Terry Pratchett - The Science of Discworld II - The Globe

Mathematicians like to pre-state the space of possibilities, but the whole point about innovation is that it opens up new possibilities that were previously not envisaged. So Kauffman suggests that a key feature of the biosphere is the inability to pre-state a phase space for it.

At risk of muddying the waters, it is worth observing that even in physics, pre-stating the phase space is not as straightforward as it might appear. What happens to the phase space of the solar system if we allow bodies to break up, or merge? Supposedly [16] See The Science of Discworld, 'A giant leap for moonkind'. the Moon was splashed off the Earth when it collided with a body about the size of Mars. Before that event, there was no Moon- coordinate in the phase-space of the solar system; afterwards, there was. So the phase space expanded when the Moon came into being. The phase spaces of physics always assume a fixed context. In physics, you can usually get away with that assumption. In biology, you can't.

There's a second problem in physics, too. That 6N-dimension phase space of thermodynamics, for example, is too big. It includes non-physical states. By a quirk of mathematics, the laws of motion of elastic spheres do not prescribe what happens when three or more collide simultaneously. So we must excise from that nice, simple 6N-dimensional space all configurations that experience a triple collision somewhere in their past or future. We know four things about these configurations. They are very rare. They can occur. They form an extremely complicated cloud of points in phase space. And it is impossible, in any practical sense, to determine whether a given configuration should or should not be excised. If these unphysical states were a bit more common, then the thermodynamic phase space would be just as hard to pre-state as that for the biosphere. However, they are a vanishingly small proportion of the whole, so we can jus about get away with ignoring them.

Nonetheless, it is possible to go some way towards pre-stating a phase space for the biosphere.

While we cannot pre-state a space of all possible organisms, we can look at any given organism and at least in principle say what the potential immediate changes are. That is, we can describe the space of the adjacent possible, the local phase space. Innovation then becomes the process of expanding into the adjacent possible. This is a reasonable and fairly conventional idea. But, more controversially, Kauffman suggests the exciting possibility that there may be general laws that govern this kind of expansion, laws that have exactly the opposite effect to the famous Second Law of Thermodynamics. The Second Law in effect states that thermodynamic systems become simpler as time passes; all of the interesting structure gets 'smeared out' and disappears. In contrast, Kauffman's suggestion is that the biosphere expands into the space of the adjacent possible at the maximum rate that it can, subject to hanging together as a biological system.

Innovation in biology happens as rapidly as possible.

More generally, Kauffman extends this idea to any system composed of 'autonomous agents'. An autonomous agent is a generalised life-form, defined by two properties: it can reproduce, and it can carry out at least one thermodynamic work cycle. A work cycle occurs when a system does work and returns to its original state, ready to do the same again. That is, the system takes energy from its environment and transforms it into work, and does so in such a manner that at the end of the cycle it returns to its initial state.

A human being is an autonomous agent, and so is a tiger. A flame is not: flames reproduce by spreading to inflammable material nearby, but they do not carry out a work cycle. They turn chemical energy into fire, but once something has been burnt, it can't be burnt a second time.

This theory of autonomous agents is explicitly set in the context of phase spaces. Without such a concept, it cannot even be described. And in this theory we see the first possibility of obtaining a general understanding of the principles whereby, and wherefore, organisms complicate themselves. We are starting to pin down just what it is about lifeforms that makes them behave so differently from the boring prescription of the Second Law of Thermodynamics. We paint a picture of the universe as a source of ever-increasing complexity and organisation, instead of the exact opposite. We find out why we live in an interesting universe, instead of a dull one.

'How can you communicate like this?' panted Ponder, as they jogged along beside a broad river.

'Since the physics of Roundworld are subordinate to the physics of the real world, I can use anything considered to be a communication device,' said the voice of Hex, slightly muffled in Rincewind's pocket. 'The owner of the device believes it to be one such. Also, I can deduce much information from this world's footprint in L-space. And the Archchancellor was right. There is much Elvish influence here.'

'You can extract information from Roundworld books?' said Ponder. 'Yes. The phase space of books that relate to this world contains ten to the power of 1,100 to the power of n volumes,' said Hex. 'That's enough books to fill the univ— hold on, what is n?' 'The number of all possible universes.'

'Then that's enough books to fill all possible universes! Well ... as close as makes no difference, anyway.'

'Correct. That is why there is never enough bookshelf space. However, because of the subordinate temporal matrix of this world, I can use virtual computing,' said Hex. 'Once you know what the answer is, the process of calculation can be seriously reduced. Once the correct answer is found, the fruitless channels of inquiry cease to exist. Besides, if you deduct all the books that are about golf, cats, slood [17] An extremely common and versatile substance, unfortunately not available in all universes. and cookery the number is really quite manageable.'

'Oook,' said the Librarian.

'He says he's not going to have a shave,' said Rincewind.

'It is essential,' said Hex. 'We are getting strange glances from people in the fields. We do not wish to attract a mob. He must be shaved, and given a robe and hat.'

Rincewind was doubtful. 'I don't think that'll fool anyone,' he said.

'My readings tell me that it will if you say he's Spanish.'

'What's Spanish?'

'Spain is a country some five hundred miles from this one.'

'And people there look like him?'

'No. But people here would be quite prepared to believe so. This is a credulous age. The elves have done a lot of damage. The greatest minds spend half their time busying themselves with the study of magic, astrology, alchemy and communion with spirits.'

'Well? Sounds just like life at home,' said Rincewind.

'Yes,' said Hex. 'But there is no narrativium in this world. No magic. None of those things work.'

'Then why don't they just stop trying it?' said Ponder.

'My inference is that they believe it should work if only they get it right.'

'Poor devils,' said Rincewind.

'They believe in those, too.'

'There's more houses ahead,' said Ponder. 'We're coming to a city. Er ... and we've got the Luggage with us. Hex, we haven't just got an orangutan with us, we've got a box on legs!'

'Yes. We must leave it in some bushes while we find a voluminous dress and a wig,' said Hex calmly. 'Fortunately, this is the right period.'

'A dress won't work, believe me!'

'It will if the Librarian sits on the Luggage,' said Hex. "That will bring him up to the right height and the dress will provide adequate cover for the Luggage.'

'Now hang on a moment,' said Rincewind. You saying that people here will believe an ape in a dress and a wig is a woman?'