Examples
Immune System
When a bacteria, virus, or some other pathogen invades the body, it is broken down by macrophages and the components are circulated through the immune system:
The proteins belonging to these foreign invaders are broken down, and a complementary pattern of proteins is reverse engineered by the immune system from scratch:
These proteins are called antibodies, and they bind to an epitope on the antigen like a lock fitting a key:
By doing so,
The immune system literally builds for itself a Model of the world with nearly 100% precision – technically speaking, Model Evidence is Maximized.
As a result, the immune system is never again surprised by the same invader – technically, it has placed an Upper bound on Surprise.
Margin of Error with respect to the Posterior Distribution – the Prediction Error - is limited, and consequently Free Energy is Minimized.
Bitcoin
Bitcoin is the most valuable digital asset in the world. Since its inception in 2008, various theses have been advanced to understand this unique asset class. Over a decade later the world appears to be in consensus on the Digital Gold narrative, largely in part, though not entirely, due to the Stock-to-Flow (S2F) Model. The S2F model is used to compute the ratio of the Stock of an asset in comparison to its Flow in order quantify its Scarcity.
This collective learning can fit into the Bayesian framework as follows:
Data
Data was gathered in the form of Bitcoin prices in relation to various currencies – mainly the U.S. Dollar.
Prior
Because Gold and related precious metals like Silver are valued significantly for their Scarcity, Digital Gold was hypothesized to also follow suit. Bitcoin is regarded as a Store of Value because of its strictly limited supply of 21 Million; only 21M Bitcoin will ever exist – making it a scarce asset, and a hedge against monetary inflation.
The Stock-to-Flow (S2F) Model has been used to approximate valuations of precious metals like Gold and Silver. Below, S2F Other represents the Prior knowledge of other scarce assets taken into consideration for this learning process.
Likelihood
After combining the BTC prices with the S2F Model, the S2F ratio for Bitcoin is computed.
A scatter plot of this S2F ratio vs the market value is created, and a line of best fit (linear regression) is drawn on the logarithmic scale to demonstrate a Pearson correlation coefficient = R² = 0.95.
This co-relation coefficient can represent the Likelihood variable in Bayes Theorem for calculating the Posterior Distribution.
This Posterior Distribution projects the future prices of Bitcoin from this Model.
Because the BTC/USD price tightly follows this S2F line, the following assumptions appear to hold:
Model Evidence is Maximized
Upper Bound is placed on Surprise
Free Energy is Minimized
Technically, maximizing model evidence is equivalent to minimizing surprise because the latter is the negative log of the probability of observations [p (o)], i.e. model evidence. So, an upper bound is placed on Surprise when Free Energy is minimized (source):
Antifragility
If you are familiar with the idea, these examples may invoke the concept of Antifragility.
The majority of insults to our immune system, and as we've observed - also Bitcoin, leads the system to become stronger. It's almost as if the systems are designed to thrive in disorder.
Is Antifragility intrinsic to bottom-up self-organizing and spontaneously ordering systems?
Lack of falsifiability and other criticisms notwithstanding, the Free Energy Principle appears to exhibit a non-trivial degree of qualitative and quantitative validity. Self-organizing biological systems are apparently modeling parts of the world. This mechanistic modelling is contingent upon the specific inputs and outputs parametrizing the system. The evidence for this Generative Model is maximized when inputs are integrated, and outputs are optimized, so as to place an upper bound on Surprise by minimizing Variational Free Energy.
In other words:
Each self-organizing system is building for itself a Model of the World so that it can accurately predict the world.
If the immune system is modeling antigens and Bitcoin is modeling gold, what might be the modeling objective of Ethereum?
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