On the Myopia of Statisticians
It’s too much to ask them to understand scale invariance
It’s too much to ask statisticians to understand scale invariance; it’s so far from a Gaussian distribution that they cannot relate.
Even such a brilliant mind as Nicholas Nassim Taleb could not break free of trying to value Bitcoin as a stock.
"All models are wrong, but some are useful." - statistician George Box
“Not everything that counts can be counted” - Einstein
“It must not be assumed that the statistics is the only method to use in research, neither should this method (be) considered the best attack for the problem.” —Croxten and Cowden
Insight
Insight is what matters. The purpose of models is to provide insight.
If it were up to statisticians, the Milky Way galaxy could not exist. We would present to them the map of the cosmic microwave background and its brightness fluctuations of one part in one hundred thousand. 0.001%.
The universe was extremely uniform when it was of age just 380,000 years.
They would look at the map and say, there is no way we could ever get a galaxy to form, it’s impossible to have a density even two times the average with such tiny fluctuations. Structure cannot form.
Cosmic Microwave Background Map (European Space Agency and Planck Collaboration)
Looking at the map, here’s what they would not know:
The cosmic microwave background radiation was released at that age for the universe, because the plasma was cooling to below 3000 Kelvin.
Below 3000 Kelvin the ionized plasma become neutral.
When ionized the photons were continually scattering off of free electrons.
As the temperature cooled below 3000 Kelvin the atomic nuclei could hold onto all the electrons and one then had a highly uniform gas consisting of atomic hydrogen and helium.
Thus the cosmic microwave background photons no longer scattered and could stream freely.
Pressure waves in the plasma had kept the density and temperature uniform.
Once the medium was neutral the regions that were slightly denser than average began collapsing under their self-gravity.
The inflation phase in the very early universe had (a) made it extremely homogeneous and (b) had also pushed it to have an average density at a critical level (c) dark energy was negligible at that time.
By around 200 million years the first stars and galaxies had formed because regions that were only 0.001% denser were above the critical density level between continued expansion and collapse.
As a gas cloud collapses it heats, and radiates away heat, and collapses further. After sufficient collapse and cooling the first generation of massive stars and of galaxies formed.
And now we are in a universe with hundreds of billions of galaxies within our horizon.
Statistically impossible, they might say.
But inevitable, according to observations, general relativity, and atomic physics.
Bitcoin
How could Bitcoin not be part of Nature when it is grounded in energy, time, cryptography, game theory, network effects and incentives for anthropoids to organize energy, time, cryptography, chip design, game theory and network effects? Power laws are naturally emergent for many complex systems.
The latest power law regressions in Block time:
Price: $54672 x (B/16)^5.4 , where B is block years elapsed (will be 16 at the Halving)
Market Cap: $1.189 trillion x (B/16)^5.97
The volatility measure is about a multiplicative factor of two (one standard deviation of residuals).
The market cap best fit is so close to a time to the 6th power law that @Giovann35084111 , who was first to notice the power law relationship for price, has proposed that we are seeing the result of Metcalfe’s Law (a square law for the growth in value of networks) convolved with a growth in addresses as the third power of time. Alternatively we see that difficulty and hashrate have risen as the 12th power of time over the full interval, and more recently as the 8th power. So one can also formulate the rise in the value of Bitcoin’s network growing as 1/2 to 2/3 power of the rise in hashrate that creates and sustains it.