The Wall Street Journal had an interesting story today, Grasping Giant Numbers Is Far From Second Nature, by Jo Craven McGinty.
The thrust of the article is that we have trouble fully grasping big numbers, and our lack of comprehension compromises our ability to judge information about things like government budgets, scientific findings, the economy, and other topics that throw around numbers like millions, billions and trillions.
It’s a great article, and uses some good examples to help readers gain an understanding of the relative size differences when numbers change in order of magnitude; i.e., from millions to billions to trillions.
However, there is one example I found troubling. McGinty notes that the President Trump’s 2018 preliminary budget proposes to cut $2.7 billion from $1.068 trillion in discretionary spending. While some people may have trouble grasping those differences in magnitude, McGinty notes that in reality such a cut is less than 1% of the total— or as she calls it, the proverbial rounding error.
The math may be right, but it is also quite misleading. Included in that $2.7 billion dollar cut is an increase of $52 billion in defense spending (simply outrageous), which means that there had to be cuts of nearly $55 billion in other programs, and that’s no rounding error.
There’s a $9 billion dollar cut in education, and while again it may be small when talking about a trillion dollar budget, just think about the number of lives of young children that will be affected by such a cut. There’s also a proposed $12.6 billion dollar cut in Health and Human Services. So much for our social safety net, and taking care of those who have the greatest need.
I know the story was about math, but in certain cases you can’t just talk about things in terms of the numbers. When there are faces behind those numbers, every number is important, even if it is just 1 person out of 319 million. If your child is that one, there’s no way you would ever refer to him or her as a “rounding error.”
OK, enough political commentary, let’s get back to the math.
Here are a couple of useful examples shared by McGinty to help visualize large numbers.
In the first one, you are asked to take a sheet of paper, and draw a line with the endpoints 0 and 1 billion. Then place a tick mark on the line where 1 million should appear. Apparently a large number of people, 40% to 50% place the mark pretty close to the middle of the line; the middle would represent 500 million.
So where should the mark go? Well if you envision the line representing 1000 miles, think about where mile 1 is on that line, just 1/1,000 of a unit away from the beginning of the line.
The second example deals with time, and trying to show the difference between a million, a billion, and a trillion. There are 1 million seconds in roughly 11½ days. There are 1 billion seconds in around 31 years. And there are 1 trillion seconds in around 31,000 years.
When you put such large numbers in a familiar context such as days, it makes it much easier to understand the scale of the numbers involved.
And speaking of really big numbers, I wish there was a way of making the concept of infinity easier to understand. But until there is, I guess I am destined to spend what seems like an infinite amount of time doing my homework…