The Math Behind Music

How is it that Beethoven, who is celebrated as one of the most significant composers of all time, wrote many of his most beloved songs while going deaf? The answer lies in the math behind his music. Natalya St. Clair employs the “Moonlight Sonata” to illustrate the way Beethoven was able to convey emotion and creativity using the certainty of mathematics.

Also see her TED blog post The math behind Beethoven’s music.

Aristotle on Excellence

“Excellence is an art won by training and habituation. We are what we repeatedly do. Excellence then is not an act, but a habit.” — Aristotle

What is a friend?

From Do Your Friends Actually Like You? – The New York Times:

…Because time is limited, so, too, is the number of friends you can have, according to the work of the British evolutionary psychologist Robin I.M. Dunbar. He describes layers of friendship, where the topmost layer consists of only one or two people, say a spouse and best friend with whom you are most intimate and interact daily. The next layer can accommodate at most four people for whom you have great affinity, affection and concern and who require weekly attention to maintain. Out from there, the tiers contain more casual friends with whom you invest less time and tend to have a less profound and more tenuous connection. Without consistent contact, they easily fall into the realm of acquaintance. You may be friendly with them but they aren’t friends.

But friendship requires the vulnerability of caring as well as revealing things about yourself that don’t match the polished image in your Facebook profile or Instagram feed, said Mr. Nehamas at Princeton. Trusting that your bond will continue, and might even be strengthened, despite your shortcomings and inevitable misfortunes, he said, is a risk many aren’t willing to take.

[…]

So it’s worth identifying who among the many people you encounter in your life are truly friends. Who makes time for you? Whose company enlivens, enriches and maybe even humbles you? Whom would you miss? Who would miss you? While there is no easy or agreed upon definition, what friendships have in common is that they shape us and create other dimensions through which to see the world. This can be for better or worse depending on whom we choose as friends. As the saying goes, “Show me your friends and I will show you who you are.”

Lisa VanDamme on The Proper Goal of Education

From the website of the VanDamme Academy:

“The proper goal of education is to foster the conceptual development of the child—to instill in him the knowledge and cognitive powers needed for mature life. It involves taking the whole of human knowledge, selecting that which is essential to the child’s conceptual development, presenting it in a way that allows the student to clearly grasp both the material itself and its value to his life, and thereby supplying him with both crucial knowledge and the rational thinking skills that will enable him to acquire real knowledge ever after. This is a truly progressive education—and parents and students should settle for nothing less.” —  Lisa VanDamme

Check out their curriculum. Pretty incredible.