Subject: Re: [stella] OT: Programming From: "Roger Williams" <mer02@xxxxxxxxxxxxx> Date: Wed, 24 Oct 2001 20:20:03 0700 
> > There are certain things you need to know no matter WHAT kind > > of programming you are doing. For example, no computer has > > ever been built that can represent a real number. > > Ummm... don't you mean a real fraction? Last time I checked, integers aren't > imaginary. :) I mean a Real Number, which has infinite precision. As a matter of fact all computers DO represent is fractions  usually fractions of 0.1 or 1/2, though other systems are encountered infrequently. What no computer does is implement real numbers that will always function as you are taught they will in algebra, trigonometry, and calculus class. The limitations of the finite math always break down somewhere. Sometimes "somewhere" is surprisingly close to home. > Aren't there some languages that actually internally represent fractions as, > well... fractions? Sure. They are limited by the extent of the numerator and denominator. There are real numbers they can't represent. Sometimes those real numbers that can't be represented become important to you. > In any case, if a computer hasn't been built that can represent them, then a > mathematical system hasn't been built that can represent them either. Of course it has. Mathematical systems have even been built  and a long, long, long time ago by the ancient Greeks  which represent numbers that aren't real, but are irrational. This is not even to get into things like limits and the methods of differential and integral Calculus, which don't work at all except as carefully controlled approximations on computers. There are an infinite number of real numbers. No computer can represent an infinite number of states. This sounds lofty and theoretical but I can tell you from experience that it sometimes has nasty and unexpected practical consequences. This is the sort of thing you should know if you are writing software whose output is important to someone. This is far OT I know, but in a sense it's not OT at all. Stella forces you to keep this truth, which is hidden in most modern environments, at the front of your mind. Programmers are like grape vines. Those that produce the best results  whether wine or software  are the ones that have to fight to produce anything at all. Roger Williams  Archives (includes files) at http://www.biglist.com/lists/stella/archives/ Unsub & more at http://www.biglist.com/lists/stella/
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