From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6148 Path: news.gmane.org!not-for-mail From: "Fred E.J. Linton" Newsgroups: gmane.science.mathematics.categories Subject: Illusion and Forthrightness in Wikipedia Date: Sun, 12 Sep 2010 20:11:15 -0400 Message-ID: <730oimakP9232S03.1284336675@web03.cms.usa.net> Reply-To: "Fred E.J. Linton" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1284402225 18888 80.91.229.12 (13 Sep 2010 18:23:45 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 13 Sep 2010 18:23:45 +0000 (UTC) To: categories Original-X-From: majordomo@mlist.mta.ca Mon Sep 13 20:23:43 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpy.mta.ca ([138.73.1.139]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1OvDgs-0004DD-21 for gsmc-categories@m.gmane.org; Mon, 13 Sep 2010 20:23:42 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:57356) by smtpy.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1OvDfg-0006AS-S9; Mon, 13 Sep 2010 15:22:29 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1OvDfa-0008WD-Ps for categories-list@mlist.mta.ca; Mon, 13 Sep 2010 15:22:23 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6148 Archived-At: These somewhat off-topic remarks are at least almost as connected with category theory as the study of knots is, as they have their = origin in my reliance on, and subsequent disillusionment with, the = Wikipedia site for basic information about a certain knot. The knot? -- the familiar trefoil knot, aka (2,3)-torus knot. The offending Wikipedia page? -- http://en.wikipedia.org/wiki/Torus_knot = =2E = The problem? A reader might be forgiven for expecting that when a page of mathematical= text offers a parametrization, in the form x =3D (2 + cos((q phi)/p))(cos(phi)) , y =3D (2 + cos((q phi)/p))(sin(phi)) , z =3D sin((q phi)/p) , of each (p,q)-torus knot, and then offers an illustration dubbed (2,3)-torus knot, that said illustration might have been produced by means of the p=3D2, q=3D3 instance of the parametrization given. But think just a moment, if you have that Torus_knot page open: for phi =3D 0, one has x =3D 3 and y =3D 0, which is *not* a point on the= (2,3)-torus knot as shown *unless* one thinks of the "x-axis" as running vertically, counter to the usual expectation. Oh, but even then, taking the x-axis as vertical and the y-axis horizonta= l, if one uses PostScript to "draw" the curve with the parametrization given= above (with p=3D2 and q=3D3, of course), the result is the "lumpy" figure= I've put up, as .ps and .png files, respectively, here: http://tlvp.net/~tlvp/Trefoil/Wiki-2-3-Torus.ps , http://tlvp.net/~tlvp/Trefoil/Wiki-2-3-Torus.png . (You can "check the math" in the text of the .ps file, or let it be displayed as a graphic using, say, GhostView; a =2Epng file is offered for those without any PostScript viewer.) Clearly the (2,3)-torus knot illustration is *not* obtained from the parametrization the Wiki page offers. Rather, it comes from a vertically oriented ellipse, with major and minor radii 3 and 1, respectively (approximately), drawn on a sheet of paper undergoing its own concurrent slow rotation as the ellipse is being drawn (in fact: an ellipse "with 30 degrees of precession for each 90 degrees of ellipse"), as shown, again in both .ps and .png files, here: http://tlvp.net/~tlvp/Trefoil/TrigTrefoilElliptic.ps , http://tlvp.net/~tlvp/Trefoil/TrigTrefoilElliptic.png . (Compare this precessional ellipse with the Wiki b/w illustration.) At first I was quite outraged that Wikipedia could be so utterly cavalier with mathematical accuracy. = Then I thought, "Well, the (2,3)-torus knot as described in the text = and the knot of the black/white illustration on that page, while = clearly different from a curvature perspective (one has 6 points = of zero curvature, the other has none), are at least equivalent = as knots, so what's the harm? = And finally I thought, "A reader who is informed of the parametrizations = for each of a family of curves, and then sees displayed what is labeled = as one of the curves in that family, has the right, if not explicitly informed otherwise, to suppose that the parametrization used for that displayed curve is the parametrization already given. For why else would the parametrization being used for the displayed curve not be mentioned? Only (presumably) because it should go *without saying*. So it's really rather dreadfully misleading -- if not downright dishonest (!) -- to lead the reader into temptation-to-err by omitting mention of the = very different parametrization being used for that display." And that's why I write here now: How does one fix such a state of affairs= ? = Or is there no better to be hoped for from Wikipedia? Cheers, -- Fred [For admin and other information see: http://www.mta.ca/~cat-dist/ ]