16 ms·

Programming as a Way of Thinking

322 points by pmcpinto 9y ago

nikki93 9y ago
Nice. I've actually found ideas in programming about modularity and complexity to be ways to approach such complexity in economics, physics, social relationships etc. "Notes on the Synthesis of Form" for example is about design in the abstract and often through examples in architecture but the ideas re: the ontology developed help and are helped by similar ideas in structuring software. This is especially the case when thinking about modeling live simulations like video games. In the vein of "Notes," our normal semantics about the "categories" of thought we have like CS, philosophy etc. might be more "categorical" than needed. Some thing I want to play with more is OS-y scheduling and AI-y thought as ways to think about time management or problem-solving for "humans."
misingnoglic 9y ago
I had a math teacher at my high school who used python and SAGE to teach us pre-calculus as well as programming, computational thinking and some mathematical logic. He was an absolute genius and I wouldn't be where I was if it wasn't for him - unfortunately the school saw him as a threat to the standard model of teaching and drove him insane before he just quit. I hope he's doing ok.
- degenerate 9y ago
  You should try to find him and say hello.
  - misingnoglic 9y ago
    I'll have to email him - I was planning on doing so once I finish my senior honors thesis in CS education (which I'm dedicating to him).
    - demonshalo 9y ago
      I had a teacher that changed me for the better, unfortunately I never got the chance to thank him as he passed away unexpectedly :/ If I were you I would send an email right away. You never know what happens.
- ionforce 9y ago
  Did anyone else, other students, find his methods effective?
  - misingnoglic 9y ago
    For sure - I can think of several other students who took his class and are now doing extremely well in Computer Science careers. Of course I don't have statistics on that or anything, but there's a large group of graduates from my school who were extremely upset when they found out what the school did to him.
- mathgladiator 9y ago
  I've had thoughts like this, using sci-py to teach kids how to hack math. Our education system is kind of sad face.
  - zokier 9y ago
    Have you heard this Wolfram TED talk about the subject: http://blog.wolfram.com/2010/11/23/conrad-wolframs-ted-talk-stop-teaching-calculating-start-teaching-math/ http://blog.wolfram.com/2010/11/23/conrad-wolframs-ted-talk-...
  - misingnoglic 9y ago
    It was definitely cool - he had us writing python functions to estimate the area under a curve (and then visualize it), and other things I don't quite remember at this moment. Once he made us define math functions just based on there being a 0, and a successor function, which happens to be what I'm doing in a graduate Math Logic course at my university.
    - mtempm 9y ago
      That's really incredible. It's sad to see educators like this get pushed out of their field. I had some incredible teachers as well, but also some awful ones. There needs to be greater competitive components added to the education system, such as statistically significant pupil success in education and career outcomes.
- fasquoika 9y ago
  I had a similar experience with my AP calculus teacher in high school. Luckily, he's dramatically overqualified for the teaching position and his classes consistently do exceptionally on standardized tests, so the administration basically gives him a wide berth.
- jodooshi 9y ago
  > People laughed at Seymour Papert in the 1960s, more than half a century ago, when he vividly talked about children using computers as instruments for learning and for enhancing creativity, innovation, and "concretizing" computational thinking.[1] [1] http://papert.org/ http://papert.org/
GrumpyNl 9y ago
The reason we went for Turbo Pascal in the old days was the readability. ( it was C or Pascal )
asavinov 9y ago
The author focuses on the algorithmic and computational aspects of programming. Yet, nowadays programming is much more than this beautiful classical view on programming. Programming is more about describing a complex system by taking into account such aspects as concurrency, cross-cutting concerns, asynchronous events, transactionality, distributed computations etc.
- mannykannot 9y ago
  That is not surprising, as this is not an article about programming in general, but about using programming for teaching in other areas. I would, however, welcome the companion article, "Thinking as a Way of Programming", to balance the prevalent notion that testing is the only way that matters.
- sn9 9y ago
  You might want to check out the author's book titled Think Complexity....
shubhamjain 9y ago
> With a computational approach, we can go “top down”, starting with libraries that implement the most important algorithms, like Fast Fourier Transform. Students can use the algorithms first and learn how they work later. This is exactly how I understood it. Three years back, WebAudio API was a new addition in browsers and I decided I should make something with it. I settled on building a Whistle Detector using a cited research paper as my basis. I barely understood anything in that paper and had to dig into DSP, FFT and other basics to get around. As I had no external help, I struggled plenty but managed to complete it after two weeks [1]. Funny enough, we had a DSP course which never made sense to me. Two weeks into my puzzle I walked away with more useful knowledge than the course ever did. What has always motivated me to learn is the application. I can work tirelessly if there is an interesting thing to build, even if I have to go through mundane theory. But, I find it utterly tedious to learn theory with no immediate goal in mind. [1]: https://stuff.shubhamjain.co/whistlerr/ https://stuff.shubhamjain.co/whistlerr/
- devoply 9y ago
  I feel the same way about math and statistics. It makes much more sense if the knowledge is applied and makes it more interesting and worth learning.
- mtempm 9y ago
  That's a very interesting comment to me because I may be perhaps the opposite. I got a slow and frustrating start learning application development--I wasnt getting it. I felt I was following instructions on how to write esoteric insutructions and not understanding how it worked. I found the book Code by Petzold and read it. Then I discussed some of this with other developers and realized they were even more clueless than I was. It seems some people love theory/understanding while some love building something practical/useful.
  - khedoros1 9y ago
    I learn best when I build something that illustrates the theory. Reading gives me a dim idea, but building something (and freely experimenting on the way) teaches me how it works.
Koshkin 9y ago
> Programming has changed. In first generation languages like FORTRAN and C, the burden was on programmers to translate high-level concepts into code. With modern programming languages—I’ll use Python as an example—we use functions, objects, modules, and libraries to extend the language... This is the first paragraph. I understand that it's just setting the stage, but it makes so little sense by itself that I had to make an effort to continue reading.
- rskar 9y ago
  Yeah, that was an odd start, given that Dr. Downey is a Professor of Computer Science. Even a charitable suggestion that he was looking to keep things as understandable as possible for a wide audience doesn't seem to give much defense. I think he was trying to articulate how much more expressive/extensive programming languages and libraries (and tools?) have gotten over the years, so that a student can get to do something interesting with much less down-and-dirty arithmetic and arcana.
  - kpil 9y ago
    What has changed its the modules and libraries, which has exploded in availability. The actual programming method haven't changed much since the dawn of Unix, or perhaps Lisp - although it took a while to spread.
  - deleted 9y ago
    [deleted]
dreamcompiler 9y ago
Nice work. Of course teaching engineering [0] and physics [1] from a computational perspective is not a new idea. [0] https://en.m.wikipedia.org/wiki/Structure_and_Interpretation_of_Computer_Programs https://en.m.wikipedia.org/wiki/Structure_and_Interpretation... [1] https://en.m.wikipedia.org/wiki/Structure_and_Interpretation_of_Classical_Mechanics https://en.m.wikipedia.org/wiki/Structure_and_Interpretation...
mybrid 9y ago
Opinion is not fact. Given this is Scientific American should we expect something, say, more scientific? Let's put this under the heading, "One Size Does Not Fit All". The underlying assumption of this opinion is that there is only one model to teach too. In the modern era we really need to take into account our differences. In this case, functional versus procedural programming. 1. Write this in a Lisp as functional. 2. Present the functional form as human readable as the given procedural. 3. Conduct a study and gather the data. 4. Present the findings. My experience has taught me that there is subset of the human population who think more naturally in functional programming. But if one model is insufficient? then why would two be? What languages are yet to be invented to meet the needs of the millions of daily programmers? It is time for experimental science to be conducted given the millions of people involved. The path has already been laid out with Usability research that is entirely experimental. It is time to do the hard science on usability of claims of functional and procedural programming languages. It is time to put to rest opinion and one size fits all.
richard_shelton 9y ago
In the beginning of 80s there was a concept called "Programming is the second literacy" [1] introduced by Soviet computer scientist A.P. Ershov. Nowadays it's obvious that there is a huge demand in special programming tools not only for professional programmers (C++, Java..), but for domain experts who use algorithms too (Python, DSLs..). There is a popular objection that "not everyone should be able to code". But it depends on the "to code" definition. A good example here is with game designers. They may not know how to do low-level coding, work with 3d math or use C++ templates. But still for a really good game designer it's very important to have algorithmic thinking and they need to have a tool for testing their algorithmic ideas on the computer. As for Python, there is an issue: it's hard to find examples of good style of Python programming (I think only few of us actually learnt Python with help of textbook). Some time ago I was happy to find notes by Peter Norvig about Python and about comparing Python and Lisp. His code is very elegant, see, for example: http://norvig.com/python-lisp.html http://norvig.com/python-lisp.html [1] http://www.sciencedirect.com/science/article/pii/0165607481900028 http://www.sciencedirect.com/science/article/pii/01656074819...
- jimmaswell 9y ago
  >it's hard to find examples of good style of Python programming I've never really bought that this matters so much as long as you just write sensibly in general. How many python users really make sure to do everything a "pythonic" way?
  - richard_shelton 9y ago
    I think, it depends on how you use Python. 1. "Executable pseudocode", almost a toy language to explain few algorithms in your article. 2. Sysadmin tool. Replacement for shell, a way to write quick throwaway scripts. 3. "A modern Lisp". Universal language for implementing AI algorithms, DSLs etc. I, personally, use 3rd variant. I write quite big programs in Python, for example I made few compilers in it. That's why code quality is important for me here.
    - noobiemcfoob 9y ago
beagle3 9y ago
The canonical, award winning version of these ideas is described in Ken Iverson's seminal 1979 paper 'Notation as a tool of thought'[0] - highly recommended to anyone who finds the ideas discussed interesting (even if they find the scientific american article lacking ... because it is) [0] http://www.jsoftware.com/papers/tot.htm http://www.jsoftware.com/papers/tot.htm
- wmacaluso 9y ago
  Peter Naur's "Programming as Theory Building" (http://pages.cs.wisc.edu/~remzi/Naur.pdf http://pages.cs.wisc.edu/~remzi/Naur.pdf) is also a closely related read.
ccleve 9y ago
This article starts to get at an idea that I've had for a while now -- that mathematicians are doing it wrong. In the software business we learned a long time ago to name our variables properly, name our functions logically, and to control complexity by breaking ideas into modules and then hiding the details inside. If you can't name something, then you don't know what it is, and that tells you that you should rethink your design. Mathematicians don't do that. They name variables "a" or "x", or worse, they use some Greek letter I can't type on my keyboard. They are entirely inconsistent in their use of variables: "phi" or "theta" can mean a zillion different things. I can't tell you the number of times I've read a computer science paper, a paper that uses entirely unnecessary equations, and doesn't bother to define symbols. This practice wastes everyone's time. It's laziness, pure and simple. Mathematics needs a general overhaul. The language of math needs to a complete redesign with a focus on understandability. And the key to it is to force mathematicians to name their variables. Yes, I realize that mathematics deals in abstractions that have little relationship to the outside world, and it makes little sense to call a variable a "dog" or a "car". So what? It just means that we need a new vocabulary, a vocabulary that includes terms like "fourier transform" or "hypotenuse". Pretty much every industry has it's own vocabulary. Chemistry has thousands of terms. Biology even more. Computer science is full of them. Math is full of symbols that have no inherent or well-understood meaning. That should change.
- umanwizard 9y ago
  Are you a mathematician? How much math have you studied?
  - ccleve 9y ago
    I'm a software developer. I need to understand computer science papers to get my work done. I've studied enough. High school and several courses in college. Enough that I should be able to take it from here and learn on my own.
    - vlasev 9y ago
      So let me get this straight...You are mainly a software developer who has an issue with math notation that is meant for mathematicians? Could it perhaps be that you haven't taken enough math to become in tune with how it's done/studied/read? I come from the other direction. I studied math first. And yes, at first I had an issue with the long variable/function names. But soon enough I realized that programming is done quite differently than math. With IDEs and autocompletion, long variable names are not really a problem. One could argue that variable names should be descriptive in programming, because there is a lot more reading involved. Whereas in math, there is a lot more writing/doing involved. I might manipulate a math variable name 1000 times in my head in the process of working on a problem. I might even WRITE it down that many times! In programming, I might READ a variable name 1000 times in debugging.
tigershark 9y ago
Not sure what I was expecting from the title, but for sure not what I read. Maybe I'm quite old now, but working with latches and switches was always a way of thinking. Writing awful BASIC with GOTO and subroutines was not that different. Writing OO code is quite different at first impact but then you discover that it is basically the same way of thinking. The real way of thinking of programmers doesn't have anything to do with the languages, it's more about finding solutions for some problem. If you can't find solutions by yourself, banging your head, it doesn't mean that you have to find a better language for your software, doing nothing in the meantime, it means that you have to start from scratch understanding how to fix things and how to solve problems. If you just wait for the next big thing or the next shiny solution that fixes everything for you then imho programming is not for you.
- yawaramin 9y ago
  Good point, I think it's about finding the 'correct' ways to break small parts together into a solution for your problem. We certainly have some tools to help us along the way--OOP, FP, etc.--but there's definitely an element of craftsmanship to it.
jackmott 9y ago
Some discussion of the efficiency cost of our current favorite higher level languages would be nice. There are things about Python that people love, and I think we should strive to provide that with something more like a 2% performance penalty instead of ~200%+ Languages like Nim are very promising on that front.
blt 9y ago
> The languages I am calling modern are not particularly new; in fact, Python is more than 25 years old. But they are not yet widely taught in high schools and colleges. Seems like a strange claim, because > eight of the top 10 CS departments, and 27 of the top 39, teach Python in introductory CS0 or CS1 courses. [1] [1] https://cacm.acm.org/blogs/blog-cacm/176450-python-is-now-the-most-popular-introductory-teaching-language-at-top-u-s-universities/fulltext https://cacm.acm.org/blogs/blog-cacm/176450-python-is-now-th...
- lazyasciiart 9y ago
  If you posit that python is a better way to teach programming, and that top universities are more likely than average to use better ways of teaching, then that data point may be skewed.
epalmer 9y ago
I saw Allen Downey speak about this concept a year ago in a small forum at the University of Richmond. Several professors in the audience challenged his thinking. I approached one after that and asked what he thought and the answer was basically that Dr. Downey's approach is spot on. This coming from a CS professor. I have just started reading his Think Stats book http://www.allendowney.com/wp/books/ http://www.allendowney.com/wp/books/ which is starting to help me better understand statistics. Not far enough into the book yet to make a complete judgement however. Got to say I like seeing different perspectives on traditional subjects. My youngest is going to Olin next year in Mechanical Engineering and seeing these sorts of articles keeps me excited about her unconventional engineering education at Olin.
- mediocrejoker 9y ago
  I don't quite understand your comment. If the professor you spoke with said "Dr. Downey's approach is spot on" then why would said professor "challenge [Dr. Downey's] thinking"
  - epalmer 9y ago
    These were testing his thinking. They wanted to find holes in it and in this one professor's view they did not.
kensai 9y ago
Also check out his companion blog post: "Python as a way of thinking". Has some nice slides there. (http://allendowney.blogspot.com/2017/04/python-as-way-of-thinking.html http://allendowney.blogspot.com/2017/04/python-as-way-of-thi...)
kccqzy 9y ago
I agree partially with this article. I think programming in a highly expressive language and runtime is a great way to get started exploring and develop intuition. I solved differential equations using mathematica in middle school, long before I even learned how to integrate. I solved instances of the traveling salesman problem long before I understood how complex it is. I played around with images and video files long before I learned anything about signal processing. I find that it is very helpful as a student to be able to learn from bottom up and top down simultaneously. Mathematica is much more forgiving than python if a student has no prior programming experience.
kkylin 9y ago
If you liked this, you may also like https://www.youtube.com/watch?v=6J1vRrozgBg https://www.youtube.com/watch?v=6J1vRrozgBg . PS There is a written version of this, but I could not find a copy that wasn't behind a paywall. Perhaps someone else can.
ethn 9y ago
"The computer revolution is a revolution in the way we think and in the way we express what we think.", SICP, 2nd Edition. The article misses what I believe is the most important point, which is the concept of the abstraction of a function. A function is more than a computer concept: a function is a hammer, a violin, and a microscope; you put an input and you get an output.
- yawaramin 9y ago
  Not only that, but you can then realise that functions are manipulable objects too, and have operations of their own--eta abstraction, reduction, composition, etc., and can be used to build all of modern mathematics pretty much from scratch.
sriku 9y ago
Pete Naur's "programming as theory building" is an excellent read on the topic. Not only on the executable code front, I've also found the type notation used in Haskell to be a great modeling tool using which I can check the consistency of what I'm designing. I'm not talking Coq level proofs here - just an elegant notation that you can use on paper as effectively as in code.
bigger_cheese 9y ago
"With a computational approach, we can go “top down”, starting with libraries that implement the most important algorithms, like Fast Fourier Transform. Students can use the algorithms first and learn how they work later." The "Learn how they work later" part sends out alarm bells to me. I don't have a lot of confidence that students will be particularly motivated to dig into how an algorithm works after their problem has been solved I fear this will lead to a generation of "just use $x package" and people blindly plugging in "magic algorithms" without understanding their choice. "Quicksort for everything" or "include leftpad" if you will... I see it a little in my industry (Engineering) "oh your data is noisy just apply a kalman filter" never mind if it is appropriate or not.
- j2kun 9y ago
  Another aspect, one that I've encountered many times, is that even when someone has to implement the idea from scratch, they don't work to understand it and instead just translate pseudocode. I once had an interview where I was asked to explain why a piece of code (that the interviewer wrote) worked, because the interviewer did not know. A benefit of the bottom up approach, of starting with the math and no reference implementation, is that you are less likely to implement it unless you understand it. And I should stress, these are tradeoffs.
neves 9y ago
BTW, the article author, Allen B. Downey, has a marvelous collection of free technical books: http://greenteapress.com/wp/ http://greenteapress.com/wp/
- neves 9y ago
  And in his books, he does what he prays: teach you complex topics using computer programs. I don't know if it is a good approach of the general population, but for us programmers, it certainly is.
- aloisama 9y ago
  Thanks for linking those!
OrangeTux 9y ago
This post reminds me of Amir Rachum's post about Knowledge Debt[1]. "This is how programming should be taught. You should do stuff way before you can figure out how it works. For a while, you should intentionally be ignorant about distracting details." "You should, intentionally and tactically, decide which piece of information you can do without, for now. But you should also, intentionally and strategically, decide when to pay back that debt." [1]: http://amir.rachum.com/blog/2016/09/15/knowledge-debt/ http://amir.rachum.com/blog/2016/09/15/knowledge-debt/

322 points by pmcpinto 9y ago

Nice. I've actually found ideas in programming about modularity and complexity to be ways to approach such complexity in economics, physics, social relationships etc. "Notes on the Synthesis of Form" for example is about design in the abstract and often through examples in architecture but the ideas re: the ontology developed help and are helped by similar ideas in structuring software. This is especially the case when thinking about modeling live simulations like video games. In the vein of "Notes," our normal semantics about the "categories" of thought we have like CS, philosophy etc. might be more "categorical" than needed. Some thing I want to play with more is OS-y scheduling and AI-y thought as ways to think about time management or problem-solving for "humans."

misingnoglic 9y ago

I had a math teacher at my high school who used python and SAGE to teach us pre-calculus as well as programming, computational thinking and some mathematical logic. He was an absolute genius and I wouldn't be where I was if it wasn't for him - unfortunately the school saw him as a threat to the standard model of teaching and drove him insane before he just quit. I hope he's doing ok.

degenerate 9y ago
You should try to find him and say hello.
- misingnoglic 9y ago
  I'll have to email him - I was planning on doing so once I finish my senior honors thesis in CS education (which I'm dedicating to him).
  - demonshalo 9y ago
    I had a teacher that changed me for the better, unfortunately I never got the chance to thank him as he passed away unexpectedly :/ If I were you I would send an email right away. You never know what happens.
ionforce 9y ago
Did anyone else, other students, find his methods effective?
- misingnoglic 9y ago
  For sure - I can think of several other students who took his class and are now doing extremely well in Computer Science careers. Of course I don't have statistics on that or anything, but there's a large group of graduates from my school who were extremely upset when they found out what the school did to him.
mathgladiator 9y ago
I've had thoughts like this, using sci-py to teach kids how to hack math. Our education system is kind of sad face.
- zokier 9y ago
  Have you heard this Wolfram TED talk about the subject: http://blog.wolfram.com/2010/11/23/conrad-wolframs-ted-talk-stop-teaching-calculating-start-teaching-math/ http://blog.wolfram.com/2010/11/23/conrad-wolframs-ted-talk-...
- misingnoglic 9y ago
  It was definitely cool - he had us writing python functions to estimate the area under a curve (and then visualize it), and other things I don't quite remember at this moment. Once he made us define math functions just based on there being a 0, and a successor function, which happens to be what I'm doing in a graduate Math Logic course at my university.
  - mtempm 9y ago
    That's really incredible. It's sad to see educators like this get pushed out of their field. I had some incredible teachers as well, but also some awful ones. There needs to be greater competitive components added to the education system, such as statistically significant pupil success in education and career outcomes.
fasquoika 9y ago
I had a similar experience with my AP calculus teacher in high school. Luckily, he's dramatically overqualified for the teaching position and his classes consistently do exceptionally on standardized tests, so the administration basically gives him a wide berth.
jodooshi 9y ago
> People laughed at Seymour Papert in the 1960s, more than half a century ago, when he vividly talked about children using computers as instruments for learning and for enhancing creativity, innovation, and "concretizing" computational thinking.[1] [1] http://papert.org/ http://papert.org/

GrumpyNl 9y ago

The reason we went for Turbo Pascal in the old days was the readability. ( it was C or Pascal )

asavinov 9y ago

The author focuses on the algorithmic and computational aspects of programming. Yet, nowadays programming is much more than this beautiful classical view on programming. Programming is more about describing a complex system by taking into account such aspects as concurrency, cross-cutting concerns, asynchronous events, transactionality, distributed computations etc.

mannykannot 9y ago
That is not surprising, as this is not an article about programming in general, but about using programming for teaching in other areas. I would, however, welcome the companion article, "Thinking as a Way of Programming", to balance the prevalent notion that testing is the only way that matters.
sn9 9y ago
You might want to check out the author's book titled Think Complexity....

shubhamjain 9y ago

> With a computational approach, we can go “top down”, starting with libraries that implement the most important algorithms, like Fast Fourier Transform. Students can use the algorithms first and learn how they work later. This is exactly how I understood it. Three years back, WebAudio API was a new addition in browsers and I decided I should make something with it. I settled on building a Whistle Detector using a cited research paper as my basis. I barely understood anything in that paper and had to dig into DSP, FFT and other basics to get around. As I had no external help, I struggled plenty but managed to complete it after two weeks [1]. Funny enough, we had a DSP course which never made sense to me. Two weeks into my puzzle I walked away with more useful knowledge than the course ever did. What has always motivated me to learn is the application. I can work tirelessly if there is an interesting thing to build, even if I have to go through mundane theory. But, I find it utterly tedious to learn theory with no immediate goal in mind. [1]: https://stuff.shubhamjain.co/whistlerr/ https://stuff.shubhamjain.co/whistlerr/

devoply 9y ago
I feel the same way about math and statistics. It makes much more sense if the knowledge is applied and makes it more interesting and worth learning.
mtempm 9y ago
That's a very interesting comment to me because I may be perhaps the opposite. I got a slow and frustrating start learning application development--I wasnt getting it. I felt I was following instructions on how to write esoteric insutructions and not understanding how it worked. I found the book Code by Petzold and read it. Then I discussed some of this with other developers and realized they were even more clueless than I was. It seems some people love theory/understanding while some love building something practical/useful.
- khedoros1 9y ago
  I learn best when I build something that illustrates the theory. Reading gives me a dim idea, but building something (and freely experimenting on the way) teaches me how it works.

Koshkin 9y ago

> Programming has changed. In first generation languages like FORTRAN and C, the burden was on programmers to translate high-level concepts into code. With modern programming languages—I’ll use Python as an example—we use functions, objects, modules, and libraries to extend the language... This is the first paragraph. I understand that it's just setting the stage, but it makes so little sense by itself that I had to make an effort to continue reading.

rskar 9y ago
Yeah, that was an odd start, given that Dr. Downey is a Professor of Computer Science. Even a charitable suggestion that he was looking to keep things as understandable as possible for a wide audience doesn't seem to give much defense. I think he was trying to articulate how much more expressive/extensive programming languages and libraries (and tools?) have gotten over the years, so that a student can get to do something interesting with much less down-and-dirty arithmetic and arcana.
- kpil 9y ago
  What has changed its the modules and libraries, which has exploded in availability. The actual programming method haven't changed much since the dawn of Unix, or perhaps Lisp - although it took a while to spread.
- deleted 9y ago
  [deleted]

dreamcompiler 9y ago

Nice work. Of course teaching engineering [0] and physics [1] from a computational perspective is not a new idea. [0] https://en.m.wikipedia.org/wiki/Structure_and_Interpretation_of_Computer_Programs https://en.m.wikipedia.org/wiki/Structure_and_Interpretation... [1] https://en.m.wikipedia.org/wiki/Structure_and_Interpretation_of_Classical_Mechanics https://en.m.wikipedia.org/wiki/Structure_and_Interpretation...

mybrid 9y ago

Opinion is not fact. Given this is Scientific American should we expect something, say, more scientific? Let's put this under the heading, "One Size Does Not Fit All". The underlying assumption of this opinion is that there is only one model to teach too. In the modern era we really need to take into account our differences. In this case, functional versus procedural programming. 1. Write this in a Lisp as functional. 2. Present the functional form as human readable as the given procedural. 3. Conduct a study and gather the data. 4. Present the findings. My experience has taught me that there is subset of the human population who think more naturally in functional programming. But if one model is insufficient? then why would two be? What languages are yet to be invented to meet the needs of the millions of daily programmers? It is time for experimental science to be conducted given the millions of people involved. The path has already been laid out with Usability research that is entirely experimental. It is time to do the hard science on usability of claims of functional and procedural programming languages. It is time to put to rest opinion and one size fits all.

richard_shelton 9y ago

In the beginning of 80s there was a concept called "Programming is the second literacy" [1] introduced by Soviet computer scientist A.P. Ershov. Nowadays it's obvious that there is a huge demand in special programming tools not only for professional programmers (C++, Java..), but for domain experts who use algorithms too (Python, DSLs..). There is a popular objection that "not everyone should be able to code". But it depends on the "to code" definition. A good example here is with game designers. They may not know how to do low-level coding, work with 3d math or use C++ templates. But still for a really good game designer it's very important to have algorithmic thinking and they need to have a tool for testing their algorithmic ideas on the computer. As for Python, there is an issue: it's hard to find examples of good style of Python programming (I think only few of us actually learnt Python with help of textbook). Some time ago I was happy to find notes by Peter Norvig about Python and about comparing Python and Lisp. His code is very elegant, see, for example: http://norvig.com/python-lisp.html http://norvig.com/python-lisp.html [1] http://www.sciencedirect.com/science/article/pii/0165607481900028 http://www.sciencedirect.com/science/article/pii/01656074819...

jimmaswell 9y ago
>it's hard to find examples of good style of Python programming I've never really bought that this matters so much as long as you just write sensibly in general. How many python users really make sure to do everything a "pythonic" way?
- richard_shelton 9y ago
  I think, it depends on how you use Python. 1. "Executable pseudocode", almost a toy language to explain few algorithms in your article. 2. Sysadmin tool. Replacement for shell, a way to write quick throwaway scripts. 3. "A modern Lisp". Universal language for implementing AI algorithms, DSLs etc. I, personally, use 3rd variant. I write quite big programs in Python, for example I made few compilers in it. That's why code quality is important for me here.
  - noobiemcfoob 9y ago

beagle3 9y ago

The canonical, award winning version of these ideas is described in Ken Iverson's seminal 1979 paper 'Notation as a tool of thought'[0] - highly recommended to anyone who finds the ideas discussed interesting (even if they find the scientific american article lacking ... because it is) [0] http://www.jsoftware.com/papers/tot.htm http://www.jsoftware.com/papers/tot.htm

wmacaluso 9y ago
Peter Naur's "Programming as Theory Building" (http://pages.cs.wisc.edu/~remzi/Naur.pdf http://pages.cs.wisc.edu/~remzi/Naur.pdf) is also a closely related read.

ccleve 9y ago

This article starts to get at an idea that I've had for a while now -- that mathematicians are doing it wrong. In the software business we learned a long time ago to name our variables properly, name our functions logically, and to control complexity by breaking ideas into modules and then hiding the details inside. If you can't name something, then you don't know what it is, and that tells you that you should rethink your design. Mathematicians don't do that. They name variables "a" or "x", or worse, they use some Greek letter I can't type on my keyboard. They are entirely inconsistent in their use of variables: "phi" or "theta" can mean a zillion different things. I can't tell you the number of times I've read a computer science paper, a paper that uses entirely unnecessary equations, and doesn't bother to define symbols. This practice wastes everyone's time. It's laziness, pure and simple. Mathematics needs a general overhaul. The language of math needs to a complete redesign with a focus on understandability. And the key to it is to force mathematicians to name their variables. Yes, I realize that mathematics deals in abstractions that have little relationship to the outside world, and it makes little sense to call a variable a "dog" or a "car". So what? It just means that we need a new vocabulary, a vocabulary that includes terms like "fourier transform" or "hypotenuse". Pretty much every industry has it's own vocabulary. Chemistry has thousands of terms. Biology even more. Computer science is full of them. Math is full of symbols that have no inherent or well-understood meaning. That should change.

umanwizard 9y ago
Are you a mathematician? How much math have you studied?
- ccleve 9y ago
  I'm a software developer. I need to understand computer science papers to get my work done. I've studied enough. High school and several courses in college. Enough that I should be able to take it from here and learn on my own.
  - vlasev 9y ago
    So let me get this straight...You are mainly a software developer who has an issue with math notation that is meant for mathematicians? Could it perhaps be that you haven't taken enough math to become in tune with how it's done/studied/read? I come from the other direction. I studied math first. And yes, at first I had an issue with the long variable/function names. But soon enough I realized that programming is done quite differently than math. With IDEs and autocompletion, long variable names are not really a problem. One could argue that variable names should be descriptive in programming, because there is a lot more reading involved. Whereas in math, there is a lot more writing/doing involved. I might manipulate a math variable name 1000 times in my head in the process of working on a problem. I might even WRITE it down that many times! In programming, I might READ a variable name 1000 times in debugging.

tigershark 9y ago

Not sure what I was expecting from the title, but for sure not what I read. Maybe I'm quite old now, but working with latches and switches was always a way of thinking. Writing awful BASIC with GOTO and subroutines was not that different. Writing OO code is quite different at first impact but then you discover that it is basically the same way of thinking. The real way of thinking of programmers doesn't have anything to do with the languages, it's more about finding solutions for some problem. If you can't find solutions by yourself, banging your head, it doesn't mean that you have to find a better language for your software, doing nothing in the meantime, it means that you have to start from scratch understanding how to fix things and how to solve problems. If you just wait for the next big thing or the next shiny solution that fixes everything for you then imho programming is not for you.

yawaramin 9y ago
Good point, I think it's about finding the 'correct' ways to break small parts together into a solution for your problem. We certainly have some tools to help us along the way--OOP, FP, etc.--but there's definitely an element of craftsmanship to it.

jackmott 9y ago

Some discussion of the efficiency cost of our current favorite higher level languages would be nice. There are things about Python that people love, and I think we should strive to provide that with something more like a 2% performance penalty instead of ~200%+ Languages like Nim are very promising on that front.

blt 9y ago

> The languages I am calling modern are not particularly new; in fact, Python is more than 25 years old. But they are not yet widely taught in high schools and colleges. Seems like a strange claim, because > eight of the top 10 CS departments, and 27 of the top 39, teach Python in introductory CS0 or CS1 courses. [1] [1] https://cacm.acm.org/blogs/blog-cacm/176450-python-is-now-the-most-popular-introductory-teaching-language-at-top-u-s-universities/fulltext https://cacm.acm.org/blogs/blog-cacm/176450-python-is-now-th...

lazyasciiart 9y ago
If you posit that python is a better way to teach programming, and that top universities are more likely than average to use better ways of teaching, then that data point may be skewed.

epalmer 9y ago

I saw Allen Downey speak about this concept a year ago in a small forum at the University of Richmond. Several professors in the audience challenged his thinking. I approached one after that and asked what he thought and the answer was basically that Dr. Downey's approach is spot on. This coming from a CS professor. I have just started reading his Think Stats book http://www.allendowney.com/wp/books/ http://www.allendowney.com/wp/books/ which is starting to help me better understand statistics. Not far enough into the book yet to make a complete judgement however. Got to say I like seeing different perspectives on traditional subjects. My youngest is going to Olin next year in Mechanical Engineering and seeing these sorts of articles keeps me excited about her unconventional engineering education at Olin.

mediocrejoker 9y ago
I don't quite understand your comment. If the professor you spoke with said "Dr. Downey's approach is spot on" then why would said professor "challenge [Dr. Downey's] thinking"
- epalmer 9y ago
  These were testing his thinking. They wanted to find holes in it and in this one professor's view they did not.

kensai 9y ago

Also check out his companion blog post: "Python as a way of thinking". Has some nice slides there. (http://allendowney.blogspot.com/2017/04/python-as-way-of-thinking.html http://allendowney.blogspot.com/2017/04/python-as-way-of-thi...)

kccqzy 9y ago

I agree partially with this article. I think programming in a highly expressive language and runtime is a great way to get started exploring and develop intuition. I solved differential equations using mathematica in middle school, long before I even learned how to integrate. I solved instances of the traveling salesman problem long before I understood how complex it is. I played around with images and video files long before I learned anything about signal processing. I find that it is very helpful as a student to be able to learn from bottom up and top down simultaneously. Mathematica is much more forgiving than python if a student has no prior programming experience.

kkylin 9y ago

If you liked this, you may also like https://www.youtube.com/watch?v=6J1vRrozgBg https://www.youtube.com/watch?v=6J1vRrozgBg . PS There is a written version of this, but I could not find a copy that wasn't behind a paywall. Perhaps someone else can.

ethn 9y ago

"The computer revolution is a revolution in the way we think and in the way we express what we think.", SICP, 2nd Edition. The article misses what I believe is the most important point, which is the concept of the abstraction of a function. A function is more than a computer concept: a function is a hammer, a violin, and a microscope; you put an input and you get an output.

yawaramin 9y ago
Not only that, but you can then realise that functions are manipulable objects too, and have operations of their own--eta abstraction, reduction, composition, etc., and can be used to build all of modern mathematics pretty much from scratch.

sriku 9y ago

Pete Naur's "programming as theory building" is an excellent read on the topic. Not only on the executable code front, I've also found the type notation used in Haskell to be a great modeling tool using which I can check the consistency of what I'm designing. I'm not talking Coq level proofs here - just an elegant notation that you can use on paper as effectively as in code.

bigger_cheese 9y ago

"With a computational approach, we can go “top down”, starting with libraries that implement the most important algorithms, like Fast Fourier Transform. Students can use the algorithms first and learn how they work later." The "Learn how they work later" part sends out alarm bells to me. I don't have a lot of confidence that students will be particularly motivated to dig into how an algorithm works after their problem has been solved I fear this will lead to a generation of "just use $x package" and people blindly plugging in "magic algorithms" without understanding their choice. "Quicksort for everything" or "include leftpad" if you will... I see it a little in my industry (Engineering) "oh your data is noisy just apply a kalman filter" never mind if it is appropriate or not.

j2kun 9y ago
Another aspect, one that I've encountered many times, is that even when someone has to implement the idea from scratch, they don't work to understand it and instead just translate pseudocode. I once had an interview where I was asked to explain why a piece of code (that the interviewer wrote) worked, because the interviewer did not know. A benefit of the bottom up approach, of starting with the math and no reference implementation, is that you are less likely to implement it unless you understand it. And I should stress, these are tradeoffs.

neves 9y ago

BTW, the article author, Allen B. Downey, has a marvelous collection of free technical books: http://greenteapress.com/wp/ http://greenteapress.com/wp/

neves 9y ago
And in his books, he does what he prays: teach you complex topics using computer programs. I don't know if it is a good approach of the general population, but for us programmers, it certainly is.
aloisama 9y ago
Thanks for linking those!

OrangeTux 9y ago

This post reminds me of Amir Rachum's post about Knowledge Debt[1]. "This is how programming should be taught. You should do stuff way before you can figure out how it works. For a while, you should intentionally be ignorant about distracting details." "You should, intentionally and tactically, decide which piece of information you can do without, for now. But you should also, intentionally and strategically, decide when to pay back that debt." [1]: http://amir.rachum.com/blog/2016/09/15/knowledge-debt/ http://amir.rachum.com/blog/2016/09/15/knowledge-debt/