"Erik Max Francis" <m...@alcyone.com> wrote in message
news:gskdnwoqpkoovztnnz2dnuvz5s2dn...@giganews.com...
On 07/20/2012 01:11 AM, Steven D'Aprano wrote:
On Thu, 19 Jul 2012 13:50:36 -0500, Tim Chase wrote:
I'm reminded of Graham's Number, which is so large that there aren't
enough molecules in the universe to write it out as a power tower
a^b^c^d^..., or even in a tower of hyperpowers a^^b^^c^^d^^... It was the
provable upper bound to a question to which experts in the field thought
the most likely answer was ... six.
(The bounds have since been reduced: the lower bound is now 13, and the
upper bound is *much* smaller than Graham's Number but still
inconceivably ginormous.)
You don't even need to go that high. Even a run-of-the-mill googol
(10^100) is far larger than the total number of elementary particles in
the observable Universe.
But you can write it down, even as a straightforward number, without any
problem. Perhaps a googolplex (10^10^100 iirc) would be difficult to write
it down in full, but I have just represented it as an exponent with little
difficulty.
These bigger numbers can't be written down, because there will never be
enough material, even using multiple systems of exponents.
(A few years ago the biggest number I'd heard of was Skewes' Number
(something like 10^10^10^34), but even that is trivial to write using
conventional exponents as I've just shown. Graham's Number is in a different
class altogether.)
--
Bartc
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