Tuesday, October 11, 2011

First approximation

In my post While we’re on the subject I talked about the difference between limiting and constricting knowledge into discrete “subjects” vs. accepting the reality that all knowledge and information is connected – somehow. Granted, the connection might be tenuous, to you, at this particular time, but at some other time, in some other circumstance, to someone else, it might be quite closely connected. Early in that post I referenced Eratosthenes and his ingenious – and simple – method for calculating the circumference of the earth 2200 years ago, with none of the resources we have today. Remembering Eratosthenes reminded me of another brilliant man whose life overlapped my own, rather than being from two millennia earlier, Enrico Fermi. If you’re not specifically familiar with him, you may recognize his name from the element named after him, fermium (Fm - element 100), or the fermion of quantum physics.

First, I’ll tell you the Fermi story which Eratosthenes’ story reminded me of, then I’ll fill in the how and why I wanna talk about it.

Fermi was one of the transcendental geniuses of his time who worked on the first atomic bomb, the Manhattan Project. All the lead-up calculations to the first test explosion were very blue-sky. They were even unsure of the order of magnitude they might be dealing with. AAMOF, there’s a story that prior to the explosion, Fermi was taking bets on whether or not it would ignite the atmosphere and destroy the entire universe, or at least the earth, maybe just New Mexico. (Yes, Fermi was a funny guy.) But that’s not the Fermi story I wanna tell. It’s this. Because they wanted to know just how much power they were producing, they set up lots and lots of sophisticated sensors and measurement devices to monitor the blast. It took quite a while after the explosion for the calculations to be completed but as the blast happened, Fermi dropped some torn-up pieces of paper and from their displacement, he quickly calculated it at about 10 kilotons.

Eventually, when the rigorous calculations were complete, the official measurement came out at around 18 kilotons. When your margin of error includes orders of magnitude, that’s incredibly precise, especially when your equipment is a torn sheet of paper vs. the most accurate, sophisticated, and expensive scientific instrumentation of the day.

Fermi was famous for his simple approach to any and all problems, even before his torn-paper A-bomb powerometer. He was so significantly know for this that nowadays it’s often called the Fermi method. You may have also heard this concept referred to as BOTE (back of the envelope) calculations, guesstimate, SWAG (scientific wild-ass guess), etc. The phrase I heard most often in my schooling was “first approximation,” thus the title of this post. Unfortunately, in popular culture, most of these phrases have lost the rigorousness and accuracy which the concept actually embodies. This is not something you pull out of your ass; if done properly, it should get you within striking distance of the ponderously-calculated answer.

Because the Manhattan project was a government/military project, a career officer named General Leslie Groves was placed in charge. In an unfortunate juxtaposition of personalities, Groves was a micromanaging, toe-the-line, precision-in-everything, engineering-mentality kinda guy. That’s not bad per se but most of the folks he was now in charge of were more, ummmnn, theoretical than that. Take the brilliant Leo Szliard who was responsible for many breakthroughs in this field. Leo did his best thinking in the bathtub or on long walks. To a guy like Groves, lying in the bathtub for half a day was not an effective use of time. Except, of course, that it was.

One of Groves’ first interactions with the scientists was when he watched them brainstorming in a room and throwing equations on the chalkboard as they talked. He was shocked to see that there was a (minor) mistake in one calculation and he was appalled that they shrugged it off when he pointed it out. Groves and Fermi had a number of interactions like this, based on their different approaches to life.

When I think about those personalities and interactions, I always see Groves as one (or several) of my math teachers. He’s the kind of guy who’d give you zero credit on a quiz or homework for making a simple mistake in your number manipulation when you had successfully defined the problem and attacked it with the proper solution. On an infinitely more significant playing field than a school math class, here were the greatest geniuses of the age, solving a problem which had never been addressed, which was possibly unsolvable, and his input to the process of saving the world from the NAZIs is to correct their arithmetic and complain about their undisciplined work habits.

The original code names for the two test bombs (two because they were experimenting with two different types of atomic bombs) were “Fat Man” and “Thin Man,” ostensibly for the Dashiell Hammett characters. “Thin Man” was later changed to “Little Boy” but “Fat Man” was retained. Despite the official explanation, scuttlebutt maintained that “Thin Man” was named for Oppenheimer and “Fat Man” was Groves, and the former was an homage but the latter was a studied insult, referring not only to Groves’ physicality but also to his fat-headedness.

One reason why we unschool, one of many reasons, each of which has its own significance, is that I hope my children will be free enough to be like Enrico Fermi or James Brown rather than Leslie Groves or Arnold Schoenberg. I know I somewhat emulate Szliard in my bathing habits and Chloe does, too. I guess that’s something.

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