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> Programming is Language. And half of mathematics is more or less the study of formal languages and their consequences? You can say that they're different in

by tel 12y ago

> Programming is Language. And half of mathematics is more or less the study of formal languages and their consequences? You can say that they're different in order to keep people who are scared of math from projecting those feelings to programming. Or you can say they're the same to draw deep insight between programming and one of the oldest fields of study of human kind. I find that people tend to reject the relation when they know of math as calculus, i.e. the analysis side of mathematics. When they bump into the algebra/proof side of it the connection is more clear. As a corollary, people who are "good at language" are probably going to be quite good at algebra/logic mathematics as well if they approached it from the right angle.

jordigh 12y ago
> And half of mathematics is more or less the study of formal languages and their consequences? No, just a small fraction is: http://www.ams.org/mathscinet/msc/msc2010.html?t=&s=68Q45++Formal+languages+and+automata&ls=s http://www.ams.org/mathscinet/msc/msc2010.html?t=&s=68Q45++F... This is but a branch of a branch (computer science): https://en.wikipedia.org/wiki/Mathematics_Subject_Classification#Applied_mathematics_.2F_other https://en.wikipedia.org/wiki/Mathematics_Subject_Classifica...
- tel 12y ago
  That's a really restrictive and explicit demarcation of "formal language". I'd happily describe logic as formal language and then go hunting for places which seem to have non-trivial interactions with logic.
  - jordigh 12y ago
    Well, if you define it to be broad enough, then you are correct by definition. My point here is that there is a big, broad cultural gap between mathematics and programming that you are not going to breach merely by saying that a lot of mathematics is about formal languages (in the nontechnical sense of "formal language"). Far from it. Most of mathematics does not talk about formal languages and most of mathematics itself uses very informal language. It looks forbidding to outsiders, but there are many linguistic styles, fashions, abbreviations, shorthands, jokes, puns, and conventions in mathematical writing, very little of which is easy to algorithmically feed into a computer.
    - tel 12y ago
      Sure, and I'm not claiming that you must unify them. Or that you can't. I'm also not saying that the language of mathematics is a formal language, but instead that it shares structure with them. The very notion of the interplay between a theory and its model is not dissimilar. I'm not trying to absolve a cultural gap. Nor am I trying to claim that if you dropped a mathematician into a programming role they would thrive, or visa versa. I'm simply trying to claim that there is a whole lot of similarity between the two and refutations of that are silly. Seeking a clear-cut demarcation between fields is a little silly as an exercise. Finally, exploiting the similarity is powerful. Both fields benefit from this fact already and the more widespread the idea is the better.
jabelk 12y ago
That was my thought too, math is obviously tied very closely to language. And programming did come from CS which came from math. Web/App dev is just so far downstream from all of the math, that people in those roles can get away with ignoring it. In fact, if you accept the premise of math as a language, most of the piece can be boiled down to: "language skills help programming skills, whether that language is mathematics or not". Another nitpick: > A common variation on this: without a CS degree, you can’t build anything substantial. Which, ha ha! Don’t tell the venture capitalists! They’re down there on Sand Hill Road giving actual money to hundreds of people building software projects without any formal qualifications whatsoever. In fact, they do it so often that the college-dropout-turned-genius-programmer is our primary Silicon Valley archetype of success. And monetarily, their strategy seems be to working out for them, if the fleets of Teslas on 280 are any indication. 1. Tesla is not a "software project" and I can't imagine that building a car is light on math. 2. Elon Musk has a degree in physics and dropped out of a Stanford EE PhD. He's not a "college dropout" or a "genius programmer." The CTO, Straubel, also has (non CS) engineering degrees from Stanford. 3. To my knowledge Tesla was initially 100% funded out of Musk's PayPal money, not venture capital. "Math is irrelevant, look at Tesla!" is simply a ridiculous thing to say.
- kluge 12y ago
  I think she was implying that college-dropouts that build software projects can afford to buy Teslas without understanding math.
  - jabelk 12y ago
    Now that you point it out I can see how it could be interpreted that way. I had trouble recognizing that because I don't think being wealthy (owning a Tesla) is an indicator that one "built something substantial".

by tel 12y ago

jordigh 12y ago

> And half of mathematics is more or less the study of formal languages and their consequences? No, just a small fraction is: http://www.ams.org/mathscinet/msc/msc2010.html?t=&s=68Q45++Formal+languages+and+automata&ls=s http://www.ams.org/mathscinet/msc/msc2010.html?t=&s=68Q45++F... This is but a branch of a branch (computer science): https://en.wikipedia.org/wiki/Mathematics_Subject_Classification#Applied_mathematics_.2F_other https://en.wikipedia.org/wiki/Mathematics_Subject_Classifica...

tel 12y ago
That's a really restrictive and explicit demarcation of "formal language". I'd happily describe logic as formal language and then go hunting for places which seem to have non-trivial interactions with logic.
- jordigh 12y ago
  Well, if you define it to be broad enough, then you are correct by definition. My point here is that there is a big, broad cultural gap between mathematics and programming that you are not going to breach merely by saying that a lot of mathematics is about formal languages (in the nontechnical sense of "formal language"). Far from it. Most of mathematics does not talk about formal languages and most of mathematics itself uses very informal language. It looks forbidding to outsiders, but there are many linguistic styles, fashions, abbreviations, shorthands, jokes, puns, and conventions in mathematical writing, very little of which is easy to algorithmically feed into a computer.
  - tel 12y ago
    Sure, and I'm not claiming that you must unify them. Or that you can't. I'm also not saying that the language of mathematics is a formal language, but instead that it shares structure with them. The very notion of the interplay between a theory and its model is not dissimilar. I'm not trying to absolve a cultural gap. Nor am I trying to claim that if you dropped a mathematician into a programming role they would thrive, or visa versa. I'm simply trying to claim that there is a whole lot of similarity between the two and refutations of that are silly. Seeking a clear-cut demarcation between fields is a little silly as an exercise. Finally, exploiting the similarity is powerful. Both fields benefit from this fact already and the more widespread the idea is the better.

jabelk 12y ago

That was my thought too, math is obviously tied very closely to language. And programming did come from CS which came from math. Web/App dev is just so far downstream from all of the math, that people in those roles can get away with ignoring it. In fact, if you accept the premise of math as a language, most of the piece can be boiled down to: "language skills help programming skills, whether that language is mathematics or not". Another nitpick: > A common variation on this: without a CS degree, you can’t build anything substantial. Which, ha ha! Don’t tell the venture capitalists! They’re down there on Sand Hill Road giving actual money to hundreds of people building software projects without any formal qualifications whatsoever. In fact, they do it so often that the college-dropout-turned-genius-programmer is our primary Silicon Valley archetype of success. And monetarily, their strategy seems be to working out for them, if the fleets of Teslas on 280 are any indication. 1. Tesla is not a "software project" and I can't imagine that building a car is light on math. 2. Elon Musk has a degree in physics and dropped out of a Stanford EE PhD. He's not a "college dropout" or a "genius programmer." The CTO, Straubel, also has (non CS) engineering degrees from Stanford. 3. To my knowledge Tesla was initially 100% funded out of Musk's PayPal money, not venture capital. "Math is irrelevant, look at Tesla!" is simply a ridiculous thing to say.

kluge 12y ago
I think she was implying that college-dropouts that build software projects can afford to buy Teslas without understanding math.
- jabelk 12y ago
  Now that you point it out I can see how it could be interpreted that way. I had trouble recognizing that because I don't think being wealthy (owning a Tesla) is an indicator that one "built something substantial".