Physicist Amok

To start, a question: why are the expositions of Landau and Lifshitz compelling? Here are ten volumes, without data. Compare them to any number of disastrous texts with an equal amount of data. Why does Landau & Lifshitz leave us credulous and so many others make us peery?

I think the answer is physical intuition. Chapters one and two of Mechanics set forth are a reference on physical intuition. A physicist believe the world has this shape, or one near to it, no matter what object we embed. For the next four volumes we get physics justified only from this intuition, and then the first chapter of volume 5 - Statistical Physics - hammers in the next piece of intuition: here is how many particles behave. The road forward is probabilistic.

These are the preconceptions a physicist carries with him into biology, where at first they seem to fail him. Some physicists become cynical and jettison this baggage (often at the behest of some biologists). Others refuse and build models that fail, fail, and fail again.

Step back for a moment. Imagine a physicist who has internalized the intuition in Mechanics but not in Statistical Physics. What is his fate? Feynman tells us (Feynman Lectures on Physics, vol.1, p.39-2):

“Anyone who wants to analyze the properties of matter in a real problem might want to start by writing down the fundamental equations and then try to solve them mathematically. Although there are people who try to use such an approach, these people are the failures of the field; the real successes come to those who start from a physical point of view, people who have a rough idea where they are going and then begin by making the right kind of approximations, knowing what is big and what is small in a given complicated situation.”

In other words, don’t neglect the first chapter of Landau and Lifshitz, vol.5.

What must we bolt onto our intuition to handle biology? The key is in Dobzhansky’s statement “Nothing in biology makes sense except in the light of evolution.”

A biologist tells a physicist, “When you have enough of X, this happens.” The naive physicist takes this literally: there exists a concentration of X at which something physically happens. But the mechanism in question probably exists in several related species, from different environments, all of which rely on similar versions of X. X probably is transcribed at different levels, into a different environment, and yet the system functions roughly the same.

More importantly, the system had to evolve, and the system had to function in all the environments leading up to the present. This is what we must add to our intuition. Exact fixed points and thresholds don’t happen. Now when we hear, “When you have enough of X, this happens,” from a biologist we filter it to, “In a bunch of organisms and places, some level of increase of X causes this to happen.” We do this with (as-is) absurd statements about mechanics and ensembles of particles every day.

This can be made rigorous in the same way as the pieces of Landau and Lifshitz. I suspect that evolutionary game theory of some form may be the proper language to express this.

What follows is abject navel gazing.

I originally studied physics. I did a lot of mathematics. I dabbled in computer science (and programmed a lot, which is something else). Now I’m immersed in biology. What do I call myself when someone asks?

These days, a mathematician.

This strikes me as odd: I don’t define my occupation by what I work on. But I think I finally understand why.

Here is the best definition I know of a physicist: someone who has been through Jackson’s E&M. If you survived it, you cemented a mindset shared by a community. In physics, everything is about time series. Anything not about time series is a statistical property of a time series.

In biology — not biophysics — trees are the natural unit. The logic of genetics deals in trees. Time series are awkward and dangerous. If we go to behavior and psychology, even the tree is inadequate.

After I settled into biology, I found myself with two deep mental frameworks, one next to the other. I spend a lot of thought trying to mesh them, and I have not yet managed it.

But wait! This is half of mathematics. Gian-Carlo Rota pointed out that axiomatic frameworks in mathematics are a sort of “hardware” for a “software” of mathematical facts. Lisp wizards who think of programs as abstract, nigh Platonic objects will interpret this the way I mean it; I hesitate to throw this analogy to anyone used to a FORTRAN descended language. A new mathematical fact is desirable; a new framework that brings known facts closer to trivial is just as novel. It itself is a mathematical fact. This way lies category theory.

The scientific equivalent of a stateless expatriate is a mathematician.

The authors of Real World Haskell just posted the first drafts for reviewers, including me. Much of the book is spent trying to explain simple concepts, while addressing the subtleties that result from Haskell’s shorthands and abstracctions. Something occurred to me as I was reading: the easiest way to learn Haskell is to learn some Lisp.

But not traditional Lisp. This Lisp is lazy, has nothing but symbols, lists, and tuples, and enforces the type differences among them. There is a let form but no define, certainly no setq. It’s lambdas are curryable. The whole realm can be explored, its lessons learned, in a couple of days.

It’s a useless language, except for its purpose. It is Limbo to Haskell’s Inferno — not Haskell itself, but sitting on the edge, where the virtuous of the past go who did not survive to the monadic revolution…

After developing the patterns of lists and lambda calculus, and the basic habits of strong typing, in this realm, the first descent into Haskell is fast. In ten minutes, you discuss the slightly changed notation, point out that we have entirely hidden the underlying cons structure of the list, and arrive at the type system.

Now the type system is an obvious extension of a habit to handle this new, more complicated world. The first unexpected structure is the algebraic data type, a transformation of a piece of BNF. I think this is the only place in computer science where the BNF is the clearest way to teach something.

Then there’s a bumpy half an hour about the syntax for defining functions, a period of clarity in general but confusion in detail about type classes, and then you arrive at

MONADS

And I don’t know how to make this one easy. sigfpe has made the beginning clear, but the rest is still obscure.

On the other hand, if a newcomer picked up a book on Haskell and was told that they were going to spend two chapters learning a dialect of Lisp they would never use again, it might not sell well.