Making Things Simpler

“How about a pumpkin spice gelato, Mr Moire?”

“I don’t think so, Jeremy. I’m a traditionalist. A double‑dip of pistachio, please.”

“Coming right up, sir. By the way, I’ve been thinking about the Math poetry you find in the circular and hyperbolic functions. How about what you’d call Physics poetry?”

“Sure. Starting small, Physics has symmetries for rhymes. If you can pivot an experiment or system through some angle and get the same result, that’s rotational symmetry. If you can flip it right‑to‑left that’s parity symmetry. I think of a symmetry as like putting the same sound at the end of each line in rhymed verse. Physicists have identified dozens of symmetries, some extremely abstract and some fundamental to how we understand the Universe. Our quantum theory for electrons in atoms is based on the symmetries of a sphere. Without those symmetries we wouldn’t be able to use Schrodinger’s equation to understand how atoms work.”

“Symmetries as rhymes … okaaayy. What else?”

“You mentioned the importance of word choice in poetry. For the Physics equivalent I’d point to notation. You’ve heard about the battle between Newton and Leibniz about who invented calculus. In the long run the algebraic techniques that Leibniz developed prevailed over Newton’s geometric ones because Leibniz’ way of writing math was far simpler to read, write and manipulate — better word choice. Trying to read Newton’s Principia is painful, in large part because Euler hadn’t yet invented the streamlined algebraic syntax we use today. Newton’s work could have gone faster and deeper if he’d been able to communicate with Euler‑style equations instead of full sentences.”


“Leonhard Euler, though it’s pronounced like ‘oiler‘. Europe’s foremost mathematician of the 18th Century. Much better at math than he was at engineering or court politics — both the Russian and Austrian royal courts supported him but they decided the best place for him was the classroom and his study. But while he was in there he worked like a fiend. There was a period when he produced more mathematics literature than all the rest of Europe. Descartes outright rejected numbers involving ‑1, labeled them ‘imaginary.’ Euler considered ‑1 a constant like any other, gave it the letter i and proceeded to build entire branches of math based upon it. Poor guy’s vision started failing in his early 30s — I’ve often wondered whether he developed efficient notational conventions as a defense so he could see more meaning at a glance.”

“He invented all those weird squiggles in Math and Physics books that aren’t even Roman or Greek letters?”

“Nowhere near all of them, but some important ones he did and he pointed the way for other innovators to follow. A good symbol has a well‑defined meaning, but it carries a load of associations just like words do. They lurk in the back of your mind when you see it. π makes you think of circles and repetitive function like sine waves, right? There’s a fancy capital‑R for ‘the set of all real numbers‘ and a fancy capital‑Z for ‘the set of all integers.’ The first set is infinitely larger than the second one. Each symbol carries implications abut what kind of logic is valid nearby and what to be suspicious of. Depends on context, of course. Little‑c could be either speed‑of‑light or a triangle’s hypotenuse so defining and using notation properly is important. Once you know a symbol’s precise meaning, reading an equation is much like reading a poem whose author used exactly the right words.”

“Those implications help squeeze a lot of meaning into not much space. That’s the compactness I like in a good poem.”

“It’s been said that a good notation can drive as much progress in Physics as a good experiment. I’m not sure that’s true but it certainly helps. Much of my Physics thinking is symbol manipulation. Give me precise and powerful symbols and I can reach precise and powerful conclusions. Einstein turned Physics upside down when he wrote the thirteen symbols his General Relativity Field Equation use. In his incredibly compact notation that string of symbols summarizes sixteen interconnected equations relating mass‑energy’s distribution to distorted spacetime and vice‑versa. Beautiful.”

“Beautiful, maybe, but cryptic.”

~~ Rich Olcott