The Official MathGeek Blog

Musical Math or Mathematical Music?

2008-03-12T06:56:36-05:00

What makes music sound good? Click here for an intriguing answer to that question from Princeton professor Dmitri Tymoczko. Here is the abstract of his paper on Geometrical Music Theory: "Western musicians traditionally classify pitch collections by disregarding the effects of five kinds of musical transformation: octave shift, permutation, transposition, inversion, and cardinality change. Here we model these transformations mathematically, showing that they generate 32 equivalence classes of chords, 243 equivalence classes of chord sequences, and 32 families of geometrical quotient spaces, in which both chords and chord-sequences are represented. This model reveals connections between diverse music-theoretical concepts, yields new tools for analyzing music, unifies many existing geometrical representations of musical structure, and suggests an answer to a longstanding question about how to represent the similarity between chord-types."

Celebrate Pi Day!

2008-03-10T07:44:21-05:00

How to Celebrate Pi Day: "Pi Day is a special day in the lives of many a nerd. Just like normal people celebrate Valentine's Day or National Pancake Day, nerds around the world will gather and join hands in the shape whose ratio of its circumference to its diameter is the most revered mathematical constant in the known universe. Below are some tips on making this day (celebrated on March 14 at 1:59pm) memorable to one and all." More...

From Wikipedia: "Pi Day and Pi Approximation Day are two unofficial holidays held to celebrate the mathematical constant π (pi). Pi Day is observed on March 14 (3/14 in American date format), due to π being equal to roughly 3.14. Sometimes it is celebrated on March 14 at 1:59 p.m. (commonly known as Pi Minute). If π is truncated to seven decimal places, it becomes 3.1415926, making March 14 at 1:59:26 p.m., Pi Second. Pi Approximation Day may be observed on any of several dates, most often July 22 (22/7 (European date format) is a popular approximation of π). March 14 also happens to be Albert Einstein's birthday." More...

Now That's a Flashlight!

2008-01-29T09:33:12-06:00

Wicked Lasers

The math behind Houston's traffic

2008-01-17T08:13:59-06:00

From KHOU.com: It doesn’t take a genius to know that accidents cause traffic jams. But it did take a genius to figure out why sometimes rush-hour traffic slows to a bewildering stop for no apparent reason at all.

In the last few months, two mathematicians at the University of Exeter in England came up with this equation, which has become something of a validation for engineers urging new approaches to traffic management. It’s changing things in Houston already.

Rice University’s Rolf Ryham explains the math.

He said for the first time, this equation takes driver “reaction time” into account. What’s revealed here could hold the key to solving Houston’s traffic problems.

Basically it’s mathematical proof that on a crowded freeway, when one driver just taps on his brakes, the driver behind him reacts and brakes a little more. The driver behind him brakes even more, and so on until drivers actually stop moving. It’s the kind of jam that happens on 290 every day.

“Slowing traffic down a little bit during peak periods is OK,” Highway 290 Expansion spokesman Stephen Hrncir said. “It’s the near-stop conditions we need to avoid.”

It’s called “cascading.” You can see it by speeding up video of 290 at rush hour. There are waves of congestion moving backward. The ripples start when someone up front does something that causes drivers behind him to brake, starting a cascade of slowing traffic.

“A few minutes ago someone may have moved lanes or done something to slow down a little bit and that’ll cause things to slow down or stop,” Ryham said. “And you’ll run into that, and you’ll be like, ‘where did this come from?’ There’s no cops or anything.’”

This is the kind of traffic that engineers think about: When cars are very close together, but they are moving. That’s when one small problem, someone changing a radio station or being on their cell phone, can create a traffic backup that seems to have no explanation.

“The last car that stopped may have stopped after the last car started moving again,’ Hrncir said. “But now his stop can be the next intersection back, and he still is causing cars behind him to stop so that’s the cascade effect.” More...

Yet Another Reason to Hate CBS...

2007-12-17T16:32:42-06:00

CBS has fired the entire production staff at a popular Web site devoted to the iconic Star Trek television series, raising questions about the site's future.

"Sadly, we must report that the CBS Interactive organization is being restructured, and the production team that brings you the StarTrek.com site has been eliminated," said a blog post from the team that appeared Friday on the Web site.

The post said that the move is "effective immediately" and added that "We don't know the ultimate fate of this site." CBS officials did not immediately return a phone call seeking comment. More...

'Mathlete' smashes human calculation record

2007-12-12T08:33:04-06:00

LONDON (AFP) - The world's fastest human calculator on Tuesday broke his own record for working out a 200-digit number using nothing but brain power to produce the answer in just over 70 seconds. ADVERTISEMENT Alexis Lemaire, a 27-year-old Frenchman, correctly calculated the 13th root of a random 200-digit number from a possible 393 trillion answers. The so-called 'mathlete' produced the answer of 2,407,899,893,032,210 in 70.2 seconds, beating his previous record of 72.4 seconds, at London's Science Museum. A computer was used to produce a random 200-digit number before he sat down to calculate the answer in his head. The museum's curator of mathematics, Jane Wess, said: "He sat down and it was all very quiet -- and all of a sudden he amazingly just cracked it. "I believe that it is the highest sum calculated mentally. "He seems to have a large memory and he's made this his life's ambition. It's quite remarkable to see it happen. A very small number of people have this extraordinary ability; nowadays there is only a handful." Lemaire, who attends the University of Reims in northern France, began demonstrating his prowess by finding the 13th root of a random 100-digit number but gave up trying to improve his performance when he calculated an answer in under four seconds in 2004. Like an athlete, he trains his brain daily for the far harder task of finding the 13th root of 200-digit numbers.

Gift Geek Wrap

2007-12-10T10:41:51-06:00

The Science of Wrapping: Bluewater reveals the formula to prevent wrapping wastage this Christmas

To ensure its customers have a green Christmas this season, Bluewater have devised an eco-friendly scientific formula on how to wrap a Christmas present after estimating British consumers will waste over one tonne^* of wrapping paper this Christmas.

Bluewater, the UKs leading shopping centre, discovered that Brits continually overestimate the amount of paper they need to wrap their Christmas presents. Following this new revelation, Bluewater today reveals the mathematical solution which will hopefully put an end to unnecessary paper wastage: A1 = 2(ab+ac+bc+c²)^**

In laymans’ terms, the length of the wrapping paper should be as long as the perimeter of the side of the gift, with no more than 2cm allowed for an overlap. The width should be just a little over the sum of the width and the depth of the gift. More...

Who Are They Calling Cheezy??

2007-11-27T17:18:58-06:00

From Wired Magazine: Having conquered television, movies, videogames, comic books, paperbacks and lunch boxes, the original Star Trek crew moves into high definition this week. The first season of Star Trek: The Original Series beams onto store shelves Tuesday in an HD DVD/DVD combo pack that looks better than ever.

To celebrate, we're reliving the glory of 10 of the best monsters and creatures to stomp, ooze or float across the screen in the groundbreaking TV series. Thanks to the magic of high def, and a painstaking digital remastering effort, you can now see these monsters in more detail than ever before -- although, to be fair, that doesn't make them look any more convincing. More...

Go!

2007-10-10T15:49:59-05:00

In 1957, Herbert A. Simon, a pioneer in artificial intelligence and later a Nobel Laureate in economics, predicted that in 10 years a computer would surpass humans in what was then regarded as the premier battleground of wits: the game of chess. Though the project took four times as long as he expected, in 1997 my colleagues and I at IBM fielded a computer called Deep Blue that defeated Garry Kasparov, the highest-rated chess player ever.

You might have thought that we had finally put the question to rest—but no. Many people argued that we had tailored our methods to solve just this one, narrowly defined problem, and that it could never handle the manifold tasks that serve as better touchstones for human intelligence. These critics pointed to weiqi, an ancient Chinese board game, better known in the West by the Japanese name of Go, whose combinatorial complexity was many orders of magnitude greater than that of chess. Noting that the best Go programs could not even handle the typical novice, they predicted that none would ever trouble the very best players.

Ten years later, the best Go programs still can't beat good human players. Nevertheless, I believe that a world-champion-level Go machine can be built within 10 years, based on the same method of intensive analysis—brute force, basically—that Deep Blue employed for chess. I've got more than a small personal stake in this quest. At my lab at Microsoft Research Asia, in Beijing, I am organizing a graduate student project to design the hardware and software elements that will test the ideas outlined here. If they prove out, then the way will be clear for a full-scale project to dethrone the best human players. More...

Han Shot First!

2007-09-27T09:47:52-05:00

From Gizmodo: The $499 Ultimate Collectors Millennium Falcon, is now shipping, 5,000-pieces and four-pound ring-binded manual included. Yes, this thing is massive. Julie Stern from LEGO confirms: "We're a bit ahead of schedule, so some people who preordered now have their sets." In other words: "Great shot kid, that was one in a million!" Spoiler: Darth Vader is Luke's father, he dies at the end and Yoda, Frank Oz is. (Thanks to Daniel L., one of our MathGeek field reporters, for sending in this item!)

Microsoft Math

2007-09-25T10:10:11-05:00

A serious bug has recently been discovered in Excel 2007. As the screenshot to the left shows, multiplying 850 by 77.1 yields 100,000 in Excel 2007, rather than the correct value of 65535. MathGeek readers will, of course, recognize that 65535 is one less than a power of 2, which raises many interesting ideas regarding the source of the bug.

Knock Knock Jokes

2007-09-12T12:48:24-05:00

Here's an interesting development: A couple of University of Cincinnati researchers have developed an artificial-intelligence program that can understand knock-knock jokes.

Knock-knock jokes, of course, frequently rely on a pun, as with: "Knock, Knock. Who is there? Wendy. Wendy who? Wendy last time you took a bath?" Humans intuitively understand when a pun is being made, because we're able to notice that a crucial word in the punchline is being misused semantically -- it's an incorrect meaning -- and is riding along purely because it sounds like the correct word. But computers have huge, huge problems with grasping semantics and homonyms.

So to create their knock-knock joke 'bot, the researchers programmed their AI with a big list of homonyms and their various meanings -- including, significantly, a lot of proper names (like "Wendy") because a lot of knock-knock jokes rely on proper names. Then whenever the AI reads a new knock-knock joke, it identifies the crucial "joke" word, then pings its database of homonyms to see if any of the words' rival meanings "fits" the joke. If it does, the bot flags the joke as "funny." More...

Wall Street Math: First Plot the Points and Then Take the Measurements

2007-08-28T08:20:56-05:00

From TechDirt: Last week, Morgan Stanley internet analyst Mary Meeker was embarrassed when it was revealed that a math mistake on her part caused her to vastly overstate (by a factor of 1000x) the revenue potential from YouTube's new ad overlay system. After having her mistake pointed out to her by none other than Henry Blodget, Meeker went back and fixed the report. But she did more than just correct the math. She also tweaked some of her original assumptions so as to boost the significance of the new advertising scheme. Whereas she originally predicted that ads would be shown on approximately 1% of streams, that number has now been boosted to yield a greater revenue impact. Meeker's new model now has the company garnering an additional $75-$189 million in net revenue over the coming year, as compared to the $720,000 that her original model predicted. This whole fiasco is quite revealing about the way Wall Street analysts sometimes operate. Rather than start out with a fixed set of assumptions and then figuring out what that will result in, they come up with an end result and then figure out what reasonable assumptions will get them there. While we're sure that this sort of thing happens all the time, it's rare to get such a stark glimpse into the way it happens.

Bach on the Trumpet!

2007-08-24T22:36:13-05:00

Geeks and Birds

2007-08-23T09:33:10-05:00

I know what you have been thinking: "This is a fantastic website about math and slide rules, but where are the parrots?" Well, your wait is over. Check out my sister's new website: www.feathersareflying.com. Enjoy!

Darwin Flunked Math!

2007-08-04T11:04:11-05:00

British astronomer Sir Fred Hoyle: “The likelihood of the formation of life from inanimate matter is 10 to the 40,000th power ... It is big enough to bury Darwin and the whole theory of evolution. There was no primeval soup, neither on this planet nor any other, and if the beginnings of life were not random, they must therefore have been the product of purposeful intelligence.” He further explains his position, using the example of a Rubik’s cube: “At all events, anyone, having even a nodding acquaintance with the Rubik’s cube will concede the near impossibility of a solution being obtained by a blind person moving the cubic faces at random. Now imagine 10 to the 50th power (that’s a number 1 with 50 zeros after it) blind people, each with a scrambled Rubik’s cube, and try to conceive of the chance of them all simultaneously arriving at the solved form. You then have the chance of arriving by random shuffling at just one of the many biopolymers on which life depends. The notion that not only biopolymers but the operating program of a living cell could be arrived at by chance in a primordial organic soup here on the earth is evidently nonsense of a high order.” He illustrates the probability of spontaneous generation like this: “Supposing the first cell originated by chance is like believing a tornado could sweep through a junkyard filled with airplane parts and form a Boeing 747.”

Dr. Michael Denton, noted molecular biologist agrees: “Considering the way the pre-biotic soup is referred to in so many discussion of the origin of life as an already established reality, it comes as something of a shock to realize that there is absolutely no positive evidence for its existence.” Dr. Denton also says: “The complexity of the simplest known type of cell is so great that it is impossible to accept that such an object could have been thrown together by some kind of freakish, vastly improbable event. Such an occurrence would be indistinguishable from a miracle.” Comments?

King me! Science of winning checkers solved

2007-07-19T15:35:29-05:00

With its uniform pieces and simple moves, checkers may seem like a simple kid's game. But it took hundreds of computers running continuously for nearly 20 years before researchers announced today that the game has officially been solved, a major benchmark in the development of artificial intelligence.

Thirteen years ago, a program named Chinook beat the reigning human world checkers champion, a feat that preceded Deep Blue's famous chess defeat of grandmaster Gerry Kasparov by three years.

Now, the programmers behind Chinook have fully solved the game, creating an unbeatable program that will choose the best move in every possible situation.

"In artificial intelligence, the chess and checkers groups have gone beyond the pale of what we thought we could do," said Michael Genesereth, an associate professor of computer science at Stanford University. "At one point, we thought we never could solve them in this way."

The team, led by University of Alberta computer science professor Jonathan Schaeffer, detailed the process Thursday on the Web site of the journal Science. The effort required up to hundreds of computers working since 1989 to analyze all possible board combinations of checkers, roughly 500 billion scenarios.

"Had I known it 18 years ago it was this big of a problem, I probably would've done something else," Schaeffer said. "But once I started, I had to finish." More...

HP-35: The Great Slide Rule Killer

2007-07-02T14:01:53-05:00

From the HP Calculator Museum: The HP-35 was HP's first pocket calculator. It was introduced at a time when most calculators (including expensive desktop models) had only the four basic functions. The HP-35 was the first pocket calculator with transcendental functions and the first with RPN.

Based on marketing studies done at the time, the HP-9100 was the "right" size and price for a scientific calculator. The studies showed little or no interest in a pocket device. However Bill Hewlett thought differently. He began the development of a "shirt pocket-sized HP-9100" on an accelerated schedule. It was a risky project involving several immature technologies. HP originally developed the HP-35 for internal use and then decided to try selling it. Based on a marketing study, it was believed that they might sell 50,000 units. It turned out that the marketing study was wrong by an order of magnitude. Within the first few months they received orders exceeding their guess as to the total market size. General Electric alone placed an order for 20,000 units. As a result, they later had to warn people to expect waiting lists in the Hewlett-Packard Journal. This was an unusual situation for HP. While many companies advertised calculators months or even years before you could buy one, HPs were normally available the day the first advertisements appeared.

Beam Me Up!

2007-06-04T21:08:00-05:00

"Scientists have set a new record in sending information through thin air using the revolutionary technology of quantum teleportation - although Mr Spock may have to wait a little longer for a Scotty to beam him up with it.

A team of physicists has teleported data over a distance of 89 miles from the Canary Island of La Palma to the neighbouring island of Tenerife, which is 10 times further than the previous attempt at teleportation through free space.

The scientists did it by exploiting the "spooky" and virtually unfathomable field of quantum entanglement - when the state of matter rather than matter itself is sent from one place to another. Tiny packets or particles of light, photons, were used to teleport information between telescopes on the two islands. The photons did it by quantum entanglement and scientists hope it will form the basis of a way of sending encrypted data.

The teleporters used in Star Trek are said to have been based on the idea of quantum entanglement and the latest study demonstrates that elements of the phenomenon could have a practical use in the real world." More...

Fahrenheit 451

2007-05-31T07:14:37-05:00

In his pastel-yellow house in upscale Cheviot Hills, where he has lived for more than 50 years, Bradbury greeted me in his sitting room. He wore his now-standard outfit of a blue dress shirt with a white collar and a jack-o’-lantern tie (Halloween is his favorite day) and white socks. This ensemble is in keeping with Bradbury’s arrested development. George Clayton Johnson, who gave us Logan’s Run, says, “Ray has always been 14 going on 15.”

Bradbury still has a lot to say, especially about how people do not understand his most literary work, Fahrenheit 451, published in 1953. It is widely taught in junior high and high schools and is for many students the first time they learn the names Aristotle, Dickens and Tolstoy.

Now, Bradbury has decided to make news about the writing of his iconographic work and what he really meant. Fahrenheit 451 is not, he says firmly, a story about government censorship. Nor was it a response to Senator Joseph McCarthy, whose investigations had already instilled fear and stifled the creativity of thousands. More...