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Forget Math to Become a Great Computer Scientist?
Coryoth writes "A new book is trying to claim that computer science is better off without maths. The author claims that early computing pioneers such as Von Neumann and Alan Turing imposed their pure mathematics background on the field, and that this has hobbled computer science ever since. He rejects the idea of algorithms as a good way to think about software. Can you really do computer science well without mathematics? And would you want to?"
Correction, make that minus one.
Who needs math? Bogosort is a good a sort algorithm as any. Hey, without math, how would you be able to tell?
Maths IS needed for computer science. Just be sure not to confuse Computer Science with Software Engineering. Software engineering is only a part of the computer science sphere.
Do the lessons of VB6 teach us nothing?
COMPUTING IS HARD. You can't dumb it down just because it would be nice to do so. And I'm sorry but mathematics is just the way in which meaning is expressed for machines. There's no free lunch here. And he's wrong about algorithms too - since a non-terminating algorithm is always expressible by deconstruction into a series of terminating algorithms.
Taking CS without math is like taking engineering without any physics.
WTF is the the author smoking?.. There are of course parts of CS that are less involved in math, but it is still overall a fundamental part.
- These characters were randomly selected.
Without mathematics, there is no internet porn.
Good luck on doing a kernel, file system, network stack, crypto, image processing, window manager, animation or 3D without math or algorithms. I look forward to reviewing some of this guys code.
This is all fine.. But it doesn't explain something I have long thrived to understand :
What is computer science ?
Computer engineering.. yeah.. I can understand that.. But man.. Computer SCIENCE ?
That's like saying 'car science', 'cooking science' or 'go at the bar and have a drink science' !
--Ivan
This is just another stupid generalization. There are some areas where you can do good computer science without math. There are other areas where you absolutely need mathematics. For example, you cannot do scientific computing without mathematics. Broad generalizations like this for a wide spread field just shows the ignorance/narrow mind of the author.
Isn't that pretty much the same as arguing that a surgeon doesn't have to know about anatomy? What we do is inherently mathematical - there exists no other way of defining and understanding complexity, computability and so on.
I agree that you do not need a good understanding of mathematics to create a homepage, but for anything remotely interesting you do.
I attained a Computer Science BS in 1986. At the time everyone was getting Math minors. I opted for a communication minor instead. I've worked in high-tech engineering environments with real-time programming for many years. What I found is that I've never needed the intense mathematics attained by those with math minors. I needed to be able to implement equations that staff mathmaticians would develop. Though math is a fundamental of computer science, I believe the ability to logically assess a situation from multiple perspectives; communicate your approach with the customer; and then implement a maintainable solution is the key components required for computer scientists.
This guy just doesn't seem to understand what math is. Substituting theory of computation with his "theory of expressions" just shifts focus on another field of math.
Mainly, he claims to want to create a "comprehensive theory of process expression". Fair enough, but as soon as you want to extract usable, reliable results from your "comprehensive theory", you've really just created a branch of mathematics. Maths is not just numbers and calculus, but any systematic treatment of relations in a symbolic fashion - unless he plans a lot of fairly useless hand waving, "Oh, my process is expressed as *insert long winded ambiguous English description", he will be working within the remit of mathematics. Heck, one of my areas of study is the development of processes (studied through the use of process calculi) - a highly mathematical tool.
He also ignores the vast array of work on non-deterministic algorithms, stating that "Any program utilising random input to carry out its process, such...is not an algorithm". Sure, it's not a deterministic algorithm, but even if you artificially restrict your definition of algorithm to just be deterministic, it's a useful tool in analysing such problems.
Finally, statements such as "Computer science does not need a theory of computation" are just so bizarre as to be funny. I suggest he forgets all he knows about formal computational theory, and I'll contract "Theseus Research" to write me a program to determine the halting problem for an arbitrary program. I wonder what his bid will be, given that he doesn't need a theory of computation (that would tell him you can't do it, at least with our models of computation - and probably with any).
Now, all of this is not to say you can't make progress in computer science without the mathematics that's currently been developed - however, you will either spend a lot of time achieving unreliable results, be reinventing the wheel, or just be creating a new branch of mathematics.
I ok. Let me see if I am able to solve the Navier Stokes equations for unstady flows without the help of a computer. And the Schrodinger equation using a tridimensional net?
Buahhh! ha, ha!
....Abstraction.
And computer science, the software side, is really the science of abstraction physics.
http://threeseas.net/abstraction_physics.html
At some point in the higher levels of abstraction creation and use you use the lower mathematical level as more or less a carrier wave of the higher level abstraction, than for the purpose of performing a mathematical calculation. The analogy is that of using radio waves to carry the music you hear over the radio, but the carrier wave is discardedafter it has done it job. Likewise, the mathematics of computers boils down to binary flipping of transistor swiches upon which the higher level of mathematics is carried upon.
With a correct approach to the abstraction manipulation machine computers really are, we can accomplish a lot more, similar to the difference between using the limitation of roman numerals in math vs. the decimal system with its zero place holder.
I feel that there are a lot of software engineering areas where you don't need much in the way of maths experience - just logical thinking. Most real world math related implementations I've done haven't relied on a high level of maths... linear interpolation and solving quadratics are probably as "tricky" as math goes outside of academia... but...
That's not the end of it. I've also done a lot of image manipulation work, and you NEED a good math background when you step over simple 2d convolution filters. Knowing your physics also helps - being able to identify trends and patterns in wave forms, and then applying the necessary maths is a great help. When dging into aliasing and reconstruction now, not just filtering, a high math proficiency is a must.
I've taken to game programming recently. If you know your maths, the physics comes easily. If you know your maths, specially advance vector and matrix theory (with integration and differentiation being prerequisites), things become a breeze. I didnt know enough. And I still struggled from time to time today. Experience is helping me, but sometimes I wish I had a math background to roll on.
I guess my ramblings are leading to a poor conclusion. Without maths you're limited in what you can do - but you're only limited by lateral field... In most cases you can take an specific soft eng field and go to town without hitting maths. I'm a very good software engineering and reverser, and I gotten here without having a math background. When I wanted to expand into games programming and image processing, things became much harder without the math.
With all that said, I'm very very guilty of obscuring simple procedures with valid but pointless math - and I know for a fact there's too much pointless formal theory in computer science now. The pointless formal theory is actually what push me away from doing a masters in computer science, and find something more vocational and rewarding!
Matt
Hmmm?
Deleted
This is something I've thought a lot about. There have been any number of times that math has helped me in my software development efforts. Things like trig to predict the path of a moving target in Robowars (back when I was in high school) to various vector and angle related maths in CustomTF for Quake 1 (www.customtf.com) to partial derivatives to calculate the slope on a surface. I've also needed math for various economics related things over the years, and probability and statistics have also been exceptionally useful to me. Currently I'm having to decipher a guy's code which is all eigenmath, so my linear algebra course is saving me from having to hire someone just to explain all the math to me.
But the kicker is that you can't just tell a student that they should "study vector math" because one day they'll write a Quake Mod, because, truth be told, they probably won't. It's the trouble with all examples you give when students ask how math will be useful -- I could pull any number of examples from my life, but the problem is, they probably won't happen in a student's life. Instead, they'll have their own trials. The best you can tell someone is to study all the math they can, because some day it *might* be useful, and they'll want to have that tool in their toolkit.
And that's just not a very satisfying answer to students who want to make sure that they'll be damn well using what you're teaching in the future.
But believe me, I thought I'd never have an application for eigenvectors, and now not only do I have to clean out my brain on the topic, but I have to parse someone else's code (PhD thesis code no less) and add functionality to it. Two other friends of mine got stuck on legacy Fortran apps which are essentially mathematical solvers (one for differential equations, the other for huge linear algebra problems), and both of them are extremely happy they paid attention in their respective math classes.
So, yeah. To CSE students out there: take math. Pay attention. It could very well save your neck some day at a job, and if it doesn't, at least try to make it interesting to yourself to think of applications where you might use them. All math through the first two years in college can find applications for it quite easily.
I sometimes run into great algorithm programmers who were poor at math, but they're rare, and usually can be explained away based on what kind of drugs they did in college. For a good algorithms guy, I love hiring good mathematicians and physicists. You can train them into great programmers a lot quicker than the other way around. However, algorithms are really a very small part of the programming space we work in. I choose to work in this space because it suits me, but most programmers never need calculus. To build a tree-based data structure and a GUI to drive it takes about an 8th grade level of knowledge. Doing a GUI really well takes creativity I've never had (apparently a lot of guys like me work at M$. I don't know where Apple finds it's GUI guys).
The summary of the author's points in the article make the book sound dead wrong on several counts, though it could just be the review. Procedural languages are the natural way to code most programs, and here's why: we've been recording recipes as a sequence of steps, with if statements and loops, since the invention of writing. It's become encoded in our genes. That's really all that early computer scientists put in our early languages like FORTRAN. It's all the stuff we've added since then that's up for debate, in my mind. The author makes money by pushing the boundaries of computing model research. I get big programs written by teams by restricting what language features are used, and how. I'd be interesting to debate the ideas, point by point.
Beer is proof that God loves us, and wants us to be happy.
Algorithms exist whether you think about them or not, but if you don't think about them, you'll accidentally create terrible ones.
Just as few telescope makers are astrophysicists, most programmers aren't computer scientists. The author himself is evidently not one. Instead, he is one of the more vocal members of an angry, ignorant mob trying to burn down the edifice of computer science. Its members do not understand it, so they fear it and try to destroy it --- look what's happened to computer science at universities!
It was bad enough when courses about a programming language replaced ones about algorithms and data structures (I'm looking at you, Java and D-flat). It was bad enough when pure profit became the raison d'etre of computer science departments. It was bad enough when I noticed my peers start to joke about how they didn't care about this "maths bullshit" and just wanted to earn more money. It was bad enough when the object, not the bit, became the fundamental unit of information.
But what this author advocates is still worse. He's proposing that we replace the study of computer science with a vocational programming, and call that emaciated husk "computer science." We already have a "theory of process expression", and that's the rigorous of algorithms and data structures. We've constructed that over the past 50-odd years, and it's served us quite well.
That field has given us not only staples, like A* pathfinding, but a whole vocabulary with which we can talk about algorithms -- how do you say that a scheduler is O(log N) the number of processes except to, well, say it's O(log N)? You can't talk about computer science without talking about algorithms.
The author's fearful denunciation of algorithms is only one manifestation of the anti-intellectualism that's sweeping computer science. "We don't need to understand the underpinnings of how things work", the angry mob chants, "but only implement the right interfaces and everything will happen automatically."
The members of this angry mob sometimes manage to cobble something of a program together, but it's more like a huge rock pile than a colonnade. It often barely works, uses too much memory, doesn't handle corner cases, and is likely to crash. (See worsethanfailure.com.) Members of this mob even think that if the same algorithm is expressed in two different languages, it's two different processes. People like this ask painful questions like, "i know quicksort in C# but can someone teach it to me in PHP?"
Argh.
Even "new" developments in programming are just new claptraps for old ideas, with fashions that come and go over the years. The only really new things are algorithms, and increasingly, we're calling people who couldn't independently create bubble sort "computer scientists." It's ridiculous. Call computer science what it is, and create a separate label and department for people who can program, but not discover new things.
It's this idea that one doesn't need to understand or think to be successful that's at the center of the article, and it's not just affecting computer science. Look around you. I wonder whether we'll fall into an old science fiction cliché and regress so far that we are unable to understand or recreate the technology of our ancestors.
I believe the author's point isn't that you don't need to know any mathematics, or that it doesn't have an important role to play in CS. He's simply arguing that some of the main issues in computer science are not fundamentally mathematical problems (even if they require some mathematics).
If you buy that argument, then treating CS as if it were merely simply another branch of mathematics will not help solve those problems.
Of course, this also takes us into the perennial debate between where to draw the line between "computer science" and "software engineering". One could certainly define away the author's problem by saying that his examples are software engineering issues rather than computer science issues. And it's true that it's software engineering has been driving a lot of the theory with respect to expressiveness (design patterns and the like). But that view also seems to really impoverish computer science - if all you leave the field of computer science is the stereotypical mathematics, why not just become an applied mathematics major?
... I've taken courses in algorithms, language theory, databases etc. and the majority of the work is not maths and if it is it's so obvious anyone can see it.
--
The majority of _your_ work might be.
Let me make this clear: your ability to write code in no way makes you a computer scientist. It's like saying that the ability to operate a forklift makes you a structural engineer. Stop it already.
That said, I'm sure you're good at what you do. I bet you can write good code in VB, as well as many other languages. This isn't a personal insult. VB, PHP, and other brutish languages are equally bad in my eyes.
These languages are brutish because they oversimplify key concepts. That oversimplification also makes them attractive to new programmers, and new programmers universally write terrible code. The languages themselves aren't bad, the coders are. That said, more experienced coders will generally choose more capable languages, so most of the time, a program written in a brutish language will be a bad one.
We need fewer programmers, not more. Maybe professional certification would help somewhat.
(Incidentally, we were lucky that Javascript became the de-facto client-side web language. We could have done far, far worse, and although we can change server languages, we can't change a user's web browser!)
"Doing a GUI really well takes creativity I've never had (apparently a lot of guys like me work at M$. I don't know where Apple finds it's GUI guys)."
Maybe the question should rather be: Why doesn't Microsoft look for the kind of GUI-guys Apple hires. And the answer to that might well be found at the top of each company. A quote from Steve Jobs' Commencement address at Stanford (June 12, 2005):
"Because I had dropped out [of college] and didn't have to take the normal classes, I decided to take a calligraphy class [...]. It was beautiful, historical, artistically subtle in a way that science can't capture, and I found it fascinating. None of this had even a hope of any practical application in my life. But ten years later, when we were designing the first Macintosh computer, it all came back to me. And we designed it all into the Mac. It was the first computer with beautiful typography. If I had never dropped in on that single course in college, the Mac would have never had multiple typefaces or proportionally spaced fonts. And since Windows just copied the Mac, its likely that no personal computer would have them. If I had never dropped out, I would have never dropped in on this calligraphy class, and personal computers might not have the wonderful typography that they do."
Read the whole thing, it's quite interesting (if not to say: inspiring).
sig? Oh, that sig...
You were off by 19787949 - 1 = 19787948 in your calculation.
However aren't they all integers, and therefore morally equivalent?
Get thee glass eyes, and, like a scurvy politician, seem to see things thou dost not.--King Lear
A lot of the criticism of this guy seems to be knee-jerk defensiveness. Read his papers on 'NULL Convention Logic' and its applicability to asynchronous circuit design and you will see where he is coming from.
It covers networking, scripting, database management, web design, hardware, etc. It's computer science without the science.
Also, Computer Science != Programming: "Computer science does not need a theory of computation; it needs a comprehensive theory of process expression." That's not computer science, that's programming. The author is confusing the two. I know many great self-taught programmers who can't tell me what O(n) means. They get a feel for what data structures to use, but rarely create their own. There's plenty of use for such people - it's probably the majority of programmers. But it isn't CS.
The author really sucks at math but heard that there's big bucks in the computer stuff, right?
Computers are (by their very definition as well as by the word used to describe them) mathematical machines. A computer can essentially do NOTHING BUT calculate. It can in its core add, subtract, shift and move data around. How is this supposed to work without math?
We used to have a Bill of Rights. Now, with the rights gone, all we have left is the bill.
I am a DSP programmer, which basically means that all the stuff I code are mathematical formulas transformed into C code. I mention DSP because writing DSP algorithms forces the programmer to know his math really well... enough so that he can distill the complex math into an efficient C code implementation.
I remember trying to get my specific algorithm to run under 500 micro seconds and the best I could get was like 10000 micro seconds. My coworker who looked at the underlying math equations for my code easily saw a better solution just by looking at the math equations for 5 minutes. After I changed my code to suit the new math equation I got my code to run at 280 micro seconds.
The whole point of this example:
When you approach the solution from a mathematical viewpoint, the mathematical viewpoint lets you see more clearly how to optimize an algorithm. In my case, I got lost looking at the C code and missed the elegant mathematical solution because I did not look at the math equations. So I ended up not being able to "distill the complex math into an efficient C code implementation" to find the elegant solution.
In my case the elegant-math-derived-solution was about 35 times faster (10000 / 280) than the original solution I had come up with.
-----
Bottom line: The syntax and complex notations used for math equations lets you look at a problem from a much higher level of abstraction and this higher level of abstraction is much more conducive to seeing the elegant best solution (solutions that improve your algorithm by an orders of magnitude rather than solutions that improve your algorithm by some linear constant).
p.s. if you were wondering what I was working on --> the function was a GMSK modulator ( http://en.wikipedia.org/wiki/GMSK ) for a transmitter.
"If all you have is a hammer, everything looks like a nail" applies to some degree to the responses to the review.
We use math for these machines because that's how they were designed. They didn't have to be, although from our perspective a half-century on, it seems impossible that they might work any other way.
Computers may need math because of how they were created, but consider that an animator didn't need math to animate, rotate or transform a figure. Though it may be reduced to math, an artist doesn't need math to give depth, shading and perspective to an image. In fact, computers make such analog tasks incredibly math-intensive, as a previous poster noted.
Despite the depth and complexity of the resulting orchestrations, no math created -- though it may describe aspects of -- Beethoven's Ninth Symphony. Learning language and grammar remain elusive to mathematicians, and even Chomsky's "universal" theories end up flummoxed by the Pirahã language. The multiple readings of T. S. Eliot's The Wasteland would take more time to track than the Internet in real time.
Even in the sciences from antiquity, increasing description and formulation result in increasing complexity, but not necessarily increasing understanding. Earth, air, fire and water made sense in societal context; then extended elements; then the periodic table; then subatomic particles, light as particles and waves, and behavior of quarks. Magnetism remains elusive, as does an elegant theory of everything.
Each of these may use math as a description or even a tool, but the careful tuning analysis of the different kinds of gamelans does not apply to the gamelans, but only their analysis. The reference is to itself, and the gamelans go on with or without analysis.
In other words, were our computers not based initially in creating algorithms to manipulate the basic elements chosen to operate them, impelling the ultimate triumph of binary data over other representations, math may have receded to its place as just one tool of computer activity.
Dennis
We Are All Mozart
Actually, "Informatics" (which is, as you say, an incorrect term in English) is used in other languages to label "Computer Science". In Dutch it is "Informatica", in German it is "Informatik" and in French is "Informatique" (sorry, I now am at the boundaries of my own language skills). All there translate to "Computer Science".
I have to admit that I prefer the English term, because it says much more than the Dutch, French and German terms. Fact is: "Informatics" is the same thing as "Computer Science".
Go to wikipedia, search for "Computer Science" and see what the languages I mention translate to. (Try "Nederlands", "Français" and "Deutsch" in the left hand column.
Ahhh...the great dumpster continuum. Many a free computer will be found there. -- sowth (748135)
> Good luck on doing a kernel, file system, network stack, crypto, image processing,
> window manager, animation or 3D without math or algorithms.
And when, may I ask, did you last do any of these things? Only a miniscule portion of us are working on the kernel, file system, or network stack (and none of them involve any math beyond simple algebra). Only one or two of us has ever written a window manager, and that's the way it should be. Only NSA people work with crypto on a regular basis; the rest of us just use premade libraries (made by cryptographers, who require years of practice to become good in their tiny little area of expertise). 3D is all done in hardware these days; software renderers went out of style in the last century and if you are still doing it, your software must be either really slow or running at 320x240. And as for image processing, most of us don't do that either, and when we do, we don't invent the algorithms; we ask mathematicians to do that.
Face it, most of us write code that has absolutely no math in it (I don't count algebra - it's just the way you write code). We make user interfaces, write database queries, and, I am sorry to say, rewrite parts of application frameworks we don't like (and there are a lot of such parts). Instead of math and algorithmic theory, these tasks would benefit from knowing how to structure your code properly, how to ensure portability and ease of localization, and, most importantly, how to correctly think about object oriented design.
> I look forward to reviewing some of this guys code.
Yeah, do look forward to it, since you'll be waiting a long time to see anyone write an "algorithm". I haven't written one in years, and even then it was for a software renderer made for fun. Real programming is about arranging objects and the control and data flow between them, not about crunching numbers. Numeric algorithms only exist in academia and in a few specialized libraries that nobody wants to, or should, rewrite. Design is what programming is about and that is what programmers should know and be taught. Mathematicians be damned!
Yes, because that's how you design and implement a file system.
"Oppression and harassment is a small price to pay to live in the land of the free." -- Montgomery Burns.
I think you are confused. The question is not 'Is Math Computer Science?', the question is 'Is Math -necessary- for Computer Science.'
To use your War analogy, Math is not War, but Math is necessary for War. (Unless you like losing, of course.) Someone may have done all the mathematics long ago, and stored it in a computer for you use, but it's still necessary. You can be infantry in a war without knowing how to add. Heck, I'd bet you could even be a low-level official without anything higher than elementary school math.
Programming is the same way. To use a PC, or script something up in VBScript, no math is necessary at all. To write a compiler (without which, computers can do nothing useful), you need college-level math. And for some applications, you need all the math that's known to humans.
For years I've heard this same 'you don't need math to program' argument, and it's like saying you don't need roads to drive cars on. Sure, it's -possible-, but it's far from efficient and you're very limited as to what you can do with it.
"If you make people think they're thinking, they'll love you; But if you really make them think, they'll hate you." - DM
I started programming at 5 - boolean algebra was the first maths I learned, because it flowed naturally from learning programming, though it took a few years before I knew it had a name. But really, boolean algebra is just logic with symbols.
You mention programmers/software engineers and computer scientists spearately, and you're right to. The two have about as much in common as a builder and an architect - they'll share some vocabulary and some understanding of methods, but what they need to do their jobs are vastly different.
I enjoy reading CS research papers, and I have an interest in some subsets of CS - particularly compiler design - but I don't particularly enjoy maths, and tend to avoid maths heavy papers simply because my interest in CS is a hobby and maths heavy papers take more effort (and in compiler design you need very little maths apart from some very basic graph theory anyway - when people write maths heavy papers on compiler design, then to me it tends to be a sign they don't understand what they are writing about well enough to explain it plainly - so far I've seen very few exceptions to that).
But ultimately CS isn't my career - software engineering IS. The two are different fields, and it's time people actually realize that... More importantly, it's time more schools realize that, and start offering differentiated computer science and software engineering degrees.
Someone with an MSc or even PhD in Computer Science can easily be useless as software engineers. You wouldn't expect an architect to be able to step right into the job of a builder, after all, and you'd be skeptical about the choices of someone who picked an education as an architect if they wanted to become a builder. I've had to deal with my share of highly educated "software engineers", and frankly none of the best software engineers who have worked for me have had anything above a BSc in CS, and many of them had no degree or unrelated degrees that gave them a good appreciation of the specific domain they developer software for, whereas very few of the people I've hired with MSc's and PhD's in CS have done particularly well (there are the odd exception) - it's marked enough that I've gotten to the point that a MSc or PhD in CS is a warning sign that cause me to probe actual engineering skills a lot more thoroughly, as well as asking some pointed questions about what drove them to pursue their degrees and why they subsequently went into software engineering.
But even in CS, the extent of maths you need depends massively on what your focus is. As I mentioned, compiler design rarely need to use much maths (some people do, but not because it's necessary - people like different tools), and a lot of other areas use only some small subset or other of maths.
I hardly took any maths at university, and it's rare for me to come across CS papers even outside of compiler/programming language design that I'd have any problems following due to the maths content. What maths content there tends to be is most often limited enough for context alone to be sufficient to get most of it. When I do run into problems, I can usually easily find papers that have no problems expressing the same information without much maths, which signals that it's very much a communications issue rather than something inherent to the problem. The cases where the maths is so integral to the message that it actually makes much difference apart from reducing the potential audience is very limited.
Unnecessary use of maths in CS papers is one of my pet peeves. I'm not advocating "dumbing down" research, but scientists that use "big words" when there is no reas
I really don't care what you do with Computer Science. There is a lot of research that requires math, as others have pointed out. And a lot of it is really valuable. Equally there is a lot of research bundled under "computer science" (because it uses computers I guess) that requires no math. Whatever.
What I'd like is an arts program that concentrates on programming. I'd like something that stresses *reading* and *writing*. I want people to learn how to *communicate* in these programming languages; not just with the computer, but also with their fellow programmers. I'd like people to do research in language design where they ask the question, "How can I allow the programmer to be more expressive about their intent?" I'd like classes on collaborative design. I could go on forever.
I was at the art gallery the other day and wandered into the modern art section. They had a display of a particular type of performance art where someone would write out a description of an artwork on 3x5 index cards. A bunch of other artists would take the description and make the art. Along with the index cards and pictures of the finished work, there were a couple of letters. The letters were describing the disappointment the original artists had in the finished work. They even went so far as to accuse the artists following the instructions as being "incompetent".
I described this to a programmer colleague of mine. His response was, "Wow... I didn't know I was a performance artist". I can count the number of times in the last 20 years that I've had to do hard math in my job as a programmer on my fingers. But questions like, "How the hell did you think *that* was readable", "How can I turn a bunch of requirements into something that isn't crap", "How do I get 10 guys working on a project and have a single vision", etc, etc, etc; those questions I ask every day.
Sure computer science is important and personally I think math is a part of that. But, someday I hope someone will realize that programming is an *artistic* endeavor and we need to do a crap load of research in that area.
Its not so much that computer science isn't related to math. Its more that CS students are assigned the wrong math courses.
Algebra is an obvious key to understanding computation. Discrete mathematics including probability and combinatorics tend to pop up in computing problems over a wide range of disciplines.
On the other hand, it would not be unfair to suggest that computing is more useful to calculus than calculus is to computer science. Continuous mathematics, like calculus, show up rarely if ever in most computer science specialties.
Fant also seems to be stuck on the word "algorithm." Computer scientists have a very different definition of an algorithm than mathematicians. LISP was the only moderately successful attempt to introduce computer scientists to the mathematical notion of an algorithm. I'll take the groans and dearth of hands raised to the question, "Is LISP your primary programming language?" as proof of just how little regard computer scienctists have for the mathematical notion of an algorithm.
Moderating "-1, Disagree" is simple censorship. Have the guts to post your opinion.
It's lucky Jobs went to his calligraphy classes; if he hadn't we'd all still be using monochrome terminals. (A pretty arrogant thing to imply)
// MD_Update(&m,buf,j);
Lots of people in this discussion mention that they don't use any of the math they were forced to take in college. I think the problem is that schools are requiring the wrong kinds of math, or maybe they're using math to "weed out" students instead of helping them. I think classes in formal logic and discrete math are invaluable to computer science students. Calc...eh, not so much.
What you have written is 100% nonsense and puts you in exactly the same crank camp as Fant. It is always interesting to hear people that don't understand computer science describe what is wrong with it. The model of interaction that you (and he) describe is normally called Reactive software, and it is true to say that it cannot be modelled by a Turing Machine as it performs interaction continuously rather than at the beginning and end of the computation.
From here you've both made a giant leap to assume that programs can't be described by an algorithm. You haven't understood that the difference between a "computation" and "reactive software" is actually a technical triviality that is easily overcome. Indeed it is so trivial that most languages simply ignore it and have stateful operations for input/output. Reactive programs are normally modelled as a sequence of algorithmic steps, everything that the program does apart from sending / receiving data is modelled by an algorithm. So we can either consider this "non-algorithm" to be a sequence of algorithms or consider the program as an algorithm operating over a larger state that includes the environment. The input/output actions become alrgorithmic state transitions over the program/environment state. Look at the way programs in CSP/CCS or other process algebra are written to how this works. To see how the theory of algorithms can be applied to reactive systems take a look at multi-headed Turing Machines.
Finally, if you're going to lob a technical term into a discussion then you should understand what it means. Automaton is a well defined term in CS, and it doesn't mean what you think. In particular what you are describing is not a decision problem and so there is not a problem of language recognition to be solved. I vaguely remembering reading the crank research that you are pointing before, and would like to ask you a simple question. Name one problem that you believe can be computed by a UBM, but not by a UTM?
Slashdot: where don knuth is an idiot because he cant grasp the awesome power of php
"The notion of the algorithm," he concludes "simply does not provide conceptual enlightenment for the questions that most computer scientists are concerned with."
The assertion that computer science is not math is similar to the assertion made in the book "The World is Flat" saying the world is now "flatter" than it used to be. In the case of the flat world, Friedman (the author of "The World is Flat") claims the world is flat to create a sense of shock that he can then use to get his message about globalization across. In the case of "computer science is not math" Fant here is trying first to shock as a method of capturing attention...
Most Americans use math in the singular. The Brits say maths. That is because there are multiple branches of mathematics. What we are discovering is that the tie between arithmetic and calculus and computer science is falsely reinforced. The fact is there are other branches of mathematics that are more important to computer science. There are also many new branches of mathematics that need to be developed in order to solve the new kinds of problems we are trying to solve in modern computer science.
I am really bothered by programmers who, when I interview them, say they have been writing software for years and can't remember ever having to use math.
I know they can't possibly mean that... or they don't know what math is...
I know that in several years of programming you must have at least been tempted to write an if statement or at least one loop of some kind.
The if statement uses a form of algebra called boolean algebra. It was named after George Boole who was very much a mathematician. I know that there are many programmers today who use the if statement and this form of mathematics makes up a large part of many programmer's jobs. I guess it must be falling out of fashion.
I know how to perform boolean algebraic operations on a white board and I have many times been confronted with a gigantic morass of if and else if statements and using simple truth tables and a little boolean math have reduced enormous sets of ifs down to just a few.
The new computer science needs to focus on solving problems involving processes. Processes are like algorithms in that they have a set of instructions but they are unlike algorithms in that they also have many temporal components and may exhibit parallelism, asynchronous invocations, and may not have a finite product. These are the types of problems addressed in newer mathematic disciplines that are trying to see information processes not as tied to computing machinery but as tied to the natural world.
Computer Science may point to a new kind of science that describes an underlying natural computational order of the universe. We are starting to observe computational processes everywhere, in the brains of animals, to the interactions of ecosystems, to quantum mechanics. We may lack the right mathematics to describe these things and we may have to invent new kinds of math but that doesn't mean that math becomes unimportant. An understanding of math can help when studying logic and so too would it help in studying any new disciplines that we may need to invent.
New kinds of math are invented every day to describe new kinds of problems. To say you don't need math to study any formal science let alone computer science is just silly. It is just something shocking to say that grabs attention... and the article nearly contradicts itself by the end... and it's only 7 paragraphs. The distinction Fant makes is nearly academic. Just as the distinction between a Statistician, a Geometer ( a mathematician who studies geometry ), and a Logician is academic. Yet that is not what the readers of the headline will read... Fant is arguing to make computer science a new kind of science much as Wolfram has. Yet it would be sil
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Most engineers never need calculus either, but we still take an awful lot. Why use does a geological engineer have for vector calculus? You'd be surprised where it shows up sometimes. But you need to know it to understand what's going on behind the scenes in various "standard" equations, modeling programs, etc., so you don't blindly follow what's laid down in a textbook. Most of the great engineers I know in industry and research (pretty closely connected in my industry actually) are also damn sharp at math.
Like saying relativity wouldn't have been discovered without Einstein.
I think it's not so much an "if" as a "when". Maybe without Eistein e=mc2 wouldn't have been know for another 20 years. Imagine how drastically that would have changed the 20th Century. Now if Jobs didn't have this artistic side to him, and that offset GUIs by 10 years, then things like the internet and the adoption of PCs might well be at about the 1997 level right now. And that's assuming that the current Federal administration would have pushed for the internet in the same way that Gore did.
We are all just people.
The web site often referred to the reliability of hardware compared to software, and argues we need a hardware methodology-like software development system. I disagree. Hardware is often incredibly difficult to design, we use procedural Verilog code to describe each process, and the rest is manual connections between them. At the manual connection level, we're not more productive designing circuits that we were when we used schematic entry. There's something called the "Design Gap", which refers to the fact that we don't yet know how to make chip designers productive enough for them to use up all the transistors now available on chips. This is one reason so many design teams where off-shored to India. We often can't afford the salaries of US engineers to design modern chips.
Many people have pointed out that programmers can describe the function of a chip in C several times faster than chip designers can do in Verilog. The point is that chips need to work no matter what system they're used in, while somewhat unreliable software can be ok. I'm releasing a 500K line program to a client this weekend. It has bugs. However, it passes hundreds of designs without failure, indicating most customers likely wont run into them. We built that system with only a dozen-ish man-years of effort, but AFAIK it's more complex than any chip ever designed. Our software methodology converges on reliability, but only to a certain quality point. Going beyond that quality point wastes resources that are needed for the next project. To get to Intel Pentium level of quality would take a team the size of Intel's processor design group.
There are several companies that now directly convert C (or SystemC - basically C++) code to hardware. The idea is to greatly improve hardware design productivity, but it only partially works. The bottle-neck is verification. If the link between the description and the hardware is difficult to see and understand, debugging and verification becomes a nightmare. A C model can be written much faster, but who cares, since it's the verification that takes all the effort? Maybe they can figure out how to improve verification flows, but until then, plain old procedural C/C++ programing with solid coding methodologies will continue to kick pants off of hardware design in terms of productivity.
Beer is proof that God loves us, and wants us to be happy.
What math do you need in computer science today? It's a tough call. But today, I'd study number-crunching rather than discrite math.
I have a classical computer science education - automata theory, number theory, combinatorics, mathematical logic - all discrite math. That's what CS was supposed to be about in the 1980s. It's hasn't been enormously useful, and I'm writing this as someone who ran a successful project to develop a proof of correctness system. Mathematical logic gets used a little, but tree-like algorithms are more important. I'm not sure automata theory is useful for much of anything. It's one of those things, like proofs in plane geometry, taught in schools because it was the first theory in the field.
Number-crunching, probability, and statistics seem to be more useful today. If you do anything in graphics, you have to have the 3D transformation math down cold. I've had to do tensor calculus and integration of non-linear differential equations (I used to do physics engines for animation) and that required plowing through difficult math books and getting consulting from university math departments. Bayesian statistics have become very important - it's used in spam filters, search engines, computer vision, and most things that have to intelligently reduce messy real-world data. I didn't get enough of that at Stanford.
On the other hand, where are you going to use this stuff? Outside of Google, Microsoft, and universities, who does real CS research any more? All the good research centers (DEC WRL, HP Labs, IBM Almaden, PARC, etc.) are gone, or a shadow of what they once were.
Oh I see. All this time I was lead to believe that Donald Knuth created TeX to satisfy the desperate need for a half decent digital typography tool and after all it must have been due to some class that steve jobs took when he dropped out of college. Knowing that TeX remains to this day the best typesetting system and knowing a bit about Adobe and the history of PostScript, I guess that that half baked assertion makes sense and must be true.
...or maybe not.
Please. Steve Jobs doesn't walk over water, nor is he behind every single thing which can be accounted as progress in the computer world. This whole jobs-worshiping thing is starting to become ridiculous.
Slashdot, fix your code or at least hire someone who is competent at it to do it for you.
I'm just a GUI programmer, but every once in a while, the need for math crops up without warning: How do I quickly find the object closest to the place where the user clicked? How do I fill that polygon that the user just drew with color? What's the matrix math for converting between color spaces?
Engineering is about building things once you understand the concept behind them. So building a jpg viewer/writer isnt science anymore, it was back circa 1980. Dont get me wrong, building one in without libraries is a mess but could be done. Or building a DES encryption box, it isnt easy, but its not science anymore. its engineering, and we need a bunch of good software engineers because they are realy hard to find.
Most coders dont really fall into the engineer category, unless they are design pattern zealots, or have a robust methodology fro producing code, they are just using logic and application. This is where most of the really cool toys get built, this is where 99.8% of the absurd buggy code comes from. Most Computer Scientists dont Engineer their experiments, IE buggy test code. Without these people we dont really value software engineers. Without Computer Science, Software Engineers are stuck using the same tools over and over.
Storm
ya... and we wouldn't have had the mouse without apple
:-p
what... the mouse was invented BEFORE apple???? gasp
-- I ignore anonymous replies to my comments and postings.
is the same as writing litterature with a programming language.
The reason computer science is so heavily influenced by math is the binary architecture that every piece of hardware is designed around. Every real world problem, right down to choosing the color of a font, has to be translated into the digital world by algorithmic approximation - a lot of math! The problem is that it is this very abstraction that makes computers so "flexible" in what they can do. Analog computers existed many years ago but they could only ever be built for a single purpose.
Unfortunately(?) it is much easier to design and mass produce something which is based on a finite lowest common denominator (bits) than it is to do so based on the continuum that a non-digital solution would require.
That said, who's to say that a beautiful painting rendered in Gimp/PhotoShop isn't a program of sorts? Certainly it has input, (from the original creator), and output, (its effect on us), and the "code" can be modified to change both!
Yes, but I wrote a new book that claims that debate is better off without logic. Early debating pioneers such as Kant and Aristotle imposed their logic background on the field, and this has hobbled debate ever since. I reject the idea of convincing arguments as a good way to resolve any conflict.
Slashdotter, ID #101. UIDs are in binary, right?
Right, well, asserting that Knuth's work had absolutely no influence on operating system fonts, as Jobs appears to have done in his statement, seems fishy.
Get thee glass eyes, and, like a scurvy politician, seem to see things thou dost not.--King Lear
Ha! I guess that's why I like to see all the variable declarations at the top of a function, and some kind of comment above that. I've also seen recipes with goto statements. I guess you could call it a spaghetti recipe? :-P
Beer is proof that God loves us, and wants us to be happy.
TeX is not a UI renderer, though. Did any OS have nice fonts back then?
True confidence comes not from realising you are as good as your peers, but that your peers are as bad as you are.
Wow. That's probably the most non-sensical statement I've read in Slashdot in a while, including the huge iraq-related threads... Quite an accomplishment!
The article completely ignores the most important part about math: It's a language. A very good language, even. More modern than any of our natural languages, capable of expressing non-Newtonian, non-Euclidian and non-Aristotelian facts of the world we today know to be true but still struggle to fit into our mother tongues.
Also, it is what Latin used to be in the middle ages - the common language of people all over the world. Scientists from different continents may be barely able to communicate in their respective mother languages or in english, but if they write down their formulas, they both know exactly what the other is talking about.
But no, the most important part is that math still evolves, and rapidly. As so many other critics, the author of the article appears to have a very limited understanding of math.
Assorted stuff I do sometimes: Lemuria.org
A few weeks ago I came across Project Euler. Most of the exercises are good examples why math is good for coding; they have brute-force solutions that take a lot of time, but clever solutions should always take less than a minute to run.
Escher was the first MC and Giger invented the HR department.
You probably aren't programming anything that requires math. Try 3D graphics programming - you need a lot of linear algebra, and some calculus if you're doing any kind of shading. Physics simulations require more differential equations than you can shake a stick at. Lossy compression requires frequency analysis and coordinate transforms. Of course, making business database front ends doesn't require much in the way of maths... *sigh* :/
Rampant carbon sequestration destroyed the Dinosaurs' tropical paradise. I'm here to help repair the damage.
... and here we find the fundamental problem. Programming != Computer Science.
More accurately, a programmer is not necessarily a computer scientist any more than a computer scientist is necessarily a programmer. Neither is better or worse than the other, and both should know something about the other's skill set, but in practice, there are many amazing programmers who are poor computer scientists, and even more great computer scientists who are poor programmers.
I would classify programmers as people who can get a computer to do what they want it to, and the measure of the skill of a programmer is how their code performs on some set of metrics (performance, reusability, readability, etc.)
On the other hand, computer scientists are people who figure out what they can get a computer to do and how to do it. More often than not, these people work in research labs and in academia, and their measure of performance is how many (usefully) novel methods they've found of doing things or how many new things they've figured out they can make computers do. In most cases, aptitude in more advanced math does help computer scientists, although in some sub-fields, there is less dependency on this.
Heh, not to reply to myself, but to reply to myself, this is the quote at the bottom of the page right now:
"A word to the wise: a credentials dicksize war is usually a bad idea on the net." (David Parsons in c.o.l.development.system, about coding in C.)
Rather apt I think!