God's Utility Function

Transcript

The problem

The question of what the utility function of biology is was raised - and answered - by Richard Dawkins in his 1995 book of River Out Of Eden.

He phrased the question as follows:

A good way to dramatize our task is to imagine that living creatures were made by a Divine Engineer and try to work it out, by reverse engineering, what the Engineer was trying to maximize: What was God's Utility Function?

The answer he gave was "DNA survival".

This essay addresses the same question - but gives a totally different answer.

Maximum entropy production

Taking a metabolic a perspective on the problem leads us back to a proposition first articulated by Lotka in 1922 - that living systems act in such a way as to maximise entropy production.

Organisms seek out sources of order, put these through a metabolic engine, use the resulting power to grow and reproduce - and, in the process, excrete degraded waste materials.

To give an example, the Earth acts more like a black body than the moon - as a result of its living systems, it more effectively degrades the Sun's radiation into heat. Tropical rain forests are expert energy degraders. Trees grow tall so they can reach the sun's energy first - to degrade it all the more rapidly.

Another example: currently, researchers at ITER in France are working on an enormous fusion reactor, to allow us to accelerate the conversion of order into entropy still further.

Some time later it was noticed that other self organizing systems (besides living ones) also acted in a manner so that their rate of entropy production was maximised. These were sometimes known as "dissipative structures" - because they dissipated order, and produced disorder.

Later still, a similar principle was extended to all irreversible dynamical systems - and a mechanism was found to explain the phenomenon:

At a low level, high-entropy states are more common than lower entropy ones - so if a dynamical system changes in some randomly-selected way, it is likely to move into a higher-entropy state. If the high-entropy states statistically share features, then the theory allows the evolution of the features of the system to be predicted. This idea was derived from Jaynes's principle of maximum entropy production by Roderick Dewar. It is a simple principle that drives irreversible dynamical systems of all kinds to move rapidly from low-entropy states towards high-entropy ones.

Viewed from this perspective, self-organizing systems are entropy-generation engines, that seek out and feed off sources of order. In fact, self-organizing systems can be seen as a degenerative type of living system - in that they propagate themselves using a primitive kind of reproduction. For example, flames give rise to more flames, crystal seeds gives rise to more crystal seeds - and so on. Living systems are the set of self-organizing systems whose reproduction involves the reliable propagation of lots of complex information.

In a sense, living systems are self-organising systems that have developed memory and then got into habits. Selection endlessly compounds and reinforces the skills of those that degraded the available order first and best. As a result, modern ecosystems are experts at entropy maximisation.

It should be noted that there are some differences between the entropy-maximisation of Dewar and that actually followed by living systems. Dewar's mechanism is a primitive one. It is totally blind to the future - while living organisms can use fat, batteries, reservoirs - and other mechanisms - to store resources in anticipation of future shortages. Also, they have brains that help them to anticipate future events. Dewar's formulation is the degenerate, special case of the maximisation principle that applies to systems with no brains - and even to non-biological systems.

Maximum entropy production represents a powerful optimisation process at the heart of all biological systems. The general principle has explanatory power not only in biology, but also in other types of self-organising systems. Indeed, a simple version of it can be applied to any irreversible system - and so it represents a genuine universal utility function.

One true utility function

So, should we go with the "DNA survival" of Dawkins, Lotka's principle of maximum entropy production - or some combination of the two?

I think the choice is clear - maximum entropy production explains roughly the same things as the DNA survi val of Dawkins - and a whole lot more besides. It is a more general and fundamental principle - and should be preferred on those grounds.

From this perspective, maximum entropy production explains why organisms act as they do - and the details of genetics are seen more as implementation details - the mechanism by which organisms operate and propagate themselves - so that they can better generate entropy.

The "driving force" that underlies biology thus gains a concrete foundation in the basic laws of statistical mechanics.

God's Utility Function

Alas, there are also some other pretenders to this throne. One is Prigogine's theorem of minimum entropy production. However, Dewar claims this to be a special case of the more general entropy maximisation theory.

Another is the the principle of least action - also known as the path integral formulation.

This principle does not involve entropy - and so doesn't its domain doesn't overlap with the idea of maximum entropy production - but again, the expected utility theorem suggests that this represents an issue that needs sorting out. However, that issue must be left for another day.

Enjoy,

References