Category: Mathematics

After Prime Proof, an Unlikely Star Rises

Follow-up on one of my favorite article from the first half of 2015 with this brilliant documentary on Yitang Zhang :

“Never heard of him. Absolutely never heard of him,” said Andrew Granville, a number theorist at the University of Montreal, in Counting From Infinity. When Granville heard about the result and the techniques that Zhang used, he recalled saying, “There’s no way that somebody I’ve never heard of has done this.”

→ Quanta Magazine

Math as Myth

A great song, Golden Ratio, and artwork from Benn Watt’s album. 

But simple, beautiful mathematical explanations can make us greedy. While we wish for all explanations of the world around us to be elegant, science often involves “the slaying of a beautiful hypothesis by an ugly fact,” in the words of biologist Thomas Henry Huxley. Before positing elliptical orbits, Kepler himself succumbed to the desire for beauty when he suggested that the planets’ orbits could be modeled as the Platonic solids nested inside each other. His theory was beautiful, but it was soundly disproved by later observations of the outer planets. In a way, it was almost too beautiful to be right.

→ Nautilus

Moving Averages and the iPad

There are myriad other ways to smooth a graph without switching to cumulative figures. One of the simplest is the moving average. In this technique, instead of plotting the raw data, you plot the average of a few data points in the neighborhood of each time value.

For many data sets, the best size of this neighborhood is not obvious. With Apple’s sales figures, though, I think it’s clear that the best choice is to average over four quarters: the quarter that you’re plotting and the three previous. This smooths over the seasonal jumpiness while not including so much past data as to ignore real trends.

→ Lean Crew

Game Theory Calls Cooperation Into Question

Vervet monkeys are known for their alarm calls. A monkey will scream to warn its neighbors when a predator is nearby. But in doing so, it draws dangerous attention to itself. Scientists going back to Darwin have struggled to explain how this kind of altruistic behavior evolved. If a high enough percentage of screaming monkeys gets picked off by predators, natural selection would be expected to snuff out the screamers in the gene pool. Yet it does not, and speculation as to why has led to decades of (sometimes heated) debate.

Researchers have proposed different possible mechanisms to explain cooperation. Kin selection suggests that helping family members ultimately helps the individual. Group selection proposes that cooperative groups may be more likely to survive than uncooperative ones. And direct reciprocity posits that individuals benefit from helping someone who has helped them in the past.

→ Quanta Magazine