This post was updated on 17 August 2022.
I have provided accounts of five striking coincidences over my lifetime. The five events individually have odds in the range 10-9 to 10-18. What are the odds that all five coincidences could happen to one individual? The answer is that the odds are way off the end of the chart. Here’s why.
To determine the probability of five independent events, A, B, C, D and E, all occurring, we need to multiply the probabilities of the individual events:
P(A and B and C and D and E) = P(A) × P(B) x P(C) × P(D) x P(E)
The five coincidences, which were independent of each another, are as follows:
A) The Chiswick Coincidence: P=10-18 = one chance in 1,000,000,000,000,000,000 = one in one quintillion (a million, million, million)
B) Coincidence or Luck?: P = 10-10 = one chance in ten billion.
C) Citizen 63 – Marion Knight: P= 2.225 x 10-10 = 2.225 chances in ten billion
D) The Flying Horseshoe: P = 1.3 x 10-12 = 1.3 chances in a million, million
E) Under the Wallpaper: P = 2.5 x 10-9 = 2. 5 chances in a billion
In the distributions of chance and non-chance events suggested in an earlier post, the five events A to E would have the positions indicated in the diagram below.
The combined probability of the five events is :
P = 10-18 x 10-10 x 2.25 x 10-10 x 1.3 x 10-12 x 2.5 x 10-9
P = 7.3125 x 10-59
This is one of the smallest probabilities imaginable. The odds are so extreme it is necessary to extend the above diagram to encompass odds of up to 10-59 and beyond.
Yet, according to the accepted scientific theory, coincidences are chance events, and so there is nothing extraordinary here.
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Update to include a sixth series of events
A sixth series of events – series F – of a personal nature is estimated to be on a par with the Chiswick coincidence. Series F also has an odds of 10-18 .
The combined probability of all six coincidences is P = 7.3125 x 10-77
Surely, this is one of the smallest and most significant probabilities in the history of this topic.
What the heck is going on here?
The above figure of 7.3 x 10-77 ignores the fact that the Chiswick Coincidence led to a correct prediction: my visit to the public house that afternoon would lead to an event that precognitively matched a key feature of Chesterton’s original story. Purely by chance, I encountered a gentleman there who would later invite me to become a member of a Secret Society to which he belonged. Incredible though this must sound, this is what actually happened.
On the terrace directly facing the river, the very spot where the tug would have taxied away Chesterton’s two main characters, a total stranger was sitting with his wife at the next table. It later emerged that this gentleman was a Freemason and, at a subsequent meeting, he invited me to join this society. I was taken aback by this turn of events but I declined his kind offer. Essentially I am too contrarian to be clubbable and I find the rituals all too silly for words.
The significant fact here is that I was actually invited to join this distinguished Secret Society, not the fictitious anarchist organisation of Chesterton’s imagination, but the real McCoy. It is impossible to give a precise estimate of the odds that I would meet a gentleman who would later invite me to join the secret society of Freemasons. I hazard to guess this has a chance in the region of one in a million. If we add 10-6 to 10-77 we end up with 7.3 x 10-83
This combination of extraordinary events in the life of a single individual leads that individual to wonder, what the heck is going on here?
How long are the odds 7.3 x 10 to the minus 83?
Here is a photo taken by NASA of the Milky Way
Courtesy NASA/JPL-Caltech
Nobody knows for certain, but it has been estimated that there are at least 100 billion planets and 400 billion stars in the Milky Way. That’s 100,000,000,000 and 400,000,000,000 respectively, i.e. 10 to the power 10 and 4 times 10 to the power 10 (using the short scale).
The odds of the six events described above are longer than the total number of stars in eight Milky Ways all multiplied together.
Another interesting reference figure is the number of galaxies in the observable universe. This number is estimated to be two trillion, i.e. 2,000,000,000,000, or 2 x 10 to the 12th power (on the short scale). Let’s call this figure ‘U’.
The odds of the six coincidences all occurring to a single individual are equal to one in U x U x U x U x U x U / 16. That’s two trillion multiplied by itself six times and then divided by 16.
According to accepted scientific theory, coincidences are purely chance events, and so nothing extraordinary happened here.