Path: g2news1.google.com!news3.google.com!proxad.net!feeder1-2.proxad.net!newsfeed.straub-nv.de!eternal-september.org!feeder.eternal-september.org!.POSTED!not-for-mail From: George Neuner Newsgroups: comp.lang.lisp Subject: Re: Is this a bug in LISP? Date: Wed, 22 Sep 2010 11:04:13 -0400 Organization: A noiseless patient Spider Lines: 25 Message-ID: <736k96pd41plj0mkl5jqgk8ldceb4tv3tj@4ax.com> References: <26f16af6-13bf-45a1-aaf4-74fb66f5ef1c@z7g2000yqg.googlegroups.com> <87fwxldrrx.fsf@kuiper.lan.informatimago.com> <9926b672-a14e-44d0-8965-f70c6bfde8d8@k9g2000vbo.googlegroups.com> <87y6avt757.fsf@mail.geddis.org> <2e181a4f-8e02-4be8-bdf0-bf5ded9f83ea@k9g2000vbo.googlegroups.com> Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Injection-Date: Wed, 22 Sep 2010 15:04:18 +0000 (UTC) Injection-Info: mx02.eternal-september.org; posting-host="qq0kN0CM1dxEbZ/R9Rsgrw"; logging-data="25798"; mail-complaints-to="ab...@eternal-september.org"; posting-account="U2FsdGVkX19UEW29bBTcQ1ZpH3YW03ZVqvCDdNWUAtY=" X-Newsreader: Forte Agent 3.2/32.830 Cancel-Lock: sha1:KODzapu4MGJxbYlBuB3xRrfvuS4= On Wed, 22 Sep 2010 03:14:37 +0000 (UTC), Peter Keller wrote: >Computer hardware simply doesn't fully represent the real number >system like how a mathematicians thinks of the real number system. >It is all approximations. There is a field of math devoted to >understanding and controlling the error one gets due to this and it >is called Numerical Methods. > >The faster you come to realize this and learn to control that error, the >better off you'll be. This happens in all programming languages and is >*inherent* to the machine. Math on a computer happens with fundamentally >different rules than math on paper. Mathematicians don't work with the real number either, they work with "significant figures" which are often a quite limited representation of the real number. Likewise mathematicians perform rounding, truncation, rebasing, etc. to keep the scale of numbers manageable. What happens on paper is not so very different from what happens in the machine. Numerical methods exist not to compensate for perceived machine deficiencies but rather because imprecise calculation is the norm everywhere. George