Definition:

1. When increasing resources of effort leads to small results.

Insights:

1. Diminishing returns can eventually turn into negative returns: extra inputs decrease overall output.
2. Our capacity for making decisions during each day is subject to the law of diminishing returns: there is only so much thinking we can do before mental fatigue kicks in.
3. Gathering additional information before making decisions is also subject to diminishing returns - information gathering takes time, and every time we delay we continue to lose value.

Definition:

1. Nonlinear relationships.

Examples:

1. Strength training will see rapid progress at the start, and then strength will plateau.
2. Kleiber's law in biology shows that animal metabolisms don't scale linearly with size.
3. Zipf's law shows that the most frequent word used in a language will occur twice as often as the second, three times as often as the third, etc.

Insights:

1. To understand the world, we should recognize that there are many non-linear relationships, or power laws.
2. Power laws govern systems where a change in one variable can lead to a very large change in another, regardless of starting conditions.
3. Power laws can have an outsize effect on outcomes when it comes to decision-making - it is important to recognize them quickly and understand the implications.
4. There are hundreds of power laws, but they can be summarized into three main categories:
   1. Exponential Growth: as quantity increases, the rate at which it grows increases
   2. Diminishing Returns: a small result is achieved for increasing amount of effort or resources
   3. Long Tail: a large percentage of impact and results are generated by a small percentage of the work or inputs
5. In analyzing systems, there are often areas where a small change in input can disproportionately affect the output - tipping points, e.g., the temperature at which water turns to ice.

Principles:

1. Focus on the few variables that have an out-weighted influence on the system.