SUO: Re: Examples! Examples! Examples!
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EEE. Note 34
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Semiotic Reflections (cont.)
There are a couple questions that come to mind
when we look at pictures of the following sort.
o-----------------------------o-------------------o-----------------------------o
| Language 1 | Object Domain | Language 2 |
o-----------------------------o-------------------o-----------------------------o
| |
| o----------o o----------o |
| /| "T" |\ 1 /| " " |\ |
| / | "x => x" |~\~~~~~~~~~~~~~~~~o~~~~~~~~~~~~~~~~/~| "(x(x))" | \ |
| / | ... | \ / \ / | ... | \ |
| / o----------o \ / \ / o----------o \ |
| / \ / \ / \ |
| / o----------o / \ / o----------o |
| / | "x" | / \ x / | "x" | |
| / | "T => x" |~~~~~~/~~~~~~~~~~~o~~~~/~~~~~~~~~~~~~| "((x))" | |
| / | | / / / | ... | |
| o----------o o----------o / / o----------o o----------o |
| | "~x" | / / / | "(x)" | / |
| | "x => F" |~~~~~~~~~~~~~/~~~~o~~~~~~~~~~~/~~~~~~| "(x(()))"| / |
| | ... | / (x) \ / | ... | / |
| o----------o / \ / o----------o / |
| \ / \ / \ / |
| \ o----------o / \ / \ o----------o / |
| \ | "F" | / \ / \ | "()" | / |
| \ | "x & ~x" |~/~~~~~~~~~~~~~~~~o~~~~~~~~~~~~~~~~\~| "x(x)" | / |
| \| ... |/ 0 \| ... |/ |
| o----------o o----------o |
| |
o-------------------------------------------------------------------------------o
Figure 7. Lattice of Objects Inducing a Diversity of Sign Partitions
o-------------------------------o------------------------------------------o
| Object Domain TLC^ ~=~ 2^TLC | Language Domain L(!TLC!) |
o-------------------------------o------------------------------------------o
| |
| o---------------o |
| /| (()) |\ |
| 1 / | (!a! (!c!)) | \ |
| o~~~~~~~~~~~~~~~~~~~~~~/~~| (!c! (!a!)) | \ |
| / \ / | ((!a! , !c!)) | \ |
| / \ / | ... | \ |
| / \ / o---------------o \ |
| ... ... / \ |
| / \ / o---------------o |
| / \ / | !a! | |
| / \ / | !c! | |
| / !a! o~~~~~~/~~~~~~~~~~~~~~~~~~| BE<!a!> | |
| / / / | BE<!c!> | |
| / / / | ... | |
| ... TLC^ ... o---------------o o---------------o |
| / / | (!a!) | / |
| / / | (!c!) | / |
| (!a!) o~~~~~~~~~~~~~~~/~~~~~~~~~| BE<(!a!)> | / |
| \ / | BE<(!c!)> | / |
| \ / | ... | / |
| \ / o---------------o / |
| ... ... \ / |
| \ / \ o---------------o / |
| \ / \ | () | / |
| \ / \ | !a! (!c!) | / |
| o~~~~~~~~~~~~~~~~~~~~~~\~~| !c! (!a!) | / |
| 0 \ | (!a! , !c!) | / |
| \| ... |/ |
| o---------------o |
| |
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Figure 19. Lattice of Propositions Inducing a Partition of Sentences
Question 1. What is the reason for the internal diversity of languages?
Question 2. What is the reason for the external diversity of languages?
By "internal diversity" I mean the fact that there are generally
so many ways to say the same thing in any language that addresses
a non-trivial object domain.
By "external diversity" I mean the fact that there are generally
so many different languages that address the same object domain.
I will hazard a guess at the first puzzle,
putting off the second for the time being.
To ask the question in a more concrete way: If languages are intended
for effective communication and efficient expression, then why not just
design them so that there is only one expression in each referential or
semiotic equivalence class, in effect, making the whole language consist
of canonical expressions?
I take my first clue to the off-canonical mystery from the experiences
that I used to have learning and teaching the "Art of the Story Problem"
in basic mathematics courses. It had been discovered fairly early on in
the pedagogy of mathematics that if students honed their formal skills on
nothing but the formal manipulations that are permissible within a single
formal language, then they would stare blankly at any realistic situation
where those very formulas might apply. And I can take another hint from
the character of the material that I was very often teaching, namely,
the practice of transforming arbitrary matrices into canonical forms.
The answer that suggests itself in the light of these reflections is this:
Problems are posed in obscure forms from outside the sphere of our own
convenience, and it is the job of language to cast a wide enough net
to catch them in the form that they initially and inchoately appear.
One observes that this is yet another variation on the
cybernetic theme of regulating variety with variety,
what Ashby called the "law of requisite variety".
Jon Awbrey
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