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I disagree. Programming is math. Highly advanced math, in fact. It's just a different type of math. And the 11 equations in the OP's article just barely touches

I disagree. Programming is math. Highly advanced math, in fact. It's just a different type of math. And the 11 equations in the OP's article just barely touches on what CS is about. There is far more to it than that.

fragsworth 15y ago
You can disagree all you want but it is pretty much objective fact that in practice, especially in the world of business, 99% of programming is not advanced at all. CS, which is not just programming, may be advanced, but you do not see the advanced concepts emerging very often in day-to-day programming.
- tikhonj 15y ago
  However, the real question is whether there's no advanced stuff because of the domain or because of the people who work there. If enough people working at a company don't like advanced math, it means that they will not use it and if you use it, your code will be harder for them to maintain, so you don't use it either. I suspect if everybody had a better grasp of these ideas, you would see them used more often.
  - rhizome 15y ago
    There are a ton of CS-trained programmers who will include advanced stuff whether the domain requires it or not. It's probably hard to have student loans hanging over your head and not have a reason to use most of the education they paid for.
slowpoke 15y ago
No. Programming is logic, and logic is a superset of math. What you need to make good programs isn't some obscure, arcane language that the few who actually understand it (mathematicians) assert to be the universal answer to everything, yet refuse to make it more accessible (when it could be), what you need is logical thinking and the ability to think in abstractions. Yes, studying math will teach you this, because - as mentioned - math is a subset of logic. But studying math by far is not the only way to gain these abilities, or to obtain a deeper understanding of CS problems. This opinion alone will get (and has got) me branded as a heretic amongst many people, and that alone proves how deeply we are stuck in this tar-pit. If we want to get more people to be interested in and eventually deeply understand CS, we need to get rid of the math barrier. Math is a tool used by computer scientists, and not the fundamental basis of our field. Limiting yourself to a single tool is bad, and you don't need abstract algebra or calculus to understand this.
- jl6 15y ago
  Do you have an example of mathematics that could be made more accessible but hasn't been?
  - slowpoke 15y ago
    A more recent example I've come across are n-dimensional spaces. I realized that most people have problems to make sense of the concept behind that because they've been stuck in thinking mathematically. I think of points in an n-dimensional space as objects holding n different types of information, which is a practical approach, and has lit a candle for some other people I explained it to this way as well. For example, images are often stored as 4 dimensional structures, with the dimensions representing height, width, depth and color value. Every point in that structure is a pixel of the image. You can easily expand this to any number of dimensions, and it still makes sense - you're just adding information (eg, add a fifth dimension for time, and you've got yourself a sequence of images - a simple video). My beef with the way math is often approached is that on the one hand, it's asserted that math is the universal solution to all problems - including practical ones - but on the other hand, more often than not math is removed so far from reality that it's nearly impossible to make any practical use of it.
    - mreid 15y ago
      The way you think of it is precisely the mathematical way of thinking about n-dimensions. Mathematically, an n-dimensional space is R^n, that is, the cross product of the real numbers (R) with itself n times. Each copy of R lets you specify a number independently of all the others. Mathematics is just careful abstraction. If you are abstracting away certain aspects of your problem and carefully making deductions about what is left, you are doing mathematics. As you point out, this can be taken too far but any tool can be used poorly in the hands of a novice.
      - slowpoke 15y ago
        >Mathematically, an n-dimensional space is R^n, that is, the cross product of the real numbers (R) with itself n times. Each copy of R lets you specify a number independently of all the others. See, that's exactly what I'm talking about. This gibberish makes sense to no one except a mathematician. The explanation I've given - while maybe the same in essence - conveys the meaning in a comprehensible way that's not completely removed from reality. My point is that mathematicians often do neither realize that they are talking gibberish that makes no sense to anyone but themselves nor do they accept that math without proper context is devoid of any meaning (outside of math, that is). NOTE: I would like to clear up that I'm not attacking math itself. I neither think math for math's sake is bad, nor do I think math is useless. I respect math as a self-contained field. The problems I'm pointing out are all happening where there is application within other fields - such as CS.
CamperBob 15y ago
For many years, computers sucked at math. In many cases the job of a programmer was not to make the computer do complicated math, but to come up with clever ways to get out of doing complicated math. That's not really true anymore, now that so many technologies from gaming to communications rely on concepts and algorithms from higher mathematics. While I'm skeptical about the importance of the particular equations on the author's list, I don't think it's reasonable any longer for software devs to plead ignorance (your humble correspondent included).
karlzt 15y ago
Programming is a branch of math.

fragsworth 15y ago

You can disagree all you want but it is pretty much objective fact that in practice, especially in the world of business, 99% of programming is not advanced at all. CS, which is not just programming, may be advanced, but you do not see the advanced concepts emerging very often in day-to-day programming.

tikhonj 15y ago
However, the real question is whether there's no advanced stuff because of the domain or because of the people who work there. If enough people working at a company don't like advanced math, it means that they will not use it and if you use it, your code will be harder for them to maintain, so you don't use it either. I suspect if everybody had a better grasp of these ideas, you would see them used more often.
- rhizome 15y ago
  There are a ton of CS-trained programmers who will include advanced stuff whether the domain requires it or not. It's probably hard to have student loans hanging over your head and not have a reason to use most of the education they paid for.

slowpoke 15y ago

No. Programming is logic, and logic is a superset of math. What you need to make good programs isn't some obscure, arcane language that the few who actually understand it (mathematicians) assert to be the universal answer to everything, yet refuse to make it more accessible (when it could be), what you need is logical thinking and the ability to think in abstractions. Yes, studying math will teach you this, because - as mentioned - math is a subset of logic. But studying math by far is not the only way to gain these abilities, or to obtain a deeper understanding of CS problems. This opinion alone will get (and has got) me branded as a heretic amongst many people, and that alone proves how deeply we are stuck in this tar-pit. If we want to get more people to be interested in and eventually deeply understand CS, we need to get rid of the math barrier. Math is a tool used by computer scientists, and not the fundamental basis of our field. Limiting yourself to a single tool is bad, and you don't need abstract algebra or calculus to understand this.

jl6 15y ago
Do you have an example of mathematics that could be made more accessible but hasn't been?
- slowpoke 15y ago
  A more recent example I've come across are n-dimensional spaces. I realized that most people have problems to make sense of the concept behind that because they've been stuck in thinking mathematically. I think of points in an n-dimensional space as objects holding n different types of information, which is a practical approach, and has lit a candle for some other people I explained it to this way as well. For example, images are often stored as 4 dimensional structures, with the dimensions representing height, width, depth and color value. Every point in that structure is a pixel of the image. You can easily expand this to any number of dimensions, and it still makes sense - you're just adding information (eg, add a fifth dimension for time, and you've got yourself a sequence of images - a simple video). My beef with the way math is often approached is that on the one hand, it's asserted that math is the universal solution to all problems - including practical ones - but on the other hand, more often than not math is removed so far from reality that it's nearly impossible to make any practical use of it.
  - mreid 15y ago
    The way you think of it is precisely the mathematical way of thinking about n-dimensions. Mathematically, an n-dimensional space is R^n, that is, the cross product of the real numbers (R) with itself n times. Each copy of R lets you specify a number independently of all the others. Mathematics is just careful abstraction. If you are abstracting away certain aspects of your problem and carefully making deductions about what is left, you are doing mathematics. As you point out, this can be taken too far but any tool can be used poorly in the hands of a novice.
    - slowpoke 15y ago
      >Mathematically, an n-dimensional space is R^n, that is, the cross product of the real numbers (R) with itself n times. Each copy of R lets you specify a number independently of all the others. See, that's exactly what I'm talking about. This gibberish makes sense to no one except a mathematician. The explanation I've given - while maybe the same in essence - conveys the meaning in a comprehensible way that's not completely removed from reality. My point is that mathematicians often do neither realize that they are talking gibberish that makes no sense to anyone but themselves nor do they accept that math without proper context is devoid of any meaning (outside of math, that is). NOTE: I would like to clear up that I'm not attacking math itself. I neither think math for math's sake is bad, nor do I think math is useless. I respect math as a self-contained field. The problems I'm pointing out are all happening where there is application within other fields - such as CS.

CamperBob 15y ago

For many years, computers sucked at math. In many cases the job of a programmer was not to make the computer do complicated math, but to come up with clever ways to get out of doing complicated math. That's not really true anymore, now that so many technologies from gaming to communications rely on concepts and algorithms from higher mathematics. While I'm skeptical about the importance of the particular equations on the author's list, I don't think it's reasonable any longer for software devs to plead ignorance (your humble correspondent included).

karlzt 15y ago

Programming is a branch of math.