If you were to ask someone “Do you believe in God?” the only possible answers are “Yes”, “No” or “I am not sure”. Very rarely do people think for very long before answering this question. Considerably more thought goes into answering the follow-up question of “Why?” and the answers are as varied as the people questioned. Very rarely, however, are such answers lacking in flaws.

            The answers are usually flawed for a simple reason. It is not that the respondents lack intelligence or that their rationale is illogical, it is simply that they rarely put as much thought into the first question as the second. When a person is asked if they believe in God, they almost always have an idea in mind of what God is and so, therefore, they do not pause to consider what they are being asked about. Given any individual’s preconceptions about “God”, the rationale they pursue in considering its existence may be completely logical. However, another person’s preconceptions will differ – even if only slightly – and the logical conclusions that they reach may be wildly differing.

            The question, therefore, that must be asked before we can decide whether “God” exists, is ‘What is “God”?’

            It is perhaps of greatest importance to determine whether God is singular or plural. All of the monotheistic religions preach a singular entity, although catholicism divides that entity into three. There are other religions and mythologies with a larger pantheon of gods. In the majority of these we find that there is a single being that is described as the ‘creator’, with the other gods usually in a subservient role (at least initially). Whilst this is not a universal view, it is useful, for the purposes of determining what “God” is, to view it as a singular entity responsible for bringing creation into being.

            This is far from a complete definition, but even this little is sufficient to cause consternation without justification and may be used to illustrate why a person’s preconceptions will lead them to flawed conclusions about whether God exists.

            A believer, upon hearing this definition, will usually respond affirmatively, as they clearly believe that the universe had a creator who was (is) God, whereas the atheist would say that it clearly did not. Any ensuing argument could be curtailed if the believer is made to realise that the “God” they believe in is merely a subset of all the possible “Gods” contained in this definition and the atheist is made to realise that what they do not believe in is also a subset of the possible “Gods”.

            A part of the problem is that some of the words used have emotive connotations. “Creator” is a term often used in religious texts to describe God himself and “entity” is usually taken to imply a being of some sort. However, in this definition “entity” must be taken in its broadest possible context and, when this entity is described as being “responsible” for creation, this must not be taken to imply conscious design.

            The latest beliefs of science are that the universe was created around thirteen billion years ago. At this time the universe was considerably smaller than it is today, occupying, according to some theories, so small a space as to be described as a ‘singularity’ – literally a point with no height, width or depth. Science does not claim to have all of the answers (yet), but can trace the evolution of the universe back to a very short time – literally a fraction of a second – after the moment when this ‘proto-universe’ began its life. To anyone willing to study the mathematics of this process, there is a logic to it that stands up well to all current investigation. (Whether the science of cosmology is telling us how the universe evolved or whether God created the universe around 4004 BC and made it look like it was evolving is not the debate here.) Suffice to say that the science is very well founded in observation and theoretical mathematics and can trace the (actual or apparent) evolution of the universe back to a very short time after it began.

            Science is faced with a number of problems in trying to trace this evolution further back those vital few moments to its beginning. The physical laws with which we are all familiar break down completely. The universe is, at that time, governed entirely by laws that – today – apply only in the microcosmic world – the world of the very small. All that science can say with any certainty (and not too much of it) about the moment of creation is that it was a “quantum event” governed by the laws of (the very poorly named) “chaos theory”. In very crude terms, creation was a random event. It is more accurate to describe it as the result of probability collapse (more on this below). This does not, however, answer such questions as why the probability collapsed when and how it did or whether such collapse was inevitable.

            One atheist view (probably the most dominant) is that science will inform us of the nature of the universe, if not now then eventually. In this way the universe can be explained without recourse to a “God”. However, if “God” is “an entity responsible for bringing creation into being”, then God, according to science, is a random probability collapse. The crude definition of “God” above does not imply intelligence or will. Therefore the atheist who rejects God based on this definition is also rejecting his own beliefs and the believer who accepts God based on the same definition is also embracing the cold mathematics of the unbeliever.

            Clearly, preconceptions must be set aside before the question of the existence of God may be answered. In fact, there are many preconceptions about both God and the Bible that misinform the opinions of many people. Each of these preconceptions tends to create greater division between the two sides of the arguments. Most of these divisions are artificial, a result of lack of understanding or, very often, a great weight of historical inertia that pushes an erroneous view for what amount to “political” reasons.

            Science and religion are usually viewed as being “opposites”, but this is mostly a result of the fact that most people do not properly understand either. Worse, many of those that do understand have historically tended to push their own agendas, almost always resulting in further misinformation. To those that have understanding of both “camps”, this is increasingly frustrating. It is clear that the “God Question” is causing unnecessary confusion to both sides and, further, it is retarding the development of both. Science is, in its pure form, the quest for truth, while religion is faith in the truth. The two should, ideally, be different facets of the same thing, yet they are increasingly seen as opponents. Too many believers are engaged in what should be a pointless defence of their faith, while too many otherwise intelligent and rational atheists are engaged in finding ways to further debase and ridicule religion. A clearer understanding of both will show, firstly, that they are nowhere near so far apart as is believed and, secondly, each can help to inform the other. With this in mind, let us return to the important issue of determining what God is.

            In addition to being the creator of the universe, the most common attribute ascribed to God is that of being infinite. This is a term that causes great confusion on all sides. “Infinite” is a quite specific term for the least specific concept in the physical universe. It means “without boundary”, but, when applied to God, we are not always certain whether this refers to space, time, knowledge or capacity. In fact, for any entity to be truly infinite in any one of these spheres, it almost certainly must be infinite in the other three and it is the generally held belief amongst religious authorities that this is the case.

            Science generally, and mathematics in particular, has a huge problem with infinity. To begin with it is not possible to pin it down to a particular definition. For example, it is the result of dividing one by zero. However, it is also the result of dividing two by zero – or any other number by zero (except, perhaps, zero itself, but that is a debate for elsewhere). Conventional thinking tells us that, since two is twice the size of one, the result of dividing two by zero should be twice the size of dividing one by zero. In fact, both result in infinity. Mathematically, this means that the presence of an infinity in a calculation is a disaster.

            Since infinity cannot be given any real mathematical meaning, it is necessary to try and find some other way of understanding it. In a very real sense this is a futile exercise, since, by its very nature, it goes beyond whatever attempts are made to rationalise it. Nevertheless, attempts are made. One such example sometimes given is that of an infinite number of monkeys with typewriters who, given sufficient time, will produce a Shakespearean play. This, however, does not give justice to infinity.

            Let us choose a particular play and count the number of letters, spaces and punctuation marks in that play. This total is then used to create a line of monkeys, each with a typewriter. Now, assume that there are an infinite number of lines of monkeys of this length and give them the absolute minimum amount of time required to strike a key on the typewriter. It is easy to imagine that, during that moment, the vast majority of the monkeys will do anything other than strike a key. It seems almost inconceivable that, even with an infinite number of lines of monkeys, there would be any in which every single monkey not only tried to strike a key, but actually succeeded. To most people, there could at best be only a few lines where this happens. In fact, there would be an infinite number of such lines. That is not to say that all of the lines would have monkeys that successfully strike a key, simply that it is in the nature of infinity that a fraction of it – even a very tiny fraction – is still infinite. Once this is realised, it should come as no surprise to find that there are lines of monkeys wherein the keys pressed give, in order, the correct combination of characters to read along the complete play that was chosen. Not only that, the number of lines of monkeys that have managed to write the play will also be infinite. (There would also be, for example, an infinite number of lines wherein the play has been written backwards; an infinite number of lines where other plays would be exhibited; and so on).

            It can be seen that infinity presents a real problem. Common sense tells us that any number divided by two is cut in half, but divide infinity by two and you still have infinity. Common sense then tells us that, surely, we have two infinities, but “adding” them together again still results in infinity. A concept that defies common sense is equally troublesome to mathematics. However, it is this very irrationality of infinity that is providing cosmologists with a wealth of hypotheses about the creation of the universe. These include the idea that, given an infinite existence, the universe simply must have happened, because all possible universes will come into existence and ours is simply one of many.

            It would be useful at this point to define what is meant by the “universe”. In theory, the universe refers to the whole of creation; literally everything. However, increasingly cosmologists talk in terms of multiple universes. To understand this, we have to consider dimensions. A dimension can be seen as a direction of measurement. Any object can be described in terms of its height, width and depth – these are the standard directions of measurement, each at right angles to the other. For this reason, our world is described as “three dimensional”. Any additional dimensions would have to be at right angles to the three “known” dimensions, but common sense tells us that this is not possible. Since Einstein, it has become evident that time may be seen as an additional dimension, but one which is constantly moving (apparently) at a steady rate in one direction. Other dimensions may exist, but they would exist outside of our experience. A common illustration given is that of the flatworlders. Imagine a universe that exists on a piece of paper. The inhabitants can only move in two directions – up or down the paper, or left or right. To those people, the world above or below the paper is beyond their understanding. Increasingly, cosmologists talk of there being additional dimensions “beyond” the conventional three-plus-time that we experience in the same way that “above” and “below” are beyond the flatworlders’ experience. Whilst even cosmologists struggle to understand this concept, these additional dimensions are readily explained mathematically. In fact, most theories about the origins of the universe require the existence of additional dimensions.

            Therefore, when we talk about the universe, we are referring to the entirety of creation within the three (plus time) dimensional existence that is within our grasp. This allows for the possibility of “other” universes that may exist along these extra dimensions. The universe is somewhat more complex than this, however, as some of these extra dimensions appear to be a part of this universe, but still beyond our everyday experience. To understand this, we have to follow the cosmologists’ model back to the very earliest days of the universe.

            It is common to think of space as being cold – and it is, but not quite as cold as it could be. Temperature is actually a measure of motion – the more particles move about, the hotter the substance is and the colder a substance is, the less the particles within it are moving. In theory, as substances get colder, they will reach a point at which the particles come to a stop. This temperature has been calculated to be around minus 273 degrees Celsius and defines the zero point of the Kelvin scale. Because it is the point at which all motion stops it is impossible, in theory, to get any colder than this, so it is known as “absolute zero”.

            The universe has been measured to be around three degrees above absolute zero (In this context, “the universe” refers to what we call “space” – the gaps between the stars, which, clearly, are considerably hotter). This small temperature manifests itself in very long wavelength radiation which can be detected in all directions in space. It is all that is left of the “big bang” – that initial burst of energy that marked the creation of the universe.

            As we travel back through time, the universe contracts. The total energy – which today averages to just a few degrees above absolute zero – remains constant (more or less), but is contained in an ever smaller universe. This means that the average temperature rises continually as we go backwards in time. Eventually a point is reached where the temperature – the average energy – is too high for ordinary matter to exist. Molecules break down into atoms and then the atoms break down into sub-atomic particles. Eventually even these cannot exist. At present, cosmologists have great difficulty explaining what this pre-particle universe would have been like. It makes sense mathematically, but defies being put into words. What can be said is that a point is reached where the ordinary rules of physics totally cease and a different set of rules apply. The universe at this point almost certainly had far more than the three dimensions that we experience today. Time did not “flow” in the way we experience it, but was, instead, a spatial dimension that could – if people could have existed – be walked along in either direction. Many other dimensions would have existed, although the exact number has not yet been settled by cosmologists.

            As the universe expanded and cooled, it seems that some of these dimensions “uncoiled”, while others remained tightly wound. For reasons not yet certain, three of these dimensions became the spatial dimensions we know today and one of them became time. The others are still there – tightly wound together on a level far below the subatomic. In this sense, some additional dimensions are part of our universe, but it is also possible that there are further dimensions that are beyond our experience. If just one additional dimension had “uncoiled”, it may have taken enough other dimensions with it to create a completely separate universe – or series of them.

            Science cannot yet tell us what happened “in the beginning”, but each new discovery brings it ever closer. To date, they can say with a great deal of certainty what happened back to a (relatively) short period after that beginning (assuming the “big bang” was the beginning. There may yet be a “before” the big bang, but that event certainly marks the beginning of this phase of the universe’s existence.) What is now certain is that what we perceive as the “normal” rules of physics did not apply in that early universe. Large particles could not exist, so all events were governed by the laws of the very small – what is known as quantum physics. In fact, those laws (or, rather, some of them) do apply today, but on the quantum level.

            One very important and measurable application of quantum laws can be seen in photosynthesis – the process by which plants capture sunlight and convert it to energy. This occurs in large molecules that work somewhat like miniature production lines. At one end the light is “captured” – it is used to “excite” an electron (that is, to give it additional energy). This excited electron is then able to escape from the atom to which it was bound and is passed along a series of atoms, like a conveyor belt, to the far end of the molecule where it finally comes to rest and can be stored or used by the plant. This seems straightforward, but the complication arises in the “conveyor belt” section of the molecule, where the excited electron is able to take any of a number of different paths to reach its destination. Consider the simplified example below, in which the electron has just two possible “conveyor” atoms that it can pass through. There are four possible routes the electron can take:

            It should be fairly clear that not all paths are equally efficient. It is a waste of time and energy for the electron to pass through both A and B on its way to the store. A similar, but far more complex, picture is found in plants, where it has been calculated that, if the electron found its way to the store simply by random chance, the efficiency would be about 50%. The problem is that this is far too low. Most plants simply could not exist with such a poor performance. In reality, measurements have shown that the efficiency of most plants is actually around 98%, which seems to defy the common sense laws of probability.

            Electrons are often described as “particles”, but this is a poor description. Although they can be seen to act like particles, their true nature is far more complex (and still far from fully understood). Taking the example above, it can be seen that the electron has, at each step, two possible paths: to A or B initially; from A to either B or the store; and from B to either A or the store. Let us assume that each possible path has an equal probability. Therefore there is a 1 in 2 chance it will go from the collector to A and the same chance to B. Similarly, if it is at A, there is a 1 in 2 chance that it will go to the store and a 1 in 2 chance of going to B, and so on. (For simplicity, assume that it cannot return to any place to which it has already been.) This means that each of the four possible paths has a 1 in 4 probability.

            In reality, the electron will travel down all of the possible paths. It can do this because an electron does not simply “exist” in one place at any one time. At any instant, an electron has a partial existence in each of a number of different places and each of these different places represents a probability that the electron exists at that location. In the example above, 25% of this probability is represented by each of the four possible paths. This is not the same as saying that the electron is 25% likely to travel down any one path – a part of the electron’s existence travels down each of the four paths. It is only when the electron interacts with the rest of the world that it acts like a particle. In the above example, the shortest path is the first, through point A. As soon as that part of the electron which takes this route reaches the store, it interacts with it. At that point of interaction, the electron acts like a particle. Further, because that interaction is a certain (i.e. probability of 100%) event, all of the other possible events (travelling along the other paths) are reduced to zero probability. In other words, as soon as the electron reaches its target, it acts as though it had simply taken the fastest route, whereas, during the journey, it had attempted to take all possible routes. This is described as quantum probability collapse. All so-called sub-atomic “particles” behave in this way. They exist as “probability density functions” – a collection of possible events, each of which is completely real, until they interact with the rest of the universe and these possibilities are forced to become a single actuality.

            Whilst this all seems somewhat bizarre, the evidence of photosynthesis provides indirect proof that this is what actually happens. Remember that, in the early universe, large particles could not exist. This means that any events that occurred during the creation of the universe must have been governed by the laws of quantum physics, no matter how strange those laws might seem to us. So, how might these laws have created our universe?

            Space is not empty. If we could travel to the most remote part of space and take out an ultra-powerful microscope, we would see that, way below the atomic level, matter is continually being created. However, for each “particle” of matter that is created, its “anti-particle” is also created. The particle travels forwards in time, the anti-particle travels backwards in time and, when the two meet, they annihilate each other. The net result is that there is nothing. However, if these particles encounter sufficient force or energy then they can be influenced to avoid their mutual annihilation. It is believed that this happens at the edge of black holes, for example, where the intense gravitational pull will drag in whichever of the particles is closest, allowing the other, eventually, to fly off into space. The probability of these particles “missing” each other, and thus avoiding annihilation, is almost infinitely small under less severe conditions than the proximity of a black hole. However, it is not zero. In the “real world”, such a probability is so low that it has probably never happened during the life of the universe. However, what if the “universe” were infinite in size and time was no longer a constraint?

            If we return to our infinite rows of monkeys, the element of time has been, effectively, removed, because each of the monkeys is only given enough of it to strike a single key – in effect, we are dealing with a “moment”. Yet, in that moment, we will find that there are an infinite number of rows in which the desired play is spelled out.

            At the moment of creation (we cannot say “before” – this is a meaningless concept, as time had not yet “started”) we have, similarly, an instant. But this “instant” is infinite in space and also in the various other dimensions. Within this particles are created, along with their anti-particle and, in almost every instance, mutually destroyed. However, in an infinity of existence, there must be many (in fact, an infinite number) instances where the particles manage to avoid such destruction, just as there would be an infinite number of monkeys that manage to strike a key. Similarly, if we have an infinite number of particles (and anti-particles) being created, it is a small step to imagine that sufficient particles may be gathered together in one “place” as to form what would then become our universe.

            This leads us to some interesting questions. Just as our monkeys would produce an infinite number of copies of our play, does the process of creation produce an infinite number of universes? On the face of it, the answer to this must be “yes”, but remember that we are talking about quantum events. The very creation of our universe creates a “certain” event. According to quantum probability collapse, this means that all of the other “possible” acts of creation acquire zero probability and thus would not happen. In our monkey analogy, this means that, in creating a line of monkeys which has the desired play, all of the other lines of monkeys instantly disappear. If this seems strange, consider another of the bizarre laws of quantum physics, which is famously illustrated by a “thought experiment” known as “Schrödinger’s Cat”.

            Imagine a box, into which is placed a cat that is very much alive and healthy. Also inside this box are a small piece of radioactive material and a sealed jar of fast-acting poisonous gas. This gas can only be released when a trigger mechanism is struck by radiation. Once the cat is inside, the box is sealed. The longer the cat is left in this box, the greater the probability that the radioactive material will decay, releasing radiation and thus triggering the release of the poison. Assuming enough time elapses that it becomes highly probable that this has happened, the question that arises is “Is the cat alive or dead?”

            Common sense tells us that, assuming the radioactive material has decayed, the cat will be dead. However, the process of radioactive decay is a quantum event and it should now come as little surprise to find that common sense has to give way to the rather bizarre rules of quantum physics. Under these rules, no event is certain until it impacts upon the rest of the universe. To be more precise, quantum events remain only probabilities until they are measured. It is the act of measuring that forces certainty. Thus, the radioactive decay, which is a probability event, may have triggered the release of gas and it may not. It is only when this is measured that the probability collapses and becomes a certainty. In practical terms, this means that, unless and until the box is unsealed and opened, the cat is both alive and dead. The more time elapses before the box is opened the greater the probability that the cat will be found dead. Let us assume that, after two minutes this is 50% and after one hour it is 99%. After two minutes, if the box is unopened, the cat is 50% alive and 50% dead. If the box is opened at that time, the cat will instantly be either 100% alive or 100% dead. If you have a thousand such boxes, then about 500 of the cats will be dead and the other 500 alive. Similarly, after an hour, the cat is 99% dead and 1% alive, but opening the box at this time also collapses the probability and the cat becomes either 100% alive or 100% dead. If there are a thousand boxes then only about ten of the cats will still be alive, but, up to the moment the box is opened, all 1,000 will be both alive and dead.

            Schrödinger’s Cat illustrates a very real law of quantum mechanics. It is not designed as a metaphysical or philosophical idea in the same way as, for example, the question “If a tree falls in the forest and there is no-one there to hear, does it make a sound?” Events on the quantum level are always only probabilities until their impact is felt by the rest of the universe. In the case of photosynthesis, the excitement of an electron and its path to the far side of the molecule are both quantum events. Once the far side is reached, the energy the electron contains is used by the plant. In making use of the energy, the plant exhibits (no matter how small) a change in behaviour that is evident to (i.e. observed by) the rest of the universe, thus causing a collapse in the probability of the path taken by the electron. This, in turn, collapses the probability of the creation of an excited electron (an excited electron has arrived, therefore an excited electron was created).

            It is often at this point that common sense attempts to re-assert itself and insist that, surely, the cat is an observer. No matter how fast-acting the poison, the brain takes time to cease activity, during which the cat is sufficiently aware to have observed the fact that it is dying. This is true as far it goes. However, so long as the box remains sealed, to the rest of the universe the demise of the cat has yet to be observed. Thus, the cat is still both alive and dead. Despite this almost impossible paradox, it is an essential part of quantum law. Without it, photosynthesis would be so inefficient that life as we know it would never have existed.

            On the one hand, we have a set of laws that utterly defy common sense and science will almost certainly discover even more bizarre laws in the future. On the other hand, belief in God is described as “irrational”. Furthermore, science is increasingly reliant on infinity to provide an explanation for creation, yet infinity is mathematical nonsense. If God exists and is infinite, then he represents all that is irrational, yet one of the fundamental aspects of God as presented in religious texts is that he is the embodiment of order.

            Once we introduce the concept of infinity, we also introduce paradox – on both sides of the arguments. It may be that paradox turns out to be a fundamental law of the universe(s), but, for now, provides little help in resolving the question of what God is.

            It may be of benefit to determine what God is not, a process that will also show how entrenched positions on all sides of the “God Question” have generated erroneous preconceptions.