Other uses of the term
In science
Scientific theories are sometimes labeled "numerology" if their primary inspiration appears to be a set of patterns rather than scientific observations. This colloquial use of the term is quite common within the scientific community and it is mostly used to dismiss a theory as questionable science.
The best known example of "numerology" in science involves the coincidental resemblance of certain large numbers that intrigued such eminent men as mathematical physicist Paul Dirac, mathematician Hermann Weyl and astronomer Arthur Stanley Eddington. These numerical coincidences refer to such quantities as the ratio of the age of the universe to the atomic unit of time, the number of electrons in the universe, and the difference in strengths between gravity and the electric force for the electron and proton. "Is the Universe Fine Tuned for Us?", Stenger, V.J., page 3.
The discovery of atomic triads, an early attempt to sort the elements into some logical order by their physical properties, was once considered a form of numerology, and yet ultimately led to the construction of the periodic table. Here the atomic weight of the lightest element and the heaviest are summed, and averaged, and the average is found to be very close to that of the intermediate weight element. This didn't work with every triplet in the same group, but worked often enough to allow later workers to create generalizations.
Large number co-incidences continue to fascinate many mathematical physicists. For instance, James G. Gilson has constructed a "Quantum Theory of Gravity" based loosely on Dirac's large number hypothesis.
Wolfgang Pauli was also fascinated by the appearance of certain numbers, including 137, in physics.
British mathematician I. J. Good wrote:
There have been a few examples of numerology that have led to theories that transformed society: see the mention of Kirchhoff and Balmer in Good (1962, p. 316) ... and one can well include Kepler on account of his third law. It would be fair enough to say that numerology was the origin of the theories of electromagnetism, quantum mechanics, gravitation.... So I intend no disparagement when I describe a formula as numerological.
When a numerological formula is proposed, then we may ask whether it is correct. ... I think an appropriate definition of correctness is that the formula has a good explanation, in a Platonic sense, that is, the explanation could be based on a good theory that is not yet known but ‘exists’ in the universe of possible reasonable ideas.
In gambling
Main article: Gambler's fallacy
Some players apply methods that are sometimes called numerological in games which involve numbers but no skill, such as bingo, roulette, keno, or lotteries. Although no strategy can be applied to increase odds in such games, players may employ "lucky numbers" to find what they think will help them. There is no evidence that any such "numerological strategy" yields a better outcome than pure chance, but the methods are sometimes encouraged, e.g. by casino owners.