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Topic: Maths as "glue languages" (martian math example)
Replies: 1   Last Post: Aug 26, 2010 7:15 PM

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kirby urner

Posts: 3,690
Registered: 11/29/05
Maths as "glue languages" (martian math example)
Posted: Aug 25, 2010 7:42 PM
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My response to Wayne's posting of the duck cartoon (Mallard Fillmore,
not depicted in circled strip) , may have appeared facetious, and
was indeed somewhat of a comic book response.

I suggested we replace mathematics with anthropology, but
then teach a lot of math *as* anthropology. To understand a
culture, one needs to study its maths.

This would mirror what has happened around philosophy in
some circles.  Having the context be "ordinary humanity"
(like in the movie 'Babies') adds a refreshing dose of realism,
especially where math and philosophy are concerned.

Things get way too "Ivory Tower" sometimes, not always a
good sign. Wittgenstein thought of his later philosophy as
providing some antibodies, some immuno-defenses against
forms of "academentia" (Mary Daly's coin) he regarded
as derailing and unproductive to the point of imprisoning

Speaking of immuno-defenses, keep on the alert for the
Mars Hoax, characterized as "a virus" by NASA, but meaning
a "meme virus" in this case (more like a rumor, untruth,
or urban legend).

The idea of "meme viruses" (which connotes "harmful" as
viruses are usually considered bad) is a powerful one. In fact
we're just talking about exponential and/or other non-linear
growth patterns, common as rain in natural environments.

So lets consider "SQL" (structured query language, ess kyoo el),
which I keep bringing up as an important topic.  How does this
topic help glue other topics together?  How does it provide a bridge?

In an obvious mathematical sense it's about intersections and
unions of sets.  One needn't get too Ivory Tower about it.  Perhaps
a library of polyhedra, all pre-sized and well organized, around
points A-Z, could be stored an a small set of related tables.
I've provided complete examples elsewhere in this archive.

Leaving aside purely technical considerations, there's the
matter of "lore" to consider (time-lines, history).  I harped on
the importance of lore in studio in Chicago in 2009 (BlipTV
recording) in a Pycon (Python conference).  I made clear that
yes, we're consciously linking to the Eugenics chapter and
WW2, talking about Hollerith machines, Cold Spring Harbor,
and all the rest of it.

"Abuse of record-keeping" is a perennial theme, and we might
next turn to the voting machine scandals around the turn of
the millennium, when North Americans, guinea pigs for
democratic principles and technologies, are having a hard
time wrapping their minds around all this IT / engineering
and its consequences. Humans are struggling with voting
technologies around the world in fact.
(how long will this link last I wonder?).

I also want to have upbeat stories, not incessantly dwell on
man's inhumanity to man.  Along those lines I segued into the
Unicode story in the Chicago context, much as that standard
has raised some ire.  Humans able to collaborate, on a global
basis:  that's not always a cause for paranoia, as without it
you'd expect even darker outcomes.  Unicode allows the
perpetuation of many more world languages in a shared
code base.

Some of the Martian Math segments I field tested recently
look at science fiction as a way of painting the future.  This is
a theme at the Science Fiction Museum in Seattle Center
as well, a part of the Experience the Music Project though
with separate admission.  I then dive in to the theme of
"what is life?" in the context of ecosystem chemistry.

When scientists look for evidence of life on other planets,
they seek evidence in the equilibrium of gases.  For example,
the presence of methane and water in the Martian ecosystem
is consistent with the presence of microbial life forms, if
not a guarantee of such.  If this is the case, then we have
reached a point anticipated by H.G. Wells in his
'War of the Worlds', another feature in my slides.  In that
story, microbial life plays a vital role and provides an
advance look at what would later become known as a
Gaia Hypothesis.

What actual mathematics did we encounter, in connecting
these dots?  I'll given an example:

The sphere packing that begins with a nuclear ball,
12 around it, then 42, then 92, conformal with a
cuboctahedron shape, is a well known lattice.

A specific transformation applied to any one of these
cuboctahedral shells, turns it into an icosahedron with
the same number of balls (1, 12, 42, 92, 162...).  Over
on mathfuture, I include the following quote, in the
context of a more in-depth investigation:

"All of these numbers are in fact found in actual viruses,
12 for certain bacteriophages, 42 for wart viruses, 92
for reovirus, 162 for herpesvirus, 252 for adenovirus
and 812 for a virus attacking crane-flies (Tipula or
daddy-long-legs)" - The Natural History of Viruses
by C.H. Andrews (W.W. Norton R Co., 1967).

Our software included a rendering of 12-around-1 which
students could inspect.  Changes to RGB (red green blue)
values would change color, a persistent theme through
several exercises.

I wasn't expecting these kids to become Python-literate
overnight. In other versions of this course, prior familiarity
with Python might be assumed (or some other language).

In a longer and more detailed version of this course, more
of the history, of the findings by x-ray diffraction and
other methods, could be investigated.

The number sequence 1, 12, 42, 92... itself is available for
lookup at the On-Line Encyclopedia of Integer Sequences.
Given each student had Internet access, all were able to
visit the relevant page.

The formula 10 * f * f + 2 may be proved using high school
mathematics and on a next turn of the spiral, that could
be the objective.

V + F = E + 2 is also relevant, as is the 1:2:3 ratio of (non-polar)
vertexes, faces and edges (non-polar just means subtract two
from the total).  This takes us off into the algebra of the geodesic
spheres and their parts (domes) in other segments.  The
chemistry of fullerenes ties to the topology of soccer balls,
and hexapents more generally:
(links to an American Scientist article)
(has a fragment of an old Kirby-to-Pam posting in this

Finally, we might revisit the notion of "powering",
introducing "Earthling Math" as 90-degree oriented
(ergo "orthodox") i.e. focused on ortho-normals X, Y
and Z.

As I've sketched here before, this hypothetical species
of ETs (or island-dwellers in other cartoons), accounts
2nd and 3rd powering differently, with triangles and
tetrahedra instead.

Putting these two language games side by side (the
Martian and the Earthling) opens up student minds
to the existence of alternative geometries, an
important teaching of the 19th and 20th centuries,
here made readily accessibly grokkable in the 21st.


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