Most everyone is familiar with Santayana’s admonition that, “Those who do not learn from history are doomed to repeat it.” What is the analagous statement for mathematics? Are those who fail to learn mathematics doomed to work in food services? Doomed to playing the lottery? Doomed to credit card debt and forclosures on the house they can’t afford?
Actually, the answer is usually none of the above. In fact, most of us probably know fairly successful people whose background and skill in mathematics was as minimal as they could get away with. I know several scientists (mostly in biology) who are extremely good at what they do, but who would be terrified to sit through even our freshman level math courses. No, it does not seem that an individual’s lack of mathematical background will necessarily cost that person anything substantial. Ah, but what of a nation or a world?
Suppose a society fails to learn mathematics? I don’t mean that all individuals fail to learn, just a number so overwhelming that they permeate the government, regulatory agencies, businesses, and schools. What if a sufficient fraction of the population learns to think intuitively, rather than critically? What if enough people agree that what feels right, is right? What if the system of checks and balances fails because the counterweights just can’t keep up? What if people start to believe that these rocks are what keep the tigers away?
I am writing this as I live the answer to these questions. To which circle of hell am I referring? Circle 9er: Airport security.
I know: It is such an easy target for scrutiny, and yet without a doubt the people who work in airport security are an honest group who are doing their job and who likely sympathize with many of the travelers inconvenienced by policies they never asked for. Am I annoyed that the security officer here at Heathrow just confiscated from me the half-full 4oz. bottle of contact lens solution—which passed through American security without notice—because 4oz. is 118mL and the British limit is 100mL?* No. I am annoyed that many people in power in both (all?) countries believe that such trivial differences matter.
*Technically, they should have confiscated it in the United States since they match Britain with a 3.4oz (roughly 100mL) limit.
How should we decide the appropriate level of security at our airports? Should experts come up with a list of reasonable ways a terrorist might attempt to take over or destroy an airplane, and then enact sufficient security measures to make those avenues of destruction prohibitively difficult? It sounds pretty good. It feels like the right solution.
Of course, if you’re one of the those anal mathematicians, then you might start questioning the definition of `reasonable ways’ and `prohibitively difficult’. At that point, it might occur to you that probability and statistics are at play here, and that these are necessary to consider before deciding upon a course of action. But those of us without a Ph.D. in pointdextery know that probability and statistics is a just a smart person’s attempt to get around the immutable law that either the plane crashes or it doesn’t; you either stop the terrorist or you don’t. Never mind the regular reports of journalists sneaking weapons or TSA agents sneaking people through security. We’d all rather be alive with a little less liberty (and contact solution) than free and dead at the bottom of the Atlantic, right?
So, I guess this is my answer: The cost of a society failing to learn mathematics is giving up some of its liberty for, well, the appearance of security? But hey, at least those badges the TSA officers wear now are keeping the tigers away.
[Update: This post was retroactively inspired (that is, I read it after I wrote this) by an article of Keith Devlin.]