> > Maybe a bit OT: > > OT: "off topic" or "over the top"? :-D
I've wondered whether we could/should instead start mathematics education > with bits as entropy (information theory first)?: > > That's an interesting suggestion. When everything seems impenetrable / indecipherable, we're in a high entropy state. Like when you first get off the airplane in some alien culture and so much of what goes on seems an utter mystery. We're more like newborns. Then as we "learn the ropes" and start to "figure it out" there's a sense of Entropy decreasing. It all makes more sense. To a point. :-D Is the self-education process itself a struggle against our own mental entropy? - base 2: 00, 01, 10, 11 (on our hands (2**?)) > - counting > - ASCII (0-127) > - how do we know the number represents an integer or a character? ... > Encoding, Types > - The number zero is actually # (code point): ___ > - Unicode > - class SpecialString(str) > > http://4dsolutions.net/ocn/mainoutline.html > - Binary and then floating point arithmetic > - unary, binary operators > - import operators: sorted(dir(operators)) > - left and right shift > - multiplication as repeated addition > - long division > - floating point (error, BigFloat) > - symbolic mathematics > - MathJax, LaTeX (how to even type this?) > I really like how I can put LaTeX between dollar signs in a Jupyter Notebook and use it inline. - CAS: SymPy, latex2sympy > > - Entropy > - Independence of observations > - Maximum Information > > Enlightenment! ... > > class Shape > class Quadrilateral > class Rectangle > class Square > class Triangle > class RightTriangle > def perimiter > def area > def vertexes > > def scale > def rotate > > class PlatonicSolid > > I started on a Polyhedrons notebook. This is where I've invested a lot of time over the years. Bob and Wayne on math-teach say my use of Quadray Coordinates is not math. Some kind of hocus pocus. I'm the only one in the world who seems to think they have a place, if only to stimulate our thinking about coordinate systems more generally. ... > > Are there computer science & mathematics curricula like this (that start > with entropy)? > > In the sense that we all start out ignorant of what these curricula aim to signal, I think we all begin in a bath of noise. Thanks as always for intriguing input. I'm on a physics teacher list where they like to argue about Entropy and how best to teach about it. They're talking thermodynamics more than information theory, but that's all the more reason to look for these unifying concepts. Perhaps Hell is pure nonsense, separated from Heaven by the thinnest of veils, like a decrypting key. Like the less redundancy in a channel, the purer the signal, the closer it comes to appearing random, if we're locked out of its meaning. Right? Kirby
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