When people complain about math
being too hard or impractical, one might expect a college math professor to
take up a defense, which Jordan
Ellenberg does in How Not to Be Wrong.
He manages to make is his argument without resorting to equations, and with
very few numbers.
Math is not all about equations and numbers (though these are important
objects in math). Ordinary people do math frequently in the form of thinking
with a little more depth, rigor and structure than usual. This is the power of
math to help us make better decisions. Though Ellenberg covers a lot of ground
in math, science
and history,
the notion of better decision making through math runs through each chapter.
Along the way, he debunks some common uses of math, even those that are
prevalently used among math-minded scientists. For instance, he takes on the
notion of statistical significance, which sometimes bothers me, too. Statistical
significance by itself is not an arbiter of the truth of something. It has a
lot more to do with a particular way of framing arguments and the sensitivity
of an experiment. If you have a large enough sample, you’re likely to have
statistically significant results, even if those results are insignificantly
small. You can “prove” ridiculous, plainly wrong things using an argument from
statistical significance because improbable things happen sometimes (actually a
lot).
Ellenberg discusses the related subject of probability, which any book
like this should. Human beings are pretty bad at grasping probability; it
requires deeper, rigorous, structured thinking that sometimes runs counter to
our intuition.
Though math is sometimes misused or misunderstood, Ellenberg is bullish
on the power of math to help us make better decisions and understand the world
more deeply. Math itself is a pretty deep world, and mathematicians have
discovered connections between things that seem to be unrelated. That is part of
the power of math. Solutions in one are often lead to applications in many
others.
Of course, math won’t eliminate uncertainty, though it can help you
understand uncertainties better. I’ve spent most of my career in and around government
and Ellenberg expresses some empathy for decision makers in the realm of policy,
writing, “Maker of public policy do not have the luxury of uncertainty that
scientist do. They have to for their best guesses and make decisions on the
basis thereof.” This guesswork can be done with humility and honesty, as is
fitting in a republic.
While Ellenberg eschews the pile of symbols many people think of as
math, he does not avoid deep, challenging questions. It’s not the math you’ll
find in journals, but it’s not fluff. He doesn’t call people to join the ranks
of academic mathematicians (though don’t give up on the idea just because it
seems hard at first), but he argues that people in all manner of professions
could benefit from education in math. If you’re interested in becoming such
person, How Not to Be Wrong is a good
introduction to how mathematicians think about the world.
If you’re interested in this book, you may also be interested in
No comments:
Post a Comment