
Notation as a Tool of Thought (1980) - vonnik
http://www.jsoftware.com/papers/tot.htm
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ThePhysicist
In Physics and Mathematics it is widely accepted that having an efficient
notation is of paramount importance when thinking about a given problem. A
good example for this are Maxwell's equations:

[https://en.wikipedia.org/wiki/Maxwell%27s_equations](https://en.wikipedia.org/wiki/Maxwell%27s_equations)

Using the vector differential operator notation those equations neatly fit on
a napkin, whereas Maxwell's original equations (written in Integral form)
would cover several pages. In fact, looking at his original manuscript always
fills me with awe for the man as he had much less sophisticated tools at hand
for his job but still managed to discover the beauty and simplicity of
electromagnetism with them, which would also provide the foundation of special
relativity.

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beagle3
Indeed. Most texts stop at the 4-equation notation that has both electric (E)
and magnetic (B) fields, but with a small extension it becomes a single
equation, which is lorentz-invariant:
[https://en.wikipedia.org/wiki/Covariant_formulation_of_class...](https://en.wikipedia.org/wiki/Covariant_formulation_of_classical_electromagnetism#Maxwell.27s_equations_in_the_Lorenz_gauge)
\- I regard it as a much more fundamental and succinct description of how EM
fields work.

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effie
The covariant notation is concise and to some even elegant, but it is also
less useful in practice. One often has to deal either with electric or
magnetic field specifically as opposed to EM field tensor, and even if one
does not need that, it is often possible and useful to work with only electric
(or magnetic) component in 3D vector notation.

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vonnik
A former hedge fund manager and all-around thoughtful guy, Brooke Allen, says
he thinks in APL. He's also the dude who does Staffup Weekend and is trying to
change how people hire. A few years ago, in a different job market and another
time, he had dozens of people learn APL as part of a job application process.
0_O

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RodgerTheGreat
Getting paid to program in APL sounds pretty fun to me- It's a shame most of
the jobs seem to be finance-based.

~~~
alexcweiner
I suggest checking out GNU APL. There are relatively few libraries, so there
is lots of room for contribution.

~~~
brudgers
Iverson's later language, J, is also open source. It doesn't require a special
keyboard, has top notch documentation and online support resources and is open
source under GPL3. It might or might not be a better place to get started than
APL depending on a person's goals.

[http://www.jsoftware.com/stable.htm](http://www.jsoftware.com/stable.htm)

~~~
jsofteh
It's not really open source. Only the "core." The development environment is
excluded.

(Looked into it recently and I was disappointed.)

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brudgers
Between the command line, scripts and Emacs the J IDE isn't really a big deal
for me. Because J was a closed source commercial product and dates to the
1980's their may be copyright licensing issues tied into the code base. It's
hard to release existing projects into open source.

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biot
See also Brett Victor's "Media for Thinking the Unthinkable":
[https://vimeo.com/67076984](https://vimeo.com/67076984)

~~~
sabertoothed
It was 2 am in the UK and I wanted to sleep. I had to watch the whole video.
It's excellent. Absolutely brilliant! Thank you for the link.

Now it's 3 am. :(

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llasram
For some context (relegated to the very end of this HTML version), this is
Iverson's Turing Award Lecture article following his winning the 1979 ACM
Turing Award. Here's the ACM's PDF photoscan of the original publication:
[http://dl.acm.org/ft_gateway.cfm?id=1283935&type=pdf](http://dl.acm.org/ft_gateway.cfm?id=1283935&type=pdf)

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Kenji
Somewhat off-topic, but the unicode symbols like Greek letters are broken in
google chrome. A shame... And also kind of ironic, because boxes with question
marks inside certainly aren't the best kind of notation.

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omaranto
They look fine on both Firefox and Microsoft Edge.

~~~
WaxProlix
lol

