So yes, I numbered the last update wrong. Numbers are always tricky. As a younger man, I read John Allen Paulos’s Innumeracy, Mathematical Illiteracy, and its Consequences. What I remember from it is that if we were as lenient with our understanding of words as we are with our knowledge of numbers, I would have written this update in a mix of Dutch, Spanish, and gibberish. And have gotten away with it.
This week, we think the world population (of humans) has passed 8 billion. There is a margin of error of some hundreds of millions. I.e., the number may be off as much as the entire population of the USA or Indonesia.
With 8 billion people, everything we do happens at scale, often a horrendous scale. For instance, my own country slaughters 1.7 million animals every day. Over 600 million annually. Globally, we’re looking at 70-80 billion animals we kill yearly for human consumption.
Because of innumeracy, we often read these numbers as prose. Factoids that shock because we’ve learned that “billion” is usually a bad word. Like “sleet” or “misogyny.” But many of us do not really have a feeling for them. We may do the quick calculation that this means we kill about 10 animals for each human being. But we ignore the more complex 600/18 to compute this ratio for the Netherlands and the consequent insight into our overconsumption of meat.
Since I started working on sustainability in the infrastructure industry, the numbers I deal with daily have increased significantly. For instance, the annual steel production is at 1.8-2.0 billion tons. Remember that “ton” is a euphemism for a thousand kilograms. The annual production of concrete is fifteen times that of steel.
This production causes carbon emissions. While we all know that carbon emissions are one of the leading causes of climate change, I’d dare to state that most of us are carbon innumerate. A quick test:
The correct answer for all three is the middle options. You could calculate the first question if you recently bought a car or studied a car ad. The second you need to know (and you need to know!) The third is where it gets really tough. What again was a kilo, a mega, and a tera? Combined with “tons,” the zeroes become hard enough fast enough.
I’ve struggled with getting comfortable with the numbers we’re trying to reduce at my job. More than once, I had to pause to avoid making an error of a factor of 1,000.
Sean Carroll recently interviewed Antonio Padilla about large numbers on his podcast. The episode serves as a nice bookend to Innumeracy. It deals with numbers too large to comprehend (or fit in our universe). For instance, I didn’t know that the famous number googol (10^100) is larger than the total number of particles in the universe (10^88).
The episode gets really interesting when Padilla talks about the number TREE(3). The number is the maximum length of a simple game in which two players draw (graph theory) trees, connecting dots with lines. The game ends when a player draws a tree that contains a part of a previous tree.
TREE(1) is the maximum number of times you can play the game if you start with one type of seed. So the answer to TREE(1) is 1. Because you play with the same seed and the first tree is only that seed, the second tree always contains that seed, and it’s game over. Similarly, TREE(2), with two types of seed, is 3. Thus, TREE(3) should be, like… 10? 50?
It turns out the number TREE(3) is too big to fit in our universe.
Padilla goes on a thought experiment (around the 30-minute mark), imagining Carroll and him playing the game at Planck speed, the fastest you can go without breaking spacetime. It turns out that even at this speed, they’ll still be playing after the heat death of the universe (1.7*10^106 years into the future).
I’m not innumerate, or at least not terribly so. Yet when it comes to TREE(3), I’m at a complete loss.
This was update 99 (almost 10^2). Thanks for reading, as always! Have a wonderful weekend, and talk soon!
— Jasper