What is a Power Law?

A power law is a type of mathematical relationship where one variable scales with another according to an exponent. It is a proportional relationship where growth scales in a consistent way across magnitude.

Power laws appear in natural systems. Earthquakes, city sizes, and wealth distributions are common examples. They describe systems that expand non-linearly rather than in straight lines. Not all systems behave this way. Some grow linearly, and others grow exponentially. A power law describes a different type of system.

In Bitcoin’s case, we observe a power law relationship between price and time. Price scales with time raised to a power, where time is measured from the start of the network, the genesis block. The exponent governs how strongly price scales as time increases.

When plotted on a log-log chart, a power law becomes a straight line. The slope of that line is the exponent. That slope describes the observed long-term structural tendency.

This does not guarantee price moves smoothly, without volatility, or cycles. Prices will fluctuate over time.

The question is whether the scaling relationship continues to hold.