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Tony Phillips' Take on Math in the Media A monthly survey of math news |

This month's topics:

- Netflix and the singular value decomposition
- "physical reality embodies simple mathematical laws"
- Math Ed in the news

Netflix and the singular value decomposition

Clive Thompson published "If You Liked This, You're Sure to Love That" in the *New York Times Magazine* for November 21, 2008. The story is about Cinematch, the "recommendation engine" Netflix uses to tell you "If you liked this, etc." Netflix depends for profits on customers' maintaining their subscriptions: "new members often have a couple of dozen movies in mind that they want to see, but after that they're not sure what to check out next, and their requests slow." Since scanning the Netflix backlist (over 100,000 movies) is impractical, users need advice; they get it from Cinematch: "its suggestions now drive a surprising 60 percent of Netflix's rentals." But the advice needs to be good, and every improvement to Cinematch is worth money. In October, 2006 Netflix decided to put the public to work: they opened their files (17,110 movies rated by 480,189 users, 200 ratings per user on overage) and offered $1 million for an algorithm that would improve the accuracy of their predictions by 10%. The contest, according to Thompson, "has galvanized nerds around the world." The first big improvement came from applying the *singular value decomposition,* a mathematical technique that "takes the mass of Netflix data and automatically sorts the films. ... it groups together movies that share qualities with predictive value." As an example of what comes out, Thompson quotes Chris Volinsky (AT&T), a member of one of the leading teams in the competition: "You can find things like 'People who like action movies, but only if there's a lot of explosions, and not if there's a lot of blood. And maybe they don't like profanity.'" But 10% turns out to have been a very elusive target: the best achieved up to now is a 9.44% improvement, and "progress seems to be stalling."

Todd Will (Wisconsin-La Crosse) has a web introduction to the topic. (The singular value decomposition is "absolutely a high point of linear algebra" according to Gilbert Strang).

"physical reality embodies simple mathematical laws"

The entire quotation runs as follows: "A highly precise calculation of the masses of strongly interacting particles, based on fundamental theory, is testament to the age-old verity that physical reality embodies simple mathematical laws." This appears at the head of a "News and Views" piece by Frank Wilczek in the November 27 2008 *Nature*. Wilczek (MIT Professor, Nobel Laureate) is commenting on an a *Science* report by Stefan Dürr and collaborators (**322** 1224-1227) entitled "Ab Initio Determination of Light Hadron Masses." Quantum Chromodynamics (QCD) is the analogue for the strong force of Quantum Electrodynamics (QED) for electromagnetism: a quantum field theory that makes predictions by minimizing the space-time integral of the *action* over all possible configurations meeting certain initial conditions. The perturbative methods (Feynman diagrams, etc.) that work so well in QED cannot be extended to QCD. The only possibility is computer simulations of the theory, huge and delicate calculations Wilczek describes as at "the frontier of ingenuity and computer power." Dürr *et al.* input three parameters (the masses of the three light quarks) and use the theory to calculate the masses of all the other light hadrons (particles subject to the strong force), including the proton and the neutron, the building blocks of our reality. What is the interest of a calculation of numbers we already know? Wilczek: "One answer is practical. The same techniques that are used to compute known hadron masses can also be used to compute other interesting quantities that are very difficult to measure experimentally."

"But perhaps a more profound answer is philosophical. A great vision of science --stretching from Pythagoras' credo 'All things are number', to Kepler's s ordering of the planets based on Platonic solids, to Wheeler's slogan 'Its from bits'-- has been that physical reality embodies ideally simple mathematical laws. As physics developed before the quantum revolutions of the twentieth century, the basic equations emphasized dynamics (how given systems evolve in time) as opposed to ontology (the science of what exists). Kepler's system was stillborn, but in the world of QCD and hadrons, the great vision lives and thrives."

* "Start-Up Teaches Math to Americans, Indian-Style" (*New York Times*, November 6, 2008). Under the "Bits" rubric: Business - Innovation - Technology - Society. India Math Online "has lessons for students in grades one through 12 and offers several packages for $12.50 to $20 a month." Started by two fathers worried about their daughters "falling behind in the global competition to be educated for the 21st century" (quote from father), now available for boys too. Includes diagnostic tests. "It sends parents a report showing the topics in which their children are strong and weak and sends students learning modules full of practice problems." Bottom line: "children of Indian and Chinese parents use the site consistently, but American children often lose interest after a couple months." Author: Claire Cain Miller.

* "Judge Halts Mandatory Algebra Testing for California 8th Graders" (AP, in *New York Times*, December 20, 2008). The California Board of Education, backed by Gov. Arnold Schwarzenegger, is trying to "meet federal testing requirements or face losing up to $4.1 million in funding." Background:

- "About half of California eighth graders receive full algebra instruction, but only about a quarter of those who take it score proficient or above on standardized tests. The rate is even lower for black, Hispanic and poor students."
- "Federal officials say California's existing math test for students not enrolled in Algebra I does not follow the rules under the No Child Left Behind Act ..."
- "David Sanchez, president of the California Teachers Association, said the algebra mandate would have required 3,000 more teachers, as well as training an additional 1,000 teachers."
- "The state is struggling with a $42 billion budget deficit through mid-2010, and both lawmakers and Mr. Schwarzenegger have suggested cutting public education financing to save money."

Tony Phillips

Stony Brook University

tony at math.sunysb.edu