[extropy-chat] Big finite numbers

[David Lubkin]

Spike wrote:

>A googleplex was once equal to google^2, so even 10^200 googleplexeths 
>still wont buy you a good cup of java.

to which I replied:

>A googolplex is not googol^2; it's 10^googol. Amusingly, this discrepancy 
>may be far away the greatest finite numeric error ever posted on this, or 
>any, list. Congrats, Spike! Even in error you distinguish yourself... :-)

Your crown may have been dramatically supplanted.

In http://www.fpx.de/fp/Fun/Googolplex/GetAGoogol.html, Don Page is quoted:

>You might be amused to note that in Information Loss in Black Holes and/or 
>Conscious Beings? to be published in Heat Kernel Techniques and Quantum 
>Gravity, edited by S. A. Fulling (Discourses in Mathematics and Its 
>Applications, No. 4, Texas A&M University Department of Mathematics, 
>College Station, Texas, 1995) (University of Alberta report 
>Alberta-Thy-36-94, Nov. 25, 1994), hep-th/9411193, I estimated a quantum 
>Poincare recurrence time for the quantum state of an extremely 
>hypothetical rigid nonpermeable box containing a black hole with the mass 
>of what may be the entire universe in one of Andrei Linde's stachastic 
>inflationary models and got 10^(10^{10^[10^(10^1.1)]}) Planck times, 
>millenia, or whatever. As I wrote in the following line, "So far as I 
>know, these are the longest finite times that have so far been explicitly 
>calculated by any physicist."

I do not know of an error in his calculations, but Page's number is 
emphatically larger than a googolplex. So if there is, he wins.

The actual paper is at http://arxiv.org/pdf/hep-th/9411193.


-- David Lubkin.