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Topic: Of Mnemonic Structures
Replies: 7   Last Post: Dec 12, 2010 10:37 PM

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kirby urner

Posts: 2,762
Registered: 11/29/05
Of Mnemonic Structures
Posted: Dec 10, 2010 11:51 PM
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Some of you may be very familiar with the Roman
art of rhetoric, which included public speech making
or oratory. We still use some of these same techniques
today. Plus the Romans probably inherited their
teachings from yet older sources. The tradition is
called "hermetic".

What techniques am I talking about? The "memory
palace" for one. In order to keep your knowledge
organized, learn to visualize a building, perhaps a
public one you'll be able to visit for real, or perhaps
an imaginary one. Store mental icons in the different
rooms (like pigeon holes) to remind yourself of various
topics, and what links to what. When you have a
speech to deliver, scatter the icons in sequential
order and mentally tour the rooms: your speech
will sound more coherent and better prepared.

Schoolish math comes with some simple mnemonics
such as "a red indian thought he might eat tobacco
in church" (of course he did, given the sacredness of
tobacco) -- a way to remember "arithmetic". Not
politically correct, but what I learned in a British
school in the 1960s. I'm sure you will think of others.
The Web is packed with such memory tricks.

However, more important than these simple rules
of thumb are mnemonic structures of a more general
sort. We speak metaphorically, yet also concretely,
about trees and networks. An outline might be in
tree form, with headings, subheadings, and sub-
subheadings. The "document object model" (DOM)
is such a nested tree structure, of nodes within
nodes.

Or consider a VRML file, or a POV-Ray file in scene
description language.... we're talking about structure
and grammar, as much as we're talking about
mathematics.

When it comes to networks, also think about polyhedrons,
their nodes as web pages, with hyperlinks for edges.
Exercise: create four web pages that all link to each
other bidirectionally along six edges. Consider that a
"mnenomic structure" of sorts (or semantic web).
The concepts of "web" "network" and "graph" all
share a lot in common. A public building of linked
rooms is early hypertext, especially if said building
is mental, i.e. is a memory palace.

In getting students to visualize the interconnectedness
of ideas in pure principle, as networks or even polyhedrons,
we're getting them to think about knowledge as a terrain.
Lou Talman uses a similar metaphor, of trails criss-
crossing every which way. There's not a single "right
way" to traverse this terrain. However, one's sense of
how it all connects is reinforced as one keeps returning
to the same "nodes" time after time, from different
directions. Pascal's Triangle is like a Grand Central
Station. Here we are again, fresh from "tetrahedral
numbers" or "combinatorics" or "binomial theorem"...

As we train up our students on the humanities side,
we will be using math texts as objects of literary criticism.
Rather than be intimidated or made to feel inferior by
the cryptic notations therein, we will apply our tools of
the trade to rank them according to various criteria. We
will think more like publishers. Why did this work get
published and what interests did it serve? What was
the agenda of this curriculum? Why was this topic
left out, why was this one included?

We don't leave such discussion to math teachers.
On the contrary, the process of learning a math is
likewise the process of investigating its location in
whatever phase spaces.

Why was Hermann Grassmann's universal algebra
considered ground-breaking? How did Cantor's work
go over at first? Are quaternions making a come-back,
thanks to game engines?

These are legitimate essay questions and would take
mathematical research, as well as historical research,
to answer. And yes, go ahead and use the free Web
as a resource. The free Web contains many excellent
reference materials, literary criticism, non-fictive accounts,
that you will not find anywhere else.

Kirby

Other recent writings by this author on math-teach:

Of Mathematics and Outdoor School:
http://mathforum.org/kb/thread.jspa?threadID=2213242&tstart=15

Of Backpacking and Sphere Packing:
http://www.mathforum.org/kb/thread.jspa?threadID=2212836&tstart=15



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