The Science of Discworld II

numerous patterns: lots of repetitions of blue pixels for the sky, for instance. The more incompressible a signal is, the more information in Chaitin’s sense it contains. And the way to compress a signal is to describe the patterns that make it up. This implies that incompressible signals are random, have no pattern, yet contain the most information. In one way this is reasonable: when each successive bit is maximally unpredictable, you learn more from knowing what it is. If the signal reads 111111111111111 then there is no great surprise if the next bit turns out to be 1; but if the signal reads 111001101101011 (which we obtained by tossing a coin 15 times) then there is no obvious guess for the next bit.
    Both measures of information are useful in the design of electronic technology. Shannon information governs the time it takes to transmit a signal somewhere else; Chaitin information tells you whether there’s a clever way to compress the signal first, and transmit something smaller. At least, it would do if you could calculate it, but one of the features of Chaitin’s theory is that it is impossible to calculate the amount of algorithmic information in a message – and he can prove it. The wizards would approve of this twist.
    â€˜Information’ is therefore a useful concept, but it is curious that ‘To be or not to be’ contains the same Shannon information as, and less Chaitin information than, ‘xyQGRlfryu&d%sk0wc’. The reason for this disparity is that information is not the same thing as meaning. That’s fascinating. What really matters to people is the meaning of a message, not its bit-count, but mathematicians have been unable to quantify meaning. So far.
    And that brings us back to stories, which are messages that convey meaning. The moral is that we should not confuse a story with ‘information’. The elves gave humanity stories, but they didn’t give them any information. In fact, the stories people came up with includedthings like werewolves, which don’t even exist on Roundworld. No information there – at least, apart from what it might tell you about the human imagination.
    Most people, scientists in particular, are happiest with a concept when they can put a number to it. Anything else, they feel, is too vague to be useful. ‘Information’ is a number, so that comfortable feeling of precision slips in without anyone noticing that it might be spurious. Two sciences that have gone a long way down this slippery path are biology and physics.
    The discovery of the ‘linear’ molecular structure of DNA has given evolutionary biology a seductive metaphor for the complexity of organisms and how they evolve, namely: the genome of an organism represents the information that is required to construct it . The origin of this metaphor is Francis Crick and James Watson’s epic discovery that an organism’s DNA consists of ‘code words’ in the four molecular ‘letters’ A C T G, which, you’ll recall, are the initials of the four possible ‘bases’. This description led to the inevitable metaphor that the genome contains information about the corresponding organism. Indeed, the genome is widely described as ‘containing the information needed to produce’ an organism.
    The easy target here is the word ‘the’. There are innumerable reasons why a developing organism’s DNA does not determine the organism. These non-genomic influences on development are collectively known as ‘epigenetics’, and they range from subtle chemical tagging of DNA to the investment of parental care. The hard target is ‘information’. Certainly, the genome includes information in some sense: currently an enormous international effort is being devoted to listing that information for the human genome, and also for other organisms such as rice, yeast, and the nematode worm Caenorhabditis elegans . But notice how easily we slip into cavalier attitudes, for here the word ‘information’ refers to the human mind as receiver, not to the developing organism. The Human Genome Project informs us , not organisms.
    This flawed metaphor leads to the equally flawed conclusion that the genome explains the complexity of an organism in terms of theamount of information in its DNA code. Humans are complicated because they have a long genome that carries a lot of information; nematodes are less