If you want to play the game well, you need to learn the rules

the gambler

Today I’m going to deal with something that’s a bit of a pet peeve of mine, albeit one that may seem nebulous at first.  The thing to which I refer is the common attitude that math and science, such as is taught in primary and secondary school, are not relevant to most people’s daily lives.

I don’t mean by this that most people don’t recognize how important math and science are to technology and to civilization.  I doubt there are many people with such a limited worldview.  I’m thinking of the people who may recognize how powerful and useful mathematics and science are, and who see all things they’ve done for humanity, but who think that their own time learning anything beyond the basics of arithmetic was a waste of time, and that they’ve never used any of it since they learned it in school.

This is silly.  This is foolish.  I have a few rejoinders to such claims.

First, I want to point out that people who exercise—by running, biking, lifting weights, doing push-up, whatever—don’t complain that they’ve never had to do push-ups in their day-to-day life or as part of their jobs.  They don’t whine that they never need to flee predators or chase down prey to survive.  The reason you don’t hear such nonsense is that most people know that the purpose of most exercise isn’t to perfect one’s ability to, say, lift weights beautifully, but to be healthier, stronger, and more physically able.  This attitude can be applied at least as well to mental exercise, whether or not you use the specific tasks with which you exercise your mind anywhere else.  Indeed, mental exercise is probably even more useful and beneficial than bodily workouts are, for a few reasons.  First, the brain has greater and more enduring plasticity and freedom to improve than the body does, and that ability of your brain to grow “stronger” can continue throughout your life, barring neurological illness.

Let’s be honest:  humans don’t rule the world because of our physical acumen.  Numerous animals are stronger, faster, and more fearsome physically than humans (though our endurance is world class).  The reason we are so powerful is because of our outrageously overgrown brains, with which we’ve created external memories and communications that allow us to be social in ways that make honeybees and termites look like hikikomori.  So, if you want to maximize and optimize what makes humans strong, you need to maximize and optimize your mind.  Math and science are among the most rigorous and effective ways to do that.

At a deeper level, though, math and science are fundamental to reality itself in ways that all other endeavors are not.  Galileo famously said that the book of nature is written in the language of mathematics, and he was not the first or the last great mind to proclaim such Pythagorean sentiments, because it is a very deep and true statement about the universe.  I like to think of it as follows:  mathematics is the programming language of reality.  Everything that happens obeys it, and it cannot be contradicted, because such contradictions—in reality—simply cannot exist.  And science is our best attempt to learn the specifics of the program is in which we live.

Any good gamer will tell you, if you want to win a game—or thrive, or get as high a score as you’re able, or last as long as you can, whatever your goal might be when playing any given game—you need to know the rules.  Math and science are the rules, ultimately, that our game follows.  Human laws and customs are parochial and provincial; laws of nature are absolute.  If you try to go against them, you’ll eventually collide with them, and when you collide with the laws of nature, it’s always you that breaks.

Also, mathematics and science are a lot of fun if you give them a chance.  Contrary to popular belief, to understand and enjoy math and science can be tremendously captivating and inspiring, and they require and stimulate the imagination in ways that mere human stories and cultural creations never could.  As J. B. S. Haldane said, nature is not only queerer than we suppose, but queerer than we can suppose.  The only thing big enough really to simulate the universe is the universe itself, so we can never completely predict all of what we’re going to find before we find it, but math and science allow us to understand as much of it as possible.

That’s pretty exciting.  And it’s deeper and more real than anything else you’ll ever encounter.  Empires rise and fall; fashion is a form of ugliness so severe that we have to change it every few months; religions come and go; politics is notoriously ephemeral.  But physics is here for good, and as the saying goes, physicists defer only to mathematicians.

And mathematicians defer only to God…if ever.

Flat-Earthers and “hate speech” are good for us

I don’t know how often most of you notice the occasional noises of Flat-Earthers online, and particularly on social media, but I notice.  Encountering such absurdities can at times lead a reasonably educated person to feel that the world is going mad, that society is collapsing, and that—despite the cornucopia of information available to us—humans are breathtakingly stupid.

However, I’ve recently been reading John Stuart Mill’s “On Liberty,” and it gave me a new insight:  The fact the we encounter such vociferous and seemingly ridiculous expressions of contra-factual ideas is a sign of the health and strength of our discourse, rather than its deterioration. Continue reading “Flat-Earthers and “hate speech” are good for us”

Odds are we should teach probability and statistics


Among the many educational reforms that I think we ought to enact in the United States, and probably throughout the world, one of the most useful would be to begin teaching all students about probability and statistics.  These should be taught at a far younger age than that at which most people begin to learn them—those that ever do.  Most of us don’t get any exposure to the concepts until we go to university, if we do even there.  My own first real, deep exposure to probability and statistics took place when I was in medical school…and I had a significant scientific background even before then.

Why should we encourage young people to learn about such seemingly esoteric matters?  Precisely because they seem so esoteric to us.  Statistics are quoted with tremendous frequency in the popular press, in advertising, and in social media of all sorts, but the general public’s understanding of them is poor.  This appears to be an innate human weakness, not merely a failure of education.  We learn basic arithmetic with relative ease, and even the fundamentals of Newtonian physics don’t seem too unnatural when compared with most people’s intuitions about the matter.  Yet in the events of everyday life, statistics predominate.  Even so seemingly straightforward a relation as the ideal gas law (PV=nRT, relating the volume, temperature, and pressure of a gas) is the product of the statistical effects of innumerable molecules interacting with each other.  In this case, the shorthand works well enough, because the numbers involved are so vast, but in more ordinary interactions of humans with each other and with the world, we do not have numbers large enough to produce reliable, simplified formulae.  We must deal with statistics and probability.  If we do not, then we will fail to deal with reality as accurately as we could, which cannot fail to have consequences, usually bad ones.  As I often say (paraphrasing John Mellencamp) “When you fight reality, reality always wins.” Continue reading “Odds are we should teach probability and statistics”