Et cetera » Math Goes Pop!

Judge v. Justices

Just as you can’t judge a book by its cover, it is not always easy to determine a person’s mathematical background based on his or her occupation. Sure, a burger flipper at McDonald’s may not look like the next Einstein, but how can you be sure she’s not just working a summer job to afford university? Conversely, just because someone is highly educated doesn’t mean he knows the difference between a prime and a composite number (although I’d argue that it should).

Case in point: Supreme Court justices may or may not know the meaning of the word orthogonal. Here’s a snippet from the oral arguments in the case of Briscoe v. Virginia (courtesy of blog The Volokh Conspiracy):

MR. FRIEDMAN: I think that issue is entirely orthogonal to the issue here because the Commonwealth is acknowledging -
CHIEF JUSTICE ROBERTS: I’m sorry. Entirely what?
MR. FRIEDMAN: Orthogonal. Right angle. Unrelated. Irrelevant.
CHIEF JUSTICE ROBERTS: Oh.
JUSTICE SCALIA: What was that adjective? I liked that.
MR. FRIEDMAN: Orthogonal.
CHIEF JUSTICE ROBERTS: Orthogonal.
MR. FRIEDMAN: Right, right.
JUSTICE SCALIA: Orthogonal, ooh.
(Laughter.)
JUSTICE KENNEDY: I knew this case presented us a problem.
(Laughter.)
MR. FRIEDMAN: I should have — I probably should have said -
JUSTICE SCALIA: I think we should use that in the opinion.
(Laughter.)
MR. FRIEDMAN: I thought — I thought I had seen it before.
JUSTICE SCALIA: Or the dissent.
(Laughter.)
MR. FRIEDMAN: That is a bit of professorship creeping in, I suppose.

While Friedman uses “orthogonal” in a bit of a metaphorical sense, this use is far from unprecedented – indeed, this use is even documented in the venerable internet database ubrandictionary.com, which defines orthogonal as a term that is “used to describe two things that are independent of one another. One does not imply the other.” Claiming that this usage is just a “bit of professorship” sounds a bit like a cop out. I wish Friedman had embraced it more completely.

In any event, the mathematical definition of orthogonal should be given in any halfway decent high school geometry course, if only as a synonym for perpendicular. The fact that Scalia and Roberts seem so unfamiliar with the concept is, at the very least, a little disappointing.

But all is not lost. On the other hand, last weekend Fox aired a special commemorating 20 years of The Simpsons, appropriately titled The Simpsons Anniversary Special: In 3-D! On Ice!. Several people contributed interviews to the special, including Mike Judge, creater of Beavis and Butthead and King of the Hill, among other comedic gems. Watch the clip below for a bombshell revelation:

That’s right – without The Simpsons, Judge believes he would be a math teacher. In fact, after doing some research online, I discovered that Judge didn’t begin playing with animation until the age of 26, while he was doing graduate studies in mathematics in the hopes of becoming a teacher.

Does this mean that Beavis and Butthead are smarter than Roberts and Scalia? Of course, some may cry out that this is an unfair comparison, but I think I can provide a fair answer.

Yes.

A Mathematical New Years Game

First, let me begin by wishing a happy 2010 to you all. If you celebrate the holidays the way I do, then the past few weeks have seen you spending time with friends and family. And if you really celebrate the holidays the way I do, then some of that time with friends and family will have been spent with mathematical puzzles.

Very recently I was with a group of friends, discussing all that would come to pass in this new year. One friend, whose anonymity I will preserve by referring to him only as “Smith,” was in the enviable position of being the only one among us whose age divided the current year (I won’t embarrass him by revealing his age, but given that it’s a divisor of 2010, this certainly restricts the possibilities). Once we realized this, it became natural to ask how common an occurrence this should be. In other words, how often can you expect your age to divide the current year? Of course, implicit in this is a choice of calendar – for our purposes, we will stick to commonly used Gregorian calendar, although the results would be equally valid under a different choice (e.g. the Hebrew calendar or Islamic calendar). For example, if you were 1, 7, 41, or 49 last year, your age divided the year (of 2009). Next year, only the one year olds will win out, since 2011 is a prime number.

Depending on the year you were born, you may find that this happens quite frequently, or not very frequently at all. For example, if you were born in the year 0, you’re in luck, because your age will divide the current year for at least part of the year for every subsequent year. The phrase “part of the year” is important, because in a given year you will be two different ages – the age before your birthday, and the age on and after your birthday. Of course, this isn’t an issue if you were born on January 1st or December 31st, but we will ignore this (simpler) case.

Let’s take a more detailed example. Suppose you were born in 1982. In 1983, after your first birthday, your age will divide the year (since 1 divides everything). Similarly, in 1984, your age will divide the year after your 2nd birthday, since 1984 is even. And in 1986 your age will divide the year until your 4th birthday, since 1986 ÷ 3 = 662. Unfortunately, you will be too young to appreciate this arithmetic coincidence at any of these opportunities, and unless you live to be 661, you’ll never again be able to say that your age divides the year.

However, if you were born just a few years earlier, in 1979, you’ll find that your age divides the year quite frequently. In fact, by the year 2000, the only years in which your age wouldn’t have divided the year at all would have been 1987, 1988, 1993, 1994, 1996, 1997, and 1999.

Why is it that some years allow for one’s age to be divisible by the year quite frequently, while other years do not? The answer is quite simple. Suppose we let b denote the birth year, and we let a denote a person’s age. That person will be a years of age from their birthday in year b + a until their birthday in year b + a + 1. Therefore, your age will divide the year from your birthday until the end of the year if a divides b + a, or from the first of the year until your birthday if divides b + a + 1. So, the question becomes: when does a divide b + a, and when does it divide b + a + 1?

In the first case, since a always divides a, we know that a divides b + a if and only if a divides b. By the second same argument, we see that a divides b + a + 1 if and only if a divides b + 1. In other words, we conclude the following:

Your age will divide the current year if, and only if, either (i) it is between January 1st and your birthday, and your age divides the year after you were born, or (ii) it is between your birthday and December 31st, and your age divides the year you were born. To put it more simply, your age will divide the year for at least part of the time you are at that age if and only if that age divides the year of your birth or the year after your birth.

With this knowledge, it’s easy to see why people born in 1979 will have their age divide the current year more frequently than people born in 1982. In the former case, determining the set of ages which will divide the current year is equivalent to finding the divisors of 1979 and 1980. 1979 is a prime number, so it will never be the case that your age will divide the year between your birthday and December 31st (except after your 1st birthday); on the other hand, 1980 has a prime factorization of 2 x 2 x 3 x 3 x 5 x 11, which gives it a large number of small factors, and consequently a large number of solutions to the problem.

By contrast, if you were born in 1982, you won’t get many factors either way: 1982 factors as 2 x 991, and 1983 factors as 3 x 661. This is why, if you are born in 1982, your age won’t divide the current year after you’re 3.

While it’s not often that mathematics comes up when I’m with my friends at home, I certainly relish every opportunity. I hope that this may serve as an example to all of you who would like to make mathematics more of a part of your everyday life, especially in social circles into which math rarely intrudes. Single guys looking for first date conversation material are especially urged to keep this sentiment in mind.

More on Nerdy T-Shirts

Recently I received an email imploring me to check out all of the “unique designs” available at a site called nerdytshirt.com. I’m not sure why I was the recipient of such an email – they could have found me through my university affiliations, or through this blog, but I’m not sure which.

If you’ve been reading my musings for a while, you may know of the problems I have with the intersection between mathematics and clothing. Most of what’s out there is junk. As one might expect, I was therefore quite skeptical when I received this solicitation. At the same time, I’d never heard of this site before, and so I hoped that perhaps a company that understood my frustrations had come to fruition.

Have my prayers been answered? Sort of. Let’s consider a few examples.

Despite claiming to have “unique designs,” the shirts at nerdytshirt.com are all variations on one theme: put a formula on the shirt, and below that make a pun related to the formula. Sometimes the results of this pairing are good:

wokka wokka wokka!

A good gift for Sarah Palin, perhaps?

Other times, however, the jokes just fall flat.

Is this even a joke?

On the plus side, the website doesn’t restrict itself to just math jokes; they also offer shirts for chemistry, physics, and statistics. The underlying principle never changes, though: take an equation, expression, or sequence, then add a pun underneath.

I certainly don’t think this is a bad strategy – on the contrary, I find some of them quite clever (as clever as one can find a pun to be, I suppose). But by restricting themselves to this one type of design, the whole enterprise seems a little one-note. Not only are they robbing us of the full power of their creative juices by using this one format, but they also exhaust this one idea fairly quickly. There are some good shirts, it’s true, but there are duds as well, and so one is left feeling that in their rush to claim that they are “now offering more than 100 unique Nerdy T-Shirt designs,” they have placed quantity over quality.

Their site is still in its infancy, and so one hopes that the masterminds behind the site will not be afraid to branch out in their shirt designs. There is potential here, and I wouldn’t mind wearing some of the shirts they have for sale, but it may be dangerous to give one of these shirts as a gift unless you are able to separate the wheat from the chaff. Also, the link to their website in small fond on the front of every t-shirt may be a dealbreaker for some.

At the very least, one could use the following t-shirt for Halloween, should one choose to be the monster group (as I’ve discussed before).

That large number is the size of the monster group.

Mathematics Awareness Month 2009

With April on its way out, it behooves me to take a moment and mention the focus of this year’s Mathematics Awareness Month. April has been bestowed with this glorious title every year since 1986 – last year the topic was Mathematics and Voting, which I discussed at some length in three earlier posts (see here, here, and here).

This year’s focus is on Mathematics and Climate. On the homepage you can find links to a variety of articles, most of which focus on the difficulty in coming up with mathematical models that can accurately reflect the complexity of the interconnected world in which we live. This is perhaps best summarized by Professor Pat Kenschaft, who writes the following in her essay, “Climate Change: A Research Opportunity for Mathematics?”:

How do we analyze the dynamics of the atmosphere, the oceans, the solid earth (especially volcanic emissions) and the biosphere (the system of plants, animals, and other living things)? Scientists have studied pieces of these systems, cutting them both conceptually and geographically, but even the pieces are not tractable by current mathematics, and the challenges as we try to understand the interplay of all phenomena involved are far beyond current conceptual and computational capabilities.

This is a theme that comes up in quite a few of the articles related to this year’s focus on the intersection of math and climate. As we begin to demand more from our models, those models will necessarily need to become more sophisticated. This requires mathematicians to create models that not only reflect reality, but are also optimized so that we can obtain results within a reasonable time frame.

There are a host of other articles discussing the interplay between climate and mathematics. Some of the articles cover related topics as well – for example, Professor Margot Garritsen’s article “Mathematics in Energy Production” provides a good example of the essential role mathematics plays in our current methods for procuring gas and oil, and briefly discusses the relationship between math and alternative energies.

With city-sized blocks of ice crumbling off of the Antarctic, there can be little doubt that climate change is happening, even if we don’t understand everything that underlies it. Will mathematics come to our rescue? Don’t worry – if it doesn’t, I’m hopeful that Captain Planet will.

Captain Planet: Math Spokesman for the 21st century?

Optimization at the Checkout

On more than one occasion, while waiting in line to buy my lunch on campus, the cashiers at the front have asked those of us in the line to split into smaller lines – one line for each cashier. This seems to be met with hesitation on the part of those of us who are in line, and rightly so. Perhaps I am simply projecting, but it seems like they all know the same thing I do: that having only one line feed into all the cashiers is the most efficient way to manage a queue.

One would think the cashiers should know this as well, but apparently not. So, if you have ever asked people to form separate lines when waiting to be helped, pay attention, because you need to learn why people in line rarely pay attention to you.

For a person waiting in a single line, there is little incentive to break into smaller lines. This is because using several lines leads to longer wait times on average. You don’t need any sophisticated machinery to explain why this is true – if you ruminate on the two choices for a moment, the benefits of the single line system should make themselves apparent.

With only one line, you never have to worry about getting stuck behind a coupon-clipper or a check-writer. You move forward whenever anyone’s transaction is completed, which means that even though a single line will be longer than several shorter lines, it will also move much faster.

This is also a plus for those of us who have trouble with decision-making. With only one queue, there is no decision to make. You needn’t worry about developing a strategy when picking your checkout line; for example, you don’t have to size up those ahead of you to discern whether or not they are the type who will take a long time paying. Just get in the line and move – it’s really as simple as that.

If only everyone could be as line savvy as Apu, perhaps we would have no need to study queue management.

How much more efficient is the single line queue? Apparently there are tools available that allow to model these sorts of situations, but here is one such example, courtesy of the blog of Dr. Michael Trick:

Suppose you have a single queue with 20 customers arriving per hour. If the cashier can handle (on average) 22 customers per hour (close to saturation, but probably roughly what “efficient” managers would aim for), then the queue will grow so long that the average wait will be 27 minutes! Five such queues would end up with about 50 people waiting in line on average. If you go over to one line (with 100 arrivals/hour) being served by five cashiers, the average wait goes down to under 5 minutes, and the number of people waiting in line is only 12 on average.

This simple example shows that the benefit to a single line is quite significant. So significant, in fact, that many grocery stores are now organizing their checkouts to have a single queue. Whole Foods is perhaps the most prominent example, because of an article the New York times wrote nearly 2 years ago, which came to the unavoidable conclusion that the single line queue is the only way to play.

2 years seems like enough time for such an unequivocal conclusion to have begun seeping into our collective consciousness, but apparently not. I welcome the day when I am no longer asked to form separate lines while buying my lunch – it’s like asking me to give you even more of my (quite valuable) time. It’s not that we can’t hear you, cashier, it’s that we know what’s in our own best interest. And frankly, so should you.

Is there any advantage to using multiple lines? There may be some psychological benefit to having many short lines rather than one longer line, especially for people who, for example, may go to the grocery store only to pick up one or two items. For them, the sight of a single line may be overwhelming, even if that line does move much faster than separate shorter lines would.

Also, there is perhaps something to be said for the use of express lines, which cater to those people who would be most turned off by a long line. However, with the single line system, that one line is already express! Neither of these points seem to matter much in the face of the data, which strongly points to having your customers stay put in a single line.

So, the next time you’re waiting in line, and the cashier asks you to split into smaller lines, feel free to hold your head up high and ask what’s in it for you. You certainly aren’t doing yourself any favors by complying.

Mariah Carey Is not a Mathematician

This may come as a surprise to some of you, but it has come to my attention that Mariah Carey is not, in fact, a mathematician. Moreover, I’m fairly certain she is not a physicist, either.

The evidence is fairly compelling. According to this article from sfgate.com, the famous crooner misappropriated Einstein’s famous mass energy equivalence formula E = mc²:

In interviews to promote the record, the singer’s eleventh studio release, Carey told reporters she re-interpreted the equation to stand for “emancipation equals Mariah Carey times two.”

Forgetting for a moment the question of what it means for Mariah Carey to be one half of emancipation, there is the arguably more important issue of her not understanding the difference between mc² and mc x 2. Granted, Mariah Carey didn’t get this far based on her math skills, but by botching what many consider to be the most famous equation in mankind’s body of knowledge, it’s hard not to shake your head a little bit.

Perhaps the interviewer caught her off guard, when she was too focused on deeper mathematical questions. Or, perhaps Mariah Carey has defined a new measurement of velocity, called the Mariah, which is equivalent to one half of the speed of light – with these units, of course, the expressions mc² and mc x 2 coincide. Unfortunately, Occam’s razor forces me to confront what is most likely the ugly truth: MC just doesn’t know her math.

“So what?” you may say. “People don’t like her because she’s good at math.” That’s a fair point. And while I enjoy a good laugh at a pop star’s expense just as much as the next guy, what may be even more troubling than her comment are the comments from everyday folks responding to the story, some of whom display a fundamental lack of mathematics knowledge that rivals Carey’s own. For example, we have the following:

Wouldn’t the correct formula then be E=MCx2? Then again, Carey’s job isn’t rocket science.

Where has America’s math education gone? Wherever it is, it certainly isn’t in the realm of pop culture.

Hey Einstein, do you like apples?
Well, Mariah Carey took your formula.
How do you like them apples?

Math as Your Wingman: Mail Goggles

As many of you with Gmail accounts may already know, Google launched a feature last week that aims to put arithmetic squarely in the shoes of your most trusted wingman. The feature, dubbed Mail Goggles, is explained in the Official Gmail Blog.

In summary, the Mail Goggles feature allows you to make Gmail aware of certain hours during the week when you should not be sending e-mail (due to exhaustion, inebriation, or the side effects of whatever other illicit things you do in your personal life). Once these hours are set, should you decide to send an e-mail during one of these highlighted times, you will first be prompted to answer a series of math questions, in an attempt to prove to Gmail that you have sufficient mental faculties to be sending e-mail.

A noble pursuit, to be sure. A trustworthy internet wingman may be just the thing for those among us who may enjoy their night life a bit too much, only to make decisions they regret in the morning. And while a wingman tied to your e-mail can’t help talk you down from every form of debauchery, there are certainly situations in which such a feature could be useful.

Unfortunately, Mail Goggles is kind of a fair weather wingman. He’ll check in on you every once in a while, but if you tell him you’re fine, he’ll leave you alone. He might tiptoe around the issue of whether or not you’ve had enough to drink, but talk forcefully enough and he’ll back down. That may sound ok, but sometimes you need a wingman who has the resolve to set boundaries for you when you’re not in a condition to set them yourself. Sadly, Mail Goggles is a bit too much of a pushover.

Maybe Mail Goggles could learn the laws of Wingmandom if it
watched more VH1. Or if it bought a big poofy hat.

I have reached this conclusion after experiencing firsthand what the Mail Goggles system has to offer. Today I went in and warned my e-mail that between the hours of 3 and 4 pm on Wednesdays, I was not to be trusted with the “Send” button. I then attempted to send an e-mail to myself, and sure enough was prompted with a list of math questions.

Now, you can tell Mail Goggles how difficult to make the questions, by setting the difficulty to be a number between 1 and 5, 1 being the easiest, and 5 being, well, the less easiest. Not wanting to peak too soon, I asked for the easiest questions, and so was not surprised when the following problems greeted me:

10 x 6 =
32 + 18 =
85 – 10 =
10 + 10 =
95 – 85 =

I was slightly more surprised by the amount of time I had to solve these questions: 60 seconds. With a whopping 12 seconds allotted per question, even someone with minimal computational ability could easily plug and chug these answers through a calculator within the allotted time – and when you’re already at the computer, the thought certainly must be tempting.

And let’s be honest – you’d have to be pretty far gone not to know what 10 + 10 is.

Itching for more of a challenge, I went back into the settings and ratcheted up the difficult to level 5. Ready to get those synapses firing, I tried another test e-mail, and was given the following questions:

477 – 138 =
72 / 9 =
8 x 8 =
242 – 98 =
30 / 10 =

Again, Mail Goggles saw fit to give me 60 seconds to answer these questions.

Seriously? This is the difference between level 1 and level 5? You give me a couple of three digit numbers, and introduce the concept of division? Is this really the best we can do? Not to mention the fact that the calculator would still function as a perfectly good cheat sheet.

With a desire to test my limits, I answered one of the above questions in error, and stuck my hand out, waiting for retribution. But did any come? Sadly, no. Instead I was just given another 5 problems, and a full 60 seconds on the clock! Come on, Mail Goggles, where’s the accountability? If you can’t divide 30 by 10, maybe you should sleep on that email to your boss telling him how attractive you find his wife. But instead, Mail Goggles says to you, “Hey buddy, it’s ok. Just try again! You’ll get to that e-mail eventually, I know it!”

There are other issues I have with this innovation from Google Labs as well, but I don’t want this to turn into a negative tirade. The idea is quite inspired, but it leaves much to be desired, especially if you really want some checks in place before you do something you may not really want to do.

In the spirit of keeping things positive, to the designer of this feature, Jon Perlow, I humbly submit some suggestions for future improvements to Mail Goggles:

1. Make questions that aren’t so easy to answer with a calculator. How about more critical thinking questions? You can use calculators on the SAT, and because of that the questions are specifically designed so that the calculator may or may not be an asset.

2. How about some significant gradation between difficulties? If you’re going to differentiate between levels of mathematics, you might as well make the problems worthwhile to people with all kinds of backgrounds. I don’t think some calculus would be too much to ask in the higher levels, even dare I say it some linear algebra. At the very least, can we get a smidgen of long division?

3. How about instead of 5 really easy problems, you just give one or two problems that require more critical thinking? This will better test mental faculties – you can test me once with a hard problem, rather than testing the same thing 5 times with simple questions.

I know you mean well, Mail Goggles, but you’re really not looking out for people when they need you. For now, ladies and gentlemen, I suggest that you stay with your flesh and blood wingmen. They will make sure to keep you away from the computer as long as you are in their sight. They will protect you, watch over you, and make sure you do nothing unsightly.

Unless they secretly hate you, in which case they will probably take incriminating photos of you and post them on the internet. In this respect, Mail Goggles offers much more protection. For now.

An Open Letter to Users of Yahoo! Answers

Dear Yahoo! Answers Users,

For every guy who has dreamed of looking like a Hoobastank concert attendee, or for every girl who has dreamed of looking like a Bratz doll, Yahoo! Answers provides you with a forum to not only construct the avatar of your dreams, but also to ask questions on a variety of topics, and get real answers from real people.

She only loved him for his soul patch.

Unfortunately, as a math educator, I feel compelled to offer criticism regarding the Mathematics section of your site. The existence of this section is not what bothers me – it is the user behavior, both of those asking questions and those answering them.

Let’s start with the askers. I’ll be blunt: please stop using the internet as your interactive cheat sheet. There are a number of users of Yahoo!’s service who have no qualms asking for answers on their homework – many do it blatantly, and with no regard to the importance of these formative years in their mathematics education.

Consider the following examples:

Exhibit A: Fractions help please =/ ughh math is so hard!?

The question is as follows:
1.] 2/3-1/2
2.] 1/2-1/8
3.] 9/5-1
4.] 3/4-1/8
5.] 1- 5/9
6.] 6/9 – 1/6
7.] 2/3 + 1/9
8.] 8/9 – 2/3
9.] 1/2 + 1/2

No attempt is made to give any sort of context: what part of these problems is difficult for this individual? Moreover, since these problems are all solved in exactly the same way, it is clear this person is only looking for quick answers to their homework, and not an understanding of how to solve these types of problems.

Exhibit B: Is there a website tht i can type in math problems and will me the answers?

This one is pretty self explanatory.

Of course, these are some of the most obvious offenders, but there are numerous other examples of students (mostly younger ones) abusing the privileges given to them by the folks at Yahoo!.

Needless to say, this is something that should be discouraged. Parents taking a more active role in monitoring their child’s internet habits will help, of course. But it is just as important to change the behavior of those answering the questions, because no matter how obvious it is that you are trying to cheat, somebody will answer you, with no questions asked.

In the case of Exhibit A, as of the time of this writing there are 16 answers to the “question.” Of these, 8 give answers to all nine parts of the question, and of those 8, 3 give answers without showing any work whatsoever (note that giving an answer is not the same as giving a correct answer). My favorite response is provided by a gentleman who chastises the questioner by saying, “It’s not fair to use Yahoo! Answers to solve your maths homeworks,” and then proceeds to write down the answer to every question.

There is only one answer to exhibit B, but sure enough, it is a link to a website that will do all the work typically asked of a middle school student in math. Not a word of reprimand is offered.

We have all heard the old adage praising the benefits of teaching someone to fish, rather than simply giving someone a fish. The people who answer these types of questions, however, don’t just give you the fish: they clean it, cook it, serve it, cut it up into tiny pieces, then chew it for you and spit it into your mouth. All that’s left for you to do is receive the regurgitation, like baby birds. The difference being that baby birds don’t need to know how to add fractions.

The thought of his daughter never learning how to
fish is enough to make this man cringe.

What can be done? While mathematical abuses at all levels of education seem to be occurring on Yahoo! Answers, it is more prevalent with the most basic material, suggesting the most common culprits are the very students who most need to build a mathematical foundation. For more advanced levels or mathematics, I shift the blame more towards the questioner, but for younger students, who may not see what long term harm a lapse in their mathematical understanding can have, the onus moves to those answering the questions, who should know better than to sell out their knowledge for some measly Yahoo! Answers “points” (the purpose of which is still not entirely clear to me).

It is with this in mind that I implore you, Yahoo! Answers users, to stop spoon feeding middle school homework answers to students. You do them a disservice, and by failing them, you are failing our collective future.

I should mention that not all of the mathematics category is corrupted. There are plenty of examples of people asking intelligent questions (questions aimed at understanding material and not just getting the right answer, for instance), and there are also many examples of people answering the questions only partially, but giving full details for the parts they do answer so as to help guide the student’s understanding. This is all well and good. But as long as someone can get answers to their homework without having to think, our work is not complete.

In conclusion, letting the internet do your homework for you is most likely a bad idea. Using the internet to help you understand your homework is, in general, a good idea. So parents, make sure you know whether your child is using the internet for good or for evil. The distinction could cost them an understanding of mathematics – or even their lives.

Well, maybe not their lives. But certainly this behavior should be discouraged.

I thank you in advance for your cooperation.

With lukewarm regards,
Matt

Designer Math

A well designed t-shirt has the power to delight and inspire; it can break the ice at the start of the evening, and seal the deal at the end. It can be a powerful tool for social interaction, and can help forge the bonds that will last a lifetime.

It is with this in mind that I bemoan the present state of mathematically themed t-shirts, many of which are asinine to the point of nausea. I also feel the need to speak out and warn those who would consider buying such t-shirts for friends or loved ones, under the misguided impression that anyone who studies math will appreciate (much less wear) a t-shirt just because it is related to math.

Let’s analyze some examples, to see just what’s gone wrong with the current state of mathematically inspired fashion. The following five designs can be found here, along with a multitude of others. However, every design seems to fall into one of the categories below:

1) The Symbol Design (epitomized by the pi design):

Many t-shirt designs seem to be of the philosophy that by throwing a bunch of math symbols on a white background, somehow their shirt is clever or interesting. In particular, there are a plethora of t-shirts focused on pi, its decimal approximation, or some pun involving pumpkins or actual pies. Pi seems to have become the poster child for mathematics, which I guess is ok, but I think you will be hard pressed to find a single mathematician who will find the transcription of a long decimal expansion of pi interesting. And for those mathematicians who already feel isolated from society, I don’t think wearing a t-shirt with a whole bunch of numbers on it will make them feel better.

I wouldn’t have as much resentment towards this particular letter if it weren’t for the fact that it always seems to be hogging the spotlight. How about a little love for e? Is it too much to ask for some love on behalf of the Euler constant? Although such similarly themed shirts would be just as unappealing, at least we would have some more variety. Perhaps it has something to do with the fact that other constants don’t lend themselves as easily to puns involving baked goods.

2) The “Why Is this on a T-shirt?” Design:

Let’s be honest: nobody is going to be impressed if you have a t-shirt with a whole lot of formulas on it. In fact, some people might be downright scared of such a shirt. And in a case like the one pictured here, why would one want a list of algebra mistakes on a t-shirt? This hardly seems like the most effective place to keep a list of common mistakes. Wouldn’t a notebook be more preferable? Not to mention the fact that while wearing the t-shirt, it would be difficult for one to read these examples; the fact that there seems to be no attempt at formatting them only compounds the matter. Such examples often make poor use of the t-shirt medium, and would seem to fit much better elsewhere.

3) The Plain Old Not Funny Design:

Come on now. Is this really the best we can do? Not only does this design juxtapose two horribly uninspired slogans, but the pun is terrible. If we’re going to go that route, shouldn’t the shirt say “Math nerd rocks rock!!”? And how can a rock hold a pencil behind its head with no ears?

4) The Minimalist Design:

Sometimes these designs can rise above mediocrity, but I don’t see how they could inspire one to make a purchase. I do appreciate the simplicity of the design pictured here – in fact, of the five displayed here, I would consider this particular design my favorite. It does not smack of effort as do so many other designs, but at the same time, it is this very same feature that keeps this type of design from rising above its brethren.

I would, however, highly recommend the thong version of this item, if you are looking for a gift for that someone special.

5) The Math Crutch Design:

Designing a t-shirt based on mathematics can be difficult: on the one hand, you want to make a joke that people who study math will find amusing, but the shirt should also be decipherable to people who do not do math. Otherwise, why should anyone wear such a shirt in public? Presumably, one wears funny t-shirts to project the impression to others that one has a keen sense of humor. But if many people don’t understand your shirt, what then?

This shirt should not be undecipherable to anyone who remembers some basic calculus – unfortunately, asking that of our citizenry seems to be a bit much. On the other hand, one can be thankful that the calculation is not difficult, so that even if your calculus is rusty you should be able to dust off the cobwebs and compute the joke. However, even though this t-shirt does give one that light bulb moment when the content is understood, the punchline itself is a bit crass for general consumption. Certainly, one should hesitate before wearing this shirt to try and get a rise out of a room full of mathematicians, at least if the mathematicians are senior to the wearer.

* * *

What then, is a fashionable young mathematician to do? Is there no safe haven from uninspired, math-themed t-shirt designs? I think one will find, upon scouring the internet, that resources are indeed limited. However, there are a few rays of hope that shine brightly through the darkness. Perhaps my favorite example is given by the image below.

This design, from threadless.com, is one I would proudly sport on my own masculine frame. It works because it is not actually a joke about mathematics, but a joke taken from pop culture that uses math to deliver the punchline. As such, it becomes accessible to a wide audience, and shows how even rappers can benefit from mathematics. While strong arguments could be made against the plausibility of a linear model as the best fit for the relationship between money and problems, the basic idea is clear, and can be easily understood and admired by people from all walks of life.

Of course, the life of a mathematician can be fraught with disappointments, and this case is no different: the design pictured here has been sold out for such a long time, one wonders if it will ever be restocked. At the same time, one can take solace in the knowledge that somewhere, somebody is looking at this shirt and having a good laugh with mathematics.

Three and a Half Things You Shouldn’t Say to a Mathematician

Mathematicians are a rare specimen to behold. While not quite endangered, they tend to congregate in areas less prone to large population densities, such as libraries, or the basements of math buildings, thus making their numbers seem lower than they actually are. This type of behavior is fortunate, for it is because of these tendencies to cluster together that breeding mathematicians in captivity has proven extremely successful – much more so than attempting to breed mathematicians in the wild with the general population (although there are successful cases of the latter phenomenon as well). The point here is that, unless you are of a certain persuasion, you could find yourself going years, possibly your whole life, without ever meeting a mathematician.

Should you be so fortunate to spot one, make sure not to approach too quickly, or you may scare the mathematician away. If you are vigilant, you may be able to engage the mathematician in conversation. In the event that this happens to you, there are a few common misconceptions about what’s appropriate to say to one who studies math. For your consideration, I present three common things people say when they find they are talking to a mathematician, and why one should avoid saying such things.

1) “You study math? You know, I never liked math.”

Ok. What exactly am I supposed to say to that? If you met a musician, would you say “You know, I’ve never liked music. Not my cup of tea.”? If you met a lawyer, would you say, “Yes, studying the law is all well and good, if you are a sucker, that is.” I should hope not. But when it comes to mathematics, people feel it is entirely acceptable to share with you how much they despise that which you devote so much of your time to. Perhaps they were abused by mathematics early in their life (in fact, for many I think this is the case). However, I am not your psychiatrist, and I have no interest in telling you that it’s ok, the math will not come out and bite you now that you are grown. Remember, when it comes to mathematicians, if you don’t have anything nice to say, tell them how good they look in their glasses.

2) “You study math? What’s 12,147 times 5,382?”

Of course, equally atrocious is any question of the form “What is n times m?” where n and m are sufficiently large. Contrary to the image of mathematicians portrayed in most popular media, we are not all socially awkward computational savants – at the very least, we are not all computational savants (even if we do have to buy all our underwear from the K-Mart on Oak and Burnett). Very little, if any, of what mathematicians do involves finding the product of very large numbers. And should we need to multiply very large numbers, we have calculators, just like the rest of you. If we are able to compute larger products than you, it is usually only because our calculators are more expensive. This brings me to a related point, of particular importance when you are out with a large group of people in a restaurant or bar, and amongst you lies a mathematician:

2.5) “Give the tab to the math guy! He’ll figure it out!”

It is precisely these kinds of prejudices that have kept mathematicians down for hundreds of years. From personal experience, under the pressure of society’s expectations on my computational abilities, I find it more difficult to figure out how to split the tab when everyone is eyeing me, wondering what is taking so long. But let’s be honest: you’re just trying to find an excuse not to figure it out yourself. Because nobody wants to figure it out. Well, mathematicians are a lot like assassins – they will do your dirty work, but they expect to be paid top dollar for their services. So the next time you think to ask a mathematician to tell you how much you owe, be careful. You may be paying a hefty, hidden premium for his or her services.

While I’m at it, we don’t enjoy doing our income taxes any more than the rest of you, either.

3) “So tell me exactly what kind of math you do.”

This one is a bit subtler. In certain contexts, such a request will endear you in the heart of a mathematician for many years. But often times, especially in party settings, such a remark is made simply to try and start a conversation. Gentle reader, before you make such a request, you must be made aware of what a deep rabbit hole you are jumping into.

The work of a mathematician tends to be extremely specialized. Specialized to the point where mathematicians will not understand what one another is doing. So unless you want an answer so general as to make it mostly useless (“Number Theory,” “Analysis,” “Geometry,” etc.), you are, in effect, demanding that the mathematician compress years of difficult study into a brief and easily comprehensible tablet. Now, of course there is something to be said for developing the skill of being able to translate one’s research to a level that can be understood, at least in a broad sense, by a large population. But at the same time, for some things, it is simply not possible to have a simple explanation up one’s sleeve. This is why mathematics is difficult. So an explanation of current research will, more often than not, take time, and be at least slightly incomprehensible.

This is not so much a problem, if one is willing to listen. The problem arises when, as mentioned before, one has merely made this remark to try and start a conversation. Not knowing what the questioners have gotten themselves into, they now must sit and listen to a mathematician talk at length about things the questioners really may have had no interest in to begin with. If this goes on too long, it can create tension, and furthermore, when the listener stops paying attention, the mathematician’s time is essentially being wasted. That time could be better spent doing research, or getting all the digits from more attractive party attendees.

In summary, I know it can be difficult knowing what to say when you meet a mathematician. But there are certain things you should not say, at least without understanding what you’re getting yourself into. It may help to pretend that instead of a mathematician, you are talking to a rock star or international supermodel – this should not be a difficult stretch of the imagination, and will help you avoid the taboos mentioned above.

Math Goes Pop!

Ruminations on the Intersection Between Mathematics and Popular Culture