[HN Gopher] Notation as a Tool of Thought (1979)
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Notation as a Tool of Thought (1979)
Author : memorable
Score : 149 points
Date : 2022-07-21 11:56 UTC (11 hours ago)
(HTM) web link (www.jsoftware.com)
(TXT) w3m dump (www.jsoftware.com)
| kubanczyk wrote:
| Eh? This line of the appendix:
|
| > Boolean: [?] [?] ~ (and, or, not-and, not-or, not)
|
| In some places in the pdf the notation looks sketchy. But this
| line demonstrates beyond any doubt that the pdf is missing chars.
| abrudz wrote:
| Thanks. I've asked someone to fix it.
| civilized wrote:
| I love the idea that notation matters for thought. I remain
| unconvinced that APL is a particularly good one, but I have
| definitely adopted "tool of thought" as a core productivity
| concept. For example, a plain text file, Google doc, or Trello
| board are all decent tools of thought, while JIRA isn't.
| zetalyrae wrote:
| Among all languages, APL has the highest ratio of times its
| founding document is posted to Hacker News to lines of code
| written.
|
| I don't mean this to be terribly dismissive: I've always been
| "tangentially fascinated", like I think a lot of people are, by
| APL and Forth. But I've never properly used it because ultimately
| it's in conflict with how I think programs should be written:
| with types, abstraction, a focus on readability etc.
| mlochbaum wrote:
| To be fair, "lines of code written" is a particularly poor
| choice of denominator when discussing APL. But I think you're
| also unaware of historical usage. There are some very large (I
| believe close to a million lines) financial applications still
| in use, and far more applications for ordinary tasks like
| scheduling, payroll, and other administration made for
| companies and universities in the 80s.
|
| Now that the ACM has made them free to access, papers from the
| APL conference are a good place to look to get a sense for
| this; APL79 was the first really huge one:
| https://aplwiki.com/wiki/APL_conference#1979
| zetalyrae wrote:
| I'm aware of kdb+. It has an SQL interface and clients in
| multiple languages. How many of their users use the APL
| interface? And how many financial companies are planning on
| building new products on top of a technological dead-end from
| the 1960's?
|
| There was a time when APL was taught in universities, and
| some computers came with APL-specialized keyboards. That time
| came and went because the bulk of mainstream software
| development went in a wildly different direction.
| mlochbaum wrote:
| For clarity, I'm talking mainly about SimCorp[0], which is
| a user of Dyalog APL, not kdb. The core of Dimension uses
| APL (with many other parts in C#), and there's a separate
| APL product bought with APL Italiana as well. They employ
| hundreds of APL programmers, preferring to hire math and
| physics majors out of college because they're easier to
| teach. Yes, SimCorp probably wouldn't start with APL today,
| and I wouldn't give it a second thought either if I were
| trying to start a big business. I pointed to the large
| codebases because they're easier to quantify, but I'm sure
| there are millions of lines written by hobbyist developers.
|
| I know you're not trying to flame, but what you've given us
| so far is a false claim that nobody writes code in APL, and
| a bare assertion that APL is a bad way to program. On that
| note, you're trying to say a language you've never used
| doesn't allow for "abstraction" or "a focus on
| readability", which I think is dead wrong. All of which is
| at best tangentially relevant to Iverson's claim in the
| paper (not APL's founding document, by the way; that would
| be A Programming Language) that APL's notation is a way to
| enhance your thinking. APL has good and bad aspects, and
| there's a lot to discuss, but can it please be a discussion
| instead of these careless remarks?
|
| [0] https://en.wikipedia.org/wiki/SimCorp
| andylynch wrote:
| Plenty. The sql-like interface (in Q) is mostly syntactic
| sugar; the functional style takes you much further. That
| said KX is making a huge push on ease of use and front end
| where you don't necessarily need to use Q.
| blululu wrote:
| FWIW APL is pretty influential to Matlab which is the
| inspiration for Numpy, etc. I think the trouble is that the
| authors are right about the importance of notation but they
| were also making the first pass and they made some choices that
| proved to be off in practice.
| skruger wrote:
| If you're familiar with both modern APL and the "Iverson
| ghost" NumPy, you'll likely find the latter a frustratingly
| crippled experience.
| blululu wrote:
| Fair. I don't think anyone transitions from Matlab or Julia
| to Numpy and feels good about it, but the broader ecosystem
| advantages are decisive there.
| buescher wrote:
| I suspect a lot of the casual fascination with APL these
| days comes from frustration with Numpy. In the same way
| that nobody had anything good to say about Ada until C++
| and Java were firmly entrenched.
| skruger wrote:
| I am an APL-fan specifically because it's like a parallel
| universe where evolution took a different path: what are
| often considered anti-patterns in main stream languages
| is best practice in APL. It's a welcome relief from the
| strait-jacket of "the Zen of Python". No libraries? It's
| a feature. Single-letter variable names? Of course.
| Terseness as a virtue? Oh yes. Right-to-left flow? Why
| not? Precedence levels? Who needs them? Tacit? Bring it
| on. APL is easily the most productive tool in my chest.
| [deleted]
| nequo wrote:
| What kinds of tasks have you used APL for?
| skruger wrote:
| I use APL for any task I previously used Python for,
| involving grabbing some data typically via a json-over-
| http API, massaging, aggregating and otherwise combining
| it to produce summaries or reports. I've gradually
| rewritten my bunch of scripts and code I use daily from
| python to APL, and seen a 10-100x reduction in code size,
| and usually a significant speed-up (admittedly, Python is
| a low bar here).
| pklausler wrote:
| I loved APL for decades but realized a while back that thing I
| appreciated most about the language wasn't how it deals with
| arrays but rather how well it supported the easy _composition_ of
| functions -- and that primed me well for languages that do that
| sort of thing even better.
|
| And yet I miss many things about APL when coding in modern
| functional languages. Specifically, having the shapes of arrays
| being a concept that's distinct from both their types and from
| their values is something that I can't reproduce in Haskell.
| auggierose wrote:
| Can you elaborate a bit more what you can do with shapes that's
| not easily replicated in other languages?
| kjellsbells wrote:
| Does the notion of suggestability extend to the notion of
| "creative breakage"? The latter is an important feature of a
| mathematical notation.
|
| For example the dy/dx notation in calculus naturally leads to
| inquisitive thinking. Can you multiply by dx? It looks like a
| division but it isnt, really, except that a soon as you get past
| Calc 101 you are spraying dys and dxs all over. the notation is
| just incredibly suggestive.
|
| Another example is exponents where m^n is introduced naively for
| natural n but instantly prompts the question around non integer
| n.
|
| i think that having a notation that is suggestive and can be
| creatively broken to use in new ways is v important
| Koshkin wrote:
| > _Can you multiply by dx?_
|
| Maybe. But can you multiply by [?] _x_?
| Blammar wrote:
| "dx" is a term rigorously defined in infinitesimal calculus
| (IMO a much easier to understand approach to
| differentiation.) So, yes, you can multiply by dx (even if x
| is a more complicated function.)
|
| [?]x would have a problematic definition, as it would require
| selecting from its components based on information not
| supplied. E.g., let x = y+z. Then dx = dy + dz. But [?]x (by
| extension) = [?]y + [?]z, but at least one of these terms on
| the right is identically zero, depending on whether y or z is
| held constant. So [?]x doesn't have a meaning.
| Koshkin wrote:
| Actually, "dx" is rigorously defined in the standard
| calculus, too, and yes, you can multiply (and divide) by
| it.
| mlochbaum wrote:
| Iverson usually expresses the derivative as an operator, which
| ties into Heaviside's operational calculus[0] but doesn't have
| multiplication rules like dx/dy (I'd probably be more on your
| side here, in favor of dx and dy). I don't think he was too
| comfortable with mathematical concepts that don't resolve into
| specific calculations. Which may be why his notation ended up
| being so easy to turn into a programming language. To me,
| Iverson's suggestivity would be more about unifying or making
| analogies between established concepts. For example, APL uses *
| for exponentiation and [?] for repeated function application.
|
| [0] https://en.wikipedia.org/wiki/Operational_calculus
| octref wrote:
| If you enjoy this, you might find this meta list on "notation and
| thought" interesting: https://github.com/k-qy/notation
| [deleted]
| samh748 wrote:
| Thank you so much for this!!
|
| The bit on "avoid ambiguity, or introduce useful ambiguity" is
| especially fascinating.
| zetalyrae wrote:
| I found this by Knuth on Iverson's notation interesting:
| https://www.maa.org/sites/default/files/images/images/upload...
| practal wrote:
| Very interesting. I did never really look at the "Concrete
| Mathematics" book, so I missed this take by Knuth on turning
| a formula F into a term [F] by defining it as 1 if F is true,
| and 0 if F is false. Note that this cannot be done in first-
| order logic, as a formula cannot be part of a term. But it is
| not a problem in simply-typed higher-order logic, for
| example, and it is not a problem in abstraction logic,
| either.
| Koshkin wrote:
| Compactness of notation is important, and verbosity of code
| (which I think became widespread since the advent of Java) only
| serves to hurt understanding. Given the right context,
| mathematical notation is easy to understand (and it often
| "computes itself"). Mathematical texts use the "literate" style
| which unfortunately has not found its adoption in software
| industry, even despite the fact that prof. D. Knuth has been
| advocating it since the 1960s...
| throwk8s wrote:
| I find that terseness has a real downside when debugging code.
| If you need to get down to the level of what is actually
| executing, having to unpack all that compact code involves many
| more things than I can keep in my short-term memory.
|
| Compactness is great for things that are true and work, but
| when there's a bug in there somewhere, terse code requires a
| lot of scribbling on paper.
| occamrazor wrote:
| Mathematicians use very terse notation in formulas, but
| accompanied by a lot of natural language text. The equivalent
| in programming would be terse code with long comments and
| documentation.
|
| Many programmers instead see self-documenting code as the
| ideal outcome: maybe not very compact, but virtually free of
| comments (and with documentation at least partially
| autogenerated).
|
| In reality, successful open-source projects tend to have many
| comments in the source code. Often not one-liners, but
| detailed descriptions of functions, their arguments and
| algorithms, motivation for the choice of the implementation
| and so on.
| melling wrote:
| Yesterday, I posted this 1974 interview with Iverson and the
| group who developed APL.
|
| https://news.ycombinator.com/item?id=32173840
|
| I started down the APL/J path last week after watching this APL
| study group with Jeremy Howard of fast.ai:
|
| https://youtu.be/CGpR2ILao5M
|
| https://forums.fast.ai/t/apl-array-programming/97188
| skruger wrote:
| If you haven't seen it, I wrote an intro to modern APL you
| might enjoy if you're starting out:
| https://xpqz.github.io/learnapl
| bfors wrote:
| Does anyone else have a long list of dense material like this
| that you have an intention of going through someday? Do you ever
| end up actually doing it?
| jimmySixDOF wrote:
| One way to go is through a text to speech reader so its the
| kind of thing you can listen to standing in line at the bank.
| Speechify is a good service for bookmarking into a listening
| list.
|
| Ps YMMV a lot based on figures code snippets and anything
| illustrated so not for all content including the featured
| article
| leobg wrote:
| Tried Speechify on my phone and found it terrible. Hated the
| navigation and found the pricing model ridiculous. Deleted it
| and stuck with Voice Dream Reader. It's the first app I
| install on every iPhone, and where I keep all my reading -
| articles, ebooks, and even physical books which I scan just
| so I can read them inside VDR. I can read with my eyes. I can
| listen to the text while doing other things. And I can take
| highlights and notes and export them.
|
| This also is my answer to OP. I save these articles to VDR.
| And when I have time to read or listen to something, I open
| the app. It helps that VDR shows me the length of each
| document in terms of reading time. When you ask me how long a
| particular book was, I'll say "It's a 12 hour book". Really
| helps to put things in perspective.
| goldfeld wrote:
| In the aftermath of a long prostrated war with tabs on browsers
| on tabs (bookmarks for me I know it's where links go to die,
| often literally so) and figuring I rather work analog than
| digital, I came to a system to debrief and save references.
|
| I always save the HN thread when applicable rather than the
| link, because it gives me short hand notation and normalization
| for writing with a pen. Now in a paper notebook I have a few
| pages where each line is a theme, a word etc. Next to it write
| the HN ids (can as well save a comment thread; superbly useful)
| to reference under that theme. Done. If particularly useful I
| can write few words in small print over the id detailing more
| the subject of a link.
|
| This is however done for a set purpose, as reference material
| for writing speculative and science fiction (HN is great for
| ideas and research) and also articles. When and whether I
| finally visit a link is staked on a piece and theme ever
| getting picked by me for writing; I find this is a great
| compromise and more realistic than simply hoarding.
| patcon wrote:
| I keep such a list in Roam, and usually neglect to pluck things
| from it. But it's more that when I go to add something and it's
| already there or has some relation to something already there
| (e.g. same author), I'll often give it more attention
| immediately. It's not the best system, but I suspect it's
| better than never writing it down :)
|
| (This perhaps a bit of an ADHD-specific tactic)
| loquor wrote:
| "Pluck" is a wonderful verb for this action of picking from a
| curated list. Thanks, I will use it from now on.
| aquajet wrote:
| I've been experimenting with a search engine/personal assistant
| to index the long list of material for me, and feed back
| snippets/articles as I want. I guess the analogy is having a
| person "read" the material for me and use it to answer general
| questions I have/point me to the article.
|
| If you want to try it for yourself id be happy to give you beta
| access. I'm still experimenting for the best UX.
| shakezula wrote:
| Funny you mention that, cause I just added this article to a
| longer-ish list of long-form posts I want to read in depth.
|
| I don't make my way to that list as often as I'd like, but I
| have found plane trips and other similar times are great for
| when I want to do something like that. Sitting down with a
| longer blog post and taking notes on a 5 hour flight is oddly
| relaxing. So yes, to answer your question, I do get around to
| it eventually when the post is worthwhile.
| stinkytaco wrote:
| So long. Bookmarks, pocket articles, org-roam notes, things
| jotted in notebooks, I even have an org capture template that
| quickly populates a list of "recommended media" (books, movies,
| etc) from friends and relations. Maintaining my list of things
| to read or watch has become a hobby unto itself.
|
| Every once and a while I go through some[1] of it and ask
| myself "Will I ever actually look at this"? Sometimes there's a
| clear answer, but more often it stays in the list because it
| still looks interesting and I only consume maybe 5-10% of what
| I saved. There's got to be some term for this. Digital hording?
| It makes me anxious to have it and anxious to just delete it.
| There are plenty of times I do remember something I saw and
| wish I could find it again, but I lean too hard into "maybe
| I'll think about this again and want it".
|
| [1]: It's so long I generally lose the will to even evaluate
| the items after a while.
| [deleted]
| [deleted]
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