"...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

"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

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

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.

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

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."

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.

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

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

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

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

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

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

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!"

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…

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.

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

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.

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

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

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.

"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.

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.

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."

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.

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.

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.

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.

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.

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.

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.

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?"

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.

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.

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.

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.

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

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"

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. "

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.

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.

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.

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.

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.

"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.

"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 .

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.

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

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

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

“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.

"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 cap