# The largest number with meaning?

1. Aug 18, 2008

### kenewbie

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 cant think of any larger number than that which has some "meaning" to it.

k

2. Aug 18, 2008

### Defennder

Numbers don't mean anything until you assign meaning to them.

3. Aug 18, 2008

### kenewbie

As random statements go, that was among the top 17.

k

4. Aug 18, 2008

### gendou2

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.

5. Aug 18, 2008

### kenewbie

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

6. Aug 18, 2008

### Kurdt

Staff Emeritus
How did you arrive at that conclusion?

7. Aug 18, 2008

### kenewbie

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

8. Aug 18, 2008

### kenewbie

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

9. Aug 18, 2008

### Jimmy Snyder

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. Aug 18, 2008

### kenewbie

Haha, that was even better. Brilliant.

k

11. Aug 18, 2008

### tmc

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. Aug 18, 2008

### Crosson

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. Aug 18, 2008

### motomax99

the largest number is definately infinity

14. Aug 18, 2008

### peter0302

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. Aug 18, 2008

### cristo

Staff Emeritus
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.