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

 

 

Heuristics or Algorithms: Confused?

The Editor of the New Scientist (Vol. 3176, 5 May 2018, Letters, p54) opined in response to Adrian Bowyer ‘swish to distinguish between ‘heuristics’ and ‘algorithms’ in AI that:

This distinction is no longer widely made by practitioners of the craft, and we have to follow language as it is used, even when it loses precision.

Sadly, I have to accept that AI folk tend to consistently fail to respect a widely held distinction, but it seems odd that their failure has led to an obligation on the New Scientist – which has a much broader readership than just AI folk. I would agree that in addressing audiences that include significant sectors that fail to make some distinction, we need to be aware of the fact, but if the distinction is relevant – as Bowyer argues, surely we should explain it.

According to the freedictionary:

Heuristic: adj 1. Of or relating to a usually speculative formulation serving as a guide in the investigation or solution of a problem.

Algorithm: n: A finite set of unambiguous instructions that, given some set of initial conditions, can be performed in a prescribed sequence to achieve a certain goal and that has a recognizable set of end conditions.

It even also this quote:

heuristic: of or relating to or using a general formulation that serves to guide investigation  algorithmic – of or relating to or having the characteristics of an algorithm.

But perhaps this is not clear?

AI practitioners routinely apply algorithms as heuristics in the same way that a bridge designer may routinely use a computer program. We might reasonably regard a bridge-designing app as good if it correctly implements best practice in  bridge-building, but this is not to say that a bridge designed using it would necessarily be safe, particularly if it is has significant novelties (as in London’s wobbly bridge).

Thus any app (or other process) has two sides: as an algorithm and as a heuristic. As an algorithm we ask if it meets its concrete goals. As a heuristic we ask if it solves a real-world problem. Thus a process for identifying some kind of undesirable would be regarded as good algorithmically if it conformed to our idea of the undesirables, but may still be poor heuristically. In particular, good AI would seem to depend on someone understand at least the factors involved in the problem. This may not always be the case, no matter how ‘mathematically sophisticated’ the algorithms involved.

Perhaps you could improve on this attempted explanation?

Dave Marsay

Artificial Intelligence?

The subject of ‘Artificial Intelligence’ (AI) has long provided ample scope for long and inconclusive debates. Wikipedia seems to have settled on a view, that we may take as straw-man:

Every aspect of learning or any other feature of intelligence can be so precisely described that a machine can be made to simulate it. [Dartmouth Conference, 1956] The appropriately programmed computer with the right inputs and outputs would thereby have a mind in exactly the same sense human beings have minds. [John Searle’s straw-man hypothesis]

Readers of my blog will realise that I agree with Searle that his hypothesis is wrong, but for different reasons. It seems to me that mainstream AI (mAI) is about being able to take instruction. This is a part of learning, but by no means all. Thus – I claim – mAI is about a sub-set of intelligence. In many organisational settings it may be that sub-set which the organisation values. It may even be that an AI that ‘thought for itself’ would be a danger. For example, in old discussions about whether or not some type of AI could ever act as a G.P. (General Practitioner – first line doctor) the underlying issue has been whether G.P.s ‘should’ think for themselves, or just apply their trained responses. My own experience is that sometimes G.P.s doubt the applicability of what they have been taught, and that sometimes this is ‘a good thing’. In effect, we sometimes want to train people, or otherwise arrange for them to react in predictable ways, as if they were machines. mAI can create better machines, and thus has many key roles to play. But between mAI and ‘superhuman intelligence’  there seems to be an important gap: the kind of intelligence that makes us human. Can machines display such intelligence? (Can people, in organisations that treat them like machines?)

One successful mainstream approach to AI is to work with probabilities, such a P(A|B) (‘the probability of A given B’), making extensive use of Bayes’ rule, and such an approach is sometimes thought to be ‘logical’, ‘mathematical, ‘statistical’ and ‘scientific’. But, mathematically, we can generalise the approach by taking account of some context, C, using Jack Good’s notation P(A|B:C) (‘the probability of A given B, in the context C’). AI that is explicitly or implicitly statistical is more successful when it operates within a definite fixed context, C, for which the appropriate probabilities are (at least approximately) well-defined and stable. For example, training within an organisation will typically seek to enable staff (or machines) to characterise their job sufficiently well for it to become routine. In practice ‘AI’-based machines often show a little intelligence beyond that described above: they will monitor the situation and ‘raise an exception’ when the situation is too far outside what it ‘expects’. But this just points to the need for a superior intelligence to resolve the situation. Here I present some thoughts.

When we state ‘P(A|B)=p’ we are often not just asserting the probability relationship: it is usually implicit that ‘B’ is the appropriate condition to consider if we are interested in ‘A’. Contemporary mAI usually takes the conditions a given, and computes ‘target’ probabilities from given probabilities. Whilst this requires a kind of intelligence, it seems to me that humans will sometimes also revise the conditions being considered, and this requires a different type of intelligence (not just the ability to apply Bayes’ rule). For example, astronomers who refine the value of relevant parameters are displaying some intelligence and are ‘doing science’, but those first in the field, who determined which parameters are relevant employed a different kind of intelligence and were doing a different kind of science. What we need, at least, is an appropriate way of interpreting and computing ‘probability’ to support this enhanced intelligence.

The notions of Whitehead, Keynes, Russell, Turing and Good seem to me a good start, albeit they need explaining better – hence this blog. Maybe an example is economics. The notion of probability routinely used would be appropriate if we were certain about some fundamental assumptions. But are we? At least we should realise that it is not logical to attempt to justify those assumptions by reasoning using concepts that implicitly rely on them.

Dave Marsay

Traffic bunching

In heavy traffic, such as on motorways in rush-hour, there is often oscillation in speed and there can even be mysterious ’emergent’ halts. The use of variable speed limits can result in everyone getting along a given stretch of road quicker.

Soros (worth reading) has written an article that suggests that this is all to do with the humanity and ‘thinking’ of the drivers, and that something similar is the case for economic and financial booms and busts. This might seem to indicate that ‘mathematical models’ were a part of our problems, not solutions. So I suggest the following thought experiment:

Suppose a huge number of  identical driverless cars with deterministic control functions all try to go along the same road, seeking to optimise performance in terms of ‘progress’ and fuel economy. Will they necessarily succeed, or might there be some ‘tragedy of the commons’ that can only be resolved by some overall regulation? What are the critical factors? Is the nature of the ‘brains’ one of them?

Are these problems the preserve of psychologists, or does mathematics have anything useful to say?

Dave Marsay

Risks to scientists from mis-predictions

The recent conviction of six seismologists and a public official for reassuring the public about the risk of an earthquake when there turned out to be one raises many issues, mostly legal, but I want to focus on the scientific aspects, specifically the assessment and communication of uncertainty.

A recent paper by O’Hagan  notes that there is “wide recognition that the appropriate representation for expert judgements of uncertainty is as a probability distribution for the unknown quantity of interest …”.  This conflicts with UK best practice, as described by Spiegelhalter at understanding uncertainty. My own views have been formed by experience of potential and actual crises where evaluation of uncertainty played a key role.

From a mathematical perspective, probability theory is a well-grounded theory depending on certain axioms. There are plausible arguments that these axioms are often satisfied, but these arguments are empirical and hence should be considered at best as scientific rather than mathematical or ‘universally true’.  O’Hagan’s arguments, for example, start from the assumption that uncertainty is nothing but a number, ignoring Spiegelhalter’s ‘Knightian uncertainty‘.

Thus, it seems to me, that where there are rare critical decisions with a lack of evidence to support a belief in the axioms, one should recognize the attendant non-probabilistic uncertainty, and that failure to do so is a serious error, meriting some censure. In practice, one needs relevant guidance such as the UK is developing, interpreted for specific areas such as seismology. This should provide both guidance (such as that at understanding uncertainty) to scientists and material to be used in communicating risk to the public, preferably with some legal status. But what should such guidance be? Spiegelhalter’s is a good start, but needs developing.

My own view is that one should have standard techniques that can put reasonable bounds on probabilities, so that one has something that is relatively well peer-reviewed, ‘authorised’ and ‘scientific’ to inform critical decisions. But in applying any methods one should recognize any assumptions that have been made to support the use of those methods, and highlight them. Thus one may say that according to the usual methods, ‘the probability is p’, but that there are various named factors that lead you to suppose that the ‘true risk’ may be significantly higher (or lower). But is this enough?

Some involved in crisis management have noted that scientists generally seem to underestimate risk. If so, then even the above approach (and the similar approach of understanding uncertainty) could tend to understate risk. So do scientists tend to understate the risks pertaining to crises, and why?

It seems to me that one cannot be definitive about this, since there are, from a statistical perspective – thankfully – very few crises or even near-crises. But my impression is that could be something in it. Why?

As at Aquila, human and organisational factors seem to play a role, so that some answers seem to need more justification that others. Any ‘standard techniques’ would need take account of these tendancies. For example, I have often said that the key to good advice is to have a good customer, who desires an adequate answer – whatever it is – who fully appreciates the dangers of misunderstanding arising, and is prepared to invest the time in ensuring adequate communication. This often requires debate and perhaps role-playing, prior to any crisis. This was not achieved at Aquila. But is even this enough?

Here I speculate even more. In my own work, it seems to me that where a quantity such as P(A|B) is required and scientists/statisticians only have a good estimate of P(A|B’) for some B’ that is more general than B, then P(A|B’) will be taken as ‘the scientific’ estimate for P(A|B). This is so common that it seems to be a ‘rule of pragmatic inference’, albeit one that seems to be unsupported by the kind of arguments that O’Hagan supports. My own experience is that it can seriously underestimate P(A|B).

The facts of the Aquila case are not clear to me, but I suppose that the scientists made their assessment based on the best available scientific data. To put it another way, they would not have taken account of ad-hoc observations, such as amateur observations of radon gas fluctuations. Part of the Aquila problem seems to be that the amateur observations provided a warning which the population were led to discount on the basis of ‘scientific’ analysis. More generally, in a crisis, one often has a conflict between a scientific analysis based on sound data and non-scientific views verging on divination. How should these diverse views inform the overall assessment?

In most cases one can make a reasonable scientific analysis based on sound data and ‘authorised assumptions’, taking account of recognized factors. I think that one should always strive to do so, and to communicate the results. But if that is all that one does then one is inevitably ignoring the particulars of the case, which may substantially increase the risk. One may also want to take a broader decision-theoretic view. For example, if the peaks in radon gas levels were unusual then taking them as a portent might be prudent, even in the absence of any relevant theory. The only reason for not doing so would be if the underlying mechanisms were well understood and the gas levels were known to be simply consequent on the scientific data, thus providing no additional information. Such an approach is particularly indicated where – as I think is the case in seismology – even the best scientific analysis has a poor track record.

The bottom line, then, is that I think that one should always provide ‘the best scientific analysis’ in the sense of an analysis that gives a numeric probability (or probability range etc) but one needs to establish a best practice that takes a broader view of the issue in question, and in particular the limitations and potential biases of ‘best practice’.

The O’Hagan paper quoted at the start says – of conventional probability theory – that  “Alternative, but similarly compelling, axiomatic or rational arguments do not appear to have been advanced for other ways of representing uncertainty.” This overlooks Boole, Keynes , Russell and Good, for example. It may be timely to reconsider the adequacy of the conventional assumptions. It might also be that ‘best scientific practice’ needs to be adapted to cope with messy real-world situations. Aquila was not a laboratory.

See Also

My notes on uncertainty and on current debates.

Dave Marsay

Assessing and Communicating Risks and Uncertainty

David Spielgelhalter Assessing and Communicating Risks and Uncertainty Science in Parliament vol 69, no. 2, pp. 21-26. This is part of the IMA’s Mathematics Matters: A Crucial Contribution to the Country’s Economy.

This starts with a Harvard study showing that “a daily portion of red meat was associated with an increase in the annual risk of death by 13% over the period of the study”. Does this mean, as the Daily Express claimed, that “10% of all deaths could be avoided”?

David S uses ‘survival analysis’ to show that “a 40 year-old  man who eats a quarter-pound burger for his working lunch each day can expect, on average, to live to 79, while his mate who avoids the burger can expect to live to 80.” He goes on: “over a lifetime habit, each daily portion of red meat is associated with about 30 minutes off your life expectancy .. ” (my emphasis.)

As a mathematician advising politicians and other decision-makers, I would not be comfortable that policy-makers understood this, and would act appropriately. They might, for example, assume that we should all be discouraged from eating too much red meat.

Even some numerate colleagues with some exposure to statistics might, I think, suppose that their life expectancy was being reduced by eating red meat. But all that is being said is that if a random person were selected from the population as a whole then – knowing nothing about them – a statistician would ‘expect’ them to have a shorter life if they eat red meat. But every actual individual ‘you’ has a family history and many by 40 will have had cholesterol tests. It is not clear what the relevance to them is of the statistician’s ‘averaged’ figures.

Generally speaking, statistics gathered for one set of factors cannot be used to draw precise conclusions about  other sets of factors, much less about individuals. David S’s previous advice at Don’t Know, Can’t Know applies. In my experience, it is not safe to assume that the audience will appreciate these finer points. All that I would take from the Harvard study is that if you eat red meat most days it might be a good idea to consult your doctor. I would also hope that there was research going on into the factors in the apparent dangers.

See Also

I would appreciate a link to the original study.

Dave Marsay

NRC’s Assessing … Complex Models

Committee on Mathematical Foundations of Verification, Validation, and Uncertainty Quantification Board on Mathematical Sciences and Their Applications Assessing the Reliability of Complex Models: Mathematical and Statistical Foundations of Verification, Validation, and Uncertainty Quantification (US) NRC, 2012

The team were tasked to “examine practices for VVUQ of large-scale computational simulations”. Such simulations are complicated. The title seems misleading in using the term ‘complex’. The summary seems like a reasonable consensus summary of the state of the art in its focus area, and of research directions, with no surprises. But the main body does provide some ammunition for those who seek to emphasise deeper uncertainty issues, considering mathematics beyond computation.

Summary

Principles

Highlighted principles include:

    1. A validation assessment is well defined only in terms of specified quantities of interest (QOIs) and the accuracy needed for the intended use of the model.
    2. A validation assessment provides direct information about model accuracy only in the domain of applicability that is “covered” by the physical observations employed in the assessment.

Comments

The notion of a model here would be something like ‘all swans are white’. The first principle suggests that we need tolerance for what is regarded as ‘white’. The second principle suggests that if we have only considered British swans, we should restrict the domain of applicability of the model.

In effect, the model is being set within a justification, much as the conclusion of a mathematical theorem is linked to axioms by the proof. This is contrary to much school science practice, which simply teaches models: we need to understand the (empirical) theory. Typically, when we read ‘all swans are white’ we should understand that it really only means ‘all British swans are white-ish’.

Swans are relatively simple. The only problem is our limited observations of them. Economics, for example, is more complex. The quantities of interest are controversial, as are the relevant observations. Such complex situations seem beyond the intended scope of this report.

Research Topics

  1. Development of methods that help to define the “domain of applicability” of a model, including methods that help quantify the notions of near neighbors, interpolative predictions, and extrapolative predictions.
  2. Development of methods to assess model discrepancy and other sources of uncertainty in the case of rare events, especially when validation data do not include such events.

Comments

These topics are easier if one has an overarching theory of which the model is a specialisation, whose parameters are to be determined. In such cases the ‘domain of applicability’ could be based on an established classifying schema, and uncertainty could be probabilistic, drawing on established probabilistic models. The situation is more challenging, with broader uncertainties, where there is no such ruling theory, as in climate science.

Recommendations

  1. An effective VVUQ [verification, validation and uncertainty quantification] education should encourage students to confront and reflect on the ways that knowledge is acquired, used, and updated.
  2. The elements of probabilistic thinking, physical-systems modeling, and numerical methods and computing should become standard parts of the respective core curricula for scientists, engineers, and statisticians.

Comments

Most engineers and statisticians will be working pragmatically, assuming some ruling theory that guides their work. This report seems most suitable for them. Ideally, scientists acting as science advisors would also be working in such a way. However, surprises do happen, and scientists working on science should be actively doubting any supposed ruling theory. Thus it is sometimes vital to know the difference between a situation where an agreed theory should be regarded as, for example, ‘fit for government work’, and where it is not, particularly where extremes of complexity or uncertainty call for a more principled approach. In such cases it is not obvious that uncertainty can be quantified. For example, how does one put a number on ‘all swans are white’ when one has not been outside Britain?

As well as using mathematics to work out the implications of a ruling theory in a particular case, one needs to be able to use different mathematics to work out the implications of a particular case for theory.

Introduction

This cites Savage,  but in his terms it is implicitly addressing complicated but ‘small’ worlds rather than more complex ‘large’ ones, such as that of interest to climate science.

Sources of Uncertainty and Error

The general issue is whether formal validation of models of complex systems is actually feasible. This issue is both philosophical and practical and is discussed in greater depth in, for example, McWilliams (2007), Oreskes et al. (1994), and Stainforth et al. (2007).

There is a need to make decisions … before a complete UQ analysis will be available. … This does not mean that UQ can be ignored but rather that decisions need to be made in the face of only partial knowledge of the uncertainties involved. The “science” of these kinds of decisions is still evolving, and the various versions of decision analysis are certainly relevant.

Comment

 It seems that not all uncertainty is quantifiable, and that one needs to be able to make decisions in the face of such uncertainties.

In the case of ‘all swans are white’ the uncertainty arises because we have only looked in Britain. It is clear what can be done about this, even if we have no basis for assigning a number.

In the case of economics, even if we have a dominant theory we may be uncertainty because, for example, it has only been validated against the British economy for the last 10 years. We might not be able to put a number on the uncertainty, but it might be wise to look for more general theories, covering a broader range of countries and times, and then see how our dominant theory is situated within the broader theory. This might give us more confidence in some conclusions from the theory, even if we cannot assign a number. (One also needs to consider alternative theories.)

Model Validation and Prediction

Comparison with reality

In simple settings validation could be accomplished by directly comparing model results to physical measurements for the QOI  …

Findings

  1. Mathematical considerations alone cannot address the appropriateness of a model prediction in a new, untested setting. Quantifying uncertainties and assessing their reliability for a prediction require both statistical  and subject-matter reasoning.
  2. The idea of a domain of applicability is helpful for communicating the conditions for which predictions (with uncertainty) can be trusted. However, the mathematical foundations have not been established for defining such a domain or its boundaries.

Comment

I take the view that a situation that can be treated classically is not complex, only at most complicated. Complex situations may always contain elements that are surprising to us. Hence bullet 1 applies to complex situations too. The responsibility for dealing with complexities seems to be shifted from the mathematicians to the subject matter experts (SMEs). But if one is dealing with a new ‘setting’ one is dealing with dynamic complexity, of the kind that would be a crisis if the potential impact were serious. In such situations it may not be obvious which subject is the relevant one, or there may be more than one vital subject. SMEs may be unused to coping with complexity or with collaboration under crisis or near-crisis conditions. For example, climate science might need not only climatologists but also experts in dealing with uncertainty.

My view is that sometimes one can only assess the relevance and reliability of a model in a particular situation, that one needs particular experts in this, and that mathematics can help – but it is a different mathematics.

Next Steps in Practice, Research, and Education for Verification, Validation, and Uncertainty Quantification

 For validation, “domain of applicability” is recognized as an important concept, but how one defines this domain remains an open question. For predictions, characterizing how a model differs from reality, particularly in extrapolative regimes, is a pressing need. … advances in linking a model to reality will likely broaden the domain of applicability and improve confidence in extrapolative prediction.

Comment

As Keynes pointed out, in some complex situations one can only meaningfully predict in the short-term. Thus in early 2008 economic predictions were not in error, as short-term predictions. It is just that the uncertain long-term arrived. What is needed, therefore, is some long-term forecasting ability. This cannot be a prediction, in the sense of having a probability distribution, but it might be an effective anticipation, just as one might have anticipated that there were non-white swans in foreign parts. Different mathematics is needed.

My Summary

The report focusses on the complicatedness of the models. But I find it hard to think of a situation where one needs a complicated model and the actual situation is not complex. Usually, for example, the situation is ‘reflexive’ because the model is going to be used to inform interaction with the world, which will change it. Thus, the problem as I see it is how to model a situation that is uncertain and possibly complex. While the report does give some pointers it does not develop them.

The common sense view of modelling is that a model is based on observations. In fact – as the report notes – it tends to be based on observations plus assumptions, which are refined into a model, often iteratively. But the report seems to suppose that one’s initial assumptions will be ‘true’. But one can only say that the model fits one’s observations, not that it will continue to fit all possible observations, unless one can be sure that the situation is very constrained. That is, one cannot say that a scientific theory is unconditionally and absolutely true, but only ‘true to’ ones observations and assumptions.

The report is thus mainly for those who have a mature set of assumptions which they wish to refine, not those who expect the unexpected. It does briefly mention ‘rare events’, but it sees these as outliers on a probability distribution whereas I would see these more as challenging assumptions.

See Also

The better nature blog provides a view of science that is complimentary to this report.

My notes on science and uncertainty.

Dave Marsay

Harris’s Free Will

This is a review of reviews of Sam Harris’s Free Will. I haven’t read the actual book. (One of Harris’s supporters says that I have no choice but to read the book: but I am not so sure.) 

New Scientist

The New Scientist has a review which says:

“We either live in a deterministic universe where the future is set, or an indeterminate one where thoughts and actions happen at random. Neither is compatible with free will.”

But why are these the only options? Harris is quoted as saying:

“You can do what you decide to do, but you cannot decide what you will decide to do.”

But what, then, is the point? 

Meissler

This is a sympathetic review. He quotes:

“Why didn’t I decide to drink a glass of juice (rather than water). The thought never occurred to me. Am I free to do that which does not occur to me to do? Of course not. And there is no way I can influence my desires–for what tools of influence would I use? Other desires? To say that I would have done otherwise had I wanted to is simply to say that I would have been in a different universe had I lived in a different universe.”

I would call such acts ‘habitual’ and often executed ‘on autopilot’, like much of driving. But does all of driving involve such ‘decisions’? Does all of life?

The next quote is:

“What I will do next, and why, remains, at bottom, a mystery–one that is fully determined by the prior state of the universe and the laws of nature (including the contributions of chance).”

This is certainly a wide-spread belief, but not one that I feel free to accept at face-value. Why? Is there any possibility of any kind of proof of this belief, or anything like it, or even a faintly convincing argument? It is stated that the actions of a person are determined by their atoms (presumable as configured into molecules etc.). But is this really true? 

Sam Harris

In his blog, Harris focusses on the ‘moral’ implications of free-will and the need for an ‘illusion of free-will’. But if we rely on a false belief, aren’t we motivated to be cynical about ‘scientific reason’? Or at least, Harris’s version of it? But do not the language and methods of science and Harris assume what Harris asserts, and thus aren’t science and Harris unable to prove their own assumptions?

See Also

An article on critical phenomena argues that they cannot be understood from a classical ‘scientific’ viewpoint, thus undermining Harris’ assertions, especially those quoted by the friendly atheist. Briefly, we are not just a mechanical assemblage of atoms.

Summary

Harris’s views seem reasonable for the type of ‘decisions’ that fill Harris’s ‘life’, and it does seem to be the case that the physical world leaves little space for free will. But there may be a critical difference between ‘little’ and ‘none’, a possibility that Harris appears preprogrammed not to address. But are the relatively automatable kinds of decisions that Harris considers all there is to his life? Is his life really like a computer simulation of life?

Addenda

Geopolicratus suggests that populations with an agricultural heritage are more institutionalised than those with a nomad heritage. If so, then those with an agricultural heritage might well be more disposed to believe things that suggest that there is no free will, since the two kinds of lives call for quite different kinds of decision making. Plato’s Republic, anyone? 

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

UK judge rules against probability theory? R v T

Actually, the judge was a bit more considered than my title suggests. In my defence the Guardian says:

“Bayes’ theorem is a mathematical equation used in court cases to analyse statistical evidence. But a judge has ruled it can no longer be used. Will it result in more miscarriages of justice?”

The case involved Nike trainers and appears to be the same as that in a recent appeal  judgment, although it doesn’t actually involve Bayes’ rule. It just involves the likelihood ratio, not any priors. An expert witness had said:

“… there is at this stage a moderate degree of scientific evidence to support the view that the [appellant’s shoes] had made the footwear marks.”

The appeal hinged around the question of whether this was a reasonable representation of a reasonable inference.

According to Keynes, Knight and Ellsberg, probabilities are grounded on either logic, statistics or estimates. Prior probabilities are – by definition – never grounded on statistics and in practical applications rarely grounded on logic, and hence must be estimates. Estimates are always open to challenge, and might reasonably be discounted, particularly where one wants to be ‘beyond reasonable doubt’.

Likelihood ratios are typically more objective and hence more reliable. In this case they might have been based on good quality relevant statistics, in which case the judge supposed that it might be reasonable to state that there was a moderate degree of scientific evidence. But this was not the case. Expert estimates had supplied what the available database had lacked, so introducing additional uncertainty. This might have been reasonable, but the estimate appears not to have been based on relevant experience.

My deduction from this is that where there is doubt about the proper figures to use, that doubt should be acknowledged and the defendant given the benefit of it. As the judge says:

“… it is difficult to see how an opinion … arrived at through the application of a formula could be described as ‘logical’ or ‘balanced’ or ‘robust’, when the data are as uncertain as we have set out and could produce such different results.”

This case would seem to have wider implications:

“… we do not consider that the word ‘scientific’ should be used, as … it is likely to give an impression … of a degree of  precision and objectivity that is not present given the current state of this area of expertise.”

My experience is that such estimates are often used by scientists, and the result confounded with ‘science’. I have sometimes heard this practice justified on the grounds that some ‘measure’ of probability is needed and that if an estimate is needed it is best that it should be given by an independent scientist or analyst than by an advocate or, say, politician. Maybe so, but perhaps we should indicate when this has happened, and the impact it has on the result. (It might be better to follow the advice of Keynes.)

Royal Statistical Society

The guidance for forensic scientists is:

“There is a long history and ample recent experience of misunderstandings relating to statistical information and probabilities which have contributed towards serious miscarriages of justice. … forensic scientists and expert witnesses, whose evidence is typically the immediate source of statistics and probabilities presented in court, may also lack familiarity with relevant terminology, concepts and methods.”

“Guide No 1 is designed as a general introduction to the role of probability and statistics in criminal proceedings, a kind of vade mecum for the perplexed forensic traveller; or possibly, ‘Everything you ever wanted to know about probability in criminal litigation but were too afraid to ask’. It explains basic terminology and concepts, illustrates various forensic applications of probability, and draws attention to common reasoning errors (‘traps for the unwary’).”

The guide is clearly much needed. It states:

“The best measure of uncertainty is probability, which measures uncertainty on a scale from 0 to 1.”

This statement is nowhere supported by any evidence whatsoever. No consideration is given to alternatives, such as those of Keynes, or to the legal concept of “beyond reasonable doubt.”

“The type of probability that arises in criminal proceedings is overwhelmingly of the subjective variety, …

There is no consideration of Boole and Keynes’ more logical notion, or any reason to take notice of the subjective opinions of others.

“Whether objective expressions of chance or subjective measures of belief, probabilistic calculations of (un)certainty obey the axiomatic laws of probability, …

But how do we determine whether those axioms are appropriate to the situation at hand? The reader is not told whether the term axiom is to be interpreted in its mathematical or lay sense: as something to be proved, or as something that may be assumed without further thought. The first example given is:

“Consider an unbiased coin, with an equal probability of producing a ‘head’ or a ‘tail’ on each coin-toss. …”

Probability here is mathematical. Considering the probability of an untested coin of unknown provenance would be more subjective. It is the handling of the subjective component that is at issue, an issue that the example does not help to address. More realistically:

“Assessing the adequacy of an inference is never a purely statistical matter in the final analysis, because the adequacy of an inference is relative to its purpose and what is at stake in any particular context in relying on it.”

“… an expert report might contain statements resembling the following:
* “Footwear with the pattern and size of the sole of the defendant’s shoe occurred in approximately 2% of burglaries.” …
It is vital for judges, lawyers and forensic scientists to be able to identify and evaluate the assumptions which lie behind these kinds of statistics.”

This is good advice, which the appeal judge took. However, while I have not read and understood every detail of the guidance, it seems to me that the judge’s understanding went beyond the guidance, including its ‘traps for the unwary’.

The statistical guidance cites the following guidance from the forensic scientists’ professional body:

Logic: The expert will address the probability of the evidence given the proposition and relevant background information and not the probability of the proposition given the evidence and background information.”

This seems sound, but needs supporting by detailed advice. In particular none of the above guidance explicitly takes account of the notion of ‘beyond reasonable doubt’.

Forensic science view

Science and Justice has an article which opines:

“Our concern is that the judgment will be interpreted as being in opposition to the principles of logical interpretation of evidence. We re-iterate those principles and then discuss several extracts from the judgment that may be potentially harmful to the future of forensic science.”

The full article is behind a pay-wall, but I would like to know what principles it is referring to. It is hard to see how there could be a conflict, unless there are some extra principles not in the RSS guidance.

Criminal law Review

Forensic Science Evidence in Question argues that:

 “The strict ratio of R. v T  is that existing data are legally insufficient to permit footwear mark experts to utilise probabilistic methods involving likelihood ratios when writing reports or testifying at trial. For the reasons identified in this article, we hope that the Court of Appeal will reconsider this ruling at the earliest opportunity. In the meantime, we are concerned that some of the Court’s more general statements could frustrate the jury’s understanding of forensic science evidence, and even risk miscarriages of justice, if extrapolated to other contexts and forms of expertise. There is no reason in law why errant obiter dicta should be permitted to corrupt best scientific practice.”

In this account it is clear that the substantive issues are about likelihoods rather than probabilities, and that consideration of ‘prior probabilities’ are not relevant here. This is different from the Royal Society’s account, which emphasises subjective probability. However, in considering the likelihood of the evidence conditioned on the suspect’s innocence, it is implicitly assumed that the perpetrator is typical of the UK population as a whole, or of people at UK crime scenes as a whole. But suppose that women are most often murdered by men that they are or have been close to, and that such men are likely to be more similar to each other than people randomly selected from the population as a whole. Then it is reasonable to suppose that the likelihood that the perpetrator is some other male known to the victim will be significantly greater than the likelihood of it being some random man. The use of an inappropriate likelihood introduces a bias.

My advice: do not get involved with people who mostly get involved with people like you, unless you trust them all.

The Appeal

Prof. Jamieson, an expert on the evaluation of evidence whose statements informed the appeal, said:

“It is essential for the population data for these shoes be applicable to the population potentially present at the scene. Regional, time, and cultural differences all affect the frequency of particular footwear in a relevant population. That data was simply not … . If the shoes were more common in such a population then the probative value is lessened. The converse is also true, but we do not know which is the accurate position.”

Thus the professor is arguing that the estimated likelihood could be too high or too low, and that the defence ought to be given the benefit of the doubt. I have argued that using a whole population likelihood is likely to be actually biased against the defence, as I expect such traits as the choice of shoes to be clustered.

Science and Justice

Faigman, Jamieson et al, Response to Aitken et al. on R v T Science and Justice 51 (2011) 213 – 214

This argues against an unthinking application of likelihood ratios, noting:

  • That the defence may reasonable not be able explain the evidence, so that there may be no reliable source for an innocent hypothesis.
  • That assessment of likelihoods will depend on experience, the basis for which should be disclosed and open to challenge.
  • If there is doubt as to how to handle uncertainty, any method ought to be tested in court and not dictated by armchair experts.

On the other hand, when it says “Accepting that probability theory provides a coherent foundation …” it fails to note that coherence is beside the point: is it credible?

Comment

The current situation seems unsatisfactory, with the best available advice both too simplistic and not simple enough. In similar situations I have co-authored a large document which has then been split into two: guidance for practitioners and justification. It may not be possible to give comprehensive guidance for practitioners, in which case one should aim to give ‘safe’ advice, so that practitioners are clear about when they can use their own judgment and when they should seek advice. This inevitably becomes a ‘legal’ document, but that seems unavoidable.

In my view it should not be simply assumed that the appropriate representation of uncertainty is ‘nothing but a number’. Instead one should take Keynes’ concerns seriously in the guidance and explicitly argue for a simpler approach avoiding ‘reasonable doubt’, where appropriate. I would also suggest that any proposed principles ought to be compared with past cases, particularly those which have turned out to be miscarriages of justice. As the appeal judge did, this might usefully consider foreign cases to build up an adequate ‘database’.

My expectation is that this would show that the use of whole-population likelihoods as in R v T is biased against defendants who are in a suspect social group.

More generally, I think that anyguidance ought to apply to my growing uncertainty puzzles, even if it only cautions against a simplistic application of any rule in such cases.

See Also

Blogs: The register, W Briggs and Convicted by statistics (referring to previous miscarriages).

My notes on probability. A relevant puzzle.

Dave Marsay 

The voice of science: let’s agree to disagree (Nature)

Sarewitz uses his Nature column to argue against forced or otherwise false consensus in science.

“The very idea that science best expresses its authority through consensus statements is at odds with a vibrant scientific enterprise. … Science would provide better value to politics if it articulated the broadest set of plausible interpretations, options and perspectives, imagined by the best experts, rather than forcing convergence to an allegedly unified voice.”

D. Sarewitz The voice of science: let’s agree to disagree Nature Vol 478 Pg 3, 6 October 2011.

Sarewitz seems to be thinking in terms of issues such as academic freedom and vibrancy. But there are arguably more important aspects. Given any set of experiments or other evidence there will generally be a wide range of credible theories. The choice of a particular theory is not determined by any logic, but such factors as which one was thought of first and by whom, and is easiest to work with in making predictions etc.

In issues like smoking and climate change the problem is that the paucity of data is obvious and different credible theories lead to different policy or action recommendations. Thus no one detailed theory is credible. We need a different way of reasoning, that should at least recognize the range of credible theories and the consequential uncertainty.

I have experience of a different kind of problem: where one has seemingly well established theories but these are suddenly falsified in a crisis (as in the financial crash of 2008). Politicians (and the public, where they are involved) understandably lose confidence in the ‘science’ and can fall back on instincts that may or may not be appropriate. One can try to rebuild a credible theory over-night (literally) from scratch, but this is not recommended. Some scientists have a clear grasp of their subject. They understand that the accepted theory is part science part narrative and are able to help politicians understand the difference. We may need more of these.

Enlightened scientists will seek to encourage debate, e.g. via enlightened journals, but in some fields, as in economics, they may find themselves ‘out in the cold’. We need to make sure that such people have a platform. I think that this goes much broader than the committees Sarewitz is considering.

I also think that many of our contemporary problems are because societies end to suppress uncertainty, being more comfortable with consensus and giving more credence to people who are confident in their subject. This attitude suppresses a consideration of alternatives and turns novelty into shocks, which can have disastrous results. 

Previous work

In a 2001 Nature article Roger Pielke covers much the same ground. But he also says:

“Take for example weather forecasters, who are learning that the value to society of their forecasts is enhanced when decision-makers are provided with predictions in probabilistic rather than categorical fashion and decisions are made in full view of uncertainty.”

 From this and his blog it seems that the uncertainty is merely probabilistic, and differs only in magnitude. But it seems to me that before global warming became significant  weather forecasting and climate modelling seemed probabilistic but that there was an intermediate time-scale (in the UK one or two weeks) which was always more complex and which had different types of uncertainty, as described by Keynes. But this does not detract from the main point of the article.

See also

Popper’s Logic of Scientific Discovery , Roger Pielke’s blog (with a link to his 2001 article in Nature on the same topic).

Dave Marsay

The Logic of Scientific Discovery

K.R. Popper The Logic of Scientific Discovery 1980 Routledge A review. (The last edition has some useful clarifications.) See new location.

Dave Marsay

Quantum Minds

A New Scientist Cover Story (No. 2828 3 Sept 2011) opines that:

‘The fuzziness and weird logic of the way particles behave applies surprisingly well to how human thinks’. (banner, p34)

It starts:

‘The quantum world defies the rules of ordinary logic.’

The first two examples are The infamous two-slit experiment and an experiment by Tversky and Shamir supposedly showing violation of the ‘sure thing principle’. But do they?

Saving classical logic

According to George Boole (Laws of thought), when a series of assumptions and applications of logic leads to a falsehood I must abandon one of the assumptions of one of the rules of inference, but I can ‘save’ whichever one I am most wedded to. So to save ‘ordinary logic’ it suffices to identify a dodgy assumption.

Two-slits experiment

The article says of the two-slits experiment:

‘… the pattern you should get – ordinary physics and logic would suggest – should be ..’

There is a missing factor here: the classical (Bayesian) assumptions about ‘how probabilities work’. Thus I could save ‘ordinary logic’ by abandoning common-sense probability theory.

Actually, there is a more obvious culprit. As Kant pointed out the assumption that the world is composed of objects with attributes and having relationships with each other belongs to common-sense physics, not logic. For example, two isolated individuals may behave like objects but when they come into communion the sum may be more than the sum of the parts. Looking at the two-slit experiment this way, the stuff that we regard as a particle seem isolated and hence object-like until it ‘comes into communion with’ the apparatus, when the whole may be un-object-like, but then a new steady-state ’emerges’, which is object-like and which we regard as a particle. The experiment is telling us something about the nature of the communion. Prigogine has a mathematization of this.

Thus one can abandon the common-sense assumption that ‘a communion is nothing but the sum of objects’, thus saving classical logic.

Sure Thing Principle

An example is given (pg 36). That appears to violate Savage’s sure-thing principle and hence ‘classical logic’. But, as above, we might prefer to abandon out probability theory rather than our logic. But there are plenty of alternatives.

The sure-thing principle applies to ‘economic man’, who has some unusual values. For example, if he values a winter sun holiday at $500 and a skiing holiday at $500 then he ‘should’ be happy to pay $500 for a holiday in which he only finds out which it is when he gets there. The assumptions of classical economic man only seem to apply to people with lots of spare money and are used to gambling with it. Perhaps the experimental subjects were different?

The details of the experiment as reported also repay attention. A gamble with an even chance of winning $200 or losing $100 is available. Experimental subjects all had a first gamble. In case A subjects were told they had won. In case B they were told they had lost. In case C they were not told. They were all invited to gamble again.

Most subjects (69%) wanted to gamble again in case A. This seems reasonable as over the two gambles they were guaranteed a gain of $100. Fewer subjects (59%) wanted to gamble again in case B. This seems reasonable, as they risked a $200 loss overall. Least subjects  (36%) wanted to gamble again in case C. This seems to violate the sure-thing principle, which (according to the article) says that anyone who gambles in both the first two cases should gamble in the third. But from the figures above we can only deduce that – if they are representative – then at least 28% (i.e. 100%-(100%-69%)+(100%-59%)) would gamble in both cases. But 36% gambled in case C, so the data does not imply that anyone would gamble for A and B but not C.

If one chooses a person at random, then the probability that they gambled again in both cases A and B is between 28% and 100%. The convention in ‘classical’ probability theory is to split the difference (a kind of principle of indifference) yielding 64% (as in the article). A possible explanation for the dearth of such subjects is that they were not wealthy (so having non-linear utilities in the region of $100s) and that those who couldn’t afford to lose $100 had good used in mind for $200, preferring a certain win of $200 to an evens chance of winning $400 or only $100. This seems reasonable.

Others’ criticisms here. See also some notes on uncertainty and probability.

Dave Marsay

Science advice and the management of risk

Science advice and the management of risk in government and business

The foundation for science and technology, 10 November 2010

An authoritative summary of the UK governments position on risk, with talks and papers.

  •  Beddington gives a good overview. He discusses probability versus impact ‘heat maps’, the use of ‘worst case’ scenarios, the limitations of heat maps and Blackett reviews. He discusses how management strategy has to reflect both the location on the heat map and the uncertainty in the location.
  • Omand discusses ‘Why wont they (politicians) listen (to the experts)?’  He notes the difference between secrets (hard to uncover) and secrets (hard to make sense of), and makes ‘common cause’ between science and intelligence in attempting to communicate with politicians. Presents a familiar type of chart in which probability is thought of as totally ordered (as in Bayesian probability) and seeks to standardise on the descriptors of ranges of probability, such as ‘highly probable’.
  • Goodman discusses economic risk management and the need to cope with ‘irrational cycles of exuberance’, focussing on ‘low probability high impact’ events. Only some risks can be quantified. Recommends ‘generalised Pareto distribution’.
  • Spielgelhalter introduced the discussion with some important insights:

The issue ultimately comes down to whether we can put numbers on these events.  … how can a figure communicate the enormous number of assumptions which underlie such quantifications? … The … goal of a numerical probability … becomes much more difficult when dealing with deeper uncertainties. … This concerns the acknowledgment of indeterminacy and ignorance.

Standard methods of analysis deal with recognised, quantifiable uncertainties, but this is only part of the story, although … we tend to focus at this level. A first extra step is to be explicit about acknowledged inadequacies – things that are not put into the analysis such as the methane cycle in climate models. These could be called ‘indeterminacy’. We do not know how to quantify them but we know they might be influential.

Yet there are even greater unknowns which require an essential humility. This is not just ignorance about what is wrong with the model, it is an acknowledgment that there could be a different conceptual basis for our analysis, another way to approach the problem.

There will be a continuing debate  about the process of communicating these deeper uncertainties.

  • The discussion covered the following:
    • More coverage of the role of emotion and group think is needed.
    • “[G]overnments did not base policies on evidence; they proclaimed them because they thought that a particular policy would attract votes. They would then seek to find evidence that supported their view. It would be more realistic to ask for policies to be evidence tested [rather than evidence-based.]”
    • “A new language was needed to describe uncertainty and the impossibility of removing risk from ordinary life … .”
    •  Advisors must advise, not covertly subvert decision-making.

Comments

If we accept that there is more to uncertainty than  can be reflected in a typical scale of probability, then it is no wonder that organisational decisions fail to take account of it adequately, or that some advisors seek to subvert such poor processes. Moreover, this seems to be a ‘difference that makes a difference’.

From a Keynesian perspective conditional probabilities, P(X|A), sometimes exist but unconditional ones, P(X), rarely do. As Spielgelhalter notes it is often the assumptions that are wrong: the estimated probability is then irrelevant. Spielgelhalter mentioned the common use of ‘sensitivity analysis’, noting that it is unhelpful. But what is commonly done is to test the sensitivity of P(X|y,A) to some minor variable y while keeping the assumptions, A. fixed. What is more often (for these types of risk) needed is a sensitivity to assumptions. Thus, if P(X|A) is high:

  • one needs to identify possible alternatives, A’, to A for which P(X|A’) is low, no matter how improbable A’ may be regarded.

Here:

  • ‘Possible’ means consistent with the evidence rather than anything psychological.
  • The criteria for what is regarded as ‘low’ or ‘high’ will be set by the decision context.

The rationale is that everything that has ever happened was, with hind-sight, possible: the things that catch us out are those that we overlooked, perhaps because we thought them improbable.

A conventional analysis would overlook emergent properties, such as booming cycles of ‘irrational’ exuberance. Thus in considering alternatives one needs to consider potential emotions and other emergencies and epochal events.

This suggests a typical ‘risk communication’ would consist of an extrapolated ‘main case’ probability together with a description of scenarios in which the opposite probability would hold.

See also

mathematicsheat maps, extrapolation and induction

Other debates, my bibliography.

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

The Precautionary Principle and Risk

Definition

The precautionary principle is that:

When an activity raises threats of harm to human health or the environment, precautionary measures should be taken even if some cause and effect relationships are not fully established scientifically.

It thus applies in situations of uncertainty: better safe than sorry. It has been criticised for holding back innovation. But a ‘precautionary measure’ can be anything that mitigates the risk, not just failing to make the innovation. In particular if the potential ‘harm’ is very mild or easy to remediate, then there may be no need for costly ‘measures’.

Measures

There may be a cancer risk from mobile phones. The appropriate response is to advise restraint in the use of mobile phones, particularly by young people, and more research.

In the run-up to the financial crisis of 2007/8 there was an (indirect) threat to human health. An appropriate counter-measure might have been to encourage a broader base of economic research, including non-Bayesians.

Criticisms

Volokh sees the principle as directed against “politically disfavoured technologies” and hence potentially harmful. In particular Matt Ridley considers that the German e-coli outbreak of 2011 might have been prevented if the food had been irradiated, but irradiation had been regarded as leading to a possible threat, and hence under the precautionary principle had not been used. But the principle ought to be applied to all innovations, including large-scale organic farming, in which case irradiation might seem to be an appropriate precautionary measure. Given the fears about irradiation, it might have been used selectively – after test results or to quash an e-coli outbreak.  In any event, there should be a balance of threats and measures.

Conclusion

The precautionary principle seems reasonable, but needs to be applied evenly, not just to ‘Frankenstein technologies’. It could be improved by emphasing the need for the measures to be ‘proportional’ to the down-side risk.

Dave Marsay