THE FINAL MYSTERY

Scientists shouldn't really be atheists

This sounds like a contradiction, but is it? Hardly anyone still imagines that God is some considerate sky daddy with a big white beard sitting on a cloud. Scientists, because they are scientists, have an automatic commitment to the laws of cause and effect. Weird though our reality is, it is still based on causality which dictates that there must be a First Cause – an ‘ultimate explanation’, if you like. To deny there is a first cause is the equivalent of saying you don’t believe in the conservation of energy, or that everything must have been created by magic.

Figure 1. 16th Century metaphor for God

Ever since humanity became conscious and able to communicate, people have been in awe of what caused everything to exist, and they called it God. The current version is the quest to find a ‘Theory of Everything’, which is what prompted the media to call the latest particle to be discovered the ‘God particle’ (i.e. the Higgs boson). Governments spend huge amounts of taxpayer’s money on fundamental science projects like the Large Hadron Collider to discover the first cause, which is simply the updated version of God. That is why a scientist claiming to be an atheist is the real contradiction.

The only conceivable way you can dispense with a first cause is if everything is infinite. Then there is no beginning and no end to anything. There is no ultimate explanation, no first cause. With all the evidence we have come across for infinities at the smallest level and infinities at the largest, there is still yet more evidence, and it comes from pure logic. Pure logic may sound a bit scary but it is easy to understand.

The Liar Paradox

It all starts with the ancient Greeks around 2,400 years ago who came up with what is called the ‘Liar Paradox’. Over the years since, just about every famous philosopher has tried to explain it, but never to everyone’s satisfaction. It consists of a single sentence: This statement is false. Although it sounds absurdly simple, it uncovers the profound fact that there is a limit to human reason!

Let’s take a look at it: This statement is false. Now if it is true it has to be false. But if it is false it can’t be true. However, if This statement is false, is false, then the statement is true, which in turn would mean that it is actually false, but this would mean that it is true...and so on forever and ever.

Kurt Gödel

Although hardly any of the general public have heard of him, Kurt Gödel is thought by many to be one of the greatest mathematicians of all time. Freeman Dyson, who occupies Einstein’s post as Professor of Physics at the Institute for Advanced Study, says of him:

“Gödel was one of the few indubitable geniuses of our century, the only one of our colleagues who walked and talked on equal terms with Einstein” 1

Figure 2. Kurt Gödel

At the beginning of the 20th century David Hilbert led an international effort to link up all of the then known theorems of mathematics. Everyone joined in believing that it was possible, but out of Vienna in 1931 came two theorems, known jointly as the Incompleteness Theorem by a brilliant young upstart. It smashed apart the whole international effort with a single punch, and devastated the world of mathematics. What Gödel did was to prove that mathematics could never be complete.

He started with the Liar Paradox but changed it to: This statement is unprovable. Very briefly, it proved that given any system of established principles in maths, there will always be statements or theorems that are undecidable on the basis of those principles. In other words, there are theorems that cannot, in principle, be shown to be either true or false. Here is how he described it:

“The human mind is incapable of formulating (or mechanising) all its mathematical intuitions, i.e., if it has succeeded in formulating some of them, this very fact yields new intuitive knowledge, e.g., the consistency of this formalism. This fact may be called the ‘incompletability’ of mathematics.” 2

The most shocking realisation that comes from the Incompleteness Theorem is simply this: it proves that there will always be a truth that lies ‘beyond’ any mathematical system’s ability to prove. So there is a truth ‘outside’…a truth ‘beyond’ mathematics. But we have already discovered that everything real, everything that ‘exists’ comes from maths. Yet in the end we find that there will always be a truth beyond mathematics. A truth that escapes definition by any means we know of. A truth which actually exists but can never be proved to exist. Sounds a bit like Cantor’s Actual Infinite (see page 3, The Magic of infinities). About the Incompleteness Theorem John Barrow says:

“any limitations of mathematical reasoning, like those uncovered by Gödel, are thus not merely limitations of our mental categories but intrinsic properties of reality and hence limitations upon any attempt to understand the ultimate nature of the universe.” 3

Alan Turing and Gregory Chaitin

Five years later Alan Turing, a British mathematician, and the founder of computer science, published a paper known as the Halting Problem. He theorised what has become known as a Universal Turing Machine which is the same as a modern digital computer, but long before they were first constructed. A problem is decidable if it can answer a yes/no question. What Turing found is that there are many problems which are undecidable by either man or machine. The Halting Problem is known to be unsolvable. What he demonstrated is that there are limits to computation. In other words, there does exist an actual limit to what can ever be known. It backs up what Cantor and Gödel discovered – that there will always be something that cannot be explained.

Figure 3. Alan Turing

Turing is better known as a hero of the 2nd World War for his role in breaking the Nazi Enigma codes at Bletchley Park which was a huge advantage for the Allies. He was also a leading figure in artificial intelligence, and his Turing Test is still considered the bench mark for assessing machine intelligence.

More recently Gregory Chaitin, a well known mathematician and computer scientist at IBM has discovered what is called Chaitin’s Constant which he calls Omega. It expresses the probability that a random computer programme will halt, but it turns out to be something definable but not computable. If you don’t understand, that’s fine, because neither do I!

Omega is infinitely complex because it is based on an unsolvable problem – Turing’s Halting Problem. But the important point is surely this; because Omega is completely unknowable, it proves yet again that there are limitations to what can ever be known by mathematical reasoning. About Chaitin’s discovery Marcus Chown says:

“Chaitin’s discovery implies there can never be a reliable ‘Theory of Everything’, neatly summarising all the basic features of reality in one set of equations.” 4

Hawking, Penrose and Weinberg

In a news report Stephen Hawking once said:

“up to now, most people have implicitly assumed that there is an ultimate theory that we will eventually discover. Indeed, I myself have suggested we might find it quite soon.”

But he then expressed his personal doubts by saying:

“Maybe it is not possible to formulate the theory of the universe in a finite number of statements.” 5

Now it seems, one of the great icons of science has admitted - that it may not be possible to formulate the theory of the universe in a finite number of statements. It carries the implication that there may be an infinite number.

Roger Penrose seems to be equally doubtful. He has said:

“it is a matter of contention whether anything resembling a ‘theory of everything’ will ever be found.” 6

About finding a Theory of Everything, even the Grand Patriarch of theoretical physics, Steven Weinberg (Nobel Prize in Physics, 1979), acknowledges:

“I don’t think that will be possible, because we can already imagine logically consistent laws of nature that don’t quite describe the world we see [read M- Theory]. We will always be somewhat disappointed...All human beings, whether religious or not, are caught in a tragic situation of never fully being able to understand the world we are in.” 7

Figure 4. Steven Weinberg

The central odyssey of human consciousness has always been the quest to discover what caused everything to exist. It has filled generations with both fear and longing, but now it seems we have perhaps arrived at an historic moment. It looks like we will never know.

From the Multiverse to M-Theory the evidence suggests that our reality is only one option among an infinite number of mathematically conceivable options. And the mystery deepens further when we realise that the mathematics from which everything is constructed is itself infinite. Yet although mathematics is demonstrably ‘outside’ and independent of space and time, and matter and energy, it still exists – if it didn’t we wouldn’t be able to access it. This legitimately allows us to ask: what entirely unimaginable entity is responsible for creating the infinities?

What God Looks Like

I believe that Gödel’s theorem is universal, as Barrow has suggested, and that there will always exist a truth which is ‘there’ but can never be proved. A truth beyond infinity. Cantor’s Actual Infinite. This is how I see that final truth. To put our reality into perspective, Freeman Dyson told us:

“Imagine if you can, four things that have very different sizes. First the entire visible universe, second, the planet Earth. Third, the nucleus of an atom. Fourth, a superstring. The step in size from each of these things to the next is roughly the same. The Earth is smaller than the visible universe by about twenty powers of ten. An atomic nucleus is smaller than the Earth by twenty powers of ten. And a superstring is smaller than a nucleus by twenty powers of ten.” 8

Figure 5. Freeman Dyson

So, if you are a super-string then the world of the nucleus of the atom (just the centre), is as big as the universe is to us. Yes, that big! And if you were an atom, then our earth would seem as big as the whole of our observable universe. I mean, our little galaxy alone is staggeringly vast. It takes eight minutes for light to arrive from our sun, and five years from our nearest star. But the light we see tonight from Andromeda, our nearest galactic neighbour, actually left there before humans existed. And Andromeda is the nearest of hundreds of billions of other galaxies!

And please, I urge you – keep imagining it. This is just our ‘home’ universe. What about the infinite universes of the multiverse? And if it were possible for anything to be more astonishing than this, then please consider that each quantum bit of every atom which exists in all those universes, is itself surrounded by an infinite number of parallel worlds! Worlds that you can do computing with. And finally, that the mathematics – the ‘blue print’ from which it all emerges - is itself infinite. This is infinity upon infinity upon infinity. And these infinities - from atomic particles to the multiverse, actually exist and are real.

Although it must be the strangest of all ironies, I am suggesting that science, our most reliable form of knowledge, the only tool we possess to keep us from ignorance, has led us to our first ever understanding of the appearance of that unspeakable three letter sequence.

I am suggesting that this infinity upon infinity which science has discovered and to which everything leads no matter where you look, is none other than the actual face of the unimaginable entity. This is surely what God looks like.

It means that the First Cause, the origin of all ‘information’, which is responsible for the infinities – does exist. But it will forever remain unfathomable by humankind. This is the Final Mystery.

May The Cause be with you!

The Book Chapter 25
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