On June 25, 2024, a quirky explanation is given on why x^2 is not always equal to x*x. Using the idea of intervals, it is shown how arithmetic with uncertainties around measurements can lead to surprising results. For example, when multiplying intervals that cover negative numbers, the traditional rules break down. The concept of intervals and their impact on mathematics, especially in computer science and manufacturing, is explored. This unconventional approach to arithmetic challenges traditional conventions and highlights the importance of considering uncertainties in calculations. The contentious debate between William Kahan and John Gustafson about interval arithmetic adds to the intrigue of this unique perspective on mathematical operations.
https://buttondown.email/hillelwayne/archive/a-brief-introduction-to-interval-arithmetic/