6 ms·

Notation as a Tool of Thought (1979)

106 points by ehudla 10y ago

qwertyuiop924 10y ago
Ah, yes. The paper that taught the world about the marvels of APL. Which is a pretty cool language, and definitely on my "to learn" list. APL's unofficial slogan, by the way, is "and you thought Perl was executable linenoise." :-)
- imglorp 10y ago
  I took a numerical methods in APL class way back. Nothing we did took more than half a line, ever.
  - JosephHatfield 10y ago
    []pw <- 80?
gardano 10y ago
Musician checking in. Reading music in the original notation I have found to be particularly enlightening. Where the manuscript writer (or print publisher) chose to put bar lines, for instance, can give clues as to intent in performance. I'm thinking specifically about Venetian publishers in the 17th century -- but there are plenty of other examples. Notation can be incredibly important when trying to discern intent in some disciplines.
- gkya 10y ago
  Would you mind to elaborate a bit more? Seems to be very interesting fact.
  - gardano 10y ago
    Picture a piece for 3 players -- 2 soprano instruments and Basso Continuo (a bass instrument + let's say, harpsichord). It's a piece with a recurring harmonic structure; say, Passamezzo or ciacona -- think Pachelbel Canon. The BC in this particular instance might only have barlines every 8 measures. The soprano parts might have barlines every 8 measures too, but might also have them where a significant change to their melodies change. Like, when a flurry of 16th notes begin to crop up. Now, this isn't always the case -- it's definitely inconsistent, but such things show up enough that those hints cannot be discounted at all, and seem to be enough of a performance hint to at least be noted and appreciated by the performer.
- tnecniv 10y ago
  Was bar placement not standardized to be at the end of every measure?
  - gardano 10y ago
    No, bars were not standardised at all! One could interpret placement of barlines as something close to paragraph markers -- not all the time, but often enough that they seem to indicate specific intent.
kaoD 10y ago
Slightly unrelated: I often find myself in the browser console, exploring data scraped off webpages (often from Wikipedia tables). I think REPLs are another kind of "tool of thought". E.g.: I recently scraped my country's election results off Wikipedia to see how voting areas affected the distribution of seats. Very insightful. Being tightly integrated to the browser offers the whole web as a data set. Unfortunately JavaScript does not lend itself very well to data analysis. What is your tool of choice for interactive data exploration? I've been looking for something similar for my phone, a sort of calculator-on-steroids even if not web-scraping ready. J for Android[0] fits the bill perfectly... except the language itself seems to get in the way with its short mnemonics, unrememberable verb train rules, function composition words and other weirdness in the construction of tacit phrases. I've (partially) learned and forgotten J three times already. Every single time I come back is like starting anew. I tried Clojure too but the Android REPL[1] is stuck on Clojure 1.4.0 and the lack of an S-expression enabled keyboard/editor makes it a pain to code. Any recommendations in this area? [0] http://www.jsoftware.com/ http://www.jsoftware.com/ [1] https://play.google.com/store/apps/details?id=com.sattvik.clojure_repl&hl=en https://play.google.com/store/apps/details?id=com.sattvik.cl...
- RodgerTheGreat 10y ago
  It may not really be what you want, but I've been developing a mobile-friendly frontend for my K interpreter which makes it essentially a K-based graphing calculator: http://johnearnest.github.io/ok/mobile.html http://johnearnest.github.io/ok/mobile.html The browser security model severely limits potential for doing web scraping with it, but I have found it pleasant to use so far. Docs can be found here: https://github.com/JohnEarnest/ok#mobile https://github.com/JohnEarnest/ok#mobile
- dTal 10y ago
  It's not Free Software, but Frink is my goto "calculator on steroids". Not sure if it's suited to what you have in mind. https://frinklang.org/ https://frinklang.org/
- carussell 10y ago
  Side note: > I often find myself in the browser console, exploring data scraped off webpages (often from Wikipedia tables) Are you aware of Wikidata? I don't have a lot of familiarity with it, only that some (a lot?) of the programmer types who were drawn to Wikipedia in its infancy have shifted their focus to Wikidata nowadays. As I understand it, Wikidata is meant to be the data source behind those tables that you're scraping. (Forgive me if you're already involved with Wikidata and one of your primary uses for scraping is in pursuit of migrating content to Wikidata.)
yummyfajitas 10y ago
If anyone is interested in a more readable version of APL, I think python/numpy qualifies. Their first few examples can be expressed the same way in standard numpy: arange(6) # Same as ⍳5 add.reduce(arange(6)) # Same as +/⍳5 add.accumulate(arange(6)) # Same as +\⍳5 I've gone partway through this document (up to chapter 3, plus skimming other bits) and have not found any examples that don't translate into standard numpy code. From what I can tell, the core learning one takes from J/K/etc is the concept of an array language and treating arrays as first class objects. And nowadays Python/R/Julia provide this same functionality in a more verbose/more readable/more mainstream package.
- _mhr_ 10y ago
  It'd be a fun project to write a an APL-like that compiles down to NumPy. Would it be pointless? Another interesting project might be to make an APL-like for probabilistic programming.
  - yummyfajitas 10y ago
    My point is that it'd be pretty easy. The semantics are pretty close, it's only the syntax ("+/" -> "add.reduce") that varies.
  - 3JPLW 10y ago
    There's a start for this in Julia[0], where custom string literals mean that you can actually write APL in native Julia: julia> apl"ι5" 1:5 julia> apl"+/ι5" 15 You can even just get the function that represents the `+/` operation and apply it to any Julia object: julia> apl"+/"(rand(100)) 52.17866879741195 0. https://github.com/shashi/APL.jl https://github.com/shashi/APL.jl
- beagle3 10y ago
  > From what I can tell, the core learning one takes from J/K/etc is the concept of an array language and treating arrays as first class objects. And nowadays Python/R/Julia provide this same functionality in a more verbose/more readable/more mainstream package. That's just part of it. Other parts (by no means a complete list): - Visual density puts the pattern matching engine in your brain to good use; e.g. the K idiom "|/0(0|+)+\" which implements maximum-subsequence-sum is a 10-character visually recognizable sequence recognizable to many K programmers, which is efficient and well specified; Similarly, ",//" flattens a list. I don't know of any other language family that has this feature. - Arrays with equivalent indices work better than structures ("column major" captures some, but not all of it) - A properly selected core set of concrete operations (in K's case, about 60 of them) makes the needed abstractions shallower and simpler than a properly selected set of abstraction constructs.
mayoff 10y ago
The year in the title should be 1979, not 2009. This was Ken Iverson's Turing Award lecture in 1979.
- mcnamaratw 10y ago
  Yep, here's a link http://delivery.acm.org/10.1145/1290000/1283935/a1979-iverson.pdf?ip=74.67.70.223&id=1283935&acc=OPEN&key=4D4702B0C3E38B35%2E4D4702B0C3E38B35%2E4D4702B0C3E38B35%2E6D218144511F3437&CFID=877503238&CFTOKEN=71658640&__acm__=1482010216_fe163a736ce0fea424a133c4270ef743 http://delivery.acm.org/10.1145/1290000/1283935/a1979-iverso...

106 points by ehudla 10y ago

Ah, yes. The paper that taught the world about the marvels of APL. Which is a pretty cool language, and definitely on my "to learn" list. APL's unofficial slogan, by the way, is "and you thought Perl was executable linenoise." :-)

imglorp 10y ago
I took a numerical methods in APL class way back. Nothing we did took more than half a line, ever.
- JosephHatfield 10y ago
  []pw <- 80?

gardano 10y ago

Musician checking in. Reading music in the original notation I have found to be particularly enlightening. Where the manuscript writer (or print publisher) chose to put bar lines, for instance, can give clues as to intent in performance. I'm thinking specifically about Venetian publishers in the 17th century -- but there are plenty of other examples. Notation can be incredibly important when trying to discern intent in some disciplines.

gkya 10y ago
Would you mind to elaborate a bit more? Seems to be very interesting fact.
- gardano 10y ago
  Picture a piece for 3 players -- 2 soprano instruments and Basso Continuo (a bass instrument + let's say, harpsichord). It's a piece with a recurring harmonic structure; say, Passamezzo or ciacona -- think Pachelbel Canon. The BC in this particular instance might only have barlines every 8 measures. The soprano parts might have barlines every 8 measures too, but might also have them where a significant change to their melodies change. Like, when a flurry of 16th notes begin to crop up. Now, this isn't always the case -- it's definitely inconsistent, but such things show up enough that those hints cannot be discounted at all, and seem to be enough of a performance hint to at least be noted and appreciated by the performer.
tnecniv 10y ago
Was bar placement not standardized to be at the end of every measure?
- gardano 10y ago
  No, bars were not standardised at all! One could interpret placement of barlines as something close to paragraph markers -- not all the time, but often enough that they seem to indicate specific intent.

kaoD 10y ago

Slightly unrelated: I often find myself in the browser console, exploring data scraped off webpages (often from Wikipedia tables). I think REPLs are another kind of "tool of thought". E.g.: I recently scraped my country's election results off Wikipedia to see how voting areas affected the distribution of seats. Very insightful. Being tightly integrated to the browser offers the whole web as a data set. Unfortunately JavaScript does not lend itself very well to data analysis. What is your tool of choice for interactive data exploration? I've been looking for something similar for my phone, a sort of calculator-on-steroids even if not web-scraping ready. J for Android[0] fits the bill perfectly... except the language itself seems to get in the way with its short mnemonics, unrememberable verb train rules, function composition words and other weirdness in the construction of tacit phrases. I've (partially) learned and forgotten J three times already. Every single time I come back is like starting anew. I tried Clojure too but the Android REPL[1] is stuck on Clojure 1.4.0 and the lack of an S-expression enabled keyboard/editor makes it a pain to code. Any recommendations in this area? [0] http://www.jsoftware.com/ http://www.jsoftware.com/ [1] https://play.google.com/store/apps/details?id=com.sattvik.clojure_repl&hl=en https://play.google.com/store/apps/details?id=com.sattvik.cl...

RodgerTheGreat 10y ago
It may not really be what you want, but I've been developing a mobile-friendly frontend for my K interpreter which makes it essentially a K-based graphing calculator: http://johnearnest.github.io/ok/mobile.html http://johnearnest.github.io/ok/mobile.html The browser security model severely limits potential for doing web scraping with it, but I have found it pleasant to use so far. Docs can be found here: https://github.com/JohnEarnest/ok#mobile https://github.com/JohnEarnest/ok#mobile
dTal 10y ago
It's not Free Software, but Frink is my goto "calculator on steroids". Not sure if it's suited to what you have in mind. https://frinklang.org/ https://frinklang.org/
carussell 10y ago
Side note: > I often find myself in the browser console, exploring data scraped off webpages (often from Wikipedia tables) Are you aware of Wikidata? I don't have a lot of familiarity with it, only that some (a lot?) of the programmer types who were drawn to Wikipedia in its infancy have shifted their focus to Wikidata nowadays. As I understand it, Wikidata is meant to be the data source behind those tables that you're scraping. (Forgive me if you're already involved with Wikidata and one of your primary uses for scraping is in pursuit of migrating content to Wikidata.)

yummyfajitas 10y ago

If anyone is interested in a more readable version of APL, I think python/numpy qualifies. Their first few examples can be expressed the same way in standard numpy: arange(6) # Same as ⍳5 add.reduce(arange(6)) # Same as +/⍳5 add.accumulate(arange(6)) # Same as +\⍳5 I've gone partway through this document (up to chapter 3, plus skimming other bits) and have not found any examples that don't translate into standard numpy code. From what I can tell, the core learning one takes from J/K/etc is the concept of an array language and treating arrays as first class objects. And nowadays Python/R/Julia provide this same functionality in a more verbose/more readable/more mainstream package.

_mhr_ 10y ago
It'd be a fun project to write a an APL-like that compiles down to NumPy. Would it be pointless? Another interesting project might be to make an APL-like for probabilistic programming.
- yummyfajitas 10y ago
  My point is that it'd be pretty easy. The semantics are pretty close, it's only the syntax ("+/" -> "add.reduce") that varies.
- 3JPLW 10y ago
  There's a start for this in Julia[0], where custom string literals mean that you can actually write APL in native Julia: julia> apl"ι5" 1:5 julia> apl"+/ι5" 15 You can even just get the function that represents the `+/` operation and apply it to any Julia object: julia> apl"+/"(rand(100)) 52.17866879741195 0. https://github.com/shashi/APL.jl https://github.com/shashi/APL.jl
beagle3 10y ago
> From what I can tell, the core learning one takes from J/K/etc is the concept of an array language and treating arrays as first class objects. And nowadays Python/R/Julia provide this same functionality in a more verbose/more readable/more mainstream package. That's just part of it. Other parts (by no means a complete list): - Visual density puts the pattern matching engine in your brain to good use; e.g. the K idiom "|/0(0|+)+\" which implements maximum-subsequence-sum is a 10-character visually recognizable sequence recognizable to many K programmers, which is efficient and well specified; Similarly, ",//" flattens a list. I don't know of any other language family that has this feature. - Arrays with equivalent indices work better than structures ("column major" captures some, but not all of it) - A properly selected core set of concrete operations (in K's case, about 60 of them) makes the needed abstractions shallower and simpler than a properly selected set of abstraction constructs.

mayoff 10y ago

The year in the title should be 1979, not 2009. This was Ken Iverson's Turing Award lecture in 1979.

mcnamaratw 10y ago
Yep, here's a link http://delivery.acm.org/10.1145/1290000/1283935/a1979-iverson.pdf?ip=74.67.70.223&id=1283935&acc=OPEN&key=4D4702B0C3E38B35%2E4D4702B0C3E38B35%2E4D4702B0C3E38B35%2E6D218144511F3437&CFID=877503238&CFTOKEN=71658640&__acm__=1482010216_fe163a736ce0fea424a133c4270ef743 http://delivery.acm.org/10.1145/1290000/1283935/a1979-iverso...