Category: Math

A screenshot of an art project showing what windows 93 would look like if it had been released

What Windows 93 would have looked like, had it been released. (Interactive! Double click on the programs!) I got that link from this piece in the New York Times about the vogue for retro-90s digital design aesthetics. The third-leading cause of death in the US is now “medical error” (via @boingboing). After 10 years of analyzing the Enron email corpus, linguists have found some pretty cool stuff: Tons of baseball metaphors, and the mundane language of “deception theory”. The “Al Capone theory of sexual harassment.” A terrific appreciation of Maryam Mirzakhani’s mathematical genius. NASA’s “advanced concepts” program is currently funding experiment designs for the airships of Mars, soft robots to disassemble asteroids, and a probe that would explore Pluto by bouncing around.


Awesomely nerdy dice

"NYC Cuisine Dice" by Eric Harshbarger

The other day on Twitter, Benjamin Edwards posted a picture of some gorgeous milled-aluminum dice a friend made for him. In response, Eric Berlin pointed us to the work of his friend Eric Harshbarger, who designs insanely cool custom dice.

Above is one of Harshbarger’s creations: A set of dice for New Yorkers who are heading out to eat dinner but are paralyzed by the paradox of choice. The dice are labeled:

Die 1: West Village, Chelsea, EV/Nolita, LES, Soho, Roller’s Choice

Die 2: Italian, Roller’s Choice, Sushi, Mexican, Asian, Ethnic

Heh. Below, an even nerdier concept: Binary dice. I’m going to order a pair of these for my son to bring to his middle-school math class …

Binary dice by Eric Harshbarger

Here’s some deep meta — a die of polyhedral shapes:

Polyhedral die by Eric Harshbarger

And here are some DNA/nucleotide dice — useful for synthetic biologists want to add some randomness when they’re inadvertently creating unstoppable superbugs!

DNA/Nucleotide dice by Eric Harshbarger

Below are perhaps my favorite — a pair of dice Harshbarger created after he posed himself a puzzle: “What is the greatest number of dots that can be removed from a die and it still be determinable what is rolled?”

Behold …

Two-pip dice by Eric Harshbarger

His fuller explanation of how to read these:

  • If the ‘center-side’ pip is face up, then a “6” was rolled, because that is the only number with a dot in that position.
  • If the center-side pip is not visible anywhere on the die, then it must be face-down. Meaning you rolled a “1”.
  • Otherwise, the center-side is on one of the four side faces. In this case, look for the ‘center-center’ pip (which, given its position relative to the center-side pip, must be the “5” face). If that center-center dot is face-up, you’ve rolled a “5”. If it is not visible, you’ve rolled a “2”. If it is also on one of the side faces, then you need to know that the 4-5-6 values are placed counterclockwise about their shared vertex (on Bicycle Dice); with that knowledge you can determine whether a “3” or “4” is face up.

This guy’s a genius. Check out the rest of the dice on his page; the ones here are only the tip of the iceberg.

What I love about Harshbarger’s work is how it leverages humanity’s longstanding fascination with randomness — a force that has long tweaked and teased society’s ideas about logic, reason, the will of God, the arc of life. Over at Aeon, Michael Schulson wrote a terrific essay on the situations where a random choice can be better than a reasoned one, and he opens by noting the peculiar allure of the random:

As moderns, we take it for granted that the best decisions stem from a process of empirical analysis and informed choice, with a clear goal in mind. That kind of decision-making, at least in theory, undergirds the ways that we choose political leaders, play the stock market, and select candidates for schools and jobs. It also shapes the way in which we critique the rituals and superstitions of others. But … [snip]

… As any blackjack dealer or tarot reader might tell you, we have a love for the flip of the card. Why shouldn’t we? Chance has some special properties. It is a swift, consistent, and (unless your chickens all die) relatively cheap decider. Devoid of any guiding mind, it is subject to neither blame nor regret. Inhuman, it can act as a blank surface on which to descry the churning of fate or the work of divine hands. Chance distributes resources and judges disputes with perfect equanimity.


You can catch “mathophobia” from your parents

Picture of plastercine doll alarmed at "math"

Are you mathophobic? You might have caught it from your parents.

“Math anxiety” is precisely what it sounds like — “a feeling of tension, apprehension, or fear that interferes with math performance”, as one scholar puts it. No-one knows how exactly how prevalent it is, but it affects a lot of folks. One study found that 25% of US college students (and 80% of community-college students!) suffer from it; a 2010 survey found that about one in five adults feel “frustrated” or “anxious” when doing math. It also found that 30% of Americans “would rather clean the bathroom than solve a math problem.”

No-one’s quite sure where mathophobia comes from. Educators have suggested all sorts of causes, ranging from abstruse math curriculum, working-memory issues in certain students, supergendered cultural messages telling girls they’re innately bad at math (women suffer from math anxiety more than men), or the high-stakes panic of “timed” math tests.

But it’s also a social thing. There’s a pile of research showing that many elementary-school teachers feel nervous about math. (Some examples: here, here and here). Since they’re the ones teaching it, kids pick up on the fact that math is freaky and scary. So mathophobia is also an emotional virus: You catch it from anxious adults.

And now a recent study identified another source of transmission — your parents!

Parents, of course, are often encouraged to be involved in their kids’ homework, because research finds that when parents are engaged in schoolwork, children are more likely to thrive academically. But recently, a group of academics noticed one aberration: Math. Sometimes, when parents get involved in their kids’ math homework, the students do worse.

Maybe, the reseachers wondered, these parents have math dread — and they’re infecting their kids:

We considered the possibility that it is specifically parents with high math anxiety whose homework help is negatively related to their children’s math achievement. These parents may have inadequate math-helping skills or rigidly use instructional strategies that conflict with those that teachers use in the classroom, which could confuse children and negatively affect their math learning. Frequent involvement of parents with high math anxiety in their children’s math homework could also create opportunities to communicate their fears about math to their children.

So they tested it. They gathered 379 first- and second-grade students (211 girls, 168 boys). They checked the children’s math abilities at the beginning and the end of the school year. Then, crucially, they checked with the children’s parents. How often did they help their kids with homework? And what were their levels of math anxiety?

The result? The scientists’ hunch was correct. When parents had high math anxiety, they passed it on. The more they helped their kids with math homework, the worse their children did.

So if you’re a mathophobic parent, what are you supposed to do? If your kid is struggling with homework, you feel like you have to help out, right?

Maybe not. The researchers also analyzed the performance of kids a) who had mathophobic parents, but b) whose parents didn’t help them out when the math got tough. And what do you know — the math performance of those kids did not decline. In effect, the parents emotionally quarantined themselves from their children, so their math-panic didn’t rub off on the younguns. Consider it the Euclidean version of Hippocratic oath: First, do no mathematical harm!

By the way, neither I — nor the researchers — are blaming mathophobic parents for their fears. The odds are high that the parents were taught math horribly too, by people who were themselves taught horribly; these biases go back generations, and deepen like a coastal shelf. So the long-term solution, the researchers argue, is palliative. We need to help parents out, by developing strategies to alleviate their mathophobia. As they suggest:

These might include structured activities that allow parents to interact with their children around math in positive ways, which could be delivered in the form of math books, computer and traditional board games, or Internet apps. Parents’ homework help could also be facilitated by providing tip sheets with general guidelines for math-homework help and through video models of effective math-homework help (Robinson, 2014). With support, parents with higher math anxiety may be less anxious while helping their children with math and be more equipped to positively affect their children’s math achievement and math attitudes (Frenkel, 2013).

A gender note here: The teachers of those kids in the study? Of the 79, fully 76 were female and only 3 were male. The vast majority of elementary-school teachers are women, and have been for decades (for a welter of economic and sociological reasons). This becomes part of the math-anxiety cycle. Because girls have been told for decades that “math class is tough”, society has, in effect, assiduously cultivated math anxiety in the very people most likely to wind up teaching the subject to young children.

So one can see how the social transmission of mathophobia is liable to happen inside the classroom, too. It’s a good lesson for why we need to stamp out all lazy generalizations about the how men “get” math better than women; these memes have consequences.

(That Creative-Commons-2.0 picture above is courtesy Jimmie at Flickr!)