Most people don’t understand exponential growth. It can be counterintuitive and is easily misinterpreted. Understanding it is particularly important right now around Covid-19.
The following eight-minute video is extremely well done and uses the historical Covid-19 data to help understand exponential growth.
There’s a magic number in this that we should be focusing on, but gets lost in the fog of hysteria. The math lesson starts at about 3:45.
The magic number is the growth factor, which is the change in new cases today divided by the change in new cases yesterday.
Right now we have a growth factor > 1, which is the fast-growing part of the exponential curve (the scary green part.) When the growth factor is < 1, we are on the slowing down part of the curve (red). We hit an inflection point when the growth factor = 1, which means that we are transitioning from rapid growth to slowing growth.
However, since we are dealing with the rate of change of new cases on a daily basis, the absolute number of cases obscures what is going on.
Look at the following table. The absolute number of change is scary, but if the growth factor hits 1, things are getting better.
Compare that to when the growth is 1.15 (15%). Note that the difference in the absolute numbers are not that significant, but the implication is dramatic.
When the growth factor is > 1, there may be orders of magnitude more growth ahead of us. When the growth factor is < 1, the most things with grow from there is 2x.
In addition, the growth rate from here has a huge outcome on number of cases. For example, if we are at a 15% growth rate from here (21,000 cases), in 61 days of 15% daily growth, we’ll be at over 100 million cases. But, if the growth rate decreases to 5% (a growth rate of 1.05, which is still > 1), in 61 days we’ll be at slightly over 400,000 cases.
The growth rate matters a huge amount right now. The more we can do to slow the growth rate, the better things will turn out. And, this activity is exponential, not linear, so massive change right now has an enormous impact on things.
If you want to track these numbers, the best three sites on the web that I’ve found that have these data and explanations organized are Our World in Data, Worldometer, and the Johns Hopkins Covid-19 site.
I rarely read physical magazines anymore. I only read in the bathroom and most are things I forget to unsubscribe to or that Amy gives me.
Today, I finished the most recent MIT Technology Review where I was reminded about the amazing MIT Science Fiction Society. As a sci-fi nut, I realized I’d screwed up by not having a lifetime membership. So, I’m now trying to figure out where to send my $260 to be a lifer.
As I was reading the other MIT thingy I get regularly (the MIT Science News and Events) I saw a mindblowing stat from the most recent Putnam Competition (the 74th). MIT took four of the top five places, won the team competition, and had 43% of the top 81 scores (depending on the rounding, that’s either 34 of 81 or 35 of 81.) Either way, it’s nuts.
When I was a freshman, I thought I was hot shit at math. I was the star of my high school Mu Alpha Theta team and as a senior had an unexpected first place finish in a Rice University national competition for Algebra. I was pretty damn good in the calculator competitions on my TI-58C. Yes, I was a nerd then, and I’m still a nerd now.
While I got an 800 on the math SAT, I booted all the AP tests except Biology (to place out at MIT you need to get a 5) – I can’t remember what I did the night before the tests but it clearly wasn’t something that I should have been doing if I wanted to pass them.
So, when I got to MIT, I took 18.011, which was the “advanced first calculus course.” It was straightforward. I then took 18.021 (“advanced second calculus course.”) It was less straightforward. If I had placed out on the Math AP test, I would have taken 18.02 and 18.03 instead. So I felt a little less like hot shit.
My friend (and future business partner Dave Jilk) knew I liked math so he encouraged me to take a course called 18.701: Algebra. I figured “Algebra – I’ve got that.” I don’t know if Dave was serious or just fucking with me, but when I got a 12 on my first test I knew I was fucked. I dropped the class shortly thereafter. Dave, of course, got an A in that one. He’s much better at math than I am.
While I ended up being “fair” at math by MIT standards, I developed a weird savant like numeric skill. I can remember crazy amounts of number and data pairs. I can also do a lot of math in my head, although I’m often off by an order of magnitude, which of course either matters a lot or is easy to adjust when you realize it.
Mitchell M. Lee, Zipei Nie, Bobby Shen, and David Yang – y’all are math studs. Well done representing the Beavers in the 2014 Putnam.