On Friday, March 23, 2018, kirby urner <kirby.ur...@gmail.com> wrote:
> > Greetings edu-siggers! > > Way back in the archives you'll find me extolling a language known as J, > by Kenneth Iverson, his son Eric, and Roger Hui. I never met any of these > guys in person, but knew of Iverson through APL, which I discovered at > Princeton, and fell in love with. Iverson helped me squish some typos in > my Jiving with J.[1] > > What I admire about J, as about R and Python via Numpy, is the inclusion > of an n-Dimensional Block (array, addressable memory with multiple axes), > as a language native, a core star. > xarray.Dataset is n-dimensional https://xarray.pydata.org/en/stable/ >From a tweet a few days ago https://twitter.com/westurner/status/973058715149578240 : Exercise: - Describe the 3D vertices of a cube: (x,y,z). - Apply a linear transformation (e.g. rotation): (t, x, y, z) - Determine how to project 3D points into 2D (first with wireframes, then with clipping) #Mayavi and #Blender can do 3D + time in Python. #Matplotlib can do 2D animated GIFs and, with #mplot3d, 3D animated GIFs And then view point density from one perspective with a hexbin chart and binned marginal distributions https://t.co/59fO6c6JSf #hexbin plot w/ marginal distributions #seaborn https://t.co/FHe3L4oOSw https://t.co/K6WI8NcF4i 2D "Linear transformations and matrices | Essence of linear algebra, chapter 3" by @3Blue1Brown https://youtube.com/watch?v=kYB8IZa5AuE ... And then special relativity and Lorentz transformations of spacetime with tensors: https://en.wikipedia.org/wiki/Lorentz_transformation "Lorentz transformation for change in coordinates | Physics | Khan Academy" https://youtube.com/watch?v=1F1tFouUGTU "Introduction to the Lorentz transformation | Special relativity | Physics | Khan Academy" https://youtube.com/watch?v=HIQ5hnm61LQ ... With time t, the cube exercise coordinates are really 4D (*), but they can be projected into a table with columns like: t, v1x, v1y, v1z, ..., v8x, v8y, v8z This (and other multidimensional data) can be represented with pandas.DataFrame or pandas.Panel, though pandas.Panel is being deprecated in favor of xarray or just multidimensional indices and pd.DataFrame: https://pandas.pydata.org/pandas-docs/stable/dsintro.html#deprecate-panel * Actually, it's all 2D: https://en.wikipedia.org/wiki/Holographic_principle > In a larger sense, the theory suggests that the entire universe can be seen as two-dimensional information on the cosmological horizon, the event horizon from which information may still be gathered and not lost due to the natural limitations of spacetime supporting a black hole, an observer and a given setting of these specific elements,[clarification needed] such that the three dimensions we observe are an effective description only at macroscopic scales and at low energies. Cosmological holography has not been made mathematically precise, partly because the particle horizon has a non-zero area and grows with time. > > J reads like a right-to-left pipeline with an nD Block going through it. > I guess we'd need to call that a Functional Programming language right? > > As the former high school math teacher (long ago -- though I'm still in > the schools, as recently as today in fact, as an after school Python > instructor), I still chafe at the fact that we don't dive in with these > tools at that age level, except in rare cases, and instead insist on > students buying all those TIs year after year. But that's me the broken > record. > > For those schools that break out, charter or public (nevermind, how they > talk in the US makes noooo sense), there's a world of wonderful technology > to explore, while learning the math that matters. y = mx + b. Turn m over > for w, and b is for bias.[2] > > Kirby > > [1] http://www.4dsolutions.net/ocn/Jlang.html > > [2] https://www.google.com/search?q=mcdonalds+upside+down+w& > safe=off&source=lnms&tbm=isch (recent meme) > >
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