This was written in response to a Year 12 Philosophy essay, title “The Probability of Existence”, early in 2004. I’m posting it here, as I thought I’d already sone so, but was unable to find it. There seems to me to be little doubt that, in some sense, we exist. Since, as Descartes suggested, the fact we can think, we must exist. Cogito ergo sum. But what of the idea of our type of existence? Is our perception of our environment real? Is our environment real? On first appearance, as Chas suggests, we observe reality, and there must be truth to it. Or, on closer examination, there must be some kind of existence. According to logic, something must either have a quality, or not have a quality. This seems reasonable, but in fact such a simple proposition can lead to a paradox. Before we examine the paradox, let us first examine the idea that something must either be or not be. The nature of our universe is universally (sorry, bad pun) accepted now to be that of the system proposed by Quantum Mechanics, and leads to some interesting ideas about, among other things, the reality of as-yet unobserved events. Take the idea of Schrodinger’s cat, and its superposition between life and death. Until we open the box, and the wave function of the cat collapses, it is neither alive nor dead, nor some percentage of both, but both alive and dead at the same time. In fact, we can take this a step further, and place some other monitoring device, connected to a computer, that opens the box after the designated time, and stores the result for us to refer to. But, in essence, this does not collapse the wave function until a human (or otherwise conscious individual) examines the results. In fact, I could argue that until I know, the state is still unsure. That is, even if you know, since I don’t, the superposition is still there until I know. Alternatively, until you know, even though I know, as far as you are concerned the cat is neither alive nor dead until I tell you. So, this idea raises some serious questions as to the validity of the statement that something is either true or not true. But let us put that aside, and examine it in purely logical, classical, real life (or maybe even mathematical) terms. The mathematical idea of sets allows us to organise things, and we can use membership of a set to classify objects. A set might consist of all of the integers, or all of the red apples, or something else, even other sets. Obviously, sets can have an infinite number of members, or no members (the empty set, called Ã˜). It is possible to build up all of arithmetic using only the theory of sets and the empty set. So, items can be classified as either belonging to a particular set, or not belonging to it. Sets can also belong to themselves. But what of the set of sets that belong to themselves? Does this set belong to itself, or not? Easy, of course it does. But that set of sets that don’t belong to themselves is a different matter. If this set belongs to itself, then it cannot, but if it doesn’t, then it must. Put this way, it may be difficult to understand. But let’s put it in a more human context. Take the Barber of Seville. Men living in Seville can be classified as belonging to one of two sets: either they shave themselves, or they are shaved by the Barber of Seville. But what of the Barber himself? Does he shave himself, or is he shaved by the Barberâ€¦wait a minute?! This paradox appears in a variety of other contexts (the above assumes that, amongst other things, every man in Seville shaves, and there is only one barber, but it proves a point). One of these is the idea of library catalogs, and books of library catalogs. Catalogs can either be in themselves or not, and a book could list all of the library catalogs that are listed in themselves. What of the catalog of catalogs that are not in themselves? In fact, this paradox invariably appears when dealing with sets that may contain themselves as members, and this caused much grief to Frege, the mathematician and philosopher who attempted to create all of mathematics from the ground up, and remove any doubt. This paradox is a precursor to GÃ¶del’s Incompleteness Theorem, which shook the foundations of mathematics to it’s core. Basically, it says that no sufficiently complex (enough to be useful) mathematical system can be complete - there will always be undecidable statements - this, however, is beyond the scope of this paper to explain. In fact, the whole idea is not usually breached until late in a mathematics degree. As an aside: what is the opposite of nothing? Something? Everything? The number zero, and it’s close friend, infinity, have enabled great leaps in mathematics, but also can create paradoxes of their own. It is possible, by throwing a division by a number that really is zero, but doesn’t look like it yet, to equate 1 and 2, or any other pair of numbers. Of course, mathematicians are taught that division by 0 is not allowed, even though a satisfactory result may be âˆž). But back onto the idea of an external world, an environment, if you will. Since our brains apparently cannot exist in isolation, there must be something ‘out there’. But is it anything like we observe it to be? The film ‘The Matrix’ contained the idea that we were ‘energy sources’, bred and nursed by robots to create an energy source, and were linked up to a computer system that created an illusory reality, by hacking directly into our nervous system. This may turn out to be a perfectly feasible method of controlling perceptions. Early experiments discovered that physically touching parts of the brain created a feeling of sense, (thus confirming the brain as the seat of the mind), and recent developments have allowed for direct interface, using electrical signals with other parts of the nervous system. Given enough understanding of the brain and body, it should be possible to totally trick the mind/body. This would also require a significant level of computing power, but according to Gordon Moore from Intel, computing power doubles every 18 months - known as Moore’s Law, this has been true since the creation of computers, even when suspected barriers have been approached. Given sufficient computing power, it would be possible to create a simulation of another kind, purely in software. Such simulations, albeit crude, exist already, as games such as Sim City, and the more advanced of it’s ilk. To a Sim living in such a world, the world would appear real. A complex enough simulation may be capable of creating Sims with self awareness, what we call consciousness. Then, a Sim in this environment, may at some stage read a philosophy essay, and write a reportâ€¦how would it know that the world it existed in was not the real world? Again, once the price of this computing power became low enough, it would be possible (probable?) to have a multitude of these simulations running, concurrently. Theoretically, one or more of these simulations could develop within it a computing technology that is capable of creating simulations of universes, nesting universes inside of one another. But, we are just one universe. Once a universe has created a simulation (or many), the odds of us being in the ‘real’ world reduce - if there is one real world, and one simulation, it’s 50-50, but it goes down pretty quickly. There’s little to suggest that the simulations would be malevolent like the robots from the Matrix - rather, if we were to create simulations we would study them, and use them to improve ideas such as evolution - thought we might have written the rules to begin with. Might the fact we live in a simulation have some side effects? If we discovered the limits of our simulation, things might be added on. Or, we might see the limits, as a ‘graininess’, apparent in quantum physics, of the limits of measurement of time/space calculated by Planck. Or, as we approach the limits, we might come across automatic controls that destroy the universe if we threaten to reach the edge (and discover that it’s all unreal, like Jim Carrey in The Truman Show). This idea was treated previously in a science fiction story, possibly by Asimov, where the concept was likened to a ring of penicillin around bacteria growing in a petri dish - those bacteria that reached the penicillin died.