Universe is a p2p network

Few examples of how p2p networks change with the scale

  1. Physics: …. →quarks & leptons→protons & electrons→ atoms →molecules →compounds → lumps of mass →earth →solar system → Milky Way →….
  1. Carbon-based biological systems: …→ atoms →molecules →organelles →cells →tissues →organs →Organism
  2. Human Societal System: … →Human →Family →Society →Village →City →State →Country →Continent →Planet →
  3. Crypto mining: Individual Miners →Mining Pools
The nature of p2p network changes with the scale.

What is a p2p network?

A p2p network is a group of similar elements (let’s say nodes) that interact with each other and can be regarded to exist and function as a single entity in some conceptual level. Three fundamental characteristics of a p2p network are:

  1. No. of nodes
  2. The upper bound for the complexity of nodes
  3. Strength & complexity of connection among the nodes

What does it mean to be decentralized?

A group (e.g. p2p network) is decentralized if its constituent elements have a similar amount of power to control the existence and functioning of the group. Decentralization of a group can be thought as a lack of order in the power of its constituent elements to act as a group i.e. power structure of the group and the ‘power’ is dependent on the type of p2p network.

  1. A PoW blockchain (e.g. Bitcoin) is a p2p network where the power of a node is its hash power exhibited by the speed at which it can solve a mathematical problem.
  2. Our solar system is a (highly centralized) p2p network where the sun and planets are nodes and the power of the nodes are their masses exhibited via gravitational force.
  3. USA is a p2p network of 50 states (nodes) and their power to govern the network (country) stem from several factors such as population, economy, political belief, etc.
  4. A human body is a p2p network of organs.
  5. A brain is a p2p network of neurons.

Using entropy to measure decentralization

Decentralization of a group is the lack of order in the power of its members, so the degree of decentralization would be equivalent to the measure of disorder or randomness, similar to the concept of entropy https://en.wikipedia.org/wiki/Entropy. Entropy is a measure of the number of different ways that a set of objects can be arranged https://link.springer.com/article/10.1186/1936-6434-6-30. In statistical mechanics, entropy is the measure of possible number of micro-states for a macro-state. For a p2p network, the equivalent would be a metric proportional to the number of possible configurations of the nodes to form the network. In information theory, entropy is the average information carried by a symbol in a system i.e. group of symbols.

Entropy in information theory

Here, I will briefly explain information-theoretic view of entropy and relate that to the decentralization of a p2p network. According to Shannon’s information theory, entropy is the average information content of an event in a system. For example, for a language with a set of symbols, it’s entropy is the average information contained in a symbol.

This provides an important insight: the probability of existence/occurrence of a node decreases with increase in its power over the network.

The probability of existence of a node decreases with its power over the network.
  1. Power = information. The probability that it will be sunny in June 21 in Boston is high, hence the information content of the event is low. However, the probability that there will be an earthquake on June 21 in Boston is extremely low, hence the information content of the event is high.
  2. Power = hash power.
Source: Gencer et al., FC’18
Source: https://www.vanderbilt.edu/AnS/physics/astrocourses/ast201/extrasolar_planets.html

Entropy in a p2p network

Let’s assume that the measure of decentralization in a p2p network can be formulated as: H + N-N

Probability of centralization P(c)

Dependence of the probability of centralization P(c) on the characteristics of a p2p network.

1. Probability of centralization P(c) increases with the increase in the upper bound of node complexity

Let’s represent a p2p network by a set of realizations of random variable X (each unique x represent a possible node) and define following quantities.

  1. Increase in centralization of bitcoin network with increase in the sophisticated technology for mining, e.g. ASICs
  2. Increase in centralization of the p2p network of countries in Earth with the advancement of the countries
  3. Increase in centralization of the corporate businesses with increase in their complexity and size (Apple ?)
  4. Increase in centralization in the organisms with increase in evolution. e.g. Homo Sapiens Sapiens are more centralized than Homo Erectus.
Probability of centralization P(c) increases with the increase in node complexity.

2. Probability of centralization P(c) decreases with the increase in no. of nodes

When the no. of nodes in a network increases, the effective support of p(x)(the ratio between the no. of actual nodes in existence and the total no. of possible nodes) increases, which in turn increases the entropy or decentralization i.e. the probability of centralization P(c) decreases.

3. Probability of centralization P(c) increases with the increase in strength and complexity of node-node interaction

Centralization is a process when nodes in a network tend to interact with each other to create an order in the power of the nodes (e.g. forming groups or sub-networks). This increase in the order decreases the entropy and decentralization. Increase in the strength and complexity of the node-node interactions will allow the nodes to communicate and interact with each other more efficiently, thereby helping the process of centralization.

  1. Globalization (a form of centralization) increased with our technological advancement in transportation and communication
  2. Internet. So many examples here.
  3. Let’s visualize an island of 100 people (100 nodes) with primitive technology. Here, distance is one of the most important factor that controls the strength of node-node interaction. With time, it is highly likely that one individual or a group of people will be dominant (e.g. one can be a tribal leader and start a tribe), leading to the centralization. If we increase the size of the island by 10 times, it is likely that there will be more than one tribe. If we keep on increasing the size of the island, the probability of the number of tribes will increase while the size of the tribes will decrease. If we increase the size of the island by a million times, it is likely that the 100 people will never meet with each other in their life time achieving a state of complete decentralization. This example shows that the decrease in node-node interaction tend to increase the decentralization of a network.

Evolutionary force vs. Entropic force

It seems there are two opposing forces in the universe: 1) Entropic force (from 2nd law of Thermodynamics) which tend to increase the entropy and 2) Evolutionary force which tend to decrease the entropy by creating an order.

Two opposing forces: entropic force and evolutionary force.
  1. Entropic force: is due to the tendency of system to increase its entropy (according to 2nd law of Thermodynamics) https://en.wikipedia.org/wiki/Entropic_force. For a p2p network, it will be the tendency of the network to increase its decentralization.
  2. Evolutionary force: (Assumption) The evolutionary force of a p2p network can be defined as the tendency of the nodes to interact with each other and create an order in the network (e.g. by forming sub-groups). (Assumption) And the particular order or a subset of orders that helps the p2p network to sustain over time tend to dominate (i.e. survival of the fittest). The evolution might happen by the increase in the node complexity and/or complexity and strength of node-node interaction. With evolution, the no. of nodes in a network tend to decrease. I think this force is what creates life.
  1. Human Societal System: (evolution from socio-economic perspective)… →Human →Family →Society →Village →City →State →Country →Continent →…(ask Elon Musk)
  2. Crypto mining: Individual Miners →Mining Pools

Is Universe expanding to increase its entropy so that it can balance the evolutionary force?

From a p2p perspective of the universe, one way of increasing the entropy (and decentralization) is to decrease the strength and complexity of the node-node interaction. Since out of 4 fundamental forces, only gravitational and electromagnetic forces have infinite ranges and both of them decrease quadratically with the distance, a good way to decrease the node-node interaction is to increase the distance between the nodes. Maybe the universe is doing the same by expanding itself? :) [The expansion of the universe doesn’t actually increase its entropy, however the expansion allows it be in a state that can attain more entropy (more choices)].

What if our universe itself is a node of a larger p2p network??

How do we design our own p2p networks learning from natural p2p networks?

next medium article

Using entropy for the comparison of PoW vs. POS vs. DPOS ?

next medium article

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