Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!watmath!clyde!burl!ulysses!allegra!mit-eddie!think!harvard!seismo!lll-crg!lll-lcc!well!hoptoad!laura From: laura@hoptoad.uucp (Laura Creighton) Newsgroups: net.cse Subject: Re: Math and CS Message-ID: <587@hoptoad.uucp> Date: Fri, 7-Mar-86 15:44:57 EST Article-I.D.: hoptoad.587 Posted: Fri Mar 7 15:44:57 1986 Date-Received: Sun, 9-Mar-86 09:26:59 EST References: <256@hropus.UUCP> <6400005@ccvaxa> <77@umcp-cs.UUCP> <1194@mit-eddie.MIT.EDU> Reply-To: laura@hoptoad.UUCP (Laura Creighton) Organization: Nebula Consultants in San Francisco Lines: 85 In article <1194@mit-eddie.MIT.EDU> gds@mit-eddie.MIT.EDU (Greg Skinner) writes: > >Actually, this brings me to a deeper question. I have always wondered >why some hackers just didn't grit their teeth and suffer through the N >years to get their degrees. Considering the fact that it was easy for >them to grind out their programs, they could have coasted through all >their programming projects and devoted some of the energy that went >into their programs into learning linear algebra, modern algebra, and >all that other stuff. I can remember putting in a lot of time on all >my courses -- I didn't like putting in all that time so much but I >considered it necessary, and felt so much better for really >understanding it. (Yet, I suppose to someone whose goals are only to >put out portable, fast code, without understanding why it is portable >and fast, understanding is of little importance.) > >I don't know, maybe I am missing some fundamental issue regarding the >difference between those who sweated out all the courses towards their >degree and those who didn't. I would appreciate some enlightenment >though. When I was an undergrad, I would have loved it if I could >whip up fast, portable code for my assignments. I envied those who >could. I was just curious why it didn't carry over into their other >courses. You have missed it totally, Greg. Computer Programming and Mathematics both require thinking, yes. But not the same sort of thinking. Case in point -- linear algebra. I am in the unfortunate position that I can't get my csc degree without the course in Linear Algebra -- and I could knock it off in one semester if I could get that course. But I can't. I have taken it three times, dropped it once, and failed it twice. The last time with a 49%. (All I need is a pass. One more mark would have done it, but I couldn't get it for blood nor money). Now I am willing to believe that there is a way to approach linear algebra which lets me use my intellect to understand the course and thus work out problems ``from general principles''. But *nobody* has been able to teach me this. I spent one semester taking no other courses but Linear Algebra (I still was working, but I picked a time when I could coast along at work) so tyhat I could finally get rid of this obstacle. That is the year that I got 49%. And the reason why is that, without understanding (which I was never able to get, despite working my ass off) linear algebra is nothing but sheer memorization. Now check out your hackers -- they can't memorise without understanding. I know more than a dozen people who don't have their degree because they couldn't get past linear algebra. I don't know *anybody* who turns out fast, portable code who doesn't understand why it is fast and portable. I just see absolutely no connection between this understanding and linear algebra. If there is one, and you can get it across to me, I might be willing to give linear algebra another crack -- after going to all that work, I would like to have the csc degree. But until then, I've had it. I just can't memorise that much. By the way, it is not that I don't have the mathematical background I have the ``calculus courses for physics majors'' and logic courses galore. Something which may be related -- when I solved a problem in any branch of mathematics until I hit linear algebra there was this tremendous rush ``aha!'' and a warm rosy glow. Since I, by and large, live for those experiences, I found programming and cs theory attractive -- I can the same feeling out of getting my code to work, or understanding of a real interesting theory or algorithm. (To tell you the truth, I have Hofstadter's malady, and can get the same feeling by contemplating recursion). But not for an nanosecond did I ever get this feeling after solving a linear algebra problem. Indeed, I didn't even get a much of a sense that it was done. (The thing I liken it to is to reducing a very large polynomial fraction. You factor the numerator and denominator and cancel out the common factors and are left with a reduced expression. As a kid I used to do them all afternoon for the joy of it. The elegence! The simplicity! But I can't get that feeling out of linear algebra. On the other hand, I can really get it out of taking a mess of code and making it protable and then speeding it up. The simplicity! The functionality! Wow.. and my mind starts glowing again...) What I don't understand is people who have never felt this at all. I have explained ``why mathematics is beautiful'' to countless people and got no reaction at all. It is all so much ``linear algebra'' to them I hope that there are other areas of their lives which give them the same feeling, though -- to live life without ever feeling this ``aha!'' feeling sounds very, very bleak to me. -- Laura Creighton ihnp4!hoptoad!laura utzoo!hoptoad!laura sun!hoptoad!laura toad@lll-crg.arpa