Notation as a Tool of Thought (1980) | Hacker News Reader

Notation as a Tool of Thought (1980)

jsoftware.com

124 pointsvonnik17 comments

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

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.

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... - I regard it as a much more fundamental and succinct description of how EM fields work.

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.

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

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

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

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

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

(Looked into it recently and I was disappointed.)

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.

I know a person who went through this program, and is still APLing today.

See also Brett Victor's "Media for Thinking the Unthinkable": https://vimeo.com/67076984

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. :(

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

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.

You can download fonts on Dyalog APL website: http://dyalog.com/apl-font-keyboard.htm

They look fine on both Firefox and Microsoft Edge.

lol

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