God's Utility Function

Transcript

Hi. I'm Tim Tyler, this is a video about God's Utility Function - the idea that biology can be usefully seen as an optimisation process, and that evolutionary change acts so as to maximise some utility function.

The problem

If you compare the natural evolutionary process with man made genetic algorithms, biological evolution looks remarkably like a gigantic optimisaton process.

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

What else do living systems maximize besides the number of copies of their genes? Clearly bodies and metabolic systems are produced in numbers which equal the number of genomes produced.

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

Now we know from the expected utility theorem that when we have a system acts in a way that seems to maximise two quantities, it is possible to seek a single maximand that is the true one.

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

So, is God's Utility Function - that quantity which is maximised during the operation of the universe - simply entropy production?

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

Bright Light - Tim Tyler - my 2002 essay on the topic - it has more references than this essay
Lotka, A. J. (1922) Contribution to the energetics of evolution
Schneider, Eric D. and Sagan, Dorion (2006) Into the Cool: Energy Flow, Thermodynamics, and Life -
Schneider, Eric D. and Sagan, Dorion (2011) The Purpose of Life
Whitfield, John (2005) Survival of the Likeliest?
Whitfield, John (2005) Complex systems: Order out of chaos -
A. Annila and E. Annila (2007) Why did life emerge?
Sharma, Vivek and Annila, Arto (2009) Natural process – Natural selection
Schneider, E.D, Kay, J.J., (1994) "Life as a Manifestation of the Second Law of Thermodynamics", Mathematical and Computer Modelling, Vol 19, No. 6-8, pp.25-48.
Martyusheva, L.M. and Seleznevb, V.D. (2005) Maximum entropy production principle in physics, chemistry and biology
Brooks, Daniel R. and Wiley, E. O. (1988) Evolution As Entropy
Snooks, G. D. (2003)The Collapse of Darwinism
Wikipedia (?) Maximum entropy thermodynamics
Kauffman, Stuart (2010) Reinventing the Sacred
Kleidon, Axel (2009) Nonequilibrium thermodynamics and maximum entropy production in the Earth system

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Title, author, date and description

Into the Cool: Energy Flow, Thermodynamics, and Life by Eric D. Schneider and Dorion Sagan (2005)
Scientists, theologians, and philosophers have all sought to answer the questions of why we are here and where we are going. Finding this natural basis of life has proved elusive, but in the eloquent and creative Into the Cool, Eric D. Schneider and Dorion Sagan look for answers in a surprising place: the second law of thermodynamics. This second law refers to energy's inevitable tendency to change from being concentrated in one place to becoming spread out over time. In this scientific tour de force, Schneider and Sagan show how the second law is behind evolution, ecology,economics, and even life's origin. Working from the precept that "nature abhors a gradient". Into the Cool details how complex systems emerge, enlarge, and reproduce in a world tending toward disorder. From hurricanes here to life on other worlds, from human evolution to the systems humans have created, this pervasive pull toward equilibrium governs life at its molecular base and at its peak in the elaborate structures of living complex systems. Schneider and Sagan organize their argument in a highly accessible manner, moving from descriptions of the basic physics behind energy flow to the organization of complex systems to the role of energy in life to the final section, which applies their concept of energy flow to politics, economics, and even human health.

The Purpose of Life by Eric D. Schneider and Dorion Sagan (2011)
What is the purpose of life? Some say it's to reproduce, others to glorify God, but behind these and other proposed purposes lies a scientific purpose. In The Purpose of Life, science writer Dorion Sagan and biophysicist Eric D. Schneider lay out the fascinating evidence for life's natural purpose -its function in an energy-driven cosmos. New evidence shows that the evolution of life on Earth over the past three-and-a-half billion years has not been random but has a clear direction, and its direction is related to life's function as a natural system. Indeed, life shares its function -its purpose -with that of certain other complex natural systems. Although the answer is simple and not exclusive -life may have other purposes -its profound implications may change the way we see ourselves, our relationships to other living beings, and our future on this shared, energy-driven planet. Sagan and Schneider provide a striking alternative to both scientific and religious views of this age-old question. Engaging recent bestsellers such as Rick Warren's The Purpose-Driven Life and Eckhart Tolle's A New Earth: Finding Your Life's Purpose, The Purpose of Life goes beyond popular science, weaving literature, philosophy, and spirituality into a highly readable narrative.

Beyond the Second Law: Entropy Production and Non-equilibrium Systems by Roderick C. Dewar, Charles H. Lineweaver and Robert K. Niven (2013)
The Second Law, a cornerstone of thermodynamics, governs the average direction of dissipative, non-equilibrium processes. But it says nothing about their actual rates or the probability of fluctuations about the average. This interdisciplinary book, written and peer-reviewed by international experts, presents recent advances in the search for new non-equilibrium principles beyond the Second Law, and their applications to a wide range of systems across physics, chemistry and biology. Beyond The Second Law brings together traditionally isolated areas of non-equilibrium research and highlights potentially fruitful connections between them, with entropy production playing the unifying role. Key theoretical concepts include the Maximum Entropy Production principle, the Fluctuation Theorem, and the Maximum Entropy method of statistical inference. Applications of these principles are illustrated in such diverse fields as climatology, cosmology, crystal growth morphology, Earth system science, environmental physics, evolutionary biology and technology, fluid turbulence, microbial biogeochemistry, plasma physics, and radiative transport, using a wide variety of analytical and experimental techniques. View on Google Books the book page, the author page, or the book contents.

Evolution As Entropy by Daniel R. Brooks and E. O. Wiley (1988)
By combining recent advances in the physical sciences with some of the novel ideas, techniques, and data of modern biology, this book attempts to achieve a new and different kind of evolutionary synthesis.

Tim Tyler | Contact | http://originoflife.net/