What Is the Largest Meaningful Number?

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Discussion Overview

The discussion revolves around the concept of the largest meaningful number, exploring its implications in relation to the universe, mathematics, and practical applications. Participants engage in philosophical considerations, mathematical reasoning, and the potential for numbers to have meaning beyond mere size.

Discussion Character

  • Exploratory, Philosophical, Technical explanation, Debate/contested

Main Points Raised

  • One participant proposes a number based on fundamental particles, volume of the universe, and time, suggesting A^B^C as a meaningful representation of all matter arrangements.
  • Another participant argues that numbers only have meaning when assigned, questioning the significance of the proposed number.
  • A different viewpoint suggests that adding one to any number does not enhance its practical use, emphasizing the search for numbers with meaningful applications.
  • Another participant presents a thought experiment involving a cube and permutations of smaller cubes, proposing a large number based on combinations over time.
  • One participant mentions that any number could have practical applications, particularly in cryptography, suggesting the existence of larger primes than any proposed number.
  • A claim is made that all integers have practical use, leading to a humorous exchange about the implications of this statement.
  • Concerns are raised regarding the existence and definitions of the quantities involved in the original proposal, suggesting they may not be meaningful in reality.
  • A participant introduces Graham's number as a mathematically significant large number, noting its size and the limitations of standard notation.
  • Another participant suggests that infinity could be considered the largest number, while also discussing physical constants like the Planck constant and their implications for meaningful numbers.
  • A final comment dismisses the thread as lacking substance and suggests it has devolved from the original topic.

Areas of Agreement / Disagreement

Participants express a range of views on the meaning and significance of large numbers, with no consensus reached on what constitutes the largest meaningful number or its practical applications. Disagreements arise regarding the existence and relevance of the quantities discussed.

Contextual Notes

Some participants highlight limitations in the definitions and assumptions underlying the proposed numbers, indicating that the discussion may rely on unverified or abstract concepts.

kenewbie
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This is silly, but I sort of wondered.. What is the largest number that has been made, which is somehow related to the world and not just made to be as large as possible?

I was thinking:

Let A be the number of fundamental particles that exist in the universe.
Let B be the volume of the universe divided by the volume of the fundamental particle.
Let C be the the age of the universe divided by the smallest significant time-unit.

A^B^C should be all possible arrangements of all the matter in the universe, at all times?

I can't think of any larger number than that which has some "meaning" to it.

k
 
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Numbers don't mean anything until you assign meaning to them.
 
As random statements go, that was among the top 17.

k
 
Philosophically speaking, Defennder is correct.
Numbers are abstract concepts.
In fact, to me, your idea seems more "random" than his response.
Besides, A^B^C is still smaller than A^B^C+1.
 
Ok, maybe I didn't explain myself very clearly.

My number can be used to describe the position of all matter at all times.

What good does adding another 1 to the number do? What use is that 1?

What I am looking for is the largest number that you can think of a use for.

I'm not disputing that you can make a larger number, I am only interested in larger numbers that have a practical use.

k
 
kenewbie said:
Ok, maybe I didn't explain myself very clearly.

My number can be used to describe the position of all matter at all times.

k

How did you arrive at that conclusion?
 
Consider a smaller item than the universe:

Say we have a cube with sides of 100 centimeters.
Inside that cube, we have 100 smaller solid cubes ("particles") with sides of 1 centimeters.

How many unique ways is there to combine the smaller cubes inside the larger one?

That should be 100^100, no?

Now say that the cube exists for 10 seconds, and we can only operate with units of time as small as 1 second (for the sake of making it simple).

Then there would be 100^100^10 different ways to combine our matter throughout time?

Maybe my math is off, but you get the idea I hope. If you combine all of time with the volume of the universe and the size of the fundamental particle, you get the number of permutations possible for that universe. I want to know if anyone can think of a larger number with practical applications :)

k
 
Come to think of it, one could argue that making better cryptography is a use for any number. As there are infinite primes, there must be a prime which is larger than my "universe" number.

So you can always find a practical number lager than N by saying the next prime after N.

k
 
If there were an integer that had no practical use, then such an integer would answer your question and so would have a practical use. Therefore all integers have a practical use.
 
  • #10
jimmysnyder said:
If there were an integer that had no practical use, then such an integer would answer your question and so would have a practical use. Therefore all integers have a practical use.

Haha, that was even better. Brilliant.

k
 
  • #11
You also run in the problem that in reality, none of your three quantities actually exist.

The number of fundamental particles fluctuates wildly, fundamental particles, as far as we can tell, have no volume, and the 'smallest significant time-unit' is absolutely meaningless.
 
  • #12
There is a standard answer to this question called Graham's number, which is the largest number ever to be used seriously in a mathematical proof. It is so large that we cannot even come close to writing it down in standard notation.

Learn about arrow notation to appreciate its size:

http://mathworld.wolfram.com/GrahamsNumber.html
 
  • #13
the largest number is definitely infinity
 
  • #14
If you mean the largest number with _physical_ meaning, we can take a cue from the Planck constant, which is on the order of 10^-35. But we have at least four dimensions to deal with, so that becomes 10^-140. There could also be more though. There's also no guarantee that the Planck length is the smallest length, so it could be smaller still.

But once you find that, raise it to the power of the number of dimensions there are, and divide 1 by it, you start to approach the highest orders of magnitude that could possibly have any physical meaning. We're probably in the 10^several hundred, maybe thousands. But probably not more than that.
 
  • #15
This thread has no substance, and has deteriorated from a pretty pointless OP, thus is done.

motomax99: to start a new thread go into the appropriate forum and select "new topic" from the top left corner.
 

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