possible DNA sequences in large strands. Comparatively, Graham's number is noted as the largest number used in a serious mathematical proof, illustrating the need for extremely large numbers in advanced mathematics.

PREREQUISITES
  • Understanding of large numbers, specifically googol and googolplex
  • Basic knowledge of combinatorial mathematics
  • Familiarity with DNA sequencing and polypeptide structures
  • Awareness of mathematical proofs and concepts like Graham's number
NEXT STEPS
  • Research the applications of large numbers in combinatorial mathematics
  • Explore the significance of Graham's number in mathematical proofs
  • Study the implications of large numbers in theoretical physics
  • Investigate the concept of infinity and its relation to large numbers
USEFUL FOR

Mathematicians, physicists, computer scientists, and anyone interested in the implications of large numbers in theoretical contexts.

ElliotSmith
Messages
167
Reaction score
104
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
 
Mathematics news on Phys.org
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¢
 
ElliotSmith said:
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.
 
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.
 
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.
 
I've heard of Graham's number, apparently it is the largest number ever even thought of..
 
ElliotSmith said:
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.
 
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.
 
  • #10
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.
 
  • Like
Likes kswgrad2012

Similar threads

  • · Replies 16 ·
Replies
16
Views
6K
  • · Replies 25 ·
Replies
25
Views
4K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 33 ·
2
Replies
33
Views
8K
  • · Replies 6 ·
Replies
6
Views
2K
Replies
6
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 10 ·
Replies
10
Views
2K