Over at Cosmic Variance, Sean Carroll has just posted a guest essay by Joe Polchinski replying to Lee Smolin’s response to Polchinski’s review of Smolin’s book. I managed to snag the first comment spot; I predict that Peter Woit will show up within ten. With any luck, the ensuing comments will contain much good talk about physics, though the signal-to-noise ratio is a perennial problem. (Even Sean admits that he doesn’t read every comment.)

I would like to skim past several details of the physics and pull out for special consideration a passage of Polchinski’s which concerns, ironically, what happens when you think in text instead of physics:

This process of translation of an idea from words to calculation will be familiar to any theoretical physicist. It is often the hardest part of a problem, and the point where the greatest creativity enters. Many word-ideas die quickly at this point, or are transmuted or sharpened. Had you applied it to your word-ideas, you would probably have quickly recognized their falsehood. Further, over-reliance on the imprecise language of words is surely correlated with the tendency to confuse scientific arguments with sociological ones.

Polchinski is speaking about the standards one must maintain while doing science, but similar concerns apply to the process of explaining science. Of course, the latter process is one ingredient in the former, but we often think of “popularizing” (or vulgarisation if we want to be Gallic) as a distinct enterprise from communicating with fellow researchers and educating the next round of students. John Armstrong’s recent post on this topic addresses the same question from the opposite direction: according to Polchinski, going from words to equations is the hard part of getting work done, while Armstrong points out that when “vulgarizing” the science, that’s the very step we omit!

Armstrong amplified his point in the comments here at Sunclipse:

Roger Penrose noted specifically in his introduction to The Road To Reality that modern physics is no longer accessible to anyone — specialists included — except through the mathematics. We understand quantum field theory as well as we do because we understand the mathematics. To avoid the mathematics in its entirely [sic] cuts the legs out from under any popularization of physics, and risks becoming The Tao of Physics or The Dancing Wu Li Masters.

A subject like the AdS/CFT correspondence is not just mathematical, but abstrusely so: not only do the individual statements we make require sophisticated jargon, but also the reasoning which connects one statement to another is mathematical in character. It seems to me that a duality between theories is among the hardest of physical notions to translate into “layman’s terms,” because one can’t appreciate a duality using words alone.

In The Character of Physical Law, Feynman gives an example which I’d like to appropriate. I can say that when a planet travels in its orbit, a line from the planet to the Sun sweeps out equal areas in equal times. I can also say that the force pulling on the planet is always directed toward the Sun. Both of these statements require a little math — “equal areas,” “equal times” — but it’s not really math, not a kind to give the layman heebie-jeebies. Given some time for elaboration, one could translate both of these statements into “layman language.” However, one cannot explain in lay terminology why the two statements are equivalent.

If planets looping around the Sun can give us so much trouble, imagine having to explain the relation between gravity in anti-de Sitter spacetime and conformal field theory. Even if you could cook up a lay explanation of either one, you’re hamstrung when you try to connect them. And if you don’t even have an analogy for the situation — if the meta-concepts of duality, equivalence, one description “reducing to” another are completely alien to you — how can you appreciate why the physicists find the situation interesting and why they want to work in that area?

[Three paragraphs added the following day] Another complicating factor is that one cannot reason about physics by thinking about the everyday meanings of words. In their dark comedy Intellectual Impostures, Alan Sokal and Jean Bricmont mention a social-studies friend of theirs who asked them, in quite a puzzled manner, how it was that quantum mechanics could say the world was both discontinuous and interconnected? Looking at the everyday meanings of these two words, they do seem rather inconsistent; at least, though we could twist and turn using various definitions of these terms, we should forgive anyone who at first glance takes them to be contradictory.

The short answer, Sokal and Bricmont say, is that scientists working with quantum phenomena do not use these words in their everyday senses, but give them meanings which depend upon a web of ideas, mathematical equations and experiments. (My best guess is that the social-studies person had heard about “entanglement,” which led to “interconnectedness,” while also receiving some garbled notion of “quantization,” the fact that systems like atoms come in states of different energies with nothing in between allowed.) One cannot think about physics as if it were a novel whose great themes were “chaos,” “probability” and “uncertainty!”

It would be like studying music by looking only at the descriptions critics gave in reviews: “bright,” “rich,” “brooding,” “colorful,” etc.

I think we find ourselves in the unhappy situation where no matter how informed the lay audience feels they are, they can’t render a reasonable judgment.

UPDATE (24 June 2007): The video of Feynman making the point I paraphrased above is now available ontube:
[VIDEO REMOVED FROM GOOGLE ARCHIVE]