Bitcoin Power Law » cyberfella ltd, since 2012.

What is a Power Law?

Quite simply, a power law is a mathematical model. Imagine you have two hands and ten fingers. If you had four hands, you’d have twenty fingers. So as the number of hands rises, the number of fingers rises faster with 100% certainty.

The relationship of hands to fingers is F=h * 5 although this is NOT a power law correlation, it’s a linear relationship because hands always have the same number of fingers.

A power law on the other hand (no pun intended), is a relationship often exhibited in nature and in cities. Wealth distribution for example, the number of people who have very little to no wealth is very high and as you progress upwards through levels of wealth held by an individual, the number of individuals who hold exponentially more wealth than the order of magnitude beneath them is the inverse of the square or the cube or ^4 and so on. Only one person can be the richest, and the number of people competing at that top tier of 1 Trillion is very small, compared to the number of people competing for a paid job with a 100 K Salary.

It’s opportune to mention at this point that the number of bitcoin that will ever exist is effectively 20 M since 1 M of Satoshi’s coins will never move. Also, many are lost. There are not enough bitcoin in existence for every millionaire to own just one. Yet priced in bitcoin over time, everything falls in value against it, evidenced here: PricedInBitcoin21 .

Bitcoin’s price in any given fiat currency rises over time and on a linear scale can appear volatile and chaotic, putting a lot of millionaires off buying bitcoin, yet over a long period of time, if you plot the price on a logarithmic price scale on the y axis and logarithmic time scale on the x axis, a 96% correlation to a straight line up can be observed.

Moreover, it has moved through sufficient orders of magnitude that mathematically, a power law is observed and scientifically, it verifies that bitcoin is a system that is extremely unlikely to deviate from its path – even though it is volatile observed over a short time span.

In fact, over the time it’s existed, bitcoin has risen in value faster then anything in human history. This is because in terms of energy (work) input, relative to monetary output, it is the most efficient system ever invented. There is no second best system. I guess the millionaires just haven’t caught up yet. This is due to being too busy to do the 100, then 1000 hours of work required to understand it for yourself, albeit easily summarised in a few paragraphs here. They’re obviously too busy. Busy doing what? Under performing bitcoin, that’s what. Amusing isn’t it, when someone points that out? I think so, anyway.

Follow the work of Former Professor of Astrophysics Giovanni Santostasi for a deeper explanation of Bitcoin’s power law correlation, here and MicroStrategy’s Michael Saylor’s explanation of there being no second best* here.