Simply Complexity (33 page)

The answer is to form a crowd of them. Damien Challet and I have shown mathematically that by taking appropriate combinations of such defective devices, a much more accurate – indeed essentially perfect – device can be made. It turns out that the mathematical theory which we developed is intimately related to the complexity associated with combining numbers. In particular, it is related to the problem of taking combinations of numbers so that their sum is as close to zero as possible. But the basic idea can be understood quite simply in terms of a few clocks. Suppose you have a clock which is five minutes fast. If you want to produce an automatic readout of the time which is perfect, just connect it to a clock which is five minutes slow and arrange for an average of the readings to be displayed instead. The resulting time from this “crowd” of clocks is perfectly accurate. Indeed this is exactly what sailors used to do to deduce the correct time at sea. They simply took a collection of clocks on board and took the average or consensus of the times. This example considers everyday clocks – but there is no reason in principle why the same idea cannot be applied to nanoscale devices, even in the quantum regime. After all, everything has a readout eventually, and it is at this stage that taking a particular subset of devices whose errors effectively
cancel, comes to the fore. Any remaining defective devices can then be recycled efficiently by repeating this process, thereby producing a further batch of devices which are themselves also quite accurate.

So let’s see how this would work for a collection of such imperfect objects. Suppose we are clockmakers and we have produced six clocks whose times, relative to the exact time, are +5, +3, –8, –2, –1, +4. We need to compete with the big manufacturers whose clocks all have a guaranteed error of 1 or less. Should we throw away the clocks we have made and make new ones, thereby running the risk that we waste additional effort and money without producing anything more accurate? No, we just go ahead and form them into suitable “crowds”. As shown in
figure 11.2
, we can form a crowd of the three clocks with errors +3, –2 and –1 in order to give a composite clock with a net error
of zero. In short, +3 – 2 – 1 = 0. We can then form a crowd of the three remaining clocks with errors +5, –8 and +4 to give a composite clock with net error +1, since +5 – 8 + 4 = +1. In addition to having used up all our otherwise useless clocks, we have actually produced two composite devices with near-perfect accuracy.

Figure 11.2
Making nothing out of something. By combining devices which are themselves inaccurate, far more accurate composite devices can be made. In the process, little or no waste is left.

So it turns out that as a by-product of our interest in Complexity and hence crowds, we have actually come up with an efficient and ecological solution for dealing with wastage. In fact, it seems such a nice idea that one could imagine Nature already using it – or mankind being able to exploit it – to correct errors at the cellular level in human biology. In particular, might such a combination-of-errors approach be used to reduce the effects of cellular imperfections?

We have seen in this book that the need to understand Complex Systems is motivated by a multitude of important practical applications, coupled with a very deep scientific significance. Examples of the collective phenomena which can emerge from real-world Complex Systems include traffic congestion, financial market crashes, wars, cancer and epidemics. Each of these phenomena represents a massive challenge to us as individuals and as a Society – from our daily commute home through to the performance of our pension funds, and from our daily health through to our life expectancy – since they can emerge spontaneously without any form of “invisible hand” or central controller. Such emergent phenomena are possible because the underlying system contains many interacting objects, and because there is some form of feedback in the system. That is why we need to understand what is going on in such Complex Systems both for scientific and for practical reasons.

Physics is used to dealing with large numbers of interacting objects. However, the answer to building a true
Theory of Complexity
is currently a bridge too far for Physics. Most physicists implicitly deal with closed systems, such as the Universe itself and systems which have reached some kind of steady state. Having said this, there is a branch of Physics which tries to avoid such
assumptions – the field of non-equilibrium statistical mechanics. So is this the answer? Unfortunately, no. Or at least, not in its current form. The problem is that statistical mechanics in general tries to look at the limit of large numbers of objects – very large numbers, of the order of the number of atoms in a drop of liquid or a balloon full of air. This is fine for a drop of liquid or a balloon full of air since they really do have an amazingly large number of atoms in them. For example, a typical everyday volume would contain ten-to-the-power-twenty-something atoms, which is more than one hundred million, million, million. And this is much larger than the number of people on the planet.

It therefore seems unlikely that theories which need to assume such a large number of objects can properly represent everyday Complex Systems where the numbers involved are typically less than a thousand, or even a hundred. After all, in a financial market the number of people who actually have enough economic clout that they move the market when they trade is relatively few – and it is this number which should feature in any realistic model or theory of the market. So applying any theory which assumes that there are essentially an infinite number of such people sounds dodgy.

This practice by physicists of developing tools and theories which work when there are extraordinarily large numbers of objects, is certainly a very powerful one for liquids, gases and solids. As mentioned above, it works physically because these systems do indeed have lots of atoms in them – and it works mathematically because there is a tendency for large numbers of identical objects to behave like the average of them all. In addition, such theories typically assume some kind of “temperature” which implies that the system is in a steady-state. In other words, you have to wait a very long time to reach this state. But in the long run, humans are dead – so again this sounds dodgy. Therefore the notion of developing a theory which works for an infinite number of identical objects when they are in some kind of steady-state is fine – as long as that is the system that it is applied to. The hope that it can then be tweaked to apply to everyday Complex Systems which feature a finite number of non-identical objects, and which are not in a steady state, seems suspect – unfortunately.

Things are, however, far from bleak for Complexity Science. Indeed there is a very bright future ahead in terms of the study of models and real-world systems which combine the two key manifestations of Complex Systems discussed throughout this book: multi-object or so-called multi-agent populations, and networks. For example, the possibility of using the decision-making within a multi-agent population in order to build and then manipulate a complex network, and then having that network feed back onto the decisions themselves, will be a very rich area for research since it is common to all the applications discussed in this book. In addition, there are many more applications which I have not mentioned waiting to be analyzed across the physical, biological and social sciences, and which cover a wide range of length-scales and time-scales: from the quantum scale right through to the structural properties of the Universe.

You can already see such research activity starting to happen, simply by typing
Complexity
or
Complex Systems
into Google. You will be flooded with lists of Workshops and Conferences focusing on a range of different topics and disciplines. Many of these aim to explore the competition or cooperation in groups or networks of decision-making agents, in order to see how this might underpin the dynamical evolution which is actually observed across the social, political, economic and biological spectrum. Examples include political instability, guerilla warfare, crime, foraging systems such as biological organisms (e.g. fungi), and animal herding phenomena. The common elements typically include the concept of an ecology of interacting agents, possibly foraging for some limited resource. In addition, these objects may be moving on some complex dynamical network, and indeed their own actions and evolution may themselves affect the network’s structure and future evolution.

This increased focus on real-world Complexity is very good news since many professionals – from scientists through to medical doctors and policy-makers – already spend their days dealing with particular manifestations of Complexity yet may not even realize it. In other words, a better appreciation of the ideas behind
Complexity, as discussed in this book, could help us all reap significant practical benefits.

In terms of academic advancement, there seems to be an increasing proportion of the research community which is taking on board the idea that there will be few major advances in human medicine, sociology or economics without a better understanding and appreciation of Complexity Science. For example, large areas of biological phenomena are beginning to be lumped together under the more general Complexity-related title of “Systems Biology”. More medically-orientated projects seem to be referred to as “Systems Medicine”, “Nanobiomedicine” or some other similar hybrid. Even in genetics there is plenty of room for using ideas from Complexity. In particular, the vast amounts of DNA code that have been measured are supposed to read like a book, with each gene representing a phrase. Yet we all know that the true meaning of any book lies in the overall combination of such phrases, and in particular their interactions. Hence the true meaning of our genetic code is likely to lie in the collective behavior of this crowd of genes – and this collective behavior will arise, as with any Complex System, through interactions and feedback. Without it, the DNA book may be readable – but nobody will understand what it means.

So as we have seen throughout this book, Complexity isn’t just important for understanding traffic jams, financial market crashes or cancer growth. It also lies at the heart of the Universe itself. It is therefore “Big Science”. However unlike all previous “Big Science”, it also has tremendous everyday importance – from our own personal health, wealth and lifestyle, through to the security and prosperity of our Society as a whole.
Complexity is indeed the science of all sciences
.

This Appendix provides further information for anyone interested in pursuing the issues, topics and research discussed in this book. In section B, I provide details of how to access the research papers themselves. However, by their very nature research papers tend to be written in a very concise style and often contain very specific terminology – so it can be hard work jumping straight into reading them. Therefore, section A provides a stepping stone in the form of general webpages on Complex Systems, Complexity and centers of study around the world, together with a list of popular science books on these topics.

By far the easiest way of obtaining up-to-date information is to type “Complexity” or “Complex Systems” into any Internet search engine, e.g. Google. Below are some Internet sites which can be used as a starting point for exploring Complexity. The list is not exhaustive – nor can I endorse individual sites or guarantee whether they are currently accurate or up-to-date. However, they do supplement the discussions in this book and provide a broad picture of how this new field is evolving.

See the following short tutorial-style accounts on Wikipedia:

Complexity:
http://en.wikipedia.org/wiki/Complexity

Chaos Theory:
http://en.wikipedia.org/wiki/Chaos_theory

Randomness:
http://en.wikipedia.org/wiki/Randomness

Quantum Physics:
http://en.wikipedia.org/wiki/Quantum_ mechanics

Entanglement:
http://en.wikipedia.org/wiki/Quantum_entanglement

Superposition:
http://en.wikipedia.org/wiki/Quantum_superposition

Cancer:
http://en.wikipedia.org/wiki/Cancer

Angiogenesis:
http://en.wikipedia.org/wiki/Angiogenesis

In addition, the following sites are worth visiting:

http://www.calresco.org/tutorial.htm
– A source of tutorials on chaos, fractals and more general Complex Systems topics