The conceptual foundations of decision-making in a democracy

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Order, Disorder and Chaos as Applied to Living Systems

When writing about entropy and the second law of thermodynamics in the part about life and information, I used ‘chaos’ and ‘order’ as if the meaning of those words were perfectly clear and unequivocal. In fact I am doubtful as to whether their status has ever been clarified to the extent that this is both possible and necessary. In any case such a work has not come to my attention. That does not invalidate the conclusions which I drew about life and information. For these conclusions are deduced in a logically correct (I hope) way from the current knowledge about living systems which does not involve chaos and order. In fact, the way concepts from physics are applied to the living world is often questionable. Even in physics they can and do generate unwarranted connotations.

1) THE APPLICATION OF PHYSICAL TERMS TO LIVING SYSTEMS. In what direction do all inert systems involved in thermodynamical processes go? The second law says: towards an increase of entropy. The ultimate destination of such a system has often been called chaos. I like the evocative power of the term. There can be no quarrel with it as long as it is used to refer to the ultimate ‘attractor point’ of thermodynamical processes, defined as: ‘wherever increase in entropy will take any inert system’. Confusion with terms like order, disorder and chaos arises whenever these terms are used in a quantitative way and are given an autonomous role in the causality of events.

For instance the second law has been described as a tendency from order to disorder, chaos, implying that negative order is commensurable with entropy. Entropy has been said to represent the direction of time, and life has been qualified, for instance by Monod, as a process ‘a remonter le temps’, i.e. which follows the trajectory of time in a direction opposite to that of the inert world.

I have the feeling that all these generalisations are misplaced except as metaphors. For any implication that life pursues in reverse a trajectory which is defined (as being the opposite to it) by a law ruling the inert world seems to me highly questionable. Such an implication would mean that if in the inert world a certain system should move from the state A to the state B, the addition of life would generate a system which from the state B would have to move to the state A. In fact, adding life renders a system unpredictable.

Thermodynamical processes in the inert world are qualified as irreversible. That only means that if a system has undergone a thermodynamical process, we cannot reconstruct de facto the original system including its surroundings, for some heat is irretrievably lost. No more, no less. We can however conceptually reconstruct the original system. We can even physically reconstruct the original system by borrowing from its surroundings the required heat. What cannot be reconstructed is, as stated, the system including its surroundings.

Even if we resurrect a person who is clinically dead, we will not have reconstructed the original state of the person, because however good the surgical and clinical work, the person will effectively and irretrievably have been changed by that experience. And I cannot see how we can

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express, in any terms applicable in physics, the change caused by having experienced death; even a close analogy to such a term will not do.

2) ORDER. Besides doubting that concepts of the inert world are adequate to ‘measure’ life, I have a problem with the use of order as an autonomously quantifiable concept. We use it to characterise a set of positional relationships between objects, events, phenomena, in space and/or time. As with all elements of the real world, the relative position of these elements in reality just ‘is’. ‘Order’ is a category, a concept we created to make a representation of that relationship, it is an instrument for gathering knowledge and making it fit for our use, just like colour and speed. It is an abstract, mathematical type of concept. Any application of that category, of that concept, requires the definition of the dimensions we will use to ‘catch’ the relative positions of the set of elements whose order we want to establish. The four classic and common-sense dimensions are the three dimensions of space plus time. We can also use fewer dimensions (1 for a line and 2 for a plane) or more (for virtual spaces).

These spatio-temporal relationships can play a role in the explanation of events, they can be part of the cause to which we ascribe the event. The sequence in space and time of the positions of a meteorite, and thus its trajectory and speed, will determine whether it will hit the atmosphere of our earth or pass it by. The importance of the position of various elements of reality in the chain of causality breeds the tendency to impute to that position an autonomous capability to influence events. Is that ever justified? I think not. and the purpose of this piece is to explain why.

The relative position of elements can have any causal effect only in conjunction with other attributes of these elements such as mass or energy. At least in physics there is no law which does not involve such additional elements. The first law of thermodynamics about the conservation of energy is applicable only if there is energy to conserve, and the laws of mechanics only if there is some mass. The ‘pure’ concept of order can be used in a purely descriptive way; but using it to explain a causal relationship can only be done in conjunction with other factors.

If order is to refer to more than the individual positions of the elements, it cannot be defined by a simple enumeration of their coordinates. It must also define a property of the relation between these positions, some rule by which we can generalize about them, like ‘all points which are grouped around a parabola’. In fact, that is its job. If we have determined such a relationship for two sets of data, we cannot from these relationships alone decide which set is more ordered than the other, unless we have a priori and in a totally conventional way defined a point of reference, such as a metre for length. Such a criterion has been developed and is widely used: the frequency distribution of points generated in a mathematical process involving probabilities of events to which we have assigned a probability. At one end are events all having the same probability, 0.5 in the case of two possible events, 0.25 with four events etc. At the other end are events which all have a probability of one (or zero, which can be converted to one by using their negation); such a set is totally determined, is not stochastic, is totally ordered. Order is measured by the place of the frequency distribution between theses extremes. As far as I know, that is the only generally accepted definition of a ‘quantity of order’.

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The above general definition unfortunately does not allow any conclusion about the causes to which the frequency distribution is to be imputed. For instance it cannot tell us whether this distribution must be attributed to the process or to a property of the elements undergoing the process. Suppose you were shown two bags containing black and white balls of identical size. In one of the bags the balls show no discernable pattern; in the other bag all the white ones lay on top and the black ones on the bottom. Which would you consider more ordered? Obviously the second one. If one bag represents its state before a process of juggling it around, and the other after, which bag would you expect on the basis of the laws of physics to be the ‘before’, and which the ‘after’ bag? Obviously, the one with all white balls on top is the ‘before’ bag, and the mixed one the ‘after’ bag. But if you knew that all white balls were lighter than the black balls, you would draw exactly the opposite conclusion. The stochastic process mixing up the balls generates a reduction of order only if the balls are homogeneous, at least in terms of mass and density. They cannot be totally identical, for then we would not have any means to distinguish them at all. In short, my contention is that by just looking at a spatio-temporal description of a set of elements, we can never determine whether there is any ‘real’ order in them, let alone quantify such an order. We can only state whether we perceive any order, and that perception rests on an a priori and therefore subjective set of properties which we expect from order.

3) DISORDER AND CHAOS. A ubiquitous form in which the notion of order pops up in various scientific theories and arguments is ‘no order’, disorder. Certain presentations of the second law of thermodynamics equate entropy with disorder, whose ultimate state is called chaos. While total disorder and chaos are used as synonyms, chaos expresses some kind of superlative for disorder. Chaos here is the final stage of an order-destroying, disorder-producing process. Using that connotation and provided we know the process which creates disorder, we can define chaos as the spatio-temporal relationship we can expect between the elements of the system after its order has - to our satisfaction, usually meaning ‘for all practical purposes’ - been destroyed. We cannot however by looking at the frequency distribution of the elements of a system decide how far removed it is from that end state, we can only compare different stages of a specific process, which is precisely its purpose. Order is only a symptom, not a constituting element of entropy. We cannot just identify an increase of entropy with a deacrease of order, for that would imply that an increase of order equates a decrease of entropy, which to my mind, and in view of the example of balls, is not correct.

The above is not a disparagement of new concepts such as developed in Prigogine's ‘Order out of chaos’ or the phenomena and theories about which Gleick writes so well in his book ‘Chaos’. Concepts like Fractals etc. open a fascinating view on the means life might use to further its process. But none of these concepts or theories provides us with sufficient means to define the process of life itself, and certainly none offers a unit of measure as to how far a living system is or has moved away from the end-state of the universe implied in the second law of thermodynamics. My intuition is that such a measure will never be found because it is in logical contradiction with the very openness of the process of life.

Whatever the merit of the above, it is in any case an explanation of why I feel justified in ignoring the above concepts and the quantification of order in my presentation of life and information, and why I compare the process of life only in a very general way with the thermody-

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namical processes of the inert world. ‘Life has to fight the second law’ is only a hopefully correct metaphor. The direction life will take if successful can only be defined in the negative, something like ‘not towards the chaos to which its physical processes would lead if not biased away from it by the information process’. I also hope that I have countered objections as to my use of the expressions like ‘a direction opposed to that implied by the second law’ or at least stimulated the search for a better formulation which is accessible to the general academic public.