"Fred's Law": The price of Bitcoin grows as the square of the interest in Bitcoin.

First: why is this true statistically? - Last year @Giovann35084111 showed that the quadratic relationship held for addresses. - roughly speaking these addresses are growing at t^3 while price is growing at t^6 - recently Gio showed that the same is true for searches.

Now: why do we think this is true? every new participant bringing buying Interest I not only bids up a coin, but also takes a coin out of the market. This ends up being a quadratic relationship. It's unique in Financial assets, because of the absolute scarcity.

One way to think of this is as an AMM. Imagine that there are 2MM "available coins" that trade in a pool with 2MM * 100K = 200 Billion USD. Now take half of that Bitcoin from the pool (Interest Doubles). Then you now have 1MM coins which at a contant product = 400 Billion = 400K

Note that this is "analagous" but not the same as Metcalfe. This is a process of people discovering and saving into a scarce asset, not communicating in a network. It doesn't work for Gold because there is no "novel discovery". Gold has existed forever.