The Law of Large Numbers is a cornerstone of statistical science. It says that, while it is very hard to predict things on an individual basis, it is much easier to predict things on an aggregate basis once you have enough individuals in the group. The whole statistical toolbox of bell curves, averages and standard deviations exists to offer accurate predictions of random events using the law of large numbers.

For example. I can’t tell you the exact height of the next person to walk through the door but I can confidently say it will be between two standard deviations of 1.78 meters if it is a man and we are in the UK. So, in effect, a random event at the micro level yields a predictable outcome at the macro level.

#### As above, NOT so below

Consider gamblers in a casino. While it is possible for an individual gambler to get lucky and win big, in the long run the casino will always win because the odds are in its favour. This is the essence of the law of large numbers. A huge number of unpredictable micro events produce an overall system is very predictable. What is more, the larger the system the more predictable it becomes. The key criterion is that the individual events are truly random; that they are not correlated at all. In the casino example, this means that the gamblers are not colluding with each other (or with the dealers) and that the cards or roulette wheels have not been rigged. In mathematical terms, this is expressed as “the system must have independent variables”. So the ‘order’ at the macro level depends on randomness or ‘chaos’ at the micro level which is summed up in the catataxic maxim :

“Order requires Chaos”

#### The macrostate and the microstate

This ‘order above, chaos below’ concept was central to the development of Statistical Thermodynamics, one of the crowning achievements of 19th Century Physics. Ludwig Boltzmann managed to forge a link between Newton’s laws of motion and the evolving field of thermodymnamics which examined pressure and temperature phenomena in steam engines. With his kinetic theory of gases, Boltzmann took a dualistic approach defining a ‘macrostate’ and a ‘microstate’ in a catataxic separation of reality.

The macrostate was the description of the whole system, observable by measuring the pressure and temperature of the gas. The microstate was was a description of the gas as a large collection of molecules all in constant, rapid, random motion. By viewing these particles as Newtonian ‘billiard balls’ banging against each other, he was able to derive the macrostate laws of temperature and pressure from the microstate motions of these particles. The pressure of the gas derived from the sum effect of these particles banging against the side of the gas container. But he could only do this by assuming that the particles were random: that interactions between them were negligible except during collisions.

#### You are just an eddy of entropy

This macrostate/microstate approach led to one of the most important theories in Physics : the Second Law of Thermodynamics. This states that the entropy of the universe must aways increase. Things naturally tend towards a state of disorder. At first glance, this seems to be inconsistent with our experience. How do you explain the evolutionary development of complex creatures such as animals from the primordial soup if the natural tendency of the universe is towards disorder ? The answer to this paradox also lies in changing the frame of reference. Take a catataxic step upwards and look at the bigger macro picture.

Imagine two metal plates, one hot and one cold in a bath of water. As they are different temperatures, the second law of thermodynamics states that heat will flow from the hot one to the cold one until they are the same temperature. This represents the highest state of disorder (maximum entropy) because there are no local ‘pockets’ of difference which would represent some sort of structure. Everything has become uniform and the system as a whole has achieved equilibrium.

If the temperature difference between the two plates is very extreme, then you might the heat flow by convection rather than simple conduction. In other words, convection cells as in Fig.3 above could spontaneously arise in order to make the transfer of heat more efficient and drive the system towards equilibrium faster. This is an example of structure naturally emerging at a local level to speed the progress towards maximum entropy. An increase in order in the microstate facilitates a decrease in order in the macrostate. As above, not so below again.

So here, at least, is one answer to the meaning of life. Life on earth exists to drive the solar system towards maximum entropy. In the metaphore above, life is the ‘convection cell’ that has spontaneously arisen in order to dissipate the heat of the sun (the hot plate). This is why the greatest diversity of species occurs where most of the heat of the sun falls – near the equator. If you have ever wondered why you are here, now you know. You are just a little eddy of entropy that exists to dissipate sunshine. Now get out there and start tanning….

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