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No, I too am talking about a hierarchy of internally consistent knowledge. Have you implemented a compiler or a interpreter for a popular language? I could be

by ksk 13y ago

No, I too am talking about a hierarchy of internally consistent knowledge. Have you implemented a compiler or a interpreter for a popular language? I could be wrong but I strongly suspect you haven't. If you have ever implemented a compiler you understand the language at a fundamental level and when stumped with a bug or a highly technical puzzle or what have you - you get that "aha" moment where its like "Ofcource ! How else could it be. This language feature must be using this construct because of X or Y reason and the compiler has to work this way because this part here doesnt allow for it to work any other way, etc ,etc and the optimizer has xyz amount of scratch registers so abc condition could never happen, and on and on."

cousin_it 13y ago
My comment was talking about a stronger kind of consistency, maybe "inevitability" would be a better word for it. You could make many different tiny changes to the rules of C and still end up with a workable programming language. (Many people have done that, there are tons of languages derived from C.) You could say that the rules of C are "random" - after learning the first n rules, you cannot use logic to predict the n+1st. So learning the rules of C is more about memorization than logic. Math is different: when you learn a piece of math, you know exactly how it follows logically from the pieces you learned before, and you know it couldn't be any other way. That's why it feels more reasonable to me to inquire about math, rather than the details of C. Lawrence Kesteloot said it well at http://www.teamten.com/lawrence/writings/what_interests_me.html http://www.teamten.com/lawrence/writings/what_interests_me.h...: On a planet far away they have universities. In those universities they have many of the same subjects we teach here, such as math, biology, philosophy, history, computer science, psychology, and literature. But although the subjects of the classes are the same, the contents are different. They teach a history class, but their history is different from ours. So are their biology and literature. I’m not interested in subjects where their content is different from ours. In some classes, though, the content is the same. They’re teaching the same physics class (assuming they’re at the same level of understanding we’re at) and the same math classes (with a different base). In computer science most of what they teach is different, but their theory of computation is surely the same. Their biology is different, but their teaching of evolution is the same. Their philosophy is vastly different (think how different Eastern and Western philosophies are on earth), but their philosophy of science is probably very similar. Even if this point of view doesn't make sense to some people, I subscribe to it because it's very inspiring to me. YMMV.
- ksk 13y ago
  >You could say that the rules of C are "random" - after learning the first n rules, you cannot use logic to predict the n+1st. You're mis-applying things here. The language is not something to be theorized by itself. Like any (edit:spell) other body of knowledge, it has its own set of initial axioms and the 'C standard' which defines the language is simply a collection of rules other meta-knowledge which are based on those. In that sense it is internally consistent. Thats what I meant.
  - patrickmclaren 13y ago
    Can you deduce the majority of the C language from these initial axioms? You misunderstand the usage of consistency regarding mathematics. It is not the same. These rules which compose C are design decisions, and whether they are entirely artificial. Mathematical consistency arises from imposing axioms, following which there are no decisions to be made.
    - ksk 13y ago
      >Can you deduce the majority of the C language from these initial axioms? Well, no. You can deduce A language but it might not be C. I sense we're going down a fruitless path here. In my first post I was only giving an analogy of someone understanding math at a fundamental level to someone understanding a programming language at a fundamental level and how they could inform similar abilities/prowess in people when it comes to dealing with complex problems/etc.
  - cousin_it 13y ago
    Yes, you could say that the C standard is a formal theory. It won't be a very interesting one to a mathematician though, because it's huge and describes only one thing, C. There are no special considerations to single out that theory from a huge pool of similar ones. It's like devoting your life to the study of one particular differential equation with a thousand terms, which was written by a committee. Why not the other equation which has a minus instead of a plus over there? Why not study differential equations in general? Compare with a formal theory like PA, which fits on a page and describes the natural numbers. Proving a theorem about PA has implications everywhere, because natural numbers are everywhere. Or if we want to talk about computation, there are many formal theories with short descriptions that have much more to say about computation in general.

by ksk 13y ago

cousin_it 13y ago

My comment was talking about a stronger kind of consistency, maybe "inevitability" would be a better word for it. You could make many different tiny changes to the rules of C and still end up with a workable programming language. (Many people have done that, there are tons of languages derived from C.) You could say that the rules of C are "random" - after learning the first n rules, you cannot use logic to predict the n+1st. So learning the rules of C is more about memorization than logic. Math is different: when you learn a piece of math, you know exactly how it follows logically from the pieces you learned before, and you know it couldn't be any other way. That's why it feels more reasonable to me to inquire about math, rather than the details of C. Lawrence Kesteloot said it well at http://www.teamten.com/lawrence/writings/what_interests_me.html http://www.teamten.com/lawrence/writings/what_interests_me.h...: On a planet far away they have universities. In those universities they have many of the same subjects we teach here, such as math, biology, philosophy, history, computer science, psychology, and literature. But although the subjects of the classes are the same, the contents are different. They teach a history class, but their history is different from ours. So are their biology and literature. I’m not interested in subjects where their content is different from ours. In some classes, though, the content is the same. They’re teaching the same physics class (assuming they’re at the same level of understanding we’re at) and the same math classes (with a different base). In computer science most of what they teach is different, but their theory of computation is surely the same. Their biology is different, but their teaching of evolution is the same. Their philosophy is vastly different (think how different Eastern and Western philosophies are on earth), but their philosophy of science is probably very similar. Even if this point of view doesn't make sense to some people, I subscribe to it because it's very inspiring to me. YMMV.

ksk 13y ago
>You could say that the rules of C are "random" - after learning the first n rules, you cannot use logic to predict the n+1st. You're mis-applying things here. The language is not something to be theorized by itself. Like any (edit:spell) other body of knowledge, it has its own set of initial axioms and the 'C standard' which defines the language is simply a collection of rules other meta-knowledge which are based on those. In that sense it is internally consistent. Thats what I meant.
- patrickmclaren 13y ago
  Can you deduce the majority of the C language from these initial axioms? You misunderstand the usage of consistency regarding mathematics. It is not the same. These rules which compose C are design decisions, and whether they are entirely artificial. Mathematical consistency arises from imposing axioms, following which there are no decisions to be made.
  - ksk 13y ago
    >Can you deduce the majority of the C language from these initial axioms? Well, no. You can deduce A language but it might not be C. I sense we're going down a fruitless path here. In my first post I was only giving an analogy of someone understanding math at a fundamental level to someone understanding a programming language at a fundamental level and how they could inform similar abilities/prowess in people when it comes to dealing with complex problems/etc.
- cousin_it 13y ago
  Yes, you could say that the C standard is a formal theory. It won't be a very interesting one to a mathematician though, because it's huge and describes only one thing, C. There are no special considerations to single out that theory from a huge pool of similar ones. It's like devoting your life to the study of one particular differential equation with a thousand terms, which was written by a committee. Why not the other equation which has a minus instead of a plus over there? Why not study differential equations in general? Compare with a formal theory like PA, which fits on a page and describes the natural numbers. Proving a theorem about PA has implications everywhere, because natural numbers are everywhere. Or if we want to talk about computation, there are many formal theories with short descriptions that have much more to say about computation in general.