Those of you who are tuning in today for my profile of Red Bull are going to have to wait until tomorrow. I mistakenly put in yesterday’s post that it would be today – I guess I was so caught up in the talk about time and light speed and no friction, that I couldn’t keep track of what day it was! So today, a bit about exponential growth.
I have gotten several comments about what happens when you fold a piece of paper 40 times (from my post Monday). I confess, it was a slight exaggeration. Well, more of a rounding error. It actually takes 42 times before the paper thickness exceeds 238,900 miles (distance to the moon). Here is the math and a chart. If you want the spreadsheet that does the calcs, just ask for it by replying to this email.
If this seems unbelievable, you are not alone. Humans are not naturally equipped to understand exponential growth. The few people that grasp the concept have been using it to their advantage. All tech start ups have a chart of their growth potential and it looks like a hockey stick on its side.
A long flat section (the stick) and then a rapid ascent to billionairredom (the blade). Exponential growth graphs all look like hockey sticks. It doesn’t matter if what number you start with, or what number you end with. If you double something enough times, the line on the graph ends going pretty close to straight up – somewhere around the 40th doubling.
When presenting their hockey stick story, these soon to be billionaires present the future as a certainty because of “Moore’s Law”. Gordon Moore, the co-founder of chip maker Intel, said in 1965 that the number of transistors on a chip would double every 2 years. Every year, everybody says this will be the last year it will be true. But, Moore’s Law has held up – for 58 years! That is 29 doublings at 2 years each, or 39 doublings at 18 months each. Gordon Moore later revised his prediction to say 18 months is a better estimate of chip making progress.
Here is a chart of the progress in chip making from our world in data.
Wait! That chart doesn’t look like a hockey stick at all. Just a plain old straight line.
Now this is where the crazy types in the white coats are not helping us very much. People that work around exponential stuff all of the time don’t use regular charts. A regular graph of an exponential thing is so extreme, it does not help the analyst see things.
When growing bacteria in a petri dish, a scientist accepts exponential growth as a certainty, and wants to make a graph that de-emphasizes the way the line makes an abrupt turn towards space. So they use a logarithmic scale on the vertical axis. You will notice on the Moore’s Law chart that each equally spaced mark is 10 times more than the prior mark. This straitens the line and makes it more readable but hides the accelerating rate of change.
Here is our going to the moon chart on a logarithmic scale.
OK, another thought experiment. Say you have a pond with a few lily pads on one side, and every day the number of lily pads doubles. For about a month, the pond looks the same, then about the second week of the second month (40 days in) one quarter of the pond is covered, then half the pond the next day, and then the entire pond on the next day. On Monday it was 25% covered and Wednesday 100% covered. Yow!
No wonder Dr. Fauci gets freaked out by some things!
This is also why Cristiano Ronaldo has over 500 million followers on Instagram.
In the 1980s there was a shampoo commercial that illustrated exponential growth, right on the screen. “And they tell two friends” became a viral meme and even made it into Wayne’s World.
Every marketing person dreams of going viral. The straight up part of the graph has got to be quite a ride!
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