Partly because it has some interesting examples of thick and thin problems, but mostly because it’s so damn much fun, I’m going to talk about The Wizard War, by R. V. Jones.
Reginald Jones (Ph.D. Oxford, 1934)was one of the first scientists to work for an intelligence service. He investigated German radio navigational systems and developed various methods of interfering with them, which often involved projecting the German’s next move in the electronic war. He was one of the developers of ‘chaff’, and also served as an expert consultant on the development of German rocketry – mainly the V-2.
Some of his successes were classically thin, as when he correctly analyzed the German two-beam navigation system (Knickebein). He realize that the area of overlap of two beams could be narrow, far narrower than suggested by the Rayleigh criterion.
During the early struggle with the Germans, the “Battle of the Beams”, he personally read all the relevant Enigma messages. They piled up on his desk, but he could almost always pull out the relevant message, since he remembered the date, which typewriter it had been typed on, and the kind of typewriter ribbon or carbon. When asked, he could usually pick out the message in question in seconds. This system was deliberate: Jones believed that the larger the field any one man could cover, the greater the chance of one brain connecting two facts – the classic approach to a ‘thick’ problem, not that anyone seems to know that anymore.
All that information churning in his head produced results, enough so that his bureaucratic rivals concluded that he had some special unshared source of information. They made at least three attempts to infiltrate his Section to locate this great undisclosed source. An officer from Bletchley Park was offered on a part-time basis with that secret objective. After a month or so he was called back, and assured his superiors that there was no trace of anything other than what they already knew. When someone asked ‘Then how does Jones do it? ‘ he replied ‘Well, I suppose, Sir, he thinks!’
West Hunter 
Grant McCracken, “Noticing 101”:
http://cultureby.com/2006/10/noticing_101.html
When I saw that he is from Aberdeen, I understood that he is (was) _the_ Jones, who experimentally established rotary ether drag: rotary analog of longitudinal Fiseau ether drag,
and transverse Fiseau effect.
E. Fermi made previously two mutually compensating errors, while calculating rotary ether drag; Jones and his student of the time, Michael Player, have corrected Fermi.
Great guy Jones !
Respectfully, F.r.
I have nothing to say about cryptographic achievements of Prof. Jones.
Therefore I would like to praise his achievements in Physical Optics.
First, let me make a step aside.
Most people, even professionals, confuse two different properties
of our { 3D+time } Universe:
a) invariance of 3D space with respect to shift in space (w. r. to translations), and
b) invariance of { 3D+time } Universe with respect to transition to a new frame, which moves with constant velocity relative to the old frame.
The first property, a), is called homogeneity of 3D space.
The second property, b), is called Galileo-invariance of Newtonian Mechanics (NM), if velocity of frame is much smaller than speed of light in vacuum; otherwise it is called Lorentz-invariance of Einstein’s Special Relativity Theory (SRT.)
Both properties, a) and b), have something to do with “momentum”.
Property a) leads to momentum conservation both, in NM, and in STO.
Property b) leads to steady motion of Center of Mass in both cases, NM, and SRT.
By the way, any statement, or mathematical theorem, seems to me (F.r.) bland, i.e. not spicy enough, if a counter-example (of violation of the statement) is not provided.
Property a) is violated for the motion of an electron in crystalline lattice; hence the notion of Bloch’s quasi-momentum.
Property b) is violated for the sound motion in a liquid: a liquid is at rest in a certain coordinate frame only. Property b) is also violated for {single Brillouin zone} description of electron’s motion, this violation manifests itself in non-parabolic dependence of energy on momentum.
Our { 3D+time } Universe _is_ invariant with respect to rotation of coordinate frame.
This property is called isotropy of 3D space.
However, there is no invariance with respect to transition into rotating coordinate frame
(repeat, there is no such invariance.) Experiment with Foucault pendulum has demonstrated the existence of additional, “Coriolis” force of inertia, in rotating frame.
So it took considerable scientific courage by Jones to study rotary ether drag, i.e. drag of polarization of light by fast-rotating piece of glass.
Yes, he did it: Jones was the first to observe this rotation of polarization.
Bravo to Professor Jones (29 September 1911–17 December 1997), FRS.
Getting back to von Neumann and ‘genius’, it would seem that a genius, or old style and I think more accurately, someone with a genius for something, is someone who takes what is thought of as a thick problem, and comes up with a thin solution to it, converting aforesaid thick problem into a thin problem. I’d say that’s more or less what guys like Newton, Einstein, and Darwin I guess, did. Also, it makes it somewhat difficult sometimes to appreciate what it is exactly what they did, since in order to understand it, one must forget, at least temporarily, their ‘thin’ solutions, in order to appreciate how ‘thick’ the problems were before they put their minds to solving them, since we learn the problem as the ‘thin’ one that is there after it’s been solved.
Just for an example I don’t think that one would learn the state of the physics of electricity and magnetism when Faraday was Mr. Electricity, given that Maxwell changed everything, we learn Maxwell’s end product, so it’s hard to appreciate exactly what it was that he did.
Problems solving ability is about connecting dots. In medicine, such ability is critical to make correct diagnosis and treatment. Dumb physicians ordered most uneeded tests due to their studipity. On the other hand, some smart doctors order uneeded tests knowingly due to defense medicine (to protect litigation).
Deductive reasoning seems also about connecting dots too.
j mct
Yes, I think that is a good point. A genius reduces a mass of data to a simple meaning. I think your example works best for Darwin.
That was my point in the previous discussion about what genius or brilliance is in the social sciences (on the Thick and Thin discussion). It is naming something that badly needed a name.
The only caveat I would add is that the discussion of “thin” here seems to imply that a lot of deduction or analyis is needed. But, in reality, the solution can be quite simple conceptually. Einstein claimed that his answers were not that difficult conceptually, and certainly Darwin’s insight was not that complex an idea in itself. (Although both these ideas can lead to a lot of mathematics.) It is rather that Einstein and Darwin had the key insights and then ruthlessly worked out all the implications. I imagine that Ricardo (I am no economist) did something similar for international trade and then of course there was Malthus himself.
I have a friend who is a tenured proffesor who was punished (not given a raise) because he successfully expanded his area of expertise. He was told he was not supposed to do that, that was not how things were done, you stuck in your specialized niche and you didn’t stray from it. Sad really, what Jones believed, the the larger the field any one man could cover, the greater the chance of one brain cionnecting two facts appears to be obvious. But to the powers that be in acedemia the obvious is negotiable. Thanks for the plug of a book that sounds very much worth reading.
It really is well worth reading.
This thick/thin description is rather fitting in light of stoke’s theorem.
Dear Tony !
Can you elaborate ?
Your F.r.
Systems that are sufficiently internally consistent can, in many cases, be fully understood by measuring a continuous property of some boundary containing them. Stoke’s theorem is a mathematically rigorous use of this tendency as it applies to EM. AdS/CFT correspondence might also be similar.
The fact that a sufficiently high energy EMP won’t penetrate a comparatively sparse Faraday cage is an example of this. If a problem is obvious enough, you only need to
work it out in wireframe to prove it.
Note: A good mathematician would eat me alive for suggesting this. I’m anticipating something similar from Greg, but perhaps not.
Tony’s clarifications are read with gratitude by F.r.
Thanks 🙂
May find this interview interesting. Is related to this topic.