Tuesday, April 8, 2014

What role does reasoning by analogy have in science?

Two weeks ago I went to an interesting history seminar by Dalia Nassar that considered a debate between the philosopher Immanuel Kant and his former student Johann Gottfried von Herder.
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?


  1. I won't miss the opportunity to plug my work and ours, where we have made use of analogies between the active orbitals of molecules to derive parametric Hamiltonians that can be applied to families of similar molecules.

    This is just another example of the utility of orbital analogies in chemical models. A great example is also Hoffman's isolobal analogies between organic and inorganic chemical reactions, which are summarised and put well in context by Shaik's article:
    Shaik, S. Is my chemical universe localized or delocalized? is there a future for chemical concepts? New J. Chem. (2007).

    There are also examples of over-analogising to be found in chemistry. A good example might be the use of multi-parameter free energy relationships, and the attempt to use these to distinguish i.e. "resonance" vs. "inductive" substituent channels. It seems that only limited analogies are useful at a time: the one-parameter Hammett equation is enormously successful, but the insight per additional parameter declines precipitously beyond 1.

    1. Hi Seth,

      Thanks for comment. I tried to think of some chemical examples.

      One case where the analogy has been problematic has been the analogy of "resonance" between oscillators and valence bond states. This seems to have only caused confusion.


      Furthermore, it is not helpful today because most students are unfamiliar with coupled oscillators.

  2. I think one can't answer the questions about whether such analogies are "helpful" until first decided what one is trying to do. Is one trying to understand the phenomenon at the phenomenon's own level? Then indeed much of the time these analogies (say between particles and many-body condensed matter physics) are frequently not super helpful. A case in point, is recent work of ours understanding some interesting bound states between domain walls in a ferromagnetic Ising chain compounds. There is analogy that one can make between their linearly confining potential and the linearly confining potential between quarks in a meson. But making this analogy doesn't really allow you to understand either system much better (as we were told correctly by a referee when making this analogy). But I think many of us in physics feel a deep fascination with the fact that the same physics is repeated over and over again in different contexts in different parts of physics. See the Higgs mechanisms in the LHC and the Higgs mechanism in superconductors for a prosaic example and the examples given typically by Volovik for more exotic ones. This repeated physics arise from the dependence on the general distinctions between long and short range forces, symmetries, dimensionalities etc. In this sense these analogies "help us" be even more fascinated with what we are doing.

    1. Hi Peter,

      Thanks for another insightful comment.
      You have an excellent point: even if analogies do not lead to new insights they can be enjoyable and motivational.

  3. PS... I haven't forgotten I owe you a reply to an email Ross.

  4. I think analogy is very important, sometimes when I do not understand something, analogy can help me to solve my problem, but when I write my paper, the analogy is not written in the manuscript, because the reviews do not believe the analogy, because they do not think the analogy is rigorous.

  5. There was a long book published very recently on this subject of analogy by Douglas R. Hofstadter and Emmanuel Sander. The English version is called: SURFACES AND ESSENCES Analogy as the Fuel and Fire of Thinking. It is not on the role of the analogy in science per say, but more generally.

    There was a very interesting hour long recent radio program with Emmanuel Sander on the subject. Unfortunately for most reader of this blog I guess, it was on a french speaking station. Anyhow, I copy the link to listen to it for those who understand french and are interested.