Feeds:
Posts

## Jeff Shallit on Numerology at Eschaton 2012

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:

$\hbar c = \sqrt{10} \times 10^{-26}$

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).

### 5 Responses

1. on April 18, 2013 at 1:04 pm | Reply Jeffrey Shallit

Good points. Verified predictions and falsifiability are part of what separates numerology from science. Another example is Mendeleyev and the periodic table. He predicted the properties several elements on the basis of his classification, which ultimately depended on numerical patterns. But, unlike Eddington, his predictions were falsifiable and later verified.

2. on April 18, 2013 at 1:45 pm | Reply Jeffrey Shallit

Oh, and I can’t resist commenting on this, either:

The deeper we go into the laws of nature, the more remarkable simplicity we uncover.

Yes, but we see a lot of arbitrariness, too. For example, why is the fine-structure constant .0072973525698… ? Why does it have this precise value?

My guess is that we will never find any deeper theory that predicts this value.

3. Assigning significance which is dependent on base-10 representation is consistent with a strongly anthropocentric theistic view of the universe. By that I mean the following assumptions:

Assumption 1: the fact that we have ten fingers/toes is not a product of chance, but the result of the Creator’s predetermined intelligent design, i.e. lowercase i.d., meaning that it can be known at the Revelation and philosophical levels, but not at the level of the scientific method. (If positivists think that the only valid knowledge is that obtained via the scientific method, it is their problem.)

Assumption 2: the universe was created for us, i.e. humans.

4. If Professor Shallit cares to read about a highly speculative hypothesis for the meaning of the value of the fine structure constant (actually of its inverse), he can have a look at the article here:

http://christ-proclaimingft.blogspot.com

To his delight, dismay, or amusement, the article even gives as an added bonus a mystical meaning of the value of the strong coupling constant. And moreover, it does so on the basis of its decimal representation! What else could he ask for? (It is in a comment on reference [5] at the end.)

5. on May 23, 2016 at 3:09 pm | Reply Georgina Daneken

For my part, I remain unimpressed by Gel-Mann’s hocus-pocus. With or without the occult “prediction”, his “eightfold way” carries no explanatory force whatsoever, It is not science, but superstition thinly disguised.