Kirby Urner posted Aug 27, 2014 11:23 PM (http://mathforum.org/kb/message.jspa?messageID=9576219) - GSC's remarks interspersed: > > On Mon, Aug 25, 2014 at 3:04 PM, kirby urner > <email@example.com> wrote: > > > > > Of course my answer is "yes", and I was just again > >watching it over pizza, > > no beer (this was my lunch break). > > > > The series is Made in France but was translated / > >dubbed into Brit > > English. Portland Cable TV, bless its little > >heart, broadcast the whole > > series and one of my neighbors ordered the DVD, > >which is why I got to > > rewatch some of it today on break: > > > > http://www.dimensions-math.org/Dim_E.htm > > > > Today on break I'm watching this video by my friend > D. Koski, with whom > I've collaborated a lot over the years, including on > an in-person > pilgrimage / visit to Magnus Wenninger, a grand-daddy > of polyhedrons in our > age. > > https://www.youtube.com/watch?v=ycADhMVa_q0 > > Dave's stuff is solidly three dimensional yet still > comes off as somewhat > alien given he has adopted the Fuller School's unit > of mensuration, the > tetrahedron, and here compares the volume of an > enneacontahedron inscribed > in a rhombic triacontahedron ("NCLB Polyhedron") in > turn compared with a > sphere. But his sphere's volume is (sqrt 2)(pi) > instead of (4/3)(pi) for > radius = 1. That's owing to our different > interpretation of L^3 i.e. 3rd > powering is a tetrahedron for us, when represented > geometrically. You'll > remember I've talked about "our branch" in the tree > of living mathematics. > > Also: getting into David's stuff more deeply requires > making room for yet > another meaning of '4D'. Let me explain... > > The Dimensions TV show cited above (it aired on > Portland Cable Television) > is what I might call Coxeter.4D in flavor, where I > use a proper name as a > "namespace" and use "dot notation" to show '4D' > "belongs to" that > namespace (GSC take note). > I have indeed "taken note", though I fail to understand the specific context in which I am to "take note", and what I should do with whatever note that I might take.
(I do broadly understand the 'dot notation' and how it is used, though Coxeter's "Regular Polytopes" and etc are now not readily accessible to me for reference. So am quite unable to make out the distinctions between meanings of various usages of ".4D" in the book/elsewhere, when he or anyone else discusses "tesseract", "time machine" etc, etc). Anyway, all of these ideas are at a higher level than the one at which I usually function.
In regard to Mr Hansen's suggestions/ claims in his postings about your lack of awareness of what "spiralling" might be, about his understanding of "teaching", "learning", etc, etc, etc and the like: these ideas of his are, in general, worth smiling at if not ROTFLOL. Mr Hansen has grandiosely proclaimed, for instance:
>>"teaching is about teaching things. That is pedagogy"
and that learning has nothing whatsoever to do with teaching (surely worth more than a couple of smiles), and that:
Children must be FORCED or GOADED to learn math!" (and doubtless everything else) [definitely more than three smiles];
and doubtless there are many other wondrous matters most of which may well be worth smiles and etc. Mr Hansen sometimes thinks I am 'mocking' him, but actually I am usually lost in admiration.
The way I myself had understood (or NOT understood) 'spiralling' was that this is in fact the way every human, every human, every infant and every child, actually deepens his/her understanding of anything and everything. You, me, even Robert Hansen. Einstein also. Groups as well. Every time we revisit an idea, our understanding of it deepens ('spirals', so to speak). Of course, Einstein's and Robert Hansen's ideas about anything are obviously very different from those that GSC may possess. Anyway, I have long believed that the power of the 'One Page Management System' (OPMS) about which I have often written at Math-teach actually arises from its characteristic of forcing the user to 'spiral' over the things he/she/they is/are seeking to understand. Doubtless Mr Hansen will disagree based on his vast 'expertise' on 'learning', 'teaching', 'spiralling', etc, etc, etc - to claim that I do not know what 'learning', 'teaching' or 'spiralling' might be.
I always did believe that I know a little about 'learning' and how it happens in the human animal - but I freely accept that I know little or nothing about:
D. Koski; Python, POVRAY; Magnus Wenninger (though I do recall that you've referred to him earlier); polyhedral (tetrahedral?) mensuration; whatever Linda Dalrymple Henderson might have written; and a great many other things many of which I should be familiar with.
As noted, I had always believed I did understand a bit about 'learning' and about 'learning'-and-'teaching' as a 'silver dyad' (though I am no teacher by any manner of means - but I definitely do believe I am a *learner*, have always been one).
I must confess that I rarely if ever look at movies and videos, even though I know there are many fascinating (perhaps even ESSENTIAL) ones: one lives in the real-life circumtances that confront one (though my computer friend had a VAST collection of movies available for viewing). (The underlying problem is, I get nagging headaches).
[I observe that my only real interest is in how 'systems' may be made more real - and *usable* to people at large and how, via 'systems thinking' (which is a trait alas all too rare even amongst systems 'experts'). My intertest is to see if people at large may be aided to tackle the problems that confront all of us from day to day].
If I find something that I *think* may help with accomplishment of the above-noted goal of mine, then I might spend some time on it it; if I think not, I don't; I fully realise that I am bound to make many misjudgments (notwithstanding OPMS), in both directions; I have made many such misjudgments; that's life, I'm afraid - and there is not a great deal I can do about that.
As you suggest, OK, back to work.
GSC > However, in some of the movie's narrative, we seem to > bleed over into > Einstein.4D wherein "time is the fourth dimension" > with x, y, z for three > "spatial" dimensions. Coxeter himself is at pains to > distinguish between > these two meanings of 4D in his 'Regular Polytopes' > i.e. "the tesseract" > and "the time machine" are two different animals, > much as science fiction > writers might want to conflate them in the popular > imagination as a way to > drive their plots. > > These are two of the great schools of thought that > survived the early 1900s > "shake out" re 4D as a meme. Linda Dalrymple > Henderson has written a fine > book on this topic: > > http://www.amazon.com/Fourth-Dimension-Non-Euclidean-G > eometry-Leonardo/dp/0262582449/ > > David's stuff comes from a third school (which Dr. > Henderson also traces), > less well known, that associates '4D' with the "four > directions" of the > regular tetrahedron, i.e. four points and four faces, > carving space into > four quadrants instead of the eight octants of the > XYZ / Cartesian > apparatus. > > Lets call that Fuller.4D. > > So we have three meanings of 4D to stay aware of, > each anchored in a > different namespace: > > Coxeter.4D : polytope R^N geometry as in Regular > Polytopes and > n-dimensional sphere packing ala Conway > > Einstein.4D : Minkowski space, Relativity, three > spatial dimensions, one > of time > > Fuller.4D: four directional tetrahedron as volume > unit and model of 3rd > powering > > More reading on this topic of namespaces in > mathematics: > http://controlroom.blogspot.com/2006/08/more-dimension > -talk.html > http://controlroom.blogspot.com/2009/02/dimension-talk > .html > http://mybizmo.blogspot.com/2006/07/practicing-multicu > lturalism.html > > OK, back to work. > > Kirby > > > Message was edited by: kirby urner