The Fourth Law, Part 1. [4/21/03]




Several years ago I was introduced to a couple of popular books on complexity theory,1 which was presented as an extension of chaos theory, with which I already had some familiarity.  However, while reading these books I resisted what appeared to be the embrace of a teleological view by many in the field, along with the related assertion that the origin and evolution of life on Earth somehow violated the Second Law of Thermodynamics.  The most vocal proponent of these views seemed to be Stuart Kauffman, who has proposed that a new "Fourth Law" of thermodynamics is necessary to explain the origins and evolution of complexity.2


Although I found the breathless enthusiasm of the advocates of complexity theory annoying, I soon realized that my understanding of complexity theory in general and evolutionary theory in particular was much too shallow to support an intelligent critique.  I felt it necessary to bone up on evolutionary theory and thermodynamics, as well as a variety of other subjects.  These investigations have led to some conclusions and observations which I believe are interesting and unique.


On the Road


In September and October of 2002, I took an extended journey across the Top End of Australia.  As I traveled across the Kimberley region in Western Australia and into the Northern Territory, my mind was occupied by a variety of seemingly unrelated topics.  The first was the transformation of aboriginal culture brought about by contact with Europeans.  I was reading a book which was based on northwest Australian aboriginal accounts of early contacts with whites around the turn of the century and Indonesians prior to then,3 as well as another book describing early white contact with the tribes of the New Guinea highlands.4


Another topic of which I was continuously reminded was the astounding biodiversity of the Australian flora.  I was amazed at the frequent transformations in the species composition of the bush as I drove through extended regions with no significant changes in geography or climate.  In addition, almost everywhere were plant communities with a level of biodiversity normally associated with rain forests or coral reefs.  For example, one national park in the Pilbara region of Western Australia had more different plant species in an area of 1000 square kilometers than the entire British Isles.  This in a region of monotonous geography and semi-arid climate.


Finally, I was reading intermittently from a popular book on consciousness that once again had raised the conjecture of a contradiction between life and the Second Law.5  This resurrected the long-standing aggravation residing in the back of my mind.  I was puzzled by the fact that intelligent scientists and science writers could seemingly miss the point that the Second Law applied only to isolated systems or (since no real systems are completely isolated) to the universe as a whole.  This error has been commented on by several authors (for instance, the physicist Paul Davies,6 frequently in reference to Kauffman).


After 40 days in the wilderness my brain was awash with the above stew of ideas.  I was headed south from Darwin through the Northern Territory.  While musing once again on the consequences of the Second Law, I had a sudden epiphany.  It came to me that a culture was composed of a “portfolio” of customs and behaviors which existed on an “efficient frontier” similar to that described by Markowitz’ Modern Portfolio Theory.  I then saw that the portfolio of species in an ecosystem would also exist along an efficient frontier.  Where Markowitz’ measure of “efficiency” was the portfolio risk (as measured by the variance of returns) relative to a given average return, efficiency for a culture or ecosystem would be the thermodynamic efficiency, with energy flux through the system substituted for average return.    


I then realized that the flow of energy through a natural system would be such that the thermodynamic efficiency of the process would be maximized, given the structural constraints on the system.  Put another way, energy flows through a system such that the increase in entropy is minimized (I later found this to be true only under certain circumstances).  The analogy I envisioned was that of water flowing through an alluvial drainage, following the path of least resistance as it meandered down a gradual slope forming fractal patterns.


I could see that this principle would apply to all types of systems, including physical, chemical, biological, ecological, economic and cultural, and would constitute a “force” that would serve as the basis of selection in the evolution of these systems.  I call this principle of maximum efficiency the “Fourth Law of Thermodynamics” in response to Kauffman and other complexity theorists who have expressed the need for new laws of physics or “laws of complexity” to explain the genesis and development of life.


A key insight (which I have since revised) was that the quantity being minimized is the net increase in entropy.  This means that the entropy increase can not only be minimized by reducing the increase in disorder (waste heat) but also by increasing the amount of order (stored information).  In other words, for two processes that throw off the same amount of waste heat relative to an equivalent input of energy, the process that generates the most information or order would be the one that satisfies the Fourth Law, since it would result in the least net increase in entropy.  Needless to say, the net entropy (disorder minus order) of the universe always increases.1


At this point I saw what Kauffman et al may have been on about in looking for new laws of nature.  The Second Law, correctly understood, does not prevent the creation of local order, but it does nothing very obvious to encourage it either.  There is the sense that something is encouraging the process, rather than just passively allowing it to happen.  This is true in the inanimate world as well as the animate, as the formation of solar systems and galaxies can also easily appear purposeful.


The Fourth Law fills this role without the burden of teleology.  It provides a selection mechanism that applies not only to biological evolution, but to all of nature.  The idea that Darwinian selection is a universal mechanism has been developed by Daniel Dennett,8 but he does not make the thermodynamic connection.  The laws of complexity that have been proposed have usually been confined to biological (or “complex”) systems and generally invoke tautologies of the following form:  Order exists because there are laws of order that operate in complex systems.


As I contemplated the Fourth Law, I realized that a similar principle operated in physics, as when an apple falls to earth along the shortest path.  It occurred to me that the Fourth Law was logically similar to the Path of Least Resistance, the Principle of Least Action and the Principle of Minimum Assumptions (Occam’s Razor).  Furthermore, where I had always regarded these maxims a rules of thumb, I now saw that they were instead laws strictly adhered to in nature.  This conclusion was later supported by the realization that Hamilton and LaGrange derived Newton’s laws directly from the Principle of Least Action, which was originally proposed by the French biologist Pierre-Louis Moreau de Maupertuis in 1746.  The most commonly cited example of  the Principle of Least Action in physics is the separation of the spectrum of light by a prism, with the different frequencies of light following the shortest possible paths through a refractive substance.


The Fourth Law and Evolution


The most interesting application of the Fourth Law is to evolutionary theory.  The call by complexity theorists for new laws to connect biology to physics is testimony to the unfilled gap between the two fields.  The nature of this gap is illustrated by the realization that the Darwinian selection criteria of Survival of the Fittest is a tautology.  Surprisingly, this seems to be almost universally unrecognized (or unacknowledged, perhaps due to its use by creationists).9  The only other place I have seen this mentioned is in Edward O. Wilson’s book Consilience,10 after which he moves on without further comment.


The Fourth Law fills this gap.  While the law of  Survival of the Fittest says nothing about why the fittest are fitter except that, in retrospect, they survived (and therefore were, by definition, the fittest), the Fourth Law says that the survivors are thermodynamically more efficient.  Application of this principle would at least theoretically allow one to predict which members of a population were more likely to survive, rather than just waiting to see which ones in fact do.  The Fourth Law therefore provides a basis for causality and prediction that is absent in the Darwinian formulation.


Since the Fourth Law acts as a universal selection mechanism , there is no conceptual discontinuity in moving from the inanimate and animate realms, no need for an élan vital or laws of nature specific to biology.  In addition, the Fourth Law is unbiased with regard to progress, purpose or complexity, since it favors those processes which maximize efficiencyThe nature of the optimum configuration is driven only by context and chance, so that a benign environment, such as the Earth has experienced over the last 600 million years, would encourage increasing complexity, while a return to Snowball Earth,11 for instance, would be accompanied by a radical simplification of life forms.  If traces of extinct life are found on Mars, it will be testimony to the fact that increasing complexity is not inevitable.


The Principle of Least Action


One may ask why someone else hasn’t thought of this?  Well, of course they have, but the antecedents seem for the most part forgotten or obscure.  Maupertuis regarded the Principle of Least Action as universal: "The laws of movement and of rest deduced from this principle being precisely the same as those observed in nature, we can admire the application of it to all phenomena. The movement of animals, the vegetative growth of plants ... are only its consequences; and the spectacle of the universe becomes so much the grander, so much more beautiful, the worthier of its Author, when one knows that a small number of laws, most wisely established, suffice for all movements."  However, the principle seems to have been largely ignored outside of dynamics, where it was elaborated by Euler, Hamilton and LaGrange and later by Feynman in his work on quantum electrodynamics.12  While ecologists occasionally discuss the efficiency of competing organisms, they appear to use the term more as a euphemism for differential survival than in its thermodynamic sense.


The only place I have seen the thermodynamic connection made in any detail is in Chris Davis’ Idle Theory of Evolution.  His theory is a fascinating variation of Darwinism, with similarities to ideas presented by Niles Eldredge in a less developed form in his book Reinventing Darwin.13


A thoughtful review of the above discussion raises a host of questions and conjectures, many of which revolve around verification and utility.  The first three laws of thermodynamics are empirical laws based on observation, as opposed to derived laws based on mathematics.  For this reason, Einstein reportedly remarked that the laws of thermodynamics were the least likely of any of the physical laws to be overturned.14  Needless to say, the Fourth Law would be difficult to experimentally confirm in open complex systems, since so many paths (and their alternatives) would need to be monitored.  Perhaps this is why it has been largely overlooked.


A more philosophical question is whether the maximization of efficiency is satisfied at every instant or whether it acts as an attractor, or both (my preference).  Note that given a fixed structure, the energy flow will follow the path of least resistance.  However, the structure will also change as a result of the energy flow in a way which is subject to higher-level constraints, and so on.  At a particular level, the structure may either be enhanced or eroded, depending on the context.  So the Fourth Law would seem to operate in a nested fashion across multiple levels of structure.  Once again, this poses verification problems, since maintaining fixed structures for experimental purposes is much more difficult for open complex systems than for the closed PVT systems used in the classical experiments leading to the first three laws of thermodynamics.



Footnotes and References:


1 M. Mitchell Waldrop, Complexity: The Emerging Science at the Edge of Order and Chaos, Simon & Schuster Adult Publishing Group, 1993.

Roger Lewin, Complexity: Life at the Edge of Chaos, University of Chicago Press, 1999.
2 Stuart Kauffman, Investigations, Oxford University Press, 2000.

3 Ian Crawford, We Won the Victory, Fremantle Arts Centre Press, 2001.

4 Jared Diamond, The Third Chimpanzee, HarperCollins Publishers, 1992.

5 Tor Nørretranders, The User Illusion, Penguin Books, 1991.

6 Paul Davies, The Fifth Miracle, Simon & Schuster Adult Publishing Group, 2000.
7 The reasoning in this paragraph was based on my then current understanding of the Second Law, which conforms with the orthodox view.  I have since realized that these statements are based on incorrect assumptions leading to faulty logic, although the general thrust of the argument remains valid.

8 Daniel Dennett, Darwin's Dangerous Idea: Evolution And The Meanings Of Life, Simon & Schuster Adult Publishing Group, 1996.

9 Philip Johnson, Darwin on Trial, InterVarsity Press, 1993.

10 Edward O. Wilson, Consilience, Random House, 1999.

11 Gabrielle Walker, Snowball Earth: The Story of the Great Global Catastrophe That Spawned Life as We Know It, Crown Publishing Group, 2003.
12 Richard Feynman, QED: The Strange Theory of Light and Matter, Princeton University Press, 1988.

13 Niles Eldredge, Reinventing Darwin, John Wiley & Sons, 1995.

14 Donald Haynie, Biological Thermodynamics, Cambridge University Press, 2001.