I’ve often been surprised how little intuitive grasp people have of basic mathematical or statistical ideas or relationships, even when they have had the education to understand with a little effort.
One example of this is what I call “unilateral mathematics” where people fixate on one term or side of an equation while ignoring that changing a term changes the equation’s other side (or to keep the other side static, something else has to give.) For example, I hear people getting so excited by the new salary they will earn when they move to a new place. Then they get to the new locale only to find that the cost of living is so much higher that even their hefty pay boost supports only a diminished quality of life. One sees this tendency a great deal in people’s policy discussions when someone will say, “just set a maximum (or minimum) price” without understanding that shortages or surpluses will come along for the ride. [The Law of Unintended Consequences is another good answer to this prompt.]
We all saw flaws in statistical thinking during the pandemic when people said things like, “See, she got the vaccine and then she got COVID, so obviously the vaccine doesn’t work!” I’m convinced this is because people don’t have good intuition for statistical thinking and — instead — they want to treat a low probability as an impossibility and a high probability as a certainty.
By the way, you see this from people of all persuasions, including those who are highly educated, conservatives, progressives, believers, atheists, etc. One can see the universality of the flaw most commonly in climate change comments. You’ll hear one person say, “See, it’s the hottest day on record, that’s evidence global warming is real!” Another person will say, “See, it’s the coldest day on record, global warming is obviously hokum!” Somehow, even with diametrically opposed viewpoints, these two manage to both be wrong because one day’s WEATHER is not instructive of what is happening to the CLIMATE. In other words, a sample of one provides no insight into state changes in the population. [Maybe it’s more appropriate to use Wolfgang Pauli’s terms and say the two are “not even wrong.”]
Tiger Riding for Beginners 