What is the significance of googolplex in mathematics and science?

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Discussion Overview

The discussion revolves around the significance and applications of the number googolplex in mathematics and science. Participants explore its size, potential uses, and comparisons with other large numbers, particularly in theoretical contexts.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants note that googolplex is significantly larger than the total number of atoms in the universe and question its practical applications in science or mathematics.
  • One participant recalls that a googol was once considered larger than the hypothesized number of particles in the universe, suggesting that googolplex may not have practical uses.
  • Another participant proposes a hypothetical scenario involving coloring atoms in the universe, suggesting that there could be a googolplex ways to do so.
  • Some participants argue that googolplex could be useful when considering the number of possible polypeptides or DNA sequences, although it may still be undersized compared to other large numbers.
  • There is a discussion about the number of possible DNA sequences in billion base pair strands, with calculations indicating that this number far exceeds a googolplex.
  • One participant mentions that while googolplex may not have direct applications, mathematics often requires very large numbers, referencing Graham's number as an example of a number used in serious proofs.
  • Several participants express fascination with Graham's number, discussing its size and the complexity of its representation.
  • A later reply humorously claims that mathematicians make statements about every member of the real numbers, implying that googolplex is involved in such discussions.

Areas of Agreement / Disagreement

Participants generally express uncertainty regarding the practical applications of googolplex, with some suggesting potential uses while others remain skeptical. There is no consensus on its significance in the scientific community.

Contextual Notes

Limitations include the lack of specific applications for googolplex and the dependence on hypothetical scenarios for its relevance. The discussion also highlights the vast differences in scale between googolplex and other large numbers like Graham's number.

ElliotSmith
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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
 
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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.
 
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