Poisson : The Law of the Unexpected
Siméon Denis Poisson. Born 1781, Pithiviers, France. Died 1840, Paris, France. He lived for 59 years. And before anything else… His name is not poison. It is: poo-SON And that matters. Because he did not study destruction. He studied someth
Siméon Denis Poisson. Born 1781, Pithiviers, France. Died 1840, Paris, France. He lived for 59 years. And before anything else… His name is not poison. It is: poo-SON And that matters. Because he did not study destruction. He studied something far more subtle. The structure of the unexpected. He was a student of Laplace. Raised in a world that believed: If you know everything… you can predict everything. Uncertainty is ignorance. That was the belief. Then came Legendre. Who showed: Even if measurements are flawed… truth can still be extracted. Error can be minimized. But Poisson stepped into a different reality. Not measurement error. But events themselves. Things that happen. A call arriving. A defect appearing. A particle striking. Not continuous. Discrete. Irregular. Unpredictable. And he asked: Are these truly random? Or is there something deeper? Now pause. Because another mind had already studied uncertainty. Gauss. Gauss looked at error. When you measure something many times… you get variation. Some slightly above. Some slightly below. And Gauss showed: These errors form a smooth curve. A bell shape. Centered around truth. Error distributes symmetrically. Predictably. That is Gaussian distribution. But Poisson is looking at something else. Not error around a value. But occurrence of events. Sometimes nothing happens. Sometimes one event. Sometimes two. Rarely many. There is no “center” in the same way. No symmetry. No smooth spread. This is different. Completely different. Now Poisson sees something. Even though events seem random… Their frequency stabilizes. Over time… patterns emerge. He describes it with a function: Now don’t rush this. This is not just a formula. It says: If events happen at an average rate λ… Then the probability of seeing exactly k events… is determined. Even if each individual event… feels random. Now feel the shift. Gauss says: Error clusters around truth Poisson says: Events cluster around rate Gauss deals with: continuous variation Poisson deals with: discrete occurrence Gauss is about: how far you are from truth Poisson is about: how often something happens This is a fundamental shift. From measurement… to reality itself. Now imagine: A call center. Calls arrive randomly. But over time… the average stabilizes. Some minutes: zero calls. Some minutes: one. Some minutes: two. Rarely more. But not chaos. Pattern. Now imagine: Defects in manufacturing. Most items perfect. Some flawed. Rarely many flawed. Again… not chaos. Structure. Poisson showed: Randomness is not the absence of order It is a different kind of order. One that emerges… only when you step back. Now connect back. Laplace believed: Everything is predictable. Poisson shows: Even when individual events are unpredictable… their pattern is not. Now connect forward. This idea becomes: queuing theory telecommunications reliability engineering stochastic processes And much later: machine learning probabilistic modeling Because reality is not just smooth curves. It is made of events. Discrete. Irregular. Yet structured. Poisson did not remove randomness. He gave it a law. And that is why his work matters. Because he showed something deeply counterintuitive: The unexpected… is not unstructured It is simply misunderstood. Remember Poisson through the following lines “Randomness is not chaos… it is order, when observed closely with the tools poisson built. ”