# A Little Ditty ‘Bout Log Regression

Humans don’t do exponential very well. Humans do linear well. Humans experience exponential all the time however since nature runs on exponential. If you get in your car and go from 8 m/s to 16 m/s and your car weighs 1000kg your kinetic energy goes from 32KJ to 128KJ double the speed 2^2 x the energy. Another example is the growth of the virus. We look at the death counter shake our heads and say WTF happened!

When we look at Crypto prices we look at variable exponential growth with variable growth oscillating in and out of bubble territory. By doing a log plot on Y axis growth v X axis time and looking for a smooth fit to the data to some formula y = b*log (x) + a you generate a log regression curve and by adjusting b and a the curve fits the data. Below is a video that describes how this is done and looks at time of the X axis v non bubble growth on the Y. The argument is ETH is 5 years behind BTC in its adoption and is just coming into the second cycle peak while BTC is coming into its third cycle peak. It’s from this kind of analysis that 500K BTC is derived.

I was listening to Raul Pal and instead of charting exponential growth against time he charted against the time it took to various amounts of account addresses. Account address expansion is Metcalf’s law. As the addresses expand the network increases in complexity.

When he did that fit, BTC and ETH were tracking exactly meaning the growth in ETH will follow the same complexity path as BTC just offset by 5 years time. Is it true? I don’t know. It is a way to think about exponential growth v a variable that may not be time, but may just be be functionally related to time in some way.

Beats hell out of standing there staring at a screen saying WTF, while non linear reality unfolds before your glazed over doe eyes. I think understanding this stuff at least at the flavor level has merit even if it’s only based on probability and Bayesian inference. For example I’ve noticed BTC and ETH don’t accelerate in time with each other. When BTC is accelerating ETH goes sideways or down and when BTC goes sideways ETH tends to explode. I think this is the basis of the diversity and risk reduction provided by owning both assets. I think the diversity is not structural but behavioral.

BTC at present is preferred. When it’s moving trading is deferred to BTC and ETH and the other alt’s go dormant. When BTC goes sideways money flows to ETH which causes it to explode because things are exponential. When BTC moves again ETH goes sideways. This effectively provides diversity and tends to reduce risk in the overall portfolio. Eventually the 2 assets will perform different economic functions and diversity will be derived on that but I think in this nascent crypto soup of barely understood assets it’s buy the FOMO that drives diversity enough to create an efficient frontier.