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**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.

**The Super-Additive Dessert**

I am on a perpetual search for super-addictive combinations of food. One of my favorites: to the traditional quesadilla combination of tortilla + melted cheddar, add tumeric + chopped celery. Unaccountably good.

**Epistemology is Hard**

I have conflicted feelings about the rationalist philosophers (Descartes, Leibniz, Spinoza, kind of Hobbes). On the one hand, I love the aesthetic of the arguments: the clear, axiomatic development modeled on mathematics.

On the other hand, this seems like a very stupid way to try to understand the world. The universe is very confusing and is never what you would have guessed. “Certain knowledge” is so elusive it’s basically an oxymoron.

I find that I’m a rationalist by inclination, but my rationalism leads to the conclusion that empiricism is the only sensible way to go.

**The Trivial Case**

Look forward to my graphic novel “The Life and Times of the Trivial Case,” which will be 400 pages of that green elf with different text on each page, like Dinosaur Comics.

**Club Obvi**

“Obviousness” is in the eye of the beholder, right?

WRONG. If it’s in the eye of the beholder, then it’s not sufficiently obvious!

Finally, a quick announcement of the results from the Know-Nothing Oscar Pool!

**219 people**filled out ballots.- The
**Ultimate Visionary**, a math(s) teacher named**Kin**, scored**33.1**(of a possible 47.1) across all categories. Kin mostly stuck with the favorites, with one masterstroke exception: picking “Heaven is a Traffic Jam on the 405,” which was the night’s biggest underdog winner. - The
**Lazy Visionary**scored**15.9**(of a possible 15.9) on the high-profile categories. - The
**Obscure Visionary,**the self-effacing**Colin Thomas**, scored**22.3**(of a possible 31.2) on the technical categories. He writes: “I must confess that I chose several at random (having looked at, and not entirely understood, the odds page.)” But he also had this key insight: “‘good’ films tend to do well in these categories even if they don’t deserve to.” **My own ballot**lost narrowly to my Oscar arch-nemesis Ryan’s,**27.4 to 27.0**. Sigh.

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semi-mythical mathematician

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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.”

Or consider this problem, from the 21^{st} century:

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.

What say you, my fellow jurors?

*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!*

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**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.”

**Parking Sign**

@DynamicsSIAM pointed me to the real-life version of this:

**Teacher Condolences**

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 ask: who the hell is this Joyce who demands so many waking hours of the few thousands I have still to live for a proper appreciation of his quirks and fancies and flashes of rendering?

**24601**

If any gifted singers out there want to belt this line at the top of their lungs and then send me the mp3, please feel encouraged!

**Rationalizing**

This cartoon generated lots of great discussion on Twitter and Facebook, and – anecdotally – I saw a cultural split. British educators identified with the teacher in the comic; American educators, with the student.

On this matter, as many others, I am a true American. Best I can tell, the reason we “rationalize the denominator” is a historical artifact: in the absence of a calculator, it’s much easier to do the long division for √2 divided by 2 than for 1 divided by √2. For pedagogical purposes, I’m with James Tanton: the standard manipulation is worth learning, but works better when accompanied by *other* manipulations. It better captures the nature of mathematical technique, and is actually more engaging and puzzle-y.

(For example, to prove that √N and √(N+1) grow infinitely close as n grows, the best path is to rationalize the *numerator*!)

**A Pedantic Birthday Card**

In 2016, I happened to have a Leap Day Child in my homeroom class. We celebrated his third birthday with enthusiasm. He’ll turn 4 in 2020.

Also, I learnt there are levels beyond extra pedantic: One commenter sagely pointed out that the comic should read “how many Leap *Days* you’ve lived through.” Touché!

**Great Moments in Conversation with My Father**

My father (a mathematician) has a quintessentially mathematical memory: it flushes out all extraneous details, stores the minimum data necessary, and reconstructs facts from the available information. That reconstructive process is characteristic of all human memory, but is especially valuable in mathematics, where it mirrors the deductive reasoning at the heart of the discipline.

**The Danger of an Art Dealer Who’s Read Thinking Fast and Slow**

You can’t see it in the scan, but the “painting” is of a smiling pig. $10,000 is a bargain if you ask me.

**Ron Weasley’s Insecurities**

I’ve been known to say a few ill words about Harry Potter’s best mate (particularly as he appears in the films, where I firmly believe the characters Fred, George, and Ron should have been folded into a single character called “Ron Weasley”). Still, I get where the guy is coming from. Also working against him: He has five older, more popular brothers, and a hot younger sister who’s in love with his best friend. Plus he’s from a demographic category subject to awful prejudice in the UK: gingers. The guy needs a break.

**The Malcolm Gladwell of Math**

In reality, I just said, “Sure, Ryland, that sounds attainable.” But this is what I said later, in my head, and it’s my blog, so that counts.

Also, it surprised me to see how many Facebook commenters hadn’t heard of Gladwell! I suppose his name recognition peaked sometime in the early-to-mid 2000s, so folks a decade younger than me may not be as familiar with his work.

**Bonus Cartoon! The Scaling Factors of Giants**

I drew this one on a $0 commission for Jim Propp’s January essay at Mathematical Enchantments. Like all his posts, it’s a fun read – check it out!

]]>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 **e** **Day**: 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 **E**uler, 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 **E**xponential, 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 **E**legance, 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 **I**rrational.

(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

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 **E**ccentric **E**ggbert, the **E**gregiously **E**rror-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 **E**vents. 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 **E**xciting **E**quality, because in calculus, the function e^{x} 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 *e*xcited? (ARE YOU NOT ENTERTAINED???) Then perhaps I should explain. (Don’t worry; it’s easy; *e*-lementary, even.)

The language by which many scientists understand reality is differential equations. These are statements describing how quantities are changing. Makes sense; we live in a universe of flux.

One of the most basic and pervasive differential equations is this: A’ = A. In other words: “how fast this quantity is changing depends directly on how big the quantity is.” A bigger quantity changes fast; a small one, slow. Think of a growing population, a nuclear chain reaction, or a burgeoning economy.

The most fundamental solution to this fundamental problem?

*e ^{x}*.

*e* is for Eggheaded Enjoyment. Where its cousin π has gone kind of mainstream, *e* remains the exclusive estate of the hard-core nerds. And they have a lot of fun with it. Examples:

- In its 2004 IPO filing, Google announced a goal of $2,718,281,828, or
*e*billion dollars.

- Google once recruited programmers by posting a billboard that said simply: “{first 10-digit prime found in consecutive digits of
*e*}.com.” (The answer is 7,427,466,391.)

- Donald Knuth, famed computer scientist, issued a program with version numbers 2, 2.7, 2.71, 2.718, and so on.

Finally,* e* is for the most **E**xquisite **E**quation in **E**xistence, **E**uler’s **e**-dentity:

Everybody loves this equation. That’s because it’s awesome. Just listen to Keith Devlin:

like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler’s equation reaches down into the very depths of existence.

The equation is known as Euler’s identity, after the deserving genius Euler. This is altogether fitting and proper, since the formula was most likely discovered by… Jacob Bernoulli’s brother Johann.

POSTSCRIPT: On the name of *e* and Euler’s identity…

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.

Here’s the link again! Good luck, visionary.

]]>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.”

]]>**Suterisms: **I recently came across the work of cartoonist David Suter. His images are hard to describe. Artful cartoons? Cartoonish art? Visual puns? More like visual wordplay; “thoughtplay?” It’s what you’d get if you hired MC Escher as a political cartoonist. This one was a favorite of mine:

**Belatedly: RIP, Voevodsky**: A tribute to the visionary mathematician Vladimir Voevodsky, who died in 2017.

“He was unfazed by authority or status,” [Nadia] Shalaby wrote in an email. “Not out of rebellion, but because he was missing the gene that detects status and makes people respect it over merit.”

I met Voevodsky briefly in September 2016. He was surrounded by young researchers, none of them saying anything, just sort of awkwardly soaking in his presence, trying to think of a question to ask.

Seizing the chance, I fumbled a few uncomprehending questions about his ambitious work in creating proof verification software. Why did his system take as its foundation not set theory, but a more algebraic structure?

He gave patient answers, then turned back to the young researchers he had come to mentor.

**A push notification from across the universe**: A gravitational wave is detected. The world pivots its telescopes and its attention to that corner of the sky. They find an extraordinary event:** **two neutron stars colliding. Dozens of research papers ensue.

According to Daniel Holz, an astrophysicist at the University of Chicago, “back-of-the-envelope calculations indicate that this single collision produced an amount of gold greater than the weight of the Earth.”

Also:

Scott Hughes, an astrophysicist… [said] “I can’t describe in family-friendly words how exciting that is.”

**Huh.** Apparently the Twitter logo is made entirely from circles.

**Defending the indefensible?** Jim Propp, a math professor at UMass Lowell, takes advantage of his tenure by staking out a position that could very well get someone with less job security fired.

He’s pro-Comic Sans.

I contend that, when it comes to a lecture topic like math that in the wrong hands can be arid and forbidding, it’s a good countermeasure to adopt a font that from the start announces “Let’s have some fun.”

**Pretty droplets: **Vox reports some cool coffee science out of MIT:

**Advice you should actually listen to. **On his blog, Terry Tao (from time to time described as “the greatest mathematician in the world”) has an index of advice spanning a whole career, from elementary school to tenure.

Whereas at the undergraduate level and below one is mostly taught highly developed and polished theories of mathematics, which were mostly worked out decades or even centuries ago, at the graduate level you will begin to see the cutting-edge, “live” stuff – and it may be significantly different (and more fun) to what you are used to as an undergraduate! (But you can’t skip the undergraduate step – you have to learn to walk before attempting to fly.)

**The mathematical fix for the wobbly table: **Tai-Danae Bradley pointed me towards a great old column of Keith Devlin’s, on how you can stabilize a wobbly table with the Intermediate Value Theorem:

Two caveats. This only works for a table with equal legs, where the wobble is caused by an uneven floor. If the table has uneven legs, you probably need the folded napkin. Also, the floor can be bumpy but has to be free of steps – if the table is on a staircase, as you often find in outdoor cafes in Tuscan hill towns like San Gimignano, the math doesn’t work. But then, if you are sitting on a restaurant terrace in Tuscany, who cares?

**BOOK OF THE MONTH**

(*I mean, not that it was published this month, but I read it this month, and you should read it next month, so you see, months are coming up all over the place)*

**Time Travel: A History**, *James Gleick*

Gleick’s superpower is to immerse you in intellectual worlds that came before our own.

Take his biography of Isaac Newton. Reading it, you slip into a pre-scientific, Aristotelian place, where words like “mass” and “motion” have only fuzzy, ancient meanings.

Or, reading *The Information – *maybe his best book – you come to see what the train and the telegraph and the dictionary did to the world and to the minds within it. You even, briefly, inhabit a preliterate worldview, an oral intelligence in a fleeting world.

And reading *Time Travel*, you find yourself in a world just discovering time. The dawn of futurism; the nascent idea of “progress”; the strange invention of “time zones.” The book is less about the travel than it is about the medium (the dimension? the substance? the psychological construct?) that you’re traveling through. Plus lots of great pop culture commentary and poking fun at ill-conceived time metaphors.

I can’t get enough of Gleick’s stuff. You could publish a delightful short story collection out of the footnotes alone.

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