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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 und

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.
      - oblique63 15y ago
        Thank you! I've had this same feeling for a long time. It strikes me as odd that probably a lot of the same people that would find it unacceptable to write cryptic C code with one-letter variable names, find typical math notation/jargon to be completely fine and legible. If code is so important that we go out of our way to make it comprehensible to future maintainers, why don't we have the same feelings about math? (which I would argue is much more important for people to comprehend, seeing as how it's the core foundation of all of science) Personally, I'm really into physics, so I've always really wanted to like math so that I could delve deeper into the subject more easily. It's not that I'm terribly bad at it, but most math texts are so obscenely terse and cryptic, that it makes you wonder whether the authors are actually even trying to teach people about what they're talking about...
paragraft 15y ago
Why do you claim logic is a superset of math? My understanding of Gödel's incompleteness theorems is they show you can't reduce arithmetic to a consistent & complete logic.
- nkassis 15y ago
  Well Godel had to use Logic to prove this. I guess what he meant is logic allows mathematicians to talk about mathematics at a meta level. I wouldn't say a superset of Math since it's still very much mathematics. http://en.wikipedia.org/wiki/Metamathematics http://en.wikipedia.org/wiki/Metamathematics
nitrogen 15y ago
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. Caution is advised when interpreting opposition to a position as justification for the position. This kind of tenuous logic is frequently used to justify continued oppression in e.g. obscure religious communities ("They all hate us, so we must be right!"). I'm not saying your position is invalid (nor as a non-mathematician am I qualified to do so), just that it could be better supported.
- slowpoke 15y ago
  True, I shouldn't argue like this. Thanks for pointing out that fallacy. What I've been trying to convey is that I've come with what I think is a sensible position, and often got responses that ranged from fervent opposition to (very occasionally) verbally violent backlash. Maybe it was just me incorrectly stating my point, though.

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.
    - oblique63 15y ago
      Thank you! I've had this same feeling for a long time. It strikes me as odd that probably a lot of the same people that would find it unacceptable to write cryptic C code with one-letter variable names, find typical math notation/jargon to be completely fine and legible. If code is so important that we go out of our way to make it comprehensible to future maintainers, why don't we have the same feelings about math? (which I would argue is much more important for people to comprehend, seeing as how it's the core foundation of all of science) Personally, I'm really into physics, so I've always really wanted to like math so that I could delve deeper into the subject more easily. It's not that I'm terribly bad at it, but most math texts are so obscenely terse and cryptic, that it makes you wonder whether the authors are actually even trying to teach people about what they're talking about...

paragraft 15y ago

Why do you claim logic is a superset of math? My understanding of Gödel's incompleteness theorems is they show you can't reduce arithmetic to a consistent & complete logic.

nkassis 15y ago
Well Godel had to use Logic to prove this. I guess what he meant is logic allows mathematicians to talk about mathematics at a meta level. I wouldn't say a superset of Math since it's still very much mathematics. http://en.wikipedia.org/wiki/Metamathematics http://en.wikipedia.org/wiki/Metamathematics

nitrogen 15y ago

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. Caution is advised when interpreting opposition to a position as justification for the position. This kind of tenuous logic is frequently used to justify continued oppression in e.g. obscure religious communities ("They all hate us, so we must be right!"). I'm not saying your position is invalid (nor as a non-mathematician am I qualified to do so), just that it could be better supported.

slowpoke 15y ago
True, I shouldn't argue like this. Thanks for pointing out that fallacy. What I've been trying to convey is that I've come with what I think is a sensible position, and often got responses that ranged from fervent opposition to (very occasionally) verbally violent backlash. Maybe it was just me incorrectly stating my point, though.