Tuesday, January 26, 2010

Have a symmetrical object named after you

WildAboutMath by Sol-I became a big fan of Marcus du Sautoy when I read his books Symmetry, and Music of the Primes. From that video I learned about du Sautoy’s fundraising page for Common Hope:

Common Hope promotes hope and opportunity in Guatemala, partnering with children, families, and communities who want to participate in a process of development to improve their lives through education, health care, and housing.

And I learned how to get my own symmetrical object:

People have stars named after them, craters on the moon, even comets…but how about naming a symmetrical object in hyperspace. For a donation of over $10 you can have a new symmetrical object named after you or a friend. A great birthday present. My new book FINDING MOONSHINE (UK) or SYMMETRY (US) narrates the discovery of these new symmetrical objects that have interesting connections with objects in number theory called elliptic curves. Here is the chance to claim one of these groups and have the group named after you. I have created infinitely many of these groups so they won’t run out!

What a great idea! So, I donated and now I’m the proud owner of a symmetry group. This could be the perfect gift for the Math lover who has everything...

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Sunday, January 24, 2010

Are primates' brains wired for math?

Like a lot of humans, monkeys might not be able to do calculus. But a new study shows that they can learn and rapidly apply abstract mathematical principles.

Previous work has shown that monkeys and birds can count, but flexible applications of higher mathematic rules, the study authors asserted, "require the highest degree of internal structuring"—one thought largely to be the domain of only humans.

So researchers based at the Institute of Neurobiology at the University of Tubingen in Germany set out to see whether rhesus monkeys could learn and flexibly apply the greater-than and less-than rule. They tested the monkeys with groups of both ordered and random dots, many of which were novel combinations to ensure that the subjects couldn't have simply memorized them. The monkeys were cued into applying either the greater-than or less-than rule by the amount of time that elapsed between being shown the first and second group of dots.

"The monkeys immediately generalized the greater than and less than rules to numerosities that had not been presented previously," the two researchers, Sylvia Bongard and Andreas Nieder, wrote.

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Thursday, January 14, 2010

200-year-old Encrypted Letter Finally Deciphered

The mathematician who deciphered the final, encrypted page of a letter sent to President Thomas Jefferson in 1801 will visit the University of Oregon to tell how he did it.

The encrypted page -- a mystery to Jefferson and everyone else -- was solved in 2007 by Smithline, then 36, an expert in code-breaking. He detailed his solution in the American Scientist.

The letter was written by Jefferson's colleague in the American Philosophical Society, Robert Patterson, a math professor at the University of Pennsylvania. The ciphered page was devoid of capital letters or spaces and scrambled in a way that left no readable segments. Preceding pages had described the nature of the code but not the specific key required to unlock this message. The code was unlike any normally used at the time. Patterson predicted it would never be broken.

The solution involved both linguistic intuition and a to find the digital key. While the required 100,000 calculations would be easy on today's computers, Smithline's method could have been done over time in Patterson's day. In his talk, Smithline will tell how he was pulled into the mystery, how he broke the code and what was written on the page.

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Emotional Bunny Says: "What's that? In the wrong hands, this information could have been fatal? Ah. I wouldn't worry about that...."

Tuesday, January 5, 2010

Simple Math Yields Intricate Visual Patterns

Polynomials, the meat and potatoes of high-school algebra, are foundational to many aspects of quantitative science. But it would take a particularly enthusiastic math teacher to think of these trusty workhorses as beautiful.

As with so many phenomena, however, what is simple and straightforward in a single serving becomes intricately detailed—beautiful, even—in the collective.

On December 5 John Baez, a mathematical physicist at the University of California, Riverside, posted a collection of images of polynomial roots by Dan Christensen, a mathematician at the University of Western Ontario, and Sam Derbyshire, an undergraduate student at the University of Warwick in England.

Polynomials are mathematical expressions that in their prototypical form can be described by the sum or product of one or more variables raised to various powers.

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