In a normally distributed system, long deviations from the average will tend to return to that average with an increasing number of observations: the so-called Law of Large Numbers. We are often fooled by regression to the mean, as with a sick
In many, perhaps most, systems, quantitative description down to a precise figure is either impossible or useless (or both). For example, estimating the distance between our galaxy and the next one over is a matter of knowing not the precise number of
The Bayesian method is a method of thought (named for Thomas Bayes) whereby one takes into account all prior relevant probabilities and then incrementally updates them as newer information arrives. This method is especially productive given the fundamentally non-deterministic world we experience:
The normal distribution is a statistical process that leads to the well-known graphical representation of a bell curve, with a meaningful central “average” and increasingly rare standard deviations from that average when correctly sampled. (The so-called “central limit” theorem.) Well-known examples include
A process can often look like a normal distribution but have a large “tail” – meaning that seemingly outlier events are far more likely than they are in an actual normal distribution. A strategy or process may be far more risky than
One of the most common processes that does not fit the normal distribution is that of a power law, whereby one quantity varies with another’s exponent rather than linearly. For example, the Richter scale describes the power of earthquakes on a power-law
One of the fundamental underlying assumptions of probability is that as more instances of an event occur, the actual results will converge on the expected ones. For example, if I know that the average man is 5 feet 10 inches tall, I
Insurance companies and subscription services are well aware of the concept of churn – every year, a certain number of customers are lost and must be replaced. Standing still is the equivalent of losing, as seen in the model called the “Red
Any reasonably educated person knows that any number multiplied by zero, no matter how large the number, is still zero. This is true in human systems as well as mathematical ones. In some systems, a failure in one area can negate great
It’s been said that Einstein called compounding a wonder of the world. He probably didn’t, but it is a wonder. Compounding is the process by which we add interest to a fixed sum, which then earns interest on the previous sum and