Example: Strength training will see rapid progress at the start, and then strength will plateau.
Example: Kleiber’s law in biology shows that animal metabolisms don't scale linearly with size.
Example: Zipf’s law, after George Zipf, 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.
Insight: To understand the world, we should understand that there are many non-linear relationships, or power laws.
Insight: Power laws govern systems where a change in one variable can lead to a very large change in another, regardless of starting conditions.
Insight: Power laws can have an outsize effect on outcomes when it comes to decision-making - it is important to recognise them quickly and understand the implications.
Insight: There are hundreds of power laws, but they can be summarised 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.
Insight: In analysing 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.
Principle: Focus on the few variables that have an out-weighted influence on the system.
Definition: Things that are scalable.
Insight: Power laws can be seen across many systems, and the exponent around critical points is the same across systems in the same group, even when many aspects of the systems are different.
Reference: Willis and Yule - noticed the power laws in biology: the richer in a species a genus is, the richer it will tend to get over time. To note - in Yule's model the species never die out.
Reference: Vilfredo Pareto - noticed the power laws the distribution of income and wealth.
Example: Academic paper citations - few papers get the majority of citations.
Example: The combined wealth of the eight richest people in the world is more than the bottom 50%.
Insight: Power laws govern wealth distribution.
Insight: Power laws create outliers in success.
Example: Kleiber’s law: shows that as life gets bigger, it slows down.
Insight: Creativity often scales exponentially - big cities are often centres of creativity.
Key Insights & Principles
Systems & Decision Making
Power laws exist in most systems - where changes in one variable can lead to very large changes in other variables, regardless of starting points.
Exponential Growth: where quantity increases, the rate at which it grows increases.
Diminishing Returns: smaller results are achieved for increasing amount of effort or resources.
Long Tails: a larger percentage of results is generated by a small percentage of the inputs.
Power laws create outliers.
When analysing systems, look for points when inputs can disproportionately affect outputs.
Focus on the few variables that have an out-weighted influence on the system.
