On Patterns (2020-)

"Each decision about what data to gather and how to analyze them is akin to standing on a pathway as it forks left and right and deciding which way to go. What seems like a few simple choices can quickly multiply into a labyrinth of different possibilities. Make one combination of choices and you’ll reach one conclusion; make another, equally reasonable, and you might find a very different pattern in the data." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

"The world is full of patterns that are too subtle or too rare to detect by eyeballing them, and a pattern doesn’t need to be very subtle or rare to be hard to spot without a statistical lens." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

"While number theory looks for patterns in sequences of numbers, dynamical systems actually produce sequences of numbers [...]. The two merge when mathematicians look for number-theoretic patterns hidden in those sequences." (Kelsey Houston-Edwards, "Mathematicians Set Numbers in Motion to Unlock Their Secrets", Quanta Magazine, 2021)

"While number theory looks for patterns in sequences of numbers, dynamical systems actually produce sequences of numbers [.] The two merge when mathematicians look for number-theoretic patterns hidden in those sequences." (Kelsey Houston-Edwards, "Mathematicians Set Numbers in Motion to Unlock Their Secrets", Quanta Magazine, 2021).

"Chaos theory is a branch of mathematics focusing on the study of chaos - dynamical systems whose random states of disorder and irregularities are governed by underlying patterns and deterministic laws that are highly sensitive to initial conditions. Chaos theory is an interdisciplinary theory stating that, within the apparent randomness of complex, chaotic systems, there are underlying patterns, interconnectedness, constant feedback loops, repetition, self-similarity, fractals, and self-organization. The butterfly effect, an underlying principle of chaos, describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state" (meaning that there is a sensitive dependence on initial conditions)." (Nima Norouzi, "Criminal Policy, Security, and Justice in the Time of COVID-19", 2022)