On Monday, September 4, 2017, kirby urner <kirby.ur...@gmail.com <javascript:_e(%7B%7D,'cvml','kirby.ur...@gmail.com');>> wrote:
> > >> Maybe a bit OT: >> >> > OT: "off topic" or "over the top"? :-D > Off topic > > 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? > Comply! > > - 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 > This looks useful; thanks! This doesn't even include the word entropy!: "Mathematics for Computer Science" https://ocw.mit.edu/courses/electrical-engineering-and- computer-science/6-042j-mathematics-for-computer- science-spring-2015/readings/MIT6_042JS15_textbook.pdf https://en.wikipedia.org/wiki/List_of_important_publications_in_theoretical_ computer_science#.22A_mathematical_theory_of_communication.22 "A Mathematical Theory of Communication" https://en.wikipedia.org/wiki/A_Mathematical_Theory_of_Communication - [...] - Entropy (Information Theory) - "bit" * - [...] https://scholar.google.com/scholar?hl=en&q=+ "A+Mathematical+Theory+of+Communication" > > >> - 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. > "A Primer on Using LaTeX in Jupyter Notebooks" http://data-blog.udacity.com/posts/2016/10/latex-primer/ SymPy has some really convenient plotting functions for symbolic equations and things: http://docs.sympy.org/latest/modules/plotting.html#plot-window-controls > > - CAS: SymPy, latex2sympy >> > If only it were possible to latex2sympy all of the sad PDF-embedded inline equations; to free them as (sensibly named) Python functions. https://github.com/augustt198/latex2sympy >> - Entropy >> - Independence of observations >> - Maximum Information >> >> > Enlightenment! > TIL that even logistic regression is a maximum entropy model: https://en.wikipedia.org/wiki/Principle_of_maximum_entropy#Maximum_entropy_models > > ... >> >> 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. > The origin is: the center of the Earth. Estimate. ... React VR flips the Y axis (and exchanges pixels for meters): https://facebook.github.io/react-vr/docs/3dcoordinates-and-transforms.html#content That c OR v+c question is complicated because *the space changes*; IDK how that affects coordinates. Apparently, there's a gradient of affect on photons around a black hole? > > > ... >> >> 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. > https://en.wikipedia.org/wiki/Entropy_in_thermodynamics_and_information_theory ... https://medium.com/the-physics-arxiv-blog/deeper-than-quantum-mechanics-david-deutschs-new-theory-of-reality-9b8281bc793a "Constructor Theory of Information" https://arxiv.org/abs/1405.5563 https://en.wikipedia.org/wiki/Constructor_theory ... "Physicists want to rebuild quantum theory from scratch" https://www.wired.com/story/physicists-want-to-rebuild-quantum-theory-from-scratch/ > Perhaps Hell is pure nonsense, separated from Heaven by the thinnest of > veils, like a decrypting key. > https://en.wikipedia.org/wiki/Greek_underworld https://en.wikipedia.org/wiki/Gehenna Books went to Pergamum and then the Library of Alexandria: https://en.wikipedia.org/wiki/Library_of_Pergamum How many minutes of time out would've been appropriate for Alexander "the great" (if any)? #EvidenceBased #OutcomeStudy > 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? > https:// HPACK (from HTTP/2) is an interesting study / modern example of Huffman coding: https://http2.github.io/http2-spec/compression.html https://en.wikipedia.org/wiki/HTTP/2#Genesis_in_and_later_differences_from_SPDY https://github.com/python-hyper/hpack
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