Tyger! Tyger! burning bright
In the forests of the night,
What immortal hand or eye
Could frame thy fearful symmetry? —William Blake, The Tyger
Evariste Galois is perhaps one of the most romantic figures in mathematics. While still in school, he sent his great breakthrough in geometry to established Parisian mathematicians; unfortunately, the breakthrough was written out in such an ungodly scrawl that the wise men had no idea what to make of it. By the age of twenty, he was languishing in prison for his revolutionary acts (political, this time); with cholera threatening, he and other prisoners were sent to a clinic where he fell in unrequited love with a doctor's daughter. Then, on May 30, 1832, he died of a wound from a gunshot fired in a duel that arose under murky circumstances.
The night before, realizing that he might not have another chance, Galois did some major cramming. He gave his best shot at explaining his ideas about geometry in the clearest language he could muster. (The name of his beloved, Stephanie, dotted the margins.)
"Maybe the fact that he stayed up all night doing mathematics was the [reason] why he was such a bad shot the next morning and got killed", said Marcus du Sautoy in his TED talk on Galois and symmetry at the 2009 TED global conference. But du Sautoy, an Oxford mathematician, owes Galois quite a bit. The young mathematician discovered the rules governing symmetric shapes, shapes that can be rotated and flipped and look unchanged. Du Sautoy calls these manipulations the "magic trick" changes. "For Galois symmetry was all about motion, what can you do to a symmetrical object so it can looks the same," du Sautoy said.
Symmetry, Marcus du Sautoy says, is "nature's language." It arranges the atoms in a ruby, and the piles of molecules that form a virus. Humans consider symmetric faces to be beautiful, he says, because symmetry, being difficult to achieve, is a token of strong genes and the sign of a desirable mate.
When Spain was under Muslim rule in the mid 14th century, the rulers built themselves a splendid palace known as the Alhambra, or the red fort. Because Muslim artists were forbidden from depicting animals or people, they found beauty in patterns and symmetry. Using Galois rules, you can determine that the gorgeous, intricate mosaics on the walls of the Alhambra contain 17 different kinds of symmetry in all, making it a treasure-trove for mathematicians. (A paper on the geometry of Islamic art appeared in Science in 2007.)
Walls and ceiling of the Alhambra. (Justus Hayes/Shoes on Wires/shoesonwires.com)
Du Sautoy goes on to say that there's no stopping mathematicians from using Galois rules to go beyond three dimensions.
His breakthrough, du Sautoy says, "allows us to create symmetrical objects in the unseen world"—four, five, six dimensions and more.
"That's where I work," he says. "I create mathematical objects, symmetric objects using Galois' language in very high dimensional spaces."
As a final treat, du Sautoy named a new mathematical object he'd created after the person who could get closest to estimating the number of symmetries in a Rubix cube. (Try it yourself - he gives the answer at the end of the talk.) Of course, you can't see a symmetric object in twelve dimensions, so the winner had to be content with a picture drawn in Galois' mathematical language.
If you fancy having your own multidimensional symmetrical object named after you, you can donate $10 to a Guatemalan charity that du Sautoy supports. He will then "stay up all night" building a new intangible, symmetric toy to stick your name on. He's raised about $3,000 this way—that's a lot of late nights!
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It looks like justice was defeated in Maine, but we got a glimmer of success in Washington (Hooray for my home state!). I think everyone who is unhappy with Maine voters should go tromp on this Canadian poll just to get it out of your system.
Absolutely, yes 21%
Sure, why not? 19%
Not really 11%
Absolutely, no 35%
I don't care either way 14%
What counts next, of course, is for activists in Maine to get back to work. Same for everyone in every state…like Minnesota.Read the comments on this post...
I am no fan of pseudoscience, as you may have guessed. Dowsing is a practice that falls squarely in that field. It’s the idea that you can detect an object — usually water, but sometimes gold, or people, or whatever — using a y-shaped[...]
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Umbrella or sunscreen? Flood or drought? The secret of flawless weather forecasting turns out to be surprisingly simple
Earthquakes far from plate boundaries can cause aftershocks centuries later
According to a new study accepted for publication in The Endocrine Society's Journal of Clinical Endocrinology & Metabolism (JCEM), eating a meal quickly, as compared to slowly, curtails the release of hormones in the gut that induce feelings of being full. The decreased release of these hormones, can often lead to overeating.
Tyrannosaurus rex and related large carnivorous dinosaurs together form the family Tyrannosauridae. A long forgotten fossil skull in the collections of the Natural History Museum in London has now provided crucial clues to the early stages of the lengthy evolutionary history of these fearsome predators.
Farming salmon hurts the environment less than rearing beef cattle, though there is still room for improvement
At first glance, I thought this story was good news: Oklahoma is going to build a Christian prison! About time, I thought, I can think of a few Christians who deserve a few years for faith-abuse. But no…it's a prison to be administered by Christians to give Christian criminals special privileges. Not quite as appropriate, but more in line with what we've gotten used to from our dominant faith tradition.
We're getting more of the same from Congress, too. Religion is being given permission to intrude on science once again, with the sanctimonious Orrin Hatch (abetted by a pair of Democrats, Kerry and Kennedy) sponsoring a provision in the mangled health care football to allow prayer to count as medicine. It's specifically a sop to Christian Science, that nonsensical superstition that believes that medicine is a betrayal of faith and that wants to charge sick people money to pray over them…and also get reimbursement from the government. Let the Christian Scientists get a foot in the door and official recognition of mumbling to Jesus as a billable service, and you know the Scientologists and Jehovah's Witnesses and Amish and Mormons and, of course, the Catholics will be surging through to take advantage of the opportunities.
I may just have to convert to Catholicism under this bill so I can charge the US and my insurance provider to cover my near-sightedness treatments at Lourdes. And the French Riviera.
You laugh. But look at the absurdity of existing loopholes.
The Internal Revenue Service, for example, allows the cost of Christian Science prayer sessions to be counted among itemized medical expenses for income tax purposes -- one of the only religious treatments explicitly identified as deductible by the IRS.
Moreover, some federal medical insurance programs, including those for military families now reimburse for prayer treatment.
The Christian Science religious tradition has always emphasized the role of trained prayer practitioners. Their job, as outlined by the church's founder, Mary Baker Eddy, is to pray for healing and charge for treatment at rates similar to those charged by doctors.
Practitioners are not regulated by the government, but many buy advertisements in a leading Christian Science publication. The publication requires an application process for the ads that includes the submission of patient testimonials, a practice that church leaders say is tantamount to a vetting process.
Davis has been trained as a practitioner and still occasionally treats the sick. "We'll talk to them about their relationship to God," he said. "We'll talk to them about citations or biblical passages they might study. We refer to it as treatment."
During the day, Davis may see multiple patients and pray for them at different moments. He charges them $20 to $40 for the day, saying, "I think that it would be considered modest by any standard."
Modest in absolute terms, but relative to the quality of the "treatment", that counts as a major ripoff.
We can at least hope that the bad publicity this provision is getting will lead to its removal…and even more optimistically, that it will lead to scrutiny of the unethical fraud of a secular government legitimizing any of these superstitious practices.
I hope the Oklahoma prison for pampered Christians is also found unconstitutional.Read the comments on this post...
It's for college students only, and first prize is $2000. Come on, students, you're used to churning out term papers, and that prize is substantial.
The topic of the essay is free expression.
The Campaign for Free Expression is a CFI initiative to focus efforts and attention on one of the most crucial components of freethought: the right of individuals to express their viewpoints, opinions, and beliefs about all subjects&mdashlespecially religion. To encourage free expression and to emphasize the importance of this fundamental right, CFI and its sister organization, The Council for Secular Humanism, are sponsoring this contest.
Given recent events in Chicago, that topic is ironic and rich in potential for discussion.Read the comments on this post...