Growth

We like to think of things as linear.

When I was young my mother had told me that driving faster used more fuel. At the time I asked, if going faster used more fuel, but you also got where you were going faster, wouldn’t it even out? I remember the pride I felt when she didn’t know.

I of course, was wrong. She had grown up with the U.S. national 55 mile per hour speed limit so knew that driving faster was more expensive. footnotes, i cant drive 55, US limit

As it turns out the relationship between the amount of gas used and the speed of your car is quadradic, meaning doubling the speed of your car will 4x the rate you burn through fuel.

Many things in life aren’t actually linear.

Let’s say your boss pays you $100 a day and you save it under your matress. This is linear growth. Each day you make the same amount. In a business week you’ll make $500, double the time to two business weeks you’ll make twice as much total $1,000.

A table for the dummies.

Exponentials are crazy.

There is another, that is just so much more interesting in my mind -

graph of X, then x^2, then 2^x, growing out.

Exponentials are when the rate of change is tied to how much you have of something.

water liles, doubling animation

A pond has a water lily. The next day it doubles to two, the day after four. Within thirty days the pond will be completely filled. How many days will it take to fill the first 25%? How many for the last 75%?

Bar and pie graph.

On day 28 a quarter of the pond will be filled. Three quarters of the pond will be filled in just the last two days.

Exponential growth takes time to start, but once it does its hard to stop. It moves like a fire through a forest. Footnote, forest fires are modeled by exponentials.

Postivie feedback loops

Expontials are surprisingly intunative. Take a microphone and put it near a speaker to know what I mean.

Postitive feedback loop system diagram.

Compound interest

This concept is one of the large reasons the rich stay rich while the poor stay poor.

Skills

People tend to think skills are linear. Put in an extra 10% each day, and you’ll be 10% better. This isn’t true. Things are related, similar, concepts build on each other. If you understand topic really well, you’ll be able to pick up similar ones much quicker than someone else.

Resource deprivation

In real life, expotentials cannot continue forever. The fire will eventuallh run out of forest.

last man to do all things