The Science Of Discworld II by Stewart Ian & Jack Cohen & Terry Pratchett

Author:Stewart, Ian & Jack Cohen & Terry Pratchett [Stewart, Ian]
Language: eng
Format: mobi
ISBN: 9781407022611
Publisher: Random House UK
Published: 2011-06-29T16:00:00+00:00

A central concept in Shannon’s information theory is something that he called entropy, which in this context is a measure of how statistical patterns in a source of messages affect the amount of information that the messages can convey. If certain patterns of bits are more likely than others, then their presence conveys less information, because the uncertainty is reduced by a smaller amount. In English, for example, the letter ‘E’ is much more common than the letter ‘Q’. So receiving an ‘E’ tells you less than receiving a ‘Q’. Given a choice between ‘E’ and ‘Q’, your best bet is that you’re going to receive an ‘E’. And you learn the most when your expectations are proved wrong. Shannon’s entropy smooths out these statistical biases and provides a ‘fair’ measure of information content.

In retrospect, it was a pity that he used the name ‘entropy’, because there is a longstanding concept in physics with the same name, normally interpreted as ‘disorder’. Its opposite, ‘order’, is usually identified with complexity. The context here is the branch of physics known as thermodynamics, which is a specific simplified model of a gas. In thermodynamics, the molecules of a gas are modelled as ‘hard spheres’, tiny billiard balls. Occasionally balls collide, and when they do, they bounce off each other as if they are perfectly elastic. The Laws of Thermodynamics state that a large collection of such spheres will obey certain statistical regularities. In such a system, there are two forms of energy: mechanical energy and heat energy. The First Law states that the total energy of the system never changes. Heat energy can be transformed into mechanical energy, as it is in, say, a steam engine; conversely, mechanical energy can be transformed into heat. But the sum of the two is always the same. The Second Law states, in more precise terms (which we explain in a moment), that heat cannot be transferred from a cool body to a hotter one. And the Third Law states that there is a specific temperature below which the gas cannot go – ‘absolute zero’, which is around -273 degrees Celsius.

The most difficult – and the most interesting – of these laws is the Second. In more detail, it involves a quantity that is again called ‘entropy’, which is usually interpreted as ‘disorder’. If the gas in a room is concentrated in one corner, for instance, this is a more ordered (that is, less disordered!) state than one in which it is distributed uniformly throughout the room. So when the gas is uniformly distributed, its entropy is higher than when it is all in one corner. One formulation of the Second Law is that the amount of entropy in the universe always increases as time passes. Another way to say this is that the universe always becomes less ordered, or equivalently less complex, as time passes. According to this interpretation, the highly complex world of living creatures will inevitably become less complex, until the universe eventually runs out of steam and turns into a thin, lukewarm soup.

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