Bad Math about Infertility in the WSJ

From the Wall Street Journal:

Infertility, defined as the inability to conceive after one year of unprotected sex, affects one in six couples of childbearing age in the U.S. In 40% of cases, the problem is with the man; in 40% it’s with the woman, and in 20%, something is amiss with both, say Zev Rosenwaks and Marc Goldstein, fertility experts at New York Presbyterian/Weill Cornell Medical College and co-authors of the 2010 book, “A Baby at Last!”

Probability is often confusing, but after running the numbers, I’m fairly certain this math is wrong. If we assume that infertility affects one in six couples, then 5/6 pairings are fertile. Assuming that people choose who they try to have children with independent of fertility, at least initially, and assuming the infertility can be equally due to either the man or the woman, the results follow quite clearly: only about 5% of cases of infertility are due to both members of the couple being infertile, while the other 95% of the time it’s either due to the man or woman only.

Anyone know how the WSJ numbers were calculated?

How my calculations were done: if 5/6 pairings are fertile, this means that the square root of 5/6, or about 91%, of the population is fertile. Of those pairings then that result in infertility (that remaining 1/6), the ones that are due to both the man and woman being infertile are only (1-0.91)^2/(1/6), or about 5%.

A Town Named Migrate, KY

In a Wall Street Journal article about winning the American green card lottery due to a computer error, there’s a great anecdote:

In the days when the lottery was paper-based, the State Department’s Kentucky Consular Center, which handles the program, created a post-office address with a fictitious city named Migrate, Ky., putting the address on applications. Applicants mailed their forms to the city and lottery winners who eventually settled in the U.S. would sometimes search in vain for Migrate on the U.S. map.

Gutenberg’s Legacy: Hypotrochoids and Wound Man

Last week I was in Germany for the Altmetrics11 workshop at the ACM Web Science 2011 conference, and had the opportunity to go to the Gutenberg Museum in Mainz.

If you love the history of technology, typography, the history of printing, or even just seeing lots and lots of old books, this museum will astonish you. From an in-depth discussion of lithography and printing presses from throughout the ages, to clear examples of how even within a few years of Gutenberg’s innovations typography was charting bold new avenues, this Museum is amazing.

Gutenberg, lauded for his creation of the printing press and movable type, did much more than simply modify a wine press. His use of technologies and innovations from an astonishing number of areas is what made his idea so powerful. He used metallurgical developments to create easily regularized metal type, chemical innovations for a better ink, and even used the concept of division of labor to make a large team of workers (many of whom were illiterate) churn out books at a rate never before seen in history. Gutenberg even employed elegant error-checking mechanisms to ensure that the type was always set properly.

And of course, his innovations unleashed changes in nearly every field: science, religion, technology, art, literature, everything. But let’s focus briefly on gears: at the museum, there is a Guilloché lathe, which is a massive and intricately geared device that is used to etch the geometric patterns seen on bank notes. These patterns, known as hypotrochoids by mathematicians and Guilloché patterns by designers, are exceedingly beautiful. So essentially, part of Gutenberg’s legacy was the Industrial Age Spirograph.

And Gutenberg also affected medicine. The Gutenberg Museum has a book with a copy of Wound Man, which is apparently a medical diagram that teaches anatomy through injury:

And want to see how a book was made in the Nineteen Forties, as companion piece to the museum? Check out this video.

Why We Need a TV Show About Academia

In a piece at Wired Science, I argue why we need a TV show about academia:

No matter what new sitcoms and dramas the networks dream up this coming fall, I can almost guarantee the absence of one type of show: a show about academia. But a television show about academics — professors, scientist and graduate students — is more necessary than ever before. And with a film being made out of Piled Higher and Deeper — an online comic about the trials and tribulations of graduate students — the time may be right to fill this gaping hole on the small screen.

The West Wing was a great success because the creators used White House staff as advisors, giving viewers a riveting window into the way policy and politics occur in our country. But this desire to see how the sausage is made should not be limited to our government. It can also be extended to how we think about the creation of knowledge.

The rest is here.

And anyone in Hollywood, please feel free to contact me.

Gaussian Genealogy: Math Masters Trace Their Intellectual Lineage

For my first piece in Wired (June issue, page 56, if you’re playing at home), I explored the Mathematics Genealogy Project, which examines the academic lineage of mathematicians and is well-known to all mathematically-inclined academics. For example, play with my “family” tree for awhile, and you’ll find a lot of academic inbreeding. For Wired, I created a heavily-annotated ancestry for Gerald Sussman, a professor at MIT, who has quite the pedigree (Leibniz, Gauss, Euler, and many more). Check out the piece here.

On the Social Fabric of Fiction, and Superheroes

Over at TheAtlantic.com, I have an essay about the social fabric of fiction: whether or not the worlds of the mind are similar to or different from the “real world” and how we can use science to help us answer this question. So, naturally, I look to the world of superheroes and social networks:

One clear way in which the fictional world seems far less dull is in the tendency to create complex connections between characters. Characters are not strangers to each other, but are connected in surprising and complicated ways. From superheroes to the world of Scooby-Doo, we are well-versed in the Big Reveal, where someone is exposed as a previously known character. Enemies are actually long-lost brothers; a secret father is discovered; and when a mask is taken off, the antagonist is exposed as a neighbor from down the street.

This isn’t a modern inclination either. In the Jewish rabbinic tradition, there is a trend towards interpreting an unnamed character — who is mentioned briefly and then never again — as someone who we have met before. For example, a man in a field is not simply a random person; instead he is the angel Gabriel. This concept is used so often that some people have a light-hearted term for this: the Conservation of Biblical Characters.

We can now bring new methods of analysis to these phenomena through the now-ubiquitous scientific study of social networks. Through research that delves into who we know and what sorts of relationships we have, we have a good handle on the overall structure and shape of social networks in the real world. In addition to the oft-mentioned six degrees of separation, there are many other statistical properties of social networks, from how individuals with lots of friends are connected to each other, to the distribution of popularity.

It turns out that similar research has begun on the social network of the Marvel Universe. The common home of Spider-Man, X-Men, and the Fantastic Four, various die-hard fans decided that collecting comic books wasn’t enough; they wanted to understand the universe in its entirety. Thus was born the collaborative Marvel Chronology Project, which details every character in the Marvel Universe, major or minor, and every issue of every comic book series that they appear in.

The whole essay is here.

Connecticut’s Panhandle and New York’s Oblong

Connecticut, like a number of other states, has its own panhandle. However, due to circumstances surrounding its creation, it created a mysterious region in New York State, known as the Oblong. Here is the story of the creation of both, in brief:

Under a new agreement of November 28, 1683 the boundary between Connecticut and New York was generally recognized as a line parallel to and twenty miles from the Hudson River north to the Massachusetts line. However, New York, acknowledging most of Connecticut’s settlements in Fairfield County, gave up a claims to a 61,660 acre rectangle east of the Byram River, which became the area sometimes referred to as Connecticut’s “panhandle” or the “handle of the cleaver”. In return, Connecticut gave up its claims to Rye and ceded to New York a strip of land 580 rods (1.81 miles) wide “equivalent” to the area of the panhandle that extended north from Ridgefield along Dutchess, Putnam, and Westchester Counties, New York, to the Massachusetts line.

While this strange region of New York is no longer particularly relevant (aside from the marker pictured below, indicating its existence), it is primarily known about within genealogical circles, as families that hail from the Oblong find it to be a genealogical black hole. Apparently, families from this region are ignored by both states, leading to some family tree dead ends.

Cultural Ontogeny Recapitulates Phylogeny

In evolutionary biology, there is a now-discredited idea that “ontogeny recapitulates phylogeny.” In other words, the development of an organism follows its evolutionary history. Human embryos look like they have gills because people evolved from fish, we have tails in utero because of the same origins, and so forth.

In a recent paper in PLoS ONE, Alex Mesoudi, a professor at the University of London, discusses this briefly, but in the realm of culture. Mesoudi’s paper, entitled Variable Cultural Acquisition Costs Constrain Cumulative Cultural Evolution, explores how to model the exponential increase in cultural complexity, whether scientific knowledge, technological innovation, or other cultural products. Mesoudi argues that in order to create any new innovation that builds on previous knowledge, an individual must first learn and master all the innovations that came before it. In other words, cultural ontogeny recapitulates phylogeny.

And Mesoudi demonstrates this in an elegant way, by looking at the age at which British students first learn various mathematical concepts, as compared to the year these concepts were actually discovered. Here is the resulting figure:

As can be seen, there is a clear, albeit nonlinear, relationship between these quantities (original data here). More complex concepts–those learned later in life–are in fact those that were discovered more recently. Specifically, since the function is actually a logarithmic curve, this means that newer concepts are being discovered more quickly, and learned more rapidly.

It’s unlikely that this works for all topics–if a field’s college courses don’t require prerequisites, this relationship is highly unlikely to hold–but it’s fascinating to see the regularity of this shape.


Mesoudi A (2011). Variable cultural acquisition costs constrain cumulative cultural evolution. PloS one, 6 (3) PMID: 21479170

The International Dateline in Jewish Law

There are many examples where geekiness meets Judaism. Sierpinski Hamantaschen, for example. Well, here’s one case where geography nerdiness combines with Jewish Law: the International Dateline.

When Jewish laws were first being debated and discussed, the spherical nature of the Earth was not on many rabbis’ minds. And crossing the Pacific? Even less so. But in the last few centuries, and especially in the last few decades, these questions have become more important.

First of all, where is the International Dateline according to Jewish Law? And more practically, if you time things correctly, can you skip the Jewish Sabbath? One need never worry about rolling on Shabbos ever again!

Enter the vast compendium of Jewish Law. And of course, there are many opinions of where the International Dateline falls (the above map is a visualization of these opinions). Here’s a sampling of the discussion:

Therefore, the halachic Dateline of the Chazon Ish avoids going through land by gerrymandering along the Russian and Korean coasts, then along the 125.2°E longitude line, through the East China Sea, Philippine Sea, and Indonesia. Finally, the line cuts eastward, around most of the Australian coast, and south towards Antarctica. According to the Chazon Ish, Japan, New Zealand, and Fiji are on the same side of the Dateline as the United States. When the Japanese and New Zealand residents say it is Saturday, halacha says it is Friday. When they say it is Sunday, it is halachically Shabbos.

And more:

Rav Yechiel Michel Tucazinsky, the author of the Gesher Hachaim, in Sefer Hayoman B’Kadur Ha’aretz, bases his ruling on Chazal’s Judaic principle that Yerushalayim is “the center of the world.” If so, the Earth “starts and ends” (i.e. the dateline) on the exact opposite side of the Earth, halfway around the globe at 144.8°W (line E). This line runs from the Gulf of Alaska through the Pacific Ocean east of Hawaii, placing Hawaii on the “other side of the Dateline” from the United States. Hawaii would then be nineteen hours ahead of Baltimore, rather than five hours behind, as it is on the same side of the Dateline as Asia. The day Hawaiians call Friday is halachically Shabbos, and the day they call Saturday is halachically Sunday.

It turns out that in the end, most opinions follow common sense (in general, whatever day the locals say it is, Jewish Law agrees), but it is quite intriguing to see how this conclusion is arrived at.