[Edu-sig] still admiring J

[Wes Turner]

On Friday, March 23, 2018, kirby urner <kirby.urner at 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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