

Enormous Integers - robinhouston
http://johncarlosbaez.wordpress.com/2012/04/24/enormous-integers/

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lotharbot
> _"These higher levels of largeness blur, where one is unable to sense one
> level of largeness from another."_

IMO that's the really neat thing about enormous integers. They simply pass
beyond our ability to reason about them in the same ways that we reason about
numbers in our everyday life. We can conceive of two and three digit numbers
simply by counting to them. We can conceive of millions and billions by
imagining piles of material (a 2 foot cube of sand might be 1-2 billion
grains). We can conceive of larger numbers by counting the number of digits,
or equivalently, using logarithms -- often comparing them to the number of
particles in the solar system or the known universe, or thinking in terms of
how many bits are needed to store the number.

At some point, though, we start dealing with numbers so big that Knuth's up-
arrows or Conway Chained Arrow Notation become necessary. We reach a point
where the numbers no longer correspond to objects, distances, or physical
quantities. These sorts of large numbers are truly abstract -- the only way we
have to measure them is with other ridiculously large numbers, which
themselves are only understood as notation.

See, for example,
[http://en.wikipedia.org/wiki/Large_numbers#Examples_of_numbe...](http://en.wikipedia.org/wiki/Large_numbers#Examples_of_numbers_in_numerical_order)

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nsns
>> It’s like seeing a seasoned tiger hunter running through the jungle,
yelling “Help! It’s a giant ant!”

I don't think anyone can top this analogy in the near future :)

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evincarofautumn
On a tangentially related note, “Dark Integers”[1] is now perhaps the best
short story I have ever read.

[1] <http://www.asimovs.com/_issue_0805/DarkINtegers.shtml>

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polymatter
I just read it and enjoyed it immensely. Thanks for the recommendation.

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hamidpalo
What about busy beaver numbers? <http://en.wikipedia.org/wiki/Busy_beaver>

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michaelochurch
Large integers are sometimes easier to think about in terms of infinities.
Coming to mind is the extremely counterintuitive Goodstein's theorem, which
becomes comprehensible when one uses (infinite) ordinal numbers:

[http://en.wikipedia.org/wiki/Goodsteins_theorem#Goodstein_se...](http://en.wikipedia.org/wiki/Goodsteins_theorem#Goodstein_sequences)

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evincarofautumn
I am not at all disturbed by heights, but very large numbers make me a bit
uncomfortable.

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16s
Yep... I think in terms of, "How many bits do I need to store one of those
things." ;)

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diminish
or can you compress the damn things?

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Someone
Of course. That text wasn't that long, and it mentioned several of them.

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ORioN63
Anyone else wondering about the problem with 26 letters?

