[Tutor] How trustworthy are pseudo-random numbers?

[Andre Engels]

On Fri, Oct 3, 2008 at 5:25 PM, Luke Paireepinart
<rabidpoobear at gmail.com> wrote:
> Is your math correct?  That's ridiculously large.

1 year equals 3600 * 24 * 365 makes about 3*10^8 seconds.
The universe is about 15.000.000.000 years old, that's about 5*10^17 seconds.
With 1 billion combinations per second, each computer does 5*10^26
combinations in that time.
There are something like 10^70 or 10^72 particles in the universe,
thus N is about 10^100, give or take a factor of thousand or so.
N2 is equal to 5*10^17 * N * N, which we will round up to 10^220.
N3 by that same calculation will be about 10^460.
The unnamed last number that way becomes something like 10^940 (in
reality, because of all the rounding up, more like 10^930). That's
less than 1/10^600 of 10^1600 - I'd say that's dwarved by any
definition of the word.

> On Fri, Oct 3, 2008 at 10:03 AM, Andre Engels <andreengels at gmail.com> wrote:
>> On Fri, Oct 3, 2008 at 4:11 PM, Daniele <d.conca at gmail.com> wrote:
>>> >From here
>>> http://en.wikipedia.org/wiki/Pseudorandom_number_generator#Periodicity
>>> and here
>>> http://en.wikipedia.org/wiki/Mersenne_twister#Advantages
>>>
>>> I think it can be argued that the randomness is pretty trustworthy :o)
>>
>> Nice understatement on that last page - "most applications do not
>> require 2^19937 unique combinations (2^19937 is approximately 4.315425
>> × 10^6001)."
>>
>> If you used every atom in the known universe as a computer, then let
>> them turn out a billion combinations a second for the entire time
>> since the big bang, and call the number of combination you get then
>> N...
>> then take N computers turning out N combinations a second for the
>> entire time since the big bang, and call the number of combinations
>> they turn out N2...
>> then take N2 computers turning out N2 combinations a second and call
>> the number of combination they turn out in the time since the big bang
>> and call that N3...
>> then the number of combinations turned out by N3 computers turning out
>> N3 combinations per second in the time since the big bang STILL
>> dwarves in comparison to that number.
>>
>>
>> --
>> André Engels, andreengels at gmail.com
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>



-- 
André Engels, andreengels at gmail.com