Life, The Mathematical Universe Hypothesis and Everything

The Mathematical Universe Hypothesis (MUH) is a science philosophy that says that our universe is nothing more than a mathematical structure. It also says that all definable mathematical structures are universes that are just as real as ours.

It doesn’t seem to be taken too seriously. The person who proposed it, Max Tegmark, refers to his MUH papers with the perspective “Every time I’ve written ten mainstream papers, I allow myself to indulge in writing one wacky one” under his home page link “Crazy Science”. Maybe this is just a disclaimer because it’s on an MIT site and he’s a well respected member of the scientific community.

Well I’m not. And I think it should be taken seriously and I’d like to explain why. But my approach will be from a finitist point of view, that any definable finite and discrete mathematical structure is a real universe. I’ll also be presuming that our universe is finite and discrete.

In this post I’ll show you some things most people haven’t seen. I’ll stretch your imagination to think of reality differently. I’ll show you You Tube clips that are truly stunning. And if these things don’t blow you right out of your chair then you’re simply reading the wrong blog.

Then as a bonus I’ll show how the MUH provides answers to some of the Big Questions, such as Why is there something rather than nothing?, What happened before the universe? and What is the meaning of life?

But I’ll begin with something simple and ask: What is strange about this picture?

Source: Public Domain

Source: Public Domain

This picture is an example of what’s come to be known as the Droste Effect. It occurs when a copy of a picture is embedded within the picture itself, creating an infinite recursion of picture-within-picture. They occur in many places, for example if you stand between two mirrors facing each other. My personal favourite is

showing Lloyd Bridges having one of many bad days in the movie Airplane! (aka Flying High) by Paramount Pictures.

I’m going to return to the Droste effect later, but now I want to introduce something that I’ve found helps in conceptualizing our universe as “just” a piece of mathematics. It’s Conway’s “Life”. It’s a set of rules for creating patterns that change. It’s the most well-known example of cellular automata and if you haven’t heard of it you’ve still probably seen it somewhere such as on a screensaver. You can play around with it here.

It consists of a rectangular grid of cells that form a pattern by being coloured black or white. The pattern changes by the following simple and arbitrary rule:

  • every black cell with 2 or 3 black adjacent cells becomes black
  • every white cell with 3 black adjacent cells becomes black
  • all other cells become white

Here’s a random pattern as a starting point:


When the Life algorithm is applied to most random starting patterns, it stays pretty chaotic. Here’s the pattern at the fortieth “generation” after the starting pattern above:


(Note: The above implementation of Life treats boundaries as joined. Squares on the right edge are considered to be neighbours of corresponding cells on the left edge. Similarly for the top and bottom edges. The examples below don’t)

Now here’s what I need you to do. I need you to think of the “universe” created by the Life algorithm in the same way that you think of our own. Life is a much simpler universe than ours. Ours is vastly bigger (than the examples I’ll show), and our universe most probably has a more complex set of rules than Life (but maybe not) and rather than being a uniform grid I believe our universe is more like a tangled network of points with lines joining them:

Tangle, 2011, In Progress

But it is essentially the same kind of object as our universe, ie a mathematically defined discrete structure. So as I discuss things about these sample universes of Life, I want you to apply my comments equally to your concept of our universe (to be considered as one of all possible universes that follow our laws of physics), but at the sub sub sub sub atomic level where science observes very discrete (or quantum) things happening.

All of the possible Life universes are defined by their size (number of rows and columns) and starting pattern. A Life universe can then be observed as a series of patterns such as the above pictures of two different generations. But there are two ways to look at the Life universe, which I’ll call “from the inside” and “from the outside”. I’ll start with looking from the inside and here’s an example

Source: Wikimedia Commons

Bill Gosper’s Glider Gun in action. This image was made by using Life32 v2.15 beta, by Johan G. Bontes. (Photo credit: Wikipedia)

This inside view flicks through successive generations. We’re no longer seeing successive applications of an algorithm that are recorded in separate sets of black and white patterns, we’re seeing motion. We’re seeing time. See the “gliders” moving to the bottom right hand corner? They are things and they are going somewhere.

Now let’s look at a Life universe from the outside. Here’s a random starting pattern of another Life universe:

lifegen1Now I’ve added its second generation which sits just slightly behind the first generation:


and here it is after several generations:


No sense of movement here. No sense of time. Just a three-dimensional pattern that does not change. You could put it in a cardboard box and stick it in the cupboard and it would be exactly the same when you come back later. In fact I have stored the moving “gliders” pattern above in a cardboard box, here’s a picture of it:

Glider All Boxed Up

Glider All Boxed Up

and if I was to open this box I’d see a series of 0’s and 1’s that haven’t changed.

Now the next thing I want to consider is What sort of organised complexities can exist within our Life universes? Quite a bit it turns out. But how far do you think that complexity can go to? More “particles” like the gliders above? A collection of nice stable patterns? Well, if you’re only going to click on one link in this post then click this one right here (6:20 video).

If a Life universe is sufficiently large and allows stable structures that reproduce and can evolve (read: life) and if they evolve sufficiently far that they have a central nervous system that can build internal models of its environment (read: intelligence) then those central nervous systems will have thought processes that perceive their universe as existing. And their sense of “existing” will be just as strong and real as ours is.

Here’s the thing: all of the complex sequences shown in the video weren’t invented, they were discovered (not doubt through great perseverance and ingenuity). They already existed, in exactly the same way as the complexity of the decimal expansion of the number pi already existed before we understood pi. We, as a species, have simply developed tools to look at Life universes from the inside. For the same reason, the sense of reality of the evolved life within Life will not depend upon another universe (eg ours) building a simulation tool to look at the Life universe, because it already existed “before” we simulated it just as much as it exists “after” we simulated it.

There is a community of enthusiasts that build these Life patterns here. And a Life Wiki here. They’ve shown that Life has patterns that can reproduce themselves. As one final example of organised complexity I want to show what some consider to be a key step in the evolution of consciousness. I mentioned above about life in Life evolving brains that can mentally build internal models of their environment. Douglas Hofstadter puts forward a compelling argument that consciousness can only arise from a yet greater ability of the brain: the ability to mentally build internal models of its own thinking processes. A kind of recursion of a model within a model. A sort of Droste Effect. Hofstadter has written some excellent popular books including Godel, Escher, Bach: An Eternal Golden Braid which includes this argument. It won the Pulitzer Prize for general non-fiction, the National Book Award for science and my personal Book-That-Most-Changed-My-Life Award.

Would it be possible to have a Droste Effect in Life, where large “metapixels” interacted with their metapixel neighbours by way of the Life algorithm? Think of all the things it would have to do. The meta pixels would have to somehow count their neighbours, and in unison update their colour. Well, it’s been done and it’s via the OTCA metapixel, discovered by Brice Due. These metapixels are 2048 squares by 2048 squares. In unison they all change colour at every meta-generation (which consists of 35328 normal generations) according to their number of black neighbours. Between the metapixels are gaps within which information is communicated between metapixels. Somewhere amongst the detail, the information from all eight neighbours is processed according to the rules of Life to instruct the metapixel what its next colour will be. And you can watch the whole process at expanding levels of size and time by clicking here (1:21 video).

So we can see that discrete systems can build huge ordered complexity from simple rules. From this we can think then maybe our universe follows a few simple discrete rules. If so, then in principle universes following our laws can be simulated, with size being the only practical limitation. In this post I’ve argued that if this is the case then a simulation of our universe would only discover our universe, not invent it. It already exists without being simulated. And that is why it exists.

I said there was a bonus section that will address some of the Big Questions in the light of the science philosophy that our universe is just a mathematical structure. So here goes:

Why is there something rather than nothing?

There are universes that correspond to all mathematically definable discrete structures. Our is one. They exist because mathematics exists and it is self-evident that mathematics does not need a creation process just as pi does not need to be created. Pi simply “is” what it needs to be, 3.14159…

What happened before the universe?

From viewing a Life universe from the outside and from the inside, you can see that time exists within, and is a property of, a discrete universe. It makes no sense to talk of “before” the Life universe existed. What happened before pi existed?

What is the meaning of life?

The Meaning of Life

The Meaning of Life (Photo credit: Jari Schroderus)

Whatever you make it to be. You have your own sense of purpose and you follow it. This comes from human evolution. Meaning evolves.

How can life have meaning if there is no eternal afterlife?

Why does something have to be infinite to have meaning? Why does eternity suddenly confer meaning onto something? This question has no meaning.

On that note I would like to wish you all a happy perception of time entering another 365 day unit!


3 thoughts on “Life, The Mathematical Universe Hypothesis and Everything

  1. Above you mention that the number pi exists necessarily and does not needed to be created. However, this statement is incompatible with your committment to mathematical finitism, in which only mathematical objects exist that can be constructed from natural numbers in a finite number of steps. Thus irrational numbers like pi do not exist in finitism but are nothing but human fictions.

    • Thank you for your comment, it is a good one. My statement about pi was sloppy so let me clarify.
      (I was trying to make the point that the concept of pi was discovered, not invented, because there is a school thought that mathematics exists only because we invented it.)
      As far as existence goes my intent was to refer to the expansion of pi to any desired finite number of places, which I would say exists. I would also say that the concept of pi exists as a limit to a definable infinite sum. However the complete decimal expansion of pi does not exist, nor does an actual physical construction of, say, a perfect circle, as this also requires a complete construction of pi.

So what do you think?

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