This is going to seem a bit off-topic, but my goal is to show how CS might recruit more liberal arts majors by focusing on namespaces in the humanities. Like I was saying earlier, every professor, of Near Eastern Studies, of Molecular Biology, of Postmodern Poetics, whatever BS, is a walking talking live specimen namespace. And when you get two or more professors in a room, what typically happens? Name collisions, and lots of them. So how has computer science helped solve the problem of name collisions, at least for the benefit of our poor slave electronic robots (AI bots), with no hope of understanding the subtlties of "context" without it? By means of dot notation, is one way. In Python, we'll see what that looks like. But let's get back to those professors for a moment, and take a good example of a name collision, familiar to everyone who studies Bucky Fuller's stuff on occasion (i.e. probably most gnu math teachers). Over on Synergeo (another obscure archive where I'm sometimes active), you'll maybe find some "chalkboard notation" like this: coxeter.4d < > einstein.4d < > fuller.4d What that refers to is the three different trajectories taken by the '4D' meme since like around 1900, when it was caught up in a maelstrom of competing schools of thought.[1] In his 'Regular Polytopes' this master geometer (who recently died -- there's new bio out), H.S.M. Coxeter takes pains to differentiate *his* meaning of "four dimensional" from that of the spacetime Relativity's.[2][3] Coxeter's *not* saying the Einsteinians are wrong to have their own namespace, just that the two schools have different usages for this same '4D' meme. Not getting that there's a difference will lead only to confusion. He mentions some science fiction that fell into this trap. The difference? In hyperspatial geometry, you have as many dimensions as you want, and they're all spatial. In Relativity, the time dimension is singled out for special treatment. Fuller, meanwhile, held back publishing his gestating meaning for '4D' until much later in life (1970s), and, upon unveiling, it turned out to be neither Coxeter's nor Einstein's, but had some family resemblance to both. Fuller's 4D is very like everyday high school's 3D, i.e. the XYZ apparatus, anchored at an origin (0,0,0) is conceived to exist independently of any specific event in spacetime. There's no "where or when" questions that need answering. XYZ exists in pure conceptuality, and gives us a refined idea of "a mathematical space" that's very like our own personal circumstances (i.e. spatial, volumetric), yet is conveniently devoid of what philosophers of the day called "secondary characteristics" e.g. color, sound, tactility -- the messy business of energetic reality. Why Fuller called it 4D instead of 3D is he was very impressed by the simple nature of the Tetrahedron, the fact that it had fewer faces, edges and vertices than the cube. In the world of hard edges, skeletons, sticks, it seemed the simplest of shapes (not a new realization -- mathematicians often call it The Simplex). Spheres seem a lot smoother, true, but in stick world they're just hugely multi-faceted and hence not simple at all. Axiomatically, one needn't buy a Continuum to practice geometry per Democritus. Buckaneering is digital, seems analog only because everything does. And the tetrahedron simply radiates 4ness, really more than 3ness, although the two complementary 3-edge spiral zig-zags always and only co-exist (as the local namespace would have it). And then, taking a page from Kant, we simply identify conceptuality with this Tetrahedron Space (a 4-space) and scoff at Abbott's 'Flatland' as a conceptual impossibility (i.e. we only *pretend* we can imagine a space of fewer dimensions -- always forgetting about the camera). Anyway, this is all a very different namespace than either Professor Coxeter or Professor Einstein were using. More philosophical, vs. Coxeter's mathematical and Einstein's physical. Each guy had his own trademark brand of 4D, and developed his thinking accordingly, systematically, consistently. Fuller came along late in the game, threw a new '4D' in the ring. So as of the 1970s, we have at least three, distinct, not-equal usage patterns, yet all using the same name. What are the chances of name collisions? Very high. But learning from computer science, and Python especially, we have this simple way of cleaning up the mess: use dot notation, to anchor names to their users, their professors (those who profess (Fuller claimed not to be "professing" but was just quibbling over verbs (always the stickler))). coxeter.4d < > einstein.4d < > fuller.4d In sum, I'm including this little chalkboard lecture on "The Three Meanings of 4D" in order to show how we, the liberal arts humanties types, have become enamoured of dot notation as a way to sort out name collisions, and the messes they sometimes engender. Ever since we in the Fuller School got clear on this "three schools" picture, we've had a lot easier time lowering the noise level in our meetings. As Fuller Schoolers, we're less likely to flounder around in BS, and we credit nearby Python Nation's high level of intelligence and civilization for helping us out. We import. We thrive. And we hope our exports are valued too (it's about trading, not stealing i.e. keeping in balance). Kirby [1] Linda Dalrymple Henderson. The Fourth Dimension and Non-Euclidean Geometry in Modern Art (Hardcover). ISBN 0691040087 [2] H.S.M Coxeter, 'Regular Polytopes' ISBN 0486614808, pg. 119 [3] The King of Infinite Space: Donald Coxeter: the Man Who Saved Geometry (Hardcover) by Siobhan Roberts -- which I just purchased about a minute ago from Amazon.com.
kirby urner wrote:
Why Fuller called it 4D instead of 3D is he was very impressed by the simple nature of the Tetrahedron, the fact that it had fewer faces, edges and vertices than the cube. In the world of hard edges, skeletons, sticks, it seemed the simplest of shapes (not a new realization -- mathematicians often call it The Simplex).
He renamed 3d, in an "I know something you don't" sort of way. Paraphrasing Atanas, in another context: Maybe he does, maybe he does't. Art
On 9/13/06, Arthur <ajsiegel@optonline.net> wrote:
He renamed 3d, in an "I know something you don't" sort of way.
Not really. We say 3D because we think height (1), width (2) and depth (3) come apart as isolatable components of volume. You can have one (any one) with out the others. Really? Anyway, if you conceive of volume as primordial, as rock bottom, then you might reconsider why a "3" and not a "4". Why start with 3 when the most primitive volume has 4 vertices and 4 faces? It's not a completely insane proposal, and it's not like you have to buy into it to the exclusion of every other paradigm. What's cool about namespaces is you can always change channels (if you're mentally limber -- there're limits...). Anyway, it's a remote namespace, quite alien and "out there". I mostly say 3D like an ordinary person. When in Rome... Kirby
Not really apropos to Python, but since the discussion veered into 4D: There's a great flash animation on how to visualize 10 dimensions (companion to a book on the same subject): http://www.tenthdimension.com/flash2.php My favorite redefinition of dimensions (but I can't find it anymore and don't remember where I came across it) was based on rotations. The idea is that we perceive 3 dimensions because the Greeks made the math work out, but we don't really live in perfect 3 spacial (height, depth, width) dimensions any more than there are dimensionless lines which go on to infinity, or infinite perfect planes, or spheres. Bucky called them on the dimensionless geometry, but I don't think he was the one who planted rotation-based dimensions in my head. So, instead of living in 3-D space, we live on a rotating sphere. The rotation of the earth on its axis is one dimension. The rotation of the earth around the sun is another dimension, the rotation of the sun around the Galactic core is another. The rotation of the galaxy relative to other galaxies is a further dimension. Of course, the dimensions go down, too. Rotation of electrons around the nucleus of an atom is one dimension, electron spin is another, etc. I think they had something like 17 dimensions labeled, and it was easy to visualize, and incorporated time (since rotations and orbits are all movement over time), so time did not have to be a seperate, isolated component. The whole thing is kind of wacky, and probably come from some fringe cult like Urantia (I sat through one of their lectures as a kid, and it seemed to have some good ideas for a science fiction novel). I forget how many dimensions are required by superstring theory this week (the 10 dimensions guy claims 10, but I know the answer has varied with the development of the theory, and not all proponents of superstring theory agree on the number of dimensions needed), but for me, thinking of them as these various rotations helps me keep it in perspective, even if it isn't an accurate map of the territory. --Dethe On 13-Sep-06, at 8:45 PM, kirby urner wrote:
On 9/13/06, Arthur <ajsiegel@optonline.net> wrote:
He renamed 3d, in an "I know something you don't" sort of way.
Not really. We say 3D because we think height (1), width (2) and depth (3) come apart as isolatable components of volume. You can have one (any one) with out the others.
Really?
Anyway, if you conceive of volume as primordial, as rock bottom, then you might reconsider why a "3" and not a "4".
Why start with 3 when the most primitive volume has 4 vertices and 4 faces?
It's not a completely insane proposal, and it's not like you have to buy into it to the exclusion of every other paradigm.
What's cool about namespaces is you can always change channels (if you're mentally limber -- there're limits...).
Anyway, it's a remote namespace, quite alien and "out there".
I mostly say 3D like an ordinary person. When in Rome...
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On 9/14/06, Arthur <ajsiegel@optonline.net> wrote:
It's not a completely insane proposal, and it's not like you have to
buy into it to the exclusion of every other paradigm.
It is, like some other of what I read in (into) Fuller, the apparent stated esoterically.
Art
Not esoteric relative to string theory. Kirby
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