The Improbability Principle: Understanding Coincidence and Chance in Everyday Life

An old woman had just lost her husband. I spoke to her on the phone. While I was talking to her, she mentioned that a butterfly flew into the room. The butterfly landed on her late husband's watch in front of her. She let out a cry of wonder and said, “This can't be a coincidence! The butterfly was his favorite animal. He comes to greet me.” 

I could understand her reaction and did not contradict her. But David J. Hand's book “The Improbability Principle” offers insight into why events we think cannot be a coincidence are more common than we think and why our intuitive responses are often misleading.

The five principles of improbability

Hand introduces the improbability principle: the principle that extremely improbable events occur  regularly due to underlying mathematical laws. He explains this on the basis of five principles:

Law	Explanation	Example
The law of inevitability	Something has to happen if there are enough opportunities.	Suppose you roll a die a thousand times, then it is almost certain that there will be a series of six identical outcomes. Although any particular sequence is highly unlikely, it is inevitable that such a sequence will eventually occur given enough attempts.
The law of large numbers	With enough attempts, rare events will occur.	So many people live in a big city that almost every day there is someone with an extremely rare disease.
The law of selection	We mainly notice the most striking events and forget the mundane ones.	The news often reports about plane crashes, but not about the thousands of safe flights. This makes plane crashes appear to occur more often than they actually do.
The law of leverage of probability	Small changes can cause big differences in probabilities.	In a lottery with one ticket, the chance of winning is minimal, but if you buy a thousand tickets, your chance is considerably greater. Although the chance still remains small, the increase is significant.
The law of 'almost enough'	Similar events are often considered identical.	Different forms of lottery winnings are often seen as one type of event, which makes them seem more common.

Correcting misconceptions

Understanding these principles is important because it helps us better deal with seemingly impossible events.

1. Avoiding incorrect conclusions: When we experience a very unlikely event, we tend to think that there must be a deeper meaning or supernatural force behind it. Hand's principles show that such events are often simply the result of probability on a large scale.
2. Promoting rational thinking: By understanding how these principles work, we can deal more rationally with chance and uncertainty in our daily lives.
3. Reducing superstition: Knowledge of these principles can help reduce superstition and irrational beliefs that often arise from misunderstood coincidences.
4. Better decision-making: In many professions, from finance to medicine, an understanding of probability is essential. These principles can help you make better, more informed decisions.

The extreme improbability of everyday specific outcomes

When you think about it straight, any specific outcome in life is extremely unlikely. Let's illustrate this with an example:

Herman is 55 years old, married, has 2 daughters, lives in Boulder, works as a project manager in IT, is a marathon runner, has a dog, and plays the piano. If we go back 40 years, when Herman was 15 and at school in Omaha, how likely would this specific life course have been? To calculate the probability of this exact situation, we must consider the probability of each individual element: the probability that he lives to the age of 55, the probability that he marries, the probability that he has exactly two children, the probability that both children are girls, the chance that he will live in Boulder (quite unlikely for someone from Omaha), the chance that he will end up in the IT sector, the chance that he will specifically become a project manager, the chance that he will become a marathon runner, the chance that he will have a dog, the chance that he plays the piano. Each of these probabilities is less than 1, and some are significantly smaller. To calculate the total probability of this exact life course, we must multiply all these probabilities together. The result is an unbelievably small number. We can increase the improbability even further by adding more specific details: the brand of car he drives, his favorite holiday destination, his shoe size, etc. With each addition, the probability of this exact combination becomes even smaller.

► This leads to an astonishing conclusion: any precise condition in our lives is, statistically speaking, extremely unlikely if we try to calculate its probability years in advance.

Why is this insight important?

1. Perspective on 'coincidence': It helps us understand why events that we consider 'coincidental' or 'impossible' are in fact very normal in the larger context of all possible outcomes.
2. Appreciation for uniqueness: It underlines how unique everyone's path in life is without having to attribute supernatural meaning to it.
3. Flexibility in future thinking: It can help us to be less rigid in our expectations for the future, knowing that any specific prediction is unlikely to come true.
4. Understanding statistical principles: It illustrates how the combination of many independent events leads to extremely small probabilities, an important concept in probability theory.
5. Promote critical thinking: It encourages us to think critically about how we interpret 'unlikely' events in our daily lives.

This paradox of specific outcomes fits in seamlessly with Hand's improbability principle. It shows how the law of large numbers (there are billions of people, each with their own unique life courses), the law of selection (we focus on one specific outcome), and the law of 'almost enough' (we see similar life courses as'the same') together explain why our lives are simultaneously unique and inevitable.

Conclusion

David J. Hand's “Improbability Principle,” together with the insight that each specific life course is statistically extremely improbable, offers a fascinating perspective on chance and coincidence in our daily lives. These principles help us to:

1. Deal more rationally with seemingly impossible coincidences.
2. To look more critically at claims of predestination or supernatural intervention or abilities
3. To appreciate the uniqueness of everyone's life path without assigning excessive meaning to it
4. Looking to the future more flexibly and openly

By recognizing that unlikely events are a natural and inevitable part of our reality, we can develop a deeper understanding of the true nature of chance and probability. This allows us to look at the world around us with more wonder and sobriety, knowing that every moment, no matter how ordinary or extraordinary it seems, is part of an infinitely complex tapestry of possibilities.

The butterfly

Looking back on my conversation with the grieving widow, I wonder if I did the right thing by not contradicting her interpretation. The improbability principle teaches us to look critically at coincidences but also to understand the human need for meaning. In this case, I chose empathy over rationality.

References:

• Hand, D.J. (2014). The Improbability Principle: Why Coincidences, Miracles, and Rare Events Happen Every Day . Farrar, Straus and Giroux.