What does randomness look like?

The post explains that random data can look clustered, and that this is often what chance produces. It uses examples from glowworms, coin tosses, shark attacks, and wartime bombings to show how the Poisson distribution helps distinguish randomness from targeted or manufactured patterns.

Reading notes

#

• Randomness can produce clumps, strands, and gaps, while uniformity is a different property.
• In the coin-toss example, the data with long runs looks random, while the data with almost no runs looks suspicious.
• Poisson’s work began with French crime statistics and the idea that observed rates can vary because the underlying process is fallible.
• Poisson’s formula estimates the odds of unusual counts when events are rare and independent.
• Bortkiewicz used the formula to show that horse-kick deaths in the Prussian army fit random variation.
• The shark-attack data for South Africa also fit a Poisson distribution, with no extra clustering beyond chance.
• R. D. Clarke applied the same logic to V-1 bomb impacts in London and found the pattern matched chance closely.
• The post generalizes the Poisson distribution to other contexts such as mutations, traffic queues, births, deaths, and typos.