Sunday, December 20, 2009

Philosophy of Mathematics


I've done some followup on the Wittgenstein list I frequent, hoping to get some wheels turning. Our current crew doesn't seem predisposed to discuss philosophy of mathematics all that much. No wait, JPDeMouy is keeping it going. That's wonderful!

I introduced the above figure as akin to something we might find in Remarks on the Foundations of Mathematics. It relates to how Fuller's philosophy uses triangles and tetrahedra to model area and volume.

Here's an excerpt of something I wrote for Lionel, another long treatise on the meaning of dimension in Fuller's writings, a topic in which I've specialized:
In Fuller's namespace, we go with 4D for the tetrahedron because of its pronounced fourness. When you draw the XYZ three, as the corner of a room, you think of another facet between you and the apex (the room corner) making four walls. That could be a symbol of the wall behind you, if your viewpoint is inside. Either way, the 3-ness of XYZ is considered incomplete, an inadequate expression of two complementary sets of three, the two zig zigs of a tetrahedron. Which is where he gets his six.

I think we maybe get worried and anxious with these alternative uses because we feel this might call into question some authority to use all our favorite math tools, such as XYZ coordinates, trigonometry, who knows what else. I think this is an unfounded stress reflex, as there is no challenge at that level. Useful tools are useful tools. You wouldn't have had free Linux without free C.

That worry may be projected such that we see someone like Kirby trying to single-handedly replace centuries of math and physics in one fell swoop (fat chance of that happening). I'm not trying to do that. I'm looking for a modest place in the sun for precious heritage we need to protect and nurture. Do US Marines know how to build domes any more? Does anyone? Have we lost the ability to build domes? Know of any big new ones, of the geodesic variety?

Call me conservative, but I'd like to keep these advances alive, don't take for granted that we will, given all the backsliding.
Given Synergetics is difficult and not typically assigned as reading-for-credit in any department, my little tempest in a teapot is ipso facto esoteric, something I often reflect on. Widening this circle would help a lot, ergo my going among academic philosophers, seeking converts to the cause (more world game players).

Tara opted out of the annual Solstice Party, hosted by good Bridge City Friends. We've been off the radar a lot; no other kids going.

What amazed me about the weather reports last night (CBS News) is the inflexibility of our car culture. The storms might be terrible, the risks rather high, yet the option of rescheduling, rewriting the script on the fly, seems even more dangerous somehow. Those dreams must come true. The airlines are smarter, with safety a chief concern. They simply cancel. Yes holiday plans are changed, that's what it means to have weather, an environment.

The word "hell bent" comes to mind, and I'm not thinking this with an aloof or superior attitude, as I'm also known to be stubborn to the point of foolhardy sometimes. Plus I realize that weather is sometimes surprising. One would have gladly stayed home, armed with advance notice, but even our best weather models have a strictly limited time horizon.

Those stories were east coast, like from I-77 in Virginia. People needed their National Guard.

Our weather in the Pacific Northwest is relatively balmy, although it's good those sleeping bags for the homeless were military grade and rated to go below freezing.

We're transporting appliances relating to food preparation to a start up community kitchen this evening. I have a small refrigerator no one is using, other household items. Uses of the company car tend to be utilitarian these days, counting doctor and physical therapy trips. I am fortunate to have stores within walking distance. Many people have lifestyles dependent on owning a car. I'm one of those people, am a part of the car culture.