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Rare events happen all the time!

Ali Hyder Mulji

If you rearrange the letters in the word William Shakespeare you can spell ‘here was I like a psalm’. In the book ‘King James Bible’ in Psalm 46, the 46th word is ‘shake’ and the 46th word from the bottom is ‘William’.  Coincidence…? Yes!

The Banality of Improbable Events.

It is funny to think how improbable events leave us mystified but it is important to understand that the amount of data humans have is massive and if you look long and hard such events will be found easily.

The book ‘Futility’ also known as ‘The Wreck of the Titan’ describes a 800ft long ship with four funnels and three propellers and not enough lifeboats to save all the passengers. The ship was believed to be ‘practically unsinkable’. It was the largest ship in the world with the finest luxuries and a handpicked crew. The ship hit an iceberg in the North Atlantic, broke in half and sank, killing most of the people on board. Few of the survivors were carried to safety by a steamer that reached the spot later.

One might think the book was based on Titanic because of its uncanny similarity but this book was actually written fourteen years before the actual Titanic sank. The book even described the orchestra that continued to play as the passengers dived into the chilling water.

Again, this is a mere coincidence just like the movie ‘contagion’ which many claimed, predicted the coronavirus. It is hard to imagine that these occurrences have no real connection to each other but with a few examples we can see how ‘improbable things happen all the time’.

Creating a Rare Event: The Baltimore Stockbroker.

The Baltimore Stockbroker is a story of the broker who could predict exactly where a stock would move in the market. This may sound fishy but the Baltimore Stockbroker only asked you to put in a large sum of minimum investment if he got ten correct predictions in a row. Obviously, if someone can predict where the stock moves ten times in a row anyone would believe in him. 

However, just like our other two events, this was merely the mathematics of coincidence. 

The Baltimore Stockbroker would send out a letter to 10000 prospective clients. 5000 of them would say that a stock will go up and the other 5000 would say that the stock will go down. Obviously, after a week the stock will have moved in either of the two directions. If the stock moved up, the broker stopped contacting the ones who received the letter which said the stock would go down and continue contacting the ones who received the correct prediction.

Now, the broker would repeat the same exercise and send a letter to the remaining 5000 people. 2500 letters said the stock would go up and the other 2500 said that the stock would go down. Naturally, the stock moved in one of those two directions. This exercise was continued ten times every time leaving the broker with half the number of prospective clients. 

After 10 cycles, some people will have received 10 correct predictions and those (no matter how few) were ready to hand over a large sum of money because they believed in the brokers ability to predict. With a sufficiently large number of trials you will eventually arrive at your desired result (In this case, 10 correct predictions)

Equidistant Letter Sequences (ELS)

ELSs are another tool that people enjoy using to either fool others into believing something or fool themselves into getting entrenched in their own preconceived notions. Equidistant Letter Sequences are obtained by picking up one letter after a fixed number of letters to form a meaningful sentence. For example, I can make an ELS by picking a letter after every 50 letters from a novel and try to make a meaningful sentence. 

Eg: If I take every fifth letter starting from the first in the following sentence:


The ELS will be DUCK.

Some rabbis used ELS to find secret messages in the Torah which they believed were sent by God. Unsurprisingly, they found several ELSs that predicted assassinations and major world events. The same process was repeated by another Catholic mathematics enthusiast to find messages in the Bible and claimed that it predicted the great war, therefore proving that God exists. You would think an omnipotent being would pull off something more spectacular to mark his presence than send secret messages through a book.


The crux of these practices is that if you try a sufficiently large number of combinations, by increasing your data you are sure to find some random sentence which will relate to another random event that occured in history or will occur in the future. This is the foundation on which fortune-tellers and astrologists make their living. In other words, it’s just a coincidence! As the volume of data increases so does the number of coincidences. It can be thought of as an extension of rare events that we experience in our usual lives like meeting someone with the same birthday as yours or dying on your birthday.


Published by mscnm

Add some excitement, Minus the boredom, multiply your skills, divide the stress. Math is an integral part of our lives, so connect with MSCNM where the fun is derived

6 thoughts on “Rare events happen all the time!

  1. Ali, this has to be your best best work. So so interesting. ❤️❤️ This will also explain the theory where the show Simpsons keeps predicting stuff in the future!


  2. This was such an interesting blog!! Absolutely loved reading this. Never knew that rare events can be predicted without luck but pure maths


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