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The Mathematical Universe
This is a large idea and will take a few pages to describe. It is in two parts. The first explains that there is no difference between a mathematical model of a universe and the “real” universe itself (to being contained within it), and the second part explains that there are an infinite number of these models.
Everything in the universe can be predicted using math. There is not one phenomenon anywhere, that we are aware of, that does not fit into a mathematical model.
Using the existing tools that we have (Classical Mechanics, General Relativity, Quantum Mechanics), and with a knowledge of the state of every particle in existence, we would be able to accurately predict the future.
We could predict that the Moon will travel around the Earth; that a leaf falling from a tree will blow twenty metres from it before landing on the ground; that the same tree, falling onto a road five minutes later, will hit the car under it.
Given enough information, we could even track the changes in the car driver’s brain and predict exactly when they will slam on the brakes.
This is because even the human brain is predictable using math.
In tests, it has been shown that it is possible for a computer to predict what choice a human will make between two separate buttons a few seconds before the human actually consciously makes the decision.
We are all computing devices. The inputs to our calculating machines are the bodily senses, and the outputs are the decisions that we make. We like to think that we have free will and that we make our decisions independent of our bodies, but if a computer can be made which can model what we are about to decide, then there is no such thing as free will.
A complex enough mathematical model will predict not just the fluid dynamics of the leaf as it swims through the air, or the Newtonian mechanics of the tree as it falls gracefully in an elliptic arc towards the ground, but also the movement of electric and chemical impulses through the human’s brain as it reacts to the sight before it.
The model would be able to carry on predicting, moment after moment, and show exactly what the human would do at each instant, including the thoughts that go through its head.
Is the human in this story “aware” of itself in the same way as we are?
Because there is nothing at all in the universe that is not calculable, the answer to this is that the human in the story is no different to the human that is reading this text. A model that can predict the interactions of every particle in a system accurately can also predict the emergent properties of those interactions.
Fluid dynamics are an emergent property of fundamental physical laws, for example. They are a simplification of the interactions of billions of basic particles. Human thought is another emergent property, which is a simplification of the interactions of billions of neurons.
The sceptical reader may point out that the difference is that the modelled human in the story is just a model and is not “real”, but then what exactly is reality?
Possibly the simplest answer to this is that reality is the world that we experience.
You are experiencing a world in which you are reading this page. A model of you, right down to the fundamental particles, is also experiencing a world in which it reads this page. If the model is exact, then the model includes all of your memories, and the modelled sensory inputs are exactly the same as well.
That model believes it is in the “real” world as well.
The “real” world is real to you.
The modelled world is real to the model.
But because there is nothing in the universe that cannot be modelled by math, there is therefore no difference between the real world and the modelled world. Everything that exists in the “real” world can also exist in the modelled world.
One of the most convincing (to me) arguments for this, is that physics has fundamental conservation laws. You cannot create or destroy energy.
This begs the question: if we cannot create or destroy energy, then how is it that we exist, and the planets exist, and we see other things that exist?
The answer, again, lies in the fact that our universe is mathematical in nature.
In quantum physics, we find that there is no such thing as “nothing”. When we look at the smallest spaces and try to examine the void that we expect to find there, we actually find that it is fizzing in energy.
We find that in the smallest spaces, tiny particles pop into existence and annihilate each other constantly. How? Because the particles are mathematical in nature, they have certain values which can be positive or negative. If you put a positive and negative thing together in the same place, they cancel out.
But, conversely, this also means that if you start with nothing, then there is no reason why this cannot spontaneously evolve into lots of positive and negative particles. As long as everything balances out to zero in the end, there is no violation of the conservation laws.
Keep spontaneously creating and interacting all of these particles that would annihilate each other if they came together, and you end up with something that looks a lot like our universe.
No matter the complexity of the object, there is a mathematical model that will predict it.
A model that predicts the entire contents of the universe you are sitting in also contains a copy of you, thinking the exact thoughts that you are currently thinking.
In fact, because there is nothing in your universe which is not predictable using math, there is no way for you to tell whether you are a “real” you (whatever “real” means), or are you a model of you.
In other words, there is no difference, to the beings contained within it, between a “real” universe, and a modeled universe.
The second part of this idea has to do with the infinite number of possible models that exist.
Consider a simple mathematical model starting with the number zero: “add 2 to the number”.
If you iterate the model on paper five times, then you will result in the number 10.
If you iterate the model five times in your head, then the answer is still 10.
Even if you don’t run the model, you know that if you were to run it, the fifth time, the answer would be 10.
This shows that the result is 10, no matter whether you actually do the math, or not. The result of that specific model is 10, after five iterations.
Now, let’s say you never even thought of the model in the first place. Let’s say you never read the above sentences and it never occurred to you to add 2 to 0 five times. Would the answer still be 10?
Yes. The set of numbers that comprises that model’s universe always has 10 as the answer after 5 iterations, even if the model has never been formulated. This is similar to saying that 3x5=15 whether you do the multiplication or not.
We’ve already established that the entire universe is indistinguishable from a mathematical model of the universe.
This means that for every second of that universe, it is possible to predict the next second. And, in fact, it is possible to predict every second for all time. Yes, quantum mechanics makes this tricky, so there are infinite results, but the fact remains that if you know the current state of the universe, you can predict the future.
Consider this hugely complex model in the same way as the simple one we considered before.
If we were to run the entire universe through a computer that applied physical rules to the numbers, we could run the universe forward so that we could see what happens, what people do, what people think or say.
But what if we don’t run the universe through a computer. Will those thoughts and events happen anyway?
In the simple model, we showed that the number 10 results if we start with 0 and add 2 five times. This is true no matter whether the model is run or not. Of course, the result (10) makes absolutely no impression on the “real” world if it is not run, but that does not stop it from being real.
Similarly, a model of the universe that begins with you reading the beginning of this line will continue to model what happens after that, whether or not the model is computed in a huge “reality” machine or is just a potential model.
In the model, all results are real to each other. In the simple model, the number 8 was real to the number 10, because the 10 is a result of a computation on 8. In the more complex model, the reality of the book or screen you are reading is not questioned, because otherwise, how could you be reading these words?
The universe exists to its inhabitants whether it is computed in a “higher reality” or not. And in fact, the reality of the universe doesn’t change at all whether it is kept in potential or is computed. The 10 in the simple model is still the same 10 whether the model is computed or not.
Now we’re ready for the largest implication of this: If all mathematical models that model a reality are “real” to the intelligent beings that are modelled whether the model is computed or not, then all mathematical models of reality are real.
All mathematical models of reality are real.
And there are an infinite number of them. There are models where you are reading this on paper, on a computer screen, through audio, through someone signing at you. There are even models where you, for some reason, are not reading this, possibly because in those realities, you don’t exist, the Earth doesn’t exist, and the entire universe itself is two-dimensional. If the math is good, the universe is real.