These cartoons appeared on Twitter and Facebook throughout February 2018, and are preserved here, museum-like, for posterity and/or people who are too cool for social media.
Funny vs. Trying To Be Funny
It has since been pointed out to me that Emily Dickinson is, in fact, hilarious. I stand by this cartoon otherwise.
“Charter” Thoughts
I spent four years teaching at a charter school. That experience makes it hard to see the charter movement either as demon or panacea. More than a new type of school, I see them mostly as individual new schools – liable to make the same sorts of ambitious moves and avoidable mistakes as any new institution.
Multivariable Woes
Sometimes the pursuit of a punch line leads you to throw more weight into the blow than your victim actually deserves.
This is probably not one of those times.
What to Name Your Math-y Band
Folks on Twitter and Facebook chimed in with their own suggestions. My favorite comes from @SpinVector: a cover band called “Partial Derivative.” If that band name isn’t taken by the end of the week, then cover bands aren’t nearly as much fun as I thought.
Statistics Education
When it comes to statistics education, I find there’s a sad mismatch between possibility and practice. I indict myself here too – I’ve at times brought too much of a “pure math” mindset (let’s prove some theorems, kids!) to a discipline with its own characteristic style of thought.
The Angel of Death
The Angel of Death comes for us all. There is no escape.
Also, my boss replied to this cartoon: “THIS IS YOU. YOU DID THIS ALL THE TIME,” which is absolutely going on my business cards now.
A Romantic Proposal
As you can perhaps tell from the old-school whiteboard photo, this dates from the early days of this blog. I revived it here because (A) It’s Valentine-themed, and (B) Hannah Fry said she liked it, and there’s no better way to take the piss out of my British friends than pretending that I am best pals with Hannah Fry.
Hyperbole and Ellipsis
Not depicted: flat statements on Euclidean geometry (e.g., “Euclidean geometry is a form of geometry that draws its name from Euclid”).
“Linear Algebra”
I shall take this opportunity to plug 3Blue1Brown’s excellent series of videos giving geometric visualizations of Linear Algebra.
I could watch 3Blue1Brown all day.
And by “could,” I mean some combination of “have done” and “shall do again.”
The Fog of Confusion
Fog is really hard to draw, okay?
This cartoon is the equivalent of those SNL sketches where the character’s first line has to be, “Hello, it’s me! Robert Mueller!” because you couldn’t follow the joke if it was any less explicit.
Bayesian on Trial
Once people know me well enough, they don’t even wait for the punch-line; instead, they sigh with resignation as soon as the set-up begins.
I’d explain the title of this post, but you already know what I’m talking about. I refer to questions like this one, from the 4th century:
I, for one, pity old Demochares—enumerating the fractions of his life, yet unable to recall his own age. It’s a bizarre, selective senility, like something from an Oliver Sacks book: “The Man Who Mistook His Life for a Math Problem.”
Over the last three millennia, much has changed. Civilizations have risen, collided, and fallen. Revolutions have left legacies in blood and ink. There have been, for good and for ill, 417 million Marvel films. Yet somehow, these age-based math puzzles have remained a constant.
What’s the case for them?
Well, they’re easy to state and tricky to solve. They take a naked mathematical structure and give it a fig leaf of narrative—just enough to require some imaginative effort. They’re a convenient variant on an algebraic theme.
And the case against them?
Well, they’re artificial. If you’re presenting such a problem to a pupil or a pal, then you’d better hope they’re already invested in the project of mathematical puzzle-solving. If not, a stilted find-my-age puzzle ain’t gonna reel them in.
I recently came across a “real-life” (well… “fictional-life”) instance of such a problem on the first page of Lolita, Vladimir Nabokov’s classic novel about a child predator who becomes infatuated with a twelve-year-old girl:
In point of fact, there might have been no Lolita at all had I not loved, one summer, an initial girl-child. In a princedom by the sea. Oh when? About as many years before Lolita was born as my age was that summer. You can always count on a murderer for a fancy prose style.
For what it’s worth, our narrator does not give quite enough information to determine the age gap. (You can count on a murderer for an under-determined system of equations.) But a few additional facts—for example, that he was 13 years old that initial summer, and 37 upon meeting Lolita—suffice to fill in the gaps. (The composition and solution of such ghastly problems is left as an exercise for the novel’s reader.)
Should we forswear such problems as carrying the ineradicable stain of Nabokov’s protagonist? Or embrace them as carrying the indisputable glow of Nabokov’s prose?
Cards on the table: I’ve rarely used such problems in my own teaching, though I have nothing against them on principle (icky Lolita associations notwithstanding). My own taste is towards heightening the weirdness and trying to nudge them towards a more open-ended form. Something like this:
Do these have the same spirit as the classics that open this post? Not really. But then again, those two openers don’t have quite the same structure, either. Love ’em or hate ’em, these age problems will stick around because they’re convenient hooks for hanging all kinds of algebra on.
NOTE: I’ve made a few edits because people weren’t loving this post’s winning combination of jokey unhelpfulness and pedophilia references. I can’t imagine why!
I’d explain the title of this post, but you already know what I’m talking about. I refer to questions like this one, from the 4th century:
I, for one, pity old Demochares—enumerating the fractions of his life, yet unable to recall his own age. It’s a bizarre, selective senility, like something from an Oliver Sacks book: “The Man Who Mistook His Life for a Math Problem.”
Over the last three millennia, much has changed. Civilizations have risen, collided, and fallen. Revolutions have left legacies in blood and ink. There have been, for good and for ill, 417 million Marvel films. Yet somehow, these age-based math puzzles have remained a constant.
What’s the case for them?
Well, they’re easy to state and tricky to solve. They take a naked mathematical structure and give it a fig leaf of narrative—just enough to require some imaginative effort. They’re a convenient variant on an algebraic theme.
And the case against them?
Well, they’re dreadfully artificial. If you’re presenting such a problem to a pupil or a pal, then you’d better hope they’re already invested in the project of mathematical puzzle-solving. If not, a stilted find-my-age puzzle ain’t gonna reel them in.
What say you, my fellow jurors? Are these problems rightful citizens of the algebraic learning process? Or guilty of loitering for centuries, impersonating something more useful?
For some, I suspect, it hinges on the question of whether anybody ever talks like that. As it turns out, I have found someone who does—though it’s hardly a witness that the defense would wish to call.
You will find the instance on the first page of Lolita, Vladimir Nabokov’s classic novel about a child predator who becomes infatuated with a twelve-year-old girl:
In point of fact, there might have been no Lolita at all had I not loved, one summer, an initial girl-child. In a princedom by the sea. Oh when? About as many years before Lolita was born as my age was that summer. You can always count on a murderer for a fancy prose style.
Here we have it: the only in-the-wild instance of a convoluted age-based word problem. And I wish to state, for the record, that it is uttered:
By a murderer.
Who is also a pedophile.
Who wishes to allude to—without making explicit—the enormous age gap between himself and his victim.
For what it’s worth, our narrator does not give quite enough information to determine the age gap. (You can count on a murderer for an under-determined system of equations.) But a few additional facts—for example, that he was 13 years old that initial summer, and 37 upon meeting Lolita—suffice to fill in the gaps. (The composition and solution of such ghastly problems is left as an exercise for the novel’s reader.)
Perhaps this doesn’t settle the question. Sure, we could forswear such problems, as carrying the ineradicable stain of Nabokov’s protagonist. Or we could embrace them as carrying the indisputable glow of Nabokov’s prose.
Or, then again, we could just say that the problems now make us feel icky, and thus refuse to show them to children again.
These cartoons first appeared on Facebook and Twitter during the wild and woolly month of January 2018. If you have ever found yourself thinking, “I wish my daily social media experience featured more math puns,” then I encourage you to (A) Follow Math with Bad Drawings! and (B) Take a long, careful look in the mirror to see what you’ve become.
Welcome to 2018
Some folks on Facebook offered optimistic predictions that the pattern is quadratic, with a negative leading coefficient. This is an adorable sentiment, so please don’t spoil their innocence by disagreeing with them.
Meanwhile, somebody on Twitter suggested sin(x)/x, which is a nice “end of history” prediction. My personal worry is that the world is more like x sin(x).
The Strangeness(es) of Languages
Although I meant this cartoon as a vicious elbow into the ribs of my British friends, folks on Facebook instead took the opportunity to educate me about the typographical differences between German and English.
Oh well. It’s like I say, “Blogging: come for the petty insults, stay for the surprisingly enlightening discussion with commenters.”
For other professions, you can cross out “teach” and replace it with “work for,” “serve,” or “interact with.” Another alternative: “I am sorry for the irrationality of the people whose children you teach.”
An Impossible Wish
This one struck a nerve: by the numbers, it’s the most popular cartoon I’ve ever shared on Facebook. My own experience: patiently drawing and discussing diagrams like the one in the second panel really ought to help folks understand how the distributive property works. And it really doesn’t. Clearly I am really bad at it.
Of Mice and Men
In contrast to the prior comic, this was one of the least popular cartoons I’ve ever posted, but I stand by it. History will judge that this is the best joke I’ve ever written.
A Tiny, Tiny Point
This is my go-to line for salvaging a useless lesson. Well… salvaging it rhetorically, anyway. It doesn’t really salvage the lesson itself. Also, note that no finite number of points can ever constitute an actual through-line for your curriculum.
Very Belated Birthday
Some folks thought the day I posted this was my birthday, which it was not – although those who wished me a happy birthday were certainly in keeping with the spirit of the comic. Also, a Spanish speaker on Facebook pointed out that the cartoon makes no sense in translation, because the Spanish word for “birthday” means something more like “year completion.” Spanish: language of love and logic.
MLK Day
Pro cartooning tip: You can get away with lousy puns if you draw a skeptical character saying how bad the puns are. Still, I was feeling shy about posting this – it’s a bit like putting a red rubber nose on the legacy of a civil rights hero – until I saw my offense pales in comparison to that egregious Super Bowl ad.
Hard-to-Remember Mnemonics
This is sort of how I feel about all mnemonics. My personal philosophy: mnemonics for definitions (e.g., SOHCAHTOA) are useful. Mnemonics for computational strategies (FOIL) and easily derived facts (ASTC), nope.
Rare Used Books
I have no interest in reading Finnegans Wake, but I find the Wikipedia page for it pretty fascinating. H.G. Wells wins for “best quote,” in a personal letter to Joyce:
[Y]ou have turned your back on common men, on their elementary needs and their restricted time and intelligence […] I..
More precisely, e is the essence of existence, the fount of human joy, and (for folks who worry that Pi Day is kinda played out) the perfect constant around which to build your mathematical festivities (e-clairs, anyone?).
Get excited, citizens of math, because Wednesday, February 7th, 2018 is eDay: 2/7/18.
(Well… in America, anyway. Our international pals may wait until Monday, July 2nd.)
In honor of this noble number, I offer an alphabetical celebration:
e is for Euler, one of the most renowned mathematicians of the last millennium. Euler discovered e, although what’s more impressive is where he discovered it: in the public writings of Jacob Bernoulli, who actually discovered it.
e is for Exponential, because Euler couldn’t very well name it after himself, could he? That would be immodest. So he named it after a word that happens to start with the same letter. What a hilarious coincidence!
e is for Elegance, because of facts like these:
[UPDATE: Thanks to those who pointed out the e-gregious error in the pink formula. Previously I had n approaching infinity, which would result in the limit approaching 1.]
e is for Economy, because e lies at the heart of compound interest.
Imagine a wildly generous savings account that pays you 100% interest per year. The question is: When do they pay it?
If they give you 100% at the end of the year, you’ll end up with $2. Not bad.
But if they give you 50% halfway through the year, and another 50% at the end, then you’ll end up with more: $2.25. (That’s because you earn interest on the first chunk of interest.)
And what if they give you 25% each quarter? Then you’ll end up with $2.44, because you earn even more interest on the interest.
And what if they give you 10% at each of ten points throughout the year? You’re up to $2.59!
What about 1% at each of 100 points during the year?
Or 0.1% at each of 1000 points during the year?
Or 0.0001% at each of 1 million points during the year?!
As you carve up the year into finer and finer slivers, each carrying a tinier and tinier interest payment, the total value converges. If you could somehow carve the year into infinite pieces, each carrying an infinitesimal payment, then you’d end up with about $2.718.
Or, more precisely: e.
e is for Irrational.
(You wish to complain that “irrational” starts with i, not e? Fool: your rationality has no place here.)
Like its colleagues π and √2—not to mention the overwhelming majority of all numbers in existence—the number e cannot be written as a ratio of two integers.
(In fact – like π, but unlike √2 – e goes beyond irrationality to achieve transcendental status, meaning that it isn’t the solution to any polynomial equation.)
e is for EEEEEEK! because e offers a simple demonstration of the dangers of gambling.
Suppose there’s a bet you’ll win 1 in 6 times. So you try it 6 times. You ought to win at least once, right?
Nope. There’s a 33.5% chance that you lose ‘em all.
Okay, what about 100 trials of a bet you win 1 in 100 times? Surely your odds are pretty good?
Not really. There’s a 36.6% probability that you won’t win a single one.
Keep going. What about a million trials at a 1-in-a-million bet? A billion trials at a 1-in-a-billion gamble? The further we go, the closer your odds of utter defeat get to roughly 36.79%.
Or, more precisely: 1/e.
e is for Eccentric Eggbert, the Egregiously Error-Prone Butler.
When the guests arrive for a party, they all give their fancy hats to Eggbert. But he forgets whose is whose, and winds up giving them all back to random guests. As the party grows ever larger, what’s the probability that nobody gets back the right hat?
1/e.
e is for Events. Why? Because as any statistician knows, aggregating many independent events will yield a normal distribution.
Diffusion of molecules. Weights of animals. Inches of rainfall. All of these can be described by the same family of bell-shaped curves.
(The normal distribution is also called a Gaussian, after legendary mathematician Carl Gauss. This makes perfect sense, seeing as the normal distribution was first discovered by de Moivre.)
And what is the formula for such a curve? Well, the simplest example is this:
Throw some π’s and square roots in there, and you’ve got yourself the normal distribution.
e is for Exciting Equality, because in calculus, the function ex has a very exciting property: at every point on its graph, the height is equal to the steepness.
Or, in more calculus-y language:
What, are you not excited? (ARE YOU NOT ENTERTAINED???) Then perhaps I should explain. (Don’t worry; it’s easy; e-lementary, even.)
Backstory: Since 2009, I’ve had an annual Oscars wager with my friend Ryan. From 2009 to 2014, Ryan always won.
Ryan’s advantage? He is much smarter than I am. (Smart friends: I don’t recommend it.) He’d go to BetFair.com and identify the favorite in each category. (For close races, he’d supplement with a little extra research.) While Ryan leveraged the wisdom of the crowds, I’d fall back on my own personal favorites and erratic judgment. I’d lose because I couldn’t keep myself from “clever” (read: stupid) underdog picks.
Then, in 2015 I devised a new scoring system to neutralize Ryan’s advantage. An Oscar pool for know-nothings like me.
Picks would be scored based on their probability of winning. If prediction markets gave a film a 1-in-2 chance of winning, then its victory was worth 2 points. If they gave it a 1-in-15 chance of winning, then its victory was worth 15 points.
This system has a simple mathematical property: it equalizes expected value. So you can follow any probabilistic strategy you like. Pick all favorites. Pick all longshots. Pick the nominees whose names make the most appealing anagrams (“Lady Bird” –> “I Dry Bald”; Phantom Thread” –> “Top Hardhat Men”; “The Post” –> “Hot Step”; “Get Out” –> “Toe Tug”).
In the long run, it will all return the same average total: 24 points a year.
Now, it didn’t matter that Ryan is a neurosurgery resident, busy saving lives by mastering the inner workings of the most complex organ in existence. None of that did him any good. What an idiot!
Anyway, this year, I am excited to open up the game to you, with the KNOW-NOTHING OSCAR POOL.
Here are five compelling reasons why you should participate:
The ultimate visionary will receive a custom-drawn Math with Bad Drawings cartoon!
The lazy visionary will receive a custom-drawn Math with Bad Drawings cartoon that takes me no more than 10 minutes to draw!
And the obscure visionary will receive a custom-drawn Math with Bad Drawings cartoon that is deliberately hard to understand!
NOTE: The probabilities will shift over time, but rest assured that your expected value will always remain 24 points. You can go back and edit your answers as often as you like.
From time to time, math folks can’t help wrestling with the old, pot-stirring question “Is [algebra/calculus/trigonometry/mathematics] class really necessary?”
The argument goes like this: At every step of education, students face math requirements.
What’s weird is that, once you’ve cleared the bar, you rarely use the math you learned.
Math is just a gatekeeper, a sorting mechanism, a bouncer used to keep some people out of the party. So why not eliminate those dumb requirements altogether?
In the ensuing debate, math folks leap to defend the discipline. Skeptics parry with counterattacks. In the end, we talk, blog, and Tweet right past each other.
Both sides dislike math education’s competitive, exclusionary nature. One side aims to overcome it by reorienting towards a higher purpose. (“Math is beautiful/useful/the best way to learn reasoning!”) The other side prefers to curtail math’s presence. (“End these foolish requirements!”) But to me, all of this dances around an obvious truth.
Why does math function as a gatekeeper?
Because our educational system is full of gates.
The judges behind these gates find themselves sifting through piles of applications. They turn to math as a simple signal of desirable qualities.
We all know it’s not a perfect indicator. But admissions and HR departments seem to find it useful anyway.
Meanwhile, even when it’s not required, students pursue mathematics in order to prove their diligence, muscle, and intellectual worth in the competitive economy. They want to get through the gates, and they see math as the key.
Mathematicians don’t necessarily encourage or desire this dynamic. It happens above and around them—sometimes even in spite of them.
This is a dreary thought for both the anti- and pro-math camps. The exclusivity comes first, and math simply rises up to fill the gap. Eliminating the gatekeeper won’t increase the number of spots at Harvard or jobs at Google. Students will just seek other grounds on which to compete, and the folks evaluating students will seek other grounds on which to distinguish them.
This frame helps me understand why each side of the algebra debate sounds so out-of-touch to the other. The purpose math-lovers would choose for the subject doesn’t necessarily match the purpose assigned to it.
The idea of “math as competitive platform” discomforts me. Still, I see a modest path forward.
First, frankly acknowledge the system’s competitive nature. We math teachers wield undeniable power over young people’s lives, and we should aim to do so responsibly, openly, and evenhandedly.
Second, just because math plays a role in sorting doesn’t mean it can’t serve eight hundred other magnificent purposes. In spite of the constraints, we should endeavor to make education as rich, meaningful, and “useful” (however you want to define that word) as possible.
Is algebra/calculus/trigonometry “necessary”? Well, apart from maple syrup, very little in life is. But is mathematics bursting with potential to inspire and to enrich students’ mental lives? The answer to that, I believe, is a resounding “yes.”
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