The God Delusion

Introduction

The book can be rightfully called thought-provoking, there are many interesting ideas and observations about religious practices being made. I found myself very much in agreement with Dawkins on the trivial points, for example when he points out the inconsistencies of literal belief in scripture, or when he argues that teaching religion to children takes away their chance to make a choice what to believe. However, I disagree with Dawkins on essentially every non-trivial count, and this is the main topic of this essay. I argue that Dawkins' presentation very much suffers from confirmation bias - he does not hold science and religion to the same standards. If he would apply the same standard which he uses to discuss religion to measure science, science would fail just as religion does in his book. On the other hand, if he would measure religion by the same standard he applies to science, clearly many religious ideas would still fail, but some would in all likelihood pass.

The essay has three parts. In the first part, I collect several points which are not really central to my argument, but still illustrate what I see as failures in Dawkins' reasoning. The second part directly aims to illustrate the roots of confidence in the scientific method, with the implication that there is no reason to assume that any other method which is based on the same roots is inferior to science. The third part finally shows the limits of rational thought as they are known in mathematics or physics and why these render Dawkins' main thesis rather meaningless.

I confine myself in the following to a scientific perspective and refrain from referring to any anecdotal evidence except in cases which are discussed in Dawkins' book. The discussion of essential ideas of quantum physics is (as no mathematics is used in the presentation) by necessity rough and a bit simplified, however the results are sound and I do not make quantum physics any more mysterious than it really is.

Text passages in smaller font contain discussions which are somewhat off the main line of reasoning. They are inserted for completeness, to indicate that I actually thought about details which are not discussed in length in the main text.

Several minor points

A fair comparison

First of all, science also has produced outcomes which are hardly a reason for pride, among them the nuclear destruction of Hiroshima and Nagasaki due to advances in physics, or gas warfare thanks to an increased knowledge in chemistry. Evolutionary biology has its own rather dark side in eugenics. While it is probably to some degree true that these examples do not represent what science is, but rather what a society can do with the tools science can provide, it can be argued similarly that what Dawkins presents is not so much what religion is but what a society may do with religion. If the worst that is coming from religion should be counted against religion, one should also count the worst that is coming from doing science against science - and I am not sure how well science would fare in this comparison.

Second, science done in real life is not quite the ideal of science. It does happen that the availability of funding determines the direction of research, that someone is less inclined to publish results which contradict established ideas because he is in need of a position or of grant money and does not want to oppose people who decide about such things, and it also happens that ideas are judged by the person who proposed them, not by their content. Postmodern philosophy has used such observations to argue that science is actually just a social construct. I vehemently oppose this view - chiefly because in my view there is an ideal of science and for sure some scientists are sometimes true to this idea even if it means a risk for their career or their funding, and every time this happens science makes progress in finding truth. But since I judge science by its ideal, I feel I should extend the same courtesy to religion.

In a broader context, Dawkins actually touches several questions. For illustration, I will in the following also discuss the equivalent questions for science:

	Religion	Science
1a)	Is there a god or an ultimate divine truth?	Is there an ultimate truth?
2a)	Is religion the right way to this truth?	Is the scientific method the way to find this truth?
2b)	Is religion beneficial for society?	Is the scientific method beneficial for society?
3a)	Is a particular form of religion the right way to the truth?	Is science as practiced by a particular group of scientists leading to truth?
3b)	Is a particular form of religion beneficial for society?	Is science as practiced by a particular group of scientists beneficial for society?

While the a) questions are connected, the b) are somewhat independent - one could be of the opinion that the impact of science on society is in general problematic and that therefore science should not be done even if it would be a way to establish truth. Or one could be of the opinion that science is in general unable to establish real truth about the world, but that it has benefits for society (in terms of the internet or teflon) nevertheless and therefore should be pursued.

Dawkins argues with respect to 1a) that there is almost certainly no god. A proof of the absence of anything, however, is difficult to make. There is a maxime in science that absence of proof is not proof of absence. Dawkins knows this, and goes for a plausibility argument instead - if every observation can be explained in terms of what we know, there is no need to introduce the supernatural. The main text of this essay will counter this statement and try to show that the rational scientific approach to understand the world is severely limited, much more than Dawkins would have us believe, and that there are quite enough unexplained things left to make one ponder if there is truth in religion.

Most of the book is however concerned with 3a) and 3b) - the way some people find truth in religion and the way some forms of religion impact on society. Dawkins is readily generalizing this to 2a) and 2b) - but falls short here. In a nutshell, what he is criticizing is the claim of some religions to final truth in scripture, the way critical thinking is discouraged in favour of belief for the sake of belief, the resulting group divisions in terms of believers and non-believers leading to religious conflicts who has the 'right truth' and who is morally just and finally the way these beliefs are transferred to children who can not in any way critically assess them.

It seems to me these things are characteristics of an ideology, not so much of a religion. Suffice to say, a religion can be made into an ideology, but a religion does not have these characteristics per se. To demonstrate this, let me draw attention to the mystical branches of religions which start from the idea that truth must be found in personal experience with the divine. As an example, let's consider Zen Buddhism. There are no children educated in Zen, instead whoever wants to practice Zen must demonstrate to a Zen master that he is mature enough. There are hardly any scriptures in Zen, instead Buddhism teaches that one has to go beyond words in order to find truth. Zen doesn't ask for any belief but for individual experience in meditation. And so on. So, while Buddhism certainly is usually grouped into the major religions, Zen has almost none of the characteristics Dawkins implicitly ascribes to a religion.

One could be argued that the Nirvana of Buddhism isn't actually a god, and that in that sense there is no god in Buddhism. However, the Nirvana shares many characteristics with concepts in other mystical branches of major religions, for example with the Cabalistic Ain Soph - but that in turn is identified with the biblical Jahwe. I will therefore in the following dodge the question of a personified god and instead refer to 'the divine'.

So, what is Dawkins saying when he argues that religion in general is a bad thing? Let's turn this around and make a gedankenexperiment. Imagine that most of the scientists would do bad science - they would do biased experiments which are not suited to find any truth, and imagine moreover that the results of this bad science would be used to deceive people, for example in order to market certain products (I don't actually believe that most scientists are like this - this is a gedankenexperiment!). What would be the implication - that science in general is bad and that it should not be done?

My guess is, Dawkins would not argue that way, but just like myself he would argue that one should fix the problem and get people to do good science instead of giving up. In the same way, I don't see how the fact that I (like Dawkins) find certain forms of religion to be neither a good way to approach andy truth nor a good influence on society would imply that religion in general is bad. I think, also from a scientific point of view, the case can be made that some religions may be on to something interesting.

The role of scripture

Did you think for a moment I wrote about the bible or any other scripture? No, actually I had the birth of quantum mechanics in mind. Initially there was Heisenberg who conceptualized everything in terms of matrix equations, and Schroedinger who had wave equations, and if you read the two descriptions, it doesn't look like the same thing at all. It looks violently inconsistent, the equations look completely different, in one case you need linear algebra to work out solutions, in the other case differential equations, in one case indexed states are the fundamental quantities, in the other case the wave function. Later came Feynman with the even different concept to sum over all potential paths a particle could take.

One can imagine how it could have gone - the school of Schroedinger vs. the school of Heisenberg, vehemently denouncing the work of the other group as not reflecting the relevant truth, the sect of Feynman inbetween, people being expelled from the school of Heisenberg because they dared to use the wave picture of the Schroedingerists, and so on. However, this is not how it went.

In reality, people realized that if you look through the technical and conceptual differences, all the approaches refer actually to the same thing. It does not matter if you use matrix mechanics or solve a wave equation - these are just different ways to describe the same underlying truth. And this story should make one cautious with respect to two things: First, there is often no value in a literal interpretation of something, instead one should search for the idea behind. And second, face value contradictions in religious texts do not necessarily mean much - in fact we expect them to be there if different people try to describe the same idea, but this idea is difficult to describe. Dawkins' approach to religion seems very much geared to be hung up on superficial differences instead of going onward to the ideas. And his treatment of science is rather different.

What, actually, is the supernatural?

To elaborate on this point further, let us consider a scientist who is confronted by a supernatural being trying to make the scientist believe in the supernatural. Starting with a classical example - would for example the transmutation of water into wine be evidence of the supernatural? In order to answer the question, let us analyze another classic first, the transmutation of lead into gold, the goal of alchemy. Far from being supernatural, this one is actually comparatively easy. I know myself how to do it with nuclear reactions - it's just technically complicated and not worth the effort since it is far cheaper to mind gold than to produce it from lead. But in principle it can be done, there is no natural law that prohibits changing one element into another. I would not know how to do it with water and wine, but this is due to my lack of knowledge in chemistry - anyone who had sufficient knowledge in chemistry along with the knowledge to induce nuclear reactions could in principle change water into wine, although I don't think anyone today knows how to do it in practice. But not being able to do something in practice is something very different from supernatural. So let us move on to a different example.

Suppose a supernatural being demonstrates to the scientist the ability to walk on water. What would a good scientist do after having clearly verified that no deception is involved? Well, he would in fact not conclude that there is something supernatural - he would assume that there is either a force at work which physics did not previously know and which he has just observed for the first time and subsequently try to understand its laws (and thus expand the definition of what a natural phenomenon is), or he would assume that our knowledge of the law of gravity may be incomplete and try to emend the law of gravity such as to incorporate the new observation. What he would not do is sit down, be awed and state that this clearly must be supernatural - that's not how scientists are.

Thus, we need something more involved - maybe an experiment where the outcome depends on belief and intention - this would clearly show something beyond universal natural laws. Or would it? Actually, in medical research it has been known for a long time that experiments depend very much on the beliefs of the subject - this has not really been explained, but given the label 'Placebo effect' and its action is accounted for in systematical double blind studies. No researcher ever claimed that the Placebo effect would be supernatural - it is not really understood, but again, this is something very different from supernatural. Maybe medical science is too vague and experimental results not precisely enough defined - so let us move to physics where measurement results are quite unambiguous. About 100 years ago, physicists were very much ad odds if light is a wave or a particle - so based on their individual belief, they designed experiments. The amazing outcome was that those physicists who believed in light as a wave could get solid experimental evidence that light is indeed a wave, but those who believed that light is a particle could get equally solid evidence that light is indeed a particle. Far from convincing anyone in the physics community of the supernatural nature of light, a solution was eventually reached in rethinking the concepts of physics: In modern physics, 'wave' or 'particle' are not considered good concepts to describe the world, rather the 'quantum state' is a good concept, and how a quantum state appears to the observer (for example if as wave or as particle) depends very much on the point of view of the observer. A bit simplified, anyone who wants to observe light as a particle will be able to do so. Thus, such experiments will also not convince our scientist of the supernatural.

So, as a final straw, what about the following? Something happens so overwhelmingly often that a universal rule is established, but sometimes something completely different and weird happens - would this be considered supernatural? You may guess the answer - it would not. Before 1964, physicists believed that the laws of nature would be CP invariant. This is a bit of a complicated concept, but in essence it means if one goes into a mirror-world and exchanges positive by negative charges, one would not see any difference to our world. A breaking of the CP invariance was considered weird, because it would imply that the time direction is uniquely identified, i.e. watching a movie in which two billard balls collide, one could actually tell if it runs forward or backward. The fact that the time direction is identified in the laws of physics may not mean much to you, but as far as the fundamental equations in any stage of physics went, time reversal invariance was a central concept and the idea that it could be broken almost unthinkable. Nevertheless, in 1964 CP violation was measured. In an overwhelmingly large number of cases CP invaniance works, but sometimes the weird thing actually happens. Again, far from convincing anyone of the supernatural, the laws of nature have just been cast into a probabilistic framework which is able to account for something happening usually and something else in rare cases.

What these examples show is that there is a problem with the definition of the supernatural - if it includes anything which exceeds our current understanding of the laws of nature, then researchers encounter the supernatural every day as they expand the frontier of knowledge. If, however, it includes all that can not potentially accounted for by future extensions and modifications of these laws, then it is in essence defined as all things that can not happen - and even a god or other supernatural being would be hard pressed to demonstrate something that cannot happen without demonstrating at the same time that is actually happening.

Given this definition, it is no surprise that no evidence for any supernatural phenomenon has ever been found - in fact, by definition none ever will be found. By definition there can't be any. If science ever encounters a god of any kind, that god will be made part of the laws of nature, not anything supernatural.

Musings on evolution

Let me state up front (in case this is actually needed) that I find the evidence for natural selection as a principle behind evolution from simple to complex organisms very compelling and therefore agree mostly with what Dawkins describes in chapter 4. However, I do have issues with chapters 5 and 6.

In many places, Dawkins seems to use what I would call the 'strong' concept of natural selection which states that Darwinian selection constantly drives replicating organisms to an optimal adaption to their environment. This is evident e.g. from his citation of Lewontin at the beginning of chapter 5: That is the one point which I think all evolutionists are agreed upon, that it is virtually impossible to do a better job than an organism is doing in its own environment. My understanding of evolution was different, but since I am not a biologist myself, I asked researchers working in genetics and molecular biology if this is true, and received what I would call the 'weak' concept of natural selection: Traits which render the performance of a replicating organism in its environment below some acceptable threshold will be weeded out by natural selection. In addition, I was given several examples of organisms which are manifestly not optimally adapted to their environment, but do in some sense 'well enough'. One striking example is the horse - despite the appearance to the contrary, a horse is not well adapted to eating grass. A system optimized to digest grass is seen in the several stomach tracts of the cow - a horse has nothing comparable. As a result, fresh, wet grass with high nutritional value (in contrast to dry steppe grass) can be actually dangerous to a horse in terms of causing colic. Neverthelss, the horse works 'well enough' in its usual environment so that natural selection never optimized the digestive tract. Thus, it seems Lewontin is in error about a consensus in the research community with regard to the strong version (unless people doing genetics don't count as evolutionists).

Adopting the strong or the weak version of the selection principle actually makes a difference, as the weak version leaves quite some room for mechanisms other than natural selection to determine the evolution of a replicator, whereas the strong doesn't. Dawkins himself actually mentions a second mechanism, genetic drift, later in chapter 5, so it is somewhat unclear to me to what degree he really advocates the strong concept.

Nevertheless, at the beginning of chapter 5, Dawkins makes, to my mind, a rather strange application of the strong concept. At the example of anting (some birds 'bathing' in ant nests), in spite of the fact that it serves no recognizeable purpose, he states that Darwinians should presume, with great confidence, that anting must be 'for' something. To spell it out more clearly: There is, on face value, evidence in anting that there may be animal behaviour which is not driven by natural selection. Nevertheless, because we 'know' the theory (natural selection) is correct, that evidence should be discarded as it surely does in fact agree with the theory, even if we don't understand how. It is unclear to me how one could actually hope to test or falsify such a theory, if any evidence against it can be discarded.

What is quite clear to me is why Dawkins needs the strong concept at this point in the book, because he needs to convince the reader that evolutionary psychology is actually sound and natural selection is the main driving principle behind the evolution of the human mind for chapters 5 and 6 to make any sense. Which doesn't seem even remotely plausible to me. I can observe continually that the mind is amazingly adaptive on short timescales. Three months after moving across the Atlantic ocean, I have caught myself unconsciously using 'home' to refer to the new place in spite of all cultural differences. During just six weeks in Japan, I went from 'Japanese people look almost alike' to 'I can spot my friend from behind halfway through a crowded store'. That a system capable of such rapid adaptions should be stuck in patterns acquired to cope with a stone-age hunter-gatherer environment doesn't actually seem very plausible. Neither does the theory that the mind is optimized to propagate the own set of genes go well with the observation that, as soon as reliable contraceptives are available, a large fraction of the population of the Western world commits voluntarily 'genetic suicide' by deciding not to have any children.

Following the last of the 'Ten New Commandmends' ('Question everything!') and good scientific practice, when faced with an implausible theory, one does well looking into the evidence underlying evolutionary psychology. It turns out there isn't really any.

Evolution of organisms by natural selection has plenty of evidence going for it in terms of lab and real life observations of animals adapting to changed environmental conditions and in terms of fossilized records of adaptive changes in species. Evolution of the mind has nothing of that sort. One can take a look at models of the mind in modern psychology where people can be observed, questioned and tested in various way to appreciate the difficulty to get a handle on the mental setup of modern homo sapiens. Trying to understand the mind of people in the Roman Empire, one at least has written documents available. However, the mental setup of stone age man is purely conjecture. There are remains to be found, and tools, and hence one can get a rough idea of the conditions of living, but to extrapolate from this how the mind of man in the stone age worked is impossible. But without knowing how the mind of people worked in the past, one can hardly determine which mechanism primarily drove its evolution.

One of the most celebrated findings of evolutionary psychology is the supposed explanation for the finding that women are more disturbed by the thought of their partner forming an emotional attachment to another woman ('emotional infidelity'), whereas men are more disturbed by the thought of their partner actually having sex with another man ('sexual infidelity'). Evolutionary psychology explains this in terms of a man's mind setup adapted to being concerned with a child of his partner carrying his genes and a woman's mind setup adapted to making sure a partner is around for the difficult time of pregnancy and child infancy, as a woman can be sure of any child of hers carrying her genes.

This 'explanation' assumes that stone age humans lived in fixed partnerships and not as a group taking care as a whole of infants, otherwise for example a woman's emotional jealousy would not be a selection advantage. But we don't actually know that - some apes (Bonobos for example) live in larger communities, not in partnerships.

Perhaps even more telling is a look at the raw data of different studies, broken down by country. In the US, typically between 60 and 70% of males find sexual infidelity more disturbing than emotional infidelity, i.e. a clear majority. In China, the numbers are vastly different - merely 21% of the male population find sexual infidelity more problematic, the majority there reacts stronger to emotional infidelity. Given that the differences driven by modern culture are so huge, it is rather unlikely that the claimed 'explanation' of evolutionary psychology has anything to do with the actual result.

In short, if one is allowed to speculate almost unconstrained about what social and environmental challenges a stone age human may have faced, one can quite probably 'explain' any modern-day behaviour in terms of this speculation. This doesn't make any of it true. Just to provide a counterexample to Dawkins' evolutionary psychology 'explanations' of religion - suppose for a moment that there is something divine in the world, and humans have an evolutionary advantage in getting into contact with it and getting a glimpse of the divine plan. Natural selection would continuously improve the ability of man to perceive the divine, accounting for the evolution of animal totems (depicting something a hunter actually encounters) to hellenistic deities (more abstract personified virtues and other properties of man) to the completely abstract concepts like the Nirvana, the Tao or the Ain Soph. It would account for the differences between religions (the divine always seen through a different human filter) and for the fact that the abstract concepts of the divine are actually rather similar (as the filter improves, the nature of the divine becomes more clearly apparent). Let me hasten to say that I don't claim that this is actually true - just that it seems at least as plausible as the evolutionary psychology explanation.

One can also look at the evolution of complexity from a radically different perspective, and then much of the whole discussion in Dawkins' book appears a bit like a red herring. If there's no 'outside' influence (like a morphogenetic field, an immortal soul or anything like that), and I am rather confident Dawkins does not want to postulate anything like that, then an organism can in principle be explained in terms of cell biology when going to a smaller scale, its environment in terms of classical physics and chemistry. Cell biology in turn should emerge from biochemistry at a yet smaller scale, all chemistry then from atomic physics. Finally, all physics ultimately at the smallest known scale emerges from quantum field theory. In this view, we would use natural selection as an effective way to understand what happens at a size scale of an organism, but if we could somehow solve the underlying quantum field theory directly, we would in fact get the same result as genetics or Darwinism provide (if this would not work, we'd have to conclude that there is in fact an outside influence, a substantial effect not known to science so far).

But now something interesting happens. There is evolution in quantum field theory, but the word means something different. It is a completely deterministic evolution. If the quantum state at one time is known, the equations of the theory allow to compute it at any other time, be it back into the past or forward into the future. Given the state at one time, one has thus complete and unique knowledge of the state at all times. This has an obvious implication for complexity - the complexity of a state in this picture neither increases nor decreases - the information content of a state is the same at all times.

In plain words, any outside observer with the knowledge of the quantum state of our universe at its beginning could in principle have computed the quantum state of our universum as it is now and could have known about Dawkins' book more than 10 billion years ago. In the more fundamental picture, there is no evolution of complexity by natural selection, there are just quantum fields undergoing a deterministic evolution from state to state by extremizing the action of their Lagrangean function. The complexity of the universe now is that with which the universe began. And this picture is no less scientific than the one outlined by Dawkins - it just describes things at a different scale.

Darwinian evolution in the quantum picture becomes a fix-point of the theory. If one does not have detailed knowledge of the quantum state, one can replace it by random configurations. This (like entropy in thermodynamics) is a calculational trick to manage our lack of detailed knowledge - it has nothing to do with what is really happening in nature. If we do so, we may find that there is something in the theory that leads the evolution to a certain similar outcome for a larger class of initial states which are not too different. Darwinian evolution is such a fixpoint - it states that even if the quantum state of the initial universe would have been somewhat different, we could expect to see life developing. But as the fundamental process, Darwinian evolution is misleading - the initial state of the universe was what it was, and it is playing out now. It does not matter what manner of life different states had produced if the universe would have begun with them. We only solve such questions to manage our lack of knowledge of what the true state was.

The nature of evidence

Direct and indirect evidence

To appreciate the difference, let us assume I return home from work, and when entering the kitchen I see the cat spilling some milk. Here, I have first hand, direct evidence that the cat spilled milk and not, say, my wife.

An interlude for people who have heard of a philosophical idea called 'Solipsism': Strictly speaking, I cannot be absolutely sure that what I saw corresponds to external reality. I might have been hallucinating when I saw the cat. I might have dreamt it, and somehow confused dream and reality. What I perceive with my senses might not correspond to any reality at all - I may be stuck in a virtual environment (as in the movie 'Matrix'), or my brain may generate the illusion of an external reality. Basically, I make the assumption that there is an external reality, and that my sensory input is somehow connected to it, and that I have a basic capability to distinguish internal images like dreams from external images like my cat spilling milk.

Now imagine I come home from work, and I see spilled milk in the kitchen, and right next to it the paw print of the cat. I would conclude that the cat spilled the milk. But I cannot be as sure as with direct evidence - my wife may have spilled the milk, and the cat may have stepped in later. It would not be the usual behaviour of my wife, so it is unlikely, but it is just possible.

There is, on closer inspection, a whole machinery of deduction rules and principles which turn indirect evidence into conclusions. These are the basis of rational thought and the scientific method. Usually we do not even think much when we apply such rules in everyday life, but it is good to spell them out once in a while. An example for a deduction rule is transitivity: If A implies B, and B implies C, then A implies C. In the example, 'a paw print is generated by the physical presence of a cat' and 'a paw print is found in the spilled milk', transitivity allows to remove the paw print and to conclude 'the cat has been physically present in the spilled milk'. An example of a guiding principle for deduction is Occam's razor. The principle states that the explanation of any phenomenon should make as few assumptions as possible. For example, it may be possible that extraterrestrial visitors from Mars landed on Earth, entered my kitchen, spilling milk in the process, and faked a cat paw print in order to hide their presence. Since this explanation requires lots of additional assumptions (life on Mars, availability of interplanetar spacecraft for the Marsian population, the ability to land undetected,...), Occam's razor makes me reject this possibility immediately.

It is important to realize that Occam's razor does not necessarily lead to truth - it leads to the explanation that it most probably true, given the (incomplete) set of indirect evidence. More evidence can change the conclusions. For example, if I learn from my wife that the cat has been at the place of a friend the whole day, my conclusion that my cat spilled the milk would change - maybe I would then tend to blame a different cat intruding into the kitchen.

This is why Dawkins' statements are not equivalent: There is direct evidence for New Zealand being on the southern hemisphere - one can see it from space. In the absence of a ticket on the space shuttle, one can also refer to countless satellite images - barring a world-wide conspiracy to publish fake earth pictures, they show the same thing. It is not really conceiveable that any future evidence would lead anyone to locate New Zealand on the northern hemisphere. On the other hand, the truth of evolution is a conclusion reached on the basis of indirect evidence like fossils (this is why Dawkins would change his mind if evidence against evolution could be found). Unlike the location of New Zealand (which requires essentially the assumptions I made above to get away from Solipsism), the truth of evolution requires that one accepts transitivity and Occam's razor. It is easy to picture a situation in which Occam's razor leads to the wrong conclusion. But interestingly enough, I know for every single deduction rule I am aware of at least one situation in which it fails. Nevertheless, I place an immense trust in these rules and principles, and I apply them with great confidence. Why is this so?

The origin of 'belief in evidence' and its limits

My confidence in the deduction rules and principles comes directly from experience, and I suspect that it is quite the same with every scientist. There are many situations where indirect evidence is available before direct evidence becomes available. For example, I might first see the spilled milk and the paw print, conclude that the cat has spilled the milk, and then learn five minutes later that my wife has been in the garden and has indeed observed the cat spilling milk through the window. Thus, I have experienced that my set of deduction rules allowed me to make the right conclusion. Like possibly most people, I have been through literally thousands of such situations and experienced that a certain set of rules works in most cases, although occasionally a conclusion turns out to be wrong.

Thus, at some point, I am confident enough to apply the same set of deduction rules which I have learned and tested in cases where ultimately direct evidence was available to cases where (in practice or even in principle) no direct evidence is available. Still, it is often in such situations possible to test the deduction by predicting how further bits of indirect evidence should look like. For example, after seeing spilled milk and the paw print, I can predict that if my cat spilled the milk, an investigation of the paw should find traces of milk. If this turns out to be true, my deduction, although still not confirmed directly, is at least indirectly substantiated.

However, it goes even beyond this. Predictions from theories based on indirect evidence turn out to be so successful that in many cases I trust them more than my direct experience when an indirect deduction contradicts direct experience. For example, direct observation tells me that the sun moves over the sky each day, and direct observation tells me that I can feel when I am in motion - out of which I would conclude that the Sun is moving around a static Earth. But there is so good indirect evidence to the contrary that I reject my direct observation that I feel motion and am convinced that strictly speaking there is no preferred frame of referece, but that for the almost flat spacetime of the solar system a frame of reference in which the sun is at rest describes the situation better (yes, general relativity allows to do all calculations in a frame where Earth is at rest - the metric of spacetime just gets very messy).

This actually should give one some pause, as the deduction rules are based on my direct experience with phenomena, but now I use them to reject some direct experiences - so the question is, is there any arbitrariness involved in the rejection process? In other words, are some experiences rejected not because they are not true, but rather because I don't want them to be true? There is no easy answer to this question (and my guess is a fair number of scientists never really asks it), but the guiding principle is something like consistency - dismiss the minimal amout of contradictory direct experience and indirect evidence such that the rest fits into a consistent picture.

That in itself raises the question where the principle of consistency comes from. Of course, at first glance it is plainly obvious. But going beyond, the question is not so easily answered. Consistency, or absence of contradictions, is something that is, at least in the sense used here, not fundamentally part of nature. Quantum field theory has a rather different concept of consistency and contradiction and allows many things to coexist which would be contradictions in almost any rational deduction system. On the other hand, consistency appears to be very much a property of the conscious mind - it is known that contradictory input from different senses is heavily edited by the mind in order to create a consistent conscious experience. So ultimately, the consistency principle may be more about how the mind works than about how nature is. But I'm afraid, I have to leave it like that - I cannot offer a more compelling solution or an ultimate argument in the defense of rational thought.

Rational deduction from indirect evidence works well in most situations one experiences, it allows to make successful predictions of how a situation will evolve based on deductions with regard to its cause and rational thought is thus a useful paradigm to make good decisions. In the absence of an ultimate philosophical argument, this in itself should be good justification for most purposes.

The role of prior 'knowledge'

The first is the claimed ability of the human mind to see patterns in randomness. This is briefly alluded to in Dawkins' book. That is evidently highly relevant for a discussion of the divine and religion, as such an ability would amout to combining random events into a meaningful pattern which appears as fate (providence, divine justice,...). The clearest example I fould was a psychologist generating random sequences of numbers on his computer, handing those to probands asking if they could detect a pattern. The study found that indeed all of the probands claimed they could detect (rather complicated) patterns. This seems to prove the case.

Unless you have some knowledge of informatics and are aware that random numbers generated on a computer are actually pseudo-random numbers which are generated according to a pattern which is just very complicated so that it appears random. So the probands were actually correct in assuming a pattern. But it goes even further - one can mathematically prove that any finite sequence of numbers can be generated by a pattern (in fact, one can prove even that for any finite sequence of numbers one can find a pattern such that the next number is 3), so it takes infinitely many numbers to mathematically distinguish a patterned sequence from true randomness. Thus, presumably most of the probands' patterns where in all likelihood mathematically correct solutions to the posed problem.

It was the assumed 'knowledge' of randomness of the sequences that led the researcher to his conclusion. But that is nothing but a subjective judgement of complexity - to him any pattern in the sequences seemed to complex that he did not spot it and judged it random - but a different mind may be able to deal with more complexity and identify a pattern in the same sequence - and is backed up by mathematics in doing so, because there is a pattern. So, one cannot rigorously prove that any given sequence of events is truly random or has a pattern to it, and that is an obstacle to most arguments based on pattern recognition in randomness. (One can, however, falsify the assumptions that events follow any particular pattern stated up front, so if somebody claims to know fate (providence, divine justice...) it can be tested.)

The second example is likewise only briefly mentioned in Dawkins' book - it has to do with brain activity scans of practicioners of meditation. While the people in meditation experience the unity with the divine and a sense of understanding the universe, brain centers responsible for making connections between different observations are seen to be active. Thus, the meditative unity with the divine is explained as a particular function of the brain which is active during meditation.

In order to understand where this goes wrong, let us assume the neurologist had not scanned the brain of a practicioner of meditation, but rather of a physicist sitting and realizing how his new theory connects with data (or a neurologist realizing the correct interpretation of brain scan data). The scans in all likelihood would have shown the same activity in the centers responsible for making connections. Nobody would be surprised of that, because that is just what these scientists do - making connections between evidence and theory in order to understand something.

In no case there is any outside sensory input, the activity in the connection centers is entirely driven by the internal state of the brain. So if, in the case of meditation, the experiment shows that the feeling of understanding is an illusion generated by the brain, the same reasoning should conclude that brain activity that generates the feeling of understanding a physics theory or brain scan images is also an illusion generated by the brain. This, however, is usually not concluded. The reason is that neurologists do the experiment being convinced that science works, and religion is an illusion. The experiment itself does nothing to prove or disprove this notion - it shows that a feeling of understanding is correlated with activity in certain brain centers. If the experiment itself could disprove the truth of meditation, it could also disprove the truth of science - since it can't undermine science, it also can't undermine the experience during meditation. Whatever is used as a criterion to distinguish what reflects reality and what is illusion comes from outside the experiment.

A similar technique may be applied to meme theory which features rather prominently in Dawkins' book - we just apply it to itself. The idea of information replicating itself using carriers is itself a meme. It is correlated with the presence of other memes in a person, say if you do science and if you believe that genetics is a valid description of how the replication of organisms works, you are much more likely to accept the idea of memes than if you believe in Intelligent Design or the morphogenetic field. The argument then goes completely as above - if the correlation of memes into a memeplex can 'explain' religion, it can also 'explain' science. Indeed, postmodern philosophy advocates precisely this explanation for science when labelling science as a social construct. The memeplex of a scientist is, using this reasoning, as internally consistent (note the re-appearance of the consistency principle in combining memes into a memeplex) as the one of a religious person, and it is therefore as true. Any scientist will of course reject the notion that science is just an arbitrary collection of consistent beliefs having no real connection to reality. But again, as above, the distinction does not come from within meme theory, it comes from somewhere outside.

This is the reason we discussed the roots of the belief in rationality in such detail - we need to understand in what way they are different from the roots of non-rational belief, and since the roots of rational thought lie in experience with rational deduction and decisionmaking, we need to understand experience with non-rational deduction and decisionmaking.

Failures of rationality

The prisoners' dilemma from game theory is a classic example in which rational decisionmaking fails. In its abstract form, the dilemma goes like this: Two players in separate locations can make a decision to co-operate or to try to exploit the other, but they can not communicate and have to make their decision independently. If both co-operate, they receive three points each (the points stand for anything the two players want, so everyone wants to leave the game with the maximal number of points). If both exploit, they essentially hinder each other and each receives just one point each. However, if one player exploits while the other decides to co-operate, the exploiting player receives five points and the co-operative player gets nothing.

The rational argument is easy to see: Try to exploit, whatever the other player does, you'll be better off. If the other player co-operates, you get five points when you exploit, but only three if you don't. On the other hand, if the other player also exploits, you get at least one point if you do it yourself, but nothing for co-operation. One can do it more formally with the apparatus of game theory, and the so-called Nash equilibrium, a situation in which no one can be better off by changing his strategy unilaterally, is reached when both players exploit.

However, it is obvious that the outcome of the rational choice (in which one is always better off than if one had chosen otherwise) leads, if both players are rational, to the result that each player gets one point, whereas they would both enjoy three points if they had thrown the rational choice out of the window and just co-operated. But that would have required a leap of faith, a trust in the other player that he likewise will not be rational. Note that many religious decisionmaking paradigms handle the dilemma well - for example a Christian may believe that exploiting the other player is bad no matter what, hence he will never be tempted to exploit. However, also non-religious principles such as Kant's categorical imperative can deal with it adequately. One can therefore attempt to extend rationality in a way that an extended rational decisionmaking paradigm can handle the prisoner's dilemma. However, other problems of similar type eventually require a 'rational' choice which consists in throwing a dice and following a particular course of action if a given number occurs - it is certainly a stretch of the meaning of 'rational' to apply it to a random choice.

Dawkins' interpretation of the success of religious paradigms in the prisoners' dilemma would probably be that they have evolved to handle exactly this kind of situation. Be that as it may, the point I want to make here is that a rational choice isn't necessarily a good choice, in order to make good decisions, we need also decisionmaking paradigms beyond rationality.

The failure of a formal, rational system to establish truth in some circumstances is evident from Gödel's incompleteness theoremes. The important one reads in formal language: Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true but not provable in the theory. What this means in plain language is that any formalization of rational logic which is not trivial but actually capable of dealing with real-world input is either not consistent, i.e. contains internal contradictions (note again the theme of consistency appearing here in mathematics) or there are statements which are true, but they cannot be proven from within the formal system. In particular, self-referencing statements have this property. A (simplified) example goes like this - assume I have a system of rules for forming logical conclusions from evidence called X. The statement 'This statement cannot be proven in X' must be true - because if it were false, we get the contradiction that one the one hand, being false, it can in fact be proven in X. But if it can be proven in X, then its content is true, and that says that it can not be proven. Since the statement cannot be false without contradictions, but it can be true without contradictions, it must be true - but then it is also true that it cannot be demonstrated to be true within X.

You may be tempted to argue that this is intellectual hair-splitting and that self-referencing statements are a rather special thing and not really relevant outside of mathematics. But unfortunately, self-referencing occurs in any discussion of the divine and science in at least two places: The incompleteness theorems states plainly that science cannot prove its consistency within itself and that there are true statements which cannot in principle be proven by science. And of course the conscious mind which makes all experiences is in itself a self-referencing system - we are aware that we are aware. Thus, self-referencing and the fact that rationality operates in a funny way when self-referencing is involved cannot be dodged.

Intuitive understanding and imaginary friends

Intuition sometimes contradicts the rational conclusion. The investigator knows that on face value, the evidence points one way, and yet, he knows somehow that there is something wrong and that the truth is different. What is really different when comparing intuition and rational deduction is that when we apply rational methods, we do not only know the conclusion, we also know why we reached that particular conclusion. We can tell others, and they can follow each step till they arrive at the same result, thus we can convince them. Not so with intuition - here we know the evidence, we know the conclusion, but we don't know anything of the link - intuition seemingly jumps across all intermediate steps. Thus, it is impossible to convince others of a conclusion reached by intuition - either they trust the conclusion, or they don't.

Intuition can go wrong. In fact, if untrained, it often does. But so does logical deduction when untrained. Intuition can however be trained and tested the same way as rational deduction. Several forms of meditation are aimed to focus the mind on intuitive understanding for example. Any trust in intuitive deductions comes from the same source as trust in rational deduction - experience. If enough intuitive conclusions turn out to agree with direct evidence found later, if intuition predicts events correctly and if intuition allows to make good decisions, then intuition is essentially justified the same way as rational deduction. I am often tempted to think that rational deduction still has the last word, but I have more than 15 years education in the rational method and none in intuition, so presumably there is some bias here.

Intuitive understanding is actually not as such opposed to rational deduction. Dramatic breakthroughs in science sometimes happen because someone is able to make a huge intuitive jump in an unexpected direction he knows to be right, and then, looking back, is able to reconstruct the logical steps leading there and in doing so can also convince others that he is indeed right. But as rationality sometimes leads to deductions which cannot be verified by direct experience or any other way and we simply have to trust that the method still works, the same way intuition sometimes leads to results which cannot be verified, and one can trust it or not.

Part of what Dawkins has to say about imaginary friends as an explanation for visions of gods may actually relate to intuition. The term 'imaginary friend' suggests that a child (or grown-up person for that matter) makes a decision to imagine someone for keeping company, and invents then the characteristics of that imagined character. In many cases, this may be what actually happens. But there may also be something else which is easily confused. The imaginary friend may just be one way intuition presents itself, or it may be even more.

First of all, while it seems easy to equate 'imaginary' with 'not real', note that 'real' is not a clear-cut decision. Most people agree that out of a cup of coffee, light and a Beethoven symphony, all are real. But what exactly is the real Beethoven symphony? The soundwaves during a performance, the notes on paper, the magnetic track on a CD, the idea of the sound in people's mind, all of those, or something else entirely? What would need to happen in order to destroy it (and hence to unmake its reality)? Things can have a rather complicated way of being real.

Then, things which are not real can still be the interface to something real. Consider the desktop on your computer screen. It is not real (that's why it is called 'virtual'), one cannot place a cup of coffee there, and there is no real structure in the computer corresponding to the desktop. In fact, one can completely alter the desktop appearance and functionality with a few mouseclicks (at least if one is a Linux user...), and one can dispense with it alltogether and operate the computer in text mode - the essential functionality of the computer remains just the same. But the desktop is an interface - even if it is not real in itself, it displays and allows to control real things which happen in the computer in an organized way. Giving a 'delete' command on the desktop causes a real change on the magnetic tracks of the harddisk.

Similarly, an apparition that is invisible to other people (a purple man, the Virgin Mary...) may well not be real in itself, but it might be a mind-generated interface to something that is real enough. The way to tell the difference is to look at the information provided by the invisible friend. If someone has an invisible friend who tells him whatever he consciously imagines him to say, then one might conclude that he indeed imagined this figure. If the invisible friend however tells things he does not know, but which he can in principle know (for example, where a key was lost, or why he feels bad, or something like this) one might conclude that the invisible friend is an interface to the subconscious mind. Finally, if the invisible friend tells things he cannot possibly know (like describing a place where he has never been, or predicting an event which he cannot have known) and these things routinely turn out to be correct, the conclusion seems justified that the invisible friend is an interface to something outside - which is in itself quite real.

If someone gets routinely good advice and information which turns out to be accurate from an invisible companion - why on earth should he accept any logical reasoning that this companion is not real? Should he not rather think that the logical reasoning is faulty? As we will see below, in the case of the miracle of the sun, sometimes an apparition makes strikingly good predictions about future events, and to explain these away as cases of imaginary friends is not very plausible - where else does the (real) information come from?

So, ultimately, if any form of intuitive understanding leads one to the divine - why should this be automatically dismissed if intuition works elsewhere and rationality is known not to work everywhere?

None of the above is meant to indicate that intuition would in any way be better than rationality, or that rationality should be abandoned in favour of intuition, or that objective truth should be replaced by everyone's private truth. Intuition has its own dangers - it is much more in danger from wishful thinking than rational deduction for starters. Quite obviously, rationality works all in all quite well for many questions, and to stop rational thinking in general is, well, rather stupid. If intuition is to be used, it must be held to the same standards as rationality - it must be tested wherever possible and moreover trained. The idea of the above is merely that intuition is a method which can potentially complement rationality, or which can be applied where rationality is known to fail, and that there is no reason to assume rationality is the only method to discover truth.

Consistency, quantum theory, and the nature of delusions

There is now an obvious catch: What if there is a contradiction - i.e. what if we have a question in which we can not have direct experience and for which a well trained intuition and rational deduction give different answers? This section will deal with how we commonly resolve such contradictions and what quantum theory implies for this question.

What is a delusion?

A false belief based on incorrect inference about external reality that is firmly sustained despite what almost everybody else believes and despite what constitutes incontrovertible and obvious proof or evidence to the contrary. The belief is not one ordinarily accepted by other members of the person's culture or subculture.

Thus, clinically a belief is not a delusion even if it is held in spite of proof or obvious evidence to the contrary of enough other people share it. This is accounting for group dynamics - since we usually don't have the time to check everything ourselves, we tend to accept a belief held by a larger group, presumably with the unspoken assumption that at least some people in the group will have checked. Group dynamics clearly is to some degree relevant for science as well - no scientist has gone through all the evidence and arguments of moden science - many things are accepted based on the understanding that other people have discussed the evidence thoroughly and that their conclusions are sound. But although this is an interesting line of inquiry, it is not what Dawkins has in mind, so I shall drop it. What Dawkins has in mind is a shortened version, presumably something like

A false belief based on incorrect inference about external reality that is firmly sustained despite what constitutes incontrovertible and obvious proof or evidence to the contrary.

An example could be a person who believes he is being observed by government secret service agents. An important thing to note is that a delusion is not about inconsequential side issues but about something that is important to a person. In the terminology used in the previous section, a delusional person makes the direct experience of being observed (he may be able to point at the people who in his view observe him). However, nobody else shares his belief, and there is incirect evidence to contradict the experience (for example, one can find out that the observer is in reality a gardener, employed in the job for a long time with no government connection). The delusion is then the refusal to reject direct experience in favour of a deduction from indirect evidence.

Note that such a refusal to accept indirect evidence over direct experience may be actually correct if other people draw the wrong conclusions from the evidence available to them. For example, when Martha Beall Mitchell, then wife of the US Attorney-General in the Nixon administration, claimed that White House officials were engaged in illegal activities, she was considered delusional. However, the Watergate scandal later on proved that she was in fact quite sane.

Consistency is, however, still a relevant principle even for a delusional belief. A delusional person does not hold a belief based on direct experience but agrees at the same time that the evidence to the contrary is correct - instead a delusional person insists that the evidence is wrong or must be interpreted in a different way. Upholding a belief despite constant confrontation with evidence to the contrary consumes a lot of mental energy - so why is it done? I think there are ultimately two tendencies in the human mind - to defend the beliefs one already holds, or to search for truth and question everything anew, and it is the first which wins out here.

There are many reasons to defend what one beliefs to 'know'. One of them is security - the world is a less threatening place as long as one beliefs one understand how it works and can thus predict and influence future events. The admission that one does not understand the world threatens this sense of security. A belief may be actively comforting - a delusional person holding the belief that a loved one, instead of having died in an accident, is just on holiday for example is using the belief as a mental barrier against pain. Abandoning the belief implies a loss of that comfort. Finally, there are special benefits linked with the three types of establishing truth mentioned above. Direct experience is usually close to the core personality which is formed and defines itself through experience. Any admission that direct experience is wrong becomes easily a threat to the self-image. Beliefs held because of rational deduction are often linked to an investment in time, effort, and sometimes (in the case of a scientist) also academic prestige - rejecting such conclusions thus renders the effort seemingly futile and may also go hand in hand with a loss of academic prestige. Finally, intuition often has an emotional component - we strongly want to trust our instincts - thus, giving up an intuitive conclusion is more difficult as giving up a rational conclusion which has no strong emotional involvement.

This is balanced by an opposing tendency to improve the mental model of the world, by a desire to really know what is going on. Dawkins suggests that the dividing line runs between science and religion, but I don't think that is true. Witnessing a scientist's public admission that he was wrong in the face of good evidence (as Dawkins tells the story) is primarily remarkable because it is so rare! While the ideal of science is the continuous quest for truth, real-life scientists have a hard time dealing with evidence contrary to their beliefs and tend to scrutinize such evidence much more closely than evidence which confirms their belief. On the other hand, while there are religions in which religious leaders claim to have all relevant answers (and Dawkins cites ample examples), there are also religions which require followers to be ready to part with cherished beliefs, to make new experiences and to find a path to truth based on perception and deduction - several forms of Buddhism come to mind here, which goes as far as pointing out that in order to find the truth, one must relinquish fixation on words and letters - which is a claim quite contrary to the validity of a holy scripture. One can find open-minded religious people as well as dogmatic scientists (although, admittedly, the numbers work probably out the way Dawkins thinks they do).

Delusion, then, is not the contradiction between direct experience and indirect evidence itself. It is a peculiar mismatch in a) the emphasis direct experience is given precedence over indirect evidence as compared to how other people place this emphasis and b) the personal direct experience as compared to the direct experience of others.

Contradicting candidates for a truth are in fact quite frequently encountered both in everyday life and in science and usually dealt with quickly. Having outlined three modes of establishing truth - direct experience, rational deduction and intuition - we can expect three different external contradictions and three different internal contradictions.

If rational deduction clashes with direct experience, usually direct experience wins out (remember the example of my cat as the culprit in the milk-spilling incident - if I see the cat coming in a transport box from a friend, I reject my deduction that my cat spilled the milk without a second thought). It is rather unusual that one trusts rational deduction more than direct experience - this required good and consistent evidence and usually also someone who has learned by experience that he can trust rational deduction. Likewise, in a case where intuition is contrary to direct experience, people usually concede that their intuition was wrong. The opposite case, preferring intuition over direct experience, seems very unusual. Finally, if intuition goes against rational deduction, people tend to 'follow their instinct' when alone, but concede to the rational argument when in a group. This seems to be connected with the fact that rational arguments can be communicated and can be used to convince the group, intuition cannot and requires trust.

Coming to internal contradictions, one observes that intuition contradicting intuition does not seem to occur frequently. A contradiction between direct experience and another direct experience (or rather, the memory of another direct experience) is potentially a severe thing and questions our reality model and ultimately our sanity. Imagine remembering clearly losing a friend in an accident and attending his funeral - and then meeting the same friend in a cafe! Clearly, this would be a very disturbing experience.

Contraditions in rational deductions are quite frequent in science. Sometimes, there are actual mistakes in applying the deduction rules - these are usually resolved quickly. But the most common case is that the indirect evidence is under dispute. Face-value evidence may not be what it seems. A measurement can be wrong, There may be a hidden bias which influences the data. A result may be a statistical fluke (if you measure something with a 95% confidence level, it means there is a 5% chance that the result is accidental - in 100 studies, it is bound to occur now and then). Rare cases have been known in which scientific data was simply faked. There is thus nothing wrong with dismissing evidence as such - it has to be routinely done in science, and usually there are good reasons to do it. The scientific principle states that one should subject each bit of evidence to close scrutiny in order to verify that it is sound.

Hume's principle and confirmation bias

Hume's principle in essence states that if any evidence (or rather, testimony of evidence) fundamentally contradicts what you believe you know, you should apply especially hard criteria on the validity of the evidence. In other words, the degree of scrutiny applied to your evidence should be proportional to your (subjective) impression how strongly it would contradict what you believe you know already. Suppose someone believes he knows all that is possible, and he thinks that hallucinations are possible. Anything that contradicts his worldview, any evidence that demonstrates that something he believes can not happen does in fact happen would then be a 'miracle'. But everything can in principle be explained with the person doing the experiment hallucinating, and this would never be a miracle - so Hume's principle states that this person should always dismiss any evidence against his model of the world. That's about as far from science as it gets!

But in fact, that is precisely what proponents of Intelligent Design do: For them, the idea that any complex lifeform just appears is not miraculous at all, but the idea that it evolved into complexity is. So they are very uncritical about findings which seem to confirm their view, but they look very careful at any evidence presented for Darwinian evolution and thus continue pointing at gaps in the reasoning (much to Dawkins' annoyance who calls this application of Hume's principle 'worship of gaps' when the other side does it). If proponents of Intelligent Design would apply the scientific method, they would have to be as critical of evidence confirming what they belief as of evidence contradicting what they believe (and then they might be significantly less certain of some things). But if Dawkins would apply the same standard to miracles which he uses to judge evolutionary psychology, he would have to accept a lot of the evidence.

So, plausible as Hume's principle seems, it is not what a scientist should apply. A scientist should not apply different standards to evidence dependent on if it agrees what he thinks or not - he should have one standard, and judge all evidence according to it. If physicists would have applied Hume's principle, there would be no Quantum Theory today - the assumption that a few people hallucinated or deluded themselves is far easier to maintain than the assumptions Quantum Theory asks one to make.

The miracle of the sun - a case study

What seems to have happened is, roughly, the following. On October 13th, about 70.000 - 100.000 people had assembled to observe what Portuguese newspapers had been ridiculing for months as the absurd claim of three shepherd children that a miracle was going to occur at high-noon in the Cova da Iria on October 13, 1917. According to many witness statements, after a downfall of rain, the dark clouds broke and the sun appeared as an opaque, spinning disk in the sky. It was said to be significantly less bright than normal, and cast multicolored lights across the landscape, the shadows on the landscape, the people, and the surrounding clouds. The sun was then reported to have moved towards the earth in a zigzag pattern, frightening some of those present who thought it meant the end of the world. Astronomers across the rest of the world did not observe any unusual activity of the sun.

Dawkins argues that about anything - history reporting it wrong, 70.000 people having the same hallucination or conspiring to make up the story for example, is more likely than the sun (or earth) actually accelerating out of its path and coming down without anyone outside Portugal noticing it. Well - of course the solar system did not alter. That is a strawman raised by Dawkins, which he goes on to defeat without addressing the real issue. Reading through witness reports, I haven't seen a single claim that the solar system was factually altered. People were describing what they saw, and they used words like 'the sun seemed to come down'. So, what is Dawkins saying here? Any event causing the observation would need to either alter the light coming from the sun at the precise time and place which was predicted or tinker with the mind of some 70.000 people simultaneuosly - and that would be somehow less remarkable because the sun didn't really move? That's a weird attitude.

As far as miracles go, this one is actually pretty close what a researcher would require as good evidence. First of all, it was witnessed by many people. Dawkins cites Hume's principle at this point to deal with the testimonies of so many witnesses. In the terminology used above this is a consistency argument - accept testimony that violates the consistency of what you believe to know only if the 'cost' of doing so is smaller than the 'cost' of rejecting the testimony. But we have dealt with Hume's principle above - the standard he asks here is ridiculously higher than what he asks of evolutionary psychology for example.

The 'cost' of rejecting 70.000 witnesses on the basis that they are collectively hallucinating or that they've conspired to make up the story is staggering. For example, the witnesses include newspaper reporters who have ridiculed the idea of a miracle occuring during the months before - it is highly unlikely that they'd be willing to swallow their own words and testify that they have indeed witnessed something extraordinary - uness there is a good cause for doing so. The witnesses also include scientists. If one is willing to make that kind of argument, one can dismiss Darwinian evolution without any problem: All paleontologists could be engaged in a deception scheme and, instead of digging fossils out of the ground, just assembling them somewhere. In fact, with the number of 70.000, one can probably include a fair number of in situ observations of evolution from biologists out in the field as being deceptions. Dawkins would immediately argue that such reasoning against Darwinism is obviously ridiculous (and I would support this) - but it doesn't get less ridiculous if it comes from him.

Several investigators have made a lot out of the fact that no observatory registered any unusual activity of the sun. Again, in what way would this make the event less remarkable? If the whole world had registered an intense solar flare (or any comparable event), then it would have been quite easy to make the point that an event that is visible throughout the whole solar system has no specific connection with a prediction of a miracle at the location of Fatima, so all that remains is a temporal coincidence - which may or may not be accident. As it is, one is left with the observation that a remarkable event occured at the time and place where a miracle was predicted, but nowhere else - which is considerably more of a coincidence.

A similar objection can be made to the fact that just 'a miracle' was predicted and no specific event, thus any unusual event could be made to agree with the prediction. However, one can also turn this argument around: If a specific event would have been predicted, there would have been a good case for mass hystria as an explanation for the observations - a crowd of religious people waiting for a specific event may, by group dynamics, convince themelves that the event happened. As it stands, the event was witnessed from people up to 18 km away who did not wait for any specific event to occur, could not have been influenced by group dynamics and could not have had any prior notion of what to expect.

By a reasonable standard in judging evidence, one can then conclude that a remarkable event was witnessed by several ten thousand people, and that place and time of the event was predicted by three children months in advance who cite the Virgin Mary as source for the prediction. None of this proves the existence of God, the existence of a creator of the universe or even the appearance or involvement of the Virgin Mary - but whatever mode of establishing truth the three children had, judged by the standard of making successful predictions it did work well. While this does not consitute evidence of the supernatural (as outlined above, due to the very definition of the supernatural that would seem impossible), it does seem to demonstrate that science is not (yet) as powerful in explaining all phenomena as Dawkins would have it, and moreover it shows to what length Dawkins goes in order to dismiss face-value evidence and make the claim that science can explain all experiences (which is absolutely needed to disprove the existence of the divine).

I can, however, entirely sympathize with any form of reluctance to admit that science cannot explain a phenomenon. The reason is that with a large number of people, the discussion from this point follows a predictable pattern. People argue that since science cannot explain it, it follows that their own explanation must be correct. It further follows that if their explanation is correct in this instance, it is also correct in all other instances and backs up all their claims. This is of course utter nonsense. The fact that I can't think of a scientific explanation and accept the event and, most importantly, the fact that it was predicted as extraordinary proves in no way that the bible is literally true.

Non-consistency and Zen

And yet, Zen Buddhism maintaines that consistency is actually an illusion of the mind, and one must go beyond. Reading through Zen Koans (short stories which illustrate Zen), one finds examples like Ganto's axe:

In examining two Zen students, the monk Ganto takes an axe and raises it, addressing the students in meditation: 'If you say a word I will cut off your heads; and if you do not say a word, I will also cut off your heads.'

What is the rational mind to do in order to survive? He is to 'speak' and 'not speak' at the same time, in other words, he is to perform an inconsistent and contradictory action. Thus he cannot pass the test.

The aim of this Koan is to illustrate to the student the non-dualistic picture in which Zen views the world. According to this, distinctions like 'speaking' or 'not speaking' are not part of how the world really is, they are just a device of the mind, and once the mind has introduced distinctions, consistency is necessary. However, in reality, there is no distinction between 'speaking' and 'not speaking', so asking someone to do it at the same time is a contradiction only in the mind, but not in reality. Zen is not the only religion with a non-dualist picture of the ultimate truth or the divine - it is joined by the mystical branches (those branches in a religion which rely on direct experience of the divine instead on scripture) of almost all major religions - one finds for example the teachings of Meister Eckhart in Christianity, Sufism in Islam, Advaita in Hinduism, the Cabala in Jewism, Sikhism or Taoism as examples of religions based on a non-dualistic picture.

Strange as Ganto's axe seems to be, one can formulate a logically equivalent sentence for quantum theory (the 'quantum axe'): If you claim light is a wave, I will falsify you, and if you claim light is not a wave, I will falsify you. This sentence claims that 'is a wave' and 'is not a wave', two logically exclusive properties, are both simultaneously realized in light. The weird thing is - this sentence is perfectly true and there is conclusive evidence to back it.

Quantum problems

Presumably, Dawkins thinks (like many others) that quantum theory is only relevant when one looks at very small things, and since human beings live at a size scale different from the atomic scale, one can safely ignore quantum effects. But, in a nutshell, that isn't really true - Schroedinger's cat is a quantum problem, and it is large. There is an important difference between a linear system and a nonlinear system. Roughly speaking, in a linear system, a small cause makes a small effect if one waits a given amount of time, whereas in a non-linear system at least some small causes can make a big effect after a given amount of time. Thus, if one combines small quantum objects into a big object which is a linear system, one can demonstrate that all the small quantum effects cancel out, and the big object behaves completely as if there would be no quantum fields. Not so for a nonlinear system. Schroedinger's cat is an extremely nonlinear system - the fate of a cat is linked via a detector to the state of a single atom (which can be 'decayed' or 'not decayed') - if the atomic state is 'decayed', the cat is killed, if the atomic state is 'not decayed' the cat stays alive - a small cause and make a very large effect here, and in this case quantum effects do not cancel when going to large objects. If the single atom is in a state which is a mixture of 'decayed' and 'not decayed', then the cat must also be in a mixture of 'dead' and 'not dead' with no cancellation of quantum effects. This example may seem academic, except that nonlinear systems are actually quite common - other examples include the global weather pattern and, well, the human brain.

The question why we don't see anything like Schroediger's cat is entirely justified. Part of the explanation lies in decoherence. We can observe quantum systems in 'weird' states in which they are a mixture of both 'X' and 'not X' only if they are (apart from the actual measurement) isolated, i.e. not in contact with the environment. A single atom is easy to isolate, but a large object (like a cat) interacts very much with its enviroment - there is, for example, heat radiation, air molecules touch the cat, and so on. However, to the degree that one can isolate a large object, the same quantum effects are seen there - at present experimentally observed for clusters of few hundred atoms - which, in a sense, are an approximation of Schroedinger's cat. There one observes what has been called decoherence or consistent histories - if the state of the atom can be 'X' or 'not X' (for the atom, that would be 'decayed' or 'not decayed') and if the larger object can have the property 'Y' or 'not Y' (for the cat, that would be 'dead' or 'not dead') and if 'X' and 'Y' are linked (in Schroedinger's example, through the detector which triggers the cat killing device), then the full quantum systems allows the states 'X and Y' and 'not X and not Y' to exist simultaneously, but not the mixed states 'X and not Y' or 'not X and Y'. The mixed states would correspond to inconsistent history ('the atom has decayed, but the cat is not dead' for example), and only consistent histories are realized - but there is no selection which one.

You may be tempted to argue that there is a huge difference between a few hundred atoms and a cat, and if it makes you sleep better at night, you can imagine that somehow properties of quantum theory break down if the number of atoms is increased further, this particular property is not actually measured for larger objects. But quantum physics as such works well for large-sized objects - superfluid helium for example is a quantum state so large that you can see it with bare eyes (if you have a cryostat), and superconducting cables in particle accelerators demonstrate quantum states with an extension in the range of several kilometers - so there really is no breakdown of quantum effects in large objects as such, and any breakdown assumption capable of solving Schroedinger's cat would involve some very strange ad hoc outside agency.

So, one can now understand how two competing histories, simultaneously realized ('the atom decayed and the cat dead' and 'the atom undecayed and the cat alive'), both of them internally consistent, spread to larger and larger objects if the system is not isolated - the box in which the cat is, the lab, the eye of the observing scientist, the optical nerve, the brain - and then comes the moment that is not understood in quantum theory, and this is the moment at which the observation reaches the conscious mind. And then, one of the histories is gone, and the other is observed.

This is where the interpretations of Quantum Theory mentioned by Dawkins come in. The Copenhagen interpretation states broadly that physics is altered by observation - a conscious observation truly erases one history and makes the other real. Which runs into problems immediately - whose conscious mind counts? Mine? Dawkins'? What about the cat? Almost all other interpretations blame it on consciousness - according to modern understanding of quantum theory, the other history is still there - the complete state is still there - only for some reason consciousness is only able to observe one part of the state, not the other. So if you do the experiment with a cat, and you observe a dead cat, the implication is that the part of the state which you can't see still contains a life cat, in reality the cat has not completely died, you just don't see it. So, according to present-day understanding, the deterministic world we see in which the cat is either dead or alive is nothing but a mind-generated illusion.

There is incontrovertible and obvious evidence that all that is true. Nevertheless - Dawkins doesn't really believe it. So, according to his own definition, he should be called delusional. Which is unfair, because I am in fact no better, I am worse. While Dawkins (presumably) has no first hand knowledge of quantum theory, I have done a lot of the relevant experiments myself in lab courses - I don't need to rely on anyone's testimony or interpretation, I have done it myself. There is no real escape. And intellectually I am convinced that what I stated above is true. I just can't get myself to accept it beyond the intellectual level, as it is so contrary to my direct experience that I reject the intellectual argument. I don't know any physicist who accepts quantum theory beyond an intellectual level. So - we're all delusional.

There is, however, some state of consciousness, which, at least judging by the description, seems to be close to what a direct experience of quantum physics would be like - and that is Zen enlightenment (or other, related experiences).

Quantum physics and Zen

Quantum physics	Zen
The reality as perceived by the senses is not the true reality.	The reality is perceived by the senses is not the true reality.
In true reality, in many cases demanding that something is either 'X' or 'not X' is meaningless.	In true reality, demanding that something is either 'X' or 'not X' is meaningless.
In true reality, quantum states are non-locally connected.	In true reality, all things are interconnected.
In order to understand true reality, one has to abandon conventional reasoning.	In order to understand true reality, one has to abandon conventional reasoning.
True reality can be understood using abstract mathematics.	True reality can be experienced in meditation.
To learn this takes years of study.	To learn this takes years of study.
In principle everyone can do it, in practice not everyone may have the ability.	In principle everyone can do it, in practice not everyone may have the ability.
Any quantum physicist can recognize any other quantum physicist by talking to him.	Anyone who has reached enlightenment can recognize anyone else who has reached enlightenment.

So, I would argue quite the opposite way from Dawkins - since I am (intellectually) convinced that quantum theory is true, if a religion should have any chance of containing truth about how the wold is, it should at least contain seemingly paradox and non-consistent statements as found in quantum physics - if a religion does not contain such statements and is formulated in a purely rational, consistent, non-paradox way, one can be sure that it misses an essential property of the world and is hence not true. This is a necessary, however not a sufficient condition. As I said, I don't know if Zen gives a true account of quantum physics (or reality) - I am not a practicioner of Zen. But it has at least a chance to do so.

Breakdown of consistency

One may ask if quantum theory is not consistent, or if the underlying mathematics is not rational. The answer to that has two aspects. First of all, quantum theory is certainly consistent when formulated in its own concepts - it is the nature of these concepts which does not agree with the usual idea of rationality. Quantum field theory focuses very much on what is observable instead of what things actually are. For example, the best quantum field theory answer to the nature of light is 'a creation operator of a U(1) gauge field acting on the vacuum Fock space' - this is an operational description of how to calculate observable properties of light, but certainly has nothing to do with what light actually is. And the description of what light is, based on the prescription to calculate what is does, is very different from how we conceptualize the world.

So, second, mathematics is certainly in a sense rational, but conventional rationality is only a rather small part of what can be expressed using mathematics. Some concepts in mathematics are so bizarre that one would have a hard time finding them in a lunatic asylum or in even the most outrageously weird religious texts. One can do mathematics in a world where 1+1=0, where a * b is not equal to b * a, where space has 10.4 dimensions or all of those together. One can classify infinities according to their relative size. And so on. So while mathematics is certainly rational, it can be very far from how we normally use the word, and it can be used to describe ideas which one would usually refer to as outright insane. In that sense, the rationality inherent in mathematics or the internal consistency of quantum physics is a small comfort.

So - where does this lead us? The scientific principle is essentially justified by its testable ability to form conclusions from indirect evidence which are later confirmed by direct experience. The principle is indeed so powerful that sometimes scientists argue that conclusions from indirect evidence should be perferred to direct experience, in other words that direct experience can be misleading. To avoid arbitrariness in when to perfer direct experience, the principle of consistency is used. But now science itself has shown that consistency (as used here) is not a fundamental principle of nature, while at the same time mathematics has proven that science cannot show its own consistency and does not contain every truth. Rationality undermines its own foundation quite impressively.

Where to go from here? Clearly, the scientific principle and rationality are not powerful enough to find any ultimate truth. They have to be replaced by something else, and it is this something else which should be used to answer the question Dawkins is posing, i.e. if there is something divine or not. There is no reason to assume science in terms of rationality as we think of it can do it.

Conclusions

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