machine figure - sci.math

Message from discussion machine figure

James Waldby

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More options Jul 25, 3:27 am

Newsgroups: sci.math

From: James Waldby <n...@no.no>

Date: Thu, 24 Jul 2008 14:27:29 -0500

Local: Fri, Jul 25 2008 3:27 am

Subject: Re: machine figure

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On Thu, 24 Jul 2008 07:24:16 -0700, mcjason wrote:
> On Jul 24, 12:01 am, James Waldby <n...@no.no> wrote:
>> On Wed, 23 Jul 2008 18:28:14 -0500, Jon Slaughter wrote:
>> > "Ray Vickson" ... wrote ...
>> >> On Jul 23, 11:33 am, mcjason <mcja...@gmail.com> wrote:
>> >>> Say pieces on a board, make each a pair with another piece.
>> >>> like...
>> >>> |55|44|66|
>> >>> |44|66|55|
[...]
>> Third, McJason didn't ask a question. He or she apparently wants to
>> present some kind of model for a machine or automaton but in posts so
>> far has been somewhat incoherent and inconsistent and hasn't clearly
>> described the ideas or rules the machine obeys.
> I meant to improve this...

What you posted below has the same problems with incoherency and
inconsistency as previous posts. I'll point out some examples:

> Say pieces on a board, make each piece a pair with another piece.

Incoherency: "piece" is not well-defined. If a piece is a pair
of pieces, then a piece is a pair of a pair of pieces, which means a
piece is a pair of a pair of a pair of pieces, ad infinitum.

Instead say something like "Let p_k (for k=1 to 6) be pieces on
a board that has 12 cells c_ij, and let each piece p consist of
two cells a and b, that is, p = (a,b)", if you mean that a "piece"
is two cells and a "pair" is two cells (which may be inconsistent
with your later usage of "pair").

[...]

> when a piece is moved to another piece, it becomes a pair with
> the piece it moves to.

Incoherency: In the paragraph above, "pair" is undefined and "piece"
refers unclearly to two different objects. If you have labels for
things, you can say (eg) "When piece p_1 is moved to the location of
piece p_2, it becomes a pair p_n with p_2," although you haven't said
what it means for two pairs p_1 and p_2 to form a new pair p_n and
haven't defined "pair".

> any piece to move to another piece is a piece that moved at the same
> time as it's pair, and moved to another piece that
> moved at the same time as it's pair too. A piece that moves to another
> piece becomes a pair with it, and the other of the pair has moved to
> become a pair with another piece.

Incoherency: In this paragraph, "piece" and "pair" each refer to
so many different objects that it isn't clear what you mean. Using
labels will help sort things out. You haven't indicated what "the
other of the pair" might mean, and need to define "pair" and "the
other of the pair".

[...]

> A pair never moves to a pair.

Inconsistency or Incoherency. "pair" is undefined, and it isn't
obvious whether you mean "piece" or "pair". If you mean that
pieces can't move, that would be inconsistent with earlier
conditions. Perhaps you mean: "Given a piece p in cells (a,b),
if p moves to (e,f), then (e,f) is a new piece." But that would
be inconsistent with your earlier condition re "when a piece is
moved to another piece, it becomes a pair".

-jiw

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