Path: utzoo!utgpu!water!watmath!clyde!att!osu-cis!tut.cis.ohio-state.edu!bloom-beacon!mit-eddie!bbn!uwmcsd1!ig!agate!ucbvax!hplabs!hp-pcd!uoregon!markv From: markv@uoregon.uoregon.edu (Mark VandeWettering) Newsgroups: comp.lang.misc Subject: Re: Universal Programming Languge (was: Universal OS) Message-ID: <2008@uoregon.uoregon.edu> Date: 14 May 88 20:18:29 GMT References: <769@imagine.PAWL.RPI.EDU> <76700017@uiucdcsp> <843@actnyc.UUCP> <4723@ihlpf.ATT.COM> <4082@killer.UUCP> Reply-To: markv@drizzle.UUCP (Mark VandeWettering) Organization: University of Oregon, Computer Science, Eugene OR Lines: 161 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...