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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?"
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 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.
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.
....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.
Hmmm?
Deleted
That's engineering !
Making better engines uses the science of Physics and chemistry..
Cooking uses the science of chemistry..
To me it's like saying : 'Lego Science'.. It's not 'science'.. You don't need to know the physical aspects of a lego block to assemble something.. Although you need some insight into how the thing works - but it's not science per-se !
Then again, it depends on how 'science' is defined !
--Ivan
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.
It's an old joke that any subject that has "Science" in it's name is not a science e.g. Political Science, Social Science, Computer Science.
The Science in Computer Science consists largely of niches carved out of other disciplines e.g. algorithm analysis and crypto are mathematics, user interface design is psychology, computer graphics is really about approximating physics, audio compression is mathematics, psychology and physiology, AI steals ideals from biology... every now and then we find out that the physics department, or the electrical engineers, or the chemists, are actually doing almost identical research to us.
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.
The term itself is a product of the academic environment, similar to the equally dubious "Library Science" and "Management Science". For what it's worth, the European term "informatics" would have been better, but never caught on.
That said, I believe there's a useful set of relationships well understood in other fields:
Science = The search for fundamental knowledge and predictive models;
Engineering = The creative application of the results of science;
Technology = The routine application of the results of engineering.
giving us, for example:
Science: Physics
Engineering: Electrical engineering
Technology: TV Repair, Cable TV Installation
The punch line is that application of this model to computing works as follows:
Science: Mathematics
Engineering: Programming, Informatics, "Computer Science"
Technology: Coding, Computer Installation, Home Computer Repair, etc.
Mathematics IS the science in "Computer Science".
Anyone who has studied advanced Mathematics knows that Math is not about numbers; think of mathematical logic, Boolean algebra, abstract algebra, set theory, topology, category theory, etc. ad infinitum. Dijkstra defined Mathematics as "the art of precise reasoning". In the same sense, "computation" doesn't mean "number crunching", but more generally the automated manipulation of information.
It is true that there are legitimate concerns in today's computational landscape (networking, concurrency, etc.) which didn't figure in the mathematical/engineering world view of the 1940s, but that's simply a sign that the field has grown up (i.e. grown beyond the limited perspectives of its founders). That's also true in many other applications of Mathematics. For example, early research in differential equations paid much more attention to linear differential equations (because they were more tractable). However, we now know that most "interesting" systems in the real world involve non-linearity.
Science, Engineering, and Technology share with living systems an important rule: "Grow or die!" Fortunately, the field of computing has grown.
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!)
Before groupthink nukes this person's comment into oblivion, could you please reflect on the last time you had to deal with someone else's shitty code? (I'm sure you don't have to think back very far.)
If you've never had to deal with someone else's poor work then you [are the luckiest bastard on the planet, but more likely you] may want to consider a career change...
Hmmm?
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.
"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
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 have studied advanced math and I can tell that it's all about analysis.
I'd say that Computer Science(or better Computational Science) should consist of logic, Boolean algebra and so on....
And should be a separate science.
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
Whether that is a sensible way to look at things or not really depends on your viewpoint. I'd argue it's pointless.
That you can explain something using maths doesn't mean that everyone thinks about maths or "use maths" in any conscious way when they do that something.
I could do the transformation in your example before I'd ever heard of boolean algebra, and learned to spot it without having to think much more about it after having thought through it step by step a few times. My guess would be I figured it out at 7-8 years old based on what I remember of the complexity of my programming back then. I'd argue that I was/am not "using" DeMorgan's law, but just learned a pattern by rote that I understood due to language, not maths.
If you still insist on calling it maths, then fine. But then the logical extension is to conclude that people complaining there is "too much maths" in CS are highly unlikely to be complaining about basic stuff like that, which people can/will figure out without any background in maths as/when neeeded.
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?
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"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.
In order to program well (by which I mean write code that performs quickly, uses minimal resources, has no (or few) bugs, is easy to change or enhance without creating new bugs, and consistently gets the correct result) you need to be able to think in a very rigorous, structured way. You also need to be able to hold many variables and logical connections in your mind all at once. It just so happens that the practice of mathematics exercises (and hence theoretically improves) this ability.
The world is full of people who oversimplify what is involved in programming (like my boss, for example...). There is a tendency to leave out relevant variables to make the problem at hand seem simpler to solve, and simpler to implement, than it really is. Because of this, a lot of people think programming is easier than it really is, and they also write programs which seem to get the job done but which wind up causing them problems further down the road. Such people usually aren't big math geeks themselves, don't see the relevance, and are very unlikely to ever become truly great programmers. When things get difficult, they will either run to a truly great programmer (who probably knows a lot about math, too), or try to make the case the the problem cannot be solved (either because there is no solution or because Microsoft didn't provide a robust enough toolset).
The times when you need to actually perform some calculus in order to write a program are quite rare (depending on the nature of your product, of course). Mostly basic arithmetic is all you need most of the time. However, the mental skills that are developed from the study of mathematics are crucial for the ability to program well.
I will also predict that the likelihood that a person will agree with me on this increases in direct propotion to their years of programming experience in the field (i.e., after completing school).
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.
Sure am glad that Donald Knuth poseur got no undeserved credit for TeX and METAFONT.
Admittedly, those tools target publishing, but still...
Get thee glass eyes, and, like a scurvy politician, seem to see things thou dost not.--King Lear
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?
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
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.