Re: U.S. to build world's fastest computer

From: Paul Schlyter (pausch_at_saaf.se)
Date: 05/30/04 

Date: Sun, 30 May 2004 09:14:16 GMT

In article <24888320.0405291746.68f9174c@posting.google.com>,
cascade <cascares@yahoo.com> wrote:
 
> "Douglas A. Gwyn" <DAGwyn@null.net> wrote in message news:<VqWdnVZ8c4UtjCXdRVn-tw@comcast.com>...
>> cascade wrote:
>>> Ckwop@hotmail.com (Simon Johnson) wrote...
>>>> Even if you had a grid of weather stations such that each station is a
>>>> metre from each other and this grid incircled the world and extended
>>>> right in to space then even with infinite computing power you still
>>>> wouldn't be able to tell whether it's going to be overcast or sunny in
>>>> new york 25 days from now.
>>>
>>> Why is that? Quantum mechanics events amplified to macroscopic dimensons?
>>
>> It has nothing to do with quantum mechanics,
>> but merely with the chaotic nature of the
>> evolution. (Sensitive dependence on initial
>> conditions.)
>
> He said "infinite computing power." With infinite computing power you
> can get infinite precision.
 
Not if your input data has only finite precision..... suppose you measured
a rectangle with 2-digit precision, and then computed its area with a
computer having 30-digit precision, would you then get an area accurate
to 30 digits, or 2 digits, of precision?
 
To obtain infinite precision weather forecasts from infinite
computing power, you'd need a grid of weather stations with infinite
density (having one weather station for each Angstrom would be far
from enough). And each of those weather stations would have to
provide measurements with infinite precision. Of course you'd also
need a network with an infinite number of nodes, each providing
infinite bandwidth, in order to transfer the input data to that
computer with infinite computing power.
 
And you wouldn't know when the forecast as ready: since you're trying
to process an infinite amount of data with infinite processing power,
the execution time would be infinity/infinity, which is an indeterminate
quantity.
 
Finally, to construct such a computer with an infinite number of
weather stations, you would need infinetily more matter than what's
available in the universe.... :-)
  

-- 
----------------------------------------------------------------
Paul Schlyter,  Grev Turegatan 40,  SE-114 38 Stockholm,  SWEDEN
e-mail:  pausch at stockholm dot bostream dot se
WWW:     http://www.stjarnhimlen.se/
         http://home.tiscali.se/pausch/

Relevant Pages

  • Re: questions raised by reading and thinking with possibly missing background
    ... > Not only infintely many samples, but infinite precision as well, ... infinite number of samples, I don't think you are going to worry much ... > It's very a useful fact that symmetric coefficient sets do not need ... > infinite width or precision to have exact perfect linear phase (as ...
    (comp.dsp)
  • Re: I believe in a supreme being
    ... there is infinite precision to real numbers, ... still only takes up a finite amount of space. ... thirds and you have finite bits of cake even though the number that ...
    (talk.origins)
  • Re: U.S. to build worlds fastest computer
    ... Tom St Denis wrote: ... > Paul Schlyter wrote: ... >> weather stations, you would need infinetily more matter than what's ... > Don't forget that if you had an infinite number of computers running ...
    (sci.crypt)
  • Re: U.S. to build worlds fastest computer
    ... Paul Schlyter wrote: ... > weather stations, you would need infinetily more matter than what's ... Don't forget that if you had an infinite number of computers running ...
    (sci.crypt)
  • Re: PI random? Debate running in circles (you try making math jokes)
    ... twins ARE NOT infinite for the more you try to find them. ... Euclid did´nt have infinite amount of computer power for demonstrating ... I know primes are infinite, ... amount of time or some reasonable amount of computing power. ...
    (sci.math)
Loading