Computer Science is Not Math

http://www.scott-a-s.com/cs-is-not-math/

by scott_s • 14 years ago

36 55 14 years ago

scott-a-s.com

zeteo7• 14 years ago

Oh yes it is. Programming is exactly equivalent to writing mathematical proofs.

http://en.wikipedia.org/wiki/Curry%E2%80%93Howard_isomorphis...

lincolnq• 14 years ago

Did you even read the article?

Edit: This is exactly what the author is arguing against. Yes, you're writing a proof, but that's not the point of what you're doing at all.

zeteo7• 14 years ago

Of course I've read it. He says just the foundations are math. He says actual programs (e.g. those implementing networking protocols) are not math. Curry and Howard beg to differ.

deltasquared• 14 years ago

I read the article and disagree. Computer science is a discipline of applied mathematics.

Saying that computer science is not mathematics because it involves real world complications, is like saying that experimental physics isn't physics because it is not done by theorists.

ColinWright4• 14 years ago

I'm having a hard time seeing how you can come to that conclusion based on the article you reference. Certainly a mathematical proof can be written in a program-style formal language, and then that type of programming becomes equivalent to those types of proofs.

However, programming in general is simply not like that, and programming in general does not, to me, seem to be anything like doing math.

And since that's a very personal statement, let me add by way of context that I have a PhD in math, I have programmed for a living, and I have written computer verified proofs.

It seems to me that most of the people who claim that "programming is math" (and there are many, but perhaps not as many as the OP is implying) have never actually done any math at an advanced level.

I'd be happier saying that programming is a lot like doing word problems, where it's essential not only to get the right answer, but also to use the the right terms, with the right grammar, and in a limited amount of space.

And it's pass/fail.

zeteo7• 14 years ago

>programming in general does not, to me, seem to be anything like doing math.

Hi Colin, can you substantiate that? PhD in CS here and I've done some pretty hardcore math in my academic life.

After writing lots of proofs and lots of programs the two activities don't seem that dissimilar. They are very different "programming languages" indeed, but debugging, modularity, recursion are important for both activities. To give a more concrete example: for my thesis I've implemented at one point a geometric algorithm. Some of the computer code proved buggy so I went to the white board and simply increased the complexity of the math formulas, which allowed me to write less code. I don't see an immense difference between this and, say, combining C and Python code in the same project.

jahewson2• 14 years ago

No, no, no. The Curry-Howard Isomorphism applies to functional programming languages only.

gatlin3• 14 years ago

And if those functional languages are Turing complete, then they are equivalent to all other Turing complete languages, and thus the C-H isomorphism would hold for all Turing complete languages.

qznc• 14 years ago

computer science = information theory + software engineering

My opinion is that education should split computer science into the information theory part and the engineering part. The information theory part might even merge back into the math departments where it came from.

cantankerous4• 14 years ago

I think the integration of software engineering as the core of a computer science program essentially destroys the computer science program. Sure, many people with CS degrees wind up doing software engineering, but comparing CS to SE is like comparing a metallurgist to a blacksmith.

xcallmejudasx2• 14 years ago

That's exactly the comparison I was looking for.

Sure the blacksmith and the SE can build the final products but without the CS or metallurgist to build the foundation they wouldn't have a job.

stcredzero• 14 years ago

education should split computer science into the information theory part and the engineering part.

Then the engineers will complain that "Software Engineering" doesn't have enough rigor to be called engineering. Actually, it's been happening for years.

http://lesswrong.com/lw/9sv/diseased_disciplines_the_strange...

scott_s9• 14 years ago

The problem is that there are two kinds of "software engineering." There's the practice of software engineering, which is the (hopefully) disciplined process of designing and implementing software. We're not sure how to best do it yet, but we all agree that it's important to get right because it's being done every day. Then there's software engineering research, which tries to evaluate ways in which people build software - but it's goal is not itself to build software. I admit I have been unimpressed by some software engineering research, but at the same time, I have no problem saying that the practice of software engineering is extremely important.

cgray4• 14 years ago

Information theory has a meaning that is (I think) distinct from the one you are giving it. https://en.wikipedia.org/wiki/Information_theory

tybris• 14 years ago

Actually, I think information theory is the only branch of science that has something genuinely useful to say about computers. Unfortunately, it has few people working on it in the context of computer systems. The world is dying for useful models of (real) CPUs and complex networks based on information theory, but that's not really happening. Computer "scientists" rather spend their time building example systems that no one will ever use, or creating theoretical models that have no connection to reality. No idea what the purpose of either is.

stiff• 14 years ago

There is an article on the same topic by Professor Donald Knuth which I find much more insightful:

http://mathdl.maa.org/images/upload_library/22/Ford/DonaldKn...

scott_s9• 14 years ago

It almost certainly is. Thanks, I had not seen it before.

jashkenas• 14 years ago

Follow up with Knuth's "Computer Programming as an Art":

http://awards.acm.org/images/awards/140/articles/7143252.pdf

ArtB3• 14 years ago

I have a problem with his analogy to physics. The experimental physicist purpose is to verify in the real world the laws discovered... but the person actually using those laws to build products (I'm skipping a few steps) is called an engineer. Physicists prove the existence of atoms then engineers use knowledge of them to build chips.

But we don't start grouping those engineers in with the physicists. We treat those as two separate disciplines. Well, lets keep computer science a theoretical science and call those people who apply those theoretical discoveries engineers. Much neater and cleaner and makes sense to me.

scott_s9• 14 years ago

Which is a fair point - I grapple with how much of what I do is science, how much is engineering, and how much is neither. But, the problem is, that's what the word "computer science" means now. We could try to retroactively redefine a word to fit what we feel is a more natural division, but how often is that successful?

ArtB3• 14 years ago

In what I do (mostly business cruds) it is mostly an art. The skill is not to get it done, but to organise the code effectively so that it will be easy to debug and adapt and reuse etc. It really doesn't feel like a science and more like being an editor of an anthology.

vbtemp• 14 years ago

Note to OP, I'm really not a huge fan of people posting links to their own blogs...

And in response to your essay, which by and large was tldr, I don't think many people run around saying that CS is math. Many computer scientists, as I'm quite sure you know, need to model their computable structures formally, show reductions or equivalences to other well-studied constructs, and then use the properties of these constucts to establish the expressiveness/complexity/whatever of their model. If outstanding questions remain then it can motivate basic research into the relevant mathematical field (particularly true with cryptography). These people "do math" - many other's from a CS background don't.

scott_s9• 14 years ago

I've been here for a few years. It's a common enough practice that I felt it was okay. Further, I wrote this because I have made the same comment here at least five times (http://news.ycombinator.com/item?id=3596446).

nollidge• 14 years ago

People post links to their own blogs all the time. There's nothing untoward about it.

alsothings• 14 years ago

is Computer Science the same as Software Engineering or Software Development? If it is then sure, this article makes a fair point, but I've always thought these were related but distinct things. And if they are in fact distinct, then Computer Science is the part that is Applied Mathematics by another name.

But really, all of this is just quibbling about semantics.

xcallmejudasx2• 14 years ago

As much as I agree that everyone is just quibbling about semantics it is something that needs to be finalized and agreed on.

In some states it's illegal to say you're an engineer unless you specifically have an engineering degree. Most CS degrees are offered as a science degree with an alternate Software Engineering degree being an engineering degree. There's also a noticeable gap in what you're taught depending on which path you take. Friends of mine who majored in software engineering ended up learning more practical languages, how to use source control, software engineering practices, and never had to take a class related to the theory side of it. Whereas half of my classes were information theory, and abstract or theory based math classes.

Does this make them better programmers because they know more languages and tools? That's subjective. However, there are times when you need a computer scientist and not a software engineer but most companies and even developers themselves couldn't tell you the difference between the two.

Purely hypothetical at this point but suppose you were tasked with creating the first ring based authentication system. This involves a decent understanding of group theory . I don't doubt for a second that a software engineer would be able to accomplish this after first teaching them self about group theory but my first bet would be to go to the person with the CS training. Sure they might not be able to code it as well but once the idea has been developed and proven to be mathematically sound it can just be sent off to the engineer.

ekm2• 14 years ago

Programmers are perfectly comfortable talking about history,psychology,philosophy,economics,the arts,but when math comes up everyone starts crafting intricate theories why it really has nothing to do with his craft(and is therefore not worth wasting time on).Is this a rationalized adult version of math phobia?

demian2• 14 years ago

There are two "extreme" ways of doing things, the "crafting" way in one side of the spectrum and the "engineering" way on the other side.

You can "craft" a car without knowing a single formula, but that proved to be inefficient.

In programming is kind of the other way around. There is a way to use formal mathematical methods to "engineer" programs, but for general use they seem to be economically "inefficient".

Dn_Ab• 14 years ago

The article can be efficiently summed as: Computer Science is not always Math, sometimes it is more of a Science or Engineering or something of all of them.

I think this is one of those places where a word has different meanings to different people and correctness takes a religious quality and fruitful discussion requires telepathy. Also often depending on the resolution of the definition and where a person stands on if the thing and its description can/should be distinguished.

People who say computer science is math I suspect are hard pressed to find anything that isn't. Myself for example, I define math as the maximal object that has something to say - about anything that has structure - in a systematic way. You magnify/exaggerate a certain aspect of the structure you think is key and explore it in a systematic way to gain insight on the whole thing. So while aspects of computer science are more engineering or science than math, I can look at the whole system of doing computer science in an engineer like function as mathematically describable.

dsirijus• 14 years ago

Still haven't read through all the articles referenced to in the comments, but please - do not equate "what I do every day as a computer scientist" to "what computer science is". Let's keep the ideals, shall we?

cprussin• 14 years ago

I would claim that Computer Science is a term that is supposed to apply to any science directly interested in computation. I really see no point in that. Mathematicians are interested in algorithms and complexity and the like, software engineers/db engineers are concerned with databases and UIs. There are different programming languages for each purpose. I see no reason to insist on clumping them in the same group.

tl;dr: every study involving computation or programming doesn't need to be in the same department.

demian2• 14 years ago

I believe that designing and building software systems is not "equivalent" to experimental physics, that it is not "experimental" computer science. Following the metaphor, I believe it's more accuarate to relate it to design and engineering. As in physics, there are very exact scientific theories that, mixed with technical/practical knowledge and insight about systems and people, can be used to create technology.

But I would also argue that there may be a way to "experiment" in a similar way physicist do, and it's by looking at "computing" as a phenomenon of the natural world.

Computing can be considered a science similar to phyisics, because it can be seen as laws that describe nature, or more specifically how information is processed in the natural world. This "computing" works at a "higher level" than physics, which studies the laws of the "hardware". The most used example is the DNA, with information in a higher level of abstraction than the chemical physical support.

I always find amusing to imagine what if Newton had developed his theories as a way to solve practical problems instead of trying to explain motion laws[1], and how maybie that's what happened to "computing".

[1](Physics = "Engine Sciences"?)

generateui• 14 years ago

And software engineering is quite dissimilar, if not completely different to computer science. Creating API's, building user interfaces, testing, has little to do with computer science, or information theory, or mathematics. Yes, it has some overlap, but not nearly as much as academics like to think.

Take an example as implementing a 3D renderer. A computer scientist might argue that underlaying 3D calculations should be correct. A software engineer might optimize for speed, and simply allow incorrect/imprecise calculations, as long as the rendered result does not look very different.

emmapersky• 14 years ago

Except underlying that 3D renderer is a whole bunch of Computer Science research that had to be done in order to allow the engineer to make an optimized implementation. And I doubt a decent Computer Scientists would argue that. In fact, you might need some more CS (or science in general) to figure out what tolerance can be allowed for. Further more, while an optimized implementation is good, an optimized algorithm is probably even better, and right there i more CS.

terio• 14 years ago

This is a problem of definition more than anything else. I feel more comfortable thinking of Computer Science as the Math used to study algorithms and processes. The rest, although based on Math and the scientific process, looks more like Engineering to me.

gatlin3• 14 years ago

Computer Science has always seemed to me to be the study of algorithms and information, correctness, methodologies, and their applications. Math is used in order to advance this knowledge. It is readily apparent to me that everything in CS is applied math and logic.

And in the same way a mechanic uses physical principles (arrived at by way of math), software engineering uses insights, practices, methods, and languages (which are mathematical entities to control a Turing machine) developed by computer science. Computer scientists in turn also learn quite a bit from challenges found and attacked by the engineers.

A few computer scientists I've met have math degrees and they enjoy exploring intersections of discrete math and formal methods; some also do research almost exclusively in engineering / application domains (e.g. computer graphics). And, some engineers I know do quite a bit of graph theorizing before hitting the keyboard (whether they recognize it or not) because it's useful.

A good SE will be a computer scientist when faced with a new, challenging problem and a CS will engineer on occasion to help her research.

Computer Science is Not Math

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