Apple in a Box
Introduction
My goal with this article is to outline a way of thinking fundamentally about the universe using reversible cellular automata.
I am not an academic or scientist, I am a found, CTO, and software engineer, this article is just my own thoughts. I don't claim to have invented any of the ideas here, nor do I have citations. This article is purely an exercise of formalising my own thoughts on reversible cellular automata.
The universe is strange, it is worth exploring every way of thinking about it. These thoughts came about through my interest in cellular automata, but more recently through an interest in on-chain blockchain games. I was thinking about how you could generate a world that was only explorable through locality (e.g. actually travelling to the place). It turns out, it is only possible to build this kind of world through either a proof of work or lottery generation. I will revisit these ideas later in the article.
Think of this article as a thought experiment. The universe that we will conceive is a REVCAR universe (REVersible Cellular Automata with interesting Rules). The thought experiment assumes that the second law of thermodynamics gives rise to the most fundamental laws and behaviours within the universe.
- TODO - the definition of REVCAR is not entirely clear at the start, it is introduced as the article progresses
Reversible Cellular Automata
Reversible cellular automata are a type of cellular automata where the same rule applies both forward and backward. Most cellular automata that we are familiar with only have rules that apply forwards not backwards, Conway's Game of Life is a good example.
The second law of thermodynamics is implied by having a reversible rule-set. This means we can reason about entropy in the same way as we do about entropy of real world systems.
You'll start with a low state of entropy, as the simulation goes on, entropy tends to increase.
The REVCAR universe will be a reversible cellular automata.
The Problem with the Game of Life
The Game of Life is a type of cellular automata that was created by mathematician John Horton Conway. The Game of Life is probably the most well known cellular automata. The problem with it is that entropy tends to decrease as the simulation progresses. This is due to the rule only applying forwards and not backwards. This is fun for creating complexity and interesting structures that emulate the behaviour of life.
However, in our case it is not going to be useful for trying to think about how fundamental constructs and behaviours in the universe emerge from the second law of thermodynamics.
Machines
In our REVCAR universe, we can start thinking about the concept of a "machine". Here we will define a machine as a repetitive structure over many iterations. In order to build a machine in a reversible cellular automata, it is either all encompassing or it "breaks down". To give some examples of what can be classified as a machine: a human, bicycle, star, atom.
In the simplest form, you could think of a simple convection current gradient as the most basic "machine".
In the Game of Life, machines are often perpetual repeating structures. A glider gun is perhaps the best example. A glider gun does not obey the second law of thermodynamics, therefore we aren't interested in these types of constructions for the sake of this thought experiment.
I'm going to introduce the idea here of the "environment dependence hypothesis". This is the idea that a machine is defined in terms of its environment, and it is only created within the context of its environment. A bicycle, for example, is not useful in space. In addition, a bicycle does not spontaneously form in space. Instead, a bicycle is only useful within a confident environment, such as roads, where there are humans that will utilise them for the purpose of leisure or transport. This is quite a complex definition, its creation is a result of billions of years of evolution and thousands of years of human progress and development.
Therefore, for our universe to be interesting, we want to see machines which work in their native environment and are created inside of an environment.
Apple in a Box
The "apple in a box" is a thought experiment, whereby if you have an apple in a perfectly closed box and wait an infinite amount of time, the apple will reform in the future into its exact same state, you may have to wait a quadrillion years. This is the exact same behaviour as you'd observe in REVCAR. If you deployed a machine, you could forward the state N number of times until the machine magically reformed back into itself.
Although this thought experiment is interesting, it is not at all helpful. This is because you'd have to wait an unreasonable amount of time before you see the apple form again.
What is more interesting is running the rules in reverse. What came before the apple? What created it?
Anti-matter
Anti-matter plays an important role in our idea of the universe. In the observable universe, we notice that anti-matter is often created spontaneously through the creation of particle and anti-particle pairs (quantum foam). This type of particle anti-particle pair creation is constantly happening, with these particles instantly annihilating. This is deeply connected with the idea of black holes evaporating and obeying the 2nd law. However, it is also important in our reversible cellular automata to enable "user input".
In order to have a concious external user provide input to our universe, while also remaining reversible, particle anti-particle pairs are necessary. Let's assume you write your name into our reversible cellular automata at iteration n. You would expect iteration n - 1 to deterministically be an empty universe. However, this is not the case in a typical reversible cellular automata construction. Our construction must satisfy the property that at iteration n - 1, the drawn name must be the empty universe. The only way to achieve this is by every input being the creation of a state anti-state pair.
In addition to this, all quantum foam is driven by user input. Only the end user can create a particle anti-particle pair.
The implications of this assumption is that it helps us better understand how black holes and space time work within this simulation.
Black Holes
Now knowing REVCAR has quantum foam, we can start to reason about black holes. A black hole is a region of space time where the curvature of space time is so large that anything that crosses the black hole's "event horizon" has a single destination, the singularity.
In the observable universe, the only information that escapes a black hole is via the gravitational affect on quantum foam, preventing the particle anti-particle pairs from annihilating each other. This property must hold in REVCAR for us to be able to identify a black hole.
A black hole is machine within REVCAR where the only information about the creation of the machine (things that fell into it) are radiated by the interaction with quantum foam. In addition, it is a region of the cellular automata where things can only fall into it, not escape.
This begs the philosophical question about our observable universe, what if the quantum foam was completely still? What if there was no user input? In this model, the black hole would not radiate any information. Is the universe making a promise that at some point in the future, a particle anti-particle pair would fall into the black hole? Without an observer, is the universe stale?
Space and Time
Based on our conclusions of the black hole hypothesis, space and time is emergent from the rules of our reversible cellular automata. Space is not defined by the lattice of the universe. The core lattice of REVCAR can be thought of as just that, the core lattice. Higher order structures are emergent. Space time is an emergent property.
Exploration
- TODO - holographic principle and how that ties with on-chain blockchain games
Holographic Principle
The Big Bang
By virtue of the reversible nature of reversible cellular automata, we can reverse the simulation and find out what created our supposed machine. The "name" construction would spontaneously form from the coaleasing of gas and dust. However, I'm here to argue that machines never form from gas and dust. Instead, they form from a series of long running processes. If we forward back in time, we should see the birth of the universe.
Given the 'apple in a box' principle, the so called 'big bang' is not the start. The big bang is the point of lowest entropy. Under this idea, the big bounce is the most likely explanation for the universe. Time is defined by iterations time is an endless sea.
Extra Thoughts and Ideas
- TODO - generalising to higher dimensions
- TODO - double slit experiment on a reality scale
- TODO - thoughts on how that ties with abstraction and how design should work
TODO
- TODO - time (emergent in a proof of work system)
- TODO - the speed of light (this is the speed of the rule set or computation)