We're huddled in the Pauling House with Mario Livio. It's time to play with "glass beads" (metaphorically), the smoothly worn stones of our scientific subculture.
I've just given a "lightning talk", or more a "thunder talk" (somewhat longer), whipping through my slides for Chicago, soliciting feedback, about 4D vs. 4D vs. 4D in particular.
Mario's comments: check out Birkhoff on Beauty; also maybe cast Stephen Hawking as a bridge figure between Einstein.4D and Coxeter.4D as his focus is making time "less special" in terms of its mathematical treatment. Mario is an astrophysicist, so I took this as good authoritative feedback. He also accepted my use of Akbar font, but suggested I vary the color in some slides. Buzz caught a typo (thanks guy).
Julian is here, as well as George Weismann. David Feinstein just walked in (Shomar out in his car, per usual). Lynne Taylor, Allen Taylor... there's a "gang's all here" feeling, although we're missing Jon Bunce (we phoned him last night), Bob McGown. Barbara is in California etc.
We have a young grad student, Valarie, a math teacher and grad student at PSU, whom Terry invited. She encourages more computer use (e.g. Maple), and reports that PCC is better equipped than PSU in this regard.
We discussed calculus, Julian hoping we don't lose the wisdom there, even as we shift the emphasis to more discrete math. Julian is eyeing a $9K differential equations solver as a possible tool for designing new sculptures.
Mario was born in Romania, with Romanian his first language, then grew up in Israel. In a more technologically well endowed "other tomorrow", we might have a live link, to Lionel in Jerusalem etc.
Now Terry is reciting his own ABCs, a complicated spiel to be sure. Buzz interrupts with his "just in time reality" meme. Mario: "nothing" (in the sense of "cosmic zero") simply reflects conservation and symmetry laws, keeps our bookkeeping tidy. From nothing, we tunnel to something.
We're kicking around a lot of "global variables" here, like "universe", absent any strongly shared namespace. This gives our meeting a Tower of Babel flavor. Mario is professionally adept at speaking about dark energy, dark matter, string theory and so on, which is helping Wanderers stay current. His use of the verb "tunneling" is interesting.
Regarding Fuller's "non-unitarily conceptual Universe" it's obvious enough we each have limited bandwidth i.e Universe never squeezes through anyone's thinking as "one thing" any more than a whole dictionary does (Fuller's analogy). We're linear creatures in that sense, chaining thoughts into "trains".
Mario clarifies that not all mathematical thinking is centered around axioms and theorems. He thinks inventiveness occurs around initial concept formation, but then the consequences, the ramifications, the realizations that stem from these concepts, is a process of discovery. Regarding "discovery", in a Wittgensteinian investigation, we'd look for grammatically related concepts like "surprise", "unanticipated", even "synergetic".
Glenn is now giving his presentation, with Allen Taylor taking over on camera. He's summarizing information about "gnomon studies" per Hamlet's Mill and other sources, doing some simple derivations of phi, root-2, root-3, root-5, with a piece of string on the white board. "You need these lengths to build the Platonic polyhedra" he says.
Glenn takes his story back thousands of years before the Greeks, guesses Ea and Enlil, the two tropics, might trace to common ancestors in Africa. A stick in the ground (a gnomon), casting a shadow, is the original computer, and the basis for all trigonometry. Each feather on the winged solar disk, popular with ancient Egyptians, describes a successive gnomon-cast shadow, a measure of big wheels turning in our solar system. Good mnemonics.
We adjourned to Tanh Thao. Mario has remained affable and diplomatic throughout, fielding pitches from every angle. He well deserves a quiet and relaxing afternoon on a beautiful spring day here in Portland.