Maths as "glue languages" (martian math example)

Previous Topic Next Topic
 
classic Classic list List threaded Threaded
2 messages Options
Reply | Threaded
Open this post in threaded view
|

Maths as "glue languages" (martian math example)

kirby urner-4
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.

http://mathforum.org/kb/message.jspa?messageID=7161230&tstart=0

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
(straitjacketing).

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).

http://science.nasa.gov/science-news/science-at-nasa/2010/25aug_marshoax/

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.

http://www.scoop.co.nz/stories/HL1008/S00167/voting-news-india-e-voting-expert-arrested.htm
(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.

http://www.4dsolutions.net/satacad/martianmath/mm7.html

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.

http://mybizmo.blogspot.com/2007/01/gnu-math-memo.html

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:

http://mybizmo.blogspot.com/2006/08/hp4e.html
(links to an American Scientist article)

http://mybizmo.blogspot.com/2006/10/hexa-wuh.html
(has a fragment of an old Kirby-to-Pam posting in this
archive)

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.

http://www.4dsolutions.net/satacad/martianmath/teacher_notes.html

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.

http://en.wikipedia.org/wiki/Grok

Kirby

Reply | Threaded
Open this post in threaded view
|

Re: Maths as "glue languages" (martian math example)

Kirby Urner-5
> 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?

<< SNIP >>

> 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.
>

Back to technical anthropology (history of artifacts,
e.g. maritime history...), here's a recap of the history
of punch cards, though it has less on their musical
instrument beginnings than Wikipedia has:

http://whatis.techtarget.com/tutorial/history-of-the-punch-card.html

http://en.wikipedia.org/wiki/Punched_card

We would read this recap as much for what it leaves out
as what it includes, per the above thread.  

There's no mention of the Eugenics movement and its
use of Hollerith technology.  That's completely
bleeped over, not even alluded to.

Now look at all the student projects on Youtube about
precisely this.  Clearly the message has gotten through,
and yes, some of these are amateurish, rely too heavily
on soundtrack and mood music.  

The video format also makes it difficult to embed
citations.  Embedding a Youtube in a blog, and giving
sources and citations in that context, makes more sense
(blog = student journal, required in many a for-credit
college course).  

These are the kinds of skills any college communications
course should be imparting, not simply leaving it to
Johnny to reinvent on his own (or get the same criticism
constructivists get:  there's no *time* to reinvent
everything, so just show us already -- why did we pay
tuition if no one lifts a finger to give us the inside
scoop? (answer:  you'll at least need to do *some* of
your own thinking, as that too is a course requirement)).

Given college kids have opportunities to develop these
advanced video editing skills, you'd wonder why a high
school would discourage its students from building
portfolios, especially around such serious subjects as
world hunger, damage to the environment, job safety,
past and present crimes against humanity and their
future prevention.  

Students naturally wish to express themselves on these
topics of vital interest, and yet many high schools
still discourage or outright ban Youtubes as a form of
self expression, and without offering any inhouse /
intranet video server to make up for that loss (this
might be a fine solution in some cases, where "write
access" is concerned, even where Youtube is "read access").

If you're completely in the boondocks without bandwidth,
that's one thing.  But if you're in a community where
the privileged go home to consume anything they like on
an unfettered Internet, while the public schools and
library block access, then clearly you live in a two-tier
double standard society where censorship is used to
enforce an oppressive, anti-democratic form of classism.  

Populations unable to combat meme viruses with media
campaigns of their own are vulnerable to media
manipulation and may be goaded into acting against
their own interests, as we've seen many times.  

A school system designed to protect a democracy and
train its students in the responsibilities of self-
government (cite "virtual presidents model" already
on file here) has to focus on communications skills
first and foremost, with mathematics and logic a core
feature of many of these communications.

Fear of Youtube is often accomplished by stirring parent
fears of what little Johnny might read if left to his
own devices.  What if he finds some A/V spelling teacher
who doesn't meet community standards in some way?  
Whatever happened to parental guidance?  That's a good
question, and adult education needs to cover a lot of
this same territory.

Is it better to foster that "corporate mentality" wherein
Johnny fears every keystroke might be monitored, every
web site logged to some manager's watch list? Is this
our "land of the free home of the brave" self image then?

Should school be about stoking fears and paranoias while
encouraging violent responses?  I'd call these "training
camps" more than schools.  What real school does is give
Johnny a lot of freedom to explore without trying to
manage the outcomes too tightly.  Let Johnny follow his
heart and discover his own strengths, just was Sally
does.  Don't force or spoon feed.  Encourage scholarship,
liberal arts, well roundedness, intellectual maturity,
by building the institutions in question around stellar
role models who practice what they preach (or "eat
their own dog food" as geeks like to put it).  

If your public schools won't do this, charter new ones
that will.

The corporate hive mind is all about killing the liberal
arts and academic freedoms wherever possible in some
cases, although enlightened corporations (such as the
Quakers) are just the opposite, as paranoid geeks will
likely control the IT department and not allow such
spying and censorship, even by busy-body other admins.  

That might be a minority of businesses these days
though, and mostly some of the smaller ones.

So what do punch cards have to do with mathematics again?
Should the science of record-keeping and statistics be
associated with our Oregon State's high school math track?

Consider that an individual punch card might encode some
data about an object, such as a star or planet.  The
objects might be Mars, Venus, Earth, Jupiter and so forth.
What is their atmospheric make up, the masses of their
moons (if any), their periods of rotation and revolution?

Every planet is a row in some tabular layout, with fields
being columns, the "vertical rows" on a spreadsheet.
So much mathematics begins right here, in the idea of a
tabular format, an array.  The XY and XYZ coordinate
system anchors here, as does the notion of "cells"
(row - column intersections) wherein information is
stored.  

A[i,j] notation is present in just about every
math book above a certain level.  Tabulations, such as
of trigonometric and logarithmic functions, have been
the bread and butter of many a reference, before computers
and calculators (and slide rules) made them less
necessary.  We still do tabulations of just about
everything.  There's simply no question that tabulations
are a legitimate core topic in any treatment of
mathematics.

[ Chapter title:  Welcome to The Matrix. (echoes of Pink
Floyd). ]

That being said, it follows that SQL is likewise a bona
fide topic for a high school math track, as the way rows
and columns get added and subtracted, extracted, is via
a formalized logic or language known as Structured Query
Language.  This language gets used to:

(a) to create the tables in the first place
(b) to grant read and write permissions to users
(c) to populate the tables with data
(d) to establish formal relationships among the tables
(e) to alter the columns in the tables or drop tables
(f) to update cells in a shared environment with no
ambiguous outcomes
(g) to select rows and columns for number crunching
activities in client systems

Is the On-Line Encyclopedia of Interger Sequences
implemented in an SQL engine?  That wouldn't surprise me,
though other record-keeping solutions exist.  

The future of medical record keeping will likely involve
more "scrap book like" collections more like Facebook,
although with formalized tables of contents and indexing
that makes finding information easy for readers, and with
embedded tabular formats (SQL engines might read and
write their data from a format shared with MRIs, cines,
doctor notes stored in a more "schemaless" database).

Why do I bring in bioinformatics?  Isn't that just another
branch of computer science?  Shouldn't mathematicians
keep to themselves and not bother themselves with the
"real world" in this way?  

In Oregon at least, we have high hopes of providing an
international clientèle with medical services, are
already doing this around heart procedures especially
(the Starr-Edwards valve was from this neck of the woods).
Oregon is also headquarters for a number of international
aid organizations such as Mercy Corps, Northwest Medical
Teams and so forth.  Physicians for Social Responsibility
has a big foot print here, helps sponsor public events
in collaboration with the city, helps publicize important
films such as 'Countdown to Zero' (recently at Cinema 21,
one of two premier art films outlets, the other being
at the Art Museum itself, where 'The Power of Nightmares'
was shown (likewise important)).
 
A lot of people come here to train, not just for
treatment, and take what they've learned back to their
home base communities.

OHSU is a pioneer in immune system replacement therapy,
other exotic treatments.  There's a cable car to the
condos, where some patients convalesce.  

The nanotechnology industry is likewise largely medical,
with new kinds of kidney dialysis in the works (more
portable).

For these services to be truly international in flavor,
local computers have to be able to accept medical records
generated overseas, in multiple languages.  They should at
least be able to display a patient name properly, in a
non-Latin-1 character set.  That's a difficult challenge,
but with open standards and clear protocols is likely to
progress by leaps and bounds -- provided we have some
well trained people willing to work on making it all
happen.

With all these opportunities for our local economy, we'd
have to be crazy not to find someplace in the high school
curriculum to shoe horn in at least a modicum of SQL.

We'd expect this at Winterhaven (a geek flagship), we'd
even expect it from the National Guard (Operation Space-
port or whatever it was -- which mostly got sneers in this
archive, for being no more than a few field trips (so will
the civilian services do better then, such as by offering
overnight and longer term boarding facilities? (cite
XRL thread))).

Understanding about internationalization requires knowing
about Unicode, which means understanding about ASCII
(Latin-1) and hexadecimals.  Doing arithmetic in different
bases has also been sneered at in this archive, as some
obsolete holdover from New Math.  

However, I don't think New Math ever completely went
away.  Parts of it still lurk beneath the surface,
such as "truth tables" and "sets" and "boolean algebra".

These components are now poised to re-emerge as Gnu Math
(pun), where we make use of our heritage (a whole lot of
free assets) in a kind of neo-Renaissance setting.  

There's a cornucopia of power tools out there, free
for the downloading, if your school is lucky enough
to be using Edubuntu or one of those, and if your math
faculty is at all hip to our global U's technology.

Kirby