The most significant concept on our journey to the higher reality is not that the universe is fundamentally unpredictable. It is not even that there may be many parallel universes apart from our own. No, the crucial idea is an apparently simple – oh, so deceptively simple – concept: one which will turn out to have the most profound consequences, and with implications that are genuinely unimaginable.

The concept is this: fundamentally, our universe is purely a pattern.

Wait, what? (I hear you say), that’s surely no big deal! There are patterns everywhere; we’re surrounded by patterns. Carpets and table covers and shirts are designed with patterns. City blocks and car parks and bricks in the wall are arranged in patterns. The beat of music and of ocean waves and of distant galactic pulsars are patterns in time. It would be far more surprising if you said that the universe wasn’t arranged in patterns!

So now we come to the nub of it. In all of the examples above, the pattern is describing an arrangement of things – colours, buildings, bricks, waves, noises, pulses of radiation. In contrast, what I am saying is that, ultimately, things themselves are purely patterns – it is the pattern itself that is fundamental!

This is going to take a fair amount of explanation, so let’s start with what we mean by a pattern. To be posh, we may call a pattern a mathematical structure. A mathematical structure is a collection of mathematical objects such as numbers which are related to each other by mathematical rules such as addition, multiplication or more complicated operations. The even numbers from 2 to 10 represent a mathematical structure. Mathematicians reserve the term for patterns that obey selected mathematical rules, but the rules are wide-ranging in scope, and for our  purposes we are going to use “pattern” and “mathematical structure” interchangeably.

So, we could just as well have said that, fundamentally, our universe is a mathematical structure. That is not a new thought. Two-and-a-half millennia ago, the followers of Pythagoras believed in “the properties and ratios of harmonies in numbers”. Currently, the most prominent proponent for the universe being purely a mathematical structure is Max Tegmark (Tegmark, M. Our mathematical universe: my quest for the ultimate nature of reality. Allen Lane (2014)).

To follow the argument that the universe is purely a mathematical structure, you start by asking what things are made of – say, for instance, a diamond. Answer: it’s a crystal made of carbon atoms. So, what is a carbon atom? It’s a tightly-knit cloud of six electrically positive protons together with six (or, sometimes, seven or eight) neutrons, surrounded by a much more dispersed cloud of six electrically negative electrons in the vicinity, balancing the electric charge. And what are protons, neutrons and electrons? The proton and the neutron are each composed of three quarks. And a quark? Well, it has properties such as spin and mass and charge, but it doesn’t seem to be made of any smaller particles, and so we call it an elementary particle. The electron is an elementary particle as well.

Since the elementary particles don’t seem to be made of anything more basic, all we can say about them is how they interact with forces and other elementary particles. These interactions can be boiled down to a short list of properties belonging to each type of particle, but that’s about as far as we can go. So, effectively, the elementary particles can be viewed as collections of numbers that determine how they interact through forces that, themselves, can be categorized in purely numerical terms.

Although that in itself is suggestive of the universe being purely a mathematical structure, there’s more. For one thing, although quantum mechanics works well for particles – for example, explaining the pattern on the screen in the double-slit experiment, or predicting the outcome of entanglement experiments as you change the detector angles – it doesn’t explain how new particles can be created or annihilated in interactions. This is where quantum fields come in – creation and annihilation of particles is par for the course in quantum field theory.