I have a rule: if I see an article by Frank Wilczek, I read it. Wilczek is a particle physicist and Nobel Prize Laureate, and recently wrote on “Why Does the Higgs Particle Matter?” for Big Questions Online:
The discovery of the Higgs particle is, first and foremost, a ringing affirmation of fundamental harmony between Mind and Matter. Mind, in the form of human thought, was able to predict the existence of a qualitatively new form of Matter before ever having encountered it, based on esthetic preference for beautiful equations.
A nice talk from Jeff Shallit from Recursivity on numerology. I’m going to forward it to a guy who keeps emailing me about his “Final Formula” of physics:
which has the same problem with units that Shallit’s marvellous Washington Monument example does.
That said, there have been a few episodes in physics where something that looks alarmingly like numerology proved successful, such as Gell-Mann’s 8-fold way. Murray Gell-Mann plotted mesons and spin-1/2 baryons on a plot with charge on a horizontal axis and strangeness on the diagonal. The particles formed an octagon with two particles at the centre. He also plotted the spin-3/2 baryons, which formed a triangle, but with the apex missing. Gell-Mann predicted the existence of the particle that would complete the triangle, together with its strangeness, charge and mass. Two years later, it was discovered.
Is this really numerology? I’m not familiar with Eddington’s argument, but my suspicion is that the difference is in predictive power. Gell-Mann predicted the existence of a particle, its properties and was ultimately led to the quark model, whereas the zero-predictive-power of Eddington’s ideas were displayed by his easy switch from pulling 136 out of a mathematical hat to producing 137.
The moral of the story seems to a combination of the following:
While successful physical theories can predict relationships between physical quantities that would otherwise appear to be coincidences, searching for such coincidences in the absence of a deeper physical theory is not a good way to discover the laws of nature.
The deeper we go into the laws of nature, the more remarkable simplicity we uncover. The applicability of group theory and symmetry to particle physics is a good illustration of this.
The power of science comes not from its ability to make assumptions about nature, but the ability to test those assumptions and discard those that fail. That’s why this quote from Mark Twain about “wholesale returns of conjecture out of such a trifling investment of fact” only tells half the story of science. In particular, one must keep an eye on the relationship between the number of free parameters and the number of data points, so that we can tell the difference between prediction (where the data tests the model) and curve-fitting (where the data creates the model).
Letters to Nature 