Kant considered that thinking by analogy had no role in science whereas Herder considered it did. Apparently, for this reason Kant thought that biology [natural history] could never be a real science. Thinking objects were fundamentally different from non-thinking objects.
One of the reasons I like going to these seminars is that they stimulate my thinking in new directions. For example, a seminar last year helped me understand that one of my "problems" is that I view science as a vocation rather than a career, perhaps in the tradition of Robert Boyle and the Christian virtuoso.
After the seminar I had a brief discussion with some of my history colleagues about what scientists today think about analogy. I think it plays a very important role, because it can help us understand new systems and phenomena in terms of things we already understand. But where people sometimes come unstuck is when they start to assume that the analogy is reality or the complete picture. Here are a few important historical examples.
* Electromagnetic radiation. The analogy of light waves with sound and water waves helped. But went array when people thought there must be a medium, i.e. the aether.
* Quantum mechanics. Particles and waves. Again the analogy helped understand interference and quantisation of energy levels. But I also think that pushing to hard the partial analogies with classical mechanics and classical waves is the source of some of the confusion about quantum measurement and the quantum-classical crossover.
* Quantum field theory and many-particle physics. Feynman diagrams, path integrals, renormalisation, symmetry breaking, Higgs boson,…. there is a lot of healthy cross-fertilisation.
* Imaginary time quantum theory and classical statistical mechanics. Path integral = Partition function.
Coincidentally, yesterday when I was in the library [yes, the real physical library not the virtual one!] trying to track down Wigner's quote I stumbled across a 1993 Physics Today review by Tony Leggett of Grigory Volovik's book Exotic properties of superfluid 3He. Leggett expresses his reservations about analogies.
As to the correspondences with particle physics, being the kind of philistine who does not feel that, for example, his understanding of the Bloch equations of nmr is particularly improved by being told that they are a consequence of Berry's phase, I have to confess to greeting the news that the "spin-orbit waves" of 3He-A are the analog of the W boson and the "clapping" modes the analog of the graviton with less than overwhelming excitement. These analogies no doubt display a certain virtuosity, but it is not clear that they actually help our concrete understanding of either the condensed matter or the particle-physics problems very much, especially when they have to be qualified as heavily as is done here.What do you think? Does analogy have an important role to play? When does it cause problems?