RE: [-empyre-] Re: semiomorphic..viral

["Jim Andrews" <jim@vispo.com>]

> > Semiotic morphism was originally developed as a way to translate
> > between different types of Graphic User Interface design. Different
> > types of interface design can represent the same information, and this
> > process can occur automatically via an algorithmic process - the
> > 'content' and the representation are separated.
> >
> > In Semiomorph (http://iconica.org/artefact/) this idea is applied to an
> > electronic space which is represented as a third person digital game.
> > All of the game elements may be represented as either text, diagrams,
> > icons or simulation (the 'natural'  mode of game spaces - realism).
> >
> > Of course, it may potentially be applied to a wide range of possible
> > systems - such as those you have described. The key element is that the
> > system can be described in mathematical / symbolic terms so that it can
> > be defined in terms of functions, variables etc.
> >
> > Troy

In terms of Abstract Algebra, you mean? That makes sense to me. I've been
developing a windowing/menuing set of behaviors for Shockwave (and Director
more generally). The elements of the algebra would be things like sprite
channels, behaviors, and members. The operations would be things like giving
a sprite channel a member or a behavior. Or destroying a sprite's member or
behavior(s) etc.

More generally (so that it isn't linked to, say, the Director
implementation), an algebra of OOP objects.

Whoever has worked with an API and done some abstract algebra may have noted
that manipulating the commands of an API to accomplish this or that is very
like doing a low-level type of abstract algebra proof where you push symbols
around, concatenate them, perform operations on them, in trying to prove
some property of the system. Only in the case of mucking with the API,
you're not trying to prove some property of the system but trying to make
the system do a certain thing.

Which is, I suppose, related to languages like Lisp which were developed
both for artificial intelligence programming and for generating mathematical
proofs. More generally, languages like Lisp were developed to instantiate
the possibility of reasoning/logic in a programming language.

ja

ps: here's the most intriguing isomorphism i've encountered. an isomorphism
between two games. first game. two players. you see the numbers 1 to 9 in a
row.
1 2 3 4 5 6 7 8 9
the object of the game is to be the first player to select three numbers
(not two or four) that add up to 15. So if you go first and select 5, say,
neither you nor I can again select 5. So now it's my turn and I select 7,
say. Then you select 6, say. Now I must choose 4 or you win. Etc.

Turns out this game is isomorphic to tic tac toe
4 3 8
9 5 1
2 7 6

Isomorphic in the sense that the two games are structurally identical. So,
for instance, as in tic tac toe, if you play the first game well, you will
never lose. The 'magic square' above is such that every horizontal,
vertical, and diagonal triplet of numbers adds to 15. Moreover, all possible
triplets made up of numbers 1 to 9 that add to 15 are represented in the
magic square. If this latter property did not reside in the magic square,
the two games would not be isomorphic.