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Sanjoy Mahajan

Street-Fighting Math MOOC Is Open

My mathematically inclined readers are cordially invited to enroll in “6.SFMx: Street-Fighting Math,” which starts today on EdX. Like most (all?) MOOC courses, it is free and open to world, as are all the course materials.

So far, I have learned that teaching an entirely online course requires far more effort than teaching in person. Maybe by a factor of 10. Partly, it is the difference between talking to a friend on the phone—you just pick up the phone and start talking—compared to writing a long letter that needs to be thought out. To this difference you add that 10,000 others will also read and depend on the letter. You get nervous about making all the pieces right. They never will be, so you never rest easy.

4/8/14

U.S. Math Education Still in the Doldrums

Every three years, the OECD, in the PISA assessment, studies 15-year-olds around the world to measure performance in reading, mathematics, and science. The results of the 2012 PISA assessment, which had a particular focus on mathematics, just came out and the United States does not fare well: “Among the 34 OECD countries, the United States performed below average in mathematics in 2012 and is ranked 26th.” I worry not so much about the rank, but about the low absolute level of proficiency to get this rank.

The U.S. students’ particular strengths and weaknesses are even more distressing:

Students in the United States have particular strengths in cognitively less-demanding mathematical skills and abilities, such as extracting single values from diagrams or handling well-structured formulae. They have particular weaknesses in items with higher cognitive demands, such as taking real-world situations, translating them into mathematical terms, and interpreting mathematical aspects in real-world problems.

12/16/13

The Marketing of Dogfish

In New England, cod and haddock are overfished and, according to WBUR, fishermen and restaurant owners are seeking cheaper and more plentiful fish like dogfish. Fish wholesalers are therefore working to promote the dogfish’s image. According to WBUR, dogfish is already used in cafeterias at some local universities and hospitals — and local lawmakers are now pushing the federal government to help by buying dogfish for prisons and military rations. What genius marketing: “Dogfish: Tasty enough for schools, hospitals, C rations, and even prisons.”

11/19/13

Transaction Costs: The American Way

The rest of the world likes to say that everything in America is big: the cars, the CO2 emissions, the buildings, even the hamburgers. The farce at the U.S. government’s website for enrollment in health insurance under the so-called Affordable Care Act (ACA) shows that we also supersize our transaction costs.

In a news report from NPR, Alaska Public Radio Network, and Kaiser Health News, even a computer programmer who had also created websites needed many attempts over many weeks to use the site to enroll for health insurance. And she still awaits the enrollment confirmation (with luck in the new year, said the radio version of the report). If it arrives, she gets affordable health insurance ($110 instead of $1200 per month), but then still has the joy of dealing with an insurance company and the claim paperwork.

11/12/13

The Nobel Prize in Physics and Traffic Priority at Roundabouts

The 2013 Nobel Prize in Physics was recently awarded for symmetry breaking and its consequence, the Higgs boson—a particle so well known that, according to the president of the American Physical Society, “[i]f you’re a physicist, you can’t get in a taxi anywhere in the world without having the driver ask you about the Higgs particle.” Teaching the symmetry unit in my own course this semester, I couldn’t help wondering about symmetry as I drove through an apparent example of symmetry: roundabouts or traffic circles.

Roundabouts use two complementary systems for controlling traffic flow: (1) Traffic in the roundabout has priority, or (2) traffic entering the roundabout has priority. The choice seems so symmetric, like choosing right- or left-hand traffic. In the United Kingdom, traffic in the roundabout has priority. In contrast, on many Massachusetts roundabouts, including one on my commute, entering traffic has priority.

10/21/13

Why It's Hard to Find a Used Bicycle in Denmark

Visiting friends in Copenhagen and cycling around the city, I wondered why so many bicycles were new (and, having experienced Scandinavian pricing, expensive). When I lived in England, I bought a three-speed BSA bicycle from the wonderful Chris Lloyd Bikes repair shop for only £60 (about $100). The bicycle had already lasted 40 or 50 years; according to Laplace’s rule of succession, it would probably last another 40 or 50 years — at least with regular maintenance. Which I provided. When any problem turned up, I took the bicycle back to Chris Lloyd, who set it right for a right price.

That’s the difference from Denmark, with one of the world’s highest hourly wages.

7/24/13

Titles of Laws as Propaganda

How illiterate do our politicians think we are?

In the old days we had plain titles of laws, such as the Voting Rights Act or the Civil Rights Act. In the United Kingdom, the titles of laws still reflect their subjects, whether the Official Secrets Act or the National Health Service Act. The modern U.S. Congress, as the least trusted institution in America, is particularly prone to these propaganda titles. Thus, modern Americans, instead of universal, government-funded healthcare, get government-funded propaganda: the Patient Protection and Affordable Care Act.

7/16/13

The Ultimate Telemarketing Database

Playing “My Country, ’Tis of Thee” on the piano for my evening relaxation and hearing my daughter sing about the “sweet land of liberty,” I thought of the NSA’s Prism surveillance system. The U.S. government should thank whistle-blower Edward Snowden for providing a way for them to reduce the U.S. budget deficit. Now that everyone knows that the U.S. government harvests data on every person on the planet not living in a cave, why doesn’t the U.S. government mine the data — after all, it has the most computing resources — and sell the results to telemarketers?

6/17/13

Minute-Wise, Hour-Foolish

In my kitchen cabinet, with the richest aroma, live baggies of ground cumin, coriander, turmeric, curry powder, cinnamon, and cloves. Four feet away are their labeled spice jars. The jars are easier to use but sit mostly empty. Whenever I cook, I need the spice now, before the main food ingredient releases its water and stops the spice from browning.

So I don’t dig out the funnel to transfer the spice into its jars. Nor do I cut up scrap paper and fold it into a funnel. I just fish out each spice from its baggie, and fumble around to reseal the plastic zipper. Each choice is rational, in the short run. In the long run, by not transferring the spices to their jars, I waste time and stress out my cooking.

Having noticed this reasoning anti-pattern, I see it all around.

6/11/13

Aaron Swartz Versus the Bankers

New Yorker article on Aaron Swartz, who committed suicide while under federal investigation for bulk downloading academic articles, leaves little to disagree with. But it missed a comparison that has troubled me: between Swartz and the bankers who tanked the world economy.

I have found myself unable to write about this topic until now. First, Swartz lived for many years in my apartment building in Cambridge, Mass., and many residents remember him as quiet and kind. Second, I share his belief in the free flow of information. Using the NonCommercial ShareAlike license from Creative Commons, MIT Press published and freely licensed my Street-Fighting Mathematics“One of the early architects” of Creative Commons was Aaron Swartz.

Swartz tried to free knowledge and expand the public domain. In contrast, the bankers took from the public domain.

5/16/13

Why Are Restroom Hand-Washing Signs By the Sinks?

All over America, restrooms for the public (for example, in restaurants or public parks) have signs warning and exhorting us that “Employees must wash hands before returning to work” or “Hand-washing stops the flu!” These are useful public-health messages. However, in almost every restroom I’ve been to, the sign stares at you from the mirror behind the sinks. What is the point of reminding the already hygiene-conscious to wash their hands?

But in the San Francisco airport a few days ago, I finally found a “Clean hands, good health!” sign at the restroom exit door. I don’t know whether it ever caused someone to U-turn and head for the sinks, but at least it isn’t carrying coals to Newcastle.

4/15/13

The Quants and the Airlines Versus the Public

Baggage fees are a small part of the misery of American air travel. There’s also connecting flights, which, to paraphrase the Nuremberg judgment, contain within themselves the accumulated evil of the whole. For if air travel were pleasant, who would mind changing planes and spending more time in the system?

Instead, the airlines make us pay to avoid the extra hours — giving airlines an incentive to make air travel less pleasant. But once in a while you can beat the system.

For a memorial service at short notice, I once had to fly with my 2-year-old daughter to New York (and throw away our return flight to Boston). The price of a nonstop, one-way flight from Phoenix, Arizona to Newark, New Jersey: $1200 (for two people).

But what if I flew slightly farther, allegedly changed planes in Newark, but just left the airport? So I went back to airline’s website and asked for a one-way flight to Manchester, New Hampshire. It was only $400 (for two people). Not only did the flight connect in Newark, but the Phoenix–Newark leg was the same flight that cost $1200 nonstop!

3/4/13

We Once Had Self-Driving Cars

A frequent response to the dysfunctions of American air travel is technological: namely, self-driving cars (also see this article). In a self-driving car, you can relax, even sleep, while being driven safely to your destination at 60 mph. We once had such a system. It’s called a train network.

Compared to air or car travel, a decent train network is cheaper, more environmentally friendly, and quicker. As an example, I’ll compare two door-to-door, city-center-to-city-center journeys.

1/22/13

The Absurdity of U.S. Air Travel: Baggage Fees

On the way home from visiting my brother-in-law’s family in Ohio, we changed planes in Chicago. To avoid the baggage fees, we, like most of our fellow passengers, schlepped our luggage through the airport to the gate in Dayton.  Of course, we had to gate-check it because the overhead bins were long-full by the time we could board (boarding group: infinity). The plane arrived in Chicago late, we waited 20 minutes for our baggage to be unloaded, and then we sprinted to (and barely caught) our connecting flight to Boston.  Naturally, we had to gate-check the luggage for that flight as well.

Baggage fees brought U.S. airlines in 2011 a total of $3.4 billion. That amount is almost one-half of the industry’s 2011 profits of $7 billion. To double the airlines’ profits, the social benefit of which is highly unclear, society incurs many costs:

1/9/13

Saving Boston's Long Wharf Park From Extinction

Have you visited the beautiful and historic Long Wharf Park on Boston Harbor? And what do you do when the government goes rogue?

The Boston Redevelopment Authority (BRA), in defiance of the Massachusetts Constitution, is trying to turn Long Wharf Park into a late-night restaurant and bar. The Massachusetts Constitution requires a two-thirds vote of the Legislature before public parkland can be converted to other uses. The vote has not happened, and the BRA is telling the world that it is unneeded. As featured in today’s Boston Globe, ten local residents, including me, have been trying to force the government to obey the constitution.

10/10/12

A Tax Taxonomy

Dan Hamermesh’s much-discussed post about taxing capital gains brought to mind my own taxonomy of taxes, so to speak, from least to most progressive:

1. Poll tax. Everyone pays the same amount. What could be fairer than this?!
England tried it in the late 14th century, leading in 1381 to Wat Tyler‘s Rebellion. Six hundred years later, England tried it again, leading to the Poll Tax Riots.

2. Sales tax. Goods are taxed at a flat rate (often 17 to 20 percent in Europe, and 5 to 8 percent in various American jurisdictions). Because the wealthy spend a smaller fraction of their income on taxable goods than do the poor, this tax is less progressive than a flat income tax.

3. Flat income tax. Everyone pays the same fraction of his or her income. This tax was the core of Steve Forbes’s platform when he ran for president in 1996 and 2000.

10/3/12

Beware the Weasel Word "Statistical" in Statistical Significance!

As Justin Wolfers pointed out in his post on income inequality last week, the Census Bureau was talking statistical nonsense. I blame the whole idea of statistical significance. For its weasel adjective “statistical” concedes that the significance might not be the kind about which you care. Here, I’ll explain what statistical significance is, and how its use is harmful to society.

To evaluate the statistical significance of an effect, you calculate the so-called p value; if the p value is small enough, the effect is declared statistically significant. For an example to illustrate the calculations, imagine that your two children Alice and Bob play 30 rounds of the card game “War,” and that the results are 20-10 in favor of Bob. Was he cheating?

To calculate the p value, you need an assumption, called the null (or no-effect) hypothesis: here, that the game results are due to chance (i.e. no cheating). The p value is the probability of getting results at least as extreme as the actual results of 20-10. Here, the probability of Bob’s winning at least 20 games is 0.049. (Try it out at Daniel Sloper’s “Cumulative Binomial Probability Calculator.”)

9/20/12

Why My Favorite American Cities Have a Chinatown

Relatives from South Africa were visiting and we got to talking about which cities to visit in America. I shared my list: San Francisco, New York, Boston, Washington, DC, Seattle, and Philadelphia. Each city has a Chinatown. Coincidence? Or maybe the connection is just that I like Chinese food. Indeed, our family has been going to a favorite dim-sum restaurant most every week since moving to Boston seven years ago.

Then the larger connection came to me. Chinatowns were made by Chinese laborers building the railroads (when the laborers had finished this vast public-works program, the Chinese Exclusion Act barred most Chinese from emigration to or citizenship of the United States). Having a Chinatown marks a city as of the railroad era, built up before the wide deployment of the automobile. As Lewis Mumford said, “The right to have access to every building in the city by private motorcar in an age when everyone possesses such a vehicle is actually the right to destroy the city.” Cities with Chinatowns had enough roots to escape carmageddon.

8/15/12

Division, Not Long Division

Division is the most powerful arithmetic operation. It makes comparisons. When the numerator and denominator have the same units, the comparison makes a dimensionless number, the only kind that the universe cares about. Long division, however, is something else entirely. In my post “Dump algebra,” many commentators objected to my loathing of long division. But long division is not division! Long division is just one way to do the computation, and is far from the most useful way.

I’ll illustrate with an actual example of division. For my environmental-protection lawsuit, now in the Massachusetts Supreme Court, I needed to divide 142,500 by 4655.

8/10/12

Obedience on the Job

On America’s first subway, Boston’s Green line, the middle doors stopped opening. When I asked the driver to open the doors, he said that he couldn’t: now all boarding and deboarding at the above-ground stops is through the narrow front door by the fare box. Ah, the MBTA: making up for the 23 percent fare hikes on July 1 with improved service!

Me: “The new policy slows the ride for everyone. Now passengers cannot board and pay their fares until all the deboarding passengers have left.”

Driver, shrugging: “It’s the new policy. I just do what my boss tells me to do. I don’t question.”

Me: “We could use some questioning.”

Driver: “Questioning isn’t part of my job. I just wait for my pay day.”

8/6/12

Towing Exchange

Fellow blogger Daniel Hamermesh recently explained the virtues of exchange as a painter helped him break into his Berlin apartment. My exchange example is not as glamorous. Shopping at the local co-op in Cambridge, I heard over the public-address system, “If you are the owner of a gray Subaru Outback, you are being towed!” I leaped over a low chain and made a break for the parking lot, as a mother nearby offered to watch my daughters (ages 1 and 4). The Subaru was hooked up and about to be hoisted onto the tow truck. In view of my timely arrival, the tow-truck operator offered two options: Pick up the car later that day in Somerville for $200, or pay $50 (cash) and he’d unhook the car now. An offer I couldn’t refuse. Everybody gained, yet I am still furious!

8/1/12

Dump Algebra

Being a good teacher, I like to think, requires a curious and freethinking mind. A supporting example is Andrew Hacker, described by a former Cornell colleague as “the most gifted classroom lecturer in my entire experience of 50 years of teaching.” His book Higher Education?: How Colleges Are Wasting Our Money and Failing Our Kids—and What We Can Do About It, co-authored with Claudia Dreifusconvinced me that tenure is harmful. His latest broadside, “Is Algebra Necessary?”, in last Sunday’s New York Times, is as provocative.

He argues that we should stop requiring algebra in schools. Despite the vitriol in several hundred comments (“We read them so you don’t have to.”), he is right.

7/31/12

Ending the Math Wars in a Treaty of QAMA

As a country, we are often at war. If it’s not against Germany, England, terrorism, or Grenada, it’s the war on poverty (that’s gone so well), the war on cancer (ditto), and, of particular interest to me, the Math Wars, which have been raging for decades. On one side, the traditionalists insist on drilling and back to basics, “on behalf of sanity and quality in math education.” On the other side, the reformers insist on conceptual understanding using computers and calculators, to “promot[e] the rational reform of mathematics education.”

Both are half-right and half-crazy. As the reformers say, students need to understand what the mathematics means. Students whose word problem for “6 x 3 = 18” is of the form “There were 6 ducks, and 3 more showed up, so 6 times 3 is 18,” understand little. (See “Children Learning Multiplication, Part 1,” in the articles by Professor Thomas C. O’Brien.) As the traditionalists say, using computers for everything leads to needing a calculator to compute what 6.5 x 10 is.

However, there’s a tool to combine the merits of both sides: the Quick, Approximate, Mental Arithmetic (QAMA) calculator.

7/13/12

Remembering Chinatown

Learning that Los Angeles’s Chinatown is fighting a Walmart store, including with a lawsuit against the city, reminded me of what I learned in that Chinatown years ago.

One midnight, fed up from revising our dissertations all day, a friend and I drove the 10 minutes from Caltech into Chinatown to dine at Full House Seafood, open until 2 AM. (My Ph.D. adviser once asked why graduate students all seem to live on Guam time.) The restaurant was lively and crowded but not packed, and we quickly got a table. While waiting to give our order, I noticed an African-American man sitting on the chairs near the front counter. Even though several tables were free, the waiters did not offer him a table. Other customers came in, and were seated. As our dumplings arrived and got eaten, and then the spicy tofu, the man still sat on the small chairs.

7/10/12

Solving Problems in the Real World

I owe my favorite local bookstore, the Harvard Bookstore, for making another day for me. Wandering the tall, packed shelves on a warm and breezy evening, I ran across Schaum’s Outline of Principles of Economics. One subtitle on the cover: “964 fully solved problems.” The problems include, for example (from page 50): “True of false: As used in economics, the word demand is synonymous with need,” or “True or false: A surplus exists when the market price is above the equilibrium price.”

I didn’t long much for either answer.

Instead, as the U.S. mortgage market has, as James Kunstler predicted on October 10, 2005, imploded “like a death star” and dragged “every tradable instrument known to man into the quantum vacuum of finance that it create[d],” as euros flee from Greece, and as bank loans dry up in Spain, I wished that the 964 fully solved problems included one or two of the real problems.

5/30/12

The Retirement Robbery

Since putting email back in its corral, I’ve turned some recovered time to reading actual books in print — the latest being Retirement Heist: How Companies Plunder and Profit from the Nest Eggs of American Workers by Ellen E. Schultz. If a nation of sheep shall beget a government of wolves, then the lesson from Retirement Heist is that today the shears are sharpened with numbers.

Retirement Heist is, as one blurb describes, a “meticulously researched and gripping as a crime thriller.” Each chapter explains, with detailed research data and outrage-generating examples, yet another method corporations use to steal retirement benefits and mask the theft behind accounting shenanigans. It is one of the few books (since Cadillac Desert) to describe outrageous behavior so well that I threw it across the room.

4/16/12

Surviving "the Tyranny of E-mail"

Like a plague of locusts, they give us no rest. They gobble our irreplaceable asset: our time. The faster we swat them away, the faster they arrive. Our modern locust plague is email.

Fortunately, I found The Tyranny of E-mail: The Four-Thousand-Year Journey to Your Inbox by John Freeman a week ago at the Harvard Bookstore, one of the few surviving independent bookstores in Cambridge, MA. Alas, the book was discounted to $5.99 — which probably means that it is on remainder. That is a shame, for it is a rich and thoughtful book, mixing history, analysis, outrage, and remedy.

The beginning of wisdom, it was said, is to call things by their right names. By that venerable standard, this is a wise book.

3/5/12

Classrooms With 500,000 Students

I am fascinated by the Stanford online courses in machine learning and artificial intelligence. My first inkling of them came when quite a few of my students started taking the artificial-intelligence class. Olin is very small, only about 400 students, so I realized that these online courses must be large. But I almost fell over when I saw that enrollment varied from 66,000, at the low-end, to 160,000.

Sebastian Thrun, who co-taught the artificial-intelligence course to 160,000 students, is now leaving Stanford teaching in order to teach courses to 500,000 students for free. What an inspiring goal!

1/30/12

Seal Training or Learning?

Yesterday I got a short and sweet insight into learning, courtesy of the New England Aquarium, where I took our daughters for our weekly visit. One of our favorite exhibits is the training session for the sea lions and fur seals. In the audience this time were about 100 school children with parents and teachers. To introduce the session, the lead trainer conducted the following discussion:

How many of you do chores? (Many hands go up.)

How many of you get an allowance for doing chores? (Most hands remain in the air.)

How many of do homework?

  • How many you have to finish your homework before you can go outside to play? (Lots of hands still in the air.)

    I see lots of hands! It makes homework not so bad because you get a reward at the end.

  • 1/20/12

    Listen Carefully as Our Menu Options Have Recently Changed

    Moving houses has always been like having three teeth removed without anesthetic. These days the pain is accentuated by having to wait on the phone hearing, “Please listen carefully as our menu options have recently changed.” That’s corporate-speak for, “Don’t even bother pressing zero hoping to speak to a human. That’ll just put you back at the beginning.”

    My latest such adventure started with an email from the phone company (Verizon). I was told that a technician would come to hook up our new service during the time “window” of 8 a.m. to 5 p.m. If a window is an opening in a wall, then 8 am to 5 p.m. is more like the whole wall. Trying to shrink the window, I spent more than an hour on hold for one person after another who could only forward me to someone else equally unhelpful. The circular chain of authority finally snapped when the last person claimed (all this discussion is at 10 a.m. on the day itself) “We have absolutely no way to reach the technician.” And then asked “Have I provided excellent service today?”

    12/19/11

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