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Still Waters

Ginormous Numbers Baffle the Mind

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A trillion. A googol. A centillion. TREE(3). Somewhere between zero and infinity is a host of finite, but mind-bogglingly huge numbers.

But while mathematicians have dreamed up large numbers for ages and they pop up frequently in physics and math, gigantic numbers are bafflingly hard to fathom.

http://www.livescien...e-the-mind.html

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I had an engineer friend once tell me "Intellectually, we can deal with huge numbers like a google. But emotionally we go One, Two, Three, Many."

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Just please, PLEASE, don't tell me I have to keep track of their accounting.

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My daughter is always telling me that the largest number is a Googolplexian. I always say "googolplex?", and she says, "NO! GOOGOLPLEXIAN!". She's 4. She insists the "...ian" on the end needs to be there.

When I was reading up on the Googolplex, it kind of rattled me to see the Scope of the number...

One Googol is presumed to be greater than the number of hydrogen atoms in the observable universe, which has been variously estimated to be between 1079 and 1081.

.....

If the entire volume of the observable universe (taken to be 3 × 1080 m3) were packed solid with fine dust particles about 1.5 micrometres in size, then the number of different ways of ordering these particles (that is, assigning the number 1 to one particle, then the number 2 to another particle, and so on until all particles are numbered) would be approximately one googolplex.

http://en.wikipedia.org/wiki/Googolplex

The number of ways of organizing the ENTIRE observable UNIVERSE packed with dust would approach a googolplex. Just the number of ways to arrange packed dust in a area the size of a bathroom would seem enormous, but to expand that to the observable universe seems Crazy. This number is super crazy big.

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I love the ways of defining large numbers.

A googolplex is actually relatively small, since you can express it with a tower of exponents (and only 2 exponents high!).

Using Knuth's up-arrow notation (and using ^ for the up arrow), 10^^^10 is ridiculously larger than a googolplex (a googolplex is less than 10^^4).

And then using Conway chained arrow notation (using -> for the arrow), 10 -> 10 -> 10 is ridiculously larger than (10^^^10 = 10 -> 10 -> 3).

Not to mention the Ackermann function; try figuring out just how large A(10,10) is, and is it bigger than 10 -> 10 -> 10 ?

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