A tension arises here between intuition as somatic tacit knowledge, and the sociological de nition of knowledge discussed in Chapter 1, where it was claimed that, sociologi- cally, personal knowledge is of no consequence to sociology. Certainly, one would be forced to admit that somatic tacit knowledge as such has no apparent sociological di- mensions, it being of an individual nature, but there are several reasons for supposing that even at this deep personal level the in uence of sociological factors is deep. In the training of young theoreticians, although the acquisition of intuitive skills is a personal affair of practical immersion, this immersion is ideally guided by a recognised expert who directs the novice in the right direction of performance. A notable result of this training method is that the novice does not just learn to solve problems, but acquires
See Polanyi (1966, p. 12-16), Wittgenstein (1953, § 626) and Merleau-Ponty (1945, p. 143). See the Editor’s Introduction in Merleau-Ponty, Maurice & Baldwin T. (ed.) (2003).
his own style of doing so which echoes the teacher’s predilections:
Romero: e way [teaching at research level] is done is like this. You talk to your student about a particular problem. Typically when you are start- ing out you have a tutor who talks to you about a problem you don’t un- derstand, and sometimes even he does not understand it! Maybe he half understands it. And he leads you towards a point where you can try to solve it. But typically, he will show you things that he himself knows how to do. He knows how to do it because he’s tried it out for other things, and he advises you to also try out the same thing. Now that I’m on the teaching side, I know that one does it with the hope that the student will turn out to be a real jewel and that he’ll be able to do something that you yourself weren’t able to do treading the same roads that you yourself once took. It really is like being an artisan’s apprenticeship. Although maybe even arti- sans are more professional than us since they’re more systematic. It’s an artisan learning process. (emphasis added)
us a theoretician will generally try to tackle a theoretical problem with the ‘tools’ he is most adept at, and these are naturally those that were learnt in his early research career. As Romero also mentioned, it is not altogether rare that despite knowing plenty of methods, theoreticians will ght to frame the problem so that it can be tackled with the tools they are most pro cient in:
Romero: If you learnt for example a lot about Laplace transforms in your PhD…we had a postdoc mate whom we made a lot of fun about. We’d joke and say, “hey, ask this guy how to solve a problem and he’ll tell you to rst do the Laplace transform.” You’d ask him and really, he’d say, “what if you take the Laplace transform rst?” He was such a good problem solver. He’d arrange the problem so that he’d be able to take the Laplace transform and he’d then have the equation. Others, they choose the Green’s function approach…everything is Green’s functions! For other everything is some other [mathematical] method.
Everyone learns particular tools, at a very early age I think, typically when your mind is still fresh. You base yourself on those tools, and you reduce
all problems to a usage of those tools. [Some theoreticians] reduce every problem to the same thing. [A] reduces every problem to a transfer matrix problem, or a dispersion matrix. [B] reduces everything to a transfer ma- trix. ey reduce every problem to obtain the same equation so that they can then do what they know how to do.
One tackles problems that can be handled through the things that you learnt know how to do; not necessarily problems that one thinks are im- portant. is is typically how one carries on. Technique is learnt at an early age, during your PhD or your postdoc, or the rst years of your pro- fessional career when you are open to learn new things, new techniques.
e content of a theoretician’s mathematical tool bag is thus shaped by his early ca- reer, though Romero did not mention whether this is a conscious phenomenon or not. It may well be that this combination of a ‘natural’ way for a theoretician to grasp a prob- lem tinged— a theoretical ‘style’— marked by the tradition that the theoretician grew up in has mixed elements of both the somatic and the collective tacit. Berry likewise re ected on how the content of his mathematical ‘bag of tricks’ was deeply in uenced by work with his PhD supervisor:
Berry: I like asymptotics and divergent series; I’ve worked a lot on them. So the tools, I like the tools; using the tools. ere’s that, and it’s an area where I can do something; there’s a fair amount of space […] It’s hard to be speci c why you like something; why you do something. Maybe histor- ically I was in it too. My PhD supervisor who just died— Bob Dingle in St. Andrews— he made utterly seminal contributions to understanding divergent series. […].
Underlying a lot of what we do are tools. And a lot of tools have to do with divergent series. One of my favourite tricks is the Poisson summation for- mula. at’s a formula for evaluating sums. And it relates a sum to another sum where the quantities in the second sum are the Fourier transforms of the ones in the rst sum. I encountered it in a paper decades ago and then I very quickly realised— but don’t ask me how because I don’t know— that this is a very general notion and it replaces a sum over quantum num- bers (one sum) by a sum over topologically different classical paths (that’s
the other sum) and this is a very valuable duality and I’ve applied it to a half a dozen different problems over many years, and it keeps being useful and it gives a huge amount of insight. So that’s another trick. So I don’t know where they come from. Asymptotics I learnt from my PhD supervi- sor Dingle, I mentioned that. He sensitised me to asymptotics.
us, although the development of the tools is a personal process, the guidance of a novice’s tool selection is determined by his senior mentor, the research group he is immersed in, and the traditional tools which are mastered within this tradition. ere are a few important historical studies that have concentrated on the development and dispersion of such theoretical ‘tools’ and the traditions and institutions which these spark, the most detailed being Kaiser’s on Feynman diagrams, with smaller work on the dispersion of General Relativity.⁴ As Kaiser (2005b) sums up the corpus of his studies on Feynman diagrams,
As physicists recognised at the time, much more than published research articles or pedagogical texts was required to spread [Feynman] diagrams around. Personal mentoring and the postdocs’ peripatetic appointments were the key. Very similar transfer mechanisms spread the diagrams to young theorists in Great Britain and Japan, while the hardening of the Cold War choked off the diagrams’ spread to physicists in the Soviet Union. Only with the return of face-to-face workshops between American and Soviet physicists in the mid-1950s, under the “Atoms for Peace” initia- tives, did Soviet physicists begin to use Feynman diagrams at anything re- sembling the pace in other countries. […] us it remains impossible to separate the research practices from the means by which various scienti c practitioners were trained.