The Science of Discworld II

some other CD to which that number has been assigned. For instance, suppose that a recording of Beethoven’s Fifth Symphony starts, in digital form, with 11001. That’s the number 25 in binary. Sothe jukebox reads the CD as ‘25’, and looks for CD number 25, which we’ll assume is a recording of Charlie Parker playing jazz. On the other hand, elsewhere in the jukebox is CD number 973, which actually is Beethoven’s Fifth Symphony. Then a CD of Beethoven’s Fifth can be ‘read’ in two totally different ways: as a ‘pointer’ to Charlie Parker, or as Beethoven’s Fifth Symphony itself (triggered by whichever CDs start with 973 in binary). Two contexts, two interpretations, two meanings, two results.
    Whether something is a message depends upon context, too: sender and receiver must agree upon a protocol for turning meanings into symbols and back again. Without this protocol a semaphore is just a few bits of wood that flap about. Tree branches are bits of wood that flap about, too, but no one ever tries to decode the message being transmitted by a tree. Tree rings – the growth rings that appear when you saw through the trunk, one ring per year – are a different matter. We have learned to ‘decode’ their ‘message’, about climate in the year 1066 and the like. A thick ring indicates a good year with lots of growth on the tree, probably warm and wet; a thin ring indicates a poor year, probably cold and dry. But the sequence of tree rings only became a message, only conveyed information, when we figured out the rules that link climate to tree growth. The tree didn’t send its message to us.
    In biological development the protocol that gives meaning to the DNA message is the laws of physics and chemistry. That is where the exformation resides. However, it is unlikely that exformation can be quantified. An organism’s complexity is not determined by the number of bases in its DNA sequence, but by the complexity of the actions initiated by those bases within the context of biological development. That is, by the meaning of the DNA ‘message’ when it is received by a finely tuned, up-and-running biochemical machine. This is where we gain an edge over those amoebas. Starting with an embryo that develops little flaps, and making a baby with those exquisite little hands, involves a series of processes that produce skeleton, muscles, skin, and so on. Each stage depends on the current state of the others, and all of them depend on contextual physical, biological, chemical and cultural processes.
    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