What logical term or concept ought to be more widely known?

Various What scientific term or concept ought to be more widely known? Edge, 2017.

INTRODUCTION: SCIENTIA

Science—that is, reliable methods for obtaining knowledge—is an essential part of psychology and the social sciences, especially economics, geography, history, and political science. …

Science is nothing more nor less than the most reliable way of gaining knowledge about anything, whether it be the human spirit, the role of great figures in history, or the structure of DNA.

Contributions

As against others on:

(This is as far as I’ve got.)

Comment

I’ve grouped the contributions according to whether or not I think they give due weight to the notion of uncertainty as expressed in my blog. Interestingly Steven Pinker seems not to give due weight in his article, whereas he is credited by Nicholas G. Carr with some profound insights (in the first of the second batch). So maybe I am not reading them right.

My own thinking

Misplaced Concreteness

Whitehead’s fallacy of misplaced concerteness, also known as the reification fallacy, “holds when one mistakes an abstract belief, opinion, or concept about the way things are for a physical or “concrete” reality.” Most of what we think of as knowledge is ‘known about a theory” rather than truly “known about reality”. The difference seems to matter in psychology, sociology, economics and physics. This is not a term or concept of any particular science, but rather a seeming ‘brute fact’ of ‘the theory of science’ that perhaps ought to have been called attention to in the above article.

Morphogenesis

My own speciifc suggestion, to illustrate the above fallacy, would be Turing’s theory of ‘Morphogenesis’. The particular predictions seem to have been confirmed ‘scientifically’, but it is essentially a logical / mathematical theory. If, as the introduction to the Edge article suggests, science is “reliable methods for obtaining knowledge” then it seems to me that logic and mathematics are more reliable than empirical methods, and deserve some special recognition. Although, I must concede that it may be hard to tell logic from pseudo-logic, and that unless you can do so my distinction is potentially dangerous.

The second law of thermodynamics, and much common sense rationality,  assumes a situation in which the law of large numbers applies. But Turing adds to the second law’s notion of random dissipation a notion of relative structuring (as in gravity) to show that ‘critical instabilities’ are inevitable. These are inconsistent with the law of large numbers, so the assumptions of the second law of thermodynamics (and much else) cannot be true. The universe cannot be ‘closed’ in its sense.

Implications

If the assumptions of the second law seem to leave no room for free will and hence no reason to believe in our agency and hence no point in any of the contributions to Edge: they are what they are and we do what we do. But Pinker does not go so far: he simply notes that if things inevitably degrade we do not need to beat ourselves up, or look for scape-goats when things go wrong. But this can be true even if the second law does not apply. If we take Turing seriously then a seeming permanent status quo can contain the reasons for its own destruction, so that turning a blind eye and doing nothing can mean sleep-walking to disaster. Where Pinker concludes:

[An] underappreciation of the Second Law lures people into seeing every unsolved social problem as a sign that their country is being driven off a cliff. It’s in the very nature of the universe that life has problems. But it’s better to figure out how to solve them—to apply information and energy to expand our refuge of beneficial order—than to start a conflagration and hope for the best.

This would seem to follow more clearly from the theory of morphogenesis than the second law. Turing’s theory also goes some way to suggesting or even explaining the items in the second batch. So, I commend it.

 

Dave Marsay

 

 

Uncertainty is not just probability

I have just had published my paper, based on the discussion paper referred to in a previous post. In Facebook it is described as:

An understanding of Keynesian uncertainties can be relevant to many contemporary challenges. Keynes was arguably the first person to put probability theory on a sound mathematical footing. …

So it is not just for economists. I could be tempted to discuss the wider implications.

Comments are welcome here, at the publisher’s web site or on Facebook. I’m told that it is also discussed on Google+, Twitter and LinkedIn, but I couldn’t find it – maybe I’ll try again later.

Dave Marsay

Evolution of Pragmatism?

A common ‘pragmatic’ approach is to keep doing what you normally do until you hit a snag, and (only) then to reconsider. Whereas Lamarckian evolution would lead to the ‘survival of the fittest’, with everyone adapting to the current niche, tending to yield a homogenous population, Darwinian evolution has survival of the maximal variety of all those who can survive, with characteristics only dying out when they are not viable. This evolution of diversity makes for greater resilience, which is maybe why ‘pragmatic’ Darwinian evolution has evolved.

The products of evolution are generally also pragmatic, in that they have virtually pre-programmed behaviours which ‘unfold’ in the environment. Plants grow and procreate, while animals have a richer variety of behaviours, but still tend just to do what they do. But humans can ‘think for themselves’ and be ‘creative’, and so have the possibility of not being just pragmatic.

I was at a (very good) lecture by Alice Roberts last night on the evolution of technology. She noted that many creatures use tools, but humans seem to be unique in that at some critical population mass the manufacture and use of tools becomes sustained through teaching, copying and co-operation. It occurred to me that much of this could be pragmatic. After all, until recently development has been very slow, and so may well have been driven by specific practical problems rather than continual searching for improvements. Also, the more recent upswing of innovation seems to have been associated with an increased mixing of cultures and decreased intolerance for people who think for themselves.

In biological evolution mutations can lead to innovation, so evolution is not entirely pragmatic, but their impact is normally limited by the need to fit the current niche, so evolution typically appears to be pragmatic. The role of mutations is more to increase the diversity of behaviours within the niche, rather than innovation as such.

In social evolution there will probably always have been mavericks and misfits, but the social pressure has been towards conformity. I conjecture that such an environment has favoured a habit of pragmatism. These days, it seems to me, a better approach would be more open-minded, inclusive and exploratory, but possibly we do have a biologically-conditioned tendency to be overly pragmatic: to confuse conventions for facts and  heuristics for laws of nature, and not to challenge widely-held beliefs.

The financial crash of 2008 was blamed by some on mathematics. This seems ridiculous. But the post Cold War world was largely one of growth with the threat of nuclear devastation much diminished, so it might be expected that pragmatism would be favoured. Thus powerful tools (mathematical or otherwise) could be taken up and exploited pragmatically, without enough consideration of the potential dangers. It seems to me that this problem is much broader than economics, but I wonder what the cure is, apart from better education and more enlightened public debate?

Dave Marsay

 

 

The End of a Physics Worldview (Kauffman)

Thought provoking, as usual. This video goes beyond his previous work, but in the same direction. His point is that it is a mistake to think of ecologies and economies as if they resembled the typical world of Physics. A previous written version is at npr, followed by a later development.

He builds on Kant’s notion of wholes, noting (as Kant did before him) that the existence of such wholes is inconsistent with classical notions of causality.  He ties this in to biological examples. This complements Prigogine, who did a similar job for modern Physics.

Kauffman is critical of mathematics and ‘mathematization’, but seems unaware of the mathematics of Keynes and Whitehead. Kauffman’s view seems the same as that due to Bergson and Smuts, which in the late 1920s defined ‘modern science’. To me the problem behind the financial crash lies not in science or mathematics or even in economics, but in the brute fact that politicians and financiers were wedded to a pre-modern (pre-Kantian) view of economics and mathematics. Kauffman’s work may help enlighten them on the need, but not on the potential role for modern mathematics.

Kauffman notes that at any one time there are ‘adjacent possibles’ and that in the near future they may come to pass, and that – conceptually – one could associate a probability distribution with these possibilities. But as new possibilities come to pass new adjacent possibilities arise. Kauffman supposes that it is not possible to know what these are, and hence one cannot have a probability distribution, much of information theory makes no sense, and one cannot reason effectively. The challenge, then, is to discover how we do, in fact, reason.

Kauffman does not distinguish between short and long run. If we do so then we see that if we know the adjacent possible then our conventional reasoning is appropriate in the short-term, and Kauffman’s concerns are really about the long-term: beyond the point at which we can see the potential possibles that may arise. To this extent, at least, Kauffman’s post-modern vision seems little different from the modern vision of the 1920s and 30s, before it was trivialized.

Dave Marsay

From Being to Becoming

I. Prigogine, From Being to Becoming: Time and Complexity in the Physical Sciences, WH Freeman, 1980 

 See new page.

Summary

“This book is about time.” But it has much to say about complexity, uncertainty, probability, dynamics and entropy. It builds on his Nobel lecture, re-using many of the models and arguments, but taking them further.

Being is classically modelled by a state within a landscape, subject to a fixed ‘master equation’ describing changes with time. The state may be an attribute of an object (classical dynamics) or a probability ‘wave’ (quantum mechanics). [This unification seems most fruitful.] Such change is ‘reversible’ in the sense that if one reverses the ‘arrow of time’ one still has a dynamical system.

Becoming refers to more fundamental, irreversible, change, typical of ‘complex systems’ in chemistry, biology and sociology, for example. 

The book reviews the state of the art in theories of Being and Becoming, providing the hooks for its later reconciliation. Both sets of theories are phenomenological – about behaviours. Prigogine shows that not only is there no known link between the two theories, but that they are incompatible.

Prigogine’s approach is to replace the notion of Being as being represented by a state, analogous to a point in a vector space,  by that of an ‘operator’ within something like a Hilbert Space. Stable operators can be thought of as conventional states, but operators can become unstable, which leads to non-statelike behaviours. Prigogine shows how in some cases this can give rise to ‘becoming’.

This would, in itself, seem a great and much needed subject for a book, but Prigogine goes on to consider the consequences for time. He shows how time arises from the operators. If everything is simple and stable then one has classical time. But if the operators are complex then one can have a multitude of times at different rates, which may be erratic or unstable. I haven’t got my head around this bit yet.

Some Quotes

Preface

… the main thesis …can be formulated as:

  1. Irreversible processes are as real as reversible ones …
  2. Irreversible processes play a fundamental constructive role in the physical world …
  3. Irreversibility … corresponds … to an embedding of dynamics within a vaster formalism. [Processes instead of points.] (xiii)

The classical, often called “Galilean,” view of science was to regard the world as an “object,” to try to describe the physical world as if it were being seen from the outside as an object of analysis to which we do not belong. (xv)

… in physics, as in sociology, only various possible “scenarios” can be predicted. [One cannot predict actual outcomes, only identify possibilities.] (xvii)

Introduction

… dynamics … seemed to form a closed universal system, capable of yielding the answer to any question asked. (3)

… Newtonian dynamics is replaced by quantum mechanics and by relativistic mechanics. However, these new forms of dynamics … have inherited the idea of Newtonian physics: a static universe, a universe of being without becoming. (4)

The Physics of Becoming

The interplay between function, structure and fluctuations leads to the most unexpected phenomena, including order through fluctuations … . (101)

… chemical instabilities involve long-range order through which the system acts as a whole. (104)

… the system obeys deterministic laws [as in classical dynamics] between two bifurcation points, but in the neighbourhood of the bifurcation points fluctuations play an essential role and determine the “branch” that the system will follow. (106) [This is termed ‘structurally unstable”]

.. a cyclic network of reactions [is] called a hypercycle. When such networks compete with one another, they display the ability the ability to evolve through mutation and replication into greater complexity. …
The concept of structural stability seems to express in the most compact way the idea of innovation, the appearance of a new mechanism and a new species, … . (109)

… the origin of life may be related to successive instabilities somewhat analogous to the successive bifurcations that have led to a state of matter of increasing coherence. (123)

As an example, … consider the problem of urban evolution … (124) … such a model offers a new basis for the understanding of “structure” resulting from the actions (choices) of the many agents in a system, having in part at least mutually dependent criteria of action. (126)

… there are no limits to structural instability. Every system may present instabilities when suitable perturbations are introduced. Therefore, there can be no end to history. [DJM emphasis.] … we have … the constant generation of “new types” and “new ideas” that may be incorporated into the structure of the system, causing its continual evolution. (128)

… near bifurcations the law of large numbers essentially breaks down.
In general, fluctuations play a minor role … . However, near bifurcations they play a critical role because there the fluctuation drives the average. This is the very meaning of the concept of order through fluctuations .. . (132)

… near a bifurcation point, nature always finds some clever way to avoid the consequences of the law of large numbers through an appropriate nucleation process. (134)

… For small-scale fluctuations, boundary effects will dominate and fluctuations will regress. … for large-scale fluctuations, boundary effects become negligible. Between these limiting cases lies the actual size of nucleation. (146)

… We may expect that in systems that are very complex, in the sense that there are many interacting species or components, [the degree of coupling between the system and its surroundings] will be very large, as will be the size of the fluctuation which could start the instability. Therefore … a sufficiently complex system is generally in a metastable state. (147) [But see Comments below.]

… Near instabilities, there are large fluctuations that lead to a breakdown of the usual laws of probability theory. (150)

The Bridge from Being to Becoming

[As foreshadowed by Bohr] we have a new form of complimentarity – one between the dynamical and thermodynamic descriptions. (174)

… Irreversibility is the manifestation on a macroscopic scale of “randomness” on a microscopic scale. (178)

Contrary to what Boltzmann attempted to show there is no “deduction” of irreversibility from randomness – they are only cousins! (177)

The Microscopic Theory of Irreversible Processes

The step made … is quite crucial. We go from the dynamical system in terms of trajectories or wave packets to a description in terms of processes. (186)

… Various mechanisms may be involved, the important element being that they lead to a complexity on the microscopic level such that the basic concepts involved in the trajectory or wave function must be superseded by a statistical ensemble. (194)

The classical order was: particles first, the second law later – being before becoming! It is possible that this is no longer so when we come to the level of elementary particles and that here we must first introduce the second law before being able to define the entities. (199)

The Laws of Change

… Of special interest is the close relation between fluctuations and bifurcations which leads to deep alterations in the classical results of probability theory. The law of large numbers is no longer valid near bifurcations and the unicity of the solution of … equations for the probability distribution is lost. (204)

This mathematization leads us to a new concept of time and irreversibility … . (206)

… the classical description in terms of trajectories has to be given up either because of instability and randomness on the microscopic level or because of quantum “correlations”. (207)

… the new concept implies that age depends on the distribution itself and is therefore no longer an external parameter, a simple label as in the conventional formula.
We see how deeply the new approach modifies our traditional view of time, which now emerges as a kind of average over “individual times” of the ensemble. (210)

For a long time, the absolute predictability of classical mechanics, or the physics of being, was considered to be an essential element of the scientific picture of the physical world. … the scientific picture has shifted toward a new, more subtle conception in which both deterministic features and stochastic features play an essential role. (210)

The basis of classical physics was the conviction that the future is determined by the present, and therefore a careful study of the present permits the unveiling of the future. At no time, however, was this more than a theoretical possibility. Yet in some sense this unlimited predictability was an essential element of the scientific picture of the physical world. We may perhaps even call this the founding myth of classical science.
The situation is greatly changed today. … The incorporation of the limitation of our ways of acting on nature has been an essential element of progress. (214)

Have we lost essential elements of classical science in this recent evolution [of thought]? The increased limitation of deterministic laws means that we go from a universe that is closed to one that is open to fluctuations. to innovations.

… perhaps there is a more subtle form of reality that involves both laws and games, time and eternity. (215) 

Comments

Relationship to previous work

This book can be seen as a development of the work of Kant, Whitehead and Smuts on emergence, although – curiously – it makes little reference to them [pg xvii]. In their terms, reality cannot logically be described in terms of point-like states within spaces with fixed ‘master equations’ that govern their dynamics. Instead, it needs to be described in terms of ‘processes’. Prigogine goes beyond this by developing explicit mathematical models as examples of emergence (from being to becoming) within physics and chemistry.

Metastability

According to the quote above, sufficiently complex systems are inherently metastable. Some have supposed that globalisation inevitably leads to an inter-connected and hence complex and hence stable world. But globalisation could lead to homogenization or fungibility, a reduction in complexity and hence an increased vulnerability to fluctuations. As ever, details matter.

See Also

I. Prigogine and I. Strengers Order out of Chaos Heinemann 1984.
This is an update of a popular work on Prigogine’s theory of dissipative systems. He provides an unsympathetic account of Kant’s Critique of Pure Reason, supposing Kant to hold that there are “a unique set of principles on which science is based” without making reference to Kants’ concept of emergence, or of the role of communities. But he does set his work within the framework of Whitehead’s Process and Reality. Smuts’ Holism and Evolution, which draws on Kant and mirrors Whitehead is also relevant, as a popular and influential account of the 1920s, helping to define the then ‘modern science’.

Dave Marsay

Reasoning and natural selection

Cosmides, L. & Tooby, J. (1991). Reasoning and natural selection. Encyclopedia of Human Biology, vol. 6. San Diego: Academic Press

Summary

Argues that logical reasoning, by which it seems to mean classical induction and symbolic reasoning, are not favoured by evolution. Instead one has reasoning particular to the social context. It argues that in typical situations it is either not possible or not practical to consider ‘all hypotheses’, and that the generation of hypotheses to consider is problematic. It argues that this is typically done using implicit specific theories. Has a discussion of the ‘green and blue cabs’ example.

Comment

 In real situations one can assume induction and lacks the ‘facts’ to be able to perform symbolic reasoning. Logically, then, empirical reasoning would seem more suitable. Keynes, for example, considers the impact of not being able to consider ‘all hypotheses’.

While the case against classically rationality seems sound, the argument leaves the way open for an alternative rationality, e.g. based on Whitehead and Keynes.

See Also

Later work

Better than rational, uncertainty aversion.

Other

Reasoning, mathematics.

Dave Marsay

Better than Rational

Cosmides, L. & Tooby, J. (1994). Better than rational: Evolutionary psychology and the invisible hand. American Economic Review, 84 (2), 327-332.

Summary

[Mainstream Psychologists and behaviourists have studied] “biases” and “fallacies”-many of which are turning out to be experimental artifacts or misinterpretations (see G. Gigerenzer, 1991). [Gigerenzer, G. “How to Make Cognitive Illusions Disappear: Beyond Heuristics and Biases,” in W. Stroebe and M. Hewstone, eds.,  European review of social psychology, Vol. 2. Chichester, U.K.: Wiley, 1991, pp. 83-115.]

… 

One point is particularly important for economists to appreciate: it can be demonstrated that “rational” decision-making methods (i.e., the usual methods drawn from logic, mathematics, and probability theory) are computationally very weak: incapable of solving the natural adaptive problems our ancestors had to solve reliably in order to reproduce (e.g., Cosmides and Tooby, 1987; Tooby and Cosmides, 1992a; Steven Pinker, 1994).

…  sharing rules [should be] appealing in conditions of high variance, and unappealing when resource accrual is a matter of effort rather than of luck (Cosmides and Tooby, 1992).

Comment

They rightly criticise ‘some methods’ drawn from mathematics etc, but some have interpreted as meaning that “logic, mathematics, and probability theory are … incapable of solving the natural adaptive problems our ancestors had to solve reliably in order to reproduce”. But this leads them to overlook relevant theories, such as Whitehead and Keynes‘.

See Also

Relevant mathematics, Avoiding unknown probabilities, Kahneman on biases

NOTE

This has been copied to my bibliography section under ‘rationality and uncertainty’, ‘more …’, where it has more links. Please comment there.

Dave Marsay

Which Mathematics of Uncertainty for Today’s Challenges?

This is a slight adaptation of a technical paper presented to an IMA conference 16 Nov. 2009, in the hope that it may be of broader interest. It argues that ‘Knightian uncertainty’, in Keynes’ mathematical form, provides a much more powerful, appropriate and safer approach to uncertainty than the more familiar ‘Bayesian (numeric) probability’.

Issues

Conventional Probability

The combination of inherent uncertainty and the rate of change challenge or capabilties.

There are gaps in the capability to handle both inherent uncertainty and rapid change.

Keynes et al suggest that there is more to uncertainty than random probability. We seem to be able to cope with high volumes of deterministic or probabilistic data, or low volumes of less certain data, but to have problems at the margins. This leads to the questions:

  • How complex is the contemporary world?
  • What is the perceptual problem?
  • What is contemporary uncertainty like?
  • How is uncertainty engaged with?

Probability arises from a definite context

Objective numeric probabilities can arise through random mechanisms, as in gambling. Subjective probabilities are often adequate for familiar, situations where decisions are short-term, with only cumulative long-term impact, at worst. This is typical of the application of established science and engineering where one has a kind of ‘information dominance’ and there are only variations within an established frame / context.

Contexts

Thus (numeric) probability is appropriate where:

  • Competition is coherent and takes place within a stable, utilitarian, framework.
  • Innovation does not challenge the over-arching status quo or ‘world view’
  • We only ever need to estimate the current parameters within a given model.
  • Uncertainty can be managed. Uncertainty about estimates can be represented by numbers (probability distributions), as if they were principally due to noise or other causes of variation.
  • Numeric probability is multiplied by value to give a utility, which is optimised.
  • Risk is only a number, negative utility.

Uncertainty is measurable (in one dimension) where one has so much stability that almost everything is measurable.

Probability Theory

Probability theories typically build on Bayes’ rule [Cox] :

P(H|E) = P(H).(P(E|H)/P(E)),

where P(E|H) denotes the ‘likelihood’, the probability of evidence, E, given a hypothesis, H. Thus the final probability is the prior probability times the ‘likelihood ratio’.

The key assumptions are that:

  • The selection of evidence for a given hypothesis, H, is indistinguishable from a random process with a proper numeric likelihood function, P( · |H).
  • The selection of the hypothesis that actually holds is indistinguishable from random selection from a set {Hi} with ‘priors’ P(Hi) – that can reasonably be estimated – such that
    • P(HiÇHj) = 0 for i ¹ j (non-intersection)
    • P(ÈiHi) = 1 (completeness).

It follows that P(E) = SiP(E|Hi).P(Hi) is well-defined.

H may be composite, so that there are many proper sub-hypotheses, h Þ H, with different likelihoods, P(E|h). It is then common to use the Bayesian likelihood,

P(E|H) = òh ÞHP(E|h).dP(h|H),

or

P(E|H) = P(E|h), for some representative hypothesis h.

In either case, hypotheses should be chosen to ensure that the expected likelihood is maximal for the true hypothesis.

Bayes noted a fundamental problem with such conventional probability: “[Even] where the course of nature has been the most constant … we can have no reason for thinking that there are no causes in nature which will ever interfere with the operations the causes from which this constancy is derived.”

Uncertain in Contemporary Life

Uncertainty arises from an indefinite context

Uncertainty may arise through human decision-making, adaptation or evolution, and may be significant for situations that are unfamiliar or for decisions that may have long-term  impact. This is typical of the development of science in new areas, and of competitions where unexpected innovation can transform aspects of contemporary life. More broadly still, it is typical of situations where we have a poor information position or which challenge our sense-making, and where we could be surprised, and so need to alter our framing of the situation. For example, where others can be adaptive or innovative and hence surprising.

Contexts

  • Competitions, cooperations, collaborations, confrontations and conflicts all nest and overlap messily, each with their own nature.
  • Perception is part of multiple co-adaptations.
  • Uncertainty can be shaped but not fully tamed. Only the most careful reasoning will do.
  • Uncertainty and utility are imprecise and conditional. One can only satisfice, not optimise.
  • Critical risks arise from the unanticipated.

Likelihoods, Evidence

In Plato’s republic the elite make the rules which form a fixed context for the plebs. But in contemporary life the rulers only rule with the consent of the ruled and in so far as the rules of the game ’cause’ (or at least influence) the behaviour of the players, the participants have reason to interfere with causes, and in many cases we expect it: it is how things get done. J.M. Keynes and I.J. Good (under A.M.Turing) developed techniques that may be used for such ‘haphazard’ situations, as well as random ones.

The distinguishing concepts are: The law of evidence; generalized weight of evidence (woe) and iterative fusion.

If datum, E, has a distribution f(·) over a possibility space, , then distributions g(·) over ,

 òlog(f(E)).f(E )  ³ òlog(g(E)).f(E).

I.e. the cross-entropy is no more than the entropy. For a hypothesis H in a context, C, such that the likelihood function g = PH:C is well-defined, the weight of evidence (woe) due to E for H is defined to be:

W(E|H:C) º log(PH:C (E)).

Thus the ‘law of evidence’: that the expected woe for the truth is never exceeded by that for any other hypothesis. (But the evidence may indicate that many or none of thehypotheses fit.) For composite hypotheses, the generalized woe is:

W(E|H:C) º suph ÞH {W(E|h:C)}.

This is defined even for a haphazard selection of h.

Let ds(·) be a discounting factor for the source, s [Good]. If one has independent evidence, Es, from different sources, s, then typically the fusion equation is:

W(E|H:C,ds) £ Ss{ds (W(Es |H:C))},

with equality for precise hypotheses. Together, generalized woe and fusion determine how woe is propagated through a network, where the woe for a hypothesis is dependent on an assumption which itself has evidence. The inequality forces iterative fusion, whereby one refines candidate hypotheses until one has adequate precision. If circumstantial evidence indicates that the particular situation is random, one could take full account of it, to obtain the same result as Bayes, or discount [Good].

In some cases it is convenient, as Keynes does, to use an interval likelihood or woe, taking the infimum and supremum of possible values. The only assumption is that the evidence can be described as a probabilistic outcome of a definite hypothesis, even if the overall situation is haphazard. In practice, the use of likelihoods is often combined with conjectural causal modelling, to try to get at a deep understanding of situations.

Examples

Crises

Typical crisis dynamics

Above is an informal attempt to illustrate typical crisis kinematics, such as the financial crisis of 2007/8. It is intended to capture the notion that conventional probability calculations may suffice for long periods, but over-dependence on such classical constructs can lead to shocks or crises. To avoid or mitigate these more attention should be given to uncertainty [Turner].

An ambush

Uncertainty is not necessarily esoteric or long-term. It can be found wherever the assumptions of conventional probability theory do not hold, in particular in multilevel games. I would welcome more examples that are simple to describe, relatively common and where the significance of uncertainty is easy to show.

Deer need to make a morning run from A to B. Routes r, s, t are possible. A lion may seek to ambush them. Suppose that the indicators of potential ambushes are equal. Now in the last month route r has been used 25 times, s 5 times and t never, without incident. What is the ‘probability’ of an ambush for the 3 routes?

Let A=“The Lion deploys randomly each day with a fixed probability distribution, p”. Here we could use a Bayesian probability distribution over p, with some sensitivity analysis.

But this is not the only possibility. Alternatively, let B =“The Lion has reports about some of our runs, and will adapt his deployments.” We could use a Bayesian model for the Lion, but with less confidence. Alternatively, we could use likelihoods.

Route s is intermediate in characteristics between the other two. There is no reason to expect an ambush at s that doesn’t apply to one of the other two. On the other hand, if the ambush is responsive to the number of times a route is used then r is more likely than s or t, and if the ambush is on a fixed route, it is only likely to be on t. Hence s is the least likely to have an ambush.

Consistently selecting routes using a fixed probability distribution is not as effective as a muddling strategy [Binmore] which varies the distribution, supporting learning and avoiding an exploitable equilibrium.

Concluding Remarks

Conventional (numeric) probability, utility and rationality all extrapolate based on a presumption of stability. If two or more parties are co-adapting or co-evolving any equilibria tend to be punctuated, and so a more general approach to uncertainty, information, communication, value and rationality is indicated, as identified by Keynes, with implications for ‘risk’.

Dave Marsay, Ph.D., C.Math FIMA, Fellow ISRS

References:

Bayes, T. An Essay towards solving a Problem in the Doctrine of Chances (1763), Philosophical Transactions of the Royal Society of London 53, 370–418. Regarded by most English-speakers as ‘the source’.

Binmore, K, Rational Decisions (2009), Princeton U Press. Rationality for ‘muddles’, citing Keynes and Turing. Also http://else.econ.ucl.ac.uk/papers/uploaded/266.pdf .

Cox, R.T. The Algebra of Probable Inference (1961) Johns Hopkins University Press, Baltimore, MD. The main justification for the ‘Bayesian’ approach, based on a belief function for sets whose results are comparable. Keynes et al deny these assumptions. Also Jaynes, E.T. Probability Theory: The Logic of Science (1995) http://bayes.wustl.edu/etj/prob/book.pdf .

Good, I.J. Probability and Weighting of Evidence (1950), Griffin, London. Describes the basic techniques developed and used at Bletchley Park. Also Explicativity: A Mathematical Theory of Explanation with Statistical Applications (1977) Proc. R. Soc. Lond. A 354, 303-330, etc. Covers discounting, particularly of priors. More details have continued to be released up until 2006.

Hodges, A. Alan Turing (1983) Hutchinson, London. Describes the development and use of ‘weights of evidence’, “which constituted his major conceptual advance at Bletchley”.

Keynes, J.M. Treatise on Probability (1920), MacMillan, London. Fellowship essay, under Whitehead. Seminal work, outlines the pros and cons of the numeric approach to uncertainty, and develops alternatives, including interval probabilities and the notions of likelihood and weights of evidence, but not a ‘definite method’ for coping with uncertainty.

Smuts, J.C. The Scientific World-Picture of Today, British Assoc. for the Advancement of Science, Report of the Centenary Meeting. London: Office of the BAAS. 1931. (The Presidential Address.) A view from an influential guerrilla leader, General, War Cabinet Minister and supporter of ‘modern’ science, who supported Keynes and applied his ideas widely.

Turner, The Turner Review: A regulatory response to the global banking crisis (2009). Notes the consequences of simply extrapolating, ignoring non-probabilistic (‘Knightian’) uncertainty.

Whitehead, A.N. Process and Reality (1929: 1979 corrected edition) Eds. D.R. Griffin and D.W. Sherburne, Free Press. Whitehead developed the logical alternative to the classical view of uniform unconditional causality.

Out of Control

Kevin Kelly’s ‘Out of Control‘ (1994) sub-titled “The New Biology of Machines, Social Systems, and the Economic World” gives ‘the nine laws of god’which it commends for all future systems, including organisations and economies. They didn’t work out too well in 2008.

The claims

The book is introduced (above) by:

“Out of Control is a summary of what we know about self-sustaining systems, both living ones such as a tropical wetland, or an artificial one, such as a computer simulation of our planet. The last chapter of the book, “The Nine Laws of God,” is a distillation of the nine common principles that all life-like systems share. The major themes of the book are:

  • As we make our machines and institutions more complex, we have to make them more biological in order to manage them.
  • The most potent force in technology will be artificial evolution. We are already evolving software and drugs … .
  • Organic life is the ultimate technology, and all technology will improve towards biology.
  • The main thing computers are good for is creating little worlds so that we can try out the Great Questions. …
  • As we shape technology, it shapes us. We are connecting everything to everything, and so our entire culture is migrating to a “network culture” and a new network economics.

In order to harvest the power of organic machines, we have to instill in them guidelines and self-governance, and relinquish some of our total control.”

Holism

Much of the book is Holistic in nature, The above could be read as applying the ideas of Smuts’ Holism to newer technologies. (Chapter 19 does make explicit reference to JC Smuts in connection with internal selection, but doesn’t reference his work.)

Jan Smuts based his work on wide experience, including with improving arms production in the Great War, and went on to found ecology and help modernise the sciences, thus leading to the views that Kelly picks up on. Superficially, Kelly’s book is greatly concerned with technology that ante-dates Smuts, but his arguments claim to be quite general, so an apostle of Smuts would expect Kelly to be consist, but applying the ideas to the new realm. But where does Kelly depart from Smuts, and what new insights does he bring? Below we pick out Kelly’s key texts and compare them.

The nine Laws of God

The laws with my italics are:

Distribute being

When the sum of the parts can add up to more than the parts, then that extra being … is distributed among the parts. Whenever we find something from nothing, we find it arising from a field of many interacting smaller pieces. All the mysteries we find most interesting — life, intelligence, evolution — are found in the soil of large distributed systems.

The first phrase is clearly Holistic, and perhaps consistent with Smuts’ view that the ‘extra’ arises from the ‘field of interactions’. However in many current technologies the ‘pieces’ are very hard-edged, with limited ‘mutual interaction’. 

Control from the bottom up

When everything is connected to everything in a distributed network … overall governance must arise from the most humble interdependent acts done locally in parallel, and not from a central command. …

The phrases ‘bottom up’ and ‘humble interdependent acts’ seem inconsistent with Smuts’ own behaviour, for example in taking the ‘go’ decision for D-day. Generally, Kelly seems to ignore or deny the need for different operational levels, as in the military’s tactical and strategic.

Cultivate increasing returns

Each time you use an idea, a language, or a skill you strengthen it, reinforce it, and make it more likely to be used again. … Success breeds success. In the Gospels, this principle of social dynamics is known as “To those who have, more will be given.” Anything which alters its environment to increase production of itself is playing the game … And all large, sustaining systems play the game … in economics, biology, computer science, and human psychology. …

Smuts seems to have been the first to recognize that one could inherit a tendency to have more of something (such as height) than your parents, so that a succesful tendency (such as being tall) would be reinforced. The difference between Kelly and Smuts is that Kelly has a general rule whereas Smuts has it as a product of evolution for each attribute. Kelly’s version also needs to be balanced against not optimising (below).

Grow by chunking

The only way to make a complex system that works is to begin with a simple system that works. Attempts to instantly install highly complex organization — such as intelligence or a market economy — without growing it, inevitably lead to failure. … Time is needed to let each part test itself against all the others. Complexity is created, then, by assembling it incrementally from simple modules that can operate independently.

Kelly is uncomfortable with the term ‘complex’. In Smuts’ usage a military platoon attack is often ‘complex’, whereas a superior headquarters could be simple. Systems with humans in naturally tend to be complex (as Kelly describes) and are only made simple by prescriptive rules and procedures. In many settings such process-driven systems would (as Kelly describes them) be quite fragile, and unable to operate independently in a demanding environment (e.g., one with a thinking adversary). Thus I suppose that Kelly is advocating starting with small but adaptable systems and growing them. This is desirable, but often Smuts did not have that luxury, and had to re-engineer systems such as production or fighting systems, ‘on the fly’

Maximize the fringes

… A uniform entity must adapt to the world by occasional earth-shattering revolutions, one of which is sure to kill it. A diverse heterogeneous entity, on the other hand, can adapt to the world in a thousand daily mini revolutions, staying in a state of permanent, but never fatal, churning. Diversity favors remote borders, the outskirts, hidden corners, moments of chaos, and isolated clusters. In economic, ecological, evolutionary, and institutional models, a healthy fringe speeds adaptation, increases resilience, and is almost always the source of innovations.

A large uniform entity cannot adapt and maintain its uniformity, and so is unsustainable in the face of a changing situation or environment. If diversity is allowed then parts can adapt independently, and generally favourable adaptations spread. Moreover, the more diverse an entity is the more it can fill a variety of niches, and the more likely that it will survive some shot. Here Kelly, Smuts and Darwin essentially agree.

Honor your errors

A trick will only work for a while, until everyone else is doing it. To advance from the ordinary requires a new game, or a new territory. But the process of going outside the conventional method, game, or territory is indistinguishable from error. Even the most brilliant act of human genius, in the final analysis, is an act of trial and error. … Error, whether random or deliberate, must become an integral part of any process of creation. Evolution can be thought of as systematic error management.

Here the problem of competition is addressed. Here Kelly supposes that the only viable strategy in the face of complexity is blind trial and error, ‘the no strategy strategy’. But the main thing is to be able to identify actual errors. Smuts might also add that one might learn from near-misses and other potential errors.

Pursue no optima; have multiple goals

 …  a large system can only survive by “satisficing” (making “good enough”) a multitude of functions. For instance, an adaptive system must trade off between exploiting a known path of success (optimizing a current strategy), or diverting resources to exploring new paths (thereby wasting energy trying less efficient methods). …  forget elegance; if it works, it’s beautiful.

Here Kelly confuses ‘a known path of success’ with ‘a current strategy’, which may explain why he is dismissive of strategy. Smuts would say that getting an adequate balance between the exploitation of manifest success and the exploration of alternatives would be a key feature of any strategy. Sometimes it pays not to go after near-term returns, perhaps even accepting a loss.

Seek persistent disequilibrium

Neither constancy nor relentless change will support a creation. A good creation … is persistent disequilibrium — a continuous state of surfing forever on the edge between never stopping but never falling. Homing in on that liquid threshold is the still mysterious holy grail of creation and the quest of all amateur gods.

This is a key insight. The implication is that even the nine laws do not guarantee success. Kelly does not say how the disequilibrium is generated. In many systems it is only generated as part of an eco-system, so that reducing the challenge to a system can lead to its virtual death. A key part of growth (above) is o grow the ability to maintain a healthy disequilibrium despite increasing novel challenges.

Change changes itself

… When extremely large systems are built up out of complicated systems, then each system begins to influence and ultimately change the organizations of other systems. That is, if the rules of the game are composed from the bottom up, then it is likely that interacting forces at the bottom level will alter the rules of the game as it progresses.  Over time, the rules for change get changed themselves. …

It seems that the changes the rules are blindly adaptive. This may be because, unlike Smuts, Kelly does not believe in strategy, or in the power of theory to enlighten.

Kelly’s discussion

These nine principles underpin the awesome workings of prairies, flamingoes, cedar forests, eyeballs, natural selection in geological time, and the unfolding of a baby elephant from a tiny seed of elephant sperm and egg.

These same principles of bio-logic are now being implanted in computer chips, electronic communication networks, robot modules, pharmaceutical searches, software design, and corporate management, in order that these artificial systems may overcome their own complexity.

When the Technos is enlivened by Bios we get artifacts that can adapt, learn, and evolve. …

The intensely biological nature of the coming culture derives from five influences:

    • Despite the increasing technization of our world, organic life — both wild and domesticated — will continue to be the prime infrastructure of human experience on the global scale.
    • Machines will become more biological in character.
    • Technological networks will make human culture even more ecological and evolutionary.
    • Engineered biology and biotechnology will eclipse the importance of mechanical technology.
    • Biological ways will be revered as ideal ways.

 …

As complex as things are today, everything will be more complex tomorrow. The scientists and projects reported here have been concerned with harnessing the laws of design so that order can emerge from chaos, so that organized complexity can be kept from unraveling into unorganized complications, and so that something can be made from nothing.

My discussion

Considering local action only, Kelly’s arguments often come down to the supposed impossibility of effective strategy in the face of complexity, leading to the recommendation of the universal ‘no strategy strategy’: continually adapt to the actual situation, identifying and setting appropriate goals and sub-goals. Superficially, this seems quite restrictive, but we are free as to how we interpret events, learn, set goals and monitor progress and react. There seems to be nothing to prevent us from following a more substantial strategy but describing it in Kelly’s terms.

 The ‘bottom up’ principle seems to be based on the difficulty of central control. But Kelly envisages the use of markets, which can be seen as a ‘no control control’. That is, we are heavily influenced by markets but they have no intention. An alternative would be to allow a range of mechanisms, ideally also without intention; whatever is supported by an appropriate majority (2/3?).

For economics, Kelly’s laws are suggestive of Hayek, whereas Smuts’ approach was shared with his colleague, Keynes. 

Conclusion

What is remarkable about Kelly’s laws is the impotence of the individuals in the face of ‘the system’. It would seem better to allow for ‘central’ (or intermediate) mechanisms to be ‘bottom up’ in the sense that they are supported by an informed ‘bottom’.

See Also

David Marsay

Holism and Evolution

Holism and evolution 1927. Smuts’ notoriously inaccessible theory of evolution, building on and show-casing Keynes’ notion of uncertainty. Smuts made significant revisions and additions in later editions to reflect some of the details of the then current understanding. Not all of these now appear to be an improvement. Although Smuts and Whitehead worked independently, they recognized that their theories were equivalent. The book is of most interest for its general approach, rather than its detail. Smuts went on to become the centennial president of the British Association for the Advancement of Science, drawing on these ideas to characterise ‘modern science’.

Holism is a term introduced by Smuts, in contrast to individualism and wholism. In the context of evolution it emphasises co-evolution between parts and wholes, with neither being dominant. The best explanation I have found is:

“Back in the days of those Ancient Greeks, Aristotle (384-322BCE) gave us:

The whole is greater than the sum of its parts; (the composition law)
The part is more than a fraction of the whole. (the decomposition law)

Composition Laws” (From Derek Hitchins’ Systems World.)

Smuts also develops LLoyd Morgan’s concept of emergence,  For example, the evolutionary ‘fitness function’ may emerge from a co-adaptation rather than be fixed.

The book covers evolution from physics to personality. Smuts intended a sequel covering, for example, social and political evolution, but was distracted by the second world war, for example.

Smuts noted that according to the popular view of evolution, one would expect organisms to become more and more adapted to their environmental niches, whereas they were more ‘adapted to adapt’, particularly mankind. There seemed to be inheritance of variability in offspring as whole as the more familiar inheritance of manifest characteristics, which suggested more sudden changes in the environment than had been assumed. This led Smuts to support research into the Wegner hypothesis (concerning continental drift) and the geographic origins of  life-forms. 

See also

Ian Stewart, Peter Allen

David Marsay

Life’s Other Secret

Ian Stewart Life’s Other Secret: The new mathematics of the living world, 1998.

This updates D’Arcy Thompson’s classic On growth and form, ending with a manifesto for a ‘new’ mathematics, and a good explanation of the relationship between mathematics and scientific ‘knowledge’.

Like most post-80s writings, it’s main failing is that it sees science as having achieved some great new insights in the 80s, ignoring the work of Whitehead et al, as explained by Smuts, for example.

Ian repeatedly notes the tendency for models to assume fixed rules, and hence only to apply within a fixed Whitehead-epoch, whereas (as Smuts also noted) life bears the imprint of having being formed during (catastrophic) changes of epoch.

The discussion provides some supporting evidence for the following, but does not develop the ideas:

The manifesto is for a model combining the strengths  the strengths of cellular automata with Turing’s reaction-diffusion approach, and more. Thus it is similar to Smuts’ thoughts on Whitehead et al, as developed in SMUTS. Stewart also notes the inadequacy of the conventional interpretation of Shannon’s ‘information’.

See also

Mathematics and real systems. Evolution and uncertainty, epochs.

Dave Marsay

Induction and epochs

Introduction

Induction is the basis of all empirical knowledge. Informally, if something has never or always been the case, one expects it to continue to be never or always the case: any change would mark a change in epoch. 

Mathematical Induction

Mathematical induction concerns mathematical statements, not empirical knowledge.

Let S(n) denote  statement dependent on an integer variable, n.
If:
    For all integers n, S(n) implies S(n+1), and
    S(k) for some integer k,
Then:
    S(i) for all integers i ≥ k .

This, and variants on it, is often used to prove theories for all integers. It motivates informal induction.

Statistical Induction

According to the law of large numbers, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed. Thus:

For two or more sufficiently large sets of results obtained by random sampling from the same distribution, the averages  should be close, and will tend to become closer as more trails are performed.

In particular, if one set of results, R1, has been obtained and another, R2, will be obtained, using the language of probability theory, if C() is a condition on a results then

P(C(R2)) = p(C(R1)), where P() is the probability and p() is the proportion.

Alternatively, p() could be given as a hypothesis and tested against the data. Note that for any given quantity of data, rare events cannot be excluded, and so one can never be sure that any p(x) is ‘objectively’ very small. That is, the ‘closeness’ in the law of large numbers always has some non-zero tolerance.

A key assumption of statistical induction is that there exists a stable ‘expectation’. This is only true within some epoch where the trials depend on that epoch, and not on any sub-epochs. In effect, the limits on an epoch are determined by the limits on the law of large numbers.

Empirical Induction

In practice we don’t always have the conditions required for straightforward statistics, but we can approximate. Using the notation as above, then:

P(C(R2)) = p(C(R1)),

provided that R1, R2 are in the same epoch. That is, where:

  • The sampling was either unbiased, had the same bias in the two cases or at least was not conditional on anything that changed between the two cases.
  • For some basis of hypotheses, {H}, the conditional likelihoods P(data|H) are unchanged between the two cases.

 Alternatively, we can let A=”same epoch” be the above assumptions and make

P(C(R2)|A) = p(C(R1)).

Induction on Hypotheses

Statistical induction only considers proportions.  The other main case is where we have hypotheses (e.g. models or theories) that fit the past data. If these are static then we may expect some of the hypotheses that fit to be ‘true’ and hence to continue to fit. That is:

If for all i in some index set I hypotheses Hi fit the current data  (R1), then for some subset, J, of I,  by default one expects that for all j in J, Hj will continue to fit (for future data, R2).

As above, there is an assumption that the epoch hasn’t changed.

Often we are only interested in some of the parameters of a hypothesis, such as a location. Even if all the theories that fit the current data virtually agree on the current value of the parameters of interest, there may be radically different possibilities for their future values, perhaps forming a multi-modal distribution. (For example, if we observe an aircraft entering our airspace, we may be sure about where it is and how fast it is flying, but have many possible destinations.)

Pragmatic induction

One common form of pragmatism is where one has an ‘established’ model or belief which one goes on using (unquestioning) unless and until it is falsified. By default the assumption A, above, is taken to be true. Thus one has

P(C(R2)) = p(C(R1)),

unless there is definite evidence that P() will have changed, e.g. a biased sample or an epochal change of the underlying random process. In effect, pragmatism assumes that the current epoch will extend indefinitely.

Rationalizing induction

The difference between statistical and pragmatic induction is that the former makes explicit the assumptions of the latter. If one has a pragmatic claim, P(C(R2)) = p(C(R1)), one in effect recover the rigour of the statistical approach by noting when, where and how the data supporting the estimate was sampled, compared with when where and how the probability estimate is to be applied. (Thus  it might be pragmatic – in this pedantic sense – to suppose that if our radar fails temporarily that all airplanes will have continued flying straight and level, but not necessarily sensible.)

Example

When someone, Alf, says ‘all swans are white’ and a foreigner, Willem, says that they have seen black swans, we should consider whether Alf’s statement is empirical or not, and if so what it’s support is. Possibly:

    • Alf defines swans in such a way that they must be white: they are committed to calling a similar black creature something else. Perhaps this is a widely accepted definition that Willem is unaware of.
    • Alf has only seen British swans, and we should interpret their statement as ‘British swans are white’.
    • Alf believes that swans are white and so only samples large white birds to check that they are swans.
    • Alf genuinely and reasonably believes that the statement ‘all swans are white’ has been subjected to the widest scrutiny, but Willem has just returned from a new-found continent

Even if Alf’s belief was soundly based on pragmatic induction, it would be prudent for him to revise his opinion, since his induction – of whatever kind – was clearly based on too small an epoch.

Analysis

We can split conventional induction into three parts:

  1. Modelling the data.
  2. Extrapolating, using the models.
  3. Consider predictions based on the extrapolations.

The final step is usually implicit in induction: it is usually supposed that one should always take an extrapolation to be a prediction. But there are exceptions. (Suppose that two airplanes are flying straight towards each other. A candidate prediction would be that they would pass infeasibly close, breaching the aviation rules that are supposed to govern the airspace. Hence we anticipate the end of the current ‘straight and level’ epoch and take recourse to a ‘higher’ epoch, in this case the pilots or air-traffic controllers. If they follow set rules of the road (e.g. planes flying out give way) then we may be able to continue extrapolating within the higher epoch, but here we only consider extrapolation within a given epoch.)

Thus we might reasonably imagine a process somewhat like:

  1. Model the data.
  2. Extrapolate, using the models.
  3. Establish predictions:
    • If the candidate predictions all agree: Take the extrapolations to be a candidate prediction.
    • Otherwise: Make a possibilistic candidate prediction; the previous ‘state’ has ‘set up the conditions’ for the possibilities.
  4. Establish credibility:
    1. If the candidate predictions are consistent with the epoch, then they are credible.
    2. If not, note lack of credibility.

In many cases a natural ‘null hypothesis’ is that many elements of a hypothesis are independent, so that they be extrapolated separately. There are then ‘holistic’ constraints that need to be applied over all. This can be done as a part of the credibility check. (For example, airplanes normally fly independently but should not fly too close.)

We can fail to identify a credible hypothesis either because we have not considered a wide enough range of hypotheses or because the epoch has ended. The epoch may also end without our noticing, leading to a seemingly credible prediction that is actually based on a false premise. We can potentially deal with all these problems by considering a broader range of hypotheses and data. Induction is only as good as the data gathering and theorising that supports it. 

Complicatedness

The modelling process may be complicated in two ways:

  • We may need to derive useful categories so that we have enough data in each category.
  • We may need to split the data into epochs, with different statistics for each.

We need to have enough data in each partition to be statistically meaningful, while being reasonably sure that data in the same partition are all alike in terms of transition probabilities. If the parts are too large we can get averaged results, which need to be treated accordingly.

Induction and types of complexity

We can use induction to derive a typology for complexity:

  • simple unconditional: the model is given: just apply it
  • simple conditional: check the model and apply it
  • singly complicated: analyse the data in a single epoch against given categories to derive a model, apply it.
  • doubly complicated: analyse the data into novel categories or epochs to drive a model, apply it.
  • complex: where the data being observed has a reflexive relationship with any predictions.

The Cynefin framework  gives a simple – complicated – complex – chaotic sense-making typology that is consistent with this, save that it distinguishes between:

  • complex: we can probe and make sense
  • chaotic: we must act first to force the situation to ‘make sense’.

We cannot make this distinction yet as we are not sure what ‘makes sense’ would mean. It may be that one can only know that one has made sense when and if one has had a succesful intervention, which will often mean that ‘making sense’ is more of a continuing activity that a state to be achieved. But inadequate theorising and data would clearly lead to chaos, and we might initially act to consider more theories and to gather more data. But it is not clear how we would know that we had done enough.

See also

StatisticspragmaticCynefin, mathematics.

David Marsay

Regulation and epochs

Conventional regulation aims at maintaining objective criteria, as in Conant and Ashby. They must have or form a model or models of their environment. But if future epochs are unpredictable or the regulators are set-up for the short-term, e.g. being post-hoc adaptive, then the models will not be appropriate for the long-term, leading to a loss of regulation at least until a new effective model can be formed.

Thus regulation based only on objective criteria is not sustainable in the long-term. Loss of regulation can occur, for example, due to innovation by the system being regulated. More sustainable regulation (in the sense of preserving viability) might be achieveable by taking a broader view of the system ‘as a whole’, perhaps engaging with it. For example, a ‘higher’ (strategic) regulator might monitor the overall situation, redirect the ‘lower’ (tactical) regulators and keep the lower regulators safe. The operation of these regulators would tend to correspond to Whitehead’s epochs (regulators would impose different rules, and different rules would call for different regulators).

See also

Stafford Beer.

David Marsay

Synthetic Modelling of Uncertain Temporal Systems

Overview

SMUTS is a computer-based ‘exploratorium’, to aid the synthetic modelling of uncertain temporal systems. I had previously worked on sense-making systems based on the ideas of Good, Turing and Keynes, and was asked to get involved in a study on the potential impact of any Y2K bugs, starting November 1999. Not having a suitable agreed model, we needed a generic modelling system, able to at least emulate the main features of all the part models. I had been involved in conflict resolution, where avoiding cultural biases and being able to meld different models was often key, and JC Smuts’ Holism and Evolution seemed a sound if hand-wavy approach. SMUTS is essentially a mathematical interpretation of Smuts. I was later able to validate it when I found from the Smuts’ Papers that Whitehead, Smuts and Keynes regarded their work as highly complementary. SMUTS is actually closer to Whitehead than Smuts.

Systems

An actual system is a part of the actual world that is largely self-contained, with inputs and outputs but with no significant external feedback-loops.  It is a judgement about what is significant. Any external feedback loop will typically have some effect, but we may not regard it as significant if we can be sure that any effects will build up too slowly. It is a matter of analysis on larger systems to determine what might be considered smaller systems. Thus plankton are probably not a part of the weather system but may be a pat of the climate.

The term system may also be used for a model of a system, but here we mean an actual system.

Temporal

We are interested in how systems change in time, or ‘evolve’. These systems include all types of evolution, adaptation, learning and desperation, and hence are much broader than the usual ‘mathematical models’.

Uncertain

Keynes’ notion of uncertainty is essentially Knightian uncertainty, but with more mathematical underpinning. It thus extends more familiar notions of probability as ‘just a number’. As Smuts emphasises, systems of interest can display a much richer variety of behaviours than typical probabilistic systems. Keynes has detailed the consequences for economics at length.

Modelling

Pragmatically, one develops a single model which one exploits until it fails. But for complex systems no single model can ever be adequate in the long run, and as Keynes and Smuts emphasised, it could be much better recognize that any conventional model would be uncertain. A key part of the previous sense-making work was the multi-modelling concept of maintaining the broadest range of credible models, with some more precise and others more robust, and then hedging across them, following Keynes et al.

Synthetic

In conflict resolution it may be enough to simply show the different models of the different sides. But equally one may need to synthesize them, to understand the relationships between them and scope for ‘rationalization’. In sense making this is essential to the efficient and effective use of data, otherwise one can have a ‘combinatorial explosion’.

Test cases

To set SMUTS going, it was developed to emulate some familiar test cases.

  • Simple emergence. (From random to a monopoly.)
  • Symbiosis. (Emergence of two mutually supporting behaviours.)
  • Indeterminacy. (Emergence of co-existing behaviours where the proportions are indeterminate.)
  • Turing patterns. (Groups of mutually supporting dynamic behaviours.)
  • Forest fires. (The gold standard in epidemiology, thoroughly researched.)

In addition we had an example to show how the relationships between extremists and moderates were key to urban conflicts.

The aim in all of these was not to be as accurate as the standard methods or to provide predictions, but to demonstrate SMUTS’ usefulness in identifying the key factors and behaviours. 

Viewpoints

A key requirement was to be able to accommodate any relevant measure or sense-making aid, so that users could literally see what effects were consistent from run to run, what weren’t, and how this varied across cases. The initial phase had a range of standard measures, plus Shannon entropy, as a measure of diversity.

Core dynamics

Everything emerged from an interactional model. One specified the extent to which one behaviour would support or inhibit nearby behaviours of various types. By default behaviours were then randomized across an agora and the relationships applied. Behaviours might then change in an attempt to be more supported. The fullest range of variations on this was supported, including a range of update rules, strategies and learning. Wherever possible these were implemented as a continuous range rather than separate cases, and all combinations were allowed.

Illustration

SMUTS enables one to explore complex dynamic systems

SMUTS has a range of facilities for creating, emulating and visualising systems.

By default there are four quadrants. The bottom right illustrates the inter-relationships (e.g., fire inhibits nearby trees, trees support nearby trees). The top right shows the behaviours spread over the agora (in this case ground, trees and fire). The bottom left shows  a time-history of one measure against another, in this case entropy versus value of trees. The top-left allows one to keep an eye on multiple displays, forming an over-arching view. In this example, as in many others, attempting to get maximum value (e.g. by building fire breaks or putting out all fires) leads to a very fragile system which may last a long time but which will completely burn out when it does go. If one allows fires to run their course, one typically gets an equilibrium in which there are frequent small fires which keep the undergrowth down so that there are never any large fires.

Findings

It was generally possible to emulate text-book models to show realistic short-run behaviours of systems. Long term, simpler systems tended to show behaviours like other emulations, and unlike real systems. Introducing some degree of evolution, adaptation or learning all tended to produce markedly more realistic behaviours: the details didn’t matter. Having behaviours that took account of uncertainty and hedged also had a similar effect.

Outcomes

SMUTS had a recognized positive influence, for example on the first fuel crisis, but the main impact has been in validating the ideas of Smuts et al.

Dave Marsay 

Statistics and epochs

Statistics come in two flavours. The formal variety are based on samples with a known distribution. The empirical variety are drawn using a real-world process. If there is a known distribution then we know the ‘rules of the situation’ and hence are in a single epoch, albeit one that may have sub-epochs. In Cybernetic terms there is usually an implicit assumption that the situation is stable or in one of the equilibria of a polystable system. Hence, that the data was drawn from a single epoch. Otherwise the statistics are difficult to interpret.

Statistics are often intended to be predictive, by extrapolation. But this depends on the epoch enduring. Hence the validity of a statistic is dependent on it being taken from a single epoch, and the application of the statistic is dependent on the epoch continuing.

For example, suppose that we have found that all swans are white. We cannot conclude that we will never see black swans, only that if:

  • we stick to the geographic area from which we drew our conclusion
  • our sample of swans was large enough and representative enough to be significant
  • we are extrapolating over a time-period that is short compared with any evolutionary or other selective processes
  • there is no other agency that has an interest in falsifying our predictions.

then we are unlikely to see swans that are not white.

In particular the ‘law of large numbers’ should have appropriate caveats.

Complexity and epochs

It is becoming widely recognized (e.g. after the financial crash of 2008) that complexity matters. But while it is clear that systems of interest are complex in some sense, it is not always clear that any particular theory of complexity captures the aspects of importance.
We commonly observe that systems of interest do display epochs, and many systems of interest involve some sort of adaptation, learning or evolution, so according to Whitehead and Ashby (Cybernetics) will display epochs. Thus key features of interest are:

  •  polystability: left to its own devices the system will tend to settle down into one or other of a number of possible equilibria, not just one.
  • exogenous changeability: the potential equilibria themselves change under external influence.
  • endogenous changeability: the potential equilibria change under internal influence.

For example, a person in an institution such as an old folk’s home is likely to settle into a routine, but their may be other routines that they might have adopted, if things had happened differently earlier on. Thus their behaviour is polyunstable, except in a very harsh institution. Their equilibrium might be upset by a change in the time at which the papers are delivered, an exogenous change.   Endogenous factors are typically slower-acting. For example, adopting a poor diet may (in the long – run) impact on their ability recover from illnesses and hence on their ability to carry on their establish routine. For a while the routine may carry on as normal,  only to suddenly become non-viable.