Chuck Grimes wrote:
> ``Bentham himself described the Panopticon as `a new mode of obtaining
> power of mind over mind, in a quantity hitherto without example'...''
>
> http://en.wikipedia.org/wiki/Panopticon
>
> .... just some notes on Doug's interview of Bill Ayers.
>
> Wow. Great stuff. While I was listening, of course all I could hear
> were all the evolving issues between education and politics that
> super-saturated my brain forty years ago...
>
> (among my part-time jobs to get through UCB, was working as an orderly
> at the student infirmary. It was a perfect model of the panopticon,
> and the congruency between a medical faculity and the unversity itself
> was stunning. Although I could see this intitatively and me and one of
> my political buddies laughed about it---curing our sink minds in
> revolt---we never formally explored that idea. It took reading Foucault
> many years later to remember all this...)
>
> Those issues continued to evolve over the years, of course in my case,
> as intellectual themes rather than practice, since I never got to
> the working teacher level.
>
> The point of these working ideas in progress were all directed at
> getting rid of the indoctrination, hierarchy, top down, of what
> Foucault called the panopticon. Ayers was just great on the theory of
> how to do that.
>
> (What people who were not part of the era may not realize is that
> breaking down the established orders included academia itself, was an
> ever present constant of discussion. The unversity system is no friend
> to democracy...)
>
> At some point in the late 70s I went on a math binge from problems in
> sculpture, and made one of the great discoveries of my own
> intellectual life, which is technically referred as linear algebra and
> group theory. Because I discovered these systems through the visual
> arts, I figured out that these contained the potential to massively
> overhaul mathematics education, and in a sense democratize
> mathematics. If that could be done in something of a systematic way,
> it would have a profound effect on developments in the sciences and
> open them up. This would in turn produce a far more literate and
> technically competent public, and in effect democratize the sciences
> and its allied technogies. These developments by turns democratizs the
> whole technological infrastructure of the society.
>
> And the point? Wrestle the skills, knowledge, and productive capacity
> out from the grip of the capital technocratic elite, mass distribute
> them, and therefore start to dismantle the hiearchies of power that
> hold the political economy together.
>
> Mathematics as a means to liberation? How is that supposed to work?
> (Now I am going to argue with myself). The first step is you have to
> re-conceive mathematics as a universe of symbolic forms. It is
> different than our more familiar universe which is almost entirely
> based on language. Mathematics does not derive directly from the world
> of language at all. It co-exists and co-evolves within the
> linquistic-cultural world. The key point of interface between language
> and mathematics is not rational thought. (Although you can develop an
> interface through symbolic logic.) The primary or foundational
> interface is the development of our spatio-temporal concepts which
> underly both the worlds of language and mathematics. Mathematics in
> this sense is a highly technical and systematic expression of
> spatio-temporal concepts, most of which reach far beyond even the
> plasticity of language to capture.
>
> So, then by re-configuring mathematics education with this broad
> concept in mind, it seems possible to design curricula to open the
> mathematical world. In effect, this is a practical application of many
> of Levi-Strauss and Jean Piaget's ideas. That is the very bete noir of
> Foucault's generation, turns out to hold what I think is the key to
> the liberation Foucault sought. (Big philosophical irony here.)
>
> Here's how that works. L-S and P were right about there being some
> form of structuralism to mathematical thinking. They just
> didn't quite get far enough into learning what those structural
> elements were. (I only barely perceive myself) The point is to use
> those structural elements to perform `open sesame' magic tricks with
> them. The trick is to teach and learn how to perform non-linquistic
> spatio-temporal thinking. It turns out with a careful analysis of
> higher level abstract algrebra, you can find all the tools you
> need.
>
> Formally speaking, each of the algebras on sets, groups, and rings
> have classes of morphisms that take the algebraic representation to a
> corresponding space representation, often one that can be modeled in
> plain geometry. So then the symmetries and ordering properties of the
> algebra, can be seen, apprehended directly, and physically
> manipulated, played with. This is often dismissed as mere
> illustration. Not so. If done carefully, these 2-d and 3-d
> representations contain, in their spatial configurations, a true
> representation of the abstract forms themselves. There is a deep
> affinity between the concept of number and the concept of shape, and
> some elements of abstract algebra reveal some of those affinities to a
> truly remarkable depth.
>
> The most well know examples are the rigid motions of a square on a
> plane, and a tetrahedron, in 3-space. In their algebraic
> representation, these motions correspond to various finite subgroups
> of the full finite symmetric group of permutations on an equivalent
> number of elements (letters, numbers, etc). The equivalence is
> obtained by one to one and onto map between the elements and the
> vertices and or midpoints (edges). The applications of these simple
> space models across mathematics and the sciences---and arts---is
> stunning. Learning these forms are why and how you get the open sesame
> effect. Here is a short, non-technical essay on why the study of
> groups is important:
>
> http://www.math.uconn.edu/~kconrad/math216/whygroups.html
>
> Now there is a whole history of this kind of new math teaching, but it
> has been miserably lacking in understanding the corresponding
> structures in mathematics, or teaching them. That's because
> ninety-percent of all mathematics instruction is done by teachers and
> educators who never got far enough in their own mathematics education
> to see these structures. And of course most also didn't take their
> anthro classes, their cognitive science, and any of the other
> background that would show them how to see and use mathematics in this
> way.
>
> Again part of the reason for this lack is due to the fact that
> university mathematics doesn't teach these topics until upper division
> levels, and more often than not, saves the really good stuff for
> graduate school. In effect, the university curriculum cancels out almost
> all people headed into education. In turn anybody with a degree in
> math can get a much better paying job just about anywhere else than
> public education. So the whole system is self-reinforcing. The
> panopticon effect is quite real.
>
> One of my oldest friends teaches eight grade algebra. I have tried for
> years to get him interested in higher algebra and adapting some of it
> to teaching at the elementary level. I've run into a brick wall! I
> tried to convince him for example to use Euclid's Algorithm to find
> the highest common factor. (For a hint at how far down the
> rabbit hole the Euclidean algorithm takes you, google it and/or
> Euclidean domains). But A. said, Forget it, Grimes.
>
> What I discovered in these conversations is that he had his own
> battles to fight within the existing math curriculum and has used some
> higher algebra and number theory (via Pascal's triangle) to teach
> methods in factoring and the set-up method (binomial formula) that
> leads to introducing the quadratic formula. It turns out that while
> these ideas, presented as neat games, help the kids in their general
> understanding, these same games are seen as a trivial waste of time by
> his peers, especially the feeder high school teachers. What was at
> issue was a noticable number of his kids did not show proficiency
> levels in algrebraic manipulation and calculation required to quickly
> move into the high school curriculum. Of course A. blamed that problem
> on the elementary level. So it goes round and round.
>
> Here is a very good article on Pascal's triangle:
>
> http://mathdl.maa.org/mathDL/23/?pa=content&sa=viewDocument&nodeId=493&bodyId=685
>
>
> (Side note. The connection to group theory is difficult to follow. To
> get from Pascal's triangle to group theory goes through number theory,
> congruences and modular arithemtic... Historically, that was the
> original path of discovery of groups via Galois. But a much more
> simple path came out of Kline's Erlangen program. Hence, that's the
> road I would advocate...)
>
> For my buddy A., once No Child Left Behind hit the district, that was
> the end of any discussion on developing broad concepts like
> mathematical thinking. Fuck it, here's your fractions homework. The
> panopticon was re-modeled and made far more effective.
>
> The right and especially the neocons have an absolute genius for
> creating these prisions of the mind. I don't know how they do it.
>
> CG
>
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