RE: [Edu-sig] RE: Concentric hierarchy / hypertoon (was pygame etc.)
-Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Arthur My position here has been that the importance of transmitting to students an understanding of scientific understanding needs to be a among the most fundamental goals of education. Wandering, again... But the basis for identifying the importance of this goal can certainly be misinterpreted. The understanding being sought perhaps being more important - in today's world - in providing a legitimate basis to resist illegitimate claims made in the name of science, as it is in appreciating science's legitimate scope. Art ___ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig
RE: [Edu-sig] RE: Concentric hierarchy / hypertoon (was pygame etc.)
From: Kirby Urner [mailto:[EMAIL PROTECTED] No major mind damage is going to be done by a different presentation. But I would like to disassociate the notion of geometry and the regularity of forms as completely and as early as possible. And this is where I seem to be most non-Fullerian. Art Not claiming to follow, but yes, we appear to diverge here. I suspect this exchange is more interesting to you and I than to others on the list and that it would be most appropriate to table it to a face-to-face at PyCon breaks - except that my schedule is conspiring against it, it now looking that I won't be able to make it there. The best I can hope for at the moment is attending Friday's sessions. The thing is, we don't disassociate playing with blocks from architecture, and by extension from geometry, at all, in current childhood education. We most intimately link a rectilinear format, with various cylinders, cones and balls, into the young (very young) imagination. Cubes are both prevalent and regular, without any doing from me. So Fuller's innovation is *not* with respect to linking shapes and geometry early (regular shapes included, in the form of blocks, toys using them), but in the particular assortment of shapes and their canonical relationships. It's much more 60 degree than we're used to (what with all the equiangular triangles everywhere), from a classical western perspective, which is more 90 degree, more into post and lintel perpendicularity. Well certainly Klein presentation makes the (not necessarily regular) tetrahedron the fundamental space form - so that Klein and Fuller are thinking in the same manner in some fundamental respects. And I happen to have a great fondness for 60 degrees - gained via the folding of flexagons, introduced to me in 4th grade by a brilliant teacher. I still can't resist making one when I see a roll of adding machine tape. I think they would be a great addition to your repertoire. I think the real competition to the tetrahedron in space is the sphere, and the real revelation is the perspective that makes the tetra more useful than it as the fundamental space form. But I guess I shouldn't forget that Klein's matrix algebra for lengths, areas, and volumes is working via a regular rectilinear coordinate system. I know you and others have thought about a coordination of space via a regular tetrahedron. *That* I find fascinating, and would probably be my best way in to more Fullerist geometric thinking. Art ___ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig
RE: [Edu-sig] RE: Concentric hierarchy / hypertoon (was pygame etc.)
-Original Message- From: Kirby Urner [mailto:[EMAIL PROTECTED] Engineering and a focus on artifacts trumps political efforts to block basic innovations in math teaching. There's really no stopping us, politically speaking (because we really don't care about politics that much (like, we're popular already)). The tragedy I see is that it is in fact the technologists - specifically those immersed in IT - who are emerging as the most formidable obstacle to progress, as I would define it. I follow the debian edu mailinglist, and what I seem to see is a complete lack of critical analysis as to the use of technology. The starting assumption is the more the merrier, and the prevailing motivation seems to be beating Microsoft at the thoughtless use of technology in the school systems. There are all kinds of ways of beating Microsoft, I guess. Art ___ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig
RE: [Edu-sig] RE: Concentric hierarchy / hypertoon (was pygame etc.)
I suspect this exchange is more interesting to you and I than to others on the list and that it would be most appropriate to table it to a face-to- face at PyCon breaks - except that my schedule is conspiring against it, it now looking that I won't be able to make it there. The best I can hope for at the moment is attending Friday's sessions. That's sad news. I'll be on the east coast near the end of May too, looks like. Not sure of all the details. Anyway, I'll continue to hope we might overlap on Friday. Kirby ___ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig
RE: [Edu-sig] RE: Concentric hierarchy / hypertoon (was pygame etc.)
Arthur: The tragedy I see is that it is in fact the technologists - specifically those immersed in IT - who are emerging as the most formidable obstacle to progress, as I would define it. More polemics it'd be interesting to use for new threads. But maybe not on edu-sig. More some other time I hope. Kirby ___ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig
Re: RE: [Edu-sig] RE: Concentric hierarchy / hypertoon (was pygame etc.)
- Original Message - From: Kirby Urner [EMAIL PROTECTED] Date: Sunday, March 20, 2005 11:19 am Subject: RE: [Edu-sig] RE: Concentric hierarchy / hypertoon (was pygame etc.) Arthur: The tragedy I see is that it is in fact the technologists - specifically those immersed in IT - who are emerging as the most formidable obstacle to progress, as I would define it. More polemics it'd be interesting to use for new threads. But maybe not on edu-sig. The problem though, in my view, is that it is on fourms like edu-sig ( and debian edu list) that the exploration of these kinds of polemics are both most relevant and least welcome. Which says something in-and-of-itself. The Free Software movement being a particular kind of threat, in that the tendency to provoke overconsumption is only enhanced by an offering that is free. Though - (god I hope I got this right) - the folks leading the debian education distribution effort did somewhat belatedly reveal that they are working from a business model based on support of the distribution in school systems. More some other time I hope. Starting now ;) Art ___ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig
RE: RE: [Edu-sig] RE: Concentric hierarchy / hypertoon (was pygame etc.)
The problem though, in my view, is that it is on fourms like edu-sig ( and debian edu list) that the exploration of these kinds of polemics are both most relevant and least welcome. Which says something in-and-of-itself. Let's just put it this way: I'm a technologist immersed in IT and I don't consider myself a formidable obstacle to progress. Nor do I feel that my innovative programming is encountering any effective resistance. Nor do I feel that I'm operating alone or in a vacuum. On top of this, I see a million ways to link up design science (Fuller's name for a disciplined approach to making headway) with open source projects. Of these million ways, I've so far exploited only about 4.5% of them (bogus stat). In other words, I'm loaded with ammo (weapons of mass instruction) but have only lightly tapped what's in inventory. The Free Software movement being a particular kind of threat, in that the tendency to provoke overconsumption is only enhanced by an offering that is free. Mathematics is free too. But to appreciate it to the level required to contribute patches takes work. The Free Software movement represents a promise of interesting hard work. The tools are free, but developing the skills to use them takes time. Making the tools free just means you have more time to practice, versus scrounging in a day job to earn the $10,000 ATT or SCO would have liked to charge any geek wanting entry level access to an OS. Microsoft was never the real enemy. It never marketed a proprietary UNIX. It only pushed a less attractive substitute that serious geeks didn't want or feel threatened by not having. Though - (god I hope I got this right) - the folks leading the debian education distribution effort did somewhat belatedly reveal that they are working from a business model based on support of the distribution in school systems. From my point of view, not a whole lot hinges on Debian's competence here, though if it proves highly competent, that'll be a big plus. But penetration of free and open source within the schools is already happening at some exponential rate, and Red Hat, Mandrake and others all have a piece of the action. I taught Adventures in Open Source to teenagers last summer for Saturday Academy with Jerritt Collord of linuxfund.org (brilliant guy). Our workstations were all Red Hat 9 boxes. Our language was Python (mixed with a lot of other stuff). Our venue was West Precinct, Hillsboro Police Department. More some other time I hope. Starting now ;) Art All the more reason I wish we had more time to talk at Pycon. Last point: free and open source does not mean not Windows of course. It's all a matter of layers. You've got a stack, like a sandwich piled high with stuff, and each layer may have different rules, about what's open versus what's proprietary and so on. Tons of highly proprietary stuff runs on top of open source (ever hear of IBM?). Per recent OSCONs, the trend is towards super apps that are online, that leverage user input (Google and Amazon both examples). Lots of open source tools gets used, but the overall app is pretty much an inhouse asset i.e. closed to the general public. However, here too I suspect open source will have an impact -- I've already suggested some large scale open source apps myself, related to the fleet of cybervans I intend to unleash from Global Data's garages (or Google's, or ESRI's...). Kirby ___ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig
Re: RE: RE: [Edu-sig] RE: Concentric hierarchy / hypertoon (was pygame etc.)
- Original Message - From: Kirby Urner [EMAIL PROTECTED] The problem though, in my view, is that it is on fourms like edu-sig ( and debian edu list) that the exploration of these kinds of polemics are both most relevant and least welcome. Which says something in-and-of-itself. Let's just put it this way: I'm a technologist immersed in IT and I don't consider myself a formidable obstacle to progress. Nor do I feel that my innovative programming is encountering any effective resistance. Nor do I feel that I'm operating alone or in a vacuum. On top of this, I see a million ways to link up design science (Fuller'sname for a disciplined approach to making headway) with open source projects. Of these million ways, I've so far exploited only about 4.5% of them (bogus stat). In other words, I'm loaded with ammo (weapons of mass instruction) but have only lightly tapped what's in inventory. I am also a technologist of a fashion. But in the business world there are factors that converge toward appropriate use. There is cost and there is benefit, and there is a measuring scale - dollars. I find the business world quite wholesome in that respect. What I see at work in the realm of education and technology is the worst of both worlds - folks working within self-interested frameworks of various kinds and degrees (as in the business world), but without a reasonable framework for defintions of goals, or measurement of costs and benefits, and therefore no ecosystem that it is reasonable to believe will converge us toward a reasonable result. The easiest shortcut, of course, being to simply define educated - because there is in fact a lot of leeway to be had in coming to a definition of that word - as fluent in working with computers. In which case - by simple tautology - working with computers becomes a centerpiece of the educational process. Too easy, IMO. Way. Art ___ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig
RE: [Edu-sig] RE: Concentric hierarchy / hypertoon (was pygame etc.)
Might they also be interested that in Egypt, long-ago, in the shadow of the Pyramids, folks not only understood this to be true, but were not content with this knowledge. A way of thinking was developed that allowed them to become satisfied that the truth of this observation makes sense - that we should in fact *expect* it to be true. http://babbage.clarku.edu/~djoyce/java/elements/bookXIII/propXIII15.html What seems surprising - given a logical progression of thought - can be found to be not surprising, really. What is the lesson to be learned from that? To me, it *is* the lesson. Art Yeah, once the relationships are established (burned in) as I put it, there's every reason to go over the reasoning in various ways. There's not just one way to cover this ground, but certainly a goal is to supply any logical apparatus (including Euclid's) that works. Basically, once you've got a tetrahedron inscribed in a parallelepiped as face diagonals, various affine transformations of said sculpture preserves the 1:3 volume relationship, i.e. this is not just about the regular tet and cube. Once you've accepted the octahedron of volume 4 (same edge length as tetrahedron), it's easy to do the tet:cube in special case: fragment the octa into eight equal chunks around the central angle of 90-90-90 (1/2 volume each) and apply four of them to the faces of a regular tet to build a cube (1 + 4*1/2 = 3). http://www.rwgrayprojects.com/synergetics/plates/figs/plate03z.html (there's a theorem you need for the octahedron in this picture: that tetrahedra with equal bases of the same height have equal volume -- you can pull that out of Euclid if you like). But with the pre-K groups etc., I find the measuring cups work well. My attitude is *not* that they should be surprised. I'm very matter of fact. My surprise is over the adults not teaching this material, not over the fact that spatial geometry has a simple, rational, whole number core. Kirby PS: ordered a new laptop (Toshiba Satellite A60), which should arrive either this morning or Monday morning (leaving for Pycon on Tuesday). ___ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig
RE: [Edu-sig] RE: Concentric hierarchy / hypertoon (was pygame etc.)
-Original Message- From: Kirby Urner [mailto:[EMAIL PROTECTED] Sent: Saturday, March 19, 2005 11:07 AM To: 'Arthur'; edu-sig@python.org Subject: RE: [Edu-sig] RE: Concentric hierarchy / hypertoon (was pygame etc.) Basically, once you've got a tetrahedron inscribed in a parallelepiped as face diagonals, various affine transformations of said sculpture preserves the 1:3 volume relationship, i.e. this is not just about the regular tet and cube. We can eventually get them to Klein's fusionist approach - fusing the algebraic and geometric, as well as the flat and spatial. Part One, Page 1 of the Klein Elementary Geometry book I have been referencing introduces us to the progression of formations of 2,3 + 4 points, which brings us from the line to the triangle to the tetrahedron. The length, area, and volume of the fundamental formations are a simple function of the determinate of the matrix of the rectangular point coordinates on the line, on the plane, and in space - respectively. He then points out that even further generalization can be achieved by giving significance to the sign of the determinate - so that given a consistent ordering of points, one can readily ascertain the volume of arbitrary polygons/ polyhedra by composing them into component triangles/tetrahedron from a given reference point either within or outside the form, and then by adding the volumes (which may be negative) of the fundamental forms. Klein's approach to geometry is to find approaches that move between dimensions and forms in such a way that best avoids the need to except any special case. Which is why projective geometry becomes the (nearly) fundamental geometry, and other geometries - affine, Euclidian - are specializations. In this view, a regular tetrahedron is a bit of a freak - perfectly placed and formed. And at least in some important senses is of much less interest than what can be said - and there is indeed a lot than can be said - of the geometry of 4 balls tossed arbitrarily into space. I choose to rarely think in terms regular forms. Besides seeming inherently less interesting to me, I truly get confused as to what traits I am observing (or calculating) which derive themselves from the regularity and which might be more general. Regularity is therefore dangerous, and potentially confusing - rather than comforting. No major mind damage is going to be done by a different presentation. But I would like to disassociate the notion of geometry and the regularity of forms as completely and as early as possible. And this is where I seem to be most non-Fullerian. Art ___ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig
RE: [Edu-sig] RE: Concentric hierarchy / hypertoon (was pygame etc.)
No major mind damage is going to be done by a different presentation. But I would like to disassociate the notion of geometry and the regularity of forms as completely and as early as possible. And this is where I seem to be most non-Fullerian. Art Not claiming to follow, but yes, we appear to diverge here. The thing is, we don't disassociate playing with blocks from architecture, and by extension from geometry, at all, in current childhood education. We most intimately link a rectilinear format, with various cylinders, cones and balls, into the young (very young) imagination. Cubes are both prevalent and regular, without any doing from me. So Fuller's innovation is *not* with respect to linking shapes and geometry early (regular shapes included, in the form of blocks, toys using them), but in the particular assortment of shapes and their canonical relationships. It's much more 60 degree than we're used to (what with all the equiangular triangles everywhere), from a classical western perspective, which is more 90 degree, more into post and lintel perpendicularity. So where I think Fuller and our concentric hierarchy challenges the status quo is in the manifest non-rectilinearity of this approach (NOT that this conflicts with Euclid in any way -- it really doesn't, except when we get into abstruse territory, such as absolute and infinite continua versus discrete and definite manifolds and such (analog vs. discrete stuff)). My view is he went up against a huge bias, but since he based himself outside of academia, in a sort of business world place, it wasn't like he could be shut out of the game. He was independently capable of mobilizing a large network. This has relevance in that a lot of what we call the open source movement may be traced to his anticipatory design science revolution concepts of the 1970s and 80s. Engineering and a focus on artifacts trumps political efforts to block basic innovations in math teaching. There's really no stopping us, politically speaking (because we really don't care about politics that much (like, we're popular already)). Kirby ___ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig
[Edu-sig] Re: Concentric hierarchy / hypertoon (was pygame etc.)
Kirby: But just the concentric hierarchy piece: you've got these few polyhedra, they organize this way, and the relative volumes are like this. It's not that big -- something we can share in K-12 no problem (and I do so). So I walk into this classroom with a box of polyhedra. Stiff paperboard jobbers with one face missing, so they serve as mixing bowls, measuring cups (a pre-K girl called 'em that, and it works). We're in the kitchen, measuring for a recipe (boys too). In the bottom of my plastic carrying case: about 3 inches of fava beans (I think that's what they are, dried white beans -- I tried corn meal but that was a disaster, got everywhere, in the floorboards even). I pick up my tetrahedron (black electrical tape on the edges, good contrast), and say Measuring cup! (I probably say more). Then I scoop up a boat load of beans. Now it's full. In my other hand, Cube. How many tetrahedron cups to fill my Cube? Guesses, kids calling out. Well, let's see... one two three. Done. It's brimming with beans, no room for more. Is the ratio exact? You betcha. So stop right here. How can this be? There's the hidden (wrong in this case) assumption that the cube edge and tetra edge must be the same length. But that's not the only logical relationship. You can intersect two tetrahedra to get what Kepler called his Stella Octangula (a star with eight points). Connect those 8 points and you have a cube. The tets inscribe as criss-crossing face diagonals. *That's* the relationship we want to burn in. *That's* how we get our 1:3 ratio. So, did anyone ever teach you, in like 3rd grade, about this simple 1:3 relationship? Do you need to study Klein or Coxeter to get that? Do *they* even tell you? It's not that they wouldn't agree, but this is just simple baby stuff, so why bother? Except why don't we tell the babies even? Moving on: here's a rhombic dodecahedron. Kepler loved it. Did you know it fills space without gaps? Plato's pentagonal dodeca is more famous. The Platonic Five. Heck, this rhombic guy ain't even an Archimedian. But look, trace the short diagonals (of its 12 diamond faces) with your finger: you get a cube. Let's make that the *same* cube of volume 3, the *duo-tet* cube, as Fuller called it. So what's the volume of this guy then, this other space-filler? Pouring a cube into the rhombic dodeca. One... two... Done. Cube was 3, so rh dodeca is 6. Simple, easy, memorable -- and never shared in any K-12 geometry book I've ever come across. But wait, there's more. Trace the *long* diagonals of our rhombic dodeca with your finger. An octahedron. Dual to the cube (we'll explain what that means later). Let's find out the volume of this very octahedron. We'll go back to our tetrahedral measuring cup (the unit). One... two... three... four. Done. Four. So what do we have so far: Tetrahedron = 1 Duo-Tet Cube = 3 Octahedron = 4 Rh Dodeca= 6 But wait, there's more. Remember Rh Dodecas fill space? Imagine a sphere or ball inside each one, perfectly encased (ball touches each diamond face center -- where the cube and octa criss-cross). Pack those babies together. Hey, that's CCP (= FCC). Kepler's Conjecture: densest possible (finally proved, 300+ years later). CCP is a branch point to a whole other set of cool topics. Another time. But hey we're there, ready to rumble. OK, so 12 rhombic dodecas snuggling around a central one, corresponds to some shape. Which one? Cuboctahedron. I've lost you ASCII readers, but in the classroom, this is all visual and/or tactile. I've got ping pong balls, I've got hypertoons (written in Python + VPython -- improved yet again as of late last night). And what's the volume of this 12-around-1 CCP embedded cuboctahedron, dual to the rhombic dodeca? Pour beans (your choice as to which combo of measuring cups). Answer: 20. So... Tetrahedron = 1 Duo-Tet Cube = 3 Octahedron = 4 Rh Dodeca= 6 Cubocta = 20 And yes, there's more. I've got a simple transformation of the cubocta that takes my to the icosahedron (incommensurable volume, and that's OK), and on to the octahedron (volume 4). Links to viruses, geodesic domes. Pentagonal dodeca comes back (yay Plato) as the dual of the icosa. And the rhombic triacontahedron, so very very close to volume 5 when shrink-wrapped around a CCP sphere -- but that's for another day, another grade maybe. Plus we can break the tetra and octa into more basic slivers of equal volume and assemble the rest of the not five-fold (other mods for them). My point: this is a very memorable spatial construct. It could be in there between the ears, along with the alphabet, the multiplication tables, and a gazillion other factoids we ask kids to remember, to learn by heart. But this one is visual, right brained, spatial, geometric. It addresses an imbalance (so much of what we remember are lists, algebraic rules, identities, with no pictures, especially
