Explaining the "black swan events"
Regular Network Norwich and Norfolk columnist James Knight continues his series on miracles by constructing a blueprint for a bridge between the realm of science and the world of miracles.
The present Horsemen following that has seen a huge number of book sales for Richard Dawkins, Christopher Hitchens, Sam Harris and Dan Dennett is, as I’ve said before, a bit of a cheat which only manages to criticise the Christian faith insofar as it can conceive the often imaginary and fabricated constructs of God and simply negate them with off-the-peg clichéd retorts that have virtually no relevance to the real issues in which we are engaging. The horsemen movement has only gained so much ground because they effectively define themselves by what they are not, by using emotional trump cards and presenting their readers with strawman caricatures and counterfactual retorts that stir the passions of those who are easily roused by poorly constructed emotional propaganda. In effect they are the atheistic equivalent of our Young Earth Creationists – unwilling and perhaps even wilfully unable to consider the real and genuine issues up for consideration and the changes that one needs to make. Instead they assert counter arguments against the existence of God that have little or nothing to do with God’s existence at all. All they are really doing is building their case for the rejecting of a god that they have entirely caricatured - a god that neither Christians nor anyone else believes in either.
Fundamental to the horsemen’s atheism is the belief that miracles are not true and never happen in the way that Christians claim they do. Using the Popperian black swan problem, the underlying situation seems to be this; with their claims that out of the ordinary ‘miraculous’ events are occurring Christians are claiming that these “black swans” exist and naturalists are telling us that they don’t. In other words, naturalism requires that paths of closely related physical prototypes must exist all the way from the big bang up to the present day. This is a process that enables the cosmic history of the physical regime to diffuse its way through to the complex cybernetic activities of natural selection, producing a world that is predictably non-miraculous, and this is the model that most naturalists have settled for.
Of course the problem for naturalists is that they cannot know that no black swans exist unless they know for sure that miracles are impossible, and they cannot know that miracles are impossible unless they are sure there are no such things as black swans. Christians do not face the exact same epistemological problems because many (if not most) have experienced some kind of miracle that has demonstrated to their satisfaction that God is active in their life. Of course the naturalists may claim that the Christians are using a debatable explanatory filter that defaults to intelligent agency as the best explanation of such events, but equally the Christian can rightly insist that the naturalist never knows what will come out of the woodwork, and this point is compounded by the fact that many unbelievers have gone on to experience things that have led to their belief in the supernatural.
Science may not provide us with all the answers, but its own rewards are evident by the human progress it has ushered in; science by its very definition should always lead to progression and every Kuhnian paradigm shift ought to qualitatively supersede the last. It is easy to look back into history and be under the illusion that many of these advancements were quick and easy, but they were not. Einstein’s relativistic standpoint didn’t swiftly supersede Maxwell’s electromagnetic standpoint or even the theories of force and motion underpinned by Newtonian mechanics, yet the retrospective viewpoint may give us the illusion that these transitions were smooth. When one thinks of the many other transitions; not just from Newton, Maxwell and Faraday to Einstein, Schrödinger and Heisenberg, but from the Ptolemaic cosmological view to the Copernican view; from classical mechanics to quantum mechanic; from Becher’s phlogiston theory to Lavoisier's caloric theory of combustion, right through to the science of thermodynamics; from Lamarckian inheritance to Darwinian natural selection and the reconsideration of Lamarck’s ideas with ‘epigenetics’ which identify possible inheritances of acquired traits; even shifts like the transition from Law of Markets ideologies to Keynesianism – what these shifts (and many others) ought to tell us is that we are always in transition and ought to be prepared for black swans and new knowledge that could rock our present foundations. Using the economic example, many thought that the neoclassical macroeconomic models had outmoded the Keynesian model (to a large degree) but the recent global financial crisis has seen a resurgence in Keynesian economics, as the unpredictability of the economic future at any one time shows the roadblock into crisis and depression is not always firm, and not always solved by government interventions and injections of cash. This does not mean that we have to develop a completely relativistic position where everyone’s viewpoint is as valid as everyone else’s, rather we must simply allow for a degree of relativism which accepts that almost any A is likely to be isomorphic with, or in the framework of, B, C, D and beyond.
One must realise that such a complex and inaccessible object as history and the vastly complex nexus of human experiences is not going to provide an easy epistemological route to satisfactory positivist naturalism. Unless one experiences something first hand then the miraculous is hardly going to be amenable to an inductive epistemology, it will require a proactively inferential epistemology where one can rate the experience against all other personal backdrops and decide for oneself whether this is out of the ordinary or not. Clearly given that the miraculous seems to be a dish that is only consumed by those that experience it first hand, it is understandable that unbelievers remain unsatisfied with second hand testimonies. However sceptics must be careful not to quarantine themselves from investigation by adopting an attitude that allows them to sit comfortably dismissing all anecdotal evidence as unsatisfactory and preclude themselves from proactive investigation, because this is lazy thinking. If God does act miraculously in people’s lives, one thing is abundantly clear, if you do not adopt some proactive search or radical thought process that brings you into contact with the real nature of the investigation the chances of you finding this truth are seriously minimised, maybe even to the point of virtual zero.
Even with empirical investigations, statements which insist that black swans do exist cannot be falsified without a rigorous search throughout the whole swan domain which would show that there are no black swans. Clearly if miracles are happening in people’s lives one might expect testimonies of their occurrence to be frequent, because given that no human can ever search the whole human population, if they were only experienced in one or two people’s lives, most sceptics could justifiably claim that finding them is near on impossible. But equally, although showing that black swans exist is not easily falsified, they are more easily verified because one example of a black swan is sufficient to verify the statement, thus one’s search for a miracle, if it is not experienced by the self, will not involve a thorough search of the whole swan domain.
In contrast, denial of miracles is very hard, even when one tries to experience them and has no success, because assigning a universal property to all items of a set and decreeing all swans are white can be falsified by one black swan. The trouble is, where the statement all swans are white is relatively easy to falsify in most empirical investigations it is not so easily verified because the whole swan domain must be searched and checked before the statement “all swans are white” can claim to be verified, and while this might be a rigorous search in empirical science, it is even harder in the case of miracles because it is not always easy to be certain whether a miracle has happened or not.
Although we have been using terms such as “falsify” and “verify” one can seldom absolutely verify or falsify things of this nature as our observations are mediated through the ontology of detailed, complex, and varying interfaces of conditions which produce countless black swans, emotions and feelings that are difficult to reify, and a whole host of anomalous events that are beyond the scope of rational investigation. The latter point is particularly true given that verification of “black swans exist” requires merely the observation of one black swan, which in the cases of uncomplicated and unambiguous empirical science is easily manageable, but verification of “miraculous events exist” cannot be achieved in the same simple way because we are zooming in on a very large, complex and inaccessible domain of experience.
Given that there is a fairly large degree of logical asymmetry when one compares empirical science and the establishing of evidence of the miraculous, the swan domain must be used interpretatively as a sense-making structure that seeks to piece together numerous testimonies and anecdotal claims (the more the better) and consider a more innovative and improvisational method of investigation. Of course this admission is likely to put sceptics’ backs up as it threatens to be demanding right the way throughout their efforts in starting and maintaining a proactive search.
Although it's an oft-used maxim about falsification and induction by, among others, Hume, Mill and Popper, Nassim Nicholas Taleb's updated black swan theory refers to those larger-impact, harder-to-predict, and rarer events beyond the realms of everyday expectations that occur in the world, so strictly speaking, with something as intractable as the miraculous not only may it be true that they are impossible to predict, they may be bound up in a deeper narrative through which it is their meaning in relation to how clearly one sees things, as per Mark 8:22-26 with the healing of a blind Man at Bethsaida – this may be the best hint of the fullest picture.
The statement ‘all swans are white’ is testable by being falsifiable, yet it should also be remembered that deductive falsification is not the same as postulating an absence of verification. In order to comprehensively falsify a grand sweeping claim, one must compresses all this hard to manage data into a true falsifying singular statement, and this gets harder and harder until one is forced to admit that empirical science gradually shades over into proactive induction as the objects it deals with get more complex, intractable and inaccessible. The epistemological pathways for miracles are highlighted by a few known dots which can be joined by large tracts of observation and a proactive search, rather like when one visits a single web page with just a few search tags typed into a search engine. But this will probably only get one as far as concluding that there are an awful lot of people claiming to have experienced healings and revelations and a personal relationship with the Holy Spirit far beyond what one would deem to be possible in the natural world.
But if one’s first steps lead him into huge sense making structures that attempt to embed a very wide degree of life into a grand narrative, he will almost certainly find it gets more exciting the further he gets into it. As I said, a search engine only needs a few search key words to sift out a few web pages from millions, so in principle if this is seen as a join the dots experiment (that may well take a lifetime of growth) a few dots may be enough to put one on a solid conceptual footing.
We talked earlier about the kind of counterfactual theism that plagues atheistic thinking. Well, the Lucretian model of interpreting religion as superstition which attributed to the gods things like disease, storms, lightning and thunder is also just another example of counterfactual theism, which doesn’t help either science or theology. I also alluded to the fact that any God simply awaiting the status of being ‘vanquished’ by science is a "god-of-the-gaps" for some lazy thinking Christians and a red herring for atheists who cannot keep whatever theological enquiries they have out of science, and that both positions were unhelpful in the grand scheme of enquiry.
This is largely because most people of today know enough about physics to know that there is no clockwork universe that God has to keep tinkering with. The concept of a Newtonian universe that has God periodically adjusting the orbits of the planets because they were unstable to perturbations (the three body problem) is outmoded because mutually perturbing gravitational attractions are easily explainable at a macroscopic level - even though it ought to be remembered that when one bears in mind the distinction between classical mechanics and quantum mechanics the three body problem consists of many classes of approximations, particularly when one considers that at a quantum level examples of the three body problem are vastly different to the celestial models that Newton used.
Newton wouldn’t have had the first idea that over three hundred years henceforward the three body problem would be applied in a ‘probability’ model to determine if two particles in gravitational masses would be in close enough proximity from one another to provide the energy from which the third particle would leave the system. What this illustrates is nothing to do with the cognitive abilities of the likes of Newton, or Kepler, or Copernicus, or Galileo, just that they were not of the age that understood the universe as we do. Equally scientists three hundred years from now will understand the universe in ways that we would marvel at if we could travel forward and take a quick peek, and this ought to make something quite clear when it comes to miracles and ‘god of the gaps’ arguments; there are black swans about all over the place, and any statement that one makes about changing patterns, changing cultures, or Kuhnian paradigm shifts is hugely restricted by the present paradigms and zeitgeists of the day in which such statements are proffered. For example, it is thought that as our understanding of science has increased the need for belief in a Deity has decreased, but this is very rash thinking, given the huge Christian proliferation in recent times (in particular with the Pentecostal churches which have been very successful in making Christianity accessible again). Growth so often yields further and more rapid growth, and given that 2000 years after Christ His words still remain the most powerful ever spoken, and His worldwide church is still increasing in numbers, I see no reason to assume that this current horsemen craze is anything other than a temporary phase on the human calendar.
Perhaps in 200 or 300 years’ time this growth will have brought about a worldwide revival and reach every nation (as Jesus said it would, and in most cases has). Perhaps our future discoveries of science will show us a universe that gives a much greater impression of being designed, or perhaps discoveries will be made that will turn people further away from God – but the point is not about which is more likely (I believe the former is) rather this is about the circumspection with which our epistemological foresights should come, and the unpredictable nature of a future that is bound to consist of more black swans than most of us care to admit.
Given the foregoing, it seems rather insensible to me for too many people to jump on their secular hobbyhorses and declare that belief in God is dying or irrelevant, just as it is insensible for theists to attempt to indoctrinate or control individuals for fear of losing them to atheism or agnosticism. I think one thing is certain here, aggressive or controlling or disrespectful behaviour from either side only causes people to become more defensive about their position and behave less well, and when people behave in such a way they are much more likely to compromise their intellectual integrity and battle for the sake of battling. If one looks at Christ’s methods, they were opposite to this – He expressed the good news with love, grace, tenderness, kindness, and in a manner which afforded respect and understanding to those who were invited to consider carefully who He was. And if one doesn’t consider it a miracle that the most exemplary moral standards ever were laid out by the only man in history to make any reasonable claims that He is the visual representation of the God of Abraham and Moses and Elijah, one might also like to consider something even more extraordinary – a point which is even more astounding given what we’ve said about the unpredictability of black swans – everything Jesus spoke about regarding the future has been spot on.
He said people would hate us because of Him; that His words would cause division and resentment; that there would be false prophets that come to deceive people; and that there would be people who thought they were offering a service to God with their sanguinary activities – all of us know that these things have all happened time and time again. He said that Jerusalem would be temporarily under the control of Gentile nations (it was); He said that the Jewish people would regain control of Jerusalem (they have); and that the Gentiles would lose control of the land (they did); that earthquakes, famines and natural disasters would increases (they have); that false prophets will perform great signs and ‘miracles’ to deceive the elect (they have); that many will turn away from the faith and betray each other (they have); that nation will fight against nation in war (they have).
But perhaps the most astounding prediction He made was about His own church and the ubiquity of the gospel, both of which would reach every nation. Given the difficulty we have even in this day of predicting things like stock markets, general elections, financial nexuses, domestic affairs, foreign policies, social interactions, fashions, success and failures and the many other things where black swans are inevitable, it is astonishing that one man in ancient Palestine was able to say with such certainty that a message He was preaching would reach such far ends (a message that met much resistance and was on the fringes of a very powerful dictatorship) – I couldn’t do that even in this day with the technology so great – let alone predict in those days that those comparably few words He spoke and miracles He performed would be heard about and preached in every nation in the world, particularly given that such ubiquitous travel and communication was unheard of in those days.
Whether these prescient words arrived by the most outrageous fortune, which would seem to me to beyond the probabilistic threshold of naturalism, or whether these were words spoken by God Himself, the implication behind those words is that omniscience is being hinted at – Jesus didn’t speak as a man making forecasts, He spoke as a man who already knew how things would turn out. Although there are no axiomatic scientific cut off points for effective negligibility of prophetic words, if negligibility is relative to a model of probability for all systems of analysis (and for most systems it is), a man would be pretty unreasonable and possibly a little foolish if he suggested that the words of Christ were to be simply brushed off as the words of a mere man without seriously considering, firstly how such a man came out with the most powerful and influential words ever spoken, and secondly why all the words of prophecy He spoke have been shown to have been right. Of course this does not prove He is who He claimed to be; but once one takes the 300+ Old Testament prophecies fulfilled in the person of Christ, the power and influence of His words, and His own prophecies about times to come, the case presented in the Gestalt whole seems remarkably compelling.
Regarding the earlier point about the Newtonian universe and God tinkering with it, if God is to be found in the person of Christ and nature is a story written by God before the physical regime was put in place, then it seems God’s ‘tinkering’ with His cosmic creation is less like an engineer making adjustments to something He has built, rather it is more like an author appearing in a stage version of His own play (where we are also appearing with the freedom to improvise) – thus when Laplace famously told Napoleon that he no need of the God hypothesis to run nature once he’d found the stability conditions of the planetary orbits distilled from a pre-existing nebula, it’s not the case that he was right, in my view, more that he was mistaking God the ‘author’ with God the physical ‘engineer’. To be fair to Laplace, he may not have been denying God’s existence, just suggesting that the laws of physics are not broken by God in the way that Hume suggested they would be – although Hume had no conception of the probabilistic nature of those laws as ‘regularities’.
A lot of people seem rather perturbed about the state of particles in quantum physics being dependent on our observing them, after all things like that do not happen at the macro level – the trajectory of a leaf blowing in a park is not affected by my observing it, so why will the act of observation make changes on the phenomenon being observed? The difference in particle physics is that the instruments one uses for detection alter the state of what they measure; for example a photon must interact with an electron before we can detect it, but if one shines a light on a particle to view it, one then affects its state, which could be avoided if we could use fractional amounts of light. But Planck’s studies demonstrated that one must use at least one quantum which will disturb the particle and make its momentum unpredictable to us. Depending on the light wavelength for measuring, Planck’s work tells us that when you try with accuracy to measure the speed of the particle the less your precision in measuring the position, and conversely when you try with accuracy to measure the position of the particle the less your precision in measuring the speed. This is Heisenberg’s uncertainty principle – the uncertainty in the position of a particle times the uncertainty in its speed is always greater than Planck's constant divided by the mass of the particle (that is, Planck's constant divided by 2π) – and this proved to be a very useful heuristic when considering Laplacean determinism. Laplace’s determinism entailed the knowledge of the positions and speeds of the particles in the universe in order to give the cosmos a full predictive value, but Heisenberg put an end to that by giving us a sort of half determinism where one can know the position of a particle at the present time, and the speed of a particle at the present time, but only one or the other.
If we are seeing the world “through a glass darkly” our full vision when we come “face to face” with the true mechanics behind the physical regime may well have to wait until kingdom comes. Certain definitions elude us as our measurements are probabilistic - as with particles and wavefunctions, where the Schrodinger equation is used to determine the wavefunction value from which we can ascertain probabilities in relation to the certainty of either speed or position, but not both. But even this semi-determinism isn’t the whole story, far from it, because there are regions of space-time that we do not observe due to gravitational warping. Moreover, when it comes to black holes it seems impossible to make a definite prediction about a particle that leaves a black hole – which, unless we can find a measuring mechanism for returning the information (which seems highly unlikely), strongly implies a further reduction in our potential for Laplacean determinism. This has practical implications for our views on the surprises contained in the universe, including perhaps the miraculous. If information is lost forever in a black hole or whether it escapes in different stages, its apparent irretrievability coupled with the fact that throughout the universe particles and information are thought to be caught up in the many tiny black holes in the many regions of space means that nature is rather cryptic and mysterious and furtive about her secrets. In other words, although nature has the degrees of uniformity and order necessary for our understanding and acting on her laws and physical systems, she is endowed with a degree of mystery that may well lend support to the notion that her creator is an engineer who has enshrouded her in a mystery:
As the heavens are higher than the earth, so are my ways higher than your ways and my thoughts than your thoughts. Isaiah 55:9
It may even be true that our present understandings are much further from being complete than we realise, in which case, laws of science haven’t even determined the precise future of the universe yet, it’s as though cosmological pages are being turned and written as we journey through past, present and future to her final dénouement. This would mean admitting the astonishing truth that at any point in the present moment the universe is bound to conceal brute randomness and mystery – the physical regime and the parameters in which we work give nature the appearance of simulating only what is absolutely necessary for thinking minds – our understanding of the cosmos and our potential to utilise our knowledge will always be commensurate with the secrets she reveals to us, and when they occur. It is here that we can refer back to my coin analogy:
“Think of the whole interlocking system of nature as represented by 1000 pennies laid out side by side on a table. Mathematical studies will reveal to us all the possible configurations of sums and values we can observe with the 1000 pennies, providing there are no higher valued coins added to the collection of pennies. For when that happens there are new sums and values to observe, but they do not change our original estimations when we had only 1000 pennies. The naturalist’s perception of a lack of any miraculous events nature are equivalent to him viewing nature as 1000 pennies – failing to realise that God has put in higher valued coins to supplement nature. In this illustration the laws of arithmetic are synonymous with the laws of nature - they tell us what will happen provided there is no Divine activity supplementing nature; that is, they tell us all the possible configurations with 1000 pennies provided no more pennies of higher valued coins are added. But one thing is certain; the laws of nature do not tell us the probability of supplementation from the outside.”
And it is here that my coin analogy can be brought in, for our knowledge of what is in the bank account, so to speak, may never be complete, and the perturbations that occur in the physical regime may be analogous to the interest in a bank account, where God either supplements the equity from without, or the system itself is endowed with its own nexus of supplementary processes where coins continuously regenerate further interest on their total value and the nexus of processes are enriched, rather like in smaller terms a biological cell which processes structures like its nucleus, and organelles, and membrane, and cytoskeleton, and acting on the flow of molecules and energy, 'self-create' the components that maintain the structure that gives rise to these components.
If God’s creatures work in a system called ‘allopoiesis’ where we produce systems that produce things other than themselves (as we do with most forms of industry) then the universe is the ultimate system that does all the production, and that may entail perturbations that take care of its own interest rates, which of course may well increase as interest on interest, produces interest on that interest, and so on, until we are left with a set of explanations which explain different systems in different ways that although remain probabilistic and incomplete to us are just different perspectives on one vast and complex physical regime that can at the will of God turn water in wine and allow people to be healed miraculously. Whether the power of God that raised from the dead is a different mode of Divine agency to turning water into wine, or whether they are all Divine acts but with higher and lower resolutions of the miraculous, we cannot say for sure. But if the modes of Divine agency within His creation are modes of infinitely complex dispensations then their ultimate context of resolution in relation to human resolutions and expressions in cognition may never be fully grasped in this lifetime.
Given the foregoing observations, it ought to be fairly obvious that we cannot disprove miracles, and equally given that they are rare and sporadic and only observed locally and by comparably few people, there will never be a universal system for proving their existence. If, like Gödel’s’ theorem, any finite system of axioms is insufficient for proving every result in mathematics, we as creatures in the cosmos must be circumscribed by our own physical involvement within that system (not to mention our own local perspectives), and are bound by the same self-referencing problem whereby something cannot be both consistent and complete, it must be one or the other, and incompleteness seems to be an inevitable truth about our epistemology, thus conferring customary limitations on many of our positivist approaches to knowledge. And in the case of consciousness and how it relates to the external world, it must to some degree be always inconsistent and incomplete with the naturalists’ model, and probably just incomplete with the theists model.
Some people will be very disappointed if there is not an ultimate theory that can be formulated as a finite number of principles. I used to belong to that camp, but I have changed my mind. I'm now glad that our search for understanding will never come to an end, and that we will always have the challenge of new discovery.
More next week
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James is a Norwich local government officer, author and Proclaimers church member in Norwich. You can access his current collections of columns here
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