# 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:

!\[A close up of text on a black background

Description automatically generated]\(<https://3692130413-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2Fethereum-a-model-of-the-world%2F-MW0eXDgHOrlV5dF8lJH%2F-MW0esoiLN4ZKV88qE1l%2F0.gif?generation=1616009465705537\\&alt=media>)

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:

![](https://3692130413-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2Fethereum-a-model-of-the-world%2F-MW0eXDgHOrlV5dF8lJH%2F-MW0esojQ8RCfvyWkkKj%2F1.gif?generation=1616009465808947\&alt=media)!\[A close up of a logo

Description automatically generated]\(<https://3692130413-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2Fethereum-a-model-of-the-world%2F-MW0eXDgHOrlV5dF8lJH%2F-MW0esoklPkd7P7OOMi0%2F2.gif?generation=1616009465784772\\&alt=media)![A> close up of a device

Description automatically generated]\(<https://3692130413-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2Fethereum-a-model-of-the-world%2F-MW0eXDgHOrlV5dF8lJH%2F-MW0esoleeeOhSl-BsrM%2F3.gif?generation=1616009465815488\\&alt=media>)

These proteins are called **antibodies**, and they bind to an **epitope** on the antigen like a ***lock fitting a key***:

![](https://3692130413-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2Fethereum-a-model-of-the-world%2F-MW0eXDgHOrlV5dF8lJH%2F-MW0esombXY51wx7QSNG%2F4.gif?generation=1616009465957048\&alt=media) !\[A picture containing object, monitor, clock, front

Description automatically generated]\(<https://3692130413-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2Fethereum-a-model-of-the-world%2F-MW0eXDgHOrlV5dF8lJH%2F-MW0eson4rJkXaiPKOBR%2F5.gif?generation=1616009465742795\\&alt=media>)

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**](https://medium.com/@100trillionUSD/modeling-bitcoins-value-with-scarcity-91fa0fc03e25). 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.

![](https://3692130413-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2Fethereum-a-model-of-the-world%2F-MW0eXDgHOrlV5dF8lJH%2F-MW0esoodhwcCExj4vGp%2F6.png?generation=1616009465738817\&alt=media)

#### 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.

![](https://3692130413-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2Fethereum-a-model-of-the-world%2F-MW0eXDgHOrlV5dF8lJH%2F-MW0esopRwpu5b7cYcWK%2F7.png?generation=1616009465747440\&alt=media)

#### Likelihood

After combining the BTC prices with the S2F Model, the S2F ratio for Bitcoin is [computed](https://medium.com/@100trillionUSD/modeling-bitcoins-value-with-scarcity-91fa0fc03e25).

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.

![](https://3692130413-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2Fethereum-a-model-of-the-world%2F-MW0eXDgHOrlV5dF8lJH%2F-MW0esoqfrcTbAyV1HSx%2F8.png?generation=1616009465733632\&alt=media)

This co-relation coefficient can represent the Likelihood variable in Bayes Theorem for calculating the Posterior Distribution.

![](https://3692130413-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2Fethereum-a-model-of-the-world%2F-MW0eXDgHOrlV5dF8lJH%2F-MW0esorLOfoWSkyDKQp%2F9.png?generation=1616009465732094\&alt=media)

This Posterior Distribution projects the future prices of Bitcoin from this Model.

![](https://3692130413-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2Fethereum-a-model-of-the-world%2F-MW0eXDgHOrlV5dF8lJH%2F-MW0esosE3vGS_np1Jgv%2F10.png?generation=1616009465738766\&alt=media)

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](https://medium.com/@solopchuk/tutorial-on-active-inference-30edcf50f5dc)):

![An upper bound is quite literally placed on Surprise (-log p) when Free Energy is minimized.](https://3692130413-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2Fethereum-a-model-of-the-world%2F-MW0eXDgHOrlV5dF8lJH%2F-MW0esotCht1Mj0rUBJW%2F11.png?generation=1616009465719929\&alt=media)

## Antifragility

If you are familiar with the idea, these examples may invoke the concept of Antifragility.

![](https://3692130413-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-MW0_lVVcWu8aAggonNE%2F-M_LbPJL-7_aqBVvLlmo%2F-M_Lfm2kq4wY_PHCshaa%2Fimage.png?alt=media\&token=25e5e402-d4aa-48ba-967f-e30a001e38fe)

*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**.*

{% hint style="info" %}
Is Antifragility intrinsic to bottom-up self-organizing and spontaneously ordering systems?
{% endhint %}

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:

{% hint style="info" %}
Each self-organizing system is **building** for itself a Model of the World so that it can accurately **predict** the world.
{% endhint %}

If the immune system is modeling antigens and Bitcoin is modeling gold, what might be the modeling objective of Ethereum?
