The limits of pragmatism

This is a personal attempt to identify and articulate a fruitful form of pragmatism, as distinct from what seems to me the many dangerous forms. My starting point is Wikipedia and my notion that the differences it notes can sometimes matter.

Doubt, like belief, requires justification. Genuine doubt irritates and inhibits, in the sense that belief is that upon which one is prepared to act.[2] It arises from confrontation with some specific recalcitrant matter of fact (which Dewey called a “situation”), which unsettles our belief in some specific proposition. Inquiry is then the rationally self-controlled process of attempting to return to a settled state of belief about the matter. Note that anti-skepticism is a reaction to modern academic skepticism in the wake of Descartes. The pragmatist insistence that all knowledge is tentative is quite congenial to the older skeptical tradition

My own contribution to things scientific has been on some very specific issues, but which I attempt to generalise:

  • It is sometimes seems much too late to wait to act on doubt for something that pragmatic folk recognize as a ‘specific recalcitrant matter of fact’. I would rather say (with the skeptics) that we should always be in some doubt, but that our actions require justification, and should only invest in relation to that justification. Requiring ‘facts’ seems too high a hurdle to act at all.
  • Psychologically, people do seek ‘settled states of belief’, but I would rather say (with the skeptics) that the degree of settledness ought to be only in so far as is justified. Relatively settled belief but not fundamentalist dogma!
  • It is often supposed that ‘facts’ and ‘beliefs’ should concern the ‘state’ of some supposed ‘real world’. There is some evidence that it is ‘better’ in some sense to think of the world as one in which certain processes are appropriate. In this case, as in category theory, the apparent state arises as a consequence of sufficient constraints on the processes. This can make an important difference when one considers uncertainties, but in ‘small worlds’ there are no such uncertainties.

It seems to me that the notion of ‘small worlds’ is helpful. A small world would be one which could be conceived of or ‘mentally modelled’. Pragmatists (of differing varieties) seem to believe that often we can conceive of a small world representation of the actual world, and act on that representation ‘as if’ the world were really small. So far, I find this plausible, even if not my own habit of thinking. The contentious point, I think, is that in every situation we should do our best to from a small world representation and then act as if it were true unless and until we are confronted with some ‘specific recalcitrant matter of fact’. This can be too late.

But let us take the notion of  a ‘small world’ as far as we can. It is accepted that the small world might be violated. If it could be violated as a consequence of something that we might inadvertently do then it hardly seems a ‘pragmatic’ notion in terms of ordinary usage, and might reasonably said to be dangerous in so far as it lulls us into a false sense of security.

One common interpretation of ‘pragmatism’ seems to be that we may as well act on our beliefs as there seems no alternative. But I shall refute this by presenting one. Another interpretation is that there is no ‘practical’ alternative’. That is to say, whatever we do could not affect the potential violation of the small world. But if this is the case it seems to me that there must be some insulation between ourselves and the small world. Thus the small world is actually embedded in some larger closed world. But do we just suppose that we are so insulated, or do we have some specific closed world in mind?

It seems to me that doubt is more justified the less our belief in insulation is justified. Even when we have specific insulation in mind, we surely need to keep an open mind and monitor the situation for any changes, or any reduction in justification for our belief.

From this, it seems to me that (as in my own work) what matters is not having some small world belief, but in taking a view on the insulations between what you seek to change and what you seek to rely on as unchanging. And from these identifying not only a single credible world in which to anchor one’s justifications for action, but in seeking out credible possible small worlds in the hope that at least one may remain credible as things proceed.

Dave Marsay

See also my earlier thoughts on pragmatism, from a different starting point.

Addendum: Locke anticipated my 3 bullet points above, by a few centuries. Pragmatists seem to argue that we don’t have to take some of Locke’s concerns too seriously. But maybe we should. It further occurs to me that there are often situations where in the short-run ‘pragmatism pays’, but in the long-run things can go increasingly awry. Locke offers an alternative to the familiar short-term utilitarianism that seems to make more sense. Whilst it may be beneficial to keep developing theories pragmatically, in the longer term one would do well to seek more logical (if less precise) theories from which one can develop pragmatic ‘beliefs’ that are not unduly affected by beliefs that may have been pragmatic in previous situations, but which no longer are. One might say that rather than stopping being pragmtic, one’s pragmatism should -from time to time – consider the potential long-run consequences, lest the long-run eventually burst upon one, creating a crisis and a need for a challenging paradigm shift.

An alternative is to recognise the issues arising from one’s current ‘pragmatic’ beliefs, and attempt to ‘regress to progress’. But this seems harder, and may be impossible under time presssure.

Are more intelligent people more biased?

It has been claimed that:

U.S. intelligence agents may be more prone to irrational inconsistencies in decision making compared to college students and post-college adults … .

This is scary, if unsurprising to many. Perhaps more surprisingly:

Participants who had graduated college seemed to occupy a middle ground between college students and the intelligence agents, suggesting that people with more “advanced” reasoning skills are also more likely to show reasoning biases.

It seems as if there is some serious  mis-education in the US. But what is it?

The above conclusions are based on responses to the following two questions:

1. The U.S. is preparing for the outbreak of an unusual disease, which is expected to kill 600 people. Do you: (a) Save 200 people for sure, or (b) choose the option with 1/3 probability that 600 will be saved and a 2/3 probability no one will be saved?

2. In the same scenario, do you (a) pick the option where 400 will surely die, or instead (b) a 2/3 probability that all 600 will die and a 1/3 probability no one dies?

You might like to think about your answers to the above, before reading on.

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The paper claims that:

Notably, the different scenarios resulted in the same potential outcomes — the first option in both scenarios, for example, has a net result of saving 200 people and losing 400.

Is this what you thought? You might like to re-read the questions and reconsider your answer, before reading on.

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The questions may appear to contain statements of fact, that we are entitled to treat as ‘given’. But in real-life situations we should treat such questions as utterances, and use the appropriate logics. This may give the same result as taking them at face value – or it may not.

It is (sadly) probably true that if this were a UK school examination question then the appropriate logic would be (1) to treat the statements ‘at face value’ (2) assume that if 200 people will be saved ‘for sure’ then exactly 200 people will be saved, no more. On the other hand, this is just the kind of question that I ask mathematics graduates to check that they have an adequate understanding of the issues before advising decision-takers. In the questions as set, the (b) options are the same, but (1a) is preferable to (2a), unless one is in the very rare situation of knowing exactly how many will die. With this interpretation, the more education and the more experience, the better the decisions – even in the US 😉

It would be interesting to repeat the experiment with less ambiguous wording. Meanwhile, I hope that intelligence agents are not being re-educated. Or have I missed something?

Also

Kahneman’s Thinking, fast and slow has a similar example, in which we are given ‘exact scientific estimates’ of probable outcomes, avoiding the above ambiguity. This might be a good candidate experimental question.

Kahneman’s question is not without its own subtleties, though. It concerns the efficacy of ‘programs to combat disease’. It seems to me that if I was told that a vaccine would save 1/3 of the lives, I would suppose that it had been widely tested, and that the ‘scientific’ estimate was well founded. On the other hand, if I was told that there was a 2/3 chance of the vaccine being ineffective I would suppose that it hadn’t been tested adequately, and the ‘scientific’ estimate was really just an informed guess. In this case, I would expect the estimate of efficacy to be revised in the light of new information. It could even be that while some scientist has made an honest estimate based on the information that they have, some other scientist (or technician) already knows that the vaccine is ineffective. A program based on such a vaccine would be more complicated and ‘risky’ than one based on a well-founded estimate, and so I would be reluctant to recommend it. (Ideally, I would want to know a lot more about how the estimates were arrived at, but if pressed for a quick decision, this is what I would do.)

Could the framing make a difference? In one case, we are told that ‘scientifically’, 200 people will be saved. But scientific conclusions always depend on assumptions, so really one should say ‘if …. then 200 will be saved’. My experience is that otherwise the outcome should not be expected, and that saving 200 is the best that should be expected. In the other case we are told that ‘400 will die’. This seems to me to be a very odd thing to say. From a logical perspective one would like to understand the circumstances in which someone would put it like this. I would be suspicious, and might well (‘irrationally’) avoid a program described in that way.

Addenda

The example also shows a common failing, in assuming that the utility is proportional to lives lost. Suppose that when we are told that lives will be ‘saved’ we assume that we will get credit, then we might take the utility from saving lives to be number of lives saved, but with a limit of ‘kudos’ at 250 lives saved. In this case, it is rational to save 200 ‘for sure’, as the expected credit from taking a risk is very much lower. On the other hand, if we are told that 400 lives will be ‘lost’ we might assume that we will be blamed, and take the utility to be minus the lives lost, limited at -10. In this case it is rational to take a risk, as we have some chance of avoiding the worst case utility, whereas if we went for the sure option we would be certain to suffer the worst case.

These kind of asymmetric utilities may be just the kind that experts experience. More study required?

 

Dave Marsay

Hercock’s Cohesion

Robert G. Hercock Cohesion: The Making of Society 2009.

Having had Robert critique some of my work, I could hardly not comment on this think-piece. It draws on modern complexity theory and a broad view of relevant historical examples and current trends to create a credible narrative. For me, his key conclusions are:

  1. “[G]iven a sufficient degree of communication … the cooperative assembly of [a cohesive society] is inevitable.”
  2. To be cohesive, a society should be “global politically federated, yet culturally diverse”.

The nature of communication envisaged seems to be indicated by:

 “From smoke signals, and the electric telegraph, through to fibre optics, and the Internet … the manifest boom in all forms of communication is bringing immense capabilities to form new social collectives and positive cultural developments.”

 I ‘get’ that increasing communication will bring immense capabilities to support the cooperative assembly of a cohesive global society, but am not convinced the effective exploitation of the capability in this way is inevitable. In chapter 6 (‘Bridges’) Robert says:

 “The truth is we now need a new shared set of beliefs. … Unfortunately, no one appears to have the faintest idea what such a common set of beliefs should look like, or where it might arise from, or who has responsibility to make it happen, or how, etc. Basically this is the challenge of the 21st century; we stand or fall on this battle for a common cultural nexus.”  

 This is closer to my own thinking.

People have different understandings of terms like ‘federated’. My preference is for subsidiarity: the idea that one has the minimum possible governance, with reliance on the minimum possible shared beliefs and common cultures. In complex situations these minimum levels are not obvious or static, so I would see an effective federations as engaging tentatively at a number of ‘levels’, ‘veering and hauling’ between them, and with strong arrangements for ‘horizon scanning’ and debate with the maximum possible diversity of views. Thus there would be not only cultural diversity but ‘viewpoint diversity within federated debate’. What is needed seems somewhat like Holism and glocalization 

Thinking of the EU, diversity of monetary policy might make the EU as an institution more cohesive while making their economies less cohesive. To put it another way, attempts to enforce cohesion at the monetary level can threaten cohesion at the political level. So it is not clear to me that one can think of a society as simply ‘being cohesive’. Rather it should be cohesive in the sense appropriate to its current situation. Cohesion should be ‘adaptive’. Leadership and vision seem to be required to achieve this: it is not automatic.

In the mid 80s many of those involved in the development of communications technologies thought that they would promote world peace, sometimes citing the kind of works that Robert does. I had and have two reservations. Firstly, the quality of communications matters. Thus [it was thought] one probably needed digital video, mobile phones and the Internet, all integrated in way that was easy to use. [The Apple Macintosh made this credible.] Thus, if there was a clash between Soviet secret police and Jewish protestors [common at the time], the whole world could take an informed view, rather than relying on the media. [This was before the development of video faking capabilities]. Secondly, while this would destabilize autocratic regimes, it was another issue as to what would happen next. It was generally felt that the only possible ‘properly’ stable states were democratic, but views differed on whether such states would necessarily stabilize.

Subsequent experience, such as the Arab spring, support the view that YouTube and Facebook undermine oppressive regimes. But I remain unconvinced that ‘the cooperative assembly of [a cohesive society] is inevitable’ in Africa, the Middle East,Russia or South America’, or that more communications would make it so. It certainly seems that if the process is inevitable, it can be much too slow.

My own thinking in the 80s was informed by the uncertainty and complexity theory Keynes, Whitehead, Turing and Smuts, which predates that which Robert cites, and which informed the development of the United Nations as a part of ‘the cooperative assembly of a cohesive global society’. Robert seems to be arguing that according to modern theory such efforts were not necessary, but even so they may have been beneficial if all they did was speed the process up by a few generations. Moreover, the EU example seems to support my view that these theories are usefully more advanced than their contemporary counter-parts.

The financial crash of 2008 occurred part way through the writing of the book. Like any history, explanations differ, and Robert gives a credible account in terms of modern complexity theory. But logic teaches us to be cautious about such post-hoc explanations. It seems to me that Keynes’ theory explains it adequately, and having been developed before the event should be given more credence.

 Robert seems to regard the global crash of 2008 as a result of a loss of cohesion :

“When economies, states and societies lose their cohesion, people suffer; to be precise a lot of people end up paying the cost. In the recession of 2008/09 … “

But Keynes shows how it is cohesion (‘sticking together’) that causes global crashes. Firstly, in a non-globalized economy a crash in one part can be compensated for by the stability of another part, a bit like China saving the situation, but more so. Secondly, (to quote Patton) ‘if everyone is thinking alike then no-one is thinking’. Once group-think is established ‘expectations’ become ossified, and the market is disconnected from reality.

Robert’s notion of cohesion is “global politically federated, yet culturally diverse”. One can see how in 2008 and currently in the EU (and North Africa and elsewhere) de jure and de-facto regulatory structures change, consistent with Robert’s view. But according to Keynes this is a response to an actual or potential crisis, rather than a causative factor. One can have a chain of  crises in which political change leads to emergent social or economic problems, leading to political change and so-on. Robert seems to suppose that this must settle down into some stable federation. If so then perhaps only the core principles will be stable, and even these might need to be continually reinterpreted and refreshed, much as I have tried to do here.

On a more conceptual note, Robert has the qualifies the conclusion with “The evidence from all of the fields considered in this text suggests …”.  But the conclusion could only be formally sustained by an argument employing induction. Now, if improved communications is really going to change the world so much then it will undermine the basis of any induction. (In Whitehead’s terms, induction only works with an epoch but here the epoch is changed.) The best one could say would be that on current trends a move towards greater cohesion appears inevitable. This is a more fundamental problem than only considering evidence from a limited range of fields. More evidence from more fields could not overcome this problem.

Dave Marsay

GLS Shackle, imagined and deemed possible?

Background

This is a personal view of GLS Shackle’s uncertainty. Having previously used Keynes’ approach to identify possible failure modes in systems, including financial systems (in the run-up to the collapse of the tech bubble), I became concerned  in 2007 that there was another bubble with a potential for a Keynes-type  25% drop in equities, constituting a ‘crisis’. In discussions with government advisers I first came across Shackle. The differences between him and Keynes were emphasised. I tried, but failed to make sense of Shackle, so that I could form my own view, but failed. Unfinished business.

Since the crash of 2008 there have been various attempts to compare and contrast Shackle and Keynes, and others. Here I imagine a solution to the conundrum which I deem possible: unless you know different?

Imagined Shackle

Technically, Shackle seems to focus on the wickeder aspects of uncertainty, to seek to explain them and their significance to economists and politicians, and to advise on how to deal with them. Keynes provides a more academic view, covering all kinds of uncertainty, contrasting tame probabilities with wicked uncertainties, helping us to understand both in a language that is better placed to survive the passage of time and the interpretation by a wider – if more technically aware – audience.

Politically, Shackle lacks the baggage of Lord Keynes, whose image has been tarnished by the misuse of the term ‘Keynesian’. (Like Keynes, I am not a Keynesian.)

Conventional probability theory would make sense if the world was a complicated randomizing machine, so that one has ‘the law of large numbers’: that in the long run particular events will tend to occur with some characteristic, stable, frequency. Thus in principle it would be possible to learn the frequency of events, such that reasonably rare events would be about as rare as we expect them to be. Taleb has pointed out that we can never learn the frequencies of very rare events, and that this is a technical flaw in many accounts of probability theory, which fail to point this out. But Keynes and Shackle have more radical concerns.

If we think of the world as a complicated randomizing machine, then as in Whitehead, it is one which can suddenly change. Shackle’s approach, in so far as I understand it, is to be open to the possibility of a change, recognize when the evidence of a change is overwhelming, and to react to it. This is an important difference for the conventional approach, in which all inference is done on the assumptions that the machine is known. Any evidence that it may have change is simply normalised away. Shackle’s approach is clearly superior in all those situations where substantive change can occur.

Shackle terms decisions about a possibly changing world ‘critical’. He makes the point that the application of a predetermined strategy or habit is not a decision proper: all ‘real’ decisions are critical in that they make a lasting difference to the situation. Thus one has strategies for situations that one expects to repeat, and makes decisions about situations that one is trying to ‘move on’. This seems a useful distinction.

Shackle’s approach to critical decisions is to imagine potential changes to new behaviours, to assess them and then to choose between those deemed possible. This is based on preference not expected utility, because ‘probability’ does not make sense. He gives an example of  a French guard at the time of the revolution who can either give access to a key prisoner or not. He expects to lose his life if he makes the wrong decision, depending on whether the revolution succeeds or not. A conventional approach would be based on the realisation that most attempted revolutions fail. But his choice may have a big impact on whether or not the revolution succeeds. So Shackle advocates imagining the two possible outcomes and their impact on him, and then making a choice. This seems reasonable. The situation is one of choice, not probability.

Keynes can support Shackle’s reasoning. But he also supports other types of wicked uncertainty. Firstly, it is not always the case that a change is ‘out of the blue’. One may not be able to predict when the change will come, but it is sometimes possible to see that there is an economic bubble, and the French guard probably had some indications that he was living in extraordinary times. Thus Keynes goes beyond Shackle’s pragmatism.

In reality, there is no strict dualism between probabilistic behaviour and chaos, between probability and Shackle’s complete ignorance. There are regions in-between that Keynes helps explore. For example, the French guard is not faced with a strictly probabilistic situation, but could usefully think in terms of probabilities conditioned on his actions. In economics, one might usefully think of outcomes as conditioned on the survival of conventions and institutions (October 2011).

I also have a clearer view why consideration of Shackle led to the rise in behavioural economics: if one is ‘being open’ and ‘imagining’ then psychology is clearly important. On the other hand, much of behavioral economics seems to use conventional rationality as some form of ‘gold standard’ for reasoning under uncertainty, and to consider departures from it as a ‘bias’.  But then I don’t understand that either!

Addendum

(Feb 2012, after Blue’s comments.)

I have often noticed that decision-takers and their advisers have different views about how to tackle uncertainty, with decision-takers focusing on the non-probabilistic aspects while their advisers (e.g. scientists or at least scientifically trained) tend to, and may even insist on, treating the problem probabilistically, and hence have radically different approaches to problem-solving. Perhaps the situation is crucial for the decision-taker, but routine for the adviser? (‘The agency problem.’) (Econophysics seems to suffer from this.)

I can see how Shackle had much that was potentially helpful in the run-up to the financial crash. But it seems to me no surprise that the neoclassical mainstream was unmoved by it. They didn’t regard the situation as crucial, and didn’t imagine or deem possible a crash. Unless anyone knows different, there seems to be nothing in Shackle’s key ideas that provide as explicit a warning as Keynes. While Shackle was more acceptable that Keynes (lacking the ‘Keynesian’ label) he also still seems less to the point. One needs both together.

See Also

Prigogine , who provides models of systems that can suddenly change ‘become’. He also  relates to Shackle’s discussion on how making decisions relates to the notion of ‘time’.

Dave Marsay

Induction, novelty and possibilistic causality

The concept of induction normally bundles together a number of stages, of which the key ones are modelling and extrapolating. Here I speculatively consider causality through the ‘lens’ of induction.

If I perform induction and what is subsequently observed fits the extrapolation then, in a sense, there is no novelty. If what happened was part of an epoch where things fit the model, then the epoch has not ended. I only need to adjust some parameter within the model that is supposed to vary with time.  In this case I can say that conformance to the model (with the value of its variables) could have caused the observed behaviour. That is, any notion of causality is entailed by the model. If we consider modelling and extrapolation as flow, then what happens seems to be flowing within the epoch. The general model (with some ‘slack’ in its variables) describes a tendency for change, that can be described as a field (as Smuts does).

As with the interpretation of induction, we have to be careful. There may be multiple inconsistent models and hence multiple inconsistent possible causes. For example, an aircraft plot may fit both civil and military aircraft, which may heading for different airports. Similarly, we often need to make assumptions to make the data fit the model, so different assumptions can lead to different models. For example, if an aircraft suddenly loses height we may assume that it had received an instruction, or that it is in trouble. These would lead to different extrapolations. As with induction, we neglect the caveats at our peril.

We can distinguish the following types of ‘surprise’:

  1. Where sometimes rare events happen within an epoch, without affecting the epoch. (Like an aircraft being struck by lightning, harmlessly.)
  2. Where the induction was only possibilistic, one of which predictions actually occurred. (Where one predicts that at least one aircraft will manoeuvre to avoid a collision, or there will be a crash.) 
  3. Where induction shows that the epoch has become self-defeating. (As when a period aircraft flying straight and level has to be ended to avoid a crash – which would end the epoch anyway).
  4. Where the epoch is ended by external events. (As when air traffic control fails.)

These all distinguish between different types of ’cause’. Sometimes two or more types may act together. (For example, when two airplanes crash together, the ’cause’ usually involves both planes and air traffic control. Similarly, if a radar is tracking an aircraft flying straight and level, we can say that the current location of the aircraft is ’caused by’ the laws of physics, the steady hand of the pilot, and the continued availability of fuel etc. But in a sense it also ’caused by’ not having been shot down.)

If the epoch appears to have continued then a part of the cause is the lack of all those things that could have ended it.  If the epoch appears to have ended then we may have no model or only a very partial model for what happens. If we have a fuller model we can use that to explain what happened and hence to describe ‘the cause’. But with a partial model we may only be able to put constraints on what happened in a very vague way. (For example, if we launch a rocket we may say what caused it to reach its intended target, but if it misbehaves we could only say that it will end up somewhere in quite a large zone, and we may be able to say what caused it to fail but not what caused it to land where it did. Rockets are designed to operate within the bounds of what is understood: if they fail ‘interesting’ things can happen.) Thus we may not always be able to give a possible cause for the event of interest, but would hope to be able to say something helpful.

In so far as we can talk about causes, we are talking about the result of applying a theory / model / hypothesis that fits the data. The use of the word ’cause’ is thus a short-hand for the situation where the relevant theory is understood.

Any attempt to draw conclusions from data involves modelling, and the effectiveness of induction feeds back into the modelling process, fitting some hypotheses while violating others. The term ’cause’ is suggestive that this process is mature and reliable. Its use thus tends to go with a pragmatic approach. Otherwise one should be aware of the inevitable uncertainties. To say that X [possibly] causes Y is simply to say that one’s experience to date fits X causes Y, subject to certain assumptions. It may not be sensible to rely on this, for example where you are in an adversarial situation and your opponent has a broader range of relevant experience than you, or where you are using your notion of causality to influence something that may be counter-adapting. Any notion of causality is just a theory. Thus it seems quite proper for physicists to seek to redefine causality in order to cope with Quantum Physics.

Dave Marsay

All watched over by machines of loving grace

What?

An Adam Curtis documentary shown on the BBC May/June 2011.

Comment

The trailers (above link) give a good feel for the series, which is entertaining, with some good video, music, pseudo-history and comment. The details shouldn’t be taken too seriously, but it is thought-provoking, on some topics that need thought.

Thoughts

The series ends:

The idea that human beings are helpless chunks of hardware controlled by software programs written in their genetic codes [remains powerfully influential in our society]. The question is, have we embraced that idea because it is a comfort in a world where everything that we do, either good or bad, seems to have terrible unforeseen consequences? …

We have embraced a fatalistic philosophy of us as helpless computing machines, to both excuse and explain our political failure to change the world.

This thesis has three parts:

  1. that everything we do has terrible unforeseen consequences
  2. that we are fatalistic in the face of such uncertainty
  3. that we have adopted a machine metaphor as ‘cover’ for our fatalism.

Uncertainty

The program demonizes unforeseen consequences. Certainly we should be troubled by them, and their implications for rationalism and pragmatism. But if there were no uncertainties then we could be rational and ‘should’ behave like machines. Reasoning in a complex, dynamic world calls for more than narrowly rational machine-like calculation, and gives purpose to being human.

Fatalism

It seems reasonable to suppose that most of the time most people can do little to influence the factors that shape their lives, but I think this is true even when people can perfectly well see the likely consequences of what is being done in their name. What is at issue here is not so much ordinary fatalism, which seems justified, as the charge that those who are making big decisions on our behalf are also fatalistic.

In democracies, no-one makes a free decision anymore. Everyone is held accountable and expected to abide by generally accepted norms and procedures. In principle whenever one has a novel situation the extant rules should be at least briefly reviewed, lest they lead to ‘unforseen consequences’. A fatalist would presumably not do this. Perhaps the failure, then, is not to challenge assumptions or ‘kick against’ constraints.

The machine metaphor

Computers and mathematicians played a big role in the documentary. Humans are seen as being programmed by a genetic code that has evolved to self-replicate. But evolution leads to ‘punctuated equilibrium’ and epochs.  Reasoning in epochs is not like reasoning in stable situations, the preserve of rule-driven machines. The mathematics of Whitehead and Turing supports the machine-metaphor, but only within an epoch. How would a genetically programmed person fare if they move to a different culture or had to cope with new technologies radically transforming their daily lives? One might suppose that we are encoded for ‘general ways of living and learning’ but then that we seem to require a grasp of uncertainty beyond that which we currently associate with machines.

Notes

  • The program had a discussion on altruism and other traits in which behaviours might disbenefit the individual but advantage those who are genetically similar over others. This would seem to justify much terrorism and even suicide-bombing. The machine metaphor would seem undesirable for reasons other than its tendency to fatalism.
  • An alternative to absolute fatalism would be fatalism about long-term consequences. This would lead to a short-term-ism that might provide a better explanation for real-world events
  • The financial crash of 2007/8 was preceded by a kind of fatalism, in that it was supposed that free markets could never crash. This was associated with machine trading, but neither a belief in the machine metaphor nor a fear of unintended consequences seems to have been at the root of the problem. A belief in the potency of markets was perhaps reasonable (in the short term) once the high-tech bubble had burst. The problem seems to be that people got hooked on the bubble drug, and went into denial.
  • Mathematicians came in for some implicit criticism in the program. But the only subject of mathematics is mathematics. In applying mathematics to real systems the error is surely in substituting myth for science. If some people mis-use mathematics, the mathematics is no more at fault than their pencils. (Although maybe mathematicians ought to be more vigorous in uncovering abuse, rather than just doing mathematics.)

Conclusion

Entertaining, thought-provoking.

Dave Marsay

Good Inferences from Utterances?

The problem of interpretation

What people say isn’t necessarily literally true. On the other hand, we may be able to deduce more from what people say than its literal content, even where that content is true. This is something of an open problem in, for example, human-machine interaction or human-trained human interaction.

A Good approach?

Here I speculate that we could simply treat utterances as events to be interpreted, rather than try to develop any special theory. I start with the approach of Keynes as developed by Turing and Good. At its simplest, in a context C we believe that if a hypothetical state H obtained we would have a likelihood P(E|H:C) of an evidential state E. In a deterministic situation this will be 1 for a unique E. The inverse will be a set of possible H. For convenience, we normally encapsulate these into a single, canonical, conjunction. The probabilistic and possibilistic cases are similar.

The interpretation of utterances can thus be broken into two parts:

  1. What is the context?
  2. What are they likely to say for different hypothetical situations within that context?

For humans we can analyse these further: what is their culture and role? what are they attending to? … There seems not to be any need to develop any novel theories or mechanisms.

Probability

When someone says ‘X, with probability 1’, it is commonplace to think that we may be justified in supposing that X holds with probability 1, particularly when the source is authoritative or trusted.

Yet suppose that the source is an academic with little experience of the real-world situation to which X pertains, based on a somewhat artificial experiment. Then all the statement  can mean is that the academic has not been able to conceive of a situation in which X is not probably true. But we, having regard to the academic’s lack of experience, might not regard X as probably true. If we are advising someone else who might have been mislead by the statement, a good comment would be to describe a possibility for which X might not be true; even better if X seems probably false.

Reflexivity

If we believe that others interpret our utterances using an interpretation process I(•:C) then if we want them to believe H we should utter some U such that I(U:C) = H, an inverse problem. More generally, we may say whatever is likely to lead to them believing H. Thus the utterance and interpretation processes depend reflexively on each other,. If they are uncertain then one has what Keynes calls reflexive probability, as in-house prices where the more people expect the price to go up, the more it does, fueling further expectations.

If utterance and interpretation are seen as enduring habits (not just one-offs) then they are strategies and there is a game-theory like relationship between them. But none of this is any different from the problem of entities who interact via other actions. Since overt actions and utterances often go together (as in ‘look at that’) it seems reasonable to treat them uniformly.

Notes

It is not implied that people actually do think like this, or that this is consistent with how people think they think. For example, people may have a unconcious emotionally reaction which determines whether they take others literally, cautiously or suspiciously. All that is claimed is that this approach will be a ‘yardstick’, showing the best that could be done.

Contexts

A context has to contain anything that might influence utterances and interpretations. It may be ‘socially constructed’, as when a meeting room is arranged subliminally to indicate the likely tone of the meeting. The context does not need to be naively or explainably ‘real’.

Implications

Some current interest is in ‘theories of mind’, which seems to introduce new complexities over and above Good’s account, for example. But we could just include an account of the ongoing social and inter-personal interactions in the context, and our theory about how the interlocutor reacts to the context into the likelihood function. The result may not be very good account of how people do actually interpret situations,  but of how they ‘should’.

For example, if we ‘share a context’ and there is no reason to doubt someone, we may normally take their words literally. If a specialist draws our attention to something within his specialism, we do not necessarily suppose that it is the most important thing that we need to attend to. If a native person says that they see big silver birds flying high, we consider other possibilities. If an adversary calls our attention to one thing, we might also look elsewhere, and so on.

Examples

‘Your cheque is in the post’, ‘Does my bum look big in this?’. Such utterances are not always intended to be taken literally, and perhaps neither is our reply. I think at least some people imagine the possible situations that may have given rise  to such utterances, and either seek to narrow down the options or hedge across them, without necessarily considering themselves to be illogical or dishonest.

Alternatives

The New Scientist (3 December 2011) has an article ‘Time to think like a computer’ or ‘Do thoughts have a language of their own?’ (On-line). This claims that we do not treat statements using ‘traditional logic’ but that what we do is more like ‘computational logic’. This latter logic is not defined, but Prolog is given as an example.

My view is that we can apply ‘traditional logic’ as long as we treat an utterance as an utterance, as is done here, and not as a ‘fact’. Computational logic, in my experience, is best regarded as a framework for developing specific logics. The article mentions default logics. If we think that someone is in a situation where particular default assumptions would be appropriate, then we would naturally employ default reasoning as a special case of the ‘good’ approach. But the good approach is clearly much more general.

The article has this example:
   If Mary has an essay to write, then she will study late in the library.
   Mary has an essay to write.

This look like ‘modus ponens’, from which we ‘should’ conclude that Mary will study late in the library. Actually, we will probably have a few caveats, which can be explained in a variety of ways. In the article it is now said that:
If the library is open, then Mary will study late in the library.

As the article says, taking this literally implies that Mary will study late even when she has no essay to write. To get around this problem the article proposes that there is a separate ‘language of thought’. This language  is not specified, but seems to include default reasoning. But it seems to me that the example is just the kind of ‘bad logic’ that many people use much of the time, and that – knowing that – we can generally decode it using traditional logic, but treating statements as data, not ‘facts’.

Conclusion

We can conceptualize our thinking about acting and re-acting as part of a generic problem of interaction, perhaps drawing on ideas about evolutionary learning in games. Our understanding of particular actors (e.g., humans) then determines what we think is relevant within contexts, and how this may influence actors.

The advantage over a more customised approach would be:

  • includes all types of activity, in conjunction
  • can draw on insights from these other areas
  • can be theoretically underpinned, and so be less ad-hoc
  • by treating ‘models of mind’ as a variable, is less likely to be culturally specific
  • it may be more fruitful in suggesting likely variations in ‘style’.

This is speculative.

See also

Thomas McCarthy, Translator’s Introduction to Habermas, Legitimation crisis, Heinemann 1976:

According to Habermas a smoothly functioning language game rests on a background consensus formed from the mutual recognition of at least four different types of validity claims … that are involved in the exchange of speech acts:

  1. claims that the utterance is understandable,
  2. that its propositional content is true,
  3. that the speaker is sincere in uttering it, and
  4. that it is right or appropriate for the speaker to be performing the speech act.

[It] is possible for one or more of them to become problematic in a fundamental way.

From the point of view of ‘Good’s approach’, it is sufficient that the context is sufficiently understood that the likelihoods P(E|H:C) are understood (1), for some set of hypotheses, {H}. Typically, a speaker cannot know that what they are saying is actually ‘true’ (2), but for a speaker to be sincere (3)  it should be the best hypothesis out of those that they have considered. It may be that the listener is considering a broader range of hypotheses, in which case the may know that the proposition is false, and yet it may still be useful.

Even in a situation where the speaker is motivated to lie, we may understand the situation (1),  regard the lie as ‘true to the situation’ and the regard the speaker as sincere and the act appropriate within that context (3, 4). Thus the key does seem to be understanding why they said what they said, and not understanding the apparent ‘content’ of the proposition.

David Marsay

Reasoning under uncertainty methods

In reasoning about or under uncertainty it is sometimes not enough to use the best method, or an accredited method: one needs to understand the limitations of method.

The limits of method

Strictly, rational reasoning implies that everything can be assigned a value and probability, so that the overall utility can me maximised. So when faced with greater uncertainties, the appearance of rationality can only achieved by faking it, which is not always effective.

Pragmatism is more general than rationalism. The key feature is that one uses a fixed model until it is no longer credible. But if the situation is complex or uncertain it may not be possible to use a definite model without making unwarranted assumptions.

Turing (a grand-student of Whitehead) demonstrated some of the limitations of definite methods more generally. We cannot be too restrictive in we consider to be ‘methodical’.

One approach to method is to link overall decisions to ‘objective’ sub-decisions, made by accredited specialist decision-makers. This relies on some conceptual linkage between the specialists and generalists, and between all collaborators on a decision. This can deal with complicatedness across specialisms and complexity and uncertainty within specialisms, in so far as they are understood across the specialisms.

The difficulty with this approach is that complexity and uncertainty often span the whole domain. One is thus left with the problem of handling complexity and uncertainty within a collaboration.

Conceptualization

It follows from the Conant-Ashby theorem that people who are good at dealing with complexity and uncertainty without having dominance must, in some sense, understand these topics, even if they have had no exposure to the relevant theories. This raises these questions:

  • How do we recognize people whose track records are such that we can be sure that they have the appropriate understanding, and weren’t reliant on others or lucky?
  • To what extent can is an understanding of complexity and uncertainty developed in one situation relevant to another? Are all complexities and uncertainties in some sense similar, or amenable to the same approaches?
  • How can such understanding and methods be communicated?

Way ahead?

The following have been found helpful in confrontation, crisis and conflict anticipation and management:

  • Developing the broadest possible theoretical base for complexity and uncertainty, using Keynes’ Treatise as a former.
  • Identifying and engaging as broadly and fully as possible with all parties to the situations (of whatever nationality etc) who show an understanding or ability to handle complexity and uncertainty.

More broadly, seeking to take an overview and engagement with practitioners who are engaged with the more challenging kinds of complexity and uncertainty, with the aim of developing practical aids to comprehension:

  • To assist those who are or may be engaged
  • To help develop understanding among those who could support those who are or may be engaged.
  • To help establish some common language etc so that the broadest possible community can have the fullest possible visibility and understanding of the process, and – where appropriate – involvement.

The core of all this would seem to be a set of resources that address complexity and uncertainty rather than complicatedness and probability, with understanding to be developed via collaborative ‘war-games’.

Pedagogic resources

The aids included in the following have proved helpful.

  • Peter Allen’s overview, allows an appreciation of most of the fields.
  • Everyday and other metaphors.
  • A Whitehall report on collaboration highlights complexity and uncertainty, including in the ‘collaborative partnership model’.
  • SMUTS, supporting exploration of key factors.

See Also

How much uncertainty?, HeuristicsKnightian uncertainty , Kant’s critique.

David Marsay

Pragmatism and mathematics

The dichotomy

Mathematics may be considered in two parts: that which is a tool supporting other disciplines in their modelling, which is considered pragmatic; and that which seeks to test underlying assumptions in methods and models, which is not so well appreciated.

Pragmatism and sustainability

Setting mathematics to one side for a moment, consider two courses of actions, S and P, with notional actual benefits as shown.

Boom and bust can be better in the short-term, but worse in the long.

Sure and steady may beat Boom and bust

‘Boom and bust’ arises when (as is usually the case) the strategy is ‘closed loop’, with activity being adjusted according to outcomes (e.g. Ashby). Even a sustainable strategy would be subject to statistical effects and hence cyclic variations, but these will be small compared with the crashes that can arise when the strategy is based on some wrong assumption (Conant-Ashby). If something happens that violates that assumption then one can expect performance to crash until the defect is remedied, when performance can again increase. In this sense, the boom-bust strategy is pragmatic.

If one has early warnings of potential crashes then it can also be pragmatic to incorporate the indicators into the model, thus switching to a safer strategy when things get risky. But, to be pragmatic, the model has to be based on earlier experience, including earlier crashes. Thus, pragmatically, one can avoid crashes that have similar causes to the old ones, but not novel crashes. This is a problem when one is in a complex situation, in which novelty is being continually generated. Indeed, if you are continually updating your model and ‘the environment’ is affected by your actions and the environment can innovate, then one is engaged in cyclic co-innovation and hence co-evolution. This is contrary to an implicit assumption of pragmatism, which seems (to me) to be that one has a fixed ‘external world’ that one is discovering, and hence one expects the process of learning to converge onto ‘the truth’, so that surprises become ever less frequent. (From a Cybernetic perspective in a reflexive situation ‘improvements’ to our strategy are likely to be met by improvements in the environmental response, so that in effect we are fighting our own shadow and driven to ever faster performance until we hit some fundamental limit of the environment to respond.)

Rationalising Pragmatism

The graph shows actual benefits. It is commonplace to discount future benefits. Even if you knew exactly what the outcomes would be, a heavy enough discounting would make the discounted return from the boom-bust strategy preferable to the sustainable one, so that initially one would follow boom-bust. As the possible crash looms the sustainable strategy might look better. However, the Cybernetic view (Conant-Ashby) is that a sustainable strategy would depend on an ‘eyes open’ view of the situation, its possibilities and the validity of our assumptions, and almost certainly on a ‘multi-model’ approach. This is bound to be more expensive than the pragmatic approach (hence the lower yield) and in practice requires considerable invest in areas that have no pragmatic value and considerable lead times. Thus it may be too late to switch before the crash.

In complex situations we cannot say when the crash is due, but only that a ‘bubble’ is building up. Typically, a bubble could pop at any time, the consequences getting worse as time goes on. Thus the risk increases. Being unable to predict the timing of a crash makes it less likely that a switch can be made ‘pragmatically’ even as the risk is getting enormous.

There is often also an argument that ‘the future is uncertain’ and hence one should focus on the short-run. The counter to this is that while the specifics of the future may be unknowable, we can be sure that our current model is not perfect and hence that a crash will come. Hence, we can be sure that we will need all those tools which are essential to cope with uncertainty, which according to pragmatism we do not need.

Thus one can see that many of our accounting habits imply that we would not choose a sustainable strategy even if we had identified one.

The impact of mathematics

Many well-respected professionals in quite a few different complex domains have commented to me that if they are in trouble the addition of a mathematician often makes things worse. The financial crash brought similar views to the fore. How can we make sense of this? Is mathematics really dangerous?

In relatively straightforward engineering, there is sometimes a need for support from mathematicians who can take their models and apply them to complicated situations. In Keynes’ sense, there is rarely any significant reflexivity. Thus we do believe that there are some fundamental laws of aerodynamics which we get ever closer to as we push the bounds of aeronautics. Much of the ‘physical world’ seems completely unresponsive to how we think of it. Thus the scientists and engineers have tended to ‘own’ the interesting problems, leaving the mathematicians to work out the details.

For complex situations there appear to be implicit assumptions embedded in science,  engineering and management (e.g. pragmatism) that are contrary to the mathematics. There would thus seem to be a natural (but suppressed) role for mathematics in trying to identify and question those assumptions. Part of that questioning would be to help identify the implications of the current model in contrast to other credible models and theories. Some of this activity would be identical to what mathematicians do in ‘working out the details’, but the context would be quite different. For example, a mathematician who ‘worked out the details’ and made the current model ‘blow up’ would be welcomed and rewarded as contributing to that ever developing understanding of the actual situation ‘as a whole’ that is necessary to sustainability.

Multi-models

It is conventional, as in pragmatism, to seek single models that give at least probabilistic predictions. Keynes showed that this was not credible for economics, and it is not a safe assumption to make for any complex system. This is an area where practice seems to be ahead of current mainstream theory. A variant on pragmatism would be to have a fixed set of models that one only changes when necessary, but the objections here still stand. One should always be seeking to test one’s models, and look for more.

It follows from Conant-Ashby that a sustainable strategy is a modelling strategy and that there will still be bubbles, but they will be dealt with as soon as possible. It may be possible to engineer a ‘soft landing’, but if not then a prediction of Conant-Ashby is that the better the model the better the performance. Thus one may have saw-tooth like boom and busts, but finer and with a more consistent upward trend. In practice, we may not be able to choose between two or more predictive models, and if the available data does not support such a choice, we need to ‘hedge’. We can either think of this as hedge across different conventional models or as a single unconventional model (such as advocated by Keynes). Either way, we might reasonably call it a ‘multi-model’. The best strategy that we have identified, then, is to maintain as good as possible a multi-model, and ‘hedge’.

If we think of modelling in terms of assumptions then, like Keynes, we end up with a graph-like structure of models, not just the side-by-side alternative of some multi-modelling approaches. We have a trade-off between models that are more precise (more assumptions) or those that are more robust(less assumptions) as well as ones that are simply different (different assumptions). If a model is violated we may be able to revert to a more general model that is still credible. Such general models in effect hedge over the range of credible assumptions. The trick is to invest in developing techniques for the more general case even when ‘everybody knows’ that the more specific case is true, and – if one is using the specific model – invest in indicators that will show when its assumptions are particularly vulnerable, as when a bubble is over-extended.

Duality

A traditional approach is to have two separate strands of activity. One – ‘engineering’ – applies a given model (or multi-model), the other – ‘science’ – seeks to maintain the model. This seems to work in complicated settings. However, in complex reflexive settings:

  • The activity of the engineers needs to be understood by the scientists, so they need to work closely together.
  • The scientists need to experiment, and hence interfere with the work of the engineers, with possible misunderstandings and dire consequences.
  • Im so far as the two groups are distinct, there is a need to encourage meaningful collaborations and manage the equities between their needs. (Neither ‘on top’ nor ‘on tap’.)

One can see that collaboration is inhibited if one group is pragmatic, the other not, and that pragmatism may win the day, leading to ‘pragmatic scientists’ and hence a corruption of what ought to be happening. (This is in addition to a consideration of the reward system.)

It may not be too fanciful to see signs of this in many areas.

The possible benefits of crashes

Churchill noted that economic crashes (of the cyclic kind) tended to clear out dead-wood and make people more realistic in their judgements, compared with the ‘good times’ when there would be a great deal of investment in things that turned out to be useless, or worse, when the crash came. From Keynes’ point of view much of the new investment in ‘good times’ are band-wagon investments, which cause the bubble which ought to be pricked.

We can take account of such views in two ways. Firstly if the apparent boom is false and the apparent crash is beneficial then we can take this into account in our measure of benefit, so that ‘boom’ becomes a period of flat or declining growth, the crash becomes a sudden awakening, which is beneficial, and the post-crash period becomes one of real growth. The problem then becomes how to avoid ‘bad’ band-wagons.

Either way, we want to identify and avoid fast growth that is ill-founded, i.e., based on an unsustainable assumption.

Conclusion

It is well recognized that mathematics is extremely powerful, and the price for that is that it is very sensitive: give it the slightest mis-direction and the result can be far from what was intended. Mathematics has made tremendous contributions to the complicated disciplines, and seems quite tame. In contrast, my experience is that for complex subjects the combination of mathematicians and numerate professionals is risky, and requires an enormous up-front investment in exchanging views, which sometimes can be nugatory. Perhaps there is some mis-direction? If so, where?

From my point of view, the problem often seems to be one of ‘scientism’. That is, certain types of method are characteristic of the complicated professions, and so people expect problems that are almost the some but complex to be addressed in the same sort of ways. Anything else would not be ‘proper science’. The mathematician, on the other hand, has the habit of rooting out assumptions, especially un-acknowledged ones, and seeking to validate them. If they can’t be then they would rather not make them. (A cynic might say that the other professionals want to work with the tools they are familiar with while the mathematician wants to develop an all-purpose tool  so that he can move on to something more interesting.)

Numerous headline failures tend to reinforce the mathematician in his view that other professionals profess certain beliefs, while he is uniquely equipped to be productively cynical. But here I focus on one belief: in pragmatism. Often, when pressed, people do not actually believe that their assumptions are literally true, only that they are ‘pragmatic’. But, as previously noted, the mixture of literal mathematics and conventional pragmatism is unsafe. But in my view mixtures of pragmatisms from different domains (without any ‘proper’ mathematics) seems to lie behind many headline problems. I have shown why pragmatism is inappropriate for solving complex problems and briefly sketched some reforms needed to make it ‘mathematics friendly’.

See Also

General approach, Sub-prime science, Weapons of Maths Destruction, Minsky moment.

Dave Marsay

Metaphors for complexity and uncertainty

Metaphors

According to psychologists we often tell ourselves stories to rationalize away complexity and uncertainty. It would be good to have some stories that reveal the complexity and uncertainty, as an antidote.

Route Planning and the Normandy Invasion

I noticed in the 80s (before SATNAV) that not everyone thinks of a common task like route-planning in the same way. Some are pragmatic, picking the best route and only considering alternatives if that one is blocked. Others have heuristics that allow for uncertainty, such as preferring routes that have ready detours, just in case. There was some discussion among geek-dom as to whether a pure Bayesian approach would be adequate or even better. Logically, it should depend on the nature of the problem. If blocks are probabilistic with learn-able distributions, and the goal is to minimise average journey times, then the assumptions of Bayes hold and hence it shouldn’t be possible to beat Bayes consistently.

One day I discovered that a friend of the family who had been strongly anti-Bayes had been involved in planning the D-day invasion, and I realised that here was a good example of a complex problem rich in uncertainties, showing the benefits of a more principled approach to uncertainty in planning. I published a brief paper (also here ), which may be helpful. It was almost a decade before I was faced with a planning situation similarly rich with uncertainty.

Navigation

Routine journeys can be thought of as a single entity, with the usual habits of driving to keep in lane and away from the car in front. If the road is blocked one may need to divert, calling for some navigation. The routine epoch is interrupted by ‘higher-level’ considerations. If one has always optimised for journey time one will never have explored the by-ways. If one occasionally uses alternative, slightly slower, routes, one will be in a better position to find a good alternative when you have to divert. Thus optimising for journey time when all goes well is at the expense of robustness: coping well with exceptional circumstances. (This is a form of the Boyd uncertainty principle.)

A more interesting ‘change of epoch’ occurred a few years back. An unprecedented police shoot-out on the M5 near Bristol caused chaos and was widely publicised. The next weekend my partner and I were about to drive down the same stretch of motorway when there were reports of a copy-cat shoot-out. Traffic jams over a large area were inevitable, but we thought that if we were quick enough and took a wide-enough loop around, we should be able to make it.

SAT-NAVs had only just become fairly common, and the previous weekend had shown up their weakness in this situation: everyone gets diverted the same way, so the SAT-NAV sends people into big queues, while others could divert around. This week-end most drivers knew that, and so we expected many to be taking wider detours. But how wide? Too narrow, and one gets into a jam. Too wide and one is too slow, and gets into jams at the far end. Thus the probability of a road actually being jammed depended on the extent to which drivers expected it to be jammed: an example of Keynes’ reflexive probability. It also an example where the existence of meaningful ‘prior probabilities’ is doubtful: the recent popularity of SAT-NAVs and the previous incident made any decision-making based on experience of dubious validity.

This is just the kind of situation for which some of my colleagues criticise ‘the mathematical approach’, so just to add to the fun I drive while my partner, who teaches ‘decision mathematics’ advised. Contrary to what some might have expected, we took a 100-mile right-hook detour, just getting through some choke points in the nick of time, thus having a lot more fun with only about a 20 minute delay from using the motorway. I noticed, though, that rather than use one of the standard decision mathematical methods she used the theory. I wonder if some of the criticisms of mathematics are when people apply a ‘mathematical’ method without considering the theory: that is not mathematics!  

Drunken walks

A man walks along the cliff edge to the pub most evenings. His partner will not let him go if it is too windy, or the forecast is poor. The landlord calls a taxi if it is too windy at closing time.

One night two walkers comment on how dangerous the walk along the cliff is. They are ignored. The drinker walks home and off the cliff.

The cliff had been unstable but had been buttressed. Some had questioned the reliability of the contractors used, but the local authorities had given assurances that the cliff was now stable. And yet the work had been poor and the cliff had collapsed, so that the drinker had followed the path to his death.

Games field

A man notices that different things are going on as he passes a games field. He decides that he can spend 10 hours over the next 10 years observing what is going on, in an attempt to work out ‘the rules of the game’. If spends 600 1 minute intervals selected at random from games over the 10 years, he may come to have a very good idea of what games are played when, but a poor idea of the rules of any one game. On the other hand if he observes the first 10 hours of play he may form a good view of the rules of the current game, but have no idea of how games are selected. This is an example of the organizational and entropic uncertainty principles, generalizations of Heisenberg’s better-known uncertainty principle.

Particle Physics

Quantum theories arose from a recognition of the limits of the classical view, and were developed by thinkers who corresponded with Whitehead and Smuts, for example, on general logical issues. The similarities can be seen in the Bohm interpretation, for example. Temporarily stable complexes interacting with and within stable fields have dynamics that follow stable rules until previously separate complexes come to interact, in which case one has a ‘collapse of the wave function’ and a discontinuity in the dynamics. These periods of relative homogenaity correspond to Whitehead’s epochs, and the mechanism for change is essentially Cybernetic. In this formalism particles have precise positions and momentum; uncertainty is measurement uncertainty.

The Bohm interpretation only applies when one has quantum equilibrium, so that higher-level epochs are fixed, and consequential changes bounded. Otherwise one has greater uncertainty. 

Quantum Cognition

 Quantum cognition notices certain ‘irrationalities’ about human cognition, and proposes a model ‘inspired by’ quantum mechanics. It is mentioned here because the inspiration seems sound, even if the details are questionable.

Under categorization-decision it notes that asking about a relevant factor can affect categorization. This seems reasonable, as it affects the context.

Under memory-process disassociation it notes that people are more likely to recognize that something had been seen on a list if they were asked about a specific list. Taking this to extremes, people may be more likely to recognize that they have met someone at some conference if a specific conference is named. This seems reasonable. Unpacking effects is similar. The questions in conceptual combinations are similar, but the contexts and results quite different.

Under the Linda problem it notes mis-ordering of probabilities in a context where probability would be hard to judge and possibly discriminatory. Respondents may have reported likelihoods instead: the two are often confused. This would be a ‘representativeness type mechanism’.

There seem to be two things going on here: the experimental subjects might not be good at estimating, and the experimenter might not be very good at analysis. Quantum probability appears to be an attempt to avoid:

  • Problems that arise when the analyst ignores the conditionality of probabilities. 
  • Problems that arise when experimental settings or terminology (e.g. probability and likelihood) are confused.
  • Variation of performance with ‘focus’, such as when a specific list is mentioned.

Quantum probability seems to be a heuristic that gives a more moderate result, thus compensating for the above effects. It seems more natural to take account of them more directly and specifically.

Anyone?

Dave Marsay

Fat tails and Epochs

Different explanations of the crash of 2007/8

The term ‘fat tails’ has been much in evidence since the crash of 2007/8. Nicholas Taleb had been warning that statistical tails were fat and of its significance, and the term has since been taken up to explain the crash.

There has also been a revival in references to Keynes and some references (e.g. by Gordon Brown) to Whitehead’s notion of epochs. Both are often seen as alternatives to the previously fashionable ‘sophisticated mathematics’ slated in the Turner Review.

Implications of fat-tails

From a mathematical view these alternative explanations are quite different. If the crash was due to a ‘fat tail’ then the problem was that it’s probability had been under-estimated. A variant of the ‘fat-tail’ notion is the one-sided fat tail. Here sample statistics tend to seriously underestimate the probability of occurrence for quite long periods, followed by an erratic ‘correction’. Thus competitive pressure favours those who optimise in the short-run, but (unless bailed out) crashes weed them out, leaving those who had carried some ‘fat’. The solution to ‘fat tails’ is to fatten up one’s body. Similarly, in evolutionary systems we would expect to see systems that are not too optimised. If one only has a fat-tail then after the event the distribution is unchanged and – assuming that the event has been survived – the best thing to do is supposedly to update the estimated probability distribution and carry on as before. This is William James’ ‘pragmatic’ approach. Even if one is aware of fat tails the best strategy might be to optimise like everyone else (to stay in the game), cope with the crisis as best one can, and then learn what one can and carry on.

Implications of epochs

The Keynes, Whitehead and Smuts view is quite different. It incorporates a different view of evolution. It informed a different management style (not particularly well documented). It was based on a different view of logic and uncertainty. It had profound impact on Keynes’ view of economics.

All observations relate to some epoch. Empirical predictions are only really extrapolations, conditional on the epoch not changing. A given epoch has characteristic behaviours. The assumption that an epoch will endure entails assumptions about those behaviours. Within an epoch one typically has distributions, which may have fat tails. Some, but not all, fat-tail events may destabilise the epoch. Thus, from this view, fat-tail events are a problem. But external events can also destabilise an epoch, leading to a change in ‘the rules of the game’.

Thus match-fixing in cricket may lead to a new epoch in the way cricket is organised. But match-fixing in rugby could also lead to a change in the way cricket is organised. If the match-fixing had been rife, one may see a significant, enduring, shift in the statistics, rather than a ‘blip’.

Distinctions

The term ‘fat-tail’ seems to be being used to indicate any shocking event (some refer to Shackle). But the term ‘fat-tail’ implies that events were probabilistic, the problem being that low-probability is not the same as no probability. The term ‘epoch’ indicates that the rules have changed, for example an assumption was violated. Thus the terms might be used to complement each other rather than using ‘fat-tail’ as a portmanteau term. ‘Shock’ would seem a suitable less precise term.

Distinctions needed?

A further problem is that in the epochs of interest the assumptions of probability theory do not necessarily hold (e.g., see Turner) so perhaps we need a different term. What are the important distinctions? Maybe we need to distinguish between:

  • Surprises that do not change our view of what may happen in the future, only of what has happened.
  • Surprises that change our view of what may happen, but which are not evidence of a fundamental change in the situation (just our view of it) and may not cause one.
  • Surprises that are not evidence of a fundamental change having actually occurred already, but which may lead to one.
  • Surprises that suggest a fundamental change in the actual situation.

Thus, for small investors, a changing view of the market does not change the market, but en mass may lead to a change. It seems inevitable that any terminology would need to address appropriate concepts of ‘causality’.

Suggestions?

Dave Marsay

Evolution and Uncertainty

The New Scientist of 29 Jan 2011 (Issue 2797) has an article by Midgley (already blogged in ‘Evolution and epochs’ ) and ‘I, algorithm’. The latter shows how ‘old AI’ can be improved by combining it with probabilistic reasoning. The model that it uses is of numeric probability distributions. Is this enough to be able to represent the evolutionary behaviour described by Midgley, or the Knightian uncertainty of financial crashes? Or is it another example of a limited metaphor ‘hijacking our thinking’?

Keynes (Treatise on Probability) and Smuts (Holism and Evolution) both built on Whitehead’s notion of epochs, claiming that ‘common sense’ probabilistic reasoning was too limited. Or have I missed some advance?

Dave Marsay

See also

Reasoning in a complex world

Evolution and epochs

In common usage, the term evolutionary suggests gradual. As Darwin observed, common sense would suggest that species should develop minor differences before the major ones. But this is the opposite of what is seen in the fossil record of the Cambrian explosion. But if we treat evolution as a special case of Whitehead’s logic, as in  JC Smuts’ ‘Holism and Evolution’, then species are epochs, and hence one expects major changes to lead to further minor speciation. (Speculation.) This has implications for ‘Social Darwinism’, as in Mary Midgley’s ‘The selfish metaphor’, New Scientist.

See also

Mathematics and real system, Cybernetics and epochs,