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Programming as a Way of Thinking

blogs.scientificamerican.com

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Re: Programming as a Way of Thinking

#41

Post by mediocrejoker »

epalmer wrote: post #39

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/ which is startin…

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"

Re: Programming as a Way of Thinking

#42

Post by fasquoika »

misingnoglic wrote: post #3

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.

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.

Re: Programming as a Way of Thinking

#43

Post by marssaxman »

yorwba wrote: post #33
ccleve wrote: post #22

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 rethin…

> ... a paper that uses entirely unnecessary equations, and doesn't bother to define symbols. This practice wastes everyone's time. I agree with you there, notation should be defined, otherwise it doesn't help explain anything. However, consider that for people who are already used to the notation those "unnecessary" equations are actually more compact and precise than reading the accompanying text. What seems diffic…

> However, consider that for people who are already used to the notation those "unnecessary" equations are actually more compact and precise than reading the accompanying text. What seems difficult to you may be easy for someone else, and vice versa.

A struggle for me over the years has been that there does not really seem to be any way of learning the notation, separate from the standard university education process. I'm not about to drop out of my career and go back to school just to learn to read mathematical notation, and it's basically impossible to look up the definitions for obscure symbols with unguessable names, so I simply remain ignorant.

Re: Programming as a Way of Thinking

#44

Post by btilly »

ccleve wrote: post #22

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 rethin…

This article starts to get at an idea that I've had for a while now -- that mathematicians are doing it wrong.

And you're making a typical programmer mistake in thinking that.

Programming is geared towards having people who are experts in programming, but not in a specific subject area, be able to develop and maintain code. Therefore practices like descriptive variable names help provide context to people who cannot be expected to have a deep understanding of their subject.

By contrast mathematics is geared towards having people who are experts in a particular branch of mathematics be able to think and communicate with other experts.

Experts naturally create jargon. Jargon is that it is short, concise and precise. This frees up the mind to be able to consider more complex statements, and removes mental friction from more complex manipulations of those statements. Over a lifetime of expertise, the mental effort of learning the jargon for your specialty gets repaid over and over again.

Mathematics takes this to an extreme. And for professional mathematicians, it is repaid in spades. There is an obvious barrier for generalists who wish to approach a mathematical topic. But your experience of how to be a generalist does not make a mathematician's experience of how to be an effective specialist any less valid.

(Note, this comment is informed by my experience having done mathematics into graduate school, followed by 20 years as a professional programmer.)

Re: Programming as a Way of Thinking

#45

Post by omaranto »

ccleve wrote: post #22

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 rethin…

Is the problem that you want formulas to make sense on their own without the surrounding text? That's not how math is meant to be read. Formulas are reserved for only a few thoughts that are best expressed in that concise notation. The bulk of most mathematical writings is text.

Re: Programming as a Way of Thinking

#46

Post by bryik »

ccleve wrote: post #22

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 rethin…

I took discrete math last semester and part of the course focused on binary relations and their properties (reflexive, symmetric, transitive...etc). I saw students memorize the mathematical definitions for all properties and yet be unable to actually apply them to a particular relation. I suspect many people ended up ignoring the definitions and coped by developing their own or using intuition. This seems like a sign that math is not being communicated effectively.

"Translating" the math into Python code[1] helped me understand what these definition were saying and identify algorithms for exam time. The downside is that it took a lot of time and may not have been as effective as grinding practice questions.

1 - https://nbviewer.jupyter.org/github/bryik/jupyter-notebooks/...

Re: Programming as a Way of Thinking

#47

Post by sqeaky »

btilly wrote: post #44
ccleve wrote: post #22

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 rethin…

This article starts to get at an idea that I've had for a while now -- that mathematicians are doing it wrong. And you're making a typical programmer mistake in thinking that. Programming is geared towards having people who are experts in programming, but not in a specific subject area, be able to develop and maintain code. Therefore practices like descriptive variable names help provide context to people who cannot…

> Programming is geared towards having people who are experts in programming

Programming is getting simpler all the time. Compare modern Python or Ruby to the earliest punch cards. We programmers are going out of way to make it as easy to understand as possible for as many as we can. There are programming languages suitable for children to use while making robots out of Legos.

It is hard to see how variable names vs single character variables creates more friction than it reduces and might even allow domain experts outside of math without higher level math degrees in.

I am curious what other practices are history vs objectively pragmatic requirements. There is much greater pressure on programmers to use time efficiently so we spent a lot of time on pragmatic thinking, and we are nowhere near done. By contrast you sound like many mathematicians and niche experts claiming that you have it solved and know the most efficient way to proceed without even considering an experiment.

Re: Programming as a Way of Thinking

#48

Post by epalmer »

mediocrejoker wrote: post #41
epalmer wrote: post #39

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/ which is startin…

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"

These were testing his thinking. They wanted to find holes in it and in this one professor's view they did not.

Re: Programming as a Way of Thinking

#49

Post by danielpatrick »

osoba wrote: post #40
eldavido wrote: post #30

Earlier quoted context omitted.

It's more standard than people realize. Offhand: x: "some real-valued variable" n: "a countable quantity, usually a total" i: "an index" k: "some kind of constant", often an integer, whose value doesn't change, "c" is also used for this e: almost never used as a variable, it's Euler's number p: some kind of probability, or a prime number, along with p and q t: some kind of parameter, often goes from [0,1] or (0,1) z:…

U, V: vector spaces u, v: elements of vector spaces G, H: groups g, h: elements of groups or g, h: homomorphisms, isomorphisms etc e: group identity K, F: fields I: ideals f: functions (x): sequences x_i: i-th element of a sequence A, B: matrices It all depends on the context it's used of course

This notation has developed over tens to hundreds of years before we had the capabilities of autocomplete and formal typing where a computer can help us write longer names more quickly. This is why single letters became prominent, they were simply easier and faster to write.

But anyone who is serious about writing maintainable code today should be using an IDE where the benefits of susinctness are entirely relegated by intellisense-like tools.

Trading readability for conciseness is near the top of my list of "crimes against future maintainers."

So I had never thought about this in the context of mathematical symbols, but this makes total sense and I'm strongly in favor of relegating mathematical conciseness in favor of readability and specificity.

Re: Programming as a Way of Thinking

#50

Post by gbrown »

danielpatrick wrote: post #49
osoba wrote: post #40

Earlier quoted context omitted.

U, V: vector spaces u, v: elements of vector spaces G, H: groups g, h: elements of groups or g, h: homomorphisms, isomorphisms etc e: group identity K, F: fields I: ideals f: functions (x): sequences x_i: i-th element of a sequence A, B: matrices It all depends on the context it's used of course

This notation has developed over tens to hundreds of years before we had the capabilities of autocomplete and formal typing where a computer can help us write longer names more quickly. This is why single letters became prominent, they were simply easier and faster to write. But anyone who is serious about writing maintainable code today should be using an IDE where the benefits of susinctness are entirely relegated…

If you're talking about mathematically rigorous programming, conciseness and readability go hand in hand. It's actually easier to read a formula with single letter components than a complex one with long descriptive names in many cases. Also, if you're doing that kind of programming, you're also doing a lot of hand or latex computation. Minimizing the visual distance between the code and the convenient handwritten or typeset notation is incredibly important.
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