Re: Is Hera****ian (aka Calvinball) Chess possible?

In message
<fc9209bf-6fe8-447f-8f9f-d6bfd023ee6c@[EMAIL PROTECTED]
>
          richardhutnik@[EMAIL PROTECTED]
 wrote:

> On Apr 8, 10:19 pm, "Wlodzimierz Holsztynski (Wlod)"
> <sennaj...@[EMAIL PROTECTED]
> wrote:
> > On Apr 8, 6:40 pm, "Wlodzimierz Holsztynski (Wlod)"
> 
> > > On Apr 7, 7:55 am, richardhut...@[EMAIL PROTECTED]
 wrote:
> >
> > > > So the basic framework for the ultimate chess variant would be:
Can
> > > > you have a framework for chess and variants that would enable a
person
> > > > to NEVER play chess the same way twice (by the exact same set of
> > > > rules)?
> >
> > > It's only to easy.
> 
> > I was very conservative. In fact, I have many more
> > of them, and each sequence consists of astronomically
> > many variants. (Variants from different sequences
> > are always different, and so are any two from any
> > given sequence).
> 
> Astronomically large isn't infinite though.  You can see one version
> laid out by George Duke, in 91 1/2 Trillion Falcon Chess variants, to
> see the boundaries here:
> http://www.chessvariants.org/index/msdisplay.php?itemid=MSninety-oneanda
> 
> The number studied has gotten larger than 91 1/2 Trillion by the way.
> However, it still isn't unbound or infinite.  Perhaps someone
> mathematically can show the number of potential rules governing any
> system is finite in nature, then Hera****ian (and its Calvinball
> version) wouldn't be possible.
> 
> - Rich

No, it's trivial to prove that there are infinite possibilities for any
rule
system:

Assume a 28 letter alphabet (A-Z plus space and full stop.)

Write down all 28^1 one-character statements A-.
Write down all 28^2 two-character statements AA-..
Write down all 28^3 three-character statements AAA-...
Write down all 28^4 four-character statements AAAA-....

And so on.

This is a countable infinity of 'statements', where each statement
consists
of one or more 'sentences'.

Even after you've crossed out all the ungrammatical ones, and all the ones
that do not pertain to Calvinball chess you'll still have a countable
infinity of rules for chess variants remaining. Then there's the infinite
number of different recipes for eggnog, and all the chess/rugby variants
where pawns are allowed to tackle, and so on.


[BTW The number of cross-posted groups for this message is a bit high.
I've removed sci.math and rec.games.design from the followups.

-- 
Simon Smith

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