Why I Love Computer Science

http://www.cs.caltech.edu/~mvanier/hacking/rants/computer_science.html

by Jebdm • 18 years ago

65 25 18 years ago

cs.caltech.edu

nslater2• 18 years ago

So much fail.

Herring• 18 years ago

This disdain for fields without rigor reminds me of the general attitude towards people using excel macros or vb. I understand it's fun & I used to feel the same way. But at some point you just have to stop playing with your tools & get some real work done.

glymor• 18 years ago

A compiled computer program is certainly a rigorous description of something, God knows what, certainly not the programmer.

This is just funny:

"I think computer science has a tremendous amount to offer the fields of logic and mathematics. Specifically, I think that requiring all formulas to be executable by a finite, deterministic system (a computer program) could lead to a great increase in the level of rigor of these fields, would make it easier for students to learn existing results, would make it easier for practitioners to develop new results, and might possibly suggest whole new approaches...*

Also he keeps refering to computers as finite. I can only assume he means in a physical sense that there are a non-infinite amount of atoms making up his CPU.

I suppose I should critic his argument seriously but it's just too far away from any actual reality.

jsrn• 18 years ago

   > Also he keeps refering to computers as finite. I can only
   > assume he means in a physical sense that there are a
   > non-infinite amount of atoms making up his CPU.

No, this is meant as 'having a finite number of states' (dictated by finite memory, finite number of registers and so on) - as opposed to, for example, a Turing Machine [which has an infinite number of states].

nslater2• 18 years ago

What, with his comment about being able to eventually understand sociology using physics, I think this essay is easily 3 Cuil.

hc• 18 years ago

what does that mean?

dhughes• 18 years ago

"I really loathe vagueness in science (or, for that matter, in philosophy and argumentation in general)."

Is he a computer, true or false no other answer? I think he's fooling himself, what happens if quantum computing becomes common and a result can be a 1, 0 or 'maybe'?

pixcavator• 18 years ago

The dichotomy he puts forward - algorithms (CS) vs. proofs (math) - is totally made up.

Dilpil• 18 years ago

The dichotomy of CS vs Math is tenuous as well.

cchooper6• 18 years ago

I think this guy has mathematics totally wrong. Maths just doesn't work today the way it did in Newton's time, and even back then people weren't satisfied with Newton's proofs, but they lacked an alternative so they had to use them anyway. If the author had his way, we would have refused to accept Newtonian physics for two centuries! Could you imagine the damage that would have done?

> [A]ny realistic mathematical proof will leave out a great many steps, which are considered to be the "required background knowledge"

Computer science papers are different how? Computer science != programs!

> [T]he inference rules are not always specified accurately, or are not believable if they are. This is why you will sometimes read a mathematical proof and say "I understand the reasoning, but I just don't buy it"

I think this guy just isn't too hot at mathematics. Omitting a trivial step (or domain specific knowledge) is not a lack of rigour, but a courtesy to the reader. The details can always be filled in cleanly. If you ever see a modern mathematical proof that is accepted by all mathematicians, but you don't "buy it", then I can assure you that it's you that's at fault, not the proof.

Oh, and computer science papers never leave out trivial steps or assume domain knowledge? Not the papers I've read. Once again, CS != programming!

> This is reminiscent of Whitehead and Russell's Principia Mathematica where hundreds of pages pass until the authors can prove that 1 + 1 = 2.

Surely Principia is a reductio ad absurdum of the argument that everyone should always spell out all the steps!

tokenadult• 18 years ago

I think this guy just isn't too hot at mathematics. Omitting a trivial step (or domain specific knowledge) is not a lack of rigour, but a courtesy to the reader. The details can always be filled in cleanly.

A very astute comment. In principle, mathematical proofs are supposed to be every bit as completely described as computer programs, but perhaps not as explicitly expressed. Edsger Dijkstra used to refer to mathematical proofs as a model for computer programming.

http://en.wikipedia.org/wiki/Program_derivation

derefr• 18 years ago

I'm not a mathematician, but I can imagine some sort of "library of derivation" whereupon, in order to prove something, say, based on arithmetic, you include (the language directive, not the verb) the specification of arithmetic derived in Principia Mathematica. Then the proving system follows your logic to its logic, and then to the logic they relied on, and so on, until everything is completely explicit. Basically, formal execution of bibliographies.

kragen2• 18 years ago

Dijkstra also used to talk about how computing science was a particularly difficult branch of mathematics, basically for the same reason that Vanier is asserting; he recommended that only particularly good mathematicians should switch to computing science, leaving the mediocre mathematicians to what they were already doing.

cabalamat• 18 years ago

> Oh, and computer science papers never leave out trivial steps or assume domain knowledge?

That's irrelevant. The guy's argument is that computer programs don't leave out information: "If all this information isn't available in some form, the program simply will not work, as the interpreter/compiler will not know what to do with the program. This forces a certain intellectual honesty on the process of executing a program; nothing can be left unspecified."

Clearly, computer science papers are written by humans and will typically lack rigour, which has both advantages and disadvantages. Human communication can contain bullshit, but you can't bullshit a computer.

cchooper6• 18 years ago

His conclusion is that computer science is more rigorous than mathematics. His argument is that programs written for computers are more explicit than proofs written for humans. The conclusion and the argument don't match up at all. Computer science, as a subject, is no more rigorous than mathematics.

jamii• 18 years ago

A mathematical proof is a series of steps each of which the listener is confident they could prove to be correct. The more difficult or surprising a result the more steps you will have to add to convince the listener.

Similarly when you are writing a program you don't know the exact inner workings of every function you call. You should, however, be confident that they work and that you could understand them if you need to. The source for a computer program omits plenty of contextual information thats needed to make it meaningful. The only completely unambiguous interpretation of the program is the machine code which is analogous to the proofs in the principia mathematica. Its nice to know how it works in principle but you dont want to work with it unless you really have to.

randomwalker• 18 years ago

Quick note: many of you are saying that this guy is totally out of touch with how math works, and that formal derivation of proofs is just fantasy. It's true that that's an extreme view, but it is in fact one that is held by some top mathematicians, even if a small minority. There are people who have built up research programs out of trying to make it a reality. See, for instance, Doron Zeilberger, who apparently describes himself as an "ultrafinitist":

http://en.wikipedia.org/wiki/Doron_Zeilberger

http://www.math.rutgers.edu/~zeilberg/OPINIONS.html

I'm not saying I agree with that, just that it's not lunacy. Carry on.

jsyedidia2• 18 years ago

I agree. The original post is echoing many of the views expressed at more length by Sussman and Wisdom in their book "Structure and Interpretation of Classical Mechanics." There they showed that a computational expression of classical mechanics was much more explicit and rigorous than the standard mathematical or physical treatments. They also have a similar long paper on differential geometry from a computational perspective: http://groups.csail.mit.edu/mac/users/wisdom/AIM-2005-003.pd...

cchooper6• 18 years ago

Their point in SICM was that traditional notation was not as ambiguous as their computational notation. That's because traditional notation is designed to be convenient rather than explicit. They are right, but this does not mean that physics lacks rigour. More explicit notations were always available and physicists, being more intelligent than computers, were capable of resolving the ambiguities to reveal the fully rigorous structure underneath.

There's a difference between using a convenient notation and lacking rigour. If you are always capable of discerning the true formal equations behind a convenient notation then everything is OK. If you can't, or people can't agree on what the formal meaning should be, then there is indeed a problem. The fact that the authors could derive a computational notation that no physicist would disagree with is proof that a lack of rigour never existed in the first place.

cchooper6• 18 years ago

It's not the claim that mathematics sometimes lacks rigour that's bothering anyone. It's the claim that computer science, as a subject, is somehow more rigorous than mathematics. It's the false equivalence of programs with computer science that's wrong.

jmorin007• 18 years ago

Links down, here's the cached version: http://209.85.173.132/search?q=cache:YchvBt7eH24J:www.cs.cal...

Why I Love Computer Science

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