Infinity: Why the universe can’t be a computer simulation

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“A person standing on frozen water in Jökulsárlón” by Joshua Earle on Unsplash

Long ago, after having spent months in Switzerland, it stroke me just what that place reminded me of: “Welt Am Draht”. The movie was filmed to look “like no other place” and therefore mixes film footage from Munich, Cologne and Paris freely, to create a city that feels familiar but that you doesn’t quite seem to recognize.

This is exactly what Switzerland looks like. It features a mixture of old styles reminiscent of Germany, Italy and France simultaneously, a lot of frills, green idyllic pastures, cows… as well as water buffalo, ostriches, llamas, plus naked, ugly, grey concrete —lots and lots of it— sometimes hastily sprayed on by someone who would like at least SOME color somewhere. Sometimes it is freshly cleaned to return it to its original (did I mention UGLY?) concrete state, but fortunately it is often elaborately decorated by a sprayer group who obviously had a lot of practice. Miles-long practice.

Why do I mention that? Well, “Welt Am Draht” portrays its world like that because — spoiler — their world is fake. So being in Switzerland makes you wonder constantly, if you are living in a real country or a weirdly mixed-up computer simulation.

It got me thinking. The good news for our Reality is, there is Pi. Everything that is a circle has this number in it: it is the ratio between the circumference and the diameter of the circle. And since all the matter in this universe is made of atoms, it ultimately all comes down to spheres and other funnily-shaped figures with spherical parts that are the electrical fields of all the particles in the universe.

What does that mean for Reality? Well, since Pi is an irrational number, it automatically means that either the diameter (or radius), or the circumference of that circle has to be an irrational number as well. (You can check the details of this in the PS.)

It also means that a computer, which is a Finite State Machine, no matter how large and powerful, can not accurately represent the number.

Why? Because irrational numbers have an infinite amount of decimal points, and can not be represented any shorter.

So if the universe would be a simulation, the computer it is running on would have to regularly represent infinitely long numbers — for every particle, every field, every wave. Which, if the computer itself is finite, is actually impossible, because representing infinitely long numbers requires infinite amounts of memory — for each (!) irrational number in the universe.

Ergo, we just built a rudimentary mathematical proof that the universe is not a simulation running on any kind of finite state machine.

Neat, eh? Congratulations are in order. Now we can rest assured that this Reality of ours is the Real deal.

Until the next part of the Infinity series — where I show why it probably is not.

PS: Why either the circumference or the radius of a sphere has to be an irrational number:

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Science Fiction, Tech, sarcasm, and philosophical ramblings about the Universe.

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