pop culture number
I was thinking the other night about common culture and the people we know who overlap. I mean this in the most superficial sense; not people we know who are close to us, or mean something tangible in our lives. Rather, the constant bombardment of celebrity figures — sports, television, movies, music — and the infinite swirl of sub-sections. My question was, how many people do we know this way? What is the number? The people who when I say Beyoncé, you know what I’m talking about? There must be thousands.
Compressed sensing
An algorithm that resolves high resolution images from next to nothing.
Compressed sensing was discovered by chance. In February 2004, Emmanuel Candès was messing around on his computer, looking at an image called the Shepp-Logan Phantom. The image — a standard picture used by computer scientists and engineers to test imaging algorithms — resembles a Close Encounters alien doing a quizzical eyebrow lift. Candès, then a professor at Caltech, now at Stanford, was experimenting with a badly corrupted version of the phantom meant to simulate the noisy, fuzzy images you get when an MRI isn’t given enough time to complete a scan. Candès thought a mathematical technique called l1 minimization might help clean up the streaks a bit. He pressed a key and the algorithm went to work.
this unique 18-minute genre has its own requirements
From a Wired article on how to ace a TED Talk:
“I’m surprised to see that half the people here know my career in some detail and the other half don’t know who I am,” he says.
Science is fine, but not when it messes with our illusions.
If she had included solar power and African child warriors, it would have been so perfect a TED talk that there would have been no need for others.
Wolfram wraps his talk by saying that when it comes to trying to boil down the universe to a simple algorithm, “it’s almost embarrassing not to at least try.”
“Just because someone has an ego,” he says, citing a writer whose name I can’t read from my scribbled notes, “doesn’t mean he’s wrong.”
math anxiety
Student math ability was not related to teacher math anxiety at the start of the school year, the researchers report in Tuesday’s edition of Proceedings of the National Academy of Sciences.
But by the end of the year, the more anxious teachers were about their own math skills, the more likely their female students — but not the boys — were to agree that “boys are good at math and girls are good at reading.”
math monkeys
A German team of neurobiologists has found that rhesus macaques can engage in abstract mathematical reasoning using specific brain cells dedicated to the comprehension of math rules and relationships.
“Even simple mathematical operations are highly abstract mental operations on quantities that are governed by overarching concepts and principles,” explained study co-author Andreas Nieder, a professor in the department of animal physiology at the University of Tubingen’s Institute of Neurobiology. “Monkeys can adopt abstract mathematical rules, and they can switch between them.”
“That means they understand very fundamental, non-symbolic mathematical principles, such as ‘greater than’ and ‘less than’,” Neider added. His team traced this ability to neurons in the prefrontal cortex region of the primate brain — an area that appears to be devoted to encoding the basic rules of math.
quote out of context
“Now,” he says with a chuckle, “I can fail in even more spectacular ways.”
Overheard
“And then things took a 360 for the worse.”
My new motto.
numerology
A=A
math is what exists and what exists is math
What is this fractal?
(via kottke)
A New THEORY of AWESOMENESS and MIRACLES
Today I’m going to talk about the idea of the miraculous, or at least the appearance of the miraculous. Humans have a strange relationship to the miraculous, but the prime emotion it seems to stimulate is awe, and awesomeness is pretty much what we’re all striving for.
Essentially, it is a reflection on the human mind’s relationship to size and complexity:
Logicomix
Logicomix is a comic (but not funny) story about the development of the Foundation of Mathematics.
from the spam
The Math lesbians
I’m thinking of a number (of dots)
Scientists had 10 volunteers watch either numerals or dots on a screen while a part of their brain known as the intraparietal cortex was scanned – it’s a region of the parietal lobe especially linked with numbers. They next rigorously analyzed brain activity to decipher which patterns might be linked with the numbers the volunteers had observed.
When it came to small numbers of dots, the researchers found that brain activity patterns changed gradually in a way that reflected the ordered nature of the numbers. For example, one might be able to conclude that the pattern for six is between that for five and seven.
Oddly, the article begins by saying scientists can also see numbers, but ends with this:
In the case of the numerals, the researchers could not detect this same gradual change. This suggests their methods simply might not be sensitive enough to detect this progression yet, or that these symbols are in fact coded as more precise, discrete entities in the brain.
So much for relaying information.
Useful and Beautiful Devices
Skinner’s July 2009 auction of Science, Technology & Clocks features the most comprehensive collection of scientific instruments to come to market in a long time. From a private collection, offerings include several important pairs of globes by Newton, a sextant by Ramsden, an octant by George Jones, equinoctial dials, astrolabes, chronometers, microscopes and nautical antiques.
Do the math.
On Hacker News on Monday, I was amused to read some people saying that writing StackOverflow was hilariously easy—and proceeding to back up their claim by promising to clone it over July 4th weekend. Others chimed in, pointing to existing clones as a good starting point.
Let’s assume, for sake of argument, that you decide it’s okay to write your StackOverflow clone in ASP.NET MVC, and that I, after being hypnotized with a pocket watch and a small club to the head, have decided to hand you the StackOverflow source code, page by page, so you can retype it verbatim. We’ll also assume you type like me, at a cool 100 WPM (a smidge over eight characters per second), and unlike me, you make zero mistakes. StackOverflow’s *.cs, *.sql, *.css, *.js, and *.aspx files come to 2.3 MB. So merely typing the source code back into the computer will take you about eighty hours if you make zero mistakes.
Except, of course, you’re not doing that; you’re going to implement StackOverflow from scratch. So even assuming that it took you a mere ten times longer to design, type out, and debug your own implementation than it would take you to copy the real one, that already has you coding for several weeks straight—and I don’t know about you, but I am okay admitting I write new code considerably less than one tenth as fast as I copy existing code.
—Benjamin Pollack, The One in Which I Call Out Hacker News, July 1, 2009
(Via Daring Fireball & Kottke, jointly making this 99.9ºF on Fever)
How industries fail
Perhaps the most fascinating bit of Michael Nielsen’s article “Is Scientific Publishing About to Be Disrupted?” is a wish list of science-oriented Web services. It’s bracketed, however, by one of the better discussions I’ve seen of how the Internet has changed the media system and why so many otherwise intelligent people are still singing LA LA LA, I CAN’T HEAR YOU:
There are two common explanations for the disruption of industries like minicomputers, music, and newspapers. The first explanation is essentially that the people in charge of the failing industries are stupid. How else could it be, the argument goes, that those enormous companies, with all that money and expertise, failed to see that services like iTunes and Last.fm are the wave of the future? Why did they not pre-empt those services by creating similar products of their own? Polite critics phrase their explanations less bluntly, but nonetheless many explanations boil down to a presumption of stupidity. The second common explanation for the failure of an entire industry is that the people in charge are malevolent. In that explanation, evil record company and newspaper executives have been screwing over their customers for years, simply to preserve a status quo that they personally find comfortable.
It’s true that stupidity and malevolence do sometimes play a role in the disruption of industries. But in the first part of this essay I’ll argue that even smart and good organizations can fail in the face of disruptive change, and that there are common underlying structural reasons why that’s the case. That’s a much scarier story. If you think the newspapers and record companies are stupid or malevolent, then you can reassure yourself that provided you’re smart and good, you don’t have anything to worry about. But if disruption can destroy even the smart and the good, then it can destroy anybody.
(Via Richard Nash and some other people)
Bernoulli Numbers
A 16-year-old Iraqi immigrant living in Sweden has cracked a maths puzzle that has stumped experts for more than 300 years, Swedish media reported on Thursday.
“When I first showed it to my teachers, none of them thought the formula I had written down really worked,” Altoumaimi told the Falu Kuriren newspaper.
the search for mersenne primes
A downloadable program called GIMPS helps mathematicians harness personal computers to search for really large prime numbers.
Chris Caldwell, a mathematician at the University of Tennessee, Martin, says that the main obstacle in proving that these numbers are prime is just doing the arithmetic with numbers that are millions of digits long. Caldwell says there is a formula for testing whether a large number is a Mersenne prime, but it’s computationally intense.
“Not only do you have to multiply a 13 million-digit number by a 13 million-digit number, but you have to do that about 13 million times,” Caldwell says. “And that just takes a tremendous amount of computation.”
GIMPS has been plugging away at this for 13 years now, and has found 12 Mersennes so far.
Why?
“Nobody there looking at the Hope Diamond ever asks, ‘Why did they bother to dig it up?’ or ‘What is it good for?’ — even though it really isn’t good for much other than to just hang there and people to look at,” Caldwell says. “And in many ways the Mersennes play that same role — that they really are the jewels of number theory.”
How Much Is A Year of Life Worth?
Fourier Analysis Solves Beatles Mystery Chord
For years the chord at the beginning of the Beatles’ ‘A Hard Day’s Night’ has remained a mystery, and provided fodder for intense debate. Now, a mathematician has broken the code.
Four years ago, Jason Brown was inspired by reading news coverage about the song’s 40th anniversary – so much so that he decided to try and see if he could apply a mathematical calculation known as Fourier transform to solve the Beatles’ riddle. The process allowed him to break the sound into distinct frequencies using computer software to find out exactly which notes were on the record.
What he found was interesting: the frequencies he found didn’t match the instruments on the song. George played a 12-string Rickenbacker, John Lennon played his 6 string, Paul had his bass – none of them quite fit what he found. He then realized what was missing – the 5th Beatle. George Martin was also on the record, playing a piano in the opening chord, which accounted for the problematic frequencies.”
So, what was the chord?
George Harrison was playing the following notes on his 12 string guitar: a2, a3, d3, d4, g3, g4, c4, and another c4; Paul McCartney played a d3 on his bass; producer George Martin was playing d3, f3, d5, g5, and e6 on the piano, while Lennon played a loud c5 on his six-string guitar.
exploring logo design with Mathematica
Chris Carlson uses Mathematica to analyze logo design, in this case the Mercedes star.
I was surprised that such a variety of designs would arise from a straightforward parameterization of this simple logo. But that’s often the case. This tiny corner of the design universe contains an infinity within itself. It’s like exploring a drop of pond water with a microscope. The universe within is dazzling.
(via kottke)
The Formula That Killed Wall Street
A year ago, it was hardly unthinkable that a math wizard like David X. Li might someday earn a Nobel Prize. After all, financial economists—even Wall Street quants—have received the Nobel in economics before, and Li’s work on measuring risk has had more impact, more quickly, than previous Nobel Prize-winning contributions to the field. Today, though, as dazed bankers, politicians, regulators, and investors survey the wreckage of the biggest financial meltdown since the Great Depression, Li is probably thankful he still has a job in finance at all. Not that his achievement should be dismissed. He took a notoriously tough nut—determining correlation, or how seemingly disparate events are related—and cracked it wide open with a simple and elegant mathematical formula, one that would become ubiquitous in finance worldwide.
The mathematics of beauty.
Horace Brock has a theory:
Designed objects, Brock writes, can be broken down into “themes” and “transformations.” A theme is a motif, such as an S-curve; a transformation might see that curve appear elsewhere in the design, but stretched, rotated 90 degrees, mirrored, or otherwise reworked.
Aesthetic satisfaction comes from an apprehension of how those themes and transformations relate to each other, or of what Brock calls their “relative complexity.” Basically – and this is the nub of it – “if the theme is simple, then we are most satisfied when its echoes are complex . . . and vice versa.”
He gives the example of a chair in his collection designed by the English Regency architect Henry Holland. The dominant design motif, which can be found in the chair’s arm, is an S-curve. (Mathematically, an S-curve, which twists in space, is complex when compared to a straight line or unidirectional curve.) The back of the chair, writes Brock, sees that S-curve first reversed and then rotated 90 degrees – a simple two-step transformation.
Complex theme, simple transformation: Voila! The chair is beautiful.
GIMPS
UCLA mathematicians have found a thirteen-million digit prime number.
“We’re delighted,” said UCLA’s Edson Smith, the leader of the effort. “Now we’re looking for the next one, despite the odds.”
It’s the eighth Mersenne prime discovered at UCLA.
Mersenne primes — named for their discoverer, 17th century French mathematician Marin Mersenne — are expressed as 2P-1, or two to the power of “P” minus one. P is itself a prime number. For the new prime, P is 43,112,609.
Thousands of people around the world have been participating in the Great Internet Mersenne Prime Search, or GIMPS, a cooperative system in which underused computing power is harnessed to perform the calculations needed to find and verify Mersenne primes.