7 ms·

Dijkstra: On the cruelty of really teaching computer science (1988) [pdf]

111 points by jackhammer2022 13y ago

zeeboo 13y ago
His page numbers are zero indexed. Cute. I would have loved to take his proposal for an introduction to computer science course.
- chas 13y ago
  You might also be interested in CMU's introductory curriculum in the same vein which is somewhat less extreme and has a particular focus on parallelism as the standard case of computing. http://existentialtype.wordpress.com/2012/08/17/intro-curriculum-update/ http://existentialtype.wordpress.com/2012/08/17/intro-curric...
- EmielMols 13y ago
  EWD831 explains zero indexing. http://www.cs.utexas.edu/users/EWD/ewd08xx/EWD831.PDF http://www.cs.utexas.edu/users/EWD/ewd08xx/EWD831.PDF
- mykhamill 13y ago
  However after the list he states "And with the sixth example I have reached imperceptibly but unavoidably, the most hairy part of this talk: Educational consequences." which is incorrect as item 6 is actually the 7th example. Zero based indexing requires that the counter be updated after appending and the counter be referenced for the cardinal value of an item. (ie. item 6 is 7th in the list).
beala 13y ago
Transcription: http://www.cs.utexas.edu/~EWD/transcriptions/EWD10xx/EWD1036.html http://www.cs.utexas.edu/~EWD/transcriptions/EWD10xx/EWD1036...
- deviltry 13y ago
  Thank you! American(?) writing style where letters do not connect is just too wierd.
GuiA 13y ago
This EWD is mind blowing in its beauty. It's 30 pages, but 30 pages that you won't regret reading. I love computer science and teaching it is some of the most fun I've ever had. With a lot of practice, you can get across concepts such as computability and turing machines to the non-mathematically initiated within the duration of a party, and it's greatly satisfying. (yes I am a lot of fun to be around) The rest of the EWD notes are highly recommended. (also it's weird to see an academic write in script). Side question: do any other HNers keep notes in written form? I still do it, using a fountain pen, and am often poked fun at by colleagues :(
- ics 13y ago
  Re: your side question, sure![0] I would love to use a fountain pen primarily but the nib that I want is out of my budget for now. I have a couple Muji fountain pens though which are great for the price, just far too thick for me to use regularly. [0]: http://academic.ianclarksmith.com/Coursera/DesignArtifacts/content/demo1.jpg http://academic.ianclarksmith.com/Coursera/DesignArtifacts/c... (Uniball .28 and mechanical pencil on blank 4x6 card) By now I probably have thousands of these scattered throughout books (I use them as bookmarks while taking notes) or in boxes. They're not particularly well sorted except for being vaguely chronological. I have a decent stash of notebooks as well but haven't used them since it was a requirement for school except for a single pocket notebook that gets filled roughly once a year.
- jl6 13y ago
  I keep extensive paper notes, mostly in sequential "lab book" style, pages dated and numbered, with a different colour pen for each day of the week. I don't fuss too much over structure beyond that, and anything for wider distribution I write up on a computer. I've seen people struggle with tablets and laptops for note taking, but I find they are some way off the free-flowing UX of pen and paper.
- ryanobjc 13y ago
  I use fountain pens and paper to take notes in meetings all the time. I am trying to do more "thinking on paper", and I wouldn't give up the fountain pen for anything. Keep at it!
- 13y ago
Pitarou 13y ago
How can a human write that much good prose without scribbling things out?
- rcthompson 13y ago
  Presumably this is a final draft.
- elwell 13y ago
  See page #7
stiff 13y ago
I think people are attracted more to the form of the EWDs and to it's melancholic tone, rather than to the content itself, which is confirmed by the huge popularity of the EWDs as compared to "The discipline of programming", which is the technical exposition of what Dijkstra really is proposing in the EWDs. As almost all of Dijkstra's writing, this piece here is a plea for teaching formal methods. It's nicely written I admit, but it is also unbelievably smug and disconnected from reality. Even in physics or mathematics, which are obviously much more mathematically tractable than computer science, people do not do significant new things by using only formal methods. In fact, the technical achievement Dijkstra is most known for, Dijkstra's algorithm, was not invented using formal methods, but like most discoveries ever it occurred in a flash of insight after a long period of thinking, as he said in an interview. No matter how much one loves rigour, the dream of formalizing all reasoning has turned out to be a pipe-dream, as evidenced for example by the failure of the Hilbert program, and people everywhere proceed about their business as usual. Mathematics is not, after all, just the manipulation of a string of symbols, and neither is Computer Science, even if all computers do is exactly this, because we humans are complex beings, largely driven by emotions, not consciously aware of all the reasoning processes going on, that are often reasoning in "fuzzy" ways (and frequently with good effects), as opposed to being machines executing chains of logical inferences. In fact, people are born with very different internal worlds, some people are really good at symbol manipulation, algebra, and language, their daily thinking consists of "talking to themselves", while some people naturally think by imagining pictures and having various loose sensual impressions, among the latter for example the great mathematician Poincare. Was Poincare in need of someone to "really teach him mathematics"? Unfortunately I think Dijkstra assumed everyone is identical to him. Before preaching this too much, look at the practical implementations of his ideas on this, for example have a look at him lecturing on a technical topic: http://www.youtube.com/watch?v=qNCAFcAbSTg http://www.youtube.com/watch?v=qNCAFcAbSTg or read "A discipline of programming". As nice as the EWD prose is, I honestly can't stand the man talking about anything technical for more than 5 minutes. The more concrete the EWDs get the worse they are. For some perspective on how science really gets done, as opposed to people's romantic images of how it is done, I recommend "The Sleepwalkers" by Arthur Koestler, about the Copernican revolution, and "The psychology of mathematical invention" by Hadamard.
- deleted 13y ago
ics 13y ago
Was this post inspired by this post (http://www.reddit.com/r/compsci/comments/1rxfze/if_you_liked_ew_dijkstras_paper_on_the_cruelty_of/ http://www.reddit.com/r/compsci/comments/1rxfze/if_you_liked...) on r/compsci by any chance? I didn't read much of the discussion there but the other links are interesting and things which I hadn't seen before.
- 10098 13y ago
  I think it's the opposite, i.e. the reddit post was inspired by the paper, which I read yesterday... but I couldn't have found the link on HN, because it has only appeared today, so it must mean that I orginally found it on reddit. Now I'm confused...
elwell 13y ago
Interestingly, I found the handwriting to more readable than most computer fonts; that is, very visually consumable.
- sgloutnikov 13y ago
  That was the fist thing that jumped out at me. Amazing handwriting!
  - cpg 13y ago
    His handwriting looks beautiful! I loved it and emailed Prof. Dijkstra during the brief time that he finally had email (I got a graduate degree from his department and attended some of his classes). I asked him for permission to one day create a font from his handwriting, not really expecting a response. However, he did eventually reply, granting me the permission to do so. I commissioned the font and it worked nice. It was distributed briefly and it may still be out there (I see one or two are found out there). My original copy may be in old backups. One day I will find it and update it! Edit: found the email reply! He retired in 11/1999 and passed away in 8/2002 Austin, Tuesday 11 April 2000 Dear Dr. Puchol, If a competent designer can use my handwriting as a source of inspiration, that is fine with me. Thank you for asking my permission, which is granted with pleasure. With my greetings and best wishes, yours ever, Edsger W.Dijkstra
10098 13y ago
I know Dijkstra's genius and all, but his papers are just so unpleasant. First, I hate his verbose style and second, I hate his attitude. "The effort of using machines to mimic the human mind has always struck me as rather silly. I would rather use them to mimic something better." Jesus, could he be any more smug?
- edejong 13y ago
  Depends on how you read it. You could mimic structures from society or nature. The isolated human mind is quite a useless thing.
- marcosdumay 13y ago
  > Jesus, could he be any more smug? Funny that I think that statement is extremely humble.
  - scaramanga 13y ago
    Indeed, the very idea that your fly by the seat of your pants intuition, memory and senses cannot be trusted is the foundational presentiment that brought us science.
randomsearch 13y ago
Who is Dijkstra to espouse about the best way of teaching mathematics to primary school children? I think it would be equivalent to a researcher in education deciding they know the best way to design a calculus. The manner in which Dijkstra writes about this is very off-putting - it sounds arrogant and one-sided, dismissive. In fact he comes across as ignorant, which of course, he is, in this area. Worryingly, I see a lot of similar writing in CS blogs. Often authors present as fact their opinions on a topic that they are not knowledgeable about. When I read something like that, I look for the balance in their argument. If they say "well, what are the good sides to teaching by analogy? When does it work best? What is the evidence that teaching basic arithmetic is done well?" then I begin to take them seriously. [edit: typo]
- Jtsummers 13y ago
  Where in this essay does he "espouse about the best way of teaching mathematics to primary school children"? It seems to be about CS education, not primary school math.
  - randomsearch 13y ago
    Page 5.
elwell 13y ago
My point today is that, if we wish to count lines of code, we should not regard them as "lines produced" but as "lines spent"
ColinWright 13y ago
It's interesting to see how attitudes to this EWD have changed over the years. Here are some of the previous submissions with comments: https://news.ycombinator.com/item?id=43978 https://news.ycombinator.com/item?id=43978 : A few comments https://news.ycombinator.com/item?id=1666445 https://news.ycombinator.com/item?id=1666445 : Many comments https://news.ycombinator.com/item?id=3553983 https://news.ycombinator.com/item?id=3553983 : Many comments In the earlier threads there are two main voices: "Where can I learn more about this," and "It's useful to see the different perspective." Both say that there are many nuggets of wisdom to be mined, even when they don't agree. There are also a few who dissent and say it's irrelevant, impractical, and inapplicable. Even in 3553983 where the top comment says it's largely irrelevant there is a useful dialogue discussing the ideas, and how they can be made to work, or at least how we can learn from them in today's context. In contrast, in this thread so far we've mostly had comments about the hand-writing, and complete dismissal of the ideas. So far there's very little attempt to say: "OK, times have changed, but can we learn something from this?" So I ask - Can we? Are there nuggets to be mined? Or are you convinced that you really do know better, and have nothing to learn from it. I'm still learning. ======== For reference, other submissions, mostly without comments: https://news.ycombinator.com/item?id=6701607 https://news.ycombinator.com/item?id=6701607 https://news.ycombinator.com/item?id=2122826 https://news.ycombinator.com/item?id=2122826 https://news.ycombinator.com/item?id=2090256 https://news.ycombinator.com/item?id=2090256 https://news.ycombinator.com/item?id=1989473 https://news.ycombinator.com/item?id=1989473 https://news.ycombinator.com/item?id=383210 https://news.ycombinator.com/item?id=383210
- crististm 13y ago
  The audience is self-selected. The ones that don't know any better see only a condescend tone instead of the material. They don't get the difference between "lines spent" and "lines produced" and they don't know that computers were used to "compute" and thus the formalism was absolutely necessary to trust the result. What we write today is WoW and stuff we don't need formalism to prove they don't crash - because, you know, who cares about that? Dijkstra comes from a time were you could reuse a piece of software and build upon it because you could understand it. Today nobody does it because the software is "disposable". Who cares about proving a piece of future garbage?
kaivi 13y ago
A wonderful read from a badass scientist. Here is a good nugget of wisdom: Software engineering, of course, presents itself as another worthy cause, but that is eyewash: if you carefully read its literature and analyse what its devotees actually do, you will discover that software engineering has accepted as its charter "How to program if you cannot".
micro_cam 13y ago
As someone who focused on proof based mathematics in collage and is largely a self taught programer I think this proposal has merit. Begin forced to confront abstraction and formalism without any crutches as a freshman in college changed and expanded the way I thought. Learning to write down a correct proof without an external way of verifying it is an experience everyone should have. However I think this needs to be coupled with an introduction to the concrete at a younger age. In mathematics we teach arithmetic to young children then step up the ladder of abstraction to high school algebra, simple proofs and linear algebra before eventually exposing them to abstract algebra (ie group theory etc). Teaching abstract algebra first would make theoretical sense but the mind tends to need to know at least one example of something before it accepts the abstraction. I imagine a playful introduction to programing for young children coupled with a strong course in formalism for young adults could produce some great programers. Though, as with the proof based math series I took, I'm sure there would also be loads of freshman drop outs/transfers to more applied courses. I also agree with others that insight rarely comes from pure formalism. The point of learning these things is to expand the way your mind works allowing you to think about abstract objects and allowing you to verify insight when it does come. For me Charlie Parker sums up the necessity of a formal education even if it is not explicitly used in practice: "Master your instrument, master the music & then forget all that & just play."
- mathattack 13y ago
  For me Charlie Parker sums up the necessity of a formal education even if it is not explicitly used in practice: "Master your instrument, master the music & then forget all that & just play." How very true across so many aspects of life! Science doesn't happen through formalism. People learn the body of material that's been proven, then they get new intuitions, then afterwards they try to formally prove their insight. This isn't entirely inconsistent with EDW either. A lot of his point is that programmers need to know how to think symbolically, and if you truly prove the correctness of things, you can build the base of knowledge on top of it. If not, you're frequently wondering why things don't work.
mrcactu5 13y ago
I am glad he was able to articulate why some types of change are accepted and other changes rejected with hostility -- that some new things can be interpreted through analogies with previous experience. It is the difference between "change" and change, "thinking" and thinking.

111 points by jackhammer2022 13y ago

His page numbers are zero indexed. Cute. I would have loved to take his proposal for an introduction to computer science course.

chas 13y ago
You might also be interested in CMU's introductory curriculum in the same vein which is somewhat less extreme and has a particular focus on parallelism as the standard case of computing. http://existentialtype.wordpress.com/2012/08/17/intro-curriculum-update/ http://existentialtype.wordpress.com/2012/08/17/intro-curric...
EmielMols 13y ago
EWD831 explains zero indexing. http://www.cs.utexas.edu/users/EWD/ewd08xx/EWD831.PDF http://www.cs.utexas.edu/users/EWD/ewd08xx/EWD831.PDF
mykhamill 13y ago
However after the list he states "And with the sixth example I have reached imperceptibly but unavoidably, the most hairy part of this talk: Educational consequences." which is incorrect as item 6 is actually the 7th example. Zero based indexing requires that the counter be updated after appending and the counter be referenced for the cardinal value of an item. (ie. item 6 is 7th in the list).

beala 13y ago

Transcription: http://www.cs.utexas.edu/~EWD/transcriptions/EWD10xx/EWD1036.html http://www.cs.utexas.edu/~EWD/transcriptions/EWD10xx/EWD1036...

deviltry 13y ago
Thank you! American(?) writing style where letters do not connect is just too wierd.

GuiA 13y ago

This EWD is mind blowing in its beauty. It's 30 pages, but 30 pages that you won't regret reading. I love computer science and teaching it is some of the most fun I've ever had. With a lot of practice, you can get across concepts such as computability and turing machines to the non-mathematically initiated within the duration of a party, and it's greatly satisfying. (yes I am a lot of fun to be around) The rest of the EWD notes are highly recommended. (also it's weird to see an academic write in script). Side question: do any other HNers keep notes in written form? I still do it, using a fountain pen, and am often poked fun at by colleagues :(

ics 13y ago
Re: your side question, sure![0] I would love to use a fountain pen primarily but the nib that I want is out of my budget for now. I have a couple Muji fountain pens though which are great for the price, just far too thick for me to use regularly. [0]: http://academic.ianclarksmith.com/Coursera/DesignArtifacts/content/demo1.jpg http://academic.ianclarksmith.com/Coursera/DesignArtifacts/c... (Uniball .28 and mechanical pencil on blank 4x6 card) By now I probably have thousands of these scattered throughout books (I use them as bookmarks while taking notes) or in boxes. They're not particularly well sorted except for being vaguely chronological. I have a decent stash of notebooks as well but haven't used them since it was a requirement for school except for a single pocket notebook that gets filled roughly once a year.
jl6 13y ago
I keep extensive paper notes, mostly in sequential "lab book" style, pages dated and numbered, with a different colour pen for each day of the week. I don't fuss too much over structure beyond that, and anything for wider distribution I write up on a computer. I've seen people struggle with tablets and laptops for note taking, but I find they are some way off the free-flowing UX of pen and paper.
ryanobjc 13y ago
I use fountain pens and paper to take notes in meetings all the time. I am trying to do more "thinking on paper", and I wouldn't give up the fountain pen for anything. Keep at it!
13y ago

Pitarou 13y ago

How can a human write that much good prose without scribbling things out?

rcthompson 13y ago
Presumably this is a final draft.
elwell 13y ago
See page #7

stiff 13y ago

I think people are attracted more to the form of the EWDs and to it's melancholic tone, rather than to the content itself, which is confirmed by the huge popularity of the EWDs as compared to "The discipline of programming", which is the technical exposition of what Dijkstra really is proposing in the EWDs. As almost all of Dijkstra's writing, this piece here is a plea for teaching formal methods. It's nicely written I admit, but it is also unbelievably smug and disconnected from reality. Even in physics or mathematics, which are obviously much more mathematically tractable than computer science, people do not do significant new things by using only formal methods. In fact, the technical achievement Dijkstra is most known for, Dijkstra's algorithm, was not invented using formal methods, but like most discoveries ever it occurred in a flash of insight after a long period of thinking, as he said in an interview. No matter how much one loves rigour, the dream of formalizing all reasoning has turned out to be a pipe-dream, as evidenced for example by the failure of the Hilbert program, and people everywhere proceed about their business as usual. Mathematics is not, after all, just the manipulation of a string of symbols, and neither is Computer Science, even if all computers do is exactly this, because we humans are complex beings, largely driven by emotions, not consciously aware of all the reasoning processes going on, that are often reasoning in "fuzzy" ways (and frequently with good effects), as opposed to being machines executing chains of logical inferences. In fact, people are born with very different internal worlds, some people are really good at symbol manipulation, algebra, and language, their daily thinking consists of "talking to themselves", while some people naturally think by imagining pictures and having various loose sensual impressions, among the latter for example the great mathematician Poincare. Was Poincare in need of someone to "really teach him mathematics"? Unfortunately I think Dijkstra assumed everyone is identical to him. Before preaching this too much, look at the practical implementations of his ideas on this, for example have a look at him lecturing on a technical topic: http://www.youtube.com/watch?v=qNCAFcAbSTg http://www.youtube.com/watch?v=qNCAFcAbSTg or read "A discipline of programming". As nice as the EWD prose is, I honestly can't stand the man talking about anything technical for more than 5 minutes. The more concrete the EWDs get the worse they are. For some perspective on how science really gets done, as opposed to people's romantic images of how it is done, I recommend "The Sleepwalkers" by Arthur Koestler, about the Copernican revolution, and "The psychology of mathematical invention" by Hadamard.

deleted 13y ago

ics 13y ago

Was this post inspired by this post (http://www.reddit.com/r/compsci/comments/1rxfze/if_you_liked_ew_dijkstras_paper_on_the_cruelty_of/ http://www.reddit.com/r/compsci/comments/1rxfze/if_you_liked...) on r/compsci by any chance? I didn't read much of the discussion there but the other links are interesting and things which I hadn't seen before.

10098 13y ago
I think it's the opposite, i.e. the reddit post was inspired by the paper, which I read yesterday... but I couldn't have found the link on HN, because it has only appeared today, so it must mean that I orginally found it on reddit. Now I'm confused...

elwell 13y ago

Interestingly, I found the handwriting to more readable than most computer fonts; that is, very visually consumable.

sgloutnikov 13y ago
That was the fist thing that jumped out at me. Amazing handwriting!
- cpg 13y ago
  His handwriting looks beautiful! I loved it and emailed Prof. Dijkstra during the brief time that he finally had email (I got a graduate degree from his department and attended some of his classes). I asked him for permission to one day create a font from his handwriting, not really expecting a response. However, he did eventually reply, granting me the permission to do so. I commissioned the font and it worked nice. It was distributed briefly and it may still be out there (I see one or two are found out there). My original copy may be in old backups. One day I will find it and update it! Edit: found the email reply! He retired in 11/1999 and passed away in 8/2002 Austin, Tuesday 11 April 2000 Dear Dr. Puchol, If a competent designer can use my handwriting as a source of inspiration, that is fine with me. Thank you for asking my permission, which is granted with pleasure. With my greetings and best wishes, yours ever, Edsger W.Dijkstra

10098 13y ago

I know Dijkstra's genius and all, but his papers are just so unpleasant. First, I hate his verbose style and second, I hate his attitude. "The effort of using machines to mimic the human mind has always struck me as rather silly. I would rather use them to mimic something better." Jesus, could he be any more smug?

edejong 13y ago
Depends on how you read it. You could mimic structures from society or nature. The isolated human mind is quite a useless thing.
marcosdumay 13y ago
> Jesus, could he be any more smug? Funny that I think that statement is extremely humble.
- scaramanga 13y ago
  Indeed, the very idea that your fly by the seat of your pants intuition, memory and senses cannot be trusted is the foundational presentiment that brought us science.

randomsearch 13y ago

Who is Dijkstra to espouse about the best way of teaching mathematics to primary school children? I think it would be equivalent to a researcher in education deciding they know the best way to design a calculus. The manner in which Dijkstra writes about this is very off-putting - it sounds arrogant and one-sided, dismissive. In fact he comes across as ignorant, which of course, he is, in this area. Worryingly, I see a lot of similar writing in CS blogs. Often authors present as fact their opinions on a topic that they are not knowledgeable about. When I read something like that, I look for the balance in their argument. If they say "well, what are the good sides to teaching by analogy? When does it work best? What is the evidence that teaching basic arithmetic is done well?" then I begin to take them seriously. [edit: typo]

Jtsummers 13y ago
Where in this essay does he "espouse about the best way of teaching mathematics to primary school children"? It seems to be about CS education, not primary school math.
- randomsearch 13y ago
  Page 5.

elwell 13y ago

My point today is that, if we wish to count lines of code, we should not regard them as "lines produced" but as "lines spent"

ColinWright 13y ago

It's interesting to see how attitudes to this EWD have changed over the years. Here are some of the previous submissions with comments: https://news.ycombinator.com/item?id=43978 https://news.ycombinator.com/item?id=43978 : A few comments https://news.ycombinator.com/item?id=1666445 https://news.ycombinator.com/item?id=1666445 : Many comments https://news.ycombinator.com/item?id=3553983 https://news.ycombinator.com/item?id=3553983 : Many comments In the earlier threads there are two main voices: "Where can I learn more about this," and "It's useful to see the different perspective." Both say that there are many nuggets of wisdom to be mined, even when they don't agree. There are also a few who dissent and say it's irrelevant, impractical, and inapplicable. Even in 3553983 where the top comment says it's largely irrelevant there is a useful dialogue discussing the ideas, and how they can be made to work, or at least how we can learn from them in today's context. In contrast, in this thread so far we've mostly had comments about the hand-writing, and complete dismissal of the ideas. So far there's very little attempt to say: "OK, times have changed, but can we learn something from this?" So I ask - Can we? Are there nuggets to be mined? Or are you convinced that you really do know better, and have nothing to learn from it. I'm still learning. ======== For reference, other submissions, mostly without comments: https://news.ycombinator.com/item?id=6701607 https://news.ycombinator.com/item?id=6701607 https://news.ycombinator.com/item?id=2122826 https://news.ycombinator.com/item?id=2122826 https://news.ycombinator.com/item?id=2090256 https://news.ycombinator.com/item?id=2090256 https://news.ycombinator.com/item?id=1989473 https://news.ycombinator.com/item?id=1989473 https://news.ycombinator.com/item?id=383210 https://news.ycombinator.com/item?id=383210

crististm 13y ago
The audience is self-selected. The ones that don't know any better see only a condescend tone instead of the material. They don't get the difference between "lines spent" and "lines produced" and they don't know that computers were used to "compute" and thus the formalism was absolutely necessary to trust the result. What we write today is WoW and stuff we don't need formalism to prove they don't crash - because, you know, who cares about that? Dijkstra comes from a time were you could reuse a piece of software and build upon it because you could understand it. Today nobody does it because the software is "disposable". Who cares about proving a piece of future garbage?

kaivi 13y ago

A wonderful read from a badass scientist. Here is a good nugget of wisdom: Software engineering, of course, presents itself as another worthy cause, but that is eyewash: if you carefully read its literature and analyse what its devotees actually do, you will discover that software engineering has accepted as its charter "How to program if you cannot".

micro_cam 13y ago

As someone who focused on proof based mathematics in collage and is largely a self taught programer I think this proposal has merit. Begin forced to confront abstraction and formalism without any crutches as a freshman in college changed and expanded the way I thought. Learning to write down a correct proof without an external way of verifying it is an experience everyone should have. However I think this needs to be coupled with an introduction to the concrete at a younger age. In mathematics we teach arithmetic to young children then step up the ladder of abstraction to high school algebra, simple proofs and linear algebra before eventually exposing them to abstract algebra (ie group theory etc). Teaching abstract algebra first would make theoretical sense but the mind tends to need to know at least one example of something before it accepts the abstraction. I imagine a playful introduction to programing for young children coupled with a strong course in formalism for young adults could produce some great programers. Though, as with the proof based math series I took, I'm sure there would also be loads of freshman drop outs/transfers to more applied courses. I also agree with others that insight rarely comes from pure formalism. The point of learning these things is to expand the way your mind works allowing you to think about abstract objects and allowing you to verify insight when it does come. For me Charlie Parker sums up the necessity of a formal education even if it is not explicitly used in practice: "Master your instrument, master the music & then forget all that & just play."

mathattack 13y ago
For me Charlie Parker sums up the necessity of a formal education even if it is not explicitly used in practice: "Master your instrument, master the music & then forget all that & just play." How very true across so many aspects of life! Science doesn't happen through formalism. People learn the body of material that's been proven, then they get new intuitions, then afterwards they try to formally prove their insight. This isn't entirely inconsistent with EDW either. A lot of his point is that programmers need to know how to think symbolically, and if you truly prove the correctness of things, you can build the base of knowledge on top of it. If not, you're frequently wondering why things don't work.

mrcactu5 13y ago

I am glad he was able to articulate why some types of change are accepted and other changes rejected with hostility -- that some new things can be interpreted through analogies with previous experience. It is the difference between "change" and change, "thinking" and thinking.