Rosalind Franklin, Lady Scientist

If you’ve been on the Google home page today, you know that the Big G has seen fit to honor Rosalind Franklin with a doodle. (On a side note, I find it amusing that clicking on the doodle sends you to the Google results page, at the top of which are news articles about how Google did another doodle. The world is funny sometimes.)

Sadly, much of Franklin’s possible greatness was cut short by cancer—but her career was also cut short by sexism. For a more humorous rendering of this part of her story, check out Hark A Vagrant!. (Check it out for all the other stuff, too, it’s a great webcomic. The one on Charles Babbage is possibly my favorite.) The short version of the story is that Franklin made massive contributions to the discovery of DNA, while Watson and Crick got the credit. Wikipedia has a decent retelling of this story, though without the humor.

Of course, in recent years society has made strides in recognizing these systematic biases (and not just with regard to sexism—this year the UK formally recognized that it’s wrong to drive someone to suicide for being gay). And Women’s & Gender Studies programs, along with African-American, Latin-American, and other programs, abound at colleges and universities around the United States. These programs are crucial points in rediscovering and reassessing the contributions of the non-privileged throughout human history. (And, as a white man, I would stress that we should all be a part of this rediscovery, whether or not we share the same identity groups as those we study.)

But the sad fact remains that much of this knowledge will always remain unknown to us. Many non-white-males were denied the opportunity to show their talents to the world at a time when record of their work—or even of their life—would not have been kept for future generations.

And so, as you toast Rosalind Franklin’s contributions to science today, remember all those who came before—men and women, of all races, creeds, and sexual orientations—who made lasting contributions to the world we’ve inherited, and whose names & stories we’ll never know.


Facing Mecca in the Modern Age

Ken Jennings beat me to it! I had been thinking recently about the mathematics of the qibla in Islam, but a full treatment of the topic just appeared on Jennings’ CNTraveler column, The Daily Traveler. With a doff of my cap (*doff*), here’s the link:

Which direction is Mecca from space?

Beethoven in the Antarctic

If you’ve ever spent time learning to play a musical instrument, you’ve undoubtedly used a metronome—depending on your age, it may have looked something like this:


(For clarity, we’ll call that little trapezoid-shaped thingie the bob, while the bottom of the rod will be the pivot point.) The design of the mechanical metronome has not differed much since Johann Maelzel received this patent in 1815—more on this in a later post.

While today’s metronomes are often electronic devices, for centuries they were based on Galileo’s pendulum principle: the time taken by one full swing of a pendulum depends only on the bob’s distance from the pivot point (and on gravity). Crucially, the time is not dependent on the mass of the bob, or the width of the swing.* In fact, one early definition of the meter was the length of a pendulum that would swing from one end to the other in the space of two seconds.

In the end, though, this definition was rejected in favor of the so-called meridional definition: the distance along a meridian of the Earth from the Equator to the North Pole. Why the change? Well, it turns out the Earth isn’t a perfect sphere—it’s an oblate spheroid (that’s math-speak for “the spin of the Earth makes it bulge outward at the Equator”). So, the force of gravity is somewhat less strong at the poles than it is at the Equator.

Now back to the history of the metronome: musicians began to adopt the metronome in their compositions; Ludwig van Beethoven was notably one of the first to do so. By the 20th century, metronome notations (given in beats per minute) were included in nearly all musical works.

Given what we know about the Earth’s gravity, you may have already noticed that there’s a minor problem with metronomes—those at polar latitudes will click at a faster rate than those at equatorial latitudes. (Swiss Scientist & Mathematician Leonhard Euler gives a good summary of the issue in his 1738 work Von der Gestalt der Erden. See pages 4-5 of Langton’s translation, available here.)

Here’s the musical takeaway: if you are playing a piece that sets a tempo of 120 beats per minute, and are using a mechanical metronome to keep time, then you will play this piece more quickly at the South Pole than you would at the Equator. I do hope there are some musicians at the Amundsen-Scott Station who are enjoying the naturally-accelerated tempos of the region!

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* I know what you’re thinking: it’s not actually this simple (it rarely is). There are some other factors in play, including the ever-menacing friction. But it’s close enough to the truth.

A Note on Research Rigor (or, What To Do About Wikipedia?)

Since this blog is academic in nature, I thought a good first post would be on citation, facts, and the reliability of information. [If you found that first sentence to be incredibly boring, feel free to skip the rest and wait for my next post! If it  got you excited, read on!]

Having taught university-level mathematics for six years, one of my pet peeves is sloppy citation and/or use of resources in research writing. Those of you in similar careers know how common it has become for students to use Wikipedia (or worse, unanalyzed Google search results) as the primary source in their papers. In spite of that, I’m only partially opposed to the use of “low-energy” (read: easy-to-find) Internet sources like this. Certainly, I think that Wikipedia should not be considered a reputable source in peer-reviewed, research publications. However, studies have also shown (see herehere, and if you like circularity, here) that much of the information on Wikipedia is accurate and reliable.

Given this conundrum, I imagine that the general reaction to Wikipedia in academic circles has been something along these lines:

I use the Wikipedia a lot. It is a good starting point for serious research, but I would never accept something that I read there without checking. —Bill Thompson [from the BBC]

I think Thompson is overstating things here. For example, when I read on Wikipedia that John F. Kennedy was born in 1917, or that Jane Austen wrote Pride and Prejudice, or that Prince William is the second in line for the British throne, I accept it without checking. Obviously, there are places where one should be more skeptical (for example, pages related to current events or controversial topics can be dodgy, at least for a time).

Since this is a blog, and not a academic research journal, I’m going to cite Wikipedia on occasion. Here’s one reason why:

“I think the trick is to know when you can rely on Wikipedia—I mean if you want to know who were all the guys in Humble Pie who weren’t Peter Frampton, who but Wikipedia is going to know that?” —Geoff Nunberg, linguist at UC Berkeley [on NPR’s Fresh Air]

Truth. Lots of obscure things can be found quickly and accurately. Lest we begin quoting from Wikipedia willy-nilly, however, consider:

“[Wikipedia] is pretty good, but you have to be careful with it. It’s good enough knowledge, depending on what your purpose is.” —Jimmy Wales, founder of Wikipedia [from The Chronicle]

So, while I won’t use any hard and fast rules about citation, I will try to be careful about it. And while this post has turned into a scholarly analysis of Wikipedia, I’ll try to be equally careful about other sources. Finally, be aware that, in the interests of time (every post could turn into a huge research paper if I’m not careful), I may occasionally cite something without checking it as rigorously as I might do in another forum.

Of course, if I get anything phenomenally wrong, please point it out in the comments—I’ll try to address mistakes as I go. Come back soon to read my future posts!


Hi everyone! Welcome to my new blog, Math/Polymath. You can read about me, and my goals for this blog, on the FAQ page. Going forward, I hope to post every 2-4 weeks on a variety of topics in mathematics, science, history, and the like. While I haven’t placed any particular conditions on the content of the blog, I want to keep the posts “bite-sized” and manageable (no manifestos here).

Thanks for dropping by! I hope you’ll enjoy the ride. I look forward to hearing your comments, suggestions, and ideas.