nevin1@ihlpf.ATT.COM (00704a-Liber) (05/06/88)
[followups to comp.lang.misc] In article <764@l.cc.purdue.edu> cik@l.cc.purdue.edu (Herman Rubin) writes: >I am not in a position to implement a language. Yes, but earlier this year you made a claim in comp.lang.misc that you could *design* a much better language. How's it going? >I have succeeded in >designing an assembler for a particular machine, which actually could >be easily made semiportable. What does 'semiportable' mean?? Is that like semipregnant? Or is it just that it has infix notation, as you have claimed many times would be much better than the current notation used now for most assemblers. >The major problem with the languages, editors, >etc., is the fantastic number of conventions. I doubt that there is any >language which has less conventional notation than any branch of mathe- >matics. Mathematics, AS A WHOLE (since you are grouping all languages together, it is only fair to group all of mathematics together for comparison purposes), has a much less conventional notation than the combination of computer languages!! >And the conventions of the languages are not usually not in an >"alphabetical" arrangement, so that one can deduce one convention from >the others. This can't be done in mathematics, either. What stops someone from inventing a convention for something which someone else has already invented for another purpose? If I write dx/dt, do I mean derivative or division?? And there are an awful lot of mathematicians who use ' in notations for vastly different things. >If you look carefully at the part of my posting quoted, you will see that >I do not believe that a few people have the intelligence, knowledge, and >imagination to design a language, editor, etc. What do you believe, then?? >How many of the screen >editors allow one to move vertically beyond the present scope of the line? >How many allow one to tie two lines together (i.e., to allow the motion of >characters in one line to move those in another)? A lot. It depends on what the editor is being used for. >Why is there no WYSIWYG >editor which produces its output in such a way that it can be translated to >another system? Assuming the other system can display a superset of the given system, there is no reason why translators can't be written (and some already have been). >Of course, one cannot include everything. But one can facilitate the >addition of those things. Facilitate the addition of everything?? >Many mathematics papers introduce notation >unknown to the reader. Some of this even persists. If a mathematician, >or group of mathematicians, attempted to force the notation of a field, >this effort would be profoundly resisted. If they suggest a notation, >they may or may not succeed, and it is quite possible that the terminology >will be later modified. Allowing ill-defined notation would be a GOOD addition to a computer language?? I think not. >This means that the extension mechanism is too weak. Most extension >procedures are overly restrictive, and do not assume that the user wants >to, say, introduce an operation which is not of the type envisaged by the >language designers. Give me a break!! Languages (other than Ada, anyway :-)) have never been designed to allow everything (even mathematics). In mathematics, where extensions are usually given in English and NOT in terms of previous formal mathematical constructs. Don't expect computer languages to do more than this (until the time when they can 'understand' English, whatever that means). Mr. Rubin, you have this obsession that mathematics is the best language for everything. You have also claimed that you can design a better computer language than currently exists or has ever been thought of. Are you claiming that this language is indeed mathematics?? If so, then why don't you FORMALLY define exactly what you mean by the language of mathematics. By formal I mean that once you have described it (you can even do so in English), it has to have all the mechanisms to allow extensions, etc. Once you have done this it has to pass a few tests: A) Addition of an extension (such as adding the notion of limits to mathematics which previously did not involve limits). We must show that this is indeed the same language as what you keep teeling us mathematics is. B) Ability to *easily* write the Unix kernal in it. After all, it's supposed to be the best possible language for all tasks. C) Must be implementable. For instance: it should not require more RAM than the number of molecules in a pin. When you can show that either your language or mathematics can satisfy these conditions, then you can continue preaching. Until you can do this, stop these silly arguments! and whatever else I can think of. -- _ __ NEVIN J. LIBER ..!ihnp4!ihlpf!nevin1 (312) 510-6194 ' ) ) "The secret compartment of my ring I fill / / _ , __o ____ with an Underdog super-energy pill." / (_</_\/ <__/ / <_ These are solely MY opinions, not AT&T's, blah blah blah
schwartz@gondor.cs.psu.edu (Scott Schwartz) (05/07/88)
In article <4658@ihlpf.ATT.COM> nevin1@ihlpf.UUCP (00704a-Liber,N.J.) writes: >In article <764@l.cc.purdue.edu> cik@l.cc.purdue.edu (Herman Rubin) writes: [ lots of stuff ] My $0.02: I'm not convinced that "mathematics" (whatever that is) would make anything like a decent programming language. First of all, assuming you agree that more is better in these things, why not use English as you programming language? The fact that nobody can possibly write a translator from English to anything else today is just a technical detail :-) The point is that what Herman really wants is a computer with natural language understanding that he can talk to in his own way. That being the case, I'm not holding my breath waiting for him to finish designing this language. Ok, so English is too hard, but "mathematics" is just notation right? Easy for computers to deal with, right? Wrong. I'm not the best mathematician in the world, but when I was getting my B.A. in it I was taught that mathematics is written in English. I think this is an important issue. Read any mathematical paper: The notation is there to augmnent the English prose that the paper is written in. To do justice to the idea of a programming language that embodies all the power of the mathematical notation we see so often is probably going to require the English language as it's extention mechanism if you expect humans to use it and get the same kinds of (good) results they get now. Second, why the fascination with mathematics? How about formal logic? This should appeal in the same way that mathematical notation does, and has the added advantage of being actually doable. Prolog is a proof-of-concept of this idea. Open to suggestions, -- Scott Schwartz schwartz@gondor.cs.psu.edu schwartz@psuvaxg.bitnet
clb) (05/10/88)
In article <3558@psuvax1.psu.edu>, schwartz@gondor.cs.psu.edu (Scott Schwartz) writes: > In article <4658@ihlpf.ATT.COM> nevin1@ihlpf.UUCP (00704a-Liber,N.J.) writes: > > I'm not convinced that "mathematics" (whatever that is) would make > anything like a decent programming language. > > First of all, assuming you agree that more is better in these things, > why not use English as you programming language? The fact that nobody... Immediately, the major problem with English, or any other spoken language is the high degree of ambiguity and redundancy that is required (?) for human speech. Computers have totally different requirements, especially more isn't better, it's just more. Computers are mathematical, and operate best on these problem, much less well on poetry, literature, ... > > Ok, so English is too hard, but "mathematics" is just notation right? > Easy for computers to deal with, right? Wrong. I'm not the best > mathematician in the world, but when I was getting my B.A. in it I was > taught that mathematics is written in English. I think this is an > important issue. Read any mathematical paper: The notation is there to > augmnent the English prose that the paper is written in. To do justice > to the idea of a programming language that embodies all the power of > the mathematical notation we see so often is probably going to require the > English language as it's extention mechanism if you expect humans to > use it and get the same kinds of (good) results they get now. > This isn't right. I have any number of books dealing with mathematical subjects (physics, astronomy, economics, etc.) and they are written in mathematics. The English merely introduces sections. To demonstrate that, get an English professor to read it and explain to you what it says. In all probability, it might as well be written in Martian. > > Second, why the fascination with mathematics? How about formal logic? > This should appeal in the same way that mathematical notation does, > and has the added advantage of being actually doable. Prolog is > a proof-of-concept of this idea. The "fascination" is the usefulness in describing real-world processes. Operations in mathematics aren't used just to make something complicated: they are used because they model natural events and problems in a way that simplifies their understanding. Formal logic is less real-world, more like an effort on the part of people to model the world in their terms. The problem most people have with mathematics is the same as anything else: it is unfamiliar and thus intimidating. If you're looking for something simple, then you find something with little power. To do complex problem, you've got to roll up your sleeves and work at it. Not because the method is hard, but because the world is complex. One more thing. Notation is a problem with mathematics because the ASCII character set is too simple (small) to allow the expression of mathematical operations in a natural way. Just try to get tensor calculus to squeeze into ASCII.
drb@praxis.co.uk (David Brownbridge) (05/11/88)
In article <3558@psuvax1.psu.edu> schwartz@gondor.cs.psu.edu (Scott Schwartz) writes: >I'm not convinced that "mathematics" (whatever that is) would make >anything like a decent programming language. > >First of all, assuming you agree that more is better in these things, >why not use English as you programming language? ... I'm not convinced mathematics is a useful *programming* language either, but it can be used as an excellent *specification* language. At Praxis we are using the "Z" notation which combines natural language text with a *stylised* form of mathematics. Z is being developed at Oxford University (England :-)). The key ideas of Z are that the natural language text is a commentary on the maths and that the maths has a well defined interpretation. Z adds a structuring concept called a "schema" which enables pieces of the maths to be named, combined, re-used etc in powerful ways. A schema is a set of variables and a predicate relating their values. Z contains a mathematical core that can be extended *in Z*, for example by adding digraphs if you happen to need them in your spec. We are using Z to specify a large CASE system. I would find an natural language spec of such a system hopelessly imprecise and an executable (programming language) specification far too concrete. Using maths you can quickly *denote* the answer in a (possibly) non-computable way which is pleasant but more precise than natural language alone. The hard part is deciding on the program once the spec is defined :-) The mathematical basis of Z is given in %T Understanding Z %A J M Spivey %I Cambridge University Press %D 1988 %O ISBN 0-521-33429-2 For an earlier introduction: %T Specification of the UNIX Filing System %A C Morgan %A B Sufrin %J IEEE Transactions on Software Engineering %V SE-10 %N 2 %P 128-142 David Brownbridge drb%praxis.uucp@ukc.ac.uk Praxis Systems plc Phone: +44 225 444700 20 Manvers St Bath Avon, UK BA1 1PX ------------------------------------------------------------------------------ .-Signature------------------------------ | s : STRING |---------------------------------------- | s elm (wittyNotes union sarkyComments) | 0 <= length(s) < Pin.noOfMolecules ` --------------------------------------- | mySignature : {Signature} ------------------------------------------------------------------------------
nevin1@ihlpf.ATT.COM (00704a-Liber) (05/12/88)
In article <4039@killer.UUCP> loci@killer.UUCP (loci!clb) writes: >Computers are mathematical, and operate best on these problem, >much less well on poetry, literature, ... This is a common fallacy, that computers are inherently mathematical. Mathematics is simply one way of abstracting what a computer does. All computers do is some electonic signal manipulations. Anything else we say about them is an abstraction or model of what they do. >This isn't right. I have any number of books dealing with >mathematical subjects (physics, astronomy, economics, etc.) >and they are written in mathematics. The English merely >introduces sections. To demonstrate that, get an English >professor to read it and explain to you what it says. In >all probability, it might as well be written in Martian. This isn't right, either. A number of professionally videotaped courses in these subjects are done using actors who usually understand next to nothing about mathematics, yet I could learn more from these tapes than from most of my teachers in college. If you believe that these subjects are written in 'mathematics', then I propose an experiment for you. Find some advanced physics topic that you don't know, buy a book about it that is written in a foreign language that you don't know, and try to learn the topic. Then come back to the net and explain why you couldn't learn it. In order to understand the things you call 'mathematical subjects', you need both mathematics *and* English. An analogy to this is buying a newspaper and reading a caption of a picture they forgot to print or seeing a picture without the caption. Neither of these circumstances tells the whole story; you need BOTH the picture and the caption. BTW, I learned mathematics (specifically calculus) from physics, not the other way around. In my calculus class, we learned how to solve integrals; in physics, we learn how to set them up and what they meant. >The "fascination" is the usefulness in describing real-world >processes. Operations in mathematics aren't used just to >make something complicated: they are used because they model >natural events and problems in a way that simplifies their >understanding. Formal logic is less real-world, more like >an effort on the part of people to model the world in their >terms. From formal logic (and computablility) branch of mathematics come the theoretical description of what we call a computer. Does this mean that computers are less real-world? :-) >The problem most people have with mathematics is the same as >anything else: it is unfamiliar and thus intimidating. If >you're looking for something simple, then you find something >with little power. To do complex problem, you've got to roll >up your sleeves and work at it. Not because the method is >hard, but because the world is complex. I got a pretty good score on the last two Putnam exams I took (especially for someone who was never a math major); I think this qualifies me as being familiar with mathematics. To solve a complex problem, you have to break it up into smaller, more manageable problems. Whether I use mathematics or another tool, this depends entirely on the problem. >One more thing. Notation is a problem with mathematics because >the ASCII character set is too simple (small) to allow >the expression of mathematical operations in a natural way. >Just try to get tensor calculus to squeeze into ASCII. Yes, but since mathematical notation is extensible, you can NEVER have enough symbols to allow the expression of mathematical operations in a natural way. Mathematics is a very powerful *formal* language. Until someone can show otherwise (by implementing the language of mathematics), I maintain that it is not a good language for writing computer programs in. -- _ __ NEVIN J. LIBER ..!ihnp4!ihlpf!nevin1 (312) 510-6194 ' ) ) "The secret compartment of my ring I fill / / _ , __o ____ with an Underdog super-energy pill." / (_</_\/ <__/ / <_ These are solely MY opinions, not AT&T's, blah blah blah
eugene@pioneer.UUCP (05/13/88)
In article <4723@ihlpf.ATT.COM> nevin1@ihlpf.UUCP (00704a-Liber,N.J.) writes: >In article <4039@killer.UUCP> loci@killer.UUCP (loci!clb) writes: >>Computers are mathematical, and operate best on these problem, >This is a common fallacy, that computers are inherently mathematical. >Mathematics is simply one way of abstracting what a computer does. Actually, if you restricted math to use ASCII [just alphanumeric and a few other characters], imposed many limitations which would mimic "storage," "execution time [speed math, your theorems must be proved quickly]," "compile" it, you could get math to look to look a lot like computers. [Knuth, Mar. 1985 AMM? Mathematicians know the value of everything and the cost of nothing modified from Perlis's Epigrams]. Consider doing math with $int$ $sum from i = 1 to inf$, etc. Certainly doable, but I am only aware of a few systems which can evaluate 2^72-1 (certainly all systems with bc) and this is just a small integer 8-). This is part of the beauty of math as well as a limitation. Another gross generalization from --eugene miya, NASA Ames Research Center, eugene@aurora.arc.nasa.gov resident cynic at the Rock of Ages Home for Retired Hackers: "Mailers?! HA!", "If my mail does not reach you, please accept my apology." {uunet,hplabs,hao,ihnp4,decwrl,allegra,tektronix}!ames!aurora!eugene "Send mail, avoid follow-ups. If enough, I'll summarize."
clb) (05/14/88)
In article <4723@ihlpf.ATT.COM>, nevin1@ihlpf.ATT.COM (00704a-Liber) writes: < In article <4039@killer.UUCP> loci@killer.UUCP (loci!clb) writes: < < >Computers are mathematical, and operate best on these problem, < >much less well on poetry, literature, ... < < This is a common fallacy, that computers are inherently mathematical. < Mathematics is simply one way of abstracting what a computer does. All < computers do is some electonic signal manipulations. Anything else we say < about them is an abstraction or model of what they do. No no! Look at the machine language for ANY processor on the market today: they include mathematical operations like add, subtract, and, or, xor, cmp, etc. Anything else you think you see isn't there. COMPUTERS ARE MATHEMATICAL. How you abstract what a computer does is irrelevant. < < >This isn't right. I have any number of books dealing with < >mathematical subjects (physics, astronomy, economics, etc.) < >and they are written in mathematics. The English merely < < This isn't right, either. A number of professionally videotaped courses in < these subjects are done using actors who usually understand next to nothing < about mathematics, yet I could learn more from these tapes than from most < of my teachers in college. I've see some of them and they are FULL of errors. It seems to be the fashion to try to use art to avoid true understanding of scientific subjects but you can't learn more than the artist knows from them, and worse, you are infected with the errors. The main advantage of mathematics is the precise way that concepts can be expressed. < < If you believe that these subjects are written in 'mathematics', then I < propose an experiment for you. Find some advanced physics topic that < you don't know, buy a book about it that is written in a foreign < language that you don't know, and try to learn the topic. Then come < back to the net and explain why you couldn't learn it. < I did just that: I learned the relativity of gravity from German, which I don't read. You best watch out underestimating what determined students of science are capable of (doing). < In order to understand the things you call 'mathematical subjects', you < need both mathematics *and* English. An analogy to this is buying a < newspaper and reading a caption of a picture they forgot to print or < seeing a picture without the caption. Neither of these circumstances < tells the whole story; you need BOTH the picture and the caption. < Cute. Analogies now? I suggest that you throw out you video- tapes, and picture books and learn some mathematics from your professors: they try very hard to get through to their students, even the deliberately dense. < BTW, I learned mathematics (specifically calculus) from physics, not the < other way around. In my calculus class, we learned how to solve < integrals; in physics, we learn how to set them up and what they < meant. BTW: I also learned from physics, for which I received a degree in 1969. Don't think that I stopped learning it then. In fact I am still learning more physics, astronomy and other scientific subjects. < < >The "fascination" is the usefulness in describing real-world < >processes. Operations in mathematics aren't used just to < >make something complicated: they are used because they model < >natural events and problems in a way that simplifies their < >understanding. Formal logic is less real-world, more like < >an effort on the part of people to model the world in their < >terms. < < From formal logic (and computablility) branch of mathematics come the < theoretical description of what we call a computer. Does this mean < that computers are less real-world? :-) Electrical engineers designed computers: logicians sat around and proved that it couldn't be done. You seem to have a serious hole in your knowledge of the history of these subjects. Next time you decide to flame somebody for expressing an opinion, make sure you know that facts. < < >The problem most people have with mathematics is the same as < >anything else: it is unfamiliar and thus intimidating. If < >you're looking for something simple, then you find something < >with little power. To do complex problem, you've got to roll < >up your sleeves and work at it. Not because the method is < >hard, but because the world is complex. < < I got a pretty good score on the last two Putnam exams I took (especially < for someone who was never a math major); I think this qualifies me as being < familiar with mathematics. To solve a complex problem, you have to break < it up into smaller, more manageable problems. Whether I use mathematics or < another tool, this depends entirely on the problem. And your ego is bigger than your test scores. Big deal. I've never been too impressed that brag on the one hand and demonstrate their ignorance on the other. "Actions speak louder than words". < < >One more thing. Notation is a problem with mathematics because < >the ASCII character set is too simple (small) to allow < >the expression of mathematical operations in a natural way. < >Just try to get tensor calculus to squeeze into ASCII. < < Yes, but since mathematical notation is extensible, you can NEVER have < enough symbols to allow the expression of mathematical operations in a < natural way. Is there any point to this, or are you still on a high horse? < < < Mathematics is a very powerful *formal* language. Until someone can show < otherwise (by implementing the language of mathematics), I maintain that it < / (_</_\/ <__/ / <_ These are solely MY opinions, not AT&T's, blah blah blah First thing to do to solve this problem is to educate people in mathematics. Then it may be possible to find good algorithms to solve differential equations in a programmable language. The lack of knowledge at present may be a problem to some, but every problem is also an opportunity for progress. -- clb@loci.uucp (CLBrunow)
faustus@ic.Berkeley.EDU (Wayne A. Christopher) (05/14/88)
In article <4082@killer.UUCP>, loci@killer.UUCP (loci!clb) writes: > No no! Look at the machine language for ANY processor on the market > today: they include mathematical operations like add, subtract, > and, or, xor, cmp, etc. Anything else you think you see isn't > there. Hmm, "jmp" isn't there? Registers aren't there? > First thing to do to solve this problem is to educate people > in mathematics. Then it may be possible to find good algorithms > to solve differential equations in a programmable language. Are you educated in mathematics? Can you find these algorithms? Come on, put your money where your mouth is. Let's see some results. Or are you going to claim that you're not a good enough mathematician to do these things yourself? If not, you shouldn't be telling your betters what's good for them. Maybe I've missed something important -- what is the problem you're trying to solve, anyway? You don't like the existing programming paradigms? Why not? Because it's too hard to write good code in them? Not for good programmers. Because they're "ugly"? That's too subjective -- I don't think they're ugly. Because you want to do something new and different, and leave your mark on the history of computing? Probably... Wayne
markv@uoregon.uoregon.edu (Mark VandeWettering) (05/15/88)
In article <4082@killer.UUCP> loci@killer.UUCP (loci!clb) writes: >In article <4723@ihlpf.ATT.COM>, nevin1@ihlpf.ATT.COM (00704a-Liber) writes: >< In article <4039@killer.UUCP> loci@killer.UUCP (loci!clb) writes: >< >< >Computers are mathematical, and operate best on these problem, >< >much less well on poetry, literature, ... >< >< This is a common fallacy, that computers are inherently mathematical. >< Mathematics is simply one way of abstracting what a computer does. All >< computers do is some electonic signal manipulations. Anything else we say >< about them is an abstraction or model of what they do. > No no! Look at the machine language for ANY processor on the market > today: they include mathematical operations like add, subtract, > and, or, xor, cmp, etc. Anything else you think you see isn't > there. COMPUTERS ARE MATHEMATICAL. How you abstract what a computer > does is irrelevant. At the risk of sounding (being rude) "Did IQs just drop sharply around here?" Computers are NOT just mathematical machines. As a matter of fact, they are particularly poor at mathematical problems. Ask any numerical analyst about estimating round off, number of significant digits, stability etc, and he will tell you all sorts of interesting stories. Computers CAN DO arithmetic, but that is not the basis, or even the most important thing they do. As for abstraction, abstraction is the KEY to all that computers can do. At some level, we can treat a computer like a black box, and disregard lower levels that aren't interesting to us. This our Symbolics Lisp Machine runs LISP, it processes SYMBOLS, ATOMS, S-EXPRESSIONS etc... The fact that it can also do math is because WE LIKE TO DO MATH, not that it is somehow the basis of all the rest. >< >This isn't right. I have any number of books dealing with >< >mathematical subjects (physics, astronomy, economics, etc.) >< >and they are written in mathematics. The English merely Written in mathematics? I think not. Most of them are written in English, with concise notation (which is often mathematical) to describe precisely the meaning of CERTAIN ELEMENTS of the topic being addressed. A fully mathematically sound and complete treatise on any of the subjects you described (ECONOMICS hah!) is impossible. [some arguments which didn't seem pertinent are deleted for brevity] >< >The "fascination" is the usefulness in describing real-world >< >processes. Operations in mathematics aren't used just to >< >make something complicated: they are used because they model >< >natural events and problems in a way that simplifies their >< >understanding. Formal logic is less real-world, more like >< >an effort on the part of people to model the world in their >< >terms. The problem with simulation or modelling is that often the modelling process abstracts out elements of the problem which are key to the actual understanding of the problem. Hence we have a nice formal model, but it is nonsense, because it contains nothing of the actual forces that we are trying to understand. Similarly, we can define and prove a program to be mathematically correct (well, a small one at least). That doesn't mean that the program works, it means that it meets its specification. Of course the hard part of the problem is ensuring that the formal meaning of the specification matches the meaning that I have concieved for this program. Mathematics cannot help that. >< From formal logic (and computablility) branch of mathematics come the >< theoretical description of what we call a computer. Does this mean >< that computers are less real-world? :-) > > Electrical engineers designed computers: logicians sat around > and proved that it couldn't be done. You seem to have a serious > hole in your knowledge of the history of these subjects. Next > time you decide to flame somebody for expressing an opinion, > make sure you know that facts. I think both of you have your wires crossed here, you are talking over each others bows. >< >The problem most people have with mathematics is the same as >< >anything else: it is unfamiliar and thus intimidating. If >< >you're looking for something simple, then you find something >< >with little power. To do complex problem, you've got to roll >< >up your sleeves and work at it. Not because the method is >< >hard, but because the world is complex. Actually, there are occasions where the methodology is hard too, there might not even be a methodology, and you might have to *gasp* search for the answer. >< I got a pretty good score on the last two Putnam exams I took (especially >< for someone who was never a math major); I think this qualifies me as being >< familiar with mathematics. To solve a complex problem, you have to break >< it up into smaller, more manageable problems. Whether I use mathematics or >< another tool, this depends entirely on the problem. But as computational complexity will teach you, there are problems that cannot be solved by this divide and conquer methodology. Period. ------------------------------------------------------------------------ The problem here is that on one hand we have a person involved with mathematics who quite honestly doesn't have a clue about computers. He is undoubtably self taught, and quite proud of his achievements. On the other hand, there are people who are well versed in various areas of computer science, who are perhaps more familiar with the UNIQUE problems that programming and computers are likely to exhibit. "CLBrunow" has said "implement" mathematics as a language. Computer science people laugh at such statements, because they are MEANINGLESS. What does it mean to implement mathematics? What branch? For what purpose? To solve what kind of problems? Using what notation? And of course much more importantly "HOW?" The fact is, there are many things in mathematics (MANY MANY THINGS) which we cannot do, even with unbounded CPU power. Many of these things are not "conceptually" complicated. Perhaps CLBrunow would be amazed to learn that simple problems like the Travelling Salesmen problem (which can be precisely defined mathematically) is computationally intractable, because it is necessary to examine ALL POSSIBLE PATHS to decide the shortest one. Mathematics will tell you that there IS one, but it does nothing to help you find it (other than telling you you have to search) [ Above presumes that NP != P ] Does CLBrunow do programming? Know more than two computer languages? I don't know about other "computer" people here, but I personally know 8, and have examined over 20 similar languages. This include imperative languages (good ole C and *ick* fortran), Lisp, Scheme, functional languages like SASL and ML, and logic programming languages such as Prolog. Has CLBrunow ever had to develop a program? How does mathematics address problems of reusability, modularity, and ease of understanding? Can it be understood only by dedicated professionals, or do common pleebs have a chance of being able to (at some level) understand it as a specification for a problem to be solved? How does one "debug" mathematics? By exhibiting a counter proof one would imagine, but that is computationally intractable as well. Now, unless mr. brunow can give us some answers to questions that computer people need answered, I think he should go back and dust of some computer science texts and raise his conciousness level before he seeks to tell dedicated professionals their business. If anyone else thinks the above statement is cocky and rude, it is. but then I didn't tell him how to do mathematics now either. mark vandewettering, better to keep ones mouth shut and have people think you are an idiot, than open it and remove all doubt...
kelly@uxe.cso.uiuc.edu (05/16/88)
/* Written 6:41 pm May 13, 1988 by loci@killer.UUCP in uxe.cso.uiuc.edu:comp.lang.misc */
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BTW: I also learned from physics, for which I received a
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Is this conversation proof that learning 'physics' fries peoples brains?
Maybe Dr. Koop should issue a public health warning.