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

Troy Innocent <troy@iconica.org> · Tue, 28 Oct 2003 08:35:47 +1100

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

There are certainly similarities between Abstract Algebra and the idea 
of Algebraic Semiotics with its use of algebra and set theory. 
Algebraic semiotics is used to describe different sign systems in terms 
of algebra / functions / theorems so that then morphisms can be 
generated. So, there are some extra rules that describe structure that 
allow for these sign systems to be more accurately defined.
With all the different types of media possible in Director cast members 
and ways to manipulate sprites, the Director OOP implementation of 
Abstract Algebra would offer some intriguing possibilities.
Once any system is defined in terms of algebraic theory then it opens 
it up to a whole range of computational processses, including automatic 
generation of new permutations by a generative system, AI etc. Many of 
these may be meaningless, but some may generate new meanings...
Troy.
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.

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>>> Troy Innocent : troy@iconica.org : iconica.org