The Fabric of Reality : : Complexity

The universal probability bound

Definition of the universal probability bound

When discussions come to the point where the anthropic bias has to be recognized, some evangelicals come up with the concept of universal probability bounds. They acknowledge that evolution doesnít have to be common (i.e. likely a priori) in order to believe that it happened the way modern biology tells us. They claim instead that the probability of evolution is so extremely low that it can hardly have happened even once in the whole universe ever.

A universal probability bound for anything to happen is built up by asking how often anything has happened or will happen in the whole universe at all. The universe (strictly speaking the visible part of it) contains roughly 10^24 solar systems. The ^-character here serves as an exponential operator, such that 10^24 describes a 1 followed by 24 zeroes: 1 000 000 000 000 000 000 000 000. The total mass of the universe contains roughly 10^80 particles. As the universe expands towards its heat death it wonít be able to form solar systems forever. After another 10^14 years passing there will be no more stars. This is an accepted fact of cosmology indeed. From quantum physics it follows that, like space, time is also discrete. Time jumps ahead in steps of 10^-43 seconds (the Planck time). With less than 10^8 seconds per year we have roughly 10^63 events possible with each of the 10^80 particles in the universe. So there is a total amount of 10^143 occasions with anything happening in the universe at all anytime anywhere.

Therefore every event with a probability of lower than, say, 10^-150 is not expected to happen even once in the universe ever. This probability, 10^-150, is called the universal probability bound.

The refined evangelical argument in three parts

The universal probability bound forms the first part of the evangelical argument.

The second part of the argument is the probability (a priori) for evolution. The claim is that evolution does violate statistical physics in a crucial way. This means that the complexity evolution has built up can neither be explained by other existing forms of low entropy nor by the ability of gradual increase of complexity nor by other principles that somehow work against the second law. On the contrary this complexity would have to be regarded in the same way as some random quantum fluctuations. The information needed to fully describe evolution contains at least the human genome. In fact the human genome only is a tiny part of the whole thing, but this alone contains a least a Gigabyte of information. The random collection of a Gigabyte of information has a probability of something like 10^-1000000000.

The third part of the argument: 10^-1000000000 is so vastly smaller than 10^-150 that the chance for evolution to happen even once in the universe ever becomes much smaller than 10^-1000000, a probability that is so ridiculously small that evolution is unthinkable without the help of god.

All three parts of this argument are simple and clear. If they are all true then there must be god indeed. If at least one of the parts is wrong the whole argument fails.

Letís recall here that evangelicals use this line of argument in order to provide scientific proof in favor of god. Therefore all of this reasoning has to meet scientific standards. And furthermore the burden of proof is on the evangelicals. They want to prove something that isnít common sense at all among scientists, namely that godís influence can be deduced from observing evolution.

Why the third part is dubious

What if we observe a miracle? Religious people will take miracles and wonders as evidence for their deities. Deities, well at least the Christian god, are often sought of as the biggest mysteries of all: ďIt has been Godís will and God moves in mysterious ways.Ē Deities have been made up for the main purpose of helping people to cope with the incomprehensible. Mysteries are being given a name and a personalization in order to make these mysteries easier to digest. In a religious way of thinking the third part of the evangelical argument is entirely obvious.

However in a scientific way of thinking it makes no sense to explain one mystery by replacing it with an even bigger one. If scientists observe something they canít explain, they instead try to make up a new theory. If their observations donít make sense in the context of existing theories or contradict them straight away, they will try to correct their theories or to get rid of them. Einstein for example did so with relativity after all attempts had failed to integrate the fact of the speed of light being constant within the existing theories. This new theory even changed the entire world view in physics. However relativity is still a scientific theory that is based on observations and that is mathematically forceful, fallible and so on. Contrary to that the argument ďtherefore it must be godĒ is a mere claim that is meaningless in a scientific way of thinking.

Part three of the evangelical argument doesnít meet scientific standards, it rather follows a religious way of thinking. However, if the first and second part would still be true, it would at least force biologists to rethink their perception of the evolutionary process.

Why the first part is wrong

Imagine you wake up in front of a tent on a meadow. You have no idea how you got there. The landscape is covered in thick fog, and you can only look as far as 100 yards. How large is the island you are on?

As long as you stay where you are and the fog doesnít disappear you have no idea. You donít even know whether you are on an island at all. This is pretty much what our situation in the universe is like. We sit on our planet and look into the foggy universe. The universe is foggy because it only came to existence some 14 billion years ago, or more precisely light only started to exist some 14 billion years ago. So if a star is further away from us than 14 billion light years, then, by the definition of a light year, light didnít have enough time to travel from that star all the way to us since the big bang. Everything further away than 14 billion light years (at the time the light photons started to moving towards us) is therefore is invisible to us. This natural limit of visibility is called the event horizon.

Like there is no reason to assume the island from the example above to have a radius of 100 yards while you happen to find yourself sitting exactly in the center, there is no reason either to assume that there is nothing in the universe behind the event horizon and that our solar system happens to be in the exact center of the universe for some odd reason.

Therefore we have no idea how big the universe is. We have strong evidence though, that the universe must be much bigger than the 13.7 billion light years radius that we can overlook.

There is no universal probability bound

Without knowledge about the size of the universe there is no universal probability bound, and therefore the whole evangelical argument falls apart, regardless of what we think about the a-priori probability of evolution.

The mathematician, theologian and proponent of intelligent design William Dembski has nonetheless written a whole rather incomprehensible book full of math only to support the evangelicalís case. He did so despise the fact that the whole argument is rather clear and simple, as described above. The suspicion arises that he made the whole subject more complicated than necessary only to cover the fact that all this is pointless without knowing the size of the universe. And of course evangelicals try to argue in the way that those 10^24 stars really is all there is in the universe. They try to make it look as if that size was the best of knowledge we have, and that other claims about the size of the universe would have to be proven. But this is wrong. We have no clue about the size of the universe. And itís the evangelicals who want to prove something. They donít accept the current state of art regarding evolution and make a claim about probabilities that in fact are unknown. It's them who would have to come up with strong evidence in favor of a sufficiently small universe.

The second part of the evangelical argument doesn't matter

As long as evangelicals donít have such evidence, again, there is no such thing as a universal probability bound. Therefore the whole evangelical's line of argument fails. Even if the a priori chance for evolution would turn out be by magnitudes smaller than 10^-1000000000, the fact evolution has been successful on earth would still be compatible with an entirely naturalistic world view.