It's here! Today is the official publication date for The Calculus Diaries: How Math Can Help You Lose Weight, Win in Vegas, and Survive a Zombie Apocalypse -- two and a half years of hard work finally comes to fruition. There are zombies, of course, and rollicking good tales about probability theory in craps, surfing in Hawaii (more than you ever wanted to know about the Fourier transform), and ferreting out parabolas and vectors at Disneyland. It's peppered with colorful historical math-y characters. There's even a couple of appendices with actual, you know, equations and stuff, for those readers who crave something a bit mathier, while still making sure the book appeals to my fellow math-phobes. I like to think of The Calculus Diaries as a gateway drug to the hard stuff. Sure, you think you're just taking a light hit, reading about catenary curves and architectural arches, but soon the Math Monkey is on your back, and you're staying awake for three days straight, solving differential equations and obsessing over whether P = NP. Not that I would know anything about that. I just sell the stuff.
Calculus is all about change and motion, and this seems as good a time as any to announce another impending change. For the last two years, I've been director of the Science & Entertainment Exchange, a fledgling program of the National Academy of Sciences to foster creative collaborations between scientists and the entertainment industry. We've had a very successful first two years, and all that hard work is beginning to bear some tangible fruit -- I'm excited about the potential of the program as it moves into Phase II. But I won't be actively involved for that phase. Effective September 24th, I'll be stepping down as director to return to writing full-time. The new director will be Marty Perreault, an industrial engineer by training who's been working at the Academy for several years, most recently heading up their President's Circle program, and recently relocated to Los Angeles.
This was not an easy decision. The short version: I'm exhausted. There just aren't enough hours in the day. I managed to write The Calculus Diaries on evenings and weekends while running the daily operations of the Exchange, but it's been tough juggling two very demanding, very different kinds of work. It became abundantly clear that I would have to choose between them. Everyone recites the mantra, "Follow your heart!", but what if your heart is divided between two equally amazing options? Still, as fulfilling as the Exchange has been, when the chips are down, writing wins out in the end. I miss being able to regularly delve deeply into nifty science, and am eager to get back in the writing game with renewed vigor. I'll still be tangentially invested in the future fortunes of the Exchange -- just on an informal, watching-from-the-sidelines basis, cheering the program on.
The next couple of months will be far from restful, as I wind down my tenure as Exchange director and work to promote the new book; you can keep track of various book-related appearances here. For those who care, I also set up a separate page on Facebook for The Calculus Diaries, making sure the feed isn't just all promo, all the time -- because don't you just hate that? There's a generous sampling of fascinating math-bits gleaned from all over the Interwebs as things catch my fancy. A sampling of cool links is below, just to whet your appetite for more things mathematical.
The Mathematics of Viking Jewelry. The beautiful bracelets and necklaces made by Viking artisans from rods of gold and silver are all twisted together into double helices. That's true regardless of whether the jewelry was found in Ireland, Scotland, the Orkney Islands or Scandinavia -- an impressive degree of regularity. Is it just a coincidence? Or could math be to blame? A couple of mathematicians at Denmark's Technical University think they've cracked the case in a paper recently submitted to the arXiv: Kasper Olsen and Jakob Bohr say that two wires become maximally twisted when no more rotations can be added with deforming the double helix. You guessed it: Viking jewelry is maximally twisted.
Mathematicians: Behind the Music. Forget mad scientists, how about mad mathematicians? Adam (Paco) Hanlon brings a refreshing dose of snark to this historical overview of some of the more colorfully insane math-y sorts during Nerd Nite NY. You gotta love any talk with slides captioned, "David Hilbert: Trash-Talking Mathematician Badass." (If Hilbert were alive today, I bet he'd put that on his business cards.)
The Mathematics of Balloon Animals. Man, there's a math paper for everything these days. In "Computational Balloon Twisting: The Theory of Balloon Polyhedra," the authors introduce the idea of ‘Bloons’: mathematical idealisations of real-world balloons (eg a doggie balloon, pictured with its associated 'bloon' below). Per Improbable Research: "The research not only provides '…algorithms to find the fewest balloons that can make exactly a desired graph or, using fewer balloons but allowing repeated traversal or shortcuts, the minimum total length needed by a given number of balloons.'”
A Math-y Take on the Perfect Roller Coaster Loop. Physics Buzz reports that Swedish mathematicians have used the same equations that describe how the planets orbit the sun to design a bunch of roller coaster loops that would give riders the visual experience of a loop without any whiplash. Good times!
Tasting the Limit, with Pie! Back in March, Ethan Siegel of Starts With A Bang took a break from blogging about astrophysics to pump out a tasty twist on infinite series and the limit -- illustrated with yummy photos of various kinds of pies. It's a fun explication, but it might make you hungry for something sweet. Forewarned!
Sunday with the St. Petersburg Paradox. Matt Springer of Built on Facts has a regular feature called the Sunday Function that quickly became one of my favorites. In this post, he takes a look at the St. Petersburg Paradox: a hypothetical gambling scenario where you win money based on the outcome of a coin toss. Per Matt: "Play this game enough times and it doesn't matter how much it costs to play, you will certainly come out ahead in the long run." There's a catch, of course: you have to play for, like, infinity. But it's a fascinating discussion, all the same.
Futurama Unveils Prisoner of Benda Theory. Psst! Did you know that Futurama writer Ken Keeler has a PhD in mathematics? Well he does! And he put his training to good use a couple of weeks ago, devising (and proving) a theorem based on group theory to explain a plot twist in the episode “The Prisoner of Benda.” (APS News leaked a spoiler back in May in an interview with executive producer David X. Cohen.) Basically, the Professor and Amy use a new invention to switch bodies. But the same two brains can’t switch twice, so they need an equation to prove that, "with enough people switching, eventually everyone will end up in their rightful form." Also? Most disturbing animated sex scene ever. Just sayin'.
NP Hard Problems Frustrate Hitler. Earlier this month, the Internet was abuzz with a new paper claiming to have solved the P vs NP conundrum. It's an esoteric math question relating to the speed at which a computer can accomplish a task such as factorising a number (eg, the Traveling Salesman problem). If P = NP, every problem that can be checked quickly can also be completed quickly. If it doesn't -- as the new proof claims -- well, that could have huge repercussions for internet security, since we keep our data safe from hackers using factoring of very large numbers. But it has an even bigger impact on Hitler, who needs to find the best route to get a KFC DoubleDown in Reichstag and doesn't have eternity to wait. ("Everyone who failed Theory of Computation, leave the room!")
Cracking Plato's Mathematical Code. Science historian and philosopher Jay Kennedy claims that Plato understood the mathematical structure of the universe quite well, 2000 years before Newton and Galileo. He bases this conclusion on analysis of Platonic texts using stichometry: the measure of ancient texts by standard line lengths. Per the Guardian: "What he found was that within a margin of error of just one or two percent, many of Plato's dialogues had line lengths based on round multiples of twelve hundred. The Apology has 1,200 lines; the Protagoras, Cratylus, Philebus and Symposium each have 2,400 lines; the Gorgias 3,600; the Republic 12,200; and the Laws 14,400." Paging Dan Brown! I smell a sequel to The Da Vinco Code!
Herbie Hancock Says Do the Math! What's the secret to a successful music career? Herbie Hancock insists it's math and science, in this LA Times exclusive interview. A taste: "I've always been interested in science. I used to take watches apart and clocks apart, and there's little screws, and a little this and that, and I found out if I dropped one of them, that thing ain't gonna work. When I was a kid, I put things back together and they never worked anyway! But just, like, going into those details, it's kind of a scientist's thing. And I have that kind of [mind], it's part of my personality.... So when synthesizers came in, they used terminology I knew. I knew what an amplifier was and I knew what it did.... I knew about wave forms. I knew what a 'sawtooth' was. I mean, if you studied physics, you'd learn those things. I was really good in math and I was good in science." Read the whole thing.
Marco Fusinato Fuses Math, Music and Art. "Music is what numbers feel like," io9 declared in this post about artist Marco Fusinato. He "brings together avant garde music and art in his work, creating imagery that looks like the results of a mad scientist's musings on how sound functions. In this series of drawings, called Mass Black Implosion, he's transformed scores for avant garde works into suggestions for what he calls "free noise," by changing the order of the notes and suggesting new relationships between them. Basically he's suggested a way to make something abstract even more abstract. In the process, he's created charts that are gorgeously strange." The whole gallery of images is worth a gander.
The Calculus of Saying I Love You. This ranks as possibly my favorite blog post ever, courtesy of Inkling Magazine, via the irrepressible Anna Gosline. She applies basic calculus to the conundrum to determine the optimal moment when the engineer her roommate is dating shoud declare his affection. The solution? "The Engineer should in fact solve for zero in the second derivative to the love-time function and say 'I love you' when love has stopped accelerating. This solves the concerning problem of having to wait until his love has stopped growing. Because zero growth in the love function is likely to make any woman, chemist, calculus enthusiast or otherwise, pretty goddamn pissed off." Wise words!
Mathematically Modeling Marital Breakups. Apparently math can also shed light on what happens when love sours. A new paper appeared in May purporting to analyze marital breakups (see graph below). Per the article: "The results of the mathematical analysis showed when both members of union are similar emotionally they have an 'optimal effort policy,' which results in a happy, long-lasting relationship. The policy can break down if there is a tendency to reduce the effort because maintaining it causes discomfort, or because a lower degree of effort results in instability. Paradoxically, according to the second law model, a union everyone hopes will last forever is likely break up, a feature Rey calls the failure paradox.'"
Teaching Calculus in Haiti.One of the Spousal Unit's former students, Eugene Lim, took some time off from his postdoc to spend a summer teaching calculus at a university in Haiti. He wrote a guest post for Cosmic Variance about his experiences as a volunteer teacher -- "a powerful and affecting look into conditions there, and the spirit of the students."
Math Skills Declined Back in 1804? Apparently the challenge of inspiring apathetic students in the face of declining math and science literacy isn't an especially new problem. Skulls in the Stars unearthed a fascinating article by one Reverend John Toplis, A.M., “On the decline of mathematical studies, and the sciences dependent upon them,” which appeared in Philosophical Magazine 20 (1805), 25-31. Among other things, Toplis lamented the pending loss of England's competitive edge: "We have long ceased to study those sciences in which we took the lead and excelled, and are content to follow, at a very humble distance, the steps of the philosophers of the continent, in those which they have in a manner discovered and made plain by their glorious exertions. We, after having discovered and conquered regions in science, suddenly quit them to be possessed and cultivated by other nations, that we may pick up a few gleanings in the countries found out and cultivated by their exertions." Plus ca change, anyone?
Math Class Needs a Makeover. I wish I could be a high school student again just to take Dan Meyer's high school math classes. He gave a fantastic TED talk on what's wrong with math education in this country, echoing many of my own thoughts and experiences -- namely, that we focus on the computational aspect (numbers crunching), which most of us forget when we leave high school, but is easy enough to relearn as an adult -- provided you also have a solid grounding in reasoning ability. And that's what high school students aren't getting. Meyers is a funny man, admitting that as a high school math teacher, "I sell a product to a market that doesn't want it, but is forced by law to buy it." But as I learned while writing The Calculus Diaries, math is still relevant outside of high school -- and it's far, far cooler than I ever imagined it could be. Folks like Meyers could change our minds about math for the better.
Huzzah for the new book! And well-wishes to the new Exchange director, too.
That P ?= NP article is out of date. See this aggregator of technical comments and links to blog/media coverage. The drastically shortened version is that according to Deolalikar's attempted proof, a problem which we already know to be easy, computationally speaking, would be hard instead. So, something ganged agley.
In more jargony terms, as phrased by computer-science guru Scott Aaronson: "[I]f you're showing that an NP-complete problem like 3SAT is not in P, then your proof had better fail for related problems like 2SAT and XOR-SAT, which are known to be in P."
Lots of other technical issues were raised, as well. Some of the experts who drove the online discussions about the proof attempt (like Fields Medalist Terry Tao) were contemplating the possibility that the shortcomings in Deolalikar's proof actually pointed the way to a new general criterion for P != NP proof attempts, a way to rule out entire classes of potential theorems at one go. Historically, such no-go results have been among the greatest advances in our understanding of the P-vs.-NP problem. Something neat may yet come of it.
Posted by: Blake Stacey | August 31, 2010 at 03:17 PM
Thx Blake! I was trying to remember where I'd seen that aggregator and never did find it!
Posted by: Jennifer Ouellette | August 31, 2010 at 05:04 PM
Glad my epic link-fu could be of service!
Posted by: Blake Stacey | August 31, 2010 at 05:12 PM
Here's another cool math-related link:
http://www.theiff.org/main.html
I found it via Vonda McIntyre's hyperbolic bead and crochet pages.
Looking forward to reading your book. I regretted for years never having studied calculus, having dropped all math when I graduated from high school, despite the fact that I'd always been pretty good at it. I finally went back to school a few years ago (at 43), took a couple of semesters of calculus, and had a real blast doing it.
Posted by: Janet | September 07, 2010 at 03:00 PM