In Stephen Hawking’s remarkable book “A Brief History of Time”, he mentions in the introduction that he was advised that each formula he put in the book would halve the sales. Zero formulas, one million sales. One formula, half a million sales. Two formulas, a quarter-million sales. And so on.
By the way, that is exponential growth (well, decay, in that case). Which is what I’m going to talk about, but it’s also why I will try to include as few formulas as possible. Let’s stick to what’s important. Like, driving a car. Gas pedal, go. Brake pedal, stop. Steer where you want to go. That’s basically it, and you don’t need to understand the magic taking place under the hood to make good use of the car.
So, speaking of cars… let’s say you’re in your car, and you want to go from 0 to 100 km/h. My first car did that in about 18 seconds. My current car does it in 2.9. Both of those numbers are insane, but for completely different reasons.
Let’s look at the new chart I’ve added, which is a logarithmic graph of all the same data… and some dotted-dashed lines I’ll explain below.
You car will follow an acceleration curve, which… interestingly, for a supercar like a Ferrari, will look a lot like the Italian line on the logarithmic chart. A more modest car, like a Kia, will look more like the South Korea line.
Ooohhh, wait a minute, we might be onto something here…
All cars eventually hit a top speed where they are no longer accelerating, and when they do, like the Kia/South Korea line almost has, it flattens out to a near-zero slope. That Ferrari/Italy line will flatten out too, eventually, but as we can see, at a much higher level, and it’s not there yet… but trending that way.
The Canada line has been skirting the left side of its attached dotted line, and is now a little on its right. What’s it most looking like? Thankfully, very evidently, not the MegaSupercharged Corvette/US line, whose pedal is still floored and heading to a scary top speed. Whether Canada trends more like South Korea or Italy depends to be seen. Eyeballing it would imply somewhere in between. The math implies something similar. The reality remains to be … [Continue Reading]