Thursday, December 27, 2007

Graham's number: Puny in God's Sight

I read a Wikipedia article recently about the Guiness World Record "Largest Number," called Graham's number. The article claims there are not nearly as many particles in the universe as this number. I am not going to go into how they even calculate it, but it makes the Googolplex seem microscopic. But Graham's number doesnt even begin to describe our God. The gap between the greatest number and infinity is still infinity. And yet even Graham's number raised to itself "G" times is not infinity. That many years from now, what will matter? Fame? Fortune? Food? No--Christ alone! He is the Image of the invisible God (Col. 1:13).
You don't want to mess with a God that big! He loves you--John 3:16.


Sbiis Saibian said...
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Sbiis Saibian said...

Actually Graham's Number is already puny in man's sight because man has already defined MUCH larger numbers that make Graham's Number & Googolplex look like they are virtually the same thing ! YIKES !!! :)

Also, "G raised to itself G times" , from the perspective of Graham's Number, isn't much larger than G itself. Your just applying an operation called tetration, which is nothing compared to the operation used to construct Graham's Number. It's like someone adding a drop of water to the ocean and claiming they increased it's volume. You might as well have said G+1, because it really makes no difference.

If a Power Tower of G's is a drop in the seemingly endless ocean of Graham's Number, then just imagine how incomprehensibly large Graham's number truly is. It almost seems to defy logic !

Large numbers are fascinating, and it's quite surprising that humans are able to concieve of numbers so much larger than anything they find in their reality. The statement about Graham's Number being "greater than the number of atoms in the universe" is an insulting understatement. The same could be said of the humble Googol, a mere 10^100. The Googolplex is also a great deal larger than most people realize.

Imagine that the entire universe was only a single subatomic particle in a 2nd order universe. Every particle in the 2nd order universe is a 1st order universe just like our own. Now imagine the 2nd order universe is only a single sub-atomic particle in a 3rd order universe ... continue this trend not to the millionth, or the billionth, but the Googolth order universe. Now count up the grand total of all the sub-atomic particles in all of the 1st order universes, and the count will be roughly a Googolplex ! Now imagine the Googolplexth order universe, this will have a Googolduplex particles. Then the Googolduplexth order universe will have a Googoltriplex, and so on. But the sequence Googol, Googolplex, Googolduplex, only represents tetrational growth !! That's right, this is TOO slow ! As I said, Graham's grows WAY WAY faster than this. There is simply no physical analogy for it's size. It just makes our universe look smaller than the point of a needle !!!

And yet Graham's Number is just the beginning! There is a whole universe overflowing with large numbers that humans have defined beyond the supposed "World Champion largest number" that make it look more proletarian then sliced bread ! :)

If anyone is interested in learning more about these extreme numbers, check out my blog.