On Fine-Tuning and the Multiverse

The Fine-Tuning Problem

I've been thinking a lot lately about the problem of fine-tuning and how it may or may not be resolved by appeal to a multiverse. This has been prompted by recent correspondence with the philosopher Philip Goff and by the book I am currently reading, The Beginning of Infinity by David Deutsch. I hope to get around to discussing Deutsch's ideas in future, but for now I'm focusing on an argument put forth by Roger White and endorsed by Goff.

The fine-tuning problem is just that the laws of physics describing the universe seem to be fine-tuned so as to allow life to exist. While trying not to be too parochial in our assumptions about what life requires to exist, at least in a universe even vaguely like ours, it seems reasonable to assume that it must at least have time and a stable environment in which to evolve, access to sources of energy and a varied assortment of building blocks from which to assemble itself.

But if the physical constants were slightly different, then perhaps stars, heavier elements or atoms could not have formed. Perhaps the universe would never have expanded from its initial hot, dense state, or would have recollapsed too quickly, or perhaps it would have expanded too quickly for particles to come together at all. When we say the universe appears to be fine-tuned, we are claiming that it appears to be delicately balanced so as to allow complex evolving self-replicators (i.e. life) to exist -- that almost any tweak we imagine to the constants or the laws of physics would result in a simpler, lifeless universe. This curious observation seems to demand an explanation.

The Universe is Made of Mathematics

Max Tegmark

A couple of years ago I was reading Anathem by Neal Stephenson and a number of ideas started to click into place for me. Without going into the novel too much (spoilers), it prompted me to think about the nature of reality and why it might be that the universe exists.

Over the course of a few sleepless nights, it all came together and it seemed too make so much sense that I could entertain no doubt: the universe was what I thought of as a "Platonic algorithm".

To my knowledge at the time, this idea had never before been proposed, and a bit of half-hearted searching at the time turned nothing up. I became more convinced of my idea over time and started developing an interest in philosophy so as to learn how to communicate and argue for the idea.

As my research ramped up, I inevitably came across Max Tegmark's Mathematical Universe Hypothesis (MUH), and with a curious mixture of disappointment and vindication realised that it was essentially the same idea.

Nevertheless, Tegmark's idea was still relatively little known, so I decided I would devote some time to building up a rigorous argument with a view to perhaps writing a book on the topic some day. That is actually the single most important reason I started this blog, as many of the arguments I have outlined in my posts will serve to support the MUH.

I have now learned (courtesy of Massimo Pigliucci's blog Rationally Speaking) that Tegmark is in fact about to publish the popular science book that is so sorely needed. I guess I can put aside that ambition for now.

But it's also time for me to put this blog to the use it was originally intended for - enough beating around the bush!

Perhaps my hesitancy to address the subject arises out of the fact that it at first seems completely mad: I am utterly convinced that the universe is made of mathematics and that the concept of physical reality is incoherent.

Now let me try to explain why.

Why the Abstract Feels Physical

I will freely admit that this at first seems like a meaningless platitude to say "the universe is mathematics", akin to statements such as "God is Love". Massimo Pigliucci quite rightly stresses on his recent blog post that we are not claiming that reality is best described by mathematics -- the claim is literally that the fundamental substance of reality is mathematical structure.

As he pointed out, it's hard to see how this can be. How can mathematics possibly explain substance? Abstract concepts such as mathematics are surely entirely different from physical stuff, and to claim the two are the same seems to be perverse.

From Pigliucci's description, Tegmark's answer to this criticism seems rather weak. He insisted that electrons are mathematical objects having mathematical properties, but apparently failed to provide a convincing reason not to regard them as physical objects having physical properties which can be described mathematically. I can see why Pigliucci feared he may have been making a category mistake.

I would take another tack. I would argue that the intuition that mathematics cannot be the stuff of, well, stuff, arises from the false belief that this is a physical universe (and indeed that the physical universe is a concept that even makes sense).

But before I elaborate on this, let me state plainly that I believe the argument in favour of the mathematical universe rests on three crucial premises.

1) All mathematical objects exist abstractly and independently of minds (mathematical Platonism)
2) The mind is a computational process (The Computational Theory of Mind or CTM)
3) The universe behaves according to laws of physics which are expressible mathematically (metaphysical naturalism)

I have made arguments in favour of all of these premises previously on the blog (Platonism, CTM, Naturalism), so for now I am going to assume them to be true.

How can I seriously doubt that the universe is physical? Two powerful analogies help to explain this.

One hypothesis gaining currency in recent years is the idea that the universe is not physical but a computer simulation, as argued rather interestingly by philosopher Nick Bostrom. If Bostrom is right, the physical universe may not exist and the fundamental stuff of the universe could be information, i.e. the bits flowing through a computer program.

Another idea, explored in the book Sophie's World and elsewhere, is the idea that our world may not physically exist because we may be fictional characters living in a fictional world being described by some author. From the point of view of a fictional character, the world seems real, so none of us can really know for sure that we are not such a character.

In both of these ideas, the universe is not real (not physically at any rate), but this fact is forever hidden from us.

The MUH is quite similar in many ways. The crucial difference is that it removes the dependence on a greater reality. Unlike the computer simulation idea, we need no external hardware to support us. Unlike the characters in a novel, we are genuinely conscious. Unlike both, there is no creator, no programmer or author.

We have no need of a programmer or author, no cosmic computer or reader. The bedrock of our existence is mathematical Platonism, and unlike all other explanations this is sufficient as an ultimate cause. Mathematical objects are not created and need nothing to sustain them. They exist necessarily of their own nature.

Let's first consider the idea that the universe is a simulation. If the physics of the universe is computable (as it seems to be), then it could certainly be simulated by a computer of sufficient power, even if such a computer would be unfeasible to construct in this universe. It therefore follows that in principle it is entirely possible that it and we ourselves are simulated, virtual entities (although if you doubt the Computational Theory of Mind then this does not follow as we are evidently conscious).

However all computer programs are mathematical structures, and as such, Platonism holds that all computer programs exist in the abstract. It follows that even if no computer could ever be built to run the simulation of the universe, this program exists as a mathematical structure, and within this structure can be found perfect descriptions of all the objects in our universe, including our minds, our thoughts, etc.

But now, if we start thinking about an abstract mathematical object containing all of our thoughts and inner experiences and determining our life stories, it seems to me that we are getting close to the idea that we may all be characters in a work of fiction.

Unlike fiction, what happens in our universe is determined by mathematical laws and these have the regularities necessary to support life, brains and real intelligence. I don't believe characters in fiction are actually conscious because their actions are not determined by internal genuine thought processes. There is consciousness there, but it is not in the minds of the characters but in that of the writer. In contrast, our consciousness is our own and is the product of our own brains.

But like the lives of characters in a novel, our lives and our thoughts are all mapped out and there for the reading. We are implicit in the structure of this mathematical object, and in principle our stories could be discovered by simulating it on a powerful computer. This is just like the way we can explore mathematical objects such as the Mandelbrot set with computers.

We are the conscious characters in a cosmic narrative determined by no author but the laws of physics. Our lives exist even if no simulation is run, just as the stories of fictional characters continue to exist even while nobody is reading the novel and just as the Mandelbrot set has always existed, even before it was discovered.

So think of our universe and our life stories as being something like an enormous fractal structure arising from some simple mathematical rules. It's a beautiful, amazing, complex, surprising thing, but it needs no creator or sustainer.

The Incoherence of the Physical Universe Hypothesis

Far more than being merely a plausible account of reality, I view the Mathematical Universe Hypothesis as being necessarily true, because it reveals the incoherence of the concept of a physical universe.

Given that the universe obeys mathematical physical laws (naturalism), there must be a mathematical object (given Platonism) which perfectly describes the universe and which contains within it structures analogous to all objects within the universe, including ourselves.

What's more, given the computational theory of mind, those structures corresponding to our minds are necessarily conscious. As such, even if there is such thing as a real, physical universe, there must also be an isomorphic (having precisely the same form or structure) abstract non-physical universe. There is a physical you and an abstract you, and both have exactly the same experiences and neither has any way of knowing which universe they find themselves in.

In fact, there is no observer anywhere who can distinguish between the physical and the abstract universes. There is nothing we can say about the physical universe that is not also true about the abstract universe, except for the fact that it is physical.

So let's unpack that. What does physical mean? In everyday speech, it is used to distinguish between objects we can interact with directly (such as rocks) and objects we can only think about and discuss (such as numbers). For something to be physical it must be present at some time and place within the universe, and for something to be abstract it must exist outside of space and time.

So what do we mean when we claim that a universe is physical? It exists in time and space? But it doesn't -- it contains time and space within it.

Ok, so let's say that the universe is a special case, that it is physical not because it is inside spacetime but because it contains spacetime.

So now let's consider a hypothetical abstract universe other than our own and ask ourselves whether it is physical. (For illustrative purposes let's say that universe is Star Wars but let's assume that the universe is not a work of fiction but a mathematical object in much the same way that I'm claiming that our universe is a mathematical object).

This universe is not present within the spacetime of our universe, so from that point of view it is not physical. It does contain its own spacetime, so by our broader definition that would make it physical.

But it's just a made-up universe! Our instinct is that it ought not to be considered physical. So let's say that only universes which contain the spacetime of our own universe are physical.

So now, only our own universe can be physical, by definition. This seems to be a rather unsatisfactory result, because there are very good reasons (such as the anthropic principle) to believe there may be other universes. We want that option to be open to us, if only so we can discuss the possibility.

It's also a patently subjective definition of physical. From the point of view of an observer in this universe, the Star Wars universe is not physical. But from the point of view of Han Solo, our universe is not real.

It seems to me that the only way out of this mess is to realise that the application of the concept of physicality to a universe is a category mistake. Physicality as a concept only makes sense within the context of a given universe.

For example, you would no doubt regard yourself as physical but Luke Skywalker as abstract. However, Luke Skywalker is physical to Han Solo, while Han would consider you to be non-existent. There is no objective, universe-agnostic way to say that you are really physical but Luke Skywalker is not.

So given that physicality as applied to universes seems to be incoherent, and given that physicality is the only (completely undetectable) property that distinguishes the mathematical universe from the physical universe, it seems to me that the only sensible conclusion is that only the mathematical version of our universe exists. This accounts for the existence of the universe, fine-tuning and everything we observe.

The Physical Universe Hypothesis is therefore unnecessary, redundant and incoherent.

Reasons to Believe

I have explained why I think the Mathematical Universe Hypothesis follows necessarily from naturalism, Platonism and the computational theory of mind, however there are plenty of people who are skeptical of some or all of these propositions. Nevertheless, I think there are independent reasons to find the MUH plausible.

Firstly, and perhaps most importantly, it explains why the universe exists. It does not tell us what caused the Big Bang, or if the Big Bang had a cause at all, but it does explain why there is something rather than nothing, without appeal to a creator or any other unsatisfying ultimate cause. This echoes my rebuttal to the Kalam Cosmological argument.

For a creator God, we are left to ask who created the creator - but if the universe is a mathematical object, it needs no creator (on Platonism at least), so this is a very satisfying answer to that eternal question. It has always existed and will always exist outside of space-time as a mathematical construct.

It also provides a powerful explanation for fine-tuning. As discussed previously, this universe seems to be perfectly calibrated to support life. Much attention in discussions of fine tuning is focused on the physical constants such as the charge of the electron or the speed of light, etc, but very rarely is it asked why are the equations and the laws of physics themselves of the form they are. Why could the universe not be completely different, not just having different constants but having completely unrecognisable physical laws?

If all possible universes exist, then we have our answer. Our universe is fine-tuned because it is one which has the ability to support conscious thought selected from an infinite multitude of mathematical structures, most of which are lifeless.

Better than other multiverse hypotheses, where it is proposed that there might be a great number of universes, the MUH posits that all possible universes exist, not merely a great many. This is actually simpler because, as Tegmark says (and as explained previously on this blog), there are no free parameters. We have no reason to wonder why universe X exists but universe Y does not. If all universes exist, nothing is arbitrary. We have an ultimate explanation of everything.

There's something attractive to me about the idea that all universes exist. After all, what's to stop any given possible universe from existing? It is not subject to the laws of other universes. No law of this universe can prevent another entirely causally disconnected universe from existing. Even if there is a multiverse with its own meta-laws (e.g. the String Theory multiverse), what's to stop another multiverse with different meta-laws from existing? Even without asserting that the universe is made of mathematics, it seems to me to be perfectly sensible to propose that all possible universes exist. Why not?

Finally, the idea that the universe is literally a mathematical object explains what physicist Eugene Wigner called "the unreasonable effectiveness of mathematics" in modelling and predicting the natural world, often leading physicists to empirical discoveries they could not otherwise have made. If the universe really is a mathematical object, it is hardly surprising that mathematics should be effective in describing it.

There are objections to the Mathematical Universe Hypothesis of course, and I intend to return to them in time.

The anthropic principle goes wild

The anthropic principle has been much discussed and it is likely that you have already come across it. It's a strange and counter-intuitive idea because it seems to place human beings in a privileged central place in our account of why our world is the way it is.

I want to raise the subject because the anthropic principle is exactly the kind of logical or philosophical argument that might have a bearing on the fundamental existential questions I mentioned in my last post.

The anthropic principle is a simple but profound idea that at first sounds like a useless tautology. It explains that we shouldn't be too surprised to find ourselves in an environment that is so well suited to us, because if our environment were not as it is then we would not be as we are.

To paraphrase Douglas Adams: to marvel at the many wonderful and hospitable aspects of our world that enable our existence is like a sentient puddle being impressed with how well its pothole fits its shape.

The anthropic principle explains why the earth is positioned in the narrow band of space at just the right distance from the sun to allow liquid water to exist. It explains how life can have come into existence despite the long odds of its arising by chance. It explains how this life can have evolved into intelligent self-reflective creatures such as ourselves.

Thinking of life, the universe and everything

The great hope of physicists such as Stephen Hawking and Lawrence Krauss is that a deep understanding of physical law will ultimately lead to an answer to the ultimate questions. Why are we here? Why does any universe exist at all? Why are the physical laws the way they are? What is the answer to the question of life, the universe and everything?

This question has been bothering me for a long time, ever since I was a small child in fact. When I was taught that we fall because of the force of gravity, I was first confused and then dissatisfied.

I have already discussed why I was confused in an earlier blog post, but essentially it was because it seemed natural to me that anything without support should fall. After all, without support, there's nothing to keep it up! There seemed to be no need to invent some mysterious force called "gravity".

This confusion did not last long. On becoming accustomed to the concept, I could see that it made sense. There is no clear logical reason why something should fall down without support any more than it should fall into the sky if not tied down. Clearly the concept of gravity makes sense.

If only it were not so dissatisfying!

A part is more complex than the whole

Here's two apparently unrelated hypotheses for you:

1. The universe contains infinite space and an infinite quantity of stuff.

2. The many worlds interpretation of quantum mechanics is true.

Both of these appear at first glance to be astonishingly wasteful, positing infinities upon infinities of things we can never observe and which can never affect us. As such, they appear to be more complex than ideas which assume that space is finite or that there is only one quantum world.

It would seem that Occam's razor weighs against them.

In this post, I will argue that in fact the reverse is true.

Something from nothing: Competing premises

In my previous post, I discussed how Dr. Carrier's argument that the universe could come into existence from nothing is cogent only if you choose to assume that anything can happen in preference to assuming that there is no dimension of time in a state of absolute nothingness.

My own viewpoint is that absolute nothingness does in fact imply a lack of a time dimension, and so Carrier's argument does not hold. So how can we choose which is the better description of absolute nothingness? In this post, I will argue for my position.

Something from nothing: Reconciliation

In my last few posts, I've been highlighting the reasons why I do not agree with Dr. Richard Carrier's argument that the universe could spring from absolute nothingness simply because there would be no laws to prevent this happening.

The focus of my argument has been that there would be no time in a state of absolute nothingness and so nothing at all could happen, including the spontaneous creation of time

In this post, I try to understand the fundamental origin of our disagreement and propose that perhaps neither of us are really wrong.

Something from nothing: Flavours of singularity

One of the ways Dr. Richard Carrier defends his contention that time can arise from a state of absolute nothingness is by giving one example where this may have happened: the singularity at the origin of our universe.

In this post, I will attempt to refute this by arguing that this singularity was not really a state of absolute nothingness at all.

Something from nothing: Time and hypertime

In continuing the discussion of my objection to Richard Carrier's argument that the universe could arise out of a state of absolute nothingness, I consider the question of whether time could arise spontaneously in a timeless environment.

The crux of my argument is that if time does not exist, then nothing can change. The state of absolute nothingness implies that there is no time. As absolute nothingness is not what we observe around us, we can safely conclude that the state of absolute nothingness has never described reality.

You are still stuck on hypertime. You seem to think we need some "extra" time in which to create time. We don't. It's instantaneous.

This is the argument I will attempt to refute in this post.

Something from nothing: The assumption of time

Dr. Richard Carrier has kindly responded to my criticism of his argument with a comment on his blog as well as a number of emails.

In the following posts, I will attempt to represent his position as accurately as I can and outline the precise points of disagreement between us. In this one, I discuss the issue of whether Carrier needs to assume that time exists in order to make his point.

Beginnings and beginnings

One of the most common and most persuasive arguments for the existence of God is the Kalam cosmological argument. William Lane Craig is perhaps its foremost proponent.

The argument has been formulated at a high level by Craig as follows (according to Wikipedia):

1. Whatever begins to exist has a cause.
2. The universe began to exist.
3. Therefore, the universe has a cause.

He then goes on to argue why this cause must be God, an argument I find unconvincing but won't get into here.

This argument is usually attacked by tackling the first premise with quantum mechanics, where events do not necessarily have causes per se, however Craig counters this by insisting that the laws of quantum mechanics themselves serve as the cause.

Premise number two is often attacked also by raising the possibility that the universe, or at least time, has always existed. Craig responds with all the evidence for the big bang (which is not actually in dispute) and with some unconvincing arguments attempting to prove that an infinite series of past events is impossible.

I propose to attack the argument from another angle. Again, I attack premise two, but not by denying the big bang or the beginning of time, but by arguing that there are beginnings, and then there are beginnings.

Something from nothing

I read an interesting blog post by a fellow named Richard Carrier the other day. In it he discusses the common idea that the universe was created from nothing, and what that might mean.

After all, a common question is why should the universe exist at all? Why is there something rather than nothing? One explanation is that God must have created the universe. Another is that for some reason nothingness is somehow unstable and will always lead to something.

And, quite apart from this question, creation from nothing is a common religious theme. It is also commonly assumed by the non-religious that all matter, time and space were created in the big bang, essentially from nothing. As such, perhaps it's worth thinking about what might happen if we can imagine such a state of nothingness.