Re: deprogramming language
Steven Gabriel (sgabriel@willamette.edu)
Tue, 26 Oct 1999 03:00:28 -0700 (PDT)
> In the meantime: surely there must be a single, basic principle from
> which those five axioms proceed? Or, to put it more particulalarly, a
> single basic principle that makes possible phenomena the particulars
> of which can be contained in 5 basic axioms? In order to develop
> axioms, there must be some generative principle that creates the
> things for which we develop axioms. Like carbon at the root of "life"
> or 1's and 0's in computer languages? Perhaps computer operations are
> a good example. They are possible only because of the difference
> between 1 and 0...between presence and absence. A single difference
> is at the root of it all. And from that single difference, we create
> an enormous and vastly complex system of signification.
Actually, the five axioms are pretty immutable. They are simple rules
like: parrallel lines never meet or meet at an infinite number of points.
For many years geometers thought they could reduce the rules to four and
failed. If you change that fifth rule you actually get a different
geometry. One such geometry yields the geometry to be found on the
surface of a sphere and not a plane, an arena wherein for example,
the angles of triangles do not add up to 180 degrees. The principle upon
which these rules were based? Well, observation of the real world really.
That bit gets really hazy, and the haziness is interesting, but I don't
think it is with regards to this discussion.
That was just an interesting anecdote, what I really want to say is that
bringing up 0's and 1's gave me the inspiration for a much better example
of that which I was trying to say. A single difference is at the root of
computation you say. Well, no not really. It is indeed a property of
binary digits that 1 does not equal 0. That's really the same as saying 5
is not equal to 7. The 1's and 0's are just numbers, in base two. So,
I'm gonna skip binary and computers for a second and talk about base ten
numbers and number systems.
Let's say then that we have all these numbers and that they are all
distinct, differentiated and named. But they're not interesting. They
might as well be books, or dogs, or love. Well, except they can't be
because they don't bark, they don't hold stories and they aren't a
fitting subject for a sonnet. What makes them interesting is other
properties that they have. For example, there is the interesting property
that every number has a successor. 2's successor is 3. From this idea we
can get other ideas. 5+3 = 8. Maybe we can get to 5*3=8. But we can't
get this from mere differentiation. We could say all we want to say about
the laws of whole numbers with a finite number of rules (the exact rules
can vary). And given a set of rules you might be able to refine and
minimize the number of rules. But rules of the form "a is not equal to b"
are not sufficient for generating rules like "each integer has an additive
inverse."
I'm not gonna have a go with regular expressions and context free
grammars as they'd only confuse matters. I think I've found another way
to express what I wanted to express without invoking those crutches
anyhow.
If you are interested in this stuff try a read through, "Goedel, Escher,
Bach" by Douglas Hofstadter (that "oe" being an "o" in dire need of an
umlaut). He delves into some very interesting stuff, in a way that makes
the subject very interesting. His work is suffused with talk of language,
formal systems, music, logic, paradox, computation and Zen. Best of all
it contains plenty of silly stories.
S.
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: Steven Gabriel -- sgabriel@willamette.edu :
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