Sunday, July 23, 2017

Melencolia I Project Articles


I'm using this post to collect together the articles and papers I have produced for my Melencolia I series. I will update this post as I produce written items.  This will mean I can use a link to this post to give access to the whole series.


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About the Melencolia I Project
In 1993, after nearly twenty years since my first encounter with quantum mechanics, I started investigating it once again. The urge to do this was brought on by a feeling that at last I just might have some insight as to the meaning of the strange world of quantum theory. This insight, if such it was, came out of my Thinknet Project, a project I had started in the 1980s. What piqued my interest was that the general structure of Thinknet theory, which in turn was based on some of ideas of the psychologist Edward de Bono, was reminiscent of quantum mechanics; in particular I fancied I saw in quantum mechanics a declarative structure not unlike my Thinknet simulations: Further detail on this matter can be found in the summing up sections of these papers here and here. To me it had started to look as if the standard imperative programming model was an inadequate metaphor for the cosmic physical laws, and instead we were dealing with something which had a declarative structure, a structure isomorphic with my Thinknet simulations. Some say the cosmos is a piece of intelligent design, but to me it had started to look more like the inside of a functioning intelligent process; so, less intelligent design, more the inside workings of a process of intelligent creation. If this was true then it would mean that the human perspective on the cosmos was a bit like the point of view of a neuro-scientist investigating the brain – down at the microscopic level the brain presents us with the relatively mundane operations of neurons, neuro-transmitters, electrical fields, signalling and the like; zooming in even further we find molecular chemistry; down at this level the traits we usually attribute to mind, namely intentionality, conscious sentience, purpose and teleology, dissolve into fragments, if indeed they appear to exist at all. In fact it’s a bit like aerial archaeology; viewed from on high the coherent patterns on the ground are clear to see, but at ground level they all but disappear. And yet those aerial patterns must somehow be impressed in subtle ground-level features, features which otherwise present a liminal threshold to the ground level observer.

Cognitive specialists are still trying put all the low level bits together in order to give a coherent third person account of the first person conscious perspective associated with the macroscopic mind. All said and done it seems that “Conscious cognition” is only meaningfully present at the integrated system level rather than the deconstructed component level observed by the third person. But there’s a paradox here; the third person scientific perspective presupposes the existence of the rational observer and scientific narrative constructor, which when traced back to its source itself entails a first person conscious perspective, the very thing under investigation. Ultimately the third person perspective presupposes a first person perspective and it’s easy to overlook this fact. Without an implicit full blown first person conscious perspective the third person account of the cosmos doesn’t make sense. In short, the third person perspective only makes sense if one presupposes the existence of an up-and-running rational first person perspective. 

If it’s a challenge to imagine how the details of the low-level biochemical perspective adds up to the integrated sentience of human beings then perhaps we have an inkling of the why, if the cosmos really is intelligence in action, we don’t readily see intentionality and teleology at work in the cosmos; we are simply too close to the stuff of the cosmos to perceive it. At first sight the cosmos looks to be an utterly meaningless and purposeless imperative computation, so much so that for many in the West there is no real substantive evidence of an immersive immanent intelligence surrounding us. In contrast I am offering, by way of an alternative (although admittedly it is a very long shot conjecture), that the cosmos is our low-level third person view of an intelligent declarative computation in operation; much like the low-level perspective a neuro-scientist has of the brain.

Human life only becomes coherent if one regards the first and third person perspectives as complimentary. If the third person examines a human being closely all they see is a complex network of biochemical structures and signals. But to make complete sense of this structure and its complex signalling network the third person must make an empathetic leap of the imagination; namely to understand that this system and its processes has a point by point conformity with the sensations & feelings of a first person perspective. But if we are going to make this empathetic leap with the human mind we may then be prompted to ask ourselves this question: Is our third person understanding of the cosmos, a cosmos with hints of a possibly declarative structure, also associated with some kind of first person perspective? This is a very speculative and conjectural leap but the beauty of being a private operator like myself is that there’s nothing to lose by seeing how much mileage one can get out of off-the-wall ideas like this. 

To allay the worries of Christian theologians about pantheism, none of this is to say that the cosmos is somehow to be identified with a sentient God; better to think of it as the manifestation of God’s thoughts about the cosmos, a cosmos which perhaps runs in the divine mind in a similar way a story runs in the mind of an author. The point of view I’m probing here is very different to that of the Intelligent Design creationists of North America who have adopted a dualistic intelligence-of-the-gaps procedure which means their inquiry stops dead once they have decided that they can’t see how so called “natural forces” give account of an object in question. In contrast I’m proposing those so-called natural forces are part of an intelligent process; hence I prefer to think of myself as heralding intelligent creation rather than intelligent design. What also sets me very much apart from de facto intelligent design is that I have to confess my ideas are highly speculative and very conjectural. I’m involved in the investigation of a hunch, a hunch which provides no pretext to spiritually abuse those who are not inclined to believe it. Moreover, I’m not coy in suggesting that the intelligence behind the conjectured intelligent cosmic processes would to all human intents and purposes be divine. Therefore I’m making no pretension to doing formal science. This is an entirely informal epistemic endeavour which can only offer a tentative take-it-or-leave-it post-facto sense making narrative (See here). Unlike the IDists and the so-called "creation scientists" I'm not making any claim to being God's gift to science. I'm a science hobbyist doing the equivalent of building a light aircraft in his shed hoping that one day it may fly, but not needing to invest too much in that hope because in the final analysis it has to be about the journey, not the destination: For, in by far and away the greater number of human endeavors a project's journey's end is about failure, not success. Therefore I'm expecting my own efforts to likely end in failure. But then as George Bernard Shaw said:


"A life spent making mistakes is not only more honourable, but more useful than a life spent doing nothing."


Critique of "Intelligent Design"
In this post I discussed some ideas by one of the de-facto IDist, Robert Sheldon. Because de facto ID conceives intelligence as a black box eminent to the objects it “designs” de facto ID has a philosophical blockage toward paradigms which may venture to propose that “natural forces” have any significant role in the formation of life. In the weltanschauung of de facto ID  “natural forces”, so-called, play a minimal role in the formation of life. Rather, in their view you need an external intelligent homunculus to do that. The idea that the world around us be so immersed in the mind of God that there is no humanly discernible distinction between scaffolding and building, between natural forces and intelligence, hasn’t occurred to them. The outcome is that the de-facto IDists are thoroughly committed to showing the inadequacy of “natural forces” to generate life:  The IDist epistemic is embodied in their “explanatory filter” which obliges them to preserve those enigmatic gaps in law and disorder science at all costs. In line with this negative tradition IDist Robert Sheldon pointed out that a random walk search, a search which proceeds to expand into its search space in proportion to the square root of time is too slow to be up to the task of finding viable living structures via evolution. The reason why random walk search is so slow is that as it proceeds the number of routes it has to explore goes up exponentially. But Sheldon’s obvious philosophical motive was to trash the idea that “Evolution did it” via random walk in favour of his belief that “God Intelligence did it”. But just how that intelligence did it the IDists do not say because they consider the detailed nature of intelligence to be beyond their terms of reference; it's almost as if the nature of intelligence is far too sacred ground for them to investigate.

In the Intelligent Design paradigm  intelligence and so-called “natural forces” are part of an unbridgeable dichotomy. It hasn’t occurred to IDists that just as the particulate low-end details of brain dynamics provides clues as to its high end operation, those so called “natural forces” we see at work across the cosmos may contain valuable clues about the operation of an intelligent process. In my blog post I've linked to I pointed out that Sheldon was reckoning without quantum mechanics; for not only does quantum mechanics have huge potential by way of its expanding parallelism, its wave motion has the effect of cancelling out the immense combinatorial sink of randomness. Thus quantum mechanics scores on at least two counts, namely a) Exponential resources and b) The cancellation of randomness. The second count means that its wave envelopes expand not with the square root of time but linearly in time. Although I would ultimately agree with Sheldon that non-locality is involved as per a declarative computational paradigm which ultimately selects from a huge array of search items, it is those so called “natural forces” which have an absolutely crucial searching role in the return of those outcomes.

The de facto ID community represented by the likes of websites such as Uncommon Descent and The Discovery Institute talk obliquely of a mysterious Intelligent Agent being the likely default means of explanation when our understanding of "natural forces" is (currently) unable to account for a phenomenon. Of course, everyone knows that these people are really talking about God and the IDists' studied detachment from theology comes over as an affectation, disingenuous even. Talking vaguely about "Intelligent causes", however, does give a scientific gloss to their work; after all, it is true that archaeology is in the business of separating out the "natural" from the "artificial". Moreover, if ever an obviously empirical situation should arise like that depicted in 2001 Space Odyssey, the question of intelligence and the nature of that intelligence would loom large in scientific circles. So arguably "Intelligent Design" is a little like archaeology and SETI and  therefore does have a prima facia claim to being  science. 

But of course we know that the de facto IDists are really thinking theologically and that is where lie their mistakes: They have in fact committed scientific, tactical and theological errors. Their error is scientific because their epistemic filter is misconceived; this misconception  leads into a natural forces vs God dichotomy which in turn helps foster scientific blunders such as the claim that evolution is inconsistent with the 2nd law of thermodynamics. Their error is tactical because their pretense at doing science uncontaminated by theology is just that; a pretense and everyone, especially atheists, can see it. Their error is theological because God is both immanent and eminent and therefore He is immanent in natural forces. It follows then that we can seek God in those so-called natural forces and not just as an ancillary outside intelligent agent; or perhaps I should say that those "natural forces" are in God. For God is the eminent and immanent context of all that his authorship permits reification in the story He tells. The immanence of God means that he is of an entirely different genus to any ancillary intelligence such as man or aliens; if we are theologically turned on then we don't expect ancillary intelligence or humunculus intelligence to be a good model for God. 

In order to maintain a scientific gloss we find that IDists will often try to avoid mention of God in their works. Not only has this tactic miserably failed but I believe it is impossible for the Christian to carry on like this. If we are dealing with immanent intelligence and not just ancillary intelligence this subject cannot be approached without mention of the immanent Sovereign Manager and Creator. That's not a mistake I intend to make myself. My project is explicit about seeking the Sovereign Manager and Creator of our cosmos. I therefore make explicit mention of Him. Also, unlike the IDists I am not making strong claims of doing exclusively science (although some parts will be science) since my epistemology is far more broad brush than spring extending and test tube precipitating scienceThis will mean that any atheist who dislikes the idea of a Sovereign God being at the heart of a study will not find grounds for accusing me of trying to pull the wool over his/her eyes. There is one thing worse than a deceiver and that is the incompetent deceiver who is oblivious to the fact that his attempt at deceiving is so obvious.

So all in all I've become increasingly displeased with the de facto ID movement and their transparent facade of studied scientific detachment. But I'm in good company: I don't think Sir John Polkinghorne is pleased with them either
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Main Papers and Articles of the Melencolia I Project

Supporting and Relevant Articles
Configuration space Series
William Dembski’s views:
Felsenstein vs. Dembski
Felsenstein and English vs. Dembski, Ewart and Marks
http://quantumnonlinearity.blogspot.co.uk/2015/11/intelligent-designs-2001-space-odyssey.html

Wednesday, July 19, 2017

No Progress on Young Earthism's Biggest Problem: Starlight. Part I

The cop out of creation weekism

After a break of a few years I thought it time to revisit Christian young earthism’s greatest unsolved conundrum and see how they are getting on with it. This problem is simply expressed as follows: How does star light cross millions of light years of space in less than 10,000 years? The cosmos is so big that any significant redistribution of cosmic energy requires millions of years.

For young earthists everything in the cosmos has to be accounted for within their tight framework of at most 10,000 years of cosmic history*; in fact the fundamentalist theme park ministry Answers in Genesis insists that one must believe that framework to actually be much nearer 6000 years or else one courts heresy.  Therefore for AiG’s young earthists everything, absolutely everything, must have happened very quickly; no process can be extended over more than a mere 6000 year duration.  Contrast this with established science which has available a huge time window to resource the processes of creation – from a few years to billions of years. Because young earthists have such a narrow window to work with they either put heavy reliance on flood geology or throw their hands up and claim it’s all a miracle of the “creation week”. Consequently in fundamentalist cosmology their resort to ad-hoc miracles is not necessarily an option they actually prefer but often it is the only option available to them, as we shall see. 

In a blog post dated July 2017 and entitled “Ingredient of Life” Discovered in Distant Star System, AiG supremo Ken Ham comments on the recent discovery of a chemical in a star system and which has been referred to by establishment scientists as an “ingredient of life”. This is what Ham says:


Infant Star Systems?
Now, it’s claimed that the star system in which this chemical was found contains “young stars in their earliest stages of evolution.” But Dr. Danny Faulkner, AiG’s PhD astronomer who taught astronomy at a secular university for over 26 years, says,

“The system in question, IRAS 16293-2422, consists of three stars, each probably having mass similar to the sun. The system is located in the Rho Ophiuchi cloud complex. Most astronomers think that stars are born in such dense clouds of dust and gas, so they have interpreted stars embedded in the cloud as having recently formed. Note that this is an interpretation, not clear evidence that these are stars in their infancy.”

These stars don’t give us a window into the formation of stars or our own solar system. We would agree that they are young stars though because all the stars are young, created just 6,000 years ago on Day Four of Creation Week.

He made the stars also. (Genesis 1:16, NKJV)
By the way, read “A Proposal for a New Solution to the Light Travel Time Problem,” a fascinating (though somewhat technical) article by Dr. Faulkner on stars and specifically on the question of starlight traveling great distances in a young universe.


Regardless of Faulkner’s qualifications it seems that too much time in the employ of AiG has blunted his  analytical abilities: See herehere and here. Moreover, judging from the above quote it looks as though Faulkner doesn’t understand the role of evidence – evidence must always be interpreted, although those interpretations have different levels of likelihood, succinctness, rationality, ad hoc-ness, special pleading, closeness to observational protocols etc. And of course those interpretations gain huge kudos if they are used to make successful predictions rather than act merely as an imaginative post-facto dot joining exercise (See herehere, here and here). The idea, as touted by Ken Ham, that one can sharply separate “observational science” from ” historical science” is just an indication that he really doesn’t understand science and that he’s an academic dunce – see here.

But what I would like to focus on here is Ham’s link to Faulkner’s proposed “new solution” to the star light problem.  This solution can be found on a web page which also provides links to numerous AiG articles on the star light problem. See here: https://answersingenesis.org/astronomy/starlight/

Faulkner’s “new solution” can be found here: https://answersingenesis.org/astronomy/starlight/a-proposal-for-a-new-solution-to-the-light-travel-time-problem/

In his paper Faulkner admits that starlight is a big, big unsolved problem for young earthists; Faulkner’s very first sentence is:

The light travel time problem is one of the greatest challenges that recent creationists face today.

Too right! But to cut a long story short Faulkner’s proposal resorts to the bottomless pit of ad hocery allowed by appeal to the miraculous: Here’s his abstract:

I identify a little-noticed issue in the normal formulation of the light travel time problem. In addition, I lay groundwork for the beginning of a new solution to the problem. This solution invokes similarity between creative acts of Day Four and other days of the Creation Week, but especially Day Three. The Day Three account suggests unusually fast growth for plants. In similar fashion, this possible new solution suggests unusually fast propagation of light on Day Four, probably by rapid expansion of space. This is an appeal to a miraculous event rather than a physical process to get distant starlight to the earth. It is not yet clear whether this suggestion could have testable predictions. If this is the correct way to look at the problem, it may be that we are seeing much of the universe in something close to real time. I briefly compare this possible solution to the light travel time to other previously published proposals

Faulkner’s “solution” is dated 23 Feb 2014. Also on the same starlight web page we can find a link to Jason Lisle’s September 2010 Anisotropic Synchrony Convention (ASC) model “solution”. So Faulkner’s “solution” has been proposed over three years after Lisle’s.  Faulkner, however, starts out afresh and proposes a “solution” that has little or no relation to Lisle’s. As I have remarked before young earthist starlight “solutions” aren’t usually progressive in the sense that they build on the work  of other young earthists that have gone before them, rather they simply clear the ground and start again; evidence of the theoretical bankruptcy of what they are doing. In fact Faulkner helpfully lists the many diverse attempts to solve the problem. Viz:


  1. Question the distances
  2. Light created in transit as part of a fully functioning universe
  3. Light follows some peculiar non-Euclidean space so that light from the entire universe can arrive in just a few years, regardless of great distance
  4. A decrease in the speed of light, allowing for light from the entire universe to reach the earth very quickly, within the Creation Week
  5. Biosphere model, or, as some critics of this model call it, the soft gap
  6. Cosmological models using general relativistic effects to get light to reach the earth very quickly during the Creation Week.
  7. Time convention (i.e. Lisle’s ASC model)

I suppose we can add Faulkner’s solution as number 8 in this list.  None of these attempts is a clear development based on previous attempts – they all branch out in different directions, clearing the ground and starting again; all signs that Christian fundamentalists are making heavy weather of the starlight problem.

However, having said that I was interested to note that on the AiG starlight web page another of AiG’s tame scholars, John Hartnett, has an article that strongly criticises Faulkner’s “solution” and then in another article Hartnett actually goes on to develop his own ideas based on Jason Lisle’s ASC model; this is actually the first time I have seen another fundamentalist building his theory on the ideas of another. You might conclude then that perhaps for AiG Lisle’s model is where the starlight problem is at; but no: Ken Ham bypasses all that and goes back to Faulkner’s work. This may indicate that Ham favours this solution in spite of Hartnett’s strong criticisms. I suspect that Ham, who is not the brightest of sparks,  probably doesn’t understand the work of Lisle and Hartnett. More to the point, however, is that Ham is head of a sales organisation whose customer base is the average scientifically challenged fundamentalist Christian: Faulkner’s idea is much more customer friendly than Lisle’s and Ham probably understands that. Ham may lack scientific aptitude but I don’t doubt his sales acumen; after all that is his job and he seems to have had some measure of success in that role. Moreover, as part of his sales technique, like all good cult leaders, he’s not past using some very spiritually intimidating language, as also did the religious salesmen Charles Taze Russel, the founder of the Jehovah’s witnesses.  Ham’s  endorsement of what really only amounts to a sales friendly solution to a big headache doesn’t help promote any confidence that AiG are making any substantive scientific progress toward solving their star light problem; rather, appearances are that fundamentalism is in disarray on this issue.

As I hope we will see in the next part of this series Hartnett’s criticises Faulkner largely on the  basis that Faulkner’s approach is far too ad hoc and disrespects known physics by simply patching in the miracles required to make everything look right. Hartnett’s criticism might work if it weren’t for the fact that Faulkner confines the light transmission miracle entirely to the creation week when who knows what God was up too. Faulkner is therefore able to wave away Hartnett’s objections which are based on the expectations of known physical laws, such as expecting that the miraculously meddled with light might betray either red or blue shifts. But according Faulkner, in the creation week God simply acts to contrive things so that it all works out fine by sheer brute authority and creative fiat; after all, what is young earthism but a belief in a miraculous “creation week” when God did His inscrutable thing His way! Faulkner admits that his solution probably isn’t scientific in that it may not be testable.  But Hartnett is very uneasy with this as he would no doubt like to do a little genuine science in order to earn his “Creation scientist” job title. But Ken Ham has shown us who and what he favours and it’s not science. He might talk about AiG loving science but let’s face it that’s just lip service – in reality he hates (established) science and much prefers sales**. So, Mr. Hartnett, stop trying to be scientific about creation!

For in the final analysis AiG, and especially Ken Ham, are not about science; they are about being a sales organisation selling anti-science products. It’s about befuddling their benighted patrons and muddying the waters with sufficiently technical sounding bafflegab to give the appearance that the difficult question of starlight is in the capable hands of AiG “experts”; that’s all that’s needed for a sales organisation like AiG. In his post linking to Faulkner’s article Ham makes special point of telling his readers that the article by Faulkner is “fascinating though somewhat technical”. That’s all the average AiG customer will really want to know.  And yet clearly John Hartnett can see that the whole thing is a scientific sham. But ever the salesman Ken Ham knows that all he need do is wave vaguely in the direction of his “research” department and make noises to the effect that they are well qualified, they’ve got the matter in hand and point to a paper or two too full of technical bafflegab, too technical for the average AiG customer to actually engage it.

Faulkner’s underlying motive, just like Jason Lisle’s, is in fact commendable. He’s hankering after creative integrity. He wants to avoid any suggestion that the light signals we see from the stars didn’t actually leave those stars; that is, the signals aren’t lying in the sense that they are not delivering a message about cosmic states of affairs that never existed. He wants, rightly, a truthful universe, not a fraudulent virtual universe. In fact Faulkner criticises fundamentalist Henry Morris favouring the idea that light was created in transit:

Thus, the stars could not fulfill their purposes unless they were visible right away, so God made them with their light already en route to earth. This has a certain amount of appeal to it, but it also could be construed as deceptive on the part of God to make light containing tremendous amount of information of physical processes that never happened. Since the vast majority of the universe is more than a few thousand light years distant, it would seem that we will never see light that actually left these distant objects, and hence much of the universe amounts to an illusion. This concern has been the primary motivation of those seeking other solutions to the light travel time problem.

But if Faulkner is looking for a cosmos of epistemic integrity he has actually got a big problem with his solution if he thinks it doesn’t entail epistemic fraud.

Let us suppose that astronomers see some event in the depths of space millions of light years away like, say, a super nova. When is that event, according to Faulkner, supposed, to have happened?  It could not have happened after the creation week because according to Faulkner the laws of physics were then settled and therefore information about the event would not have arrived at Earth in time. This leaves Faulkner with only two options. Either

a)     Information about the  event was already embedded in the ray of light that God stretched out between earth and the distant stars during the creation week or

b)      The event occurred during the creation week.

I take it that Faulkner wouldn’t like option a) since we would then be “seeing” an event that never took place. But if he selects b) he has some tricky questions to deal with.  We see distant super nova events occurring months, years and centuries apart. Somehow all these events have to be squeezed into the creation week and the miraculous light transmission stretching process has to be so contrived that the information about these events, after the end of the creation week when standard physics applies, is embedded in the light beam sufficiently close to Earth and correctly spread out in space in order to give us the impression of an ongoing process of stellar evolution occurring over months and years. Thus what we see as apparently a process conforming to known laws of physics in actual fact occurred during the miraculous creation week. In a word we are looking directly into the creation week, but are unaware of it; and when we do it's as if the "creation week" was stretched over a much longer period of time than just one week! I think this is somewhat straining the idea of a cosmos that has epistemic integrity.

Another issue is this: Unless Faulkner is also going to miraculously speed up cosmic processes during the creation week he has a poser regarding such things as colliding galaxies or galaxies in gravitational interaction  – processes that take millions of years to mature because gravitational communication doesn't exceed the speed of light. But in any case since time, in the final analysis, is measured in terms of the number of distinguishable events between two states it is arguable that time measured in this way entails a cosmos billions of years in the development – unless of course one is going to argue like fundamentalist John Byle who actually proposes that the cosmos is some kind holy deception designed by God to deceive wicked human scientists! The latter is essentially the same as waving it all away under the heading of “mature creation” thus hamstringing scientific epistemology. If fundamentalists like Faulkner want to get away from positing the bogus history bogey young earthists have got their work cut out.

 All these problems trace back to one prejudice:  Fundamentalists just won't accept that Biblical prose is not always to be read literally but mythologically. But as we have seen anyone who doesn't accept fundamentalism's prose-literalism is liable to be spiritually abused and threatened with divine displeasure. 

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This series is likely to consist of two more parts: 1) I’ll have look at the spat between Faulkner and Hartnett and then 2) have a look at Hartnett's development of Jason Lisle’s whole new can of worms.


Footnotes

* Russell’s Humphreys white hole solution may be an exception to this: He allows billions of year of time to pass in the wider cosmos, although gravitationally dilated earth time only sees 6000 years passing.


** Ken Ham's advertising announcement blog post dated 18/7/2017 is entitled "Get quick answers to tough questions".  Quick answers: That's the problem! Scientific answers are not always quick and sales friendly as Ken would no doubt prefer them to be. Ken's use of Faulkner's quick bodge perhaps reflects Ken's preference for sales over science. 

Monday, July 10, 2017

Aumann's Agreement Theorem & Group Think

This lot seldom agree to disagree. 

Quoting from the wiki entry on Aumann's agreement theorem:

Aumann's agreement theorem says that two people acting rationally (in a certain precise sense) and with common knowledge of each other's beliefs cannot agree to disagree. More specifically, if two people are genuine Bayesian rationalists with common priors, and if they each have common knowledge of their individual posterior probabilities, then their posteriors must be equal.[1] This theorem holds even if the people's individual posteriors are based on different observed information about the world. Simply knowing that another agent observed some information and came to their respective conclusion will force each to revise their beliefs, resulting eventually in total agreement on the correct posterior. Thus, two rational Bayesian agents with the same priors and who know each other's posteriors will have to agree.


Studying the same issue from a different perspective, a research paper by Ziv Hellman considers what happens if priors are not common. The paper presents a way to measure how distant priors are from being common. If this distance is ε then, under common knowledge, disagreement on events is always bounded from above by ε. When ε goes to zero, Aumann's original agreement theorem is recapitulated.[4] In a 2013 paper, Joseph Halpern and Willemien Kets argued that "players can agree to disagree in the presence of ambiguity, even if there is a common prior, but that allowing for ambiguity is more restrictive than assuming heterogeneous priors."


The big question here is, of course, why the model on which this theorem is based doesn't describe the real world. It reminds me of Olbers' paradox: From fairly basic mathematics Olbers "showed" that the night sky should be bright with star light, but because it isn't this leads to profound questions about the nature of the universe. In that sense Olbers' work was a stroke of genius. Aumman's theorem may have a similar status. Both analyses deal with signalling and both draw conclusions from this signalling using models with inbuilt but self-aware assumptions. Hence, both prompt profound questions about why their respective models don't quite capture reality: where have they gone wrong? 

On one level the theorem is common sense: The average (wo)man, whatever they might say when in a philosophical mood, tends not to be a relativist and actually has a working belief that there is such a thing as a true picture of reality to be aimed at and applicable to all interlocutors. Surely then in open, transparent, fair and unprejudiced dialogue where the evidences are equally apparent to all and where everyone is being meticulously logical, this true reality can, given sufficient discussion time, be agreed open. Thus any one with common sense knows that in theory we should be able to agree to agree, because there is a truth out there to be agreed upon. But real life isn't that simple. Real world epistemics ensures that. If you are not a relativist (like myself) then you know that "Agreeing to disagree" is an unsatisfactory state of affairs, but nevertheless epistemic practicalities cut across  the ideal and often precludes final agreement.  

As the Wiki entry implies Aumann's theorem can be questioned on several of its assumptions: Are humans Bayesian rationalists? If not why not? Do people act rationally? If not why not? Do they share common knowledge of priors? (which seems to be Hellman's tack). Is there an arbitrariness about evidences?  Other questions can also be raised: Are the communication channels non-corrupting? Do human social and relational factors have a bearing? Is it always an adaptive heuristic for a complex adaptive organism like a human to follow the truth? (In particular it might be safer to follow the crowd!)  Can all the signals we get from our environment be shared by all?

In a Facebook discussion group I attempted to get a handle on just one of the factors which may scupper Aumman's model.  In this discussion I had in mind some concerns I had about the extreme left-wing - in particular the "Socialist Workers Party" who I had contact with in the 1980s and who were as assured of their position as are the Christian fundamentalists: Significantly, like the Christian fundamentalists, their arguments entailed a strong moral and group identification components. Moreover, at times their class warfare theory sounded a bit like conspiracy theorism.

Here are my recent Facebook notes: 

Idealists have minimal doubts. They are on a mission, a mission usually tied to a group think and – this is the killer – a morality which suggests defection is an immoral act in the face of what the group will claim is “obviously true”, the plain reading of reality. Ergo, they have no sense of epistemic distance & doubt and believe there is no room to agree to disagree; defectors, apostates and detractors are all immoral, to be condemned in the strongest possible terms. If anyone defects the defector will have a nagging sense of betrayal and of cutting across moral standards. This ethos is sufficient to keep many people in place who might otherwise have doubts.

This general picture was certainly true of the socialist workers I met in the 1980s: The notion that one is betraying one’s class if one doesn’t subscribe to Marxist theory was very prevalent. And of course betrayal is regarded as the lowest form of immorality, so the pressures are tremendous.
As you can probably see most of the above comments port readily to religious groups.

One more thing: If you do have strong doubts whether of fundamentalism or Marxism there are strong group & moral pressures which encourage self-examination of one's doubts; one is encouraged to believe one has made some kind of mistake in one's thinking if it goes against the "manifest truth" of the group think.

What worries me is that we are seeing some hints of this process in the Corbyn camp. No surprise the SWP have signed up to him

People well immersed in the group-think genuinely believe it I think; any difficulties are waved away with the thought that the clever members of the group have got it all in hand. In short the authenticity of the group is effectively posited as an axiom in one's thinking. Given all that is at stake when one has thrown one's lot into kind of epistemological protection racket, this behavior of giving group-think an axiomatic status may have adaptive value and it needs to be factored in when talking to committed members of groups.

Basically what I'm saying here is that one's social identifications have a big influence on one's world view. Social links take a lot of time and mental resources to form and therefore if one's cultural identifications are effectively being posited as an axiom in one's thinking it's no surprise if people who identify with different communities can't agree even over protracted periods of discussion.