random

[David C. Ullrich]

On Thu, 31 May 2001 19:52:28 -0400 (EDT), "Steven D. Majewski"
<sdm7g at Virginia.EDU> wrote:

>
>
>On 31 May 2001, Mark 'Kamikaze' Hughes wrote:
>
>>   "Anyone who considers arithmetical methods of producing random numbers
>> is, of course, in a state of sin." -John Von Neumann
>> 
>>   Unless you have random-number-generating hardware, you don't really
>> have truly random numbers.
>
>
>That's what I was always taught, however in the light of 
>Gregory Chaitin's work or randomness in arithmetic: 
>
>	<http://www.cs.auckland.ac.nz/CDMTCS/chaitin/>
>
>JVN may have been wrong. 

??? There's a _lot_ of stuff there. 

Could you give us a hint regarding exactly what work
of Chaitin's shows we can get "truly random" numbers from
arithmetic algorithms?

A physical RNG can have the property that one cannot make
any prediction about the value of the next bit even given
_complete_ information about how the numbers are being
generated. An arithmetic algorithm with this property seems
obviously impossible - if you know the algorithm and you
know the current state of the RNG you can predict the
next number... whatever the algorithm is, someone with all
this information can devise a "randomness test" that the
RNG will fail miserably. Or so it seems.

>-- Steve Majewski
>
>
>
>



David C. Ullrich
*********************
"Sometimes you can have access violations all the 
time and the program still works." (Michael Caracena, 
comp.lang.pascal.delphi.misc 5/1/01)