The Science of Discworld II

might appear. What happens to the phase space of the solar system if we allow bodies to break up, or merge? Supposedly 5 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 6 N -dimensional phase space of thermodynamics, for example, is too big. It includes non-physical states. By a quirk of mathematics, the laws of motion for elastic spheres do not prescribe what happens when three or more collide simultaneously. So we must excise from that nice, simple 6 N- 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 just 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.
    1 There’s a Special Theory as well, but no one bothers with it much because it’s self-evidently a load of marsh-gas. [This footnote is a footnote in the original quotation. So this is a metafootnote.]
    2 The bean-counters don’t even know how to count beans sensibly. Are we surprised?
    3 A tour of any airport bookshop will show that this is reasonable.
    4 But Joycean