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Notation as a Tool of Thought

jsoftware.com

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Re: Notation as a Tool of Thought

#3

Post by blululu »

azhenley wrote: post #2

This is Kenneth Iverson's 1979 Turing Award lecture.

Yes. There are some deep insights in this exposition. The irony is (in my opinion) APL is the worst Array/Matrix based programming language. In fairness it was also the first, but compared to Matlab or Julia it is not as expressive and feels much harder to use.

Re: Notation as a Tool of Thought

#4

Post by solinent »

blululu wrote: post #3
azhenley wrote: post #2

This is Kenneth Iverson's 1979 Turing Award lecture.

Yes. There are some deep insights in this exposition. The irony is (in my opinion) APL is the worst Array/Matrix based programming language. In fairness it was also the first, but compared to Matlab or Julia it is not as expressive and feels much harder to use.

There's a certain mathematical elegance to APL, I think. When the language is terse enough it helps you visualize and work with the language as a tool of thought--Matlab attempts to map actual mathematics to ASCII which is not that successful for me at least, since it meets a middle ground where it's too difficult for me to think quickly purely in Matlab and it's too high level for it to be useful as a practical language.

Engineers love it for prototyping, though, so maybe I just haven't worked with Matlab enough.

Re: Notation as a Tool of Thought

#6

Post by emmanueloga_ »

On this subject I love this strangeloop talk [1]: the right notation allowed John Conway to solve in an afternoon a knot problem that took another mathematician (Little) 6 years to solve!

Another example is juggling notation, that allowed not only the sharing of patterns but the discovery of new ones [2].

1: https://www.youtube.com/watch?v=Wahc9Ocka1g

2: https://en.wikipedia.org/wiki/Juggling_notation

Re: Notation as a Tool of Thought

#8

Post by blululu »

solinent wrote: post #4
blululu wrote: post #3

Earlier quoted context omitted.

Yes. There are some deep insights in this exposition. The irony is (in my opinion) APL is the worst Array/Matrix based programming language. In fairness it was also the first, but compared to Matlab or Julia it is not as expressive and feels much harder to use.

There's a certain mathematical elegance to APL, I think. When the language is terse enough it helps you visualize and work with the language as a tool of thought--Matlab attempts to map actual mathematics to ASCII which is not that successful for me at least, since it meets a middle ground where it's too difficult for me to think quickly purely in Matlab and it's too high level for it to be useful as a practical lang…

Fair point - personally I found APL to be a little too terse to be readable in ASCII. I think that there is a big difference in the affordances of a chalkboard/paper and a monospaced text editor, and to me APL is too close to paper based notation where it is easy to read and write a larger set of symbols. Matlab has some dedicated notation around matrices but uses more text heavy descriptions beyond that which feels better suited to a command line. Julia takes an even more text based approach and supports notations like list comprehensions which feel easier to learn, read and use than a set glyphs.

Re: Notation as a Tool of Thought

#10

Post by moonchild »

sxp wrote: post #9

For those unfamiliar with the power of APL, see this demo of someone livecoding the Game of Life: https://www.youtube.com/watch?v=a9xAKttWgP4 Its modern descendent are https://en.wikipedia.org/wiki/J_(programming_language) & https://en.wikipedia.org/wiki/K_(programming_language) .

APL itself continues to be developed; dyalog APL (the version demonstrated in that video) has added many of the features introduced by j. Roger hui (one of the original j developers) now works on dyalog.

There's also bqn[0], among others.

0. https://github.com/mlochbaum/bqn

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