Though this is primarily about mathematics, and there are some complicated equations, it is more about the philosophy of probability theory. One is presented with technical terms and headings such as: ‘De Finetti’s Theorem on Exchangeability’, ‘Kolmogorov’s View of the Infinite in Probability Spaces’, ‘Borel Paradox’, ‘Hard-Core Frequentism’, The Ergodic Hierarchy’, Boltzmann Redux’, ‘What about the Quantification of Ignorance?’
What interested me was the eighth chapter, ‘Algorithmic Randomness’, which begins by stating something that a mathematics student told me years ago, that computers that generate supposedly random numbers do not in fact do so. This raises the much larger issue, that probability theory is entirely based on the assumption that it is dealing with random events. This is often dubious. The authors do quote the first ever writer about probability, Geralomo Cardano in the sixteenth century, who sometimes made a living at gambling, and “knew about shaved dice and dirty deals”. The first English language book on rigged dice appeared as long ago as 1553.
This uncomfortable fact has many implications. The basis of the science of population genetics is the Hardy-Weinberg Law, which assumes “a random-mating population”. In human terms, this would mean that there was no tendency of Jews to mate with other Jews, for instance. This is obviously not true, and it is doubtful if it is true for other living things, either. Even in the case of plants that mate by cross-pollination, for all we know, the insects that perform this function for them may prefer one species of flower to another. The whole subject rests upon this shaky foundation.
In a similar way a Scientific Ufologist, whose name I forget, said something to the effect that, anyone who can believe in ‘repeaters’, that is, people who have had several UFO sightings when most of us have not had even one, cannot know anything about statistics. This man, whoever he was, had missed his vocation as a population genetics theorist.
To take analogies: after my mother died, her cousin stayed in her house for three months. She remarked to me that there were a lot of airplanes going overhead. Since my late mother’s home lay directly under the approach path to Birmingham International Airport, this was hardly surprising. But her cousin normally lived in the Llyn Peninsula, which is fifty miles from the nearest airport, and that only a small one, so she was not used to them. There is nothing odd about the fact that rare birds are mostly spotted by ornithologists.
As I write, the news comes of the death of Guy Lyon Playfair. I never knew him personally, but I knew him well by sight, as he lived not far from me in Earls Court, probably in Lexham Gardens, which is where I most often passed him. I do not suppose that the average person has had even one sighting of this particular psychic investigator. The same kind of factors that govern sightings of identified objects may also be present with the unidentified. There are obvious reasons why, whatever UFOs may be, some people might be much more liable to see them than others. Rare atmospheric phenomena, which probably account for at least some UFO reports, may only occur in certain areas. If aliens are secretly surveying the earth, then it is unlikely that they do so completely at random. – Gareth J. Medway