Category: Math

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N is for Numbers

Blackadder: Right Baldrick, let’s try again shall we? This is called adding. If I have two beans, and then I add two more beans, what do I have?
Baldrick: Some beans.
Blackadder: Yes… and no. Now try again. One, two, three, four. So how many are there?
Baldrick: Three.
Blackadder: What?
Baldrick: …and that one.
Blackadder: Three and that one.  Let’s try again shall we? I have two beans, then I add two more beans. What does that make?
Baldrick: A very small casserole.

Blackadder episode, “Head”
Student geometry problem in Babylonian cuneiform @1500 BCE. Photo by Rama in the Louvre.

Yes, dear readers, there will be math today. I know you can do it. I know you can run intellectual circles around Baldrick.

The definitive work on this topic is The History of Mathematics by Merzbach and Boyer, which is already in a Third Edition, even though not much has changed for the Egyptians and Sumerians, who used what we’d consider basic counting systems to construct giant pyramids. Mainly, Merzbach and Boyer have added a “Logic and Computing” and “Recent Trends” chapters at the end. Remember when Computer Science was about logic and not Belarussians creating algorithms to stuff your social media full of outrage porn? How quaint!

Anyway, I digress. Today, I want to describe how different cultures approached numbers–not specifically whether they were smart enough to figure out Fermat’s theorem or Poincare’s theory–but how we as humans figured out what Baldrick apparently couldn’t. Thinking about math is hard, but we’ll also see that there are harder and easier ways to do it.

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Benjamin Banneker, First Black American Intellectual: Part 2, Benjamin’s Abolitionist Almanac

Herein shall we continue the story of Benjamin Banneker, surveyor, farmer, astronomer, polymath, and noted abolitionist. Be sure to read Part One, the history of Banneker’s family and his acquisition of mathematical knowledge.

Benjamin Banneker was nearly sixty when he hit upon the idea of publishing an almanac of natural information. As a farmer, he had kept copious notes, documenting the practices of bees and noting the 17-year cycle of cicadas. Unmarried, he worked his land mostly alone, though he still chatted with his neighbor, George Ellicott. One day, Ellicott brought over a telescope. It turned Banneker’s last two decades into a whirlwind of calculation, publication, and provocation. It would make him famous again for a brief time. He would also poke the hornet’s nest.

“Do you have an answer, Ben?” the schoolmaster’s voice barked out. Startled, Ben looked up and scanned the class, faces turned to stare and giggle. “What is 23 by 7?” Without any calculation, Ben replied, “14 in the tens place and 21 which is 161.” Still, he had not been paying attention. The master picked up the book that had absorbed his young pupil, Newton’s Principia. “I’m sorry, sir,” Ben said. “I forgot to ask if I could…” The master squinted but tried to suppress a grin. “Practicing your Latin?” “Yes, sir. Perhaps you could explain this part … ‘precession of the equinoxes…'”

Alone with a Telescope

In 1788, Benjamin at 57 had continued to eke out a small harvest of apples and wheat, even as the Ellicott Mills and other larger farms had grown around him. His minor celebrity status as a clock maker had died down a bit, although the clock still kept time and the occasional passerby poked his head in to gawk. The Revolution had come and gone. The War had come and gone, too.

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Y is for Yield Curve

The Yield Curve is a simple idea with surprising predictive power. The Yield Curve is a magic eight ball, which tells the interpreter what they want to hear. The Curve is a bunch of numbers. The Curve tells you everything that happened, but only in retrospect.

All of the above.

Basic yield curve shapes, colotrust.com.

People really wax poetic about the yield curve. There’s one guy at NPR that goes ga-ga over the yield curve and has done podcasts on it with clock-like regularity:

GARCIA: …I got to say, it is one of my favorite indicators.
SMITH: Cardiff, you love the yield curve.
GARCIA: Very much.
SMITH: Every time we talk about the yield curve, you kind of light up. And I have no idea why this is the case.

NPR podcast, Apr 6, 2021.
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