Holidays » Math Goes Pop!

e day?

If you come here regularly, you know of my complaints regarding so-called “math holidays” that get plenty of press, but rarely have anything to do with actual mathematics. The most well known is pi day, celebrated here in the states on March 14th, also known here as 3/14.

Aside from the mathematical arguments one can make for or against this holiday, there is a larger problem. It’s all well and good to celebrate pi day on the date representing the first three digits of pi, but this is only possible if we write dates in the MM/DD format. Most of the world, however, uses the (more logical) DD/MM format, therefore depriving them of such a delicious play on numbers. Many loyal international fans of this holiday no doubt decry the fact that April has only 30 days, for otherwise they could simply celebrate pi day on 31/4. As it is, they are left with two options: Celebrate on 3/14 like those of us in the states, or enjoy a neutered version of this play on numbers by celebrating on 3/1.

Today I would like to propose an alternative to those for whom the DD/MM notation is standard. Rather than trying to work with imperfect solutions to the pi day problem, take a different number and celebrate it in your own way: the number e.

While e may not be as popular as its irrational sibling pi, it is no less important. No doubt many would argue that it is more important. It is certainly not as well-known in popular discourse, and so highlighting it, I would argue, is more important than highlighting the attention-whore known as pi. Moreover, since the decimal expansion of e begins with 2.71828183…, countries that use the DD/MM format could celebrate e day today, January 27th. Sadly, since February does not have 71 days, and since there are not 27 months in a year, people in America would be unable to celebrate in quite the same way – but given all the press that pi day has received over the past few years, I think that’s fair.

Of course, in order to celebrate the holiday properly, one needs activities. Topics could include the ways in which this fantastic number arises naturally, or a discussion of exponential growth (and orders of magnitude in general). One could also prove that e is irrational, a fact which follows quite easily from the Taylor series expansion of the exponential function e^x at x = 1. Perhaps I’m being overly optimistic though – such a holiday would probably include less exciting activities, such as a recitation of the decimal expansion of e to a certain number of digits (a mind numbing activity which is practiced without fail every pi day).

Special consideration needs to be given to a replacement for the act of eating pie, which seems like a suitable activity to do on pi day, but not on e day (especially since the surfaces of pies are circular). I’m not sure what natural analogue exists – there is one thing that comes to mind when one wants to celebrate a day called “e day,” but I don’t want to promote drug use. Perhaps instead one could eat foods that start with the letter e, like eclairs, eggplants, and elephants. But these foods don’t work on a higher level, in that they don’t really relate to the number e in the way that the circular shape of a pie can be related to the number pi itself.

Eggs for e day?

There are obstacles to overcome, that much is certain. But if we’re going to celebrate holidays related to math, we may as well do a halfway decent job of it. So happy e day to you – don’t do anything I wouldn’t do.

Happy Birthday, Riemann Hypothesis!

Big ups to Liz Landau for bringing attention to one of the most important unsolved math problems of our time, the Riemann Hypothesis. Over at the CNN SciTechBlog, she has written a nice article on the problem aimed at a general audience.

This year marks the 150th anniversary of the publication of Riemann’s manuscript, where he proposed the now famous conjecture on the zeros of the Riemann-zeta function, and November was the month in which it was published. However, as Landau points out, the exact date of publication isn’t known, which makes having a birthday celebration a little tricky. The American Institute of Mathematics picked today to celebrate, and in honor of Riemann talks were held all around the world.

The Riemann Hypothesis has held the attention of the mathematical community for a century and a half, but it’s also made occasional forays into the realm of popular culture. For starters, there are quite a few books on the conjecture that are aimed for a general audience (one of the more recent ones is by Dan Rockmore). It has also made cameos in television shows such as Law and Order and Numb3rs. The Numb3rs episode is particularly notable because in it, the Riemann Hypothesis is solved by none other than Neil Patrick Harris. While he may not be a major contender to solve the problem in real life, it may be a bit too early to make a final verdict.

This is what NPH looks like when he thinks about mathematics.

While the Riemann Hypothesis may not be as simple to state to a general audience as, say, the statement of Fermat’s Last Theorem, there is ample room for its inclusion in popular discourse. This is important not just because the conjecture excites mathematicians, but also because it shows that the work mathematicians do involves more than multiplying large numbers and being awkward in social situations.

In an ideal world, we would celebrate the Riemann Hypothesis every November 18th, just as we celebrate Pi Day on March 14th. The difference would be that 11/18 would commemorate something substantive within mathematics. For that reason, the idea probably won’t take hold. But at least a man can dream. Thanks again, Liz, for doing your part!

Math Goes Trick Or Treating Again

Around this time last year, I wrote up some suggestions for math-themed Halloween costumes. Based on the traffic I received from that article, I can tell that many people are desperate to integrate their holiday festivities with mathematics. For this reason, and in the interest of not breaking tradition, I thought it would be fitting to suggest a few more ideas for this year.

1) Mathemagician.

In the strictest sense, a mathemagician is simply a mathematician who does magic. Or, perhaps it is a magician who does mathematics. You may (rightfully) be tempted to say that every mathematician does magic, but the tricks of the mathemagician are geared more towards a general audience, although they do often feature mathematics in a starring role. Sadly, the same cannot always be said for the typical magician.

There are examples of mathemagicians in real life, including Arthur Benjamin, who has been the subject of an earlier article (unfortunately not for his skills in mathemagic). However, the mathemagician I have in mind is closer to the kind portrayed in the episode “Grade School Confidential” from season 8 of The Simpsons. Sadly, a clip of the scene in question isn’t available online – the best I can do is show this picture, which should be enough to jog the memory of any fan of the series.

Thanks for the screen cap, University of Connecticut Mathematics Department.

2) Mathematician Who Died in a Spectacular Fashion

Some people may think it sufficient to simply dress as their favorite mathematician for Halloween, and depending on the party, that may be true. But to give your costume that extra bit of Halloween pizazz, I recommend restricting yourself to deceased mathematicians. Not only are dead people big hits at Halloween parties, but in some cases you can incorporate the cause of death to create an even more compelling costume.

Regarding mathematicians who met an untimely demise, my top two choices would be Évariste Galois, who died in a duel under mysterious circumstances at the tender age of 20, and Jørgen Gram, who was killed by a bicycle.

Jaunty joy-rider, or cold-hearted killer?

3) Quant for Hire

This is a good costume if you are going to a party with friends who think themselves political. It’s also good if you really are an unemployed quant. The key here is to wear an outfit that at one point could have been quite valuable, even if it now looks like something you pulled out of the garbage. Failing that, you could always see if they make the costume below in adult sizes.

That’s right, Jimmy – never give up on your dreams.

4) The Monster Group

The monster group is a very large finite simple group. How large? As that Wikipedia link will tell you, it contains 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,
000,000,000 elements. In case you are curious, this reads as eight hundred eight sexdecillion, seventeen quindecillion, four hundred twenty-four quattuordecillion, seven hundred ninety-four tredecillion, five hundred twelve duodecillion, eight hundred seventy-five undecillion, eight hundred eighty-six decillion, four hundred fifty-nine nonillion, nine hundred four octillion, nine hundred sixty-one septillion, seven hundred ten sextillion, seven hundred fifty-seven quintillion, five quadrillion, seven hundred fifty-four trillion, three hundred sixty-eight billion.

If you wanted your costume to be completely impenetrable, you could just make a t-shirt with the two 196,882 x 196,882 matrices that generate this group. Alternatively, you could simply dress up like a monster. Although technically, I suppose you’d need to dress up as a group of monsters.

I think this would be suitable.

5) Your favorite knot.

While many people no doubt reserve a special place in their hearts for the trefoil knot, there is certainly room for creativity here. For example, check out this dude!

This is but a small sample of what you can do to combine Halloween with mathematics. I would encourage you to think of your own ideas as well. As I’m sure you know, every holiday can be made better with just a splash of math.

Make Money Money, Make Money Money Money! (and Learn Math, too)

Let me begin by saying that, in response to the question Why is 9/09/09 so special?, my response is simple: it’s not.

In fact, I would argue that 09/08/09 is much more interesting. This claim has nothing to do with numerology, and everything to do with President Obama’s speech to the youth of America on the value of education. The speech made very clear the importance of taking education seriously, and hopefully convinced students that a good education benefits not only themselves, but also society at large. In case you missed the speech, the transcript can be found here.

Although the speech was about education in general, mathematics got a little bit of love too. Here’s one such example:

What you make of your education will decide nothing less than the future of this country. What you’re learning in school today will determine whether we as a nation can meet our greatest challenges in the future.

You’ll need the knowledge and problem-solving skills you learn in science and math to cure diseases like cancer and AIDS, and to develop new energy technologies and protect our environment. You’ll need the insights and critical thinking skills you gain in history and social studies to fight poverty and homelessness, crime and discrimination, and make our nation more fair and more free. You’ll need the creativity and ingenuity you develop in all your classes to build new companies that will create new jobs and boost our economy.

What a bunch of socialist propaganda. Even so, I’m glad the President decided to emphasize the importance of education today, and I hope that students were able to take something away from it.

As an addendum to this theme, I’d like to point out that while mathematics is an essential tool for fighting disease or curbing global warming, there is perhaps a more immediate benefit to studying math that was not highlighted in today’s speech; a benefit that appeals more to our self-interest than a sense of duty, but with the end result still being a knowledge of mathematics. That benefit, of course, is the almighty dollar.

Last month, the Free Exchange blog over at the Economist highlighted a paper by Joshua Goodman that analyzed the returns on learning math in high school. For some reason Mr. Goodman’s website seems to be down, so the link to the paper is broken, but you can also find the paper here.

What were his findings? While earlier authors had found that each year of schooling is correlated with an eventual earnings increase of 10-15%, Mr. Goodman found that a significant amount of this increase can be attributed to coursework in mathematics (results which were strongest for low-income black males).

Of course, we all know that correlation does not imply causation, so it’s a little disingenuous to say that if you take more math classes in high school, you’ll get more money as an adult (and certainly for those of us in graduate school, it’s easy to imagine that the opposite is true). However, as pointed out on the Economist’s blog:

One reason why people who learn more mathematics earn more is because doing maths makes you smarter and more productive. According to Clancy Blair, a professor of psychology at NYU, the act of performing mathematical calculations improves reasoning, problem-solving skills, behaviour, and the ability to self-regulate. These skills are associated with the pre-frontal cortex part of the brain, which continues to develop into your early 30s.

So, while math may not make you richer, it will probably make you smarter – and this in turn can (hopefully) help you live a more comfortable lifestyle.

Then again, how could a lifestyle involving mathematics not be comfortable?

USA Today, you are also on my list

It bothered me when USA Today, in an article celebrating “math holidays” centered on the numerology of certain dates, linked to a post I had written about how these holidays are stupid, without even mentioning my contrary opinion. However, I was willing to let it slide, since I was able to say that I was linked in an article from USA Today.

However, an article posted today is just too much. USA Today, you have officially made it onto my list.

The headline for the article really speaks for itself: “Rare time/date alignment could mean opportunities.” This refers to the fact that in the wee hours of the morning today, it was 4:05:06 on the date 07/08/09.

Money quote:

Although the alignment may not mean anything specific, it could be a good day to do something for yourself and others, said Betsy Carlson, a Palm Springs tarot card reader and numerology expert.

“It’s a good day to make money and have good health,” she said.

When is it not a good day to have good health? Who wakes up, looks out the window, and decides that no, today is really a day for rather poor health? What does this even mean?

And how can someone be a “numerology expert?” Would any self-respecting newspaper publish a story from a phrenology expert? Why does numerology so often seem to get a pass? If you want to know why nobody reads newspapers anymore, this serves as an excellent indication. Is this seriously what passes for journalism in 2009? I guess because it’s in the “Offbeat” section, that makes it all ok.

Money-er quote:

Joy Meredith, owner of Crystal Fantasy in Palm Springs, Calif., noticed the alignment, but she’s more focused on this morning’s lunar eclipse, she said.

Nonetheless, she’s a fan of numerology and sometimes tries to determine if numbers have meaning.

“I feel they could be significant, so I’m looking for that,” she said. “If they’re not, they’re not. But I am looking to see if there is any significance.”

Dear Joy, I think I can help you out. I have discovered that numbers do indeed have meaning. The meaning of the number 12, for example, is the number of eggs you’ll get if you go to the store and buy a dozen eggs. The number 1 represents the number of newspapers that thought such a crackpot story was worth publishing. And so on.

Here’s another question: how does one go about “looking” for significance in a given “time/date alignment?” What oracle does one consult in search of insights into the mysterious nature of 4:05:06 07/08/09? God, I hope USA Today follows up on this article, so that all of my burning questions can be answered.

The worst thing about this article is that if you’re going to post garbage, at least post the most interesting garbage possible. The fact that 4:05:06 07/08/09 occurs today (or slightly less than a month from today, for those of us outside of the states) is not nearly as interesting as the fact that 12:34:56 07/08/09 occurs (twice!) today. If you’re into this sort of thing, I see no reason to find the first time/date alignment more interesting than the second. I must admit, even I cannot resist publishing this post at the appropriate time.

Number partyyy!!! Courtesy of Kitsune Noir, by way of Meebobebo.

Watch out, USA Today, because I’ve got you in my sights. My influence is vast, and my resources infinite. Let’s dance.

Ron Gordon, you are on my list

Not this again. I’ve now discovered that the mastermind behind these so-called math “holidays” is a teacher named Ron Gordon. Not only was he the one to spearhead the Odd Day initiative 2 months ago, but he’s gone so far as to double dip and call today Odd Day as well, citing the fact that standard date notation for most of the world is DD/MM/YY, rather than MM/DD/YY.

Thanks for double dipping, Mr. Gordon, so that I can read these pointless articles yet again. Mr. Gordon has even set up a web page and a contest, with cash prizes for those who can celebrate Odd Day the most enthusiastically. Needless to say, I don’t think I will be the recipient of any such prize.

The road to hell is paved with good intentions, Mr. Gordon. I’m just sayin’.

When will this stop?

Ok, now it’s just getting annoying. Odd day? Give me a break.

My thoughts on this irritating trend can be found here, here, and here.

Numerology Goes on Holiday (Again)

I made my reservations fairly clear regarding the double dose of math holidays last month. Despite my objections, I remained confident that the headlines they gathered would quickly fade away, and I wouldn’t have to worry about these faux math headlines for the next 12 months. In this way, I was able to sleep peacefully at night.

Unfortunately, it seems there are those who wish to disturb my slumber.

Dan Vergano over at USA Today recently wrote a brief article which highlighted the fact that this year there are a whopping 2 “square days,” one of which is today, 4/01/2009. The day is called a square day because if you read the date as a number, the number turns out to be square. In this case, 4,012,009 = 2003 * 2003.

The article attempts to be relevant by making a tenuous link between this sort of mathematical wizardry and the latest film excursion into numerology – Nicolas Cage’s most recent triumph, Knowing. Mr. Vergano was also kind enough to link to my article on Square Root Day, although based on the tone of his article, I’m not sure he appreciated the point I was trying to make. Perhaps he intended to address my concerns, but in the process of writing he got lost in Nic Cage’s eyes. Lord knows it can happen to the best of us.

What’s that, Mr. Cage? Sorry, I got a little distracted.

So, Mr. Vergano, if you’re reading this, I beg of you: use your powers for good. With a readership as large as I’m assuming yours must be, you have a venue to help dispel stereotypes about people who study mathematics. Of course, those stereotypes include, but are not limited to, the idea that mathematicians spend their days looking for significance in arbitrary dates.

To his credit, Mr. Vergano does point out the insignificance of these types of diversions. But if there isn’t any significance, what’s the point in writing about it? Does this happen in other fields besides mathematics?

I get that advances in math may not seem as sexy to the lay person as certain advances in the sciences, and sometimes the ideas can be difficult to communicate. But there are opportunities for those willing to look. Here’s one: why not write an article celebrating the contributions of Mikhail Gromov, recent recipient of the Abel prize? This, it seems to me, would be a much more worthy topic for a writer with such exposure.

I don’t think I’m alone in this, either. A look at the comments to Mr. Vergano’s article reveals many others who fail to see the importance of today as a square day.

Perhaps one day the USA Today blog will discuss some real mathematics. And on that day, I shall declare a legitimate math holiday. Until then, I will remain here and nervously await Pi Day 2010.

Pi Day

Hot on the heels of Square Root Day comes Pi Day, a day held in honor of arguably the most famous mathematical constant, π. And like Square Root Day, I am forced to approach this holiday with a certain degree of hesitation.

There is no doubt that Pi Day is the most prestigious mathematical holiday, but this recognition usually only serves to illustrate the sad state of mathematical literacy in this country. For example, one year I remember reading a news article about Pi Day where the author described π as a number whose decimal expansion “was believed to go on forever.” Of course, belief has nothing to do with it – this is a simple consequence of the irrationality of π, a fact which is apparently lost amidst the pie eating hubbub of this holiday.

Unfortunately, this is not an isolated incident – for as much as Pi Day aims to educate people about π, it seems to do just as good a job of showing how little people actually know. Searching Google News for articles on the upcoming holiday, it’s possible to find a number of stories that say a whole lot of garbage. For example, there’s this quote from a Pi Day article on SF Gate:

Pi, as [Pi Day co-organizer Ron] Hipschman noted, is strange because it’s both an irrational number (its decimal expansion never ends or repeats) and yet the number is also transcendental (no finite sequence of algebraic functions could ever produce it).

To a physicist like Shaw, that kind of contradiction and beauty was all the inspiration he needed to contemplate a Pi Day.

This sort of writing is like nails on a chalkboard to anyone who knows better. Forgetting the convoluted definition of a transcendental number given above, the more important point is that there is no “contradiction” in the statement. There is nothing special about the fact that π is both transcendental and irrational – as is immediate from the definition of a transcendental number, any transcendental number is automatically irrational.

No doubt there will be other examples of this mathematical butchery as Pi Day draws near. Here are a couple more. From the Times Online:

[S]ince 1988 mathematicians across the land have been celebrating pi day each year by tucking into a feast of [sticky pudding]. The number has obsessed generations of mathematicians for millennia, and not because it’s an excuse to eat pudding.

As I’ve said before, there’s not a working mathematician today (nor can I think of one over the past several hundred years) who has made a career studying the number pi. No mathematician is “obsessed” with this number – although numerologists and Max Cohen certainly may argue otherwise.

Some sources don’t even seem to know what π is. From Jacksonville, FL:

The next big day to celebrate in the math community this year [after Square Root Day] is pi day, March 14th. It represents 3.14 – a common mathematical expression.

And from Montgomery, AL:

On March 14 math lovers can celebrate Pi, the mathmatical [sic] formula used to find the circumference of a circle’s diameter, which is 3.14.

Not only is π defined incorrectly in both of these quotes, but it’s clear that the authors don’t know that π is neither a formula, nor an expression, any more than the number 12 is a formula or an expression.

One could argue that perhaps I am just nitpicking. For the general reader, such details are of no consequence, you may say. Unfortunately, history has shown that misinterpretations of the number π can lead to quite embarrassing consequences. One need look only to the good people of Indiana for proof.

As discussed in the article linked above, around the turn of the last century, a man named Edwin J. Goodwin claimed to have done what mathematicians already knew was impossible: he claimed to be able to square the circle (i.e., he claimed he had found a way to construct a square with the same area as a given circle, using only a compass, straightedge, and a finite number of steps).

Not content to keep the discovery to himself, Dr. Goodwin decided to share his discovery with his fellow countrymen in Indiana:

The stalwart Hoosier determined that the great state of Indiana should be the first to benefit from what he fervently believed to be a “new mathematical truth.” He would allow the state to use his discovery and to put it in the school textbooks free of charge. There would be no need for Indiana to ever pay him any royalties.

On January 18, 1897, after emerging from the House Swamplands and Education Committees (legislatures sometimes work in mysterious ways), Indiana House Bill 246 was introduced to codify Dr. Goodwin’s discovery. Legislators freely admitted they did not understand the jargon-filled bill, although they were certain it had something to do with circles. Of course they passed it unanimously.

While his heart was certainly in the right place, his mathematical rigor was not. His construction relied upon the unfortunate claim that π = 3.2. Thankfully, the error was pointed out before the bill was able to do any damage. The story does go to show, however, that we have a long history of not understanding π.

Eating pie is certainly an activity I can support, but other than that, I’m not really sure of this holiday’s purpose. On the official Pi Day website, for instance, the three questions on the front page up for discussion are: “Why do you like Pi?”, “What are you doing at your school to celebrate Pi Day?”, and “How many digits of Pi have you memorized?” Note that two of these questions actually have nothing to do with the number π, and the one that does deal with π doesn’t ask about any actual mathematics.

If you’re going to delve into this number, at least ask some interesting questions. How about “How can you show that π is irrational?” (here is a simple proof that only requires some basic calculus) or the related question, “How can you show that π is transcendental?” For younger students who may not understand or appreciate such proofs, how about “Where are some unusual places that π appears?” (You could show them the infinite series π/4 = 1 – 1/3 + 1/5 – 1/7…, which is usually quite surprising to a first time viewer). Or, for a more philosophical question, “Why does π appear in so many places in mathematics?”

I’m also a reluctant supporter of this holiday because I don’t really see a reason for π to steal all the limelight from other constants that may not have the PR that π does. There are other constants equally deserving of our attention. This is a slippery slope, of course, and once we say this, it’s natural to say that there are certainly more important concepts in mathematics, each one deserving of its own day to celebrate.

Perhaps in time, we will see more effective use of these “math holidays.” For now, though, I think that this is about the best we can expect to get:

Square Root Day?

I just noticed this article on the front page of Yahoo, which discusses the pending celebrations for tomorrow, in honor of the square root function. Tomorrow is given the name “Square Root Day,” naturally enough, because the date is 3/3/09. Seeing as how there are only 9 square root days per century, apparently the sparsity of this phenomenon is enough to make some people excited when such dates do occur.

Tonight we’re gonna party like it’s 3,996,001^1/2.

I don’t want to sound like a curmudgeon, but I’m not really sure who deemed this story worthy of inclusion on the front page of Yahoo. Similarly, I don’t know what it means when the article says that tomorrow’s “holiday” is met with great enthusiasm by “math buffs.” The article seems to suggest that a celebration like this falls within the realms of mathematics, when it more appropriately falls into the realm of numerology.

One could just as easily put significance on equally unimportant sets of dates. For example, I could decide to celebrate the “Doubling Dates” – dates in which the day is twice the month, and the year is twice the day. 02/04/08 has already passed, but it’s certainly not too late to start planning celebrations for 03/06/12, or 04/08/16.

Or, why don’t I start celebrating “Fibonacci Days,” days in which the year must be equal to the sum of the day and the month (those familiar with the process of generating the Fibonacci sequence will understand this choice of name). These days may seem quite plentiful – there will be 8 such days this year alone, for instance – but in any given century, there will be 57 years in a row with no Fibonacci Days! That must make them special, right?

The problem with these sorts of faux “math holidays” is that while they may seem to be an invitation to learn about and explore mathematics, for the general populace they simply perpetuate the stereotype that the bulk of a mathematician’s career is spent multiplying really big numbers together, or trying to find the 10^10¹⁰th digit of pi. This shortchanges the beauty of mathematics and the work of those who make a career out of it.

I’m all for mathematics appreciation days, but if we’re going to have them, let’s have them appreciate something substantive. Why not have appreciation days on the birthdays of some of our most famous mathematical historical figures? Rather than learning that sometimes, the square root of the last two digits of a given year is equal to both the month and day of a given date, which is both uninteresting and limited in scope, why not spend April 15th learning about the contributions of Euler, set aside April 30th to celebrate the work of Gauss, or take September 17th to gain some insight into the prolific work of Riemann? Those with less lofty ambitions could take a day to warn of the pitfalls of combining mathematics with sport by observing the tragic deaths of Galois or Gram, who died in a duel and after getting hit by a bicycle, respectively.

There are enough mathematicians in the history to supply content for every school day of the year, but most students would be hard pressed to name even a handful of important historical mathematical figures. Why this is deemed less important than the observation that 3 * 3 = 9 is slightly beyond me. But then again, maybe I’m just a curmudgeon.

Happy Square Root day, for whatever it’s worth.

Math Goes Pop!

Ruminations on the Intersection Between Mathematics and Popular Culture