Set Definition of the Metaverse

Introducing the emergent properties that I believe make up the foundations of universes with the aim to formulate a generalized definition of the Metaverse.

Set Definition of the Metaverse

In describing Assembly Theory and the origins of life, the approach that the theorists take leverages not only the biological, chemical & physical properties but also the emergent properties of the universe. Instead of attempting to explain the processes that have resulted in life, as we know it, through physics, Assembly Theory founds its basis upon selection, evolution and complexity.

Similarly for the Metaverse, there have been attempts at definitions based on the physical properties of the environments humans have thus far experienced. This level of abstraction prevents a generalized definition and limits the ability to understand the relationship between the different environments agents are able to access.

My thesis is that the definition should be based on the emergent properties of the Experience Runtime that can be generally applied to any universe. This abstraction, I hope will aid in expanding the conversations of systems & applications in and between the universes whether they are physical, imagined or digital.

Following, in this first part, I am introducing the emergent properties that I believe make up the foundations of universes with the aim to formulate a generalized definition of the Metaverse.

Experience Runtime

It is beyond scope of this paper to consider if the laws of physics of the physical universe came first or if the universe itself existed prior to it. In any case, it’s undeniable that the physical universe operates by the laws of physics (some of which we have been able to grok). These laws dictate the properties of light, movement and interactivity of all things in the physical universe. While deep layers of laws make up the physical reality, only a subset of these laws are directly experienced by humans in the physical universe. In different universes, the laws experienced by the agents will differ.

For example, in the physical universe, when a ball is thrown in the air, it is possible to describe the quantum mechanics behind the movement. But, as humans we experience the Newtonian mechanics of the ball’s movements. This is the Experience Runtime.

This is fundamental because each universe’s Experience Runtime dictates the possibilities and limitations for the agents in the universe while the layers that make up the runtime are opaque to the participants of the unverse.

Universes

There is a set of universes, physical, imagined and digital that can be notated as: \[ U =\{U_0, U_1, U_2, ..., U_n\} \]

Let’s assume \( U_0 \) is a physical universe, \( U_1 \) a digital universe & \( U_2 \) is an imaginary universe. These very different universes may intersect offering unique experiences. The physical universe & a digital one may intersect through augmented reality. The physical universe & an imaginary one intersect through make-believe games. These intersections can be represented as \( U_0 \bigcap U_1 \) and \( U_0 \bigcap U_2 \) respectively.

Universe-intersections

Figure 1: Example of intersection of Experience Runtimes

Features & Agents

In every universe, there is a vast number of properties that participate in the Experience Runtime. In the physical universe, there are stars, planets, atmospheres, biospheres and more. In digital & imagined universes, there are transmutations of some of these properties. Let’s call the properties that undergo transmutation, Features. For an universe \( U_x \), Features can be represented as: \[ F_x = \{F_0, F_1, F_1, ..., F_n\} \]

Agents are also properties that participate in an Experience Runtime. While Features transmute between universes, Agents transfigure while traveling between universes. For an universe \( U_x \), Agents can be represented as:
\[ A_x =\{A_0, A_1, A_2, ..., A_n\} \]

The properties of the universe then can be represented as: \[ U_x = F_x \bigcup A_x \]

When a Feature undergoes the process of transmutation between universes, it exists as different Features that may have shared properties. A tree in the physical universe may have only two of its properties represented in a digital universe. The shared properties can then be represented as \( U_0F_0 \bigcap U_1F_0 \).

Feature-properties

Figure 2: Example of transmutated properties between universes

When an Agent undergoes the process of transfiguration, similar to Features, it exists as different Agents that may share properties. But, unlike Features, Agents may retain ownership of its properties across universes. The shared properties can be represented as \( U_0A_0 \bigcap U_1A_0 \) and the Agent’s ownership of the properties can be represented as \( U_1A_0 \subset U_0A_0 \).

Agent-ownership

Figure 3: Example of properties owned by Agents between universes

These processes of transmutation and transfiguration are not limited to the universes that have a physical & digital separation. These processes are also applied to Features & Agents among multiple digital universes as well.

Causal Graph

Cause & effect are built into the fabric of the laws that govern the Experience Runtime of the physical universe. The relationship of causes & effects is best represented in a graph. Let’s call this the Causal Graph. This graph describes the relationship of all properties in the universe as Agents & Features interact, build relationships and participate in systems such as societies and commerce. Causal Graphs between universes should always remain disconnected even when Features undergo transmutation & Agents undergo transfiguration. But, since Agents can retain ownership of properties across universes, this ownership can be represented in Causal Graphs.

For an universe \( U_x \) the nodes of this graph \( N_x \) are correlated by the links of the graph \( L_x \) and can be represented as: \[ L_x = \{{N_i, N_j} | N_i, N_j \in N_x\} \]

Where \( N_i \) and \( N_j \) are nodes and since an universe is described as: \[ U_x = F_x \bigcup A_x \]

The nodes of the graph in an universe must be a subset of Features & Agents of \( U_x \) represented as \( N_x \subset U_x \).

Metaverse

Given these abstractions, I propose a generalized definition that the Metaverse is the representation of transmutation of Features, transfiguration of Agents and the Causal Graphs between Experience Runtimes of different universes.

In subsequent parts, I will explore how the existing systems and applications as well as new ones align with these abstractions & definition.


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