Most folks, when they are asked whether $1 million is a lot of money, will answer yes. Still more people are impressed by $1 billion — as they should be. But try asking them what the NASA budget ought to be. How much money does a large government agency need to survive from year to year? Five billion? Ten?
These questions aren’t particularly sexy, and indeed most Yalies don’t really care about them. And that’s fine. We don’t need an entire college campus to scrutinize the minutiae of federal accounting. What concerns me, however, is why Yalies don’t concern themselves with these types of questions: an antipathy toward mathematics.
As John Allen Paulos writes in his book “Innumeracy: Mathematical Illiteracy and its Consequences,” it’s not socially acceptable to say that you’re “bad with words.” No self-respecting politician would be caught dead suggesting that we should cut back grammar instruction in schools. Yet, as recently as 2012, The New York Times published a piece suggesting that algebra — arguably the basis for most of mathematics — wasn’t so important.
Similar sentiments can be found all around campus. How many times have we heard, “I’m not a math person?” In course reviews, complaints about mathematical rigor are common. It puzzles me that students are willing to adopt such a mentality. There seems to be an institutionalized fear of quantitative reasoning — and it’s not just tolerated, but celebrated. I’ve heard students take pride in getting through high school and college without taking calculus. The number of people who chuckle at their inability to perform basic mental math is equally strange. It’s not that I think calculus is particularly useful for most people, but it’s concerning that a significant contingent of Yalies find it acceptable to go four years without doing much more than arithmetic.
So, how much mathematics do we need to know? I obviously don’t think that everyone needs to be able to spell out the divides between Bayesian and frequentist statisticians. I’ll even admit that learning how to take a partial derivative is probably a lot less practical than learning how to write an essay. I do, however, think that a good grasp of orders of magnitude — and some general numerical intuition — is important.
Take the NASA example I brought up earlier. As of 2016, NASA’s budget is a little less than $20 billion. That sounds like a huge sum indeed — which may be why its budget has been shrinking as a percentage of the federal budget for the past few decades. In fact, politicos often tout their fiscal prudence when they salvage billions of dollars for the American public. But this is incredibly misleading. NASA’s supposedly huge budget is a meager 0.6 percent of the federal budget. Why?
Because the federal budget is a whopping $3 trillion. Let’s put that number into perspective. A million seconds is about 12 days; a billion seconds is about 32 years. One trillion seconds is almost 32,000 years.
Understanding basic concepts of mathematics, such as the huge difference between a billion and a trillion, is a crucial prerequisite for meaningful policy discussions. I hope every economics major on campus, for instance, understands how much revenue can be generated or lost by even a 1 percent change in tax rates. Yalies shouldn’t be able to graduate without being able to tell when numbers just don’t add up. This is why Fermi approximations should be considered more than just another topic to learn before a McKinsey interview.
I don’t think that the majority of Yalies are inept at mathematics. It’s clear, however, that many are indifferent to basic mathematical literacy. That QR requirement is far less scary than you think.
Shreyas Tirumala is a sophomore in Trumbull College. His column runs on alternate Fridays. Contact him at firstname.lastname@example.org .