Computers don't always do what they're told to

Thinking about computers, we know that one of these days they're going to stop obeying Moore's law, at least for silicon microprocessors. Moore's law was a prediction made by a man called Gordon Moore in a paper published in 1965. It predicted that the number of transistors on processors would double every year. Surprisingly this law stayed true for a time long after the ten year period Moore initially suggested. However, unfortunately all good things must come to an end and Moore's law was no exception. Gradually the doubling period has lengthened to 18 months and in 2010 it became 3 years. There is of course a reason for this and these are the limitations of manufacturing silicon computer processors with too many chips. Firstly is the fact that, when we have too many tiny transistors in too small a space, they will generate immense amounts of heat, hot enough to burn themselves up, which we obviously don't want. The second limitation is what I'm interested in however, and that is that there is of course a limit on how small we can make transistors, since the universe is made up of atoms which are of a limited size!

This might not have been something Moore had thought of, or even a stage he thought it was possible to get to, for which this might become a problem, but the reality is that this problem is one which is actually very close to becoming a major issue for the future of computing.

But why is it an increasing problem to have transistors made up from smaller and smaller numbers or atoms. Surely we should be able to go down to one atom transistors theoretically, since in reality this is all that is needed to either let electricity flow, or not to let electricity flow.

But in reality our limits are set to five atoms. Why you may ask? Well, it is due to the unpredictability of electrons when we look at them closely. Something which a part of quantum theory.

Quantum theory, Schrödinger's cat, electron cloud - they all make up this weird and wonderful modern model of atoms. The main principle behind this theory is that, contrary to what you might think, electrons cannot only be thought of as particles, but a more accurate description is 'clouds' of space where the negative charge might be at any point in time, and has a certain probability of existing within. Yes, probability and physics. Not something I would've thought might go hand in hand, but apparently, electrons can be anywhere. It doesn't just stop there however. At this small a level, these electrons can demonstrate having equal probabilities of existing everywhere within this cloud, and since we have no method of determining the exact position of electrons at this small a level, we simply have to RELY on this theory of chance - making it really difficult to build computers with transistors this small. But of course we can use this to our advantage in fact, and this can be seen in the modern quantum counters, but that's a story for another day.

What I'm interested in is the fact that this underlying principle of atoms becoming unpredictable at a nanoscopic level is actually present throughout the world of probability and statistics. It's actually not a remote and unexplained scientific theory, but something we experience on a daily basis. Let me explain.

Think of the age old model of probability - flipping a coin to get either heads or tails. There is an equally likely probability of getting each outcome, as many of us know from the hours well spent working out probability problems in our maths workbooks at school. And as we know, often probability is actually correct. Plotting a graph of the cumulative outcomes of an infinite number of trials would eventually give us an eerily accurate 50% outcome for both events. However, as we flip less and less coins the probability will probably become less accurate, up to the point where you have only flipped two coins and can get only four outcomes: heads then tails, tails then heads, heads then heads, and finally tails then tails. Looking at these outcomes they are all equally likely. But only two of them fit the overall model of probability, with a 50:50 outcome for heads and tails. This means there is actually only a 50% likelihood of getting an accurate probability, making it very difficult to predict the number of heads and tails. However, it doesn't stop there, since things take a turn for the worse when you get into the realms of flipping just one coin. There are only two outcomes - heads or tails - and neither fits the conditions needed for our 50% probability! It's physically impossible! The only way to get half heads and half tails would be for both to happen at exactly the same time. Sounding familiar?

Now we see that the behaviour of electrons at smaller and smaller levels is weirdly similar. At a large level, the properties of substances are quite predictable - give or take some slight universal randomness - just as the number of heads and tails are after flipping a coin umpteen times. However, just as the probability becomes less and less 'probable' as we get less and less trials for heads and tails, with less and less atoms, it becomes less and less likely for us to be able to say where the electrons are and predict how the material will behave as a result. Finally we get into the realms of just a few atoms and the probability gets very weird and out of hand, just as it did when we had just two flips of the coin. Imagine this, but on the scale of electrons having an infinite number of equally likely possible locations they can take, rather than just two outcomes as with the coin. Since there are infinite outcomes and probabilities for the locations of electrons, the probability is very hard to predict even on a large scale. We can simply say a certain number of electrons at least will PROBABLY exist in certain 'clouds' as a result, using an equation called Schrödinger's equation, which is basically an equation like "number of trials divided by two" for the number of heads in a certain number of trials of a coin, except applied to an infinite number of locations for electrons. Finally we reach the one atom scenario, where predicting where the electrons are going to be becomes an impossible chore, without saying that the electrons are at each and every point at once. Perhaps this apparent physical impossibility explains the existence of alternate universes with infinite numbers of possible events. Perhaps it might one day prove the existence of God. Who knows? Well, maybe the scientists in another universe, but none in this one - most probably not at least.