October 2003 - mathfun@mailman.xmission.com

[math-fun] odometer word game
by Richard Schroeppel 03 Jun '04

03 Jun '04

zimb zinc chromatic chromatid Rich

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[math-fun] The spatial universe is finite !!!???
by asimovd＠aol.com 01 Dec '03

01 Dec '03

I just heard a report on an NPR station -- it was probably BBC news -- in which freelance mathematician Jeff Weeks (who wrote the book "The Shape of Space") was being interviewed after he had announced that the spatial universe is finite. There was not enough time allotted for him to give even a brief layperson's sketch of his reasoning. But it seemed to have something to do with the fluctuations in the background radiation from the Big Bang having bounded wavelengths. Does anyone know more about this research? Or where it might be written up? --Dan

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[math-fun] Prentice Hall strikes again
by R. William Gosper 08 Nov '03

08 Nov '03

My tutoree is now in 8th grade, and, miraculously, didn't carry home another Prentice Hall "science" book. But he just got a smearox of three pages which smell familiar. Remember "The weak force is the key to the power of the Sun."? "Because of the air within it, a huge ocean liner can float on the surface of the ocean."? The ridiculous eclipse drawing that showed both limbs of Sun, moon, and Earth lying on just two straight lines? Now they're "doing" biology. Not, as Einstein prescribed, as simply as possible. Way simpler than that. Summary: the brighter and more curious the student, the more discouraged and confused this crap will leave him. Anyone getting an A on this material is a parrot who has been misled to believe s/he has learned something. I'll indent their text. P 88. 4-2 Respiration: Using the Energy in Food Green plants (autotrophs) I'm glad they cleared that up. I thought they meant photoautotrophs. make their own food. Animals (heterotrophs) eat green plants or other animals that eat green plants. Let's see, so fish eat mosquito larvae and mosquitos eat green plants. Carnivores have an agreement not to eat each other. You have learned that energy is stored in the bonds that link together atoms in foods, such as glucose. That comma makes the sentence wrong. You can think of the energy stored in food as a savings account. You eat food to add to your energy savings account. Huh?? You eat food to add to the energy stored in food? P89 During aerobic respiration, food enters the mitochondria. Burgers, fries, Ding-Dongs with taco sauce, oysters with Cool Whip, ... The food is broken down when it combines with oxygen. During this process, water and carbon dioxide are produced as waste products. Yeah, that water stuff is pretty useless. A worse greenhouse gas than CO2. But respiration produces BOTH! We must save the Earth by banning respiration. And club soda. Maybe if we could consume enough anti-oxidants ... The energy released from food during respiration is not always used right away by the cell. Often, it is stored in a chemical compound called ATP. But sometimes the cell just needs a hit of warm club soda? Basically, ATP is a chemical substance that can be used to store energy. How does a chemical store energy without becoming some other chemical? When a cell needs energy, it breaks down the ATP and uses the energy released. Is this like breaking down food? Although respiration occurs in a series of complex steps, the overall process can be written down as a word equation and as a chemical equation, as follows: Glucose + Oxygen --> Carbon Dioxide + Water + ATP (energy) or C6H12O6 + 6O2 --> 6CO2 + 6H2O + ATP Gee, I thought the P in ATP had something to due with phosphorus. But there's no phosphorous on the left side. Wow, cells can make phosphorus out of glucose. Nuclear transmutation! Notice anything familiar about the equation for respiration? You are quite right if you said it is the opposite of the equation for photosynthesis. Yeah except there's no chlorophyll in respiration and you didn't mention ATP in photosynthesis. Maybe that's what you mean by "opposite". p90 So how do anaerobic organisms get their energy? The answer is that anaerobic organisms undergo a different type of respiration, appropriately called anaerobic respiration. I'm sure glad you told me it was appropriately. Scientists use the term fermentation when they speak of anaerobic respiration. Do they mean the same thing, or does one occur during the other, or is one an example of the other, or are they just wishing they had a beer? Carbon dioxide is also the source of bubbles in alcoholic beverages such as beer and wine. But not soda? Hey, my dad's Chianti doesn't bubble. Must be some new kind of emissions control. 4-2 Section Review 2. Why are the mitochondria appropriately called the powerhouses of the cell? Beats the hell out of me, but I'm sure glad you told me it was appropriately.

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Re: [math-fun] Simple EF (unnatural numberklaature)
by asimovd＠aol.com 03 Nov '03

03 Nov '03

Mike Speciner writes: << ... If you're going to invent new words (and I'm pretty sure I'd rather stick with "nonnegative") they really ought to be clearly better than the alternative. I understand the awkwardness of phrases like "greater than or equal to", but it's only a problem when speaking. Otherwise, I can write ">=", or, in my favorite programming language, "ge". >> But "only a problem when speaking" can be significant if one likes to talk about math, such as when collaborating or teaching. I hope that simple concepts like nonnegative can be expressed with fewer syllables in the future. Maybe using just "nonneg" and "nonpos" will catch on. --Dan

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Re: [math-fun] Simple EF
by Henry Baker 01 Nov '03

01 Nov '03

I'm sure that you have read a lot more math papers than have I, but I can tell you that I have _never_ seen a math or computer science paper in which |N excluded 0. At least in the CS community, if you want the positives only, you need to say |N^+ (i.e., |N superscript +). Re "unsigned": actually in C/C++, "unsigned" means modular arithmetic relative to the word size, so "unsigned 5" (written "5U"), means 5 modulo 2^n (n=8, 16, 32, 64, etc.). At 01:40 PM 10/31/03 -0500, John Conway wrote: >On Fri, 31 Oct 2003, Henry Baker wrote: > >> Whatever happened to |N, as in "Natural" numbers? Call it a "natural". > >There are two objections to this. The first is that my request was for >a word meaning "at least zero". This won't be applied only to integers. >The second is that there are still two schools of thought about "natural >number", the "inclusivists" (like me) who count 0 as one, and the >"exclusivists" who don't. Until the great day when the inclusivists >win, it remains ambiguous. > >> Computer languages such as Ada have had to deal with this same problem -- >> that of naming the set of non-negative numbers. >> >> I think that C/C++ call these "unsigned ints", or unsigned's, for short. > > Those are slightly different again, since the "unsigned integer 5" is >really the quotient concept {5, -5} rather than the sub-concept +5. > > John Conway

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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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