Most people who have studied some physics or chemistry know that it is important to keep the units of our numbers straight when we do calculations. Failure to attend to units usually leads to wrong answers.
What is not well known is that the analysis of units can often help scientists to derive formulas, even when the underlying physics is not well understood. How it works seems a bit mysterious, and the technique was not understood or appreciated until about 1870, when the great physicist James Clerk Maxwell laid out the principles of the technique, which is formally known as Dimensional Analysis.

Most people who have been exposed to probability and statistics have come across Bayes’ Formula, but I suspect that many have not fully understood and internalized what the formula tells us. This is unfortunate because, as we will see, the formula applies to situations where our intuition about probability can lead to wildly incorrect judgments. What is more, those situations often involve critical issues, such as interpreting the results of medical tests.
The importance of the formula is such that a whole branch of thought in science and statistics, Bayesian inference, or Bayesianism, springs directly from the formula and its implications.