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The author conflates abstract and immaterial. Computer programs don't have to be abstract, and often are not. And that's precisly what makes them more approacha

The author conflates abstract and immaterial. Computer programs don't have to be abstract, and often are not. And that's precisly what makes them more approachable than mathematics: you manipulate actual structures, see the results in real time and get to see how the actual process is carried out without language ambiguity. In short you get a concrete feeling of things that you can build a mental representation of that's closer to the senses. Now some software engineer should explain to the author how programming is central to his understanding of mathematics and see how things develop.

cheatsheet 12y ago
Software development helps me understand 'kinds' of information, and that the applicability of mathematics is dependent on the kind. But mathematics is not a sense, and neither is a program. These are the best conceptual constructions we have to represent our senses as humans collectively. They are both meant to be representations, models. This is something I continue to find difficult to understand, from both mathematical and computational perspectives, because computational and mathematical concepts are intuituve to me. However, I have the awareness that they shape how I naturally parse the raw data I get from my senses. That means it's important to let go of either model when it ceases to accurately represent reality. I found this very relatable: http://en.m.wikipedia.org/wiki/Conway%27s_law http://en.m.wikipedia.org/wiki/Conway%27s_law
yodsanklai 12y ago
Computer programs are formal objects, just like let say Euclidean geometry is. Their syntax and semantics is entirely abstract and mathematics, even though they can be run on a machine that gives you a concrete feeling. And conversely, most maths aren't that abstract. Mathematicians constantly draw diagrams, plot curves, and use various concrete representations of the object they manipulate. Geometric intuition is a very important tool. I wonder if it's not our best strength compared to machines.
- johnchristopher 12y ago
  > And conversely, most maths aren't that abstract. Mathematicians constantly draw diagrams, plot curves, and use various concrete representations of the object they manipulate. Geometric intuition is a very important tool. I wonder if it's not our best strength compared to machines. That would fit with the whole gestalt theory and how our brains are really good at intuitively* finding shapes within shapes (literally). * read: not with predefined conscious algorithms
- gohrt 12y ago
  Perl and Javascript programs are not formal objects, anymore than an essay is. Any language where "the implementation is the spec" is not a formal object.
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  - yodsanklai 12y ago
    It is. The spec is just more complicated. The meaning of a such a program is entirely defined by the code of the compiler and the underlying architecture. But it's true that some systems are so complex that we study them empirically like natural objects rather than formally.
jordigh 12y ago
> The author conflates abstract and immaterial. How do you define "abstract" then? Looks like it's just a matter of degree, and one hacker's abstraction is another hacker's concreteness.

cheatsheet 12y ago

Software development helps me understand 'kinds' of information, and that the applicability of mathematics is dependent on the kind. But mathematics is not a sense, and neither is a program. These are the best conceptual constructions we have to represent our senses as humans collectively. They are both meant to be representations, models. This is something I continue to find difficult to understand, from both mathematical and computational perspectives, because computational and mathematical concepts are intuituve to me. However, I have the awareness that they shape how I naturally parse the raw data I get from my senses. That means it's important to let go of either model when it ceases to accurately represent reality. I found this very relatable: http://en.m.wikipedia.org/wiki/Conway%27s_law http://en.m.wikipedia.org/wiki/Conway%27s_law

yodsanklai 12y ago

Computer programs are formal objects, just like let say Euclidean geometry is. Their syntax and semantics is entirely abstract and mathematics, even though they can be run on a machine that gives you a concrete feeling. And conversely, most maths aren't that abstract. Mathematicians constantly draw diagrams, plot curves, and use various concrete representations of the object they manipulate. Geometric intuition is a very important tool. I wonder if it's not our best strength compared to machines.

johnchristopher 12y ago
> And conversely, most maths aren't that abstract. Mathematicians constantly draw diagrams, plot curves, and use various concrete representations of the object they manipulate. Geometric intuition is a very important tool. I wonder if it's not our best strength compared to machines. That would fit with the whole gestalt theory and how our brains are really good at intuitively* finding shapes within shapes (literally). * read: not with predefined conscious algorithms
gohrt 12y ago
Perl and Javascript programs are not formal objects, anymore than an essay is. Any language where "the implementation is the spec" is not a formal object.
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- yodsanklai 12y ago
  It is. The spec is just more complicated. The meaning of a such a program is entirely defined by the code of the compiler and the underlying architecture. But it's true that some systems are so complex that we study them empirically like natural objects rather than formally.

jordigh 12y ago

> The author conflates abstract and immaterial. How do you define "abstract" then? Looks like it's just a matter of degree, and one hacker's abstraction is another hacker's concreteness.