3/15/2010

Pedantry and Mastery

Pedantry and mastery are opposite attitudes toward rules. To apply a rule to the letter, rigidly, unquestioningly, in cases where it fits and in cases where it does not fit, is pedantry... To apply a rule with natural ease, with judgment, noticing the cases where it fits, and without ever letting the words of the rule obscure the purpose of the action or the opportunities of the situation, is mastery. -George Polya, professor of mathematics (1887-1985)

2/25/2010

Richard Feynman - Wikiquote

Richard Feynman - Wikiquote: "I can live with doubt, and uncertainty, and not knowing. I think it's much more interesting to live not knowing than to have answers which might be wrong. I have approximate answers, and possible beliefs, and different degrees of certainty about different things, but I’m not absolutely sure of anything, and in many things I don’t know anything about, such as whether it means anything to ask why we’re here, and what the question might mean. I might think about a little, but if I can’t figure it out, then I go to something else. But I don’t have to know an answer. I don’t feel frightened by not knowing things, by being lost in a mysterious universe without having any purpose, which is the way it really is, as far as I can tell, possibly. It doesn’t frighten me. The Pleasure of Finding Things Out."

2/18/2009

Absolutely Best Math Videos

The absolutely best math videos I've ever seen are at http://www.dimensions-math.org/. Each one of the nine is about 10 minutes long and the graphics are incredible.

1/30/2009

John Updike

After reading the September 1967 Scientific American, John Updike composed the following poem. All things are Atoms: Earth and Water, Air And Fire, all, Democritus foretold. Swiss Paracelsus, in's alchemic lair, Saw Sulfur, Salt, and Mercury unfold Amid Mellennial hopes of faking Gold. Lavoisier dethroned Phlogiston; hen Molecular Analysis made bold Forays into the gases: Hydrogen Stood naked in the dazzled sight of Learned Men. ... read the entire poem on Scientific American's web site

Elevating Science, Elevating Democracy

In Jan. 26th New York Times there was an excellent article by Dennis Overbye entitled "Elevating Science, Elevating Democracy". Two paragraphs warrant reading. "The knock on science from its cultural and religious critics is that it is arrogant and materialistic. It tells us wondrous things about nature and how to manipulate it, but not what we should do with this knowledge and power. The Big Bang doesn’t tell us how to live, or whether God loves us, or whether there is any God at all. It provides scant counsel on same-sex marriage or eating meat. It is silent on the desirability of mutual assured destruction as a strategy for deterring nuclear war." and "Science is not a monument of received Truth but something that people do to look for truth. That endeavor, which has transformed the world in the last few centuries, does indeed teach values. Those values, among others, are honesty, doubt, respect for evidence, openness, accountability and tolerance and indeed hunger for opposing points of view. These are the unabashedly pragmatic working principles that guide the buzzing, testing, poking, probing, argumentative, gossiping, gadgety, joking, dreaming and tendentious cloud of activity — the writer and biologist Lewis Thomas once likened it to an anthill — that is slowly and thoroughly penetrating every nook and cranny of the world."

11/21/2007

"...all my moral and intellectual being is penetrated by an invincible conviction that whatever falls under the dominion of our senses must be in nature and, however exceptional, cannot differ in its essence from all the other effects of the visible and tangible world of which we are a self-conscious part. The world of the living contains enough marvels and mysteries as it is; marvels and mysteries acting upon our emotions and intelligence in ways so inexplicable that it would almost justify the conception of life as an enchanted state. No, I am too firm in my consciousness of the marvellous to be ever fascinated by the mere supernatural, which (take it any way you like) is but a manufactured article, the fabrication of minds insensitive to the intimate delicacies of our relation to the dead and to the living, in their countless multitudes; a desecration of our tenderest memories; an outrage on our dignity." Joseph Conrad, The Shadow Line

11/14/2007

"To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature. If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in." -- Richard P. Feynman

9/05/2007

play it out

In Robert Draper’s book on the Bush presidency, “Dead Certain,” Bush says the goal of his Iraq strategy is to play it out until “October-November.” That is when he hopes the Iraq troop increase will finally show enough results to help him achieve the central goal of his remaining time in office: “To get us in a position where the presidential candidates will be comfortable about sustaining a presence,” and, he said later, “stay longer.”

"As flies to wanton boys are we to the gods; They kill us for their sport."

Gloucester in Shakespeare’s King Lear

12/08/2006

The Cassandra Chronicles

Paul Krugman, ever interesting, has a reference to a Weekly Standard article published April 21,2003 entitled "The Cassandra Chronicles" which is vicious in its condemnation of the Iraqi war naysayers. Here's a link to his column entotled "They told you so" with some additional quotes. What is so incredible is that the editor of the Weekly Standard didn't know the Cassandra story who was given the gift of profecy but cursed so that no one would ever believe her predictions. This is testimony to the sad state of education on the right.

12/07/2006

Conventional Wisdom

"It was John Kenneth Galbraith, the hyperliterate economic sage, who coined the phrase 'conventional wisdom.' He did not consider it a compliment. 'We associate truth with convenience,' he wrote, 'with what most closely accords with self-interest and personal well-being or promises best to avoid awkward effort or unwelcome dislocation of life. We also find highly acceptable what contributes most to self-esteem.' Economic and social behavior, Galbraith continued, 'are complex, and to comprehend their character is mentally tiring. Therefore we adhere, as though to a raft, to those ideas which represent our understanding.' "So the conventional wisdom in Galbraith’s view must be simple, convenient, comfortable, and comforting--though not necessarily true. It would be silly to argue that the conventional wisdom is never true. But noticing where the conventional wisdom may be false--noticing, perhaps, the contrails of sloppy or self-interested thinking--is a nice place to start asking questions." Steven D. Levitt, Freakonomics, Harper Collins, 2005, pp. 89-90.

Reason and free inquiry

"Reason and free inquiry are the only effectual agents against error… They are the natural enemies of error, and of error only… It is error alone which needs the support of government. Truth can stand by itself… is uniformity of opinion desirable? No more than of face and stature. Difference of opinion is advantageous in religion… What has been the effect of coercion? To make one half the world fools, and the other half hypocrites. To support roguery and error all over the earth… Free inquiry must be indulged; and how can we wish others to indulge it while we refuse it ourselves." Thomas Jefferson, Sources of the American Republic, Volume I, p. 277-278

10/20/2006

Television and Autism

Online magazine Slate had an article on Television and Autism and while I find the premise interesting the study appears flawed. In passing they mention the four hours the average child spends watching television daily. To me mentioning that fact without comment is incredible. Here's my comment that Slate featured as one of the selected responses. "If children were doing anything else for an average of four hours a day (except for school or sleeping) society would be worried. Imagine if children were spending on average 4 hours a day knitting, playing checkers or collecting stamps. We'd say that's it's too much, unhealthy, need a balance. But when it comes to TV four hours a day is normal and hardly a peep of protest. Autism connection aside, for your child's sake, limit TV to as little as possible, it'll make the world of difference to their life. Life is too special to waste watching television. Encourage your child to be active not passive, particpate not vegetate, think for yourself, not be programmed by someone else."

10/12/2006

Taxes and Freedoms

"Montesquieu's Limits of Absolutism: General rule: one can raise higher taxes in proportion to the liberty of the subjects: and one is forced to moderate them to the degree that servitude increases. This has always been, and will always remain so." James MacDonald, A Free Nation Deep in Debt, Farrar, Straus, 2003, pp. 253-5.

9/29/2006

Torture

"...the United States reaffirms its commitment to the worldwide elimination of torture. Freedom from torture is an inalienable human right, and we are committed to building a world where human rights are respected and protected by the rule of law." President Bush, June 26, 2005 "The bill...systematically distinguishes "severe pain"—the hallmark of torture—from (mere) "serious" pain—the hallmark of cruel and degrading treatment, usually thought to denote mistreatment short of torture. But then it defines serious physical pain as "bodily injury that involves ... extreme physical pain."" Slate Sept 29th on the Terrorist Detainee Bill

9/28/2006

Computers and Computer Programmers

For a long time it puzzled me how something so expensive, so leading edge, could be so useless, and then it occurred to me that a computer is a stupid machine with the ability to do incredibly smart things, while computer programmers are smart people with the ability to do incredibly stupid things. They are, in short, a perfect match. - Bill Bryson, Notes from a Big Country

6/16/2006

In a medium in which a News Piece takes a minute and an In-Depth Piece takes two minutes, the Simple will drive out the Complex. - Frank Mankiewicz

10/06/2005

Obviously, a man's judgement cannot be better than the information on which he has based it. Give him the truth and he may still go wrong when he has the chance to be right, but give him no news or present him only with distorted and incomplete data, with ignorant, sloppy or biased reporting, with propaganda and deliberate falsehoods, and you destroy his whole reasoning processes, and make him something less than a man. - Arthur Hays Sulzberger

9/15/2005

If a child is to keep alive his inborn sense of wonder, he needs the companionship of at least one adult who can share it, rediscovering with him the joy, excitement, and mystery of the world we live in. - Rachel Louise Carson, 1907 - 1964

9/13/2005

JFK and GWB - Compare and Contrast If this nation is to be wise as well as strong, if we are to achieve our destiny, then we need more new ideas for more wise men reading more good books in more public libraries. These libraries should be open to all - except the censor. We must know all the facts and hear all the alternatives and listen to all the criticisms. Let us welcome controversial books and controversial authors. For the Bill of Rights is the guardian of our security as well as our liberty. - John Fitzgerald Kennedy, 1917 - 1963 One of the great things about books is sometimes there are some fantastic pictures. George W. Bush: January 3, 2000

8/24/2005

Simon Singh's "Code Book" An interactive CD-Rom version of Simon Singh's "Code Book" is now available as a FREE download on his website. Note the download is a 600 MB file and takes 2 to 4 hours to download on a typical broadband connection. But it's worth it as Arthur C. Clarke says "It is a fascinating CD-ROM, and I can see how one could get obsessed with the subject!"

6/21/2005

Generational Commitment This morning on Fox News Sunday, Secretary of State Condoleezza Rice was asked if “the Bush administration fairly [can] be criticized for failing to level with the American people about how long and difficult this commitment will be?” Rice responded: [T]he administration, I think, has said to the American people that it is a generational commitment to Iraq. That’s not true. To build support for the war the administration told the American people that the conflict in Iraq will be short and affordable. Vice President Dick Cheney, 3/16/03: [M]y belief is we will, in fact, be greeted as liberators. . . . I think it will go relatively quickly. . . (in) weeks rather than months Donald Rumsfeld, 2/7/03: It is unknowable how long that conflict will last. It could last six days, six weeks. I doubt six months. Former Budget Director Mitch Daniels, 3/28/03: The United States is committed to helping Iraq recover from the conflict, but Iraq will not require sustained aid…

6/14/2005

Math Fun Facts The Mellon Foundation and Harvey Mudd College have set up a Math Fun Facts. Many are interesting, some are bizarre. Take a look at the man with the square wheel bike.

6/08/2005

Small gaps between primes or almost primes An exciting paper has been re-released by Goldston, Graham, Pintz and Yilidrim which is a correction of their monumental announcement of two years ago on the first real progresss in decades on the age old twin prime problem. After working for twenty years, Goldston has not solved the twin prime conjecture but an affirmative anwser is given to a similar question : "Can you find an infinite number of primes that may not be twins, but that are much closer together than average". Read the paper here

2/11/2005

Television and Children. Toronto's Globe and Mail newspaper recently published an article extolling the benefits of educational television over entertainment television for children. To me it's akin to arguing that children playing with a toy hand gun is better than a child playing with a toy assault weapon. Yes I did both as a child, but I certainly would not allow my son to do it. Times have changed, most parents have learned. The same should be true for television. It's not needed. Below is my letter to the editor thet the Globe and mail published on Feb 11th responding to the virtues of television article. Regarding Television and Children While educational programs for children may be better than entertainment programs, no television is still the best. Children learn from doing not from watching. Programs like Sesame Street with its short entertaining segments destroy a child's attention span. Children become passive consumers of television programs instead of active participants in the real world. As a parent I know it's a lot of extra work to shut off the television baby sitter and spend time with my child, but childhood is too wonderful to surrender to television.

1/27/2005

April is Math Awareness Month April is Math Awareness month with this year's theme being "Math and the Cosmos". "Mathematics is at the core of our attempts to understand the cosmos at every level: Riemannian geometry and topology furnish models of the universe, numerical simulations help us to understand large-scale dynamics, celestial mechanics provides a key to comprehending the solar system, and a wide variety of mathematical tools are needed for actual exploration of the space around us." See www.mathaware.org for details

1/19/2005

Harvard President's remarks on Women and science. In the light of Harvard President Lawrence Summers disparaging remarks on women in science it is instructive for comparison to reflect on the remarks of two great mathematicians and their views of women in mathematics. Gauss’s remaks when he discovered that his correspondent “Monsieur Leblanc” was actually a woman, Sophie Germain: "But how to describe to you my admiration and astonishment at seeing my esteemed correspondent Monsieur LeBlanc metamorphose himself into this illustrious personage who gives such a brilliant example of what I would find it difficult to believe. The enchanting charms of this sublime science reveal only to those who have the courage to go deeply into it. But when a woman, who because of her sex and our prejudices encounters infinitely more obstacles that an man in familiarizing herself with complicated problems, succeeds nevertheless in surmounting these obstacles and penetrating the most obscure parts of them, without doubt she must have the noblest courage, quite extraordinary talents and superior genius." Carl Friedrich Gauss - see here for more details on Sophie Germain On the frustration faced by David Hilbert in trying to get an appointment for Emmy Noether at the University of Gottingen. ``I do not see that the sex of the candidate is an argument against her admission as Privatdozent (lecturer). After all, we are a university, not a bathing establishment.'' see here

1/11/2005

January 27th is Family Literacy Day January 27th is Family Literacy Day. Shut off the television, power down the computer and read, especially with your children. If your child is younger, read them their favourite book. If your child is older, read the same book as your child and discuss it. Every twelve year old know who Sirius Black is, you should too. For more ideas go to Family Literacy Tips.

12/16/2004

"Programming today is a race between software engineers striving to build bigger and better idiot-proof programs and the universe trying to produce bigger and better idiots. So far, the universe is winning." Rich Cook

An invitation to additive prime number theory A.V. Kumchev and D.I. Tolev have compiled a short document entitled An Invitation to Additive Prime Number Theory. From the introduction to the article : "The main purpose of this survey is to introduce the inexperienced reader to additive prime number theory and some related branches of analytic number theory. We state the main problems in the field, sketch their history and the basic machinery used to study them, and try to give a representative sample of the directions of current research." There are over 250 references in the article, it's quite extensive.

12/10/2004

COMPUTATIONAL METHODS AND EXPERIMENTS IN ANALYTIC NUMBER THEORY Here's a 74 page article on computational aspects of analytic umber theory by Michael Rubinstein. I haven't read it all, egad who would, but the section titled Experiments involving L-functions has some interesting applications to the Riemann Zeta Function.

12/08/2004

Google Scholar "Google Scholar is a search specifically for scholarly literature, including peer-reviewed papers, theses, books, preprints, abstracts and technical reports from all broad areas of research. Use Google Scholar to find articles from a wide variety of academic publishers, professional societies, preprint repositories and universities, as well as scholarly articles available across the web."

11/02/2004

URL for Meht's 3rd Edition of his book on Random Matrices The amazon.com URL for the third edition of Mehta's book on random Matrices is here.

10/26/2004

Meht's Random Matrices - Third Edition A third edition to Madan Lal Meht's classic Random Matrices is being released on November 28th by Elsevier Academic Press. It's doubly good news as the old one was perpetually out of print and the new one is cheaper ($90 US instead on $110 US). I'm sure this book will find its way into many a Christmas stocking this year.

The real story on Gauss All mathematicians have read the story of Gauss's precociousness when at the age of 10 was given by an exasperated teacher the problem of adding all the numbers from 1 to 100 and then returned the answer in seconds. Well apparently, like Newton's apple, it didn't quite happen that way. Ivars Peterson in Science News relates a somewhat more interesting story involving a more challenging arithmetic progression.

10/22/2004

Google Saves Kidnapped Journalist in Iraq A kidnapped Australian journalist was freed by his captors in Iraq after they searched on Google to confirm his identity as a journalist and not a CIA agent. See the full article here.

10/19/2004

Followup to Ten Trillion Zeta Zeros Ed Pegg in an article in Math Games at MAA online has an informative article placing the calculation of the 10 trillionth non trivial Zero of the Zeta function in context. It's an excellent article with some very informative historical links to the Zeta function's history.

10/14/2004

Math in the Media The American Mathematical Society has created a new online periodical called Math in the Media. Not only doews it contain news about mathematics, as well as sections on books, plays, movies or television shows related to mathematics. If you scroll to the bottom you'll see a reference to a article in La Repubblica, one of Italy's leading newspapers, about a Lebanese engineer who has recently announced a proof of Euclid's Fifth Postulate. That proof can be filed in the same draw as perpetual motion machines.

10/13/2004

New Riemann Hypothesis verification record Xavier Gourdon with the help of Patrick Demichel have verified the first 10 to the 13th power crtical line zeros of the Riemann function and reports the results as well as describing their technique in this 37 page paper. Additionally to test the GUE hypothesis concerning the distribution of zeros the paper describes how to calculate zeros at very large height on the critical line.

10/12/2004

Death of philosopher Jacques Derrida The father of deconstructionism has himself deconstructed. Jacques Derrida died in a Paris hospital on Friday at the age of 74 from pancreatic cancer. His voluminus output may have stopped by we need not stop the creation of new texts. See the Postmodernism Generator written by Andrew C. Bulhak using the Dada Engine, a system for generating random text from recursive grammars. On a similar note not to be missed is Alan Sokal's "Social Text Affair".

Fourteen Proofs Robin Chapman of the Univesity of Exeter's home page has an interesting paper that gives fourteen proofs that the sum of the reciprocals of the squares of the natural numbers equals pi squared over six (see Evaluating zeta(2) ) Given this result you can tproove another amazing result. If you pick any two positive integers at random, the probability of them having no common divisor is 6 divided by pi squared.

10/06/2004

Interesting Links A free referred mathematical journal is available online at DOCUMENTA MATHEMATICA. Let's hope to see more like this. Science.ca is an interesting link for information about Canadian science. Check out their take on that age old question "How many baseballs could fit inside the earth?"

10/05/2004

The Wall Street Journal's new motto - All the news that we want to see. The WSJ has sidelined Farnaz Fassihi, the Wall Street Journal's Middle East correspondent, until after the Nov. 2 election. Apparently it didn't like her private e-mail sent to friends that got reprinted on the web. See here for a copy. This is not befitting of a newspaper that employed Daniel Pearl.

9/28/2004

Which Springer-Verlag Graduate Text in Mathematics are you? Try this amusing multiple choice questionaire developed by David Savitt, a postdoctoral fellow in Mathematics at McGill to determine what Graduate mathematics text best suits your personality.

9/27/2004

Free Books on the Net HHM.com.ar has a pretty good repository of Free books in the net. Not warez or pirate stuff, but legal downloads of computer and math related books.

9/24/2004

Ice Cream Headache Explained Are you one of approximately 1/3 of people like myself that's susceptible to "brain freeze", the common name for ice cream headache. This article in the British Medical Journal describes the phenomenon. There's lots of medical talk about the experience, but the common sense solution is to keep cold substance away from the back of the palate. Now that you know the solution, if you're in Toronto go to Ed's Real Ice Cream on Queen Street in Toronto Beach neighbourhood and try their Pumpkin flavoured ice cream.

9/20/2004

Mathsoft's List of Unsolved Math Problems Mathsoft has a list of interesting unsolved math problems

9/15/2004

Potpourri "In Potpourri[47 pp,pdf], Stephen William Semmes covers a variety of basic topics in graduate-level mathematics. The book's contents come from class notes and are "very much influenced by the participants and the discussions in the class." There is a short chapter for each of about 18 sections and this may make a good supplementary or reference text to more thorough texts"

9/14/2004

Manifolds in the Genesis mission "Ed Pegg Jr. gives a wonderful history of the mathematical research leading up to the recently recovered Genesis spacecraft in his latest column. The story began in the late 19th century when King Oscar II of Norway and Sweden offered reward money to anyone who can solve a number of problems. One such problem was to prove whether Newton's and Kepler's equations were stable for our solar system. Poincare accepted this challenge and submitted a proof which, although it contained a large error which he later fixed, won the prize money (Poincare had to spend more money to stop publication of his original proof than what he won). The error in the paper itself led to the origins of chaos theory. The mathematics he used to solve the problem became the tool used in space exploration today. "

9/07/2004

Claimed proof of the Poincaré conjecture is back in the news The Poincaré conjecture, first proposed in 1904 by H. Poincaré, one of the problems that the Clay Mathematics Institute is offering one million for a solution in math is back in the news as mathematicians are coming closer to accepting the solution of Dr Grigori Perelman, of the Steklov Institute of Mathematics. The conjecture states that every simply connected closed 3-manifold is homeomorphic to the 3-sphere. The BBC has a nice story on it, as does the Scotsman. Don’t believe what you read in the Scotsman about the proof of the Riemann hypothesis, that problem is still to be solved.

9/05/2004

Wonderful new author I've found While checking out books from the library last week I noticed on the recommended shelf a book on naval history by James L. Nelson entitled "The Reign of Iron: The story of the first battling ironclads, the monitor and the Merrimack". Picking it up on a whim, I found a first -rate historical writer. The book is more than a dry historical account of this American civil war confrontation, but describes in detail the personalities involved, the confusion of the time and the parallel developments that brought these two revolutionary ships together in Hampton Roads in March of 1862. You can read the first chapter online here to get a taste of the author's style. The author, a former professional sailor also has written fiction about the American revolutionary war and I'm anxious to see if his fiction is as compelling as his non-fiction.

9/03/2004

On-Line Encyclopedia of Integer Sequences For an off beat web site of interest to math nerds try out On-line Encycloperdia of Integer Sequences. Neil A.J. Sloane of AT&T Shannon Labs in Florham Park, N.J., has been collecting number sequences ever since he was a graduate student at Cornell University in the 1960s. Sloane has some number sequence puzzles at http://www.research.att.com/~njas/sequences/Spuzzle.html. When you give up, you can just click on a link to see the answer.

9/02/2004

Music of the Primes Professor Marcus du Sautoy website www.musicoftheprimes.com , based upon his best selling book (at least in math circles) Music of the Primes is finally up. The book was a wonderful, combining history, personalities and just enough math. The web site has a rather non-standard design but once you figure out how to navigate there's some intersting gems. Of non mathematical interest there's the photo gallery of prime numbers with lots of prime numbers left to photograph and submit.

9/01/2004

e - The second most famous transcendental number Of the irrational, transcendental numbers, pi seems to get all the attention. Its digits have been computed to 1,241,100,000,000 decimal places. In the silver medal place is e (2.71828 18284 59045 23536....). Only 1,250,000,000 of its decimal digits have been computed so far. It's been called the logarithmic constant, Napier's number, Euler's constant, and the natural logarithmic base. I call it just plain e. It was the first transcendatal number I calculated on my old Apple II computer over 20 years ago. Running all night it calculated e to more than 50,000 decimal places. Two Math nerds, inventor Harlan J. Brothers and meteorologist John A. Knox, have a web site with over 20 ways to calculate this fundamental constant. Of particular interst is a recent paper just published this year entitled "Improving the convergence of Newton's series approximation for e". It's a good read and makes me want to tackle the computation with a more substantial computer than a 1 MHz 8 bit processor of 20 years ago.

8/30/2004

"Progressives" in the news David Brooks has an interesting article in last Sunday's New York Times Magazine outlining a new "progressive" U.S. Republican party to replace the mess of policies Bush and the new-con's have created. He's hedges his criticisms but advocates a form of policy that seems to be very much in line with the Clinton/Gore years. It baffles me how intelligent conservatives can stick with that party. It must be the greed from the tax cuts that clouds their judgement. The second form of Progressives in the news is a new record of 23 progressive primes. Markus Frind, Paul Jobling, and Paul Underwood announced that they had discovered the first sequence consisting of 23 prime numbers in arithmetic progression. This surpasses the previous record of 22 primes in arithmetic progression, set in 1993. The new record holder starts with the prime 56,211,383,760,397 and adds 44,546,738,095,860 for each successive term in the sequence.

8/19/2004

"Catalan's Conjecture predicts that 8 and 9 are the only consecutive perfect powers among positive integers. The conjecture, which dates back to 1844, was recently proven by the Swiss mathematician Preda Mihailescu. A deep theorem about cyclotomic fields plays a crucial role in his proof. Like Fermat's problem, this problem has a rich history with some surprising turns. " See the review article here .

8/16/2004

Dan Segal's of Review book Gamma There's an excellent review of the book by Julian Havil on the AMS web site on Gamma.

5/14/2004

"Planning for the future without a sense of history is like planting cut flowers." Daniel Boorstin

4/07/2004

TV linked to attention problems From my letter in today's Globe and Mail Toronto -- As a parent of a young child, I couldn't agree more about the negative effects of television (TV Linked To Attention Problems -- April 6). Children need people to interact with, not a flickering screen. Parents should take the $50 a month spent on cable and buy craft supplies or a soccer ball. They should get books from the library and read to their children. Books are slow and peaceful, television is fast and frantic. Life is too wonderful for a child to waste in front of a TV. See Throw out the TV

3/16/2004

Isn't it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too? - Douglas Adams

3/11/2004

“Everything should be made as simple as possible, but not simpler.” Albert Einstein, physicist Albert Einstein was born 125 years ago March 14. For a list of all things Einstien go to Albert Einstein Online. A good explanation of Special Relativity is found at Helen Quinn's Site at Stanford.

3/03/2004

"Mathematics, rightly viewed, possesses not only truth, but supreme beauty -- a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry." Bertrand Russell - Study of Mathematics

3/01/2004

Lord of the Rings Perhaps to celebrate the Lord of the Rings winning eleven Oscars, Nasa has released this glorious new image of Saturn from NASA's Cassini spacecraft acquired this on February 9th from a range of 69.4 million kilometers. The resolution enables viewing of features down to 540 km across. The picture shows multicolored bands in the planet's atmosphere, the Cassini Division and Encke Gap in the rings, and the icy moon Enceladus to Saturn's upper left.

Programmer's Drinking Song: 99 programming bugs in the code 99 programming bugs Fix one bug, compile it again Now there's 100 bugs in the code! (Repeat until bugs=0)

2/23/2004

Threads on Mars Check out this article and image from Space.com showing small thread-like objects in the Martian regolith. Before getting too excited they may simply be threads from the space crafts air bags.

2/17/2004

"The mathematician may be compared to a designer of garments, who is utterly oblivious of the creatures whom his garments may fit. To be sure, his art originated in the necessity for clothing such creatures, but this was long ago; to this day a shape will occasionally appear which will fit into the garment as if the garment had been made for it. Then there is no end of surprise and delight." D'Alembert, Jean Le Rond (1717-1783) for more quotes see Mathematical Quotation Server

2/12/2004

HAPPY BIRTHDAY DARWIN Today, February 12, 1809, is the 195th birthday of Charles Darwin. And now, with some irony, it will also go down in history as the date that the first serious scientific announcement of successful human cloning was made. See the article in the NY Times and Science magazine

2/03/2004

"Next the statesmen will invent cheap lies, putting the blame upon the nation that is attacked, and every man will be glad of those conscience-soothing falsities, and will diligently study them, and refuse to examine any refutations of them; and thus he will by and by convince himself that the war is just, and will thank God for the better sleep he enjoys after this process of grotesque self-deception." — Mark Twain

1/28/2004

A Child's Guide to Using Daddy's Computer © 1994 Gene Ziegler Bits Bytes Chips Clocks Bits in bytes on chips in box. Bytes with bits and chips with clocks. Chips in box on ether-docks. Chips with bits come. Chips with bytes come. Chips with bits and bytes and clocks come. Look, sir. Look, sir. read the book, sir. Let's do tricks with bits and bytes, sir. Let's do tricks with chips and clocks, sir. First, I'll make a quick trick bit stack. Then I'll make a quick trick byte stack. You can make a quick trick chip stack. You can make a quick trick clock stack. And here's a new trick on the scene. Bits in bytes for your machine. Bytes in words to fill your screen. Now we come to ticks and tocks, sir. Try to say this by the clock, sir. Clocks on chips tick. Clocks on chips tock. Eight byte bits tick. Eight bit bytes tock. Clocks on chips with eight bit bytes tick. Chips with clocks and eight byte bits tock. Here's an easy game to play. Here's an easy thing to say.... If a packet hits a pocket on a socket on a port, and the bus is interrupted as a very last resort, and the address of the memory makes your floppy disk abort then the socket packet pocket has an error to report! If your cursor finds a menu item followed by a dash, and the double-clicking icon puts your window in the trash, and your data is corrupted cause the index doesn't hash, then your situation's hopeless, and your system's gunna crash. You can't say this? What a shame, sir! We'll find you another game, sir. If the label on the cable on the table at your house says the network is connected to the button on your mouse, but your packets want to tunnel on another protocol, that's repeatedly rejected by the printer down the hall, and your screen is all distorted by the side-effects of gauss, so your icons in the window are as wavy as a souse, then you may as well reboot and go out with a bang, cause as sure as I'm a poet, the sucker's gunna hang! When the copy of your floppy's getting sloppy on the disk, and the microcode instructions cause unnecessary risc, then you have to flash your memory and you'll want to RAM your ROM. quickly turn off your computer and be sure to tell your mom!

Word of the day - great dirhombicosidodecacron. See this entry at mathworld for an explanation

1/26/2004

Read the classics Seventy five years ago astronomers knew only of the Milky Way. To them our galaxy was the universe. Edwin Hubble in a paper entitled "A relation Between Distance and Radial Velocity Among Extra-Galactic Nebulae" published in January 1929 changed all this and in the process gave birth to the entire branch of astronomy known as cosmology. His famous paper proved with observational evidence that galaxies are moving away from us with a speed proportional to their distance and expanded our knowledge of the universe from one galaxy to billions of galaxies.

1/21/2004

So you're cold. Take a look at this image taken January 15 from NASA's Earth Observatory showing the veil of snow on the Northeastern U.S.

1/20/2004

In one's life there may come a moment when one has to put one's principles to the test and realize that there are some moral absolutes and that the end justifies the means isn't a valid method of moral reasoning. That moment came for Katharine Gun, a translator at Britain’s top-secret Government Communications Headquarters. When confronted with the plan by British and American intelligence last year to bug U.N. security council members' telephones and e-mails she leaked the plan to the press. She now faces up to two years in prison for breaking the official secrets act. Read about it in this NY Times article or at commondreams.org.

1/09/2004

I am the enemy you killed, my friend. I knew you in this dark: for so you frowned Yesterday through me as you jabbed and killed. I parried; but my hands were loath and cold. Let us sleep now. —Wilfred Owen, "Strange Meeting"

"Simply stated, there is no doubt that Saddam Hussein now has weapons of mass destruction," Dick Cheney on Aug. 26, 2002. "We know for a fact that there are weapons there," Ari Fleischer on Jan. 9, 2003. "We know that Saddam Hussein is determined to keep his weapons of mass destruction, is determined to make more," Colin Powellon Feb. 5, 2003. "We know where they are," about these weapons. "They are in the area around Tikrit and Baghdad," Donald Rumsfeld on March 30, 2003. "We have sources that tell us that Saddam Hussein recently authorized Iraqi field commanders to use chemical weapons," George W. Bush on Feb. 8, 2003. Since the war in Iraq started, 500 American soldiers and thousands of Iraqi's have died for these lies. "If in some smothering dreams you too could pace Behind the wagon that we flung him in, And watch the white eyes writhing in his face, His hanging face, like a devil's sick of sin; If you could hear, at every jolt, the blood Come gargling from the froth-corrupted lungs, Obscene as cancer, bitter as the cud Of vile, incurable sores on innocent tongues,? My friend, you would not tell with such high zest To children ardent for some desperate glory, The old Lie: Dulce et decorum est Pro patria mori." Wilfred Owen, prior to his death on November 4, 1918,

10/07/2003

This just in New York (CNN). At John F. Kennedy International Airport today, a Caucasian male (later discovered to be a high school mathematics teacher) was arrested trying to board a flight while in possession of a compass, a protractor and a graphical calculator. According to law enforcement officials, he is believed to have ties to the Al-Gebra network. He will be charged with carrying weapons of math instruction.

10/03/2003

New Scientist reports that an asteroid about the size of a small house passed just 88,000 kilometres from the Earth by on Saturday 27 September - the closest approach of a natural object ever recorded. Geostationary communication satellites circle the Earth 42,000km from the planet's centre. The asteroid, designated 2003 SQ222, came from inside the Earth's orbit and so was only spotted after it had whizzed by.

Take a look at the new Canadian Magazine, The Walrus. I just got mine yesterday and it's professional, well written and so-far very informative.

"Even though I'm a tranquil guy now at this stage of my life, I have nothing but contempt and anger for those who betray the trust by exposing the name of our sources. They are, in my view, the most insidious of traitors." — George H. W. Bush, 1999 See the Article in TomPaine.com entitlted Conscience Before Career by Ray McGovern, a former CIA analyst .

9/29/2003

"The BBC is reporting that a village in eastern India was struck by a meteorite Saturday evening, wrecking several houses and injuring about twenty people. Fortunately, no one appears to have been killed by the impact or subsequent fires. CNN suggests that a second village near the impact site may have also been struck by part of the meteorite." Human/meteorite encounters are not entirely unheard of.

9/17/2003

There's a spectacular image of hurricane Isabel on Nasa's Earth's Observatory

8/27/2003

The fetters imposed on liberty at home have ever been forged out of the weapons provided for defence against real, pretended, or imaginary dangers from abroad. -James Madison, 4th US president (1751-1836)

7/14/2003

Published on Sunday, July 13, 2003 by the lndependent/UK 20 Lies About the War Falsehoods Ranging from Exaggeration to Plain Untruth Were Used to Make the Case for War. More Lies are Being Used in the Aftermath by Glen Rangwala and Raymond Whitaker 1. Iraq was responsible for the 11 September attacks A supposed meeting in Prague between Mohammed Atta, leader of the 11 September hijackers, and an Iraqi intelligence official was the main basis for this claim, but Czech intelligence later conceded that the Iraqi's contact could not have been Atta. This did not stop the constant stream of assertions that Iraq was involved in 9/11, which was so successful that at one stage opinion polls showed that two-thirds of Americans believed the hand of Saddam Hussein was behind the attacks. Almost as many believed Iraqi hijackers were aboard the crashed airliners; in fact there were none. 2. Iraq and al-Qa'ida were working together Persistent claims by US and British leaders that Saddam and Osama bin Laden were in league with each other were contradicted by a leaked British Defense Intelligence Staff report, which said there were no current links between them. Mr Bin Laden's "aims are in ideological conflict with present-day Iraq", it added. Another strand to the claims was that al-Qa'ida members were being sheltered in Iraq, and had set up a poisons training camp. When US troops reached the camp, they found no chemical or biological traces. 3. Iraq was seeking uranium from Africa for a "reconstituted" nuclear weapons program The head of the CIA has now admitted that documents purporting to show that Iraq tried to import uranium from Niger in west Africa were forged, and that the claim should never have been in President Bush's State of the Union address. Britain sticks by the claim, insisting it has "separate intelligence". The Foreign Office conceded last week that this information is now "under review". 4. Iraq was trying to import aluminum tubes to develop nuclear weapons The US persistently alleged that Baghdad tried to buy high-strength aluminum tubes whose only use could be in gas centrifuges, needed to enrich uranium for nuclear weapons. Equally persistently, the International Atomic Energy Agency said the tubes were being used for artillery rockets. The head of the IAEA, Mohamed El Baradei, told the UN Security Council in January that the tubes were not even suitable for centrifuges. 5. Iraq still had vast stocks of chemical and biological weapons from the first Gulf War Iraq possessed enough dangerous substances to kill the whole world, it was alleged more than once. It had pilotless aircraft which could be smuggled into the US and used to spray chemical and biological toxins. Experts pointed out that apart from mustard gas, Iraq never had the technology to produce materials with a shelf-life of 12 years, the time between the two wars. All such agents would have deteriorated to the point of uselessness years ago. 6. Iraq retained up to 20 missiles which could carry chemical or biological warheads, with a range which would threaten British forces in Cyprus Apart from the fact that there has been no sign of these missiles since the invasion, Britain downplayed the risk of there being any such weapons in Iraq once the fighting began. It was also revealed that chemical protection equipment was removed from British bases in Cyprus last year, indicating that the Government did not take its own claims seriously. 7. Saddam Hussein had the wherewithal to develop smallpox This allegation was made by the Secretary of State, Colin Powell, in his address to the UN Security Council in February. The following month the UN said there was nothing to support it. 8. US and British claims were supported by the inspectors According to Jack Straw, chief UN weapons inspector Hans Blix "pointed out" that Iraq had 10,000 liters of anthrax. Tony Blair said Iraq's chemical, biological and "indeed the nuclear weapons program" had been well documented by the UN. Mr Blix's reply? "This is not the same as saying there are weapons of mass destruction," he said last September. "If I had solid evidence that Iraq retained weapons of mass destruction or were constructing such weapons, I would take it to the Security Council." In May this year he added: "I am obviously very interested in the question of whether or not there were weapons of mass destruction, and I am beginning to suspect there possibly were not." 9. Previous weapons inspections had failed Tony Blair told this newspaper in March that the UN had "tried unsuccessfully for 12 years to get Saddam to disarm peacefully". But in 1999 a Security Council panel concluded: "Although important elements still have to be resolved, the bulk of Iraq's proscribed weapons programs has been eliminated." Mr Blair also claimed UN inspectors "found no trace at all of Saddam's offensive biological weapons program" until his son-in-law defected. In fact the UN got the regime to admit to its biological weapons program more than a month before the defection. 10. Iraq was obstructing the inspectors Britain's February "dodgy dossier" claimed inspectors' escorts were "trained to start long arguments" with other Iraqi officials while evidence was being hidden, and inspectors' journeys were monitored and notified ahead to remove surprise. Dr Blix said in February that the UN had conducted more than 400 inspections, all without notice, covering more than 300 sites. "We note that access to sites has so far been without problems," he said. : "In no case have we seen convincing evidence that the Iraqi side knew that the inspectors were coming." 11. Iraq could deploy its weapons of mass destruction in 45 minutes This now-notorious claim was based on a single source, said to be a serving Iraqi military officer. This individual has not been produced since the war, but in any case Tony Blair contradicted the claim in April. He said Iraq had begun to conceal its weapons in May 2002, which meant that they could not have been used within 45 minutes. 12. The "dodgy dossier" Mr Blair told the Commons in February, when the dossier was issued: "We issued further intelligence over the weekend about the infrastructure of concealment. It is obviously difficult when we publish intelligence reports." It soon emerged that most of it was cribbed without attribution from three articles on the internet. Last month Alastair Campbell took responsibility for the plagiarism committed by his staff, but stood by the dossier's accuracy, even though it confused two Iraqi intelligence organizations, and said one moved to new headquarters in 1990, two years before it was created. 13. War would be easy Public fears of war in the US and Britain were assuaged by assurances that oppressed Iraqis would welcome the invading forces; that "demolishing Saddam Hussein's military power and liberating Iraq would be a cakewalk", in the words of Kenneth Adelman, a senior Pentagon official in two previous Republican administrations. Resistance was patchy, but stiffer than expected, mainly from irregular forces fighting in civilian clothes. "This wasn't the enemy we war-gamed against," one general complained. 14. Umm Qasr The fall of Iraq's southernmost city and only port was announced several times before Anglo-American forces gained full control - by Defense Secretary Donald Rumsfeld, among others, and by Admiral Michael Boyce, chief of Britain's Defense staff. "Umm Qasr has been overwhelmed by the US Marines and is now in coalition hands," the Admiral announced, somewhat prematurely. 15. Basra rebellion Claims that the Shia Muslim population of Basra, Iraq's second city, had risen against their oppressors were repeated for days, long after it became clear to those there that this was little more than wishful thinking. The defeat of a supposed breakout by Iraqi armour was also announced by military spokesman in no position to know the truth. 16. The "rescue" of Private Jessica Lynch Private Jessica Lynch's "rescue" from a hospital in Nasiriya by American special forces was presented as the major "feel-good" story of the war. She was said to have fired back at Iraqi troops until her ammunition ran out, and was taken to hospital suffering bullet and stab wounds. It has since emerged that all her injuries were sustained in a vehicle crash, which left her incapable of firing any shot. Local medical staff had tried to return her to the Americans after Iraqi forces pulled out of the hospital, but the doctors had to turn back when US troops opened fire on them. The special forces encountered no resistance, but made sure the whole episode was filmed. 17. Troops would face chemical and biological weapons As US forces approached Baghdad, there was a rash of reports that they would cross a "red line", within which Republican Guard units were authorized to use chemical weapons. But Lieutenant General James Conway, the leading US marine general in Iraq, conceded afterwards that intelligence reports that chemical weapons had been deployed around Baghdad before the war were wrong. "It was a surprise to me ... that we have not uncovered weapons ... in some of the forward dispersal sites," he said. "We've been to virtually every ammunition supply point between the Kuwaiti border and Baghdad, but they're simply not there. We were simply wrong. Whether or not we're wrong at the national level, I think still very much remains to be seen." 18. Interrogation of scientists would yield the location of WMD "I have got absolutely no doubt that those weapons are there ... once we have the co-operation of the scientists and the experts, I have got no doubt that we will find them," Tony Blair said in April. Numerous similar assurances were issued by other leading figures, who said interrogations would provide the WMD discoveries that searches had failed to supply. But almost all Iraq's leading scientists are in custody, and claims that lingering fears of Saddam Hussein are stilling their tongues are beginning to wear thin. 19. Iraq's oil money would go to Iraqis Tony Blair complained in Parliament that "people falsely claim that we want to seize" Iraq's oil revenues, adding that they should be put in a trust fund for the Iraqi people administered through the UN. Britain should seek a Security Council resolution that would affirm "the use of all oil revenues for the benefit of the Iraqi people". Instead Britain co-sponsored a Security Council resolution that gave the US and UK control over Iraq's oil revenues. There is no UN-administered trust fund. Far from "all oil revenues" being used for the Iraqi people, the resolution continues to make deductions from Iraq's oil earnings to pay in compensation for the invasion of Kuwait in 1990. 20. WMD were found After repeated false sightings, both Tony Blair and George Bush proclaimed on 30 May that two trailers found in Iraq were mobile biological laboratories. "We have already found two trailers, both of which we believe were used for the production of biological weapons," said Mr Blair. Mr Bush went further: "Those who say we haven't found the banned manufacturing devices or banned weapons - they're wrong. We found them." It is now almost certain that the vehicles were for the production of hydrogen for weather balloons, just as the Iraqis claimed - and that they were exported by Britain. © 2003 Independent Digital (UK) Ltd

6/05/2003

Introduction to Primes The American Mathematical Society has an excellent introduction to Prime Numbers by Joseph Malkevitch of York College (CUNY) in its What's New in Math Section. Also covered is Agrawal, Kayal, and Saxena recent Primes in P paper.

5/28/2003

Earth and Moon as viewd from Mars Take a look at this first image of the Earth and Moon showing them as disks taken from another planet.

5/25/2003

"Objectivity cannot be equated with mental blankness; rather, objectivity resides in recognizing your preferences and then subjecting them to especially harsh scrutiny — and also in a willingness to revise or abandon your theories when the tests fail (as they usually do)." Stephen Jay Gould

5/21/2003

Looking for some summer reading If you're looking for some summer reading, there's a growing number of math books available for either reading online or downloading. Check out Edwin H. Connell's Elements of Abstract and Linear Algebra or the excellent A=B by Marko Petkovsek, Herbert Wilf and Doron Zeilberger. On a completely different subject, the book that arguably started modern science, Copernicus' De Revolutionibus preserved in the Jagiellonian Library in Cracow is available to view online.

5/07/2003

"A very bright fireball illuminated the sky over Austria on an April evening last year. The fireball was visible throughout central Europe and was photographed by the observatories of the European Fireball Network, a system set up for just such an eventuality. The calculated trajectory led to a 1.75-kg meteorite, found 6 km way from the Schloss Neuschwanstein, one of King Ludwig II's palaces. Now known as the Neuschwanstein meteorite, this is only the fourth meteorite to have been photographed in its final fall." See the article in the latest Nature.

Viking Kittens Again The original Viking kittens have been replaced by what I feel is a sub-standard offerring. To see the original Viking Kittens go to the link

5/01/2003

Future directions in algorithmic number theory The American Institute of Mathematics has a summary of work presented at the March 24 to 28 ARCC workshop that was motivated by the recent paper "Primes in P". See this link for the 32 page paper.

4/23/2003

Quantum Mechanical Approach to Hilbert's Tenth Problem Hilbert's tenth problem deals with determination of the solvability of a Diophantine equation. One formulation is "Given a diophantine equation with any number of unknown quantities and with rational integral numerical coefficients: To devise a process according to which it can be determined by a finite number of operations whether the equation is solvable in rational integers." In an oral contribution to SPIE, Orlando, Tien D Kieu of the Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Australia uses the Quantum adiabatic theorem to analyse various Diophantine equations. This is another in a intersting series of papers that have been publish recently where physics is shedding light on problems in Number Theory. It's only fair as for years physics has borrowed results from mathematicians, now perhaps, physics can return the favour.

4/17/2003

World's Largest Digital Camera The world's largest digital camera was unveiled last week at the Canada-France-Hawaii Telescope atop Mauna Kea in Hawaii. The 340-million-pixel, $100-million (US)MegaPrime camera is roughly 100 times more powerful than a commercial digital camera, say its creators. The telescope's unusually broad field of view will allow the device to photograph huge panoramas. "This camera will allow us to do some unique stuff," says Christian Veillet, executive director for the telescope. For example, researchers plan to use the camera to look for the distant explosions of dying stars and also to observe the Kuiper belt, a ring of asteroid-like objects beyond the orbit of Neptune.

Upcoming Public Lecture at The Fields Institute Manindra Agrawal of the Indian Institute of Technology will give a lecture at the Fields Institute (222 College Street, Toronto, Ontario) on May 23 at 3:30 on his recent work on a polynomial-time algorithm for primality testing. See this link for lecture details and this link for his ground breaking paper.

4/14/2003

Bush's Legacy I opposed this war and still do due to what I feel was the needless loss of U.S., British and Iraqi lives, but this is not the purpose of this blog entry. The Bush administration deemed the oil wells important enough to send special troops in advance to ensure their safety. Rumsfeld even called their torching a crime against humanity. But the Bush war mongers, despite warning from U.S. academics, did nothing to prevent the looting of the Iraqi national museum. The Iraqi nation's soul has been lost and the world has lost much of its connection with the cradle of civilization. Shame on you President Bush. But it's no surprise: it's oil that matters to this administration, not Iraqi lives, not history or not culture. To undertake nation-building in a divided, shattered country like Iraq, you need to draw on many resouces, not all of them being what you pump out of the ground. A country must rediscover its potential for greatness and purpose, and Iraq's long and important past as the cradle of civilization is a pillar of that rebuilding. This is the much worse than the Taliban shelling of the Buddhist statues. One tank and a platoon of soldiers could have prevented this loss (as one did for half an hour), but no one in the Bush admininstrations cared. Rumsfeld's comment was "Stuff happens." Shame on you President Bush. This is another part of your legacy that the Iraqi people and the world will remember for centuries.

4/11/2003

New Images of Mars Nasa has posted eleven thousand new images of Mars taken by the orbiting Mars Global Surveyor. "The new batch, taken between February and July 2002, brings the total number of images in the online gallery to more than 123,800," NASA said in a statement.

4/09/2003

Nasa's view of Baghdad
Nasa's Earth Observatory program released this March 31st image of Baghdad showing the environmental hazard of the burning pools of oil.

"War, like any other racket, pays high dividends to the very few. But what does it profit the masses? ... The cost of operations is always transferred to the people who do not profit. ... But there is a way to stop this racket. ... It can be effectively smashed only by taking the profit out of war." Marine Corps Major General Smedley Butler (1881 - 1940)

4/04/2003

Programming Language for a Quantum Computer No one has built one yet, no one really knows how to build one, but that didn't stop Stefano Bettelli of Paul Sabatier University in Toulouse, France from starting the process of designing a programming language for this non-existent quantum computer. In an article in the European Physical Journal, the author describes quantum registers, quantum operators and quantum bits (qubits). Those qubits can then be manipulated by the program by operators employing unitary transformations. Pretty heady stuff, but possiby the beginning of a new programming paradigm.

3/31/2003

More Interesting Prime News More interesting developments in the world of primes. Goldston and Yildrim have published results of their recent work that is a major step along in finding out is there is a infinite number of twin primes. For more general information on primes check out the prime number page.

3/28/2003

Answers to Questions Who am I? What am I? Where am I? Why am I? This web site can help you with the first three question, but good luck with the last. Go to Googlism and type in your own name, and discover yourself.

3/27/2003

Need to Calculate Prime Numbers I found an excellent little routine to calculate lists of prime numbers. See John Moyers page at the Research Solutions of Oklahoma. I want to so some further testing of it and refine it to look at prime number distributions.

3/26/2003

Tried of CNN et al.'s Iraq War Coverage Take a look at a BBC reporters war log page. BBC reporters in the war zone are logging their reports in real time.

Accurracy not so important In a chilling move the U.S. Justice department has lifted the restriction that the data in the FBI database run by its National Crime Information Center be accurate. The information in the database is used by law enforcement agencies, who routinely access it to determine whether to monitor, detain, or arrest individuals. No I'm not kidding, check out this AP story or abcnews. Perhaps Michael Moore was right, we do live in fictitious times.

3/25/2003

Prime numbers not so random? A team of physicists at Boston University testing a statistical tool they had developed to study heartbeat rythyms. (see Kumar, P. Ivanov, P. C. Stanley, H. E. Information entropy and correlations in prime numbers. Preprint. ). The team was looking into the interval between successive primes and conculded that the intervals were not random. The Boston team's findings are not supported by any kind of rigorous mathematical proof. So sadly they can't shed any light on one of the biggest problems in maths: the Riemann hypothesis.

3/20/2003

Causa Belli by Andrew Motion They read good books, and quote, but never learn a language other than the scream of rocket-burn Our straighter talk is drowned but ironclad; elections, money, empire, oil and Dad.

3/19/2003

The Quiet Astronaut Speaks Neil Armstrong, the first man on the moon, spoke his "giant leap fort mankind" statement while stepping off the lunar lander and hasn't hardly been heard from since. ery protective of his privacy, he has finally commissioned James Hansen, an Auburn University history professor, to write his biography. Several presses are already getting ready to bid for the book and a movie version is getting talk. See the article at space.com

3/18/2003

"Why of course the people don't want war ... But after all it is the leaders of the country who determine the policy, and it is always a simple matter to drag the people along, whether it is a democracy, or a fascist dictatorship, or a parliament, or a communist dictatorship ...Voice or no voice, the people can always be brought to the bidding of the leaders. That is easy. All you have to do is to tell them they are being attacked, and denounce the pacifists for lack of patriotism and exposing the country to danger." Hermann Goering, Nazi leader, at the Nuremberg Trials after World War II

"To announce that there must be no criticism of the President, or that we are to stand by the President, right or wrong, is not only unpatriotic and servile, but is morally treasonable to the American public." Theodore Roosevelt (1918)

3/17/2003

Beachballs in the Crab Nebula Researchers at New Mexico Tech and the NRAO have used the Aricebo radio telescope in Puerto Rico and some specilized equipment to more closely examine the pulses from the Crab Nebula pulsar. Some of the signals lasted less than two nanoseconds, meaning the originated from a volume no bigger than beach ball. Stories are here and here

Least Competent Criminals From News of the Wierd comes the story of "Timothy Baker ..., in January, hours after he had escaped while being held for aggravated robbery. His getaway had taken him to Baylor University, where he broke into a building in order to find a change of clothes from his orange jumpsuit. The building was the Fine Arts Center, where Baker raided a costume closet. He apparently thought he would be inconspicuous if he changed into a 19th-century green wool costume (with rubber galoshes) that made him look like a "leprechaun," said the sheriff later, after Baker was spotted on the street and re-arrested. Said the chairman of the theater department, "He just really stood out." [Waco Tribune Herald, 1-7-03]

Welcome to the Periodic Table of Haiku Do you need a little poetry in you life, a respite from the world news that goes from bad to worse with each morning paper. Check out the Periodic Table of Haiku where you'll find such gems as 80 Mercury Liquid silver flows like Hermes wings and shield made molten by the sun. and 6 Carbon Dead stars reborn as diamonds, buckeyballs, and beings

3/12/2003

Frozen Solid As anyone who's lived around the Great Lakes knows, this winter's been very cold. To confirm the obvious Nasa has published these remarkable images showing the ice cover in 3 of the 5 Great Lakes (Can you name them all, in order of increasing size?). Take a look at the detailed image to really see the ice cover. It's interesting that the western side of the frozen lakes show a bit of water that's ice free. I wonder if that's due to prevailing winds from the West?

Really Pertinent Questions On cold days why do tongues stick to exposed metal? Why do floor boards creak? Whay can you only fold a piece of paper eight times? See these questions and many others at Quirks and Quarks Ask Bob web site.

3/10/2003

I’m incredulous Can any level headed person think that by going to war with Iraq is going to heighten U.S. security? Iraq poses no immediate risk to the US (unlike Iran or North Korean), has no proven link to al Qaeda (unlike Pakistan, Iran and Saudi Arabia) and is being effectively contained with continued inspections. Yes Iraq has probably broken resolution 1441, but there’s so far no substantial “smoking gun”. Inspections may not be as macho as watching precision munitions fall from great heights or tales of one sided tank battles, but the immediate saving of hundreds or thousands of American lives and tens or hundreds of thousands or Iraqi lives (yes they count too) is worth it. Inspect for a year, with quadruple the number of inspectors and then see. If a “smoking gun” emerges during that time, one can then seek to justify war. If the U.S. attacks Iraq it risks inflaming more terrorists, alienating allies, and eviscerating the United Nations.

Jimmy Carter's Comments on Iraq War If you haven't read former U.S. president and Nobel Peace Prize winner Jimmy Carter's comment about the rationalization of going to war in Iraq, click on this link to commondreams.org reprint of his NY times op-ed. In simple, strainght forward terms he outlines why an Iraqi conflict at this time could not be justified as a "just war".

3/08/2003

Bush is not scared of Safddam, but he won't face Helen Veteran journalist Helen Thomas (now with Hearst newspapers) was snubbed at the president's news conference for the first time in living memory. Was he afraid of the real questions she might ask instead of the cream-puff queries from the other journalists? Was he afraid she would demand clarification of his obtuse responses? Or was he mad that she described his as "worst president in all of American history".

3/07/2003

Europan Life In Doubt A newly discovered gas cloud around Jupiter, created by ion radiation hitting the surface of Europa, has cast doubt on possible life on the moon. See also the Cassini-Huygens, NASA web page for updates on the Cassini mission.

Another online Petition "The U.N. Security Council should back tough inspections, not war." MoveIOn.Org emergency petition to the U.N. Security Council has been nothing short of extraordinary. Less than two days after the petition was launched, over 550,000 people have signed, from over 200 countries. It's a strong message from the peoples of the world that the Security Council should support tough inspections in Iraq, not war. Please sign up. It's a small gesture, but every gesture counts.

3/06/2003

Sign a petition for human rights Sign Amnesty International’s online petition, urging the Government of Canada to take a leadership role in drafting and implementing a plan of action to protect the rights and safety of the citizens of Iraq.

Major Breakthrough In 1997 John Horgan released a controversial book entitled "The End of Science : Facing the Limits of Knowledge in the Twilight of the Scientific Age" where he argued that because of human and engineering limitations all major discoveries have been made. To prove him wrong a physics Grad student has come up with the formula that generations of Saturday morning cooks have searched for, the elusive mathematical formula of how to flip a pancake and have it land in the pan. This even one ups my invention, adding unpopped popcorn to pancakes, they taste awful but they flip themselves.

3/04/2003

Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game. Hardy, Godfrey H. (1877 - 1947) A Mathematician's Apology, London, Cambridge University Press, 1941.

Sample Recomendation Letter Dear Search Committee Chair, I am writing this letter for XXXXXXXX who has applied for a position in your department. I should start by saying that I cannot recommend him too highly. In fact, there is no other student with whom I can adequately compare him, and I am sure that the amount of mathematics he knows will surprise you. His dissertation is the sort of work you don't expect to see these days. It definitely demonstrates his complete capabilities. In closing, let me say that you will be fortunate if you can get him to work for you. Sincerely, YYYYYYY

2/28/2003

Pioneer 10 Spacecraft send last Signal Another Energizer Bunny has finally given out: Pioneer 10's generators have decayed to the point that DSN can no longer detect the probe's signals. It was the first spacecraft to penetrate the asteroid belt (1972) and fly by Jupiter (1973). So long and thanks for all the pic's.

The union of the mathematician with the poet, fervor with measure, passion with correctness, this surely is the ideal. James, William (1842 - 1910) Collected Essays.

2/27/2003

Pluto Mission a Go! The U.S. Congress has approved funding for the 'New Horizons' mission to send a probe to Pluto and the Kuiper Belt. Space.com has the story here. NASA had actually fought the idea, but Congress approved the money anyway. By that time the probe arrives (12 years after liftoff) most of the Plutonian (sic?) atmosphere would have frozen, but the opportunity to see close up the largest member of the Kuiper belt is too attractive to resist.

2/26/2003

London by Night On Feb 11, I linked to Nasa's Earth Observatory's picture of London in the day. Now Earh Obsevatory has published one of London at night, a picture taken on February 4th by the International Space Station.

2/25/2003

God made the integers, all else is the work of man. Kronecker, Leopold (1823 - 1891) Jahresberichte der Deutschen Mathematiker Vereinigung.

Give'm Hellen They don't make journalists like her any more. Read this transcript between Helen Thomas and Ari Fleischer at a January 6th White House press briefing. While you're at CommonDreams.org, check out 12 Reasons to Oppose a War with Iraq

2/24/2003

Win Without War Win Without War is a "coalition" of groups "that aim to Keep America Safe by advocating alternatives to pre-emptive war in Iraq," according to its Web site—where you can view three related TV ads.

Top 11 Unusual Source Code Comments 11. /* This part doesn't really do any thing yet. It's just here in case we need it */ 10. //** This should never execute **// 9. # This is the second of three impossible errors 8. /* Emergency fix to fix emergency Turkey Day Fix */ 7. # Insert meaningful comments here 6. /* I didn't write this code */ 5. # This code was hard to write. It should be hard to understand also 4. /* Break out the Ragu. The following is spaghetti code */ 3. /* Quiet!!! This is orthogonal code */ 2. /* Ryan don't comment code! */ 1. /* Optimize THIS, code boy! */ To see the unabridged, expanded and heavily annotated go to list of unusual source code comments

Two new Mathematica Resources The new Mathematica Information Center is a collection of nearly five thousand Mathematica programs and documents categorized for easy browsing and searching. Contribute your own items too.. Also visit the new Mathematica Graphics Gallery online...

2/21/2003

"The trouble with integers is that we have examined only the small ones. Maybe all the exciting stuff happens at really big numbers, ones we can't even begin to think about in any very definite way. Our brains have evolved to get us out of the rain, find where the berries are, and keep us from getting killed. Our brains did not evolve to help us grasp really large numbers or to look at things in a hundred thousand dimensions." - Ronald Graham "Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry. What is best in mathematics deserves not merely to be learned as a task, but to be assimilated as a part of daily thought, and brought again and again before the mind with ever-renewed encouragement. Real life is, to most men, a long second-best, a perpetual compromise between the real and the possible; but the world of pure reason knows no compromise, no practical limitations, no barrier to the creative activity embodying in splendid edifices the passionate aspiration after the perfect from which all great work springs. Remote from human passions, remote even from the pitiful facts of nature, the generations have gradually created an ordered cosmos, where pure thought can dwell as in its natural home, and where one, at least, of our nobler impulses can escape from the dreary exile of the natural world. " –– Russell, Bertrand, The Study of Mathematics: Philosophical Essays (London, 1910), p.73.

2/20/2003

''The ego, so important to our sense of identity, magically slips away when we're creating.'' -- Physicist and author Alan Lightman

Dr. Math Do you have Math questions? Why does 0.999... = 1? What is 0 to the 0th power? Check out the Dr. Math website. The web site started using Swathmore college math students as 'Math Doctors' (called the Swat Team). Increased interest required recruiting more 'Doctors' from all over the world and now 300 volunteers field questions from K-12 students. Use the 'Dr. Math Searcher' to locate a problem by topic.

2/19/2003

Gardner, Martin
Biographical history, as taught in our public schools, is still largely a history of boneheads: ridiculous kings and queens, paranoid political leaders, compulsive voyagers, ignorant generals -- the flotsam and jetsam of historical currents. The men who radically altered history, the great scientists and mathematicians, are seldom mentioned, if at all. In G. Simmons Calculus Gems, New York: McGraw Hill, 1992.

Feynman, Richard Philips (1918 - 1988)
We have a habit in writing articles published in scientific journals to make the work as finished as possible, to cover up all the tracks, to not worry about the blind alleys or describe how you had the wrong idea first, and so on. So there isn't any place to publish, in a dignified manner, what you actually did in order to get to do the work. Nobel Lecture, 1966.

2/18/2003

Strings In A Bar These two strings walk into a bar and sit down. The bartender says, “So what'll it be?”. The first string says, "I think I'll have a beer è+? +›++ “=/¦) ¦=-+¦+Pquag f b o^CjfdLk jk3 #f67 ho^U r9n vy ~~o wmc 63 ^Dz." “Please excuse my friend,” the second string says, “He isn't null-terminated.”

2/17/2003

Read a Classic The First Six Books of the Elements of Euclid in Which Coloured Diagrams and Symbols are Used Instead of Letters for the Greater Ease of Learners by Oliver Byrne. London: William Pickering. 1847. "An unusual and attractive edition of Euclid was published in 1847 in England, edited by an otherwise unknown mathematician named Oliver Byrne. It covers the first 6 books of Euclid, which range through most of elementary plane geometry and the theory of proportions. ... we have had the entire edition photographed ... [and] have mounted all of Byrne's book, but in the organization of the site is by no means final. We are still experimenting with the images to improve their quality, and sooner or later the structure found for Book VI, which is much better than the rest, will be transported to the other books. If you have any suggestions we'll be pleased to hear from you."

NonEuclidian Java Software "NonEuclid is Java Software for Interactively Creating Ruler and Compass Constructions in both the Poincaré Disk and the Upper Half-Plane Models of Hyperbolic Geometry for use in High School and Undergraduate Education. Hyperbolic Geometry is a geometry of Einstein's General Theory of Relativity and Curved Hyperspace." The software can be run online or downloaded as a .zip file. There is a primer of basic concepts: What is Non-Euclidean Geometry l The Shape of Space l The Pseudosphere l Parallel Lines l Axioms and Theorems l Area l X-Y Coordinate System l Disk and Upper Half-Plane Models. There is also a section "For The Teacher: Why is it Important for Students to Study Hyperbolic Geometry?"

[The universe] "...cannot be read until we have learnt the language and become familiar with the characters in which it is written." - Galileo Galilei, astronomer

2/14/2003

Murchison Meteorite Still Contentious The well-known 1969 meteorite that fell 60 miles north of Melbourne, Australia, remains remarkably contentious today. The 100 kilogram carbon rock : a) contains pre-biotic proteins and 12% water; b) harbors 50 amino acids not found on Earth; c) favors the tell-tale signature of biochemistry based on a dominant left-handed chirality, compared to random mixtures found in test-tube syntheses. While terrestrial contamination (even interior to the meteor) may discount this so-called 'Murchison meteor', its light isotopes of carbon and nitrogen suggest the left-handed amino acids not found elsewhere on Earth have the same ratios as the right-handed ones. This would not be the case if, say, bacteria was just making the left-handed ones after impact. Seems quite a controversy from down-under.

2/12/2003

For Columbia "When you have tasted flight, you will forever walk the earth with your eyes turned skyward, for there you have been. and there you will always long to return."
--Leonardo da Vinci We shall not cease from exploring, and the end of our exploring will be to arrive where we started and know the place for the first time --T.S. Eliot

First Cosmological Results From MAP The Wilkinson Microwave Anisotropy Probe, a NASA Explorer mission has announced the first results based on a year of observations from the L2 Lagrangian point. MAP carries two back-to-back microwave telescopes to study variations in the cosmic microwave background, to much greater accuracy than the COBE satellite. The excruciating details of the results on the age, geometry and composition of the universe can be found in this paper. Executive summary: 13.7 billion years old, flat, 4.4% baryons, 22% dark matter and 73% dark energy."

2/11/2003

Earth Obsevatory's Picture of London, England There's a fascinatinating picture pf London at Earth Obsevatory, a Nasa sponsered site showing incredible images of our planet. If you have the bandwidth, download the 2MB version of the files as well.

2/10/2003

Is the British Parliment Master of its own Domain? Nobody is quite sure. This is not a political comment, but an Internet one. The British House of Parliment uses www.parliament.uk as its URL but according to the Register Article parliment.uk (along with 13 other .uk domains) were registered before Aug 1, 1996, before Nominet (the British top level domain registry) was created. The anomoly came to light when the extensive web site decided to start conducting e-commerce and were unable to get an SSL cerificate from Thwate.

2/06/2003

Which Canadian Sex Symbol are you/ Yes you read that right, CANADIAN sex symbol. We're not all William Shatner and Celine Dion. Click here if you're male and here if you're female to answer a quick 8 question quiz.

2/05/2003

Shakespeare, William (1564 - 1616)
I cannot do it without comp[u]ters. The Winter's Tale.

Adler, Alfred In the company of friends, writers can discuss their books, economists the state of the economy, lawyers their latest cases, and businessmen their latest acquisitions, but mathematicians cannot discuss their mathematics at all. And the more profound their work, the less understandable it is. Reflections: mathematics and creativity, New Yorker, 47(1972), no. 53, 39 - 45.

If You're Happy And You Know It Bomb Iraq original author unknown
If you cannot find Osama, bomb Iraq. If the markets are a drama, bomb Iraq. If the terrorists are Saudi, And your alibi is shoddy, And your tastes remain quite gaudy, Bomb Iraq. If you never were elected, bomb Iraq. If your mood is quite dejected, bomb Iraq. If you think that SUVs, Are the best thing since sliced cheese, And your father you must please, Bomb Iraq. If the globe is quickly warming, bomb Iraq. If the poor will soon be storming, bomb Iraq. We assert that might makes right, Burning oil is a delight, For the empire we will fight, Bomb Iraq. If we have no allies with us, bomb Iraq. If we think that someone's dissed us, bomb Iraq. So to hell with the inspections, Let's look tough for the elections, Close your mind and take directions, Bomb Iraq. If corporate fraud is growin', bomb Iraq. If your ties to it are showin', bomb Iraq. If your politics are sleazy, And hiding that ain’t easy, And your manhood’s getting queasy, Bomb Iraq. Fall in line and follow orders, bomb Iraq. For our might now knows no borders, bomb Iraq. Disagree? We’ll call it treason, It's the make war not love season, Even if we have no reason, Bomb Iraq.

Kasparov vs. Deep Junior. In order to thwart Deep Juniors extensive chess database and ability to analyse 3 million moves a second, Kasporov has been employing risky unorthodox moves. In an article in the Globe and Mail Kasparove is quoted as "I think I made a brilliant move to get Deep Junior out of book and make it think on its own. If you play aggressive chess and throw in a little twist you can get great positions against the strongest computer programs." Of additional note the end of the article states "Deep Junior was so stumped by an off-book Kasparov move that it spent 25 minutes mulling its next move before appearing to black out. Although times limits were not a concern, a minor panic gripped the members of the programming team as they debated whether to reboot the computer, before somebody realized that the problem was simply that Deep Junior's screensaver had activated. They moved the mouse, and the screen came back on."
The ganes can be followed live at http://www.x3dworld.com.

2/04/2003

Math Problem of the week How many primes are there that, in the usual base 10 notation, begin and end with a "1" and have alternating "0"s and "1"s? To subscribe the "Math Problem of the Week", send e-mail to majordomo@mathforum.org with ONLY the following words in the message body: subscribe macpow

The Song Of The Dead - Rudyard Kipling
We were dreamers, dreaming greatly, in the man-stifled town; We yearned beyond the sky-line where the strange roads go down. Came the Whisper, came the Vision, came the Power with the Need, Till the Soul that is not man's soul was lent us to lead. ... Follow after -- we are waiting, by the trails that we lost, For the sounds of many footsteps, for the tread of a host. Follow after -- follow after -- for the harvest is sown: By the bones about the wayside ye shall come to your own!

1/31/2003

Petition to put Stan Rogers into the Canadian Music Hall of Fame Geist magazine is sponsering a petition to put Stan Rogers into the Canadian Music Hall of Fame. His songs such as "Northwest Passage," "Barrett's Privateers" and "The Mary Ellen Carter" are Canadian classics. Ah, for just one time I would take the Northwest Passage To find the hand of Franklin reaching for the Beaufort Sea; Tracing one warm line through a land so wild and savage And make a Northwest Passage to the sea. "Northwest Passage", written and recorded by Stan Rogers

Matroids and Abstraction Joseph Malkevitch of York College (CUNY) gives an Introductory lecture on Matroids, a mathematical construct, such as a group, a field, or a topology having a somewhat surprisingly large number of associated operators or special collections of subsets. Rather than hide from the inherent abstraction of the field, the author uses it as an example of how mathematical abstraction is key in determining the utility of mathematics and enabling its growth.