For example, tiger DNA turns into a baby tiger only in the presence of an egg, supplied by a mother tiger. The same DNA in the presence of a mongoose egg, would not make a tiger at all.
Now, it could be that this is just a technical problem: that for each DNA code there is a unique kind of mother-organism that turns it into a living creature, so that the form of that creature is still implicit in the code. But theoretically, at least, the same DNA code could make two totally different organisms. We give an example in The Collapse of Chaos where the developing organism first 'looks' to see what kind of mother it is in, and then develops in different ways depending on what it sees.
Complexity guru Stuart Kauffman has taken this difficulty a stage further. He points out that while in physics we can expect to pre-stage the phase space of a system, the same is never true in biology. Biological systems are more creative than physical ones: the organisation of matter within living creatures is of a different qualitative nature from the organisation we find in inorganic matter. In particular, organisms can evolve, and when they do that they often become more complicated. The fish-like ancestor of humans was less complicate than we are today, for example. (We've not specified a measure of complexity here, but that statement will be reasonable for most sensible measures of complexity, so let's not worry about definitions.
Evolution does not necessarily increase complexity, but it's at its mo puzzling when it does.)
Kauffman contrasts two systems. One is the traditional thermodynamic model in physics, of N
gas molecules (modelled as hard spheres) bouncing around inside their 6N-dimensional phase space. Here we know the phase space in advance, we can specify the dynamic precisely, and we can deduce general laws. Among them is the Second Law of Thermodynamics, which states that with overwhelming probability the system will become more disordered as time passes, and the molecules will distribute themselves uniformly throughout their container.
The second system is the 'biosphere', an evolving ecology. Here, it is not at all clear which phase space to use. Potential choices are either much too big, or much too limited. Suppose for a moment that the old biologists' dream of a DNA language for organisms was true. Then we might hope to employ DNA-space as our phase space.
However, as we've just seen, only a tiny, intricate subset of that space would really be of interest
-but we can't work out which subset. When you add to that the probable non-existence of any such language, the whole approach falls apart. On the other hand, if the phase space is too small, entirely reasonable changes might take the organisms outside it altogether. For example, tiger- space might be defined in terms of the number of stripes on the big cat's body. But if one day a big cat evolves that has spots instead of stripes, there's no place for it in the tiger phase space.
Sure, it's not a tiger ... but its mother was. We can't sensibly exclude this kind of innovation if we want to understand real biology.
As organisms evolve, they change. Sometimes evolution can be seen as the opening-up of a region of phase space that was sitting there waiting, but was not occupied by organisms. If the colours and patterns on an insect change a bit, all that we're seeing is the exploration of new regions of a fairly well-defined 'insect-space'. But when an entirely new trick, wings, appears, even the phase space seems to have changed.
It is very difficult to capture the phenomenon of innovation in a mathematical model.
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? Supposedly16 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.