From mboxrd@z Thu Jan 1 00:00:00 1970 X-Spam-Checker-Version: SpamAssassin 3.4.4 (2020-01-24) on polar.synack.me X-Spam-Level: X-Spam-Status: No, score=-1.3 required=5.0 tests=BAYES_00,INVALID_MSGID, WEIRD_QUOTING autolearn=no autolearn_force=no version=3.4.4 X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: 103376,1042f393323e22da X-Google-Attributes: gid103376,public X-Google-Thread: 1014db,1042f393323e22da X-Google-Attributes: gid1014db,public X-Google-Thread: 109fba,1042f393323e22da X-Google-Attributes: gid109fba,public From: ceris@dai.ed.ac.uk (Ceri Stagg) Subject: Re: Off topic response to an off topic message--> was:Re: Software Engineering and Dreamers Date: 1997/06/09 Message-ID: <5nh4d2$7gm@scotsman.ed.ac.uk>#1/1 X-Deja-AN: 247732657 Sender: ceris@minerva.dai.ed.ac.uk (Ceri Stagg) References: <5m57nu$7si@bcrkh13.bnr.ca><5mcp5o$ei7$3@news.cc.ucf.edu> <5md1fl$9f4@bcrkh13.bnr.ca><5mmvgj$61k@squire.cen.brad.ac.uk> <01bc7042$609289e0$cb61e426@DCorbit.solutionsiq.com> <33947E2F.3F1A31A7@fuller.com> <5n2csg$1c6@mtinsc04.worldnet.att.net> <3394E51B.7A5A@flash.net> Organization: Dept of Artificial Intelligence, Edinburgh University, Scotland Newsgroups: comp.lang.c++,comp.lang.c,comp.lang.ada Date: 1997-06-09T00:00:00+00:00 List-Id: |> > Because of this, it is clearly only in our minds even more than math |> > is. I think Mr. Goats point can be made clearer once you realize that |> > math is about symbols and how you can transform them into one another. |> > "2 + 2 = 4" seems to be expressing a relationship of some sort that |> > exists externally in nature, but what it means and how we interpret |> > is actually quite close to how we process langauge. You wouldn't say |> > English exists in nature, and is not solely the product of our brains, |> > just because you can point to a big leafy green thing and say "tree". |> > It is not like the word "tree" was laying about, just waiting to be |> > discovered, any more than the symbol "2" was. In this sense (and in |> > many others as well) math is a product of our brains. I think a distinction should be made between NUMBERS and NUMERALS. Our mathematical system's rules are not arbitrary, they have been chosen because of their mapping to the laws of numbers we see in nature, e.g. if we have 4 things (I mean the number 4, not the numeral) and remove 2, we clearly have only 2 remaining. Admittedly, maths is not a science per se because most of it deals with platonic ideas that cannot be directly seen or touched, making it trickier to get a handle on in these areas than e.g. physics, but I think it's wrong to suggest that something like the Mandelbrot set doesn't exist outside people's minds.....surely the Mandelbrot set is a discovery, not an invention? I don't think mathematical systems can have the arbitrariness of languages. The numerals and symbols can be arbitrary, but their transformation rules MUST consistently map onto and track the relationships of numbers. But getting your head around the verifications involved in this is indeed tricky stuff...... ____ ____/....\____ C.P.Stagg |____ Ceri ____| ------------------ / \____/ \ ceris@dai.ed.ac.uk """"""""""""""""