Re: protons in the universe

[Larry.Smith@snow.edu (Larry Smith)]

Jim Green asked about the number of protons in the universe because of a
conversation between him and me about the following e-mail I received from
a student about the biggest fastest possible physical computer.  The number
10^80 had stuck in my head from somewhere, so I didn't know where the
10^126 (below) came from.  (I looked up the article myself and the numbers
below are accurate quotes.)  A quick calculation of how many protons could
_fit_ in the known universe (a sphere with a radius of 15 billion l.y.)
gives 2 x 10^123.  This may be where the 10^126 comes from (with more
carefully chosen numbers and formulae).

Larry Smith




> I read an
> article listed on the additional readings; "Intrinsically Difficult
> Problems" by Stockmeyer and Chandra, Scientific American - May 1979.  I
> found a few interesting points that I thought I'd share with the rest of
> the class.
>
>
> This quote from the introduction basically sums up he article:
>
> "Some kinds of computational problems require for their solution a computer
> as large as the universe running for at least as long as the age of the
> universe.  They are nonetheless solvable in principle."
>
> ** I apologize if the research or any scientific measurements are not
> completely correct.  The article was written in 1979 and some things have
> obviously changed since then.
>
> - There are certain limitations of building an "all powerful" computer
> 1)  It could not be bigger than the known universe (100 billion light years
>    in diameter).
> 2)  It could not have any hardware smaller than a proton (10 to the -13 cm in
>    diameter).
> 3)  It could not transmit information faster than the speed of light (3*10 to
>    8 meters per second)
> 4)  It could have no more than 10 to the 126 pieces of hardware
>    * I'm not sure why this one's true
>
> Given these limits, it would take 20 billion years (several times the age
> of the earth) to solve certain mathematical problems that are known to be
> solvable in principle.