by Jonathan Kujawa

In a miracle we neither understand nor deserve, some of the most outlandish inventions of mathematicians’ fevered imaginations have later prove eminently useful in the real world. We’ve talked about some of these here at 3QD. From using the stretchy math of topology to identify data clusters in medicine, to using exotic measures of distance to fill in large amounts of missing data, to using number systems coming from elliptic curves to create strong encryption systems. These are only a few of the gifts we’ve received over the years from mathematics. Several years ago the mathematicians who congregate at mathoverflow compiled a list of applications for each of the main areas of modern mathematics.

Many of these applications contribute billions of dollars of value to our modern world, and yet in nearly every case the mathematics underpinning these were developed years, decades, or even centuries earlier. Bringing a little math to things often pays off bigly.

Plus, doing math is just plain fun! I may be biased, but I say the (fun + value)/cost ratio of math is pretty close to unbeatable. To quote Steve Earle, “I’ll stand on Bob Dylan’s coffee table in my cowboy boots and say that”.

Last month I asserted one explanation for the “unreasonable effectiveness” of mathematics is its insistence on precision in our language and thought. There is a real power in the mere act of mathematization. Even if you can’t solve the problem using actual mathematics, thinking mathematically often lays bare the real questions, the real obstacles, and the possible paths to a solution.

That’s easier said than done. As any calculus student will tell you, one of the most difficult parts of using mathematics on a real-world problem is turning the messy, ambiguous chaos of the real world into something on which you can try to do math. Read more »

by Brooks Riley

by Amanda Beth Peery

by Brooks Riley

For someone who spent most of his life trying to get on Page Six, (the New York Post’s iconic gossip column), hitting Page One was pay dirt for Donald Trump. Now that he’s there, he means to stay there, devouring our attention for the foreseeable future. One could even argue that all his lies and deplorable actions are motivated by a single, sorry ambition, to be the center of attention at all times and in all places. Outrage sells.

Outrage is also tiresome. Trump Outrage Fatigue set in long ago, but we still can’t ignore him. Or can we? If the fate of the world wasn’t at stake we would have dropped this guy long ago from our field of vision.

I’m spending more and more time off the grid of mainstream news coverage. There are other stories out there to excite us, to outrage us or to move us. I haven’t left the grid altogether. I do keep up. But my mind now homes in on stories at the bottom of the internet page, or the seemingly trivial fillers that pepper the meal of misery at the top. Here’s a small sample:

Ötzi’s Last Meal

What could be more important than the contents of Ötzi’s stomach? Certainly not the Big Mac wending its way through our leader’s digestive system. I’m not being facetious here. Ötzi is the gift that keeps on giving, ever since the 5300-year-old man who lay buried in ice for millennia was discovered by tourists in 1991 in the Ötztal Alps bordering Austria and Italy. Since then I have followed every gripping new revelation about Ötzi—what he wore, what he carried with him, how he was murdered. Ötzi is a time capsule spilling forth impossible secrets about life in the Copper Age. Now that his stomach has been found, lurking shriveled under his lungs, we know that his last meal was a hefty portion of ibex fat—not the meat itself but the subcutaneous fat that would help him withstand the bitter cold and give him endurance at high altitudes. According to a researcher, ibex meat tastes okay, but ibex fat tastes awful, so that the act of eating it must have been prophylactic, derived from some knowledge of survival strategies. Read more »

Sophia Al Maria. … on Gulf futurism …

More here, here, and here.

Thanks to Anjuli Raza Kolb.

by Gabrielle C. Durham

Folks love to pick on passive constructions. “Passive sentences are too wordy. They are unclear. They gave me a bruise.” Two out of three of these are objectively wrong. The third I can’t help you with.

Passive voice provides a valuable service. We all know when something bad happens, even if we do not know who or what caused the bad. The perfect opportunity to use the passive presents itself on such an occasion. If you insist on using active voice, you are forced to use the sloppy “someone” or “something” as the agents of nefariousness.

The house was destroyed, the livestock abducted, and the women were observed to be strangely beatific.

Something destroyed the house, someone abducted the livestock, and the absence of useless husbands pleased the women greatly.

Don’t get it twisted: The passive is not going to fit the bill every time. Reagan’s professing that “Mistakes were made” illustrates the weakness of the passive voice. No one is accountable in the passive, unless you consider whatever mealy-mouthed alleged subject follows the preposition “by.”

Your bicycle was run into by me in my car.

Eww. This is the verbiage of bureaucratic nightmare. Read more »

by Brooks Riley

by Christopher Bacas

Because we remained so long in Housing Court’s trash-strewn orbit, Management assigned us our own agent. Every week, I saw Hassidim in our lobby. One was bigger than the others, with a jellied midsection spilling over pants, bowing his long black lapels. He moved like a man barely acclimated to walking; legs chugging ahead, thighs rubbing, wisps of beard waving cilia-like from his jowls.

To introduce our new handler, Matthew, the property manager, came by. He was a small man who always spoke quickly, words folding back on each other, nervous laughter erasing their authority.

“This is Jo-El. He doesn’t work for me (chuckle, chuckle), the landlord brought him on to work with the building.”

In fact, our landlord’s name was posted on a public list of “New York’s Worst Landlords”. I submitted the open violations in our building to the Public Advocate and within days, his name appeared. The new arrangement was designed to get the owner off that embarrassing list. Jo-El wasn’t a lawyer by training, he was a fixer. His fixing kept broken things broken.

We shook hands. Jo-El didn’t smile. He pressed his lips together and looked down. Read more »

by Max Sirak

It turns out you learn a lot when you write a book. This may seem counterintuitive. Perhaps you think, “Well, that’s dumb. If you write a book about something you should already be an expert on it.”

That’s a fair way to feel and thing to say.

However, my situation is slightly more unique. See, I don’t write books on subjects I’m an expert in. (I’m not even sure if such subjects exist.) My job as a ghostwriter is to help other people write books in their fields of expertise. It goes like this: most people spend their lives practicing and learning all they can in their fields. Then, after years of gaining proficiency, there almost inevitably comes a time for them to share their hard- won wisdom. The best way to do this, they figure, is to write a book.

That’s where I come in. Usually, the process of becoming a badass in a given field doesn’t entail much writing. Sometimes it does, certainly. But most occupations don’t involve a lot of “writing.” Paperwork? Probably. Reports to fill and file? Likely. But there’s where the pen stops.

So, most folks have spent all their time working toward being the best whatever-it-is-they-are, not writing. I, on the other hand, write every day. Which means, when it comes time for others to share what they’ve learned with the masses, I can help.

And that, friends, is why you are now being treated to a single, kidless guy’s thoughts on parenting. Read more »

by Thomas R. Wells

Tyrants like Vladamir Putin and Kim Jong Un seem to win a lot of their geopolitical contests against democratic governments. How do they do it?

A common explanation is that these tyrants are better at playing the game. They are strategic geniuses leading governments with decades of experience in foreign affairs and characterised by single-mindedness and a long-term horizon. Of course they are going to make better geopolitical moves than democratic governments riven by political factionalism and only able to think as far ahead as the next election.

This explanation is wrong. Tyrants don’t succeed because they are especially skilled at the game of geopolitics, but because they are baddies. Tyrants make bold moves because they are willing to subject their country (and the whole world) to more risk. They can do that because they care less than democrats, and hence worry less, about bringing harms to their people. Like a hedge fund manager, they can afford to take big risks because they are not playing with their own money. When tyrants win it is because of luck, not brilliance. This is easier to see when tyrants lose – as they nearly all do in the end, when their luck runs out.

I. The Clownish Incompetence of Tyranny

The myth of the strategic brilliance of tyrants is driven by cognitive biases. There is the assumption that significant events must have significant agency behind them (the same bias that drives conspiracy thinking). And there is the tendency to fill in the murky mysteries of tyrants’ decision-making by projecting our own worst fears. But if you actually think it through it is rather unlikely that tyrannies would be more competent than democracies, let alone bastions of brilliance. Read more »

by Hari Balasubramanian

Optimization – the search for the best among many – is at the heart of the statistical and machine learning models that get used so extensively these days. Take the simple concept that underlies many of these models: fitting a mathematical curve to data points, better known as regression. In the simplest two-dimensional case, the curve is a line; in three dimensions, it is a plane, as seen in the figure. Among all possible planes – there are infinitely many of them, obtained by changing the angle and orientation: imagine rotating the plane every which way – we would like the one that passes ‘closest’ to as many of the data points (shown in red) as possible. Thus regression, often called the workhorse of machine learning, is really an optimization problem.

It turns out that optimization is fundamentally connected to even basic statistical quantities. Common statistics we we now reflexively use to summarize data – means, medians and percentiles – are themselves answers to certain optimization questions. We are not used to looking at them in this way.

Let’s take the average or sample mean, which, despite its obvious limitations, everyone turns to first. Suppose we have five numbers in a sample: 3,4,5,8 and 12. The sample mean is given by the straightforward calculation:

(3+4+5+8+12)/5 = 6.4

But there is another way to think of the sample mean: as the optimal answer to the following problem. We seek to find the x that minimizes (produces the lowest value of) the sum of the squared difference between x and each observation in the sample. Mathematically, we can write the function as:

(x-3)² + (x-4)² + (x-5)² + (x-8)² + (x-12)²

At what value of x does the function have its lowest value? In the figure below, the horizontal axis shows the values that x can take (I restricted myself to the range of the data points, 3 to 12). The vertical axis shows value of the sum of squares function corresponding to each value of x.

We see that the function follows a U-shape with the lowest/best value, x=6.4, occurring at the bottom of the U. Simple high school calculus – finding that point on the continuous curve at which the derivative is 0 – will yield the same answer. In fact, the formula for the mean, adding up all the sample values and dividing by the total number in the sample, can be derived using such calculus. Read more »

Nicholas Kahn and Richard Selesnick. Forgotten Crowns, 2013.

Archival pigment print.

More here and here.

by Emrys Westacott

Why do people care about sport? With hundreds of millions of human beings (myself included) obsessively following the world cup that is being played out in Russia, it’s a good time to reflect once again on this perennially interesting question.

Of course, it’s also true that hundreds of millions don’t give a damn about sport. I know the type: I’m closely related to a disproportionate number of them. To these people, the passion aroused by twenty-two men in shorts trying to force a ball between two sticks is a great mystery, and not something they find it easy to respect. In their view, even if they don’t say this out loud, getting all worked up over a soccer match is a) dumb, and b) good evidence that one needs to get a life. And they may be right. But that still leaves the phenomenon of sport-induced passion unexplained.

Since it is arguably the sporting event that occasions the most consuming passions, let’s focus on the world cup (although many of the points made will naturally apply to other sports also). And let’s distinguish, at the outset, between enjoyment and passion.

Why is soccer entertaining?

It isn’t so hard to understand why soccer provides enjoyable entertainment. First, and most obviously, a good match is dramatic; it has a compelling narrative. But unlike a play or a film, it is unscripted, which means the outcome is not determined in advance, and that makes a game genuinely exciting. Read more »