Is the Universe simple or complex?

On the face of it the Universe is a fairly complex place. There are nine million known species of life on Earth, at least 500 billion planets in the Milky Way, and an estimated trillion galaxies containing 10²⁴ stars and 10⁷⁸ atoms in the visible Universe. The scales are mind-boggling. For centuries, scientists have made it their life's work to understand these complexities. "My goal is [...] a complete understanding of the Universe, why it is as it is and why it exists at all," Stephen Hawking once said, as quoted by John Boslough in Stephen Hawking's Universe.

A theory of everything?

In fact, scientists have unearthed an enormous amount of simplicity in nature. The laws of physics can often be expressed as relatively simple mathematical equations, and they are the same no matter where in the Universe you are and which direction you're looking in. Over the centuries physicists have discovered that seemingly different things are in fact just two sides of the same coin: for example, electricity and magnetism were combined into a single theory of electromagnetism by James Clerk Maxwell in the 19th century. Today we know that there are just three fundamental forces and twelve basic building blocks of matter (see this Plus article for more information).

What is still lacking however is a so-called "theory of everything" — a self-contained mathematical model that describes all the fundamental forces and particles. Such a theory would have to bridge the gap between quantum mechanics and Einstein's theory of general relativity, which in their current form contradict each other. Currently the strongest contenders for such a united theory of quantum gravity are string theory and a related theory which grew our of it, called M-theory (see this Plus article).

The hope is that the fundamental description of the Universe resulting from these theories will be fairly simple, though in their current incomplete form they seem more complex than the theories they are seeking to replace. String theory allows for the existence of a very large set of radically different universes, each with a different collection of particles and forces. Opinion within the scientific community divides sharply as to whether these possible universes really exist, but surely the emergence of the multiverse model suggest that our physical reality could be even more complex than originally thought?

Don Page, a theoretical physicist at the University of Alberta, Canada, says this may not be the case. He argues that it is possible for the basic principles of a scientific theory to be simple even if the constituent parts are complex, pointing to evolution as an obvious example. "The human genome is extremely complex and we are part of a whole biological evolution going back thousands of years but the principles governing [evolution] are much simpler than the details."

This could mean that the underlying principles of the Universe may still yet be simple, even if the multiverse model turns out to be true. But as string theory has yet to be verified experimentally, Page says, the jury is still out. So given the lack of empirical evidence, are there any other reasons to believe that string theory, or any other theory for that matter, should be taken seriously as a theory of everything?

Logical simplicity

When it comes to choosing between scientific theories, there are a number of indicators which lead scientists to believe that one theory is more probable than another. Observations are key: a theory must be able to predict them correctly. New theories must also fit in with other theories of neighbouring fields. Unfortunately, string theory does not make any new predictions that can be tested in the lab with current methods, nor are there neighbouring theories to compare it with. So naturally scientists have appealed to an alternative assessment; simplicity.

Richard Dawkins has argued [in his book The God delusion] that adding particular additional hypotheses to explain the nature of the Universe is making its explanation more complex, and so is less useful than not adding them. His is a straightforward appeal to an idea called Occam's razor. If the data supports multiple theories equally, a simple explanation is more likely to be true than a complex one — or as Einstein wryly put "everything should be made as simple as possible, but no simpler."

Richard Swinburne, Emeritus Professor of Philosophy at the University of Oxford, says that simplicity in terms of scientific theories consists in postulating few objects, few kinds of objects, few kinds of properties and mathematically simple relations between the properties. "I think simplicity can be codified in an objective way. My account of it is that one mathematical concept x is simpler than another concept y if you can only understand y by understanding x and not the other way round," Swinburne says.

When it comes down to the complexity of the Universe, Swinburne says the final explanation will be fairly simple. There is a large number of entities which make things complicated but only a few properties attributed to each. "We don't know what the final theory will be but it will only have a few fundamental properties like mass or charge and each of these will have a numerical value," he adds.

Under the principle of Occam's razor, a new hypothesis such as string theory should only be accepted if it leads to new data, which so far, it hasn't, or alternatively if it's simpler than current theories. As string theory seeks to unite quantum mechanics and general relatively, many scientists expect it to be simpler than those two. But Swinburne has an explanation for the existence of the Universe that he believes is far simpler than any theory of physics could ever be ... God.

Swinburne's God is a simple being — it's one entity for a start whereas the Universe is made up of a billion entities — with zero limits to its power, zero limits to its knowledge and zero constraints on its freedom. This, says Swinburne, is the simplest God there could be. "It's a matter of degree between what is simple and what is complex but all things being equal you ought to believe the simplest explanation. The hypothesis I'm putting forward is that it doesn't get simpler than God."

Unsurprisingly, some factions of the scientific community reject the idea that God is a simpler explanation of the existence of the Universe than string theory. Richard Dawkins, for example, has argued [in The God delusion] that an entity that monitors and controls every particle in the Universe and listens to all our thoughts and prayers would require a "mammoth explanation" of its own and thus cannot be simple. It's a metaphysical argument that is unlikely to be resolved anytime soon, so it seems we require a more objective assessment of complexity. This what we'll look at in the second part of this article.

Next ... mathematical complexity

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About the author

Faye Kilburn is a freelance science writer and a staff writer at a financial technology publication in London. She has a Master's degree in Physics and Philosophy from the University of Bristol and is interested in astrophysics, the relationship between physics and philosophy and trying to answer the big questions in life.