Replying to LO24239 --
At conlcudes his missive on linguistic (culturally relative?) Degrees of
Freedom with:
"Fortunately, fast amounts of information on/of any system is still not
the capacity to deal effectively with the system. Fear not computers
because they cannot think. Fear them because they can control your
thinking if you are not watchful."
Quite true, At. Quite true. As a once and future linguistic, I have
learned two sure things about language, human and otherwise.
The first is a simple enough fact: words in an of themselves convey
information, but the relationships between them impart knowledge.
The second has some fuzziness attached: all other forms of written
symbolic communication are interpolated from language. This little gem
took me from a high school student who was caught in the self-fulfilling
prophesy of math incompetency to a graduate student with a sound and
creative ablility to utilize mathematics and statistics to show some of
the relationships in learning number 1.
Someone on the list asked me offline to try to explain this. I was in the
process of changing operating systems on this machine when that occured
and I lost some data, including that letter, when I was distracted by some
interesting features of the new operating system and veered from my
migration path to a new path of discovery. A sad mistake, but one that is
and old habit. But I will try to answer that question now.
What I see in At's DF is something I remember from my youth. In my
neighborhood there were English, Italian, Polish, Russian, and Ukrainian
speakers. All ate different foods, attended different churches, sang
different songs and nourished different prejudices, loves, and fears. In
each of these ethnic groups, there was 1 degree of freedom, or perhaps,
1.1. With time, this grew to 2, and with more time, it grew back to 1.
There are no longer different clothes, not so much different food, less
song, and the prejudices, loves, and hates have shifted focus. In
families which have preserved at least some of the ethnic traditions
(including the language), there is an observable difference in levels of
tolerance, in levels of education. There is still the notion of children
being "better" than their parents through education and hard work. They
are still "becoming".
Having more degrees of freedom than some, I can limp along in many
european languages and am trying to learn more of the indic in order to
understand more about the young engineers who come to us from the
subcontinent where Hindu and Urdu lend themselves to wonderful poetry and
give us engineers who are more intellectual than most of the technical
minds we are accustomed to. But the point, from language to mathematics,
is indeed involved with degrees of freedom.
In linguistics, there's an old saying that all spoken sentences are
unique. Looking at the overall speech production mechanism which
encompasses the length of vocal folds, cultural relativity (did Mom or Dad
speak this language with an accent? Did they have a richer semantics?) it
is indeed possible to make many interpretations of the same five or six
words strung together, regardless of the language. The differences are
both historical (hermeneutic) and contextual (socio/cultural), at both the
production and the interpretation end. Because of this rich pallette of
space, time, and relatives, both human and in-, from which to draw, we can
argue the law, write poetry, or sell donkey dung most creatively. The
degrees of freedom are very, very large at both ends of a sentence. We
can, indeed, place apples and oranges on different sides of an equation,
even one with identity as the connective and make others believe. It is
wonderful, and frightening.
Math, on the other hand, has fewer degrees of freedom, even set
theoretical notions are simple when compared to the possible worlds
described in a simple declarative sentence. The concatenation of two
numbers, the reduction to the least common, is always the same.
Mathematics describes the kernels of some linguistic notions. Language
describes the universe. This is the philosophical gem that allows me to
sit happily over a step-wise multiple regression model of a complex
process in a very large factory and extract information from the iterative
runs at the data without having a nervous breakdown. Understanding that
math is derived from language, which, in turn, is derived from experience
and used to describe it, makes math a tame and useful tool. It is also
why I rebel at the little symbols running around between sentences which
are trying to describe human behavior. The behavior of planets can be
described with numbers, the behavior of the brain, perhaps, to some
extent, with neural networks, but not the behavior of a human. For this,
we need language, lots of it.
I always come back to Ortega y Gasset's little gem "the task of philosophy
is to describe the universe". It was one of the reasons my dissertation
grew for so long, because I failed to understand that it really meant "the
task of the philosopher is to understand the relationships among things in
the universe". We can describe much with language, and also explain. The
key to having a theory of learning that works for everyone is the elegance
of simplicity.
What that, I'm off to learn something else. I'll let you know what it was
when it finds me.
John
John F. Zavacki
jzavacki@greenapple.com <mailto:jzavacki@greenapple.com>
--"John Zavacki" <jzavacki@greenapple.com>
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