What is Good Mathematics? by Terence Tao

Terence Tao is a gift to the mathematical community. He is an excellent collaborator, a talented communicator, and one of the broadest and sharpest minds working today. Eighteen years ago, when he was just past thirty years old, he wrote the essay What is Good Mathematics?. I discovered this when Steven Strogatz invited Tao onto his podcast The Joy of Why to discuss how well this essay holds up.

Both of these are great, but start with the opening section of Tao’s essay, where he lists twenty-one ways to measure mathematics as being “good.” It displays his impressive clarity of thought and writing ability and evinces how the professional mathematics scene isn’t what one may have expected.

I Just Learned What BBCOR Means

In early high school, I remember all the hubbub about requiring metal baseball bats to align to the BBCOR standard. Given the pronunciation of this (“Bee-Bee-Core”), I always assumed it was a regulation about what specific materials must be used to make the bat. That’s only true insofar as the standard actually defines a material property.

BBCOR stands for “Batted Ball Coefficient of Restitution”. In other words, the standard tells you how elastic the collision between ball and bat is allowed to be. This standard was designed to dull metal bats in an effort to protect pitchers, the most likely players to be grievously injured by a batted ball. It was adopted by the NCAA in 2011, and most youth leagues that I’m aware of followed their lead. I used BBCOR-certified bats throughout high school, and continue to do so in my adult league.

You can read through the NCAA protocol for BBCOR, where the most fascinating part is the testing procedures starting on page 5. There is a table defining what the moment of inertia must be a distance of 6 inches from the knob of the bat—where the batter grips the bat—to ensure the bat isn’t “too easy” to swing. Then they use a ball cannon—that’s the term they provide—with a muzzle velocity of at least 150 mph which imparts spin at a rate of less than 10 rpm to fire fresh baseballs at clamped-down bats.

They perform six consecutive valid trials to measure the restitution of the bat using three sensors placed along the trajectory of the ball (which must be accurately placed to a tolerance of 0.005 inches.) After all that, the average measured BBCOR must be no more than 0.500.

I loved reading this, and I now want this to be a physics problem in some college class.

2022 Blogmas Day 21 – Fielding Percentage and Range Factor

Leading into the home stretch, let’s discuss some defensive statistics. As a category, these represent recent innovations in baseball, as defense is the most dynamic aspect of the game. Players can change where they are positioned, which affects their ability to get to a ball. As we gather more data — ball speed off the bat and launch angle — we can better analyze defensive ability. But it’s still messy.

Continue reading “2022 Blogmas Day 21 – Fielding Percentage and Range Factor”