[FOM] Feasible and Utterable Numbers

[Kreinovich, Vladik]

Dear Vladimir, 

Qualitatively, you are right, and I agree with you 100%, but the number
needs to be adjusted. 

According to modern cosmology, there are about 10^80 non-0-mass
particles (protons and electrons) in the Universe + about 10^88 photons.
When we do computations, we can perform many steps with each particle. 

The overall number of steps can be obtained by divising the lifetime of
the Universe by the shortest amount of time possible -- the time during
which the fastest process - light - goes thorugh the smallest-size
particle, which is 10^40.

Thus, if we make a computational cell as small as a particle, we still
have no more than 10^88 particles performing 10^40 steps - to the total
of no more than 10^128 steps overall. 

This translated to 2^430 computational steps which is slightly larger
than 2^100. 

In short, your argument remains valid if you add one more 0, and talk
about 2^1000 instead of 2^100. 

Vladik

P.S. A detailed analysis of different relations between big physical
numbers and computability can be found in our paper 

 Vladik Kreinovich and Andrei M. Finkelstein,
  "Towards Applying Computational Complexity to
  Foundations of Physics'',
  Notes of Mathematical Seminars of St. Petersburg
  Department of Steklov Institute of Mathematics,
  2004, Vol. 316, pp. 63-110.

Avaliable at http://www.cs.utep.edu/vladik/2004/tr04-13c.pdf



-----Original Message-----
> From V.Sazonov at csc.liv.ac.uk

> Richard Feinman asserted 
> that the number of electrons in the universe is less than a number 
> which is in fact less than 2^100.