Talk:Ruffini's rule/Archive

message: Just a quick POV comment: I strongly urge against beginners learning and using this technique, since it involves abdicating your role as a thinking human being. Unless you see what's going on, step by step, when applying Ruffini's rule -- and this article doesn't focus on helping you see it -- you're just pushing numbers around on paper. So do polynomial long-division the real way! Respect yourself! Doops 22:18, 30 Jun 2004 (UTC)
replies: text: Well, the whole POINT of easy-to-use algorithms is to "abdicate your role as a thinking human being". Do you really want to think through WHY Gaussian elimination works and write out systems of equations in all variables? I don't. Of course, I DO understand why G-J works, and can justify when pressed, but once I learned why, I forgot it. This seems to be a similar situation. Asking that people understand why an algorithm works before using it is helpful and instructive...demanding that they SHOULDN'T use it unless they understand it is ridiculous. If that were true, I'd have to throw away my TI-85, since I'm not familiar with many of the internal algorithms programmed into the computer. Revolver 23:21, 30 Jun 2004 (UTC)

text: I might hasten to add that polynomial division ITSELF is a notational algorithm, so by your logic, we should stop doing that, too. (I would guess many people don't understand why polynomial long division works.) Revolver 23:23, 30 Jun 2004 (UTC)
replies: text: Sorry; I was just being grumpy. :) You're right that they're both algorithms; but the reason why I like polynomial division better is that is more transparent -- that is to say, if you look at it while you're doing it you can see what's going on. (Maybe that would be true with synthetic division too if I practiced it a lot.) To be perfectly honest, my math career's been mostly theoretical and I've never really been in the situation of needing to use any of these algorithms much; so I should get off my high horse. Doops 00:13, 1 Jul 2004 (UTC)
replies: text: My math career is pretty theoretical, too (algebraic number theory), but I still don't want to give up MAPLE or MuPad! :-) Revolver 00:20, 1 Jul 2004 (UTC)
replies: text: I think this is simply long division applied. I added that as a remark to the article Eef (A) 12:17, 1 Jul 2004 (UTC)
thread_title:  A digression on ''thinking vs. algorithms'' 

message: If so many people think I'm wrong and they give that bunch of reasons, that should mind something. And that should mind more when I'm only a 15-year-old student. The experience is a status that must be achieved: in my country, we say that the Devil's knowledge does not come from its demonic nature, but from its old age...
OK, I'm changing my mental concept of "factor"... But you haven't beaten me!! MUHAHAHA!! I shall return with new ways to take you out of your minds, just like computer engineering, object-oriented and/or procedural programming, distributed network theory... (and I know a heavy bunch of that, I can bet!) :D
:Habbit 22:30, 5 Jul 2004 (UTC)
replies: text: Don't feel bad. A lot of mental concepts require "adjusting" when you first take algebra...(zero divisors?!, non-associative operations?!) If you're particularly interested in polynomials, the most readable account is probably chapter 16-17 of Gallian's book (Contemporary Abstract Algebra). Revolver 22:57, 6 Jul 2004 (UTC)
thread_title: OK, Habbit gives up against wiser (and probably more experienced) people