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[math-fun] abelian VS commutative & capitalization
by Marc LeBrun 31 Oct '03

31 Oct '03

Is there any rule or convention about "abelian" VS "commutative"? For example, I see "abelian group" but "commutative monoid"? With just a little grousing I can accept the non-descriptive but honorific "abelian" as the preferred synonym, but then why not use it consistently? Also, what about capitalization? I've seen it both ways, but personally prefer lower-case on the grounds that once a proper name is *modified* into an adjective (as opposed to used unchanged, as in "Erdos number") the word no longer "properly" refers to the person (similarly for "riemannian"). And then what about "the" "gudermannian" and "pfaffian" which are adjectival forms of names now apparently used as either nouns or adjectives?

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[math-fun] The Ghosts of Departed Quantities (1734) -- (long)
by Thane Plambeck 31 Oct '03

31 Oct '03

Since it's Halloween: Here's the continuation of the "ghosts" passage from Berkeley's THE ANALYST; OR, A DISCOURSE Addressed to an Infidel MATHEMATICIAN. WHEREIN It is examined whether the Object, Principles, and Inferences of the modern Analysis are more distinctly conceived, or more evidently deduced, than Religious Mysteries and Points of Faith (here is the "ghosts" passage, in a larger context than it's usually quoted) There is indeed reason to apprehend, that all Attempts for setting the abstruse and fine Geometry on a right Foundation, and avoiding the Doctrine of Velocities, Momentums, &c. will be found impracticable, till such time as the Object and the End of Geometry are better understood, than hitherto they seem to have been. The great Author of the Method of Fluxions felt this Difficulty, and therefore he gave in to those nice Abstractions and Geometrical Metaphysics, without which he saw nothing could be done on the received Principles; and what in the way of Demonstration he hath done with them the Reader will judge. It must, indeed, be acknowledged, that he used Fluxions, like the Scaffold of a building, as things to be laid aside or got rid of, as soon as finite Lines were found proportional to them. But then these finite Exponents are found by the help of Fluxions. Whatever therefore is got by such Exponents and Proportions is to be ascribed to Fluxions: which must therefore be previously understood. And what are these Fluxions? The Velocities of evanescent Increments? And what are these same evanescent Increments? They are neither finite Quantities nor Quantities infinitely small, nor yet nothing. May we not call them the Ghosts of departed Quantities? XXXVI. Men too often impose on themselves and others, as if they conceived and understood things expressed by Signs, when in truth they have no Idea, save only of the very Signs themselves. And there are some grounds to apprehend that this may be the present Case... (At the very end, Berkeley poses a list of questions. He introduces them as follows) L. Of a long Time I have suspected, that these modern Analytics were not scientifical, and gave some Hints thereof to the Public about twenty five Years ago. Since which time, I have been diverted by other Occupations, and imagined I might employ my self better than in deducing and laying together my Thoughts on so nice a Subject. And though of late I have been called upon to make good my Suggestions; yet, as the Person, who made this Call, doth not appear to think maturely enough to understand, either those Metaphysics which he would refute, or Mathematics which he would patronize, I should have spared my self the trouble of writing for his Conviction. Nor should I now have troubled you or my self with this Address, after so long an Intermission of these Studies; were it not to prevent, so far as I am able, your imposing on your self and others in Matters of much higher Moment and Concern. And to the end that you may more clearly comprehend the Force and Design of the foregoing Remarks, and pursue them still further in your own Meditations, I shall subjoin the following Queries. (And here is a selection of the questions) Qu. 43. Whether an Algebraist, Fluxionist, Geometrician, or Demonstrator of any kind can expect indulgence for obscure Principles or incorrect Reasonings? And whether an Algebraical Note or Species can at the end of a Process be interpreted in a Sense, which could not have been substituted for it at the beginning? Or whether any particular Supposition can come under a general Case which doth not consist with the reasoning thereof? Qu. 51. Whether any thing but Metaphysics and Logic can open the Eyes of Mathematicians and extricate them out of their Difficulties? Qu. 54. Whether the same things which are now done by Infinites may not be done by finite Quantities? And whether this would not be a great Relief to the Imaginations and Understandings of Mathematical Men? Qu. 55. Whether those Philomathematical Physicians, Anatomists, and Dealers Animal Oeconomy, who admit the Doctrine of Fluxions with an implicit Faith, can with a good grace insult other Men for believing what they do not comprehend? Qu. 64. Whether Mathematicians, who are so delicate in religious Points, are strictly scrupulous in their own Science? Whether they do not submit to Authority, take things upon Trust, and believe Points inconceivable? Whether they have not their Mysteries, and what is more, their Repugnancies and Contradictions? Anyway, the complete text is online http://www.maths.tcd.ie/pub/HistMath/People/Berkeley/Analyst/Analyst.html Thane Plambeck 650 321 4884 office 650 323 4928 fax http://www.qxmail.com/ehome.htm

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RE: [math-fun] Simple EF
by Andy Latto 31 Oct '03

31 Oct '03

> -----Original Message----- > From: John Conway [mailto:conway@Math.Princeton.EDU] > Sent: Wednesday, October 29, 2003 4:55 PM > To: math-fun > Subject: Re: [math-fun] Simple EF > > > On Wed, 29 Oct 2003, Jon Perry wrote: > > > This may be completely dumb, but is it always possible to > solve x/y = a/b + > > c/d, where all algebraic quantities are positive integers, > for all x and y? > > How about a=x, b=y, c=0, d=1 ? John Conway 0 isn't a positive integer. But how about a=c=x, b=d=2y? Andy Latto andy.latto(a)pobox.com

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[math-fun] Simple EF
by Jon Perry 31 Oct '03

31 Oct '03

This may be completely dumb, but is it always possible to solve x/y = a/b + c/d, where all algebraic quantities are positive integers, for all x and y? Jon Perry perry(a)globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths/ http://www.users.globalnet.co.uk/~perry/DIVMenu/ BrainBench MVP for HTML and JavaScript http://www.brainbench.com

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[math-fun] Dover Books
by Thane Plambeck 31 Oct '03

31 Oct '03

Why are they so inexpensive? Or: why is everything else not? Thane Plambeck 650 321 4884 office 650 323 4928 fax http://www.qxmail.com/ehome.htm

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Re: [math-fun] Matrix Arithmetic Compendium
by Henry Baker 31 Oct '03

31 Oct '03

Knuth has lots of cool stuff. There's a large 3 volume (?) set on determinants (?) from 1880 or so, which tries to be encyclopedic. There are some cool matrix algorithms to find & characterize roots of polynomials. At 10:22 PM 10/28/03 -0700, Schroeppel, Richard wrote: >Does anyone know of a compendium of matrix arithmetic? >I'm imagining a collection of numerical & simple algebraic >facts about matrices-- things like the determinant of a >Vandermonde matrix, or the inverse of a finite section >of Pascal's Triangle. > >Rich rcs(a)cs.arizona.edu

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[math-fun] Glider
by Richard Schroeppel 30 Oct '03

30 Oct '03

Ed Pegg Jr <ed(a)mathpuzzle.com> reports Eric Raymond is advocating that open source computer programmers (hackers) use the Game of Life Glider as their emblem. http://www.catb.org/~esr/hacker-emblem/ This opens up all sorts of possibilities. Eric is claiming only the shape .o. ..o ooo There are 15 others available for other purposes or organizations. I've always been partial to ooo ..o .o. which seems more upward looking. Covert hackers might use oo. .oo o.. a suitably obscure glider. NASA could adopt .ooo o..o ...o ...o ..o. and the State of Utah might use .o. o.o o.o .o. Rich rcs(a)cs.arizona.edu

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RE: [math-fun] Simple EF
by Dan Hoey 30 Oct '03

30 Oct '03

> > > This may be completely dumb, but is it always possible to > > > solve x/y = a/b + c/d, where all algebraic quantities are > > > positive integers, for all x and y? How can we make this not completely dumb? Given that x,y are positive and relatively prime, can you give formulas for a,b,c,d that guarantee that all are positive and that (a,b)=(c,d)=1? Hmm, still pretty dumb. Suppose we also require that a,b,c,d are four different positive integers? I've gotten b and d different, but I haven't managed all four. In case that's still dumb, can all of a,b,c,d be made relatively prime in pairs? Dan

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[math-fun] MathWorld
by Jon Perry 30 Oct '03

30 Oct '03

at http://mathworld.wolfram.com/ makes the strange boast of having 0 animated GIF's and 0 live Java applets. Jon Perry perry(a)globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths/ http://www.users.globalnet.co.uk/~perry/DIVMenu/ BrainBench MVP for HTML and JavaScript http://www.brainbench.com

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[math-fun] archimedian kaleidoscope
by Shel Kaphan 29 Oct '03

29 Oct '03

This is a nice Java applet. I've always wanted something like this: http://www.csd.uwo.ca/~morey/CogEng/AK.html

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