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).
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.
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:
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.