AW: [basicstamps] Re: Tricky Random Question

Archiver

Hey all you people,

hey John, it is worth more than a glance, all of you helped me a lot,
really!!!
I like the idea of finding the order first and then play the poem because a
pause of some seconds before each new version is good anyways.

I think I didnt reflect on the impossibility of keeping track of all the
versions already played, maybe it is almost Goedel stuff: there can be no
system that is smaller than the number of possibillities that keeps track of
them... (maybe you can say that in better English... :-)

As far as Dennis is concerned: if this sentence is true I have spent all my
life doing things that are not worth doing them good...see for yourself on
www.u-winters.de


Thank you all, Uli

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Urspr

Archiver

>I like the idea of finding the order first and then play the poem because a
>pause of some seconds before each new version is good anyways.

Hi Uli,

I think it is a good idea too.

>I think I didnt reflect on the impossibility of keeping track of all the
>versions already played, maybe it is almost Goedel stuff: there can be no
>system that is smaller than the number of possibillities that keeps track of
>them... (maybe you can say that in better English... :-)

Yes, but sometimes simple rules generate very complicated behavior.
That is what pseudo-random number generators do, or other systems
like the "game of life" that generate complex patterns or fractals
from simple rules.

For a permutation generator, you want to shuffle the numbers, for
simplicity, say, 123445678, into all possible orders and each time
play them from left to right as a poem or as a "peal" of bells.
There are some very systematic ways to go about that by permuting one
pair of numbers at each step. (Bell ringers call them "changes").
But I am not sure if their is a way to associate a pseudo-random
number with the sequence, so that a simple rule can get you from one
to the next with the assurance that you will play each one, once and
only once.

Most shuffling methods will eventually repeat a pattern (not that
anyone would notice or remember!).

In your case each permutation is a sequence of 90 unique symbols
(symbols in an information theory sense). 123456789ABCD... that
you are going to play from left to right. Associated with that, I
am imagining an 89 bit sequence, a binary number that you will use to
randomize the sequence. At each step, you randomize that 89 bit
number (see below), and then for each "1" bit you permute the
corresponding two symbols in the sequence, and if the bit is 0 you
leave the pair alone. So if the first few bits of the sequence are
100110..., then the 123456789 sequence becomes
1 2 3 4 5 6 7...
1 0 0 1 1 0...
2 1 3 5 6 4 7 ...

The rule executed the permutations from left to right.

To randomize the 89 bit binary number, you take feedback from bits at
positions 83, 84, 86 and 89, XOR them together and feed 0 or 1 that
back into the first bit, while shifting up one bit. That is known
<http://www.rsl.ukans.edu/~mlinhart/magic/files/vlsi/lfsr/misc/info>
to provide a maximal length 89 bit sequence. I don't know how long
that sequence is, but consider that a maximal length 39 bit sequence
repeats after 549755813887 steps. Whatever is 2^89 - 1. Big but
much much much less than 1.485715964481761497309522733621e+138.

Will that algorithm get you all 1.485715964481761497309522733621e+138
possible permutations of your 90 symbols? I have no idea. Very
arcane stuff. That is where Goedel might come in. It may take
longer to prove it than to compute it. On the other hand, somebody
(not me!) might find it easy to prove that it does _not_ go through
them all.


>As far as Dennis is concerned: if this sentence is true
> > > to mind the engineering slogan: a job that's not worth doing is not
> > > worth doing well.
>I have spent all my life doing things that are not worth doing them
>good...see for yourself on www.u-winters.de

Maybe Dennis can explain exactly what he meant by that, but, knowing
Dennis, my guess is that it was not meant to be at all pejorative.

-- regards,
Tracy Allen
electronically monitored ecosystems
mailto:tracy@e...
http://www.emesystems.com

Archiver

thanks, Dennis, but don't you think that admirable is a bit too much? ;-)

have a nice day,

Uli

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Urspr