Why I disown the de facto Intelligent Design Movement

Be careful who you yolk with

I thought it might be a good idea to bring together the major reasons why I’m not enthusiastic about the de-facto intelligent design movement.

Firstly, let me say that as far as I can tell the gurus of de facto ID are generally nice enough people. (And their followers? That’s another story!). They are mainly, I think, moderate evangelical Christians with a scattering of other traditions. It would be wholly wrong to compare them to the temperamentally dour fundamentalists who speak censoriously about all those who don’t follow their views (including other fundies with whom they disagree).  As I always say: Fundamentalism is 1 part doctrine and 2 parts attitude, mostly bad attitude; ID leaders don’t usually share the latter I’m glad to say. And yet it is the fundies who often parrot the conclusions of the ID gurus.

Secondly, I must also make it clear that I think it likely that intelligence is fundamental to the workings of the cosmos. But I differ radically from the de facto IDists in that my investigation into the subject proceeds on the basis that the intelligence concerned is both eminent and immanent to the cosmos. I am developing and exploring this theme in my Thinknet and Melencolia series.  I must emphasise, however, that this is a highly speculative blue skies project and it is no basis on which I can badger people into “belief”.

As I have said before the de facto IDists have been a big disappointment to me: They have managed to botch a variety of important theoretical themes, themes which I collect together below:

The explanatory filter epistemic

Many of de facto-ID’s problems trace back to the epistemic method of their explanatory filter, an epistemic which assumes a sharp distinction between intelligent agency and so-called “natural forces”.  This may work in archaeology and SETI  (although I qualify that statement below) but it is bad for theology. It has helped polarise further an already polarised debate and the effect has been to widen the divide between so-called "naturalists" and "supernaturalists", although of course the "surpernaturalists" prefer to identify as "IDists".  See here for more:

http://quantumnonlinearity.blogspot.co.uk/2015/06/idists-heres-another-fine-mess-theyve.html

http://quantumnonlinearity.blogspot.co.uk/2015/05/soft-core-science.html

http://quantumnonlinearity.blogspot.co.uk/2015/01/misplaced-concreteness-theology-of.html

The God of the gaps trap

The explanatory filter epistemic favours god-of-the-gaps thinking. When de facto IDists attempt to explain their position it seems that they just can’t help but fall into the god-of-the-gaps-trap: Here are some examples:

Vincent Torley:

http://quantumnonlinearity.blogspot.co.uk/2014/04/more-god-of-gaps-from-north-american-id.html

http://quantumnonlinearity.blogspot.co.uk/2014/11/western-dualism-in-north-america.html

Kirk Durston:

http://quantumnonlinearity.blogspot.co.uk/2015/07/deistical-god-of-gaps-thinking.html

William  Lane-Craig and Paul Nelson

http://quantumnonlinearity.blogspot.co.uk/2012/12/paul-nelson-computer-simulations-and.html

Barry Arrington:

http://quantumnonlinearity.blogspot.co.uk/2013/10/north-american-ids-god-of-gaps-theology.html
Stephen Meyer

http://quantumnonlinearity.blogspot.co.uk/2013/04/theology-and-north-american-id-part-1.html

http://quantumnonlinearity.blogspot.co.uk/2013/06/theology-and-north-american-id-part-2.html

ID = design detection only?

Some of the IDists I have read will tell you that ID is all about “design detection” and that the nature of the designer is secondary, if not beyond their brief.  And yet IDists in practice make interpolations about the nature of the intelligent agent concerned. The latter is inevitable because one must have some inkling about the intrinsic nature of intelligence if one seeks to not only identify the works of intelligence but also to make predictions. Here are some examples of IDists making implicit assumptions about the intelligent agent they posit:

Here we find Vincent Torley claiming to be reluctant to say much about the designing intelligence:

http://quantumnonlinearity.blogspot.co.uk/2015/05/soft-core-science.html

And yet here Vincent Torley interpolates a “minimum effort” principle:

http://quantumnonlinearity.blogspot.co.uk/2014/04/more-god-of-gaps-from-north-american-id.html

Homunculus ID: ID is inevitably saturated with implicit assumptions about the designer:

http://quantumnonlinearity.blogspot.co.uk/2011/09/does-intelligent-design-make-testable.html

A very negative science

Taken together, the IDists explanatory filter, their belief that the nature of intelligence is secondary to ID detection and their God-of-the-gaps theology all adds up to a very negative kind of science. Its epistemic method largely involves trying to shoot down current evolutionary explanations. And when they think they have achieved this IDists will conclude, using the explanatory filter, that “intelligence did it”.  It is almost as if these IDists are endeavoring to operate with an apophatic definition of intelligence – that is, intelligence is defined in terms of what it is not. The ambivalent behavior of IDists where on the one hand they claim to withdraw from identifying the nature of the intelligence concerned and yet on the other hand must grasp something about intelligence in order to identify its works, seems to be an outcome of the defensive position that is the unenviable lot of the de facto IDists.

In view of this, I may actually be doing archaeology an injustice when I sometimes compare it with ID: More often than not archaeology doesn’t have much trouble identifying the works of human intelligence; the lion’s share of the problem in archaeology is identifying the human meaning of what it digs up – and to do that requires knowledge of human beings; that is, knowledge of the intelligence behind the artifacts. So it is no surprise to find IDist Vincent Torley admitting that ID is a negative science. In a post on the ID website Uncommon Descent entitled Larry Moran commits the genetic fallacy, dated October 20th we read:

As for Professor Moran’s claim that Intelligent Design proponents’ focus is primarily aimed at discrediting unguided evolution rather than building a positive case for design, I can only reply that a design inference in ID can only be made after other explanations have been ruled out, so as a matter of necessity, much of what ID researchers do will be negative, and aimed at eliminating conventional explanations, before any positive conclusion can be reached that a given object was designed.

If from science’s third person perspective we manage to trace all human activity back to the operation of the “natural causes” of neural communities we cannot then conclude that intelligence isn’t involved; human intelligence is a high level system feature which is not easily observed down at the low neural level. Neurons are "things" and not sentient personalities; it takes a very large organised group of them to possess the property of conscious cognition.  From this example we can see how artificial it is to drive a wedge between "natural causes" and intelligence to the extent that they are thought of as all but mutually exclusive. Moreover, I would expect any genuine science to be interested in the workings of the intelligent agent and how it relates to the ontology of our world. It is almost as if IDists are trying to create a space of spiritual quietus where they can worship in peace and where the role of ID science is protective rather than proactive. The quasi-apophatic approach of de facto ID looks suspiciously like a rear-guard defence of theism rather than a presentation of positive evidence

Irreducible Complexity

This is actually not a bad idea if formulated properly: Potentially the idea of irreducible complexity is a killer concept as far as evolution is concerned. But the de facto ID community continues to use Michael Behe’s inadequate low resolution rendering of IC which talks only about interdependent functional parts. The loop hole in Behe’s concept of IC is found in the fact that the functional parts he talks of are themselves made of smaller parts, all with the potential to morph  molecule by molecule, atom by atom into other sets of interdependent parts. This allows the imaginative devil’s advocate to conceive of ways in which each interdependent function morphs in unison with all the other functions in such way that the whole conglomerate remains functional. Anti-IDists have attempted to do just this (see the first link below). The remedy is to use a concept of IC formulated at the particulate level; such a formulation would amount to a denial of the existence of the “sponge” structure in configuration space (The spongeam), a concept I describe in the second two links below. Having said that let me express my suspicion that the spongeam doesn’t exist, so the IDists may actually have the last laugh here!

Screwing up IC: http://quantumnonlinearity.blogspot.co.uk/2014/07/north-american-idists-screw-up.html

Defining IC: http://quantumnonlinearity.blogspot.co.uk/2015/06/algorithms-searches-dualism-and_13.html

Defining IC: http://quantumnonlinearity.blogspot.co.uk/2013/05/configuration-space-via-mathematical.html

The Second Law of Thermodynamics

IDists continue to be seduced by the erroneous argument that the second law of thermodynamics contradicts evolution. The basis of this argument clearly fails in the case of the growth of living organisms which organise matter in huge quantities without violating the second law by using the information in their genes and associated mechanisms. Likewise, if evolution does in fact work, it would be using the implicit information present in the spongeam of configuration space and which presumably is in turn implicit in the laws of physics. Although I doubt the existence of the spongeam, nevertheless if it is present it would effectively guide evolution just as molecular configurational information guides the annexation and organisation of matter in the growth of life. In this latter context local decreases in entropy are more than compensated for by an overall increase in entropy.

http://quantumnonlinearity.blogspot.co.uk/2015/03/the-first-law-of-holes-and-second-law.html

http://quantumnonlinearity.blogspot.co.uk/2010/07/idiot-proofing-thermodynamics.html

http://quantumnonlinearity.blogspot.co.uk/2010/02/thermodynamics-and-evolution-again.html

http://quantumnonlinearity.blogspot.co.uk/2015/06/algorithms-searches-dualism-and_13.html

Creating Information

Many clients in the fundamentalist and ID communities will offer up the cliché like “natural processes cannot create information”.  This belief is supported in part by William Dembski’s “conservation of Information” but without regard to the terms reference and limitations of Dembski’s otherwise interesting and thought provoking work. And yet natural processes can quite obviously create information: Viz: Consider for example the human brain; it creates information in any practical sense of the word and yet, as far as we can tell from the third person perspective of science, human activity is a “natural process”. However, the issues surrounding the creation of information are somewhat technical and so I will be dealing with them in more detail in a separate post. I have partially dealt with the matter here, but further clarification is needed in the light of the work I have done in  the Thinknet project.

In the meantime here is a quote from fundamentalist Ken Ham as he makes dogmatic assertions about a subject he doesn’t understand:

For example, evolution requires the addition of huge amounts of brand-new information into the DNA of a creature in order for new features to arise. But there is no known process that adds brand-new information into the genome of a creature.)  But without new information you absolutely cannot turn an amoeba into an astronaut no matter how much time you have! Evolution just cannot happen.

As I’ve already said we do know of a natural process capable of adding brand-new information into a genome - namely, human activity.  As for "Evolution just cannot happen" Ham has no notion of the spongeam and the crucial question of whether or not it exists; he is never likely to come anywhere near addressing this question.

The Christian Right and Fundamentalism

The ID community are too close to the right wing and the anti-science Christian fundamentalists. I see this in part as due to the common conceptual ground afforded by the epistemic filter which favours a form of dualism: Viz: A broad spectrum of evangelicals, fundamentalists and cultists think in terms of a God vs. natural forces dichotomy. And yet within this spectrum there is in fact a huge spread of ideas all the way from Flat Earth to the quasi-theistic evolution of William Dembski.  This creates tensions within the movement. See for example this post by Vincent Torley on Uncommon Descent where in the comments section Torley is accused of supporting “Darwinism” (Sic; See comment 86).

So, what other factors might bring together this disparate diversity of opposing opinions?  Probably even more pertinent than the philosophical dualism implicit in the explanatory filter is the common political cause of communities who otherwise find it difficult to get on. That common politics, I propose, is that they all reside to the right of the political fault line which runs between government and the private sector; especially in the USA.  In particular, both fundies and the de facto IDists find themselves alienated from the public sector academics who one fundie talks disparagingly of under the rubric  "the main stream science community".

See also here: http://quantumnonlinearity.blogspot.co.uk/2014/03/public-vs-private-polarisation.html

As a further illustration of the academic alienation and marginalisation of IDists we find evangelical atheist Larry Moran and public servant scientist trying (probably vainly) to hand an olive branch to the less extreme IDists. In a post entitled  Intelligent design needs to clean up its act if it expects to be taken seriously he says:

I hope that the knowledgeable, informed, members of the ID community will abandon the ridiculous path they've taken where they try to make a scientific case for ID knowing full well that the majority of their supporters disagree strongly with their premises (e.g. common descent). That's an untenable position.

We've seen recently that some ID proponents are attempting to do this. I'm thinking of Jonathan McLatchie and Vincent Torley right now but there are others. How is it working out? Look at the Torley post on Uncommon Descent where he's trying to explain evolution to IDiots: Human and chimp DNA: They really are about 98% similar. It's an uphill battle. The kooks are accusing him of becoming a Darwinist.

But that's exactly what the ID community needs to do in order to gain credibility. They need to shed the kooks and the IDiots who make them look silly. When they do that, they may find that more of us are willing to have a serious discussion about science

And there’s also this:

We also judge [ID] by the people who post comments on blogs and Facebook and by those politicians who support it in the public sphere….

Wouldn't it be nice to see a scientific debate between Michael Behe and David Klinghoffer on the meaning of evolution? Not going to happen as long as ID is primarily a religious movement.

Along the lines of the latter comment, I’ve never seen the ID community engage Dembki’s statement which I showcase here. But would an evangelical atheist like Moran ever entertain anyone who entertains the notion that intelligence is fundamental to the cosmos without being tempted to make recourse to appellations like “superstition” and “IDiot”? The converse is not going to happen either: The ID gurus will not be prised apart from their followers; they owe those followers a huge debt: It is those followers who have given them their platform, their accolades and the market for their books and conferences.

Forget it!

The Thinknet Project Part 3: The Intersection Product

The third part of my "The Thinknet Project" can be downloaded from here.  I reproduce the introduction to part 3 below: 

***

1.      Introduction

This is the third in the series where I explore Edward de Bono’s ideas about thinking and my development of them using mathematical and computer modelling. Just how far this modelling captures the process of thinking remains to be seen, of course; it is quite likely that even if these ideas are a step in the right direction they will nevertheless be at best a simple toy-town depiction of the immense complexities of the brain! We have to be content with the idea that my Thinknet project is perhaps only capturing one small aspect of human conscious cognition.  However, all I can do is continue on the road I have set myself and see where it leads…..

***

In his book The Mechanism of Mind de Bono describes a very general metaphor of thinking: In this metaphor consciousness is identified with a “pool of light”, or “pool of attention”, which flows like water over a surface contoured by a network of channels. That network of channels represents the thought space potentially available to the exploratory motion of consciousness as it moves around that space.  The network of thought space is a product of two things:  Sensory input impacting and impressing itself onto the surface and the etching effects of the motion of the conscious thought itself. 

Whilst the pool of attention has the property of consciousness associated with it, thought space does not. This raises an obvious question. Why is the ebb and flow of the pool of attention associated with that first person sense of a conscious perspective? Has this something to do with the physical properties associated with the pool? If so, what are those crucial consciousness bestowing properties? I don’t think such a question is answered easily, but de Bono does at least bring that question into sharper focus. In the meantime we can at least develop the mechanics of conscious attention.

In de Bono’s models the pool of attention moves around according to the dynamics set by the network, a dynamics that is local in nature and not wholly dissimilar to the way a mass of particles might move in a potential field under the influences of local forces. For example, in the activity of elementary association attention moves passively whereby one thought leads to another in a succession that depends in part on how strongly the thoughts are locally linked to one another in thought space. But we can get a vision of a much more proactive non-local dynamics if we go beyond the one-to-one links of simple association to the more complex entities of compound associations. For example consider this compound stimulus:

Small domestic meat eating mammal.

In ordinary one-to-one association  each of the tokens above can be used as a separate input stimuli in order to yield the most likely association: e.g. On entering ‘meat’ we might find  it associates  with ‘food’; on entering  ‘eating’ we might find is associates  with ‘teeth’. But the above compound stimulus cannot be solved in this way. Because of the way our own minds work we can see that a solution which fits all the ‘evidence’ contained in the compound stimulus is probably ‘domestic cat’; perhaps not ‘dog’ because the qualifier ‘small’ is more probably  fulfilled in ‘ domestic cat’.   In effect we are looking here for a single token that resolves a set of competing input tokens. It is not possible to achieve this kind of resolution by simple association.  So the question is; what is the mathematical basis for the solution to this kind of compound problem?  The following mathematics is based on my notes of 14^th  September 1991.

***

Relevant Links.

The Thinknet project is really part of my Melencolia I series. The links relating to this series are below:

http://quantumnonlinearity.blogspot.co.uk/2014/01/melencolia-i-and-great-plan.html

http://quantumnonlinearity.blogspot.co.uk/2014/06/the-melencolia-i-manifesto-part-2.html

http://quantumnonlinearity.blogspot.co.uk/2014/08/melencolia-i-part-3-sharpening-focus.html

http://quantumnonlinearity.blogspot.co.uk/2014/11/melencolia-i-part-4-generating.html

http://quantumnonlinearity.blogspot.co.uk/2014/12/melencolia-i-part-5-creating-information.html

Also relevant are these links:

http://quantumnonlinearity.blogspot.co.uk/2015/05/algorithms-searches-dualism-and.html

http://quantumnonlinearity.blogspot.co.uk/2015/05/algorithms-searches-dualism-and_12.html

http://quantumnonlinearity.blogspot.co.uk/2015/06/algorithms-searches-dualism-and.html

http://quantumnonlinearity.blogspot.co.uk/2015/06/algorithms-searches-dualism-and_13.html

http://quantumnonlinearity.blogspot.co.uk/2013/02/dembski-im-not-denying-evolutionary.html

http://quantumnonlinearity.blogspot.co.uk/2013/04/theology-and-north-american-id-part-1.html

http://quantumnonlinearity.blogspot.co.uk/2013/06/theology-and-north-american-id-part-2.html

Twere to consider too curiously, to consider so.

Could MI6 have an interest in my little story? Probably not, because I try not to live in the real world.

I spotted the following material online over a year ago, but as I'm currently short of time for blogging I thought I would tell this odd little tale in lieu of my otherwise absence from the blogosphere......

This paper on solid state physics written by Chinese authors  Xiang-Ying Ji and Xi-Qiao Feng is rather curious. Why so? .....because my book Gravity and Quantum Non-Linearity is referenced in it. Honours like this don't often come my way, so it's time to play it for all it's worth and bask in the glory.  Here's where in the paper's text the reference occurs: 

The reference 14 attached to their biased diffusion equation (4) appears in their reference list as follows:

I wonder if these guys know who I am and what I'm about because there is a bit of "but" in all this! The equation in my book Gravity and Quantum Non-Linearity  that is nearest in form to equation (4) above is equation (3.13) below:

If you can read equations like this then you will understand that apart from a couple of differences my equation (3:13) is more or less of the same form as Xiang-Ying Ji and Xi-Qiao Feng's equation (4). Those differences are in the constants and also the appearance of the last term on the right hand side of (3.13). 

But .. and here's that "but" I spoke of..... notice  I have "i" ( that is, root minus one) in front of the diffusion constant. When you add this complex factor to the diffusion term it changes an ordinary biased diffusion equation into a wave equation. The other thing to notice is the appearance of the last term on the right hand side - this is to compensate for the fact that in the kind of diffusion represented by (3.13) the diffusion is a process where in the underlying random walk the stepping agent bifurcates and steps both left and right at the same time. To prevent such a system violating conservation laws the third compensating term on the right hand side must be subtracted.  (This is not a point that appears in my book, but is something that has occurred to me more recently). It is this feature that gives my equation its relativistic character.

Xiang-Ying Ji and Xi-Qiao Fengstop stop short (wisely perhaps) of this "relativistic complexification" of biased diffusion - after all, their paper is really all about the ordinary diffusion of real particles in materials and not about a quantum equation or its extension into quantum gravity. It is perhaps a little strange that they should reference some weird and eccentric amateur theory of quantum gravity when the derivation of the non-imaginary form of their equation (4) is pretty standard fare! But I'm honoured that our esteemed Chinese friends have chosen to use this reference! I wonder if there are some security issues entailed here? I'll leave MI6 to decide on that one!

Fundies and Nihilists

There have been a couple of interesting posts on PZ Myers' blog

1.  The first one here is a take down of a brash Christian fundamentalist named Wilson who claims to have a one-liner disproof of evolution Viz:

EVOLUTION THEORY'S BIGGEST BLOW: Wilson's Law of Evolution. Where Are All The Fossils of Failed Mutations?

Myers walks through the huge loop-hole here and savages Wilson's superficial sales-talk patter and then throws the scraps into his Parana pool of commenters for further savaging. The fundamentalist clearly has no idea about statistics and the nature of mutations; whatever you think of evolution this is not the way to refute it. But I'm less interested here in yet another embarrassing argument from a Christian fundie than I am his very frequent disparaging references to the "mainstream science community". This is a sign of fundamentalism's intellectual marginalization and  alienation from the scientific establishment. It is this anti-establishment drift which is helping to drive some fundamentalists into the ultimate conspiracy theory, a theory which is also based on superficial sales-talk. 

2. The second post here is about the lastest mass shooting in America by someone claiming to be anti-religion. Myers objects to Sam Harris' consequent reactive defense of atheism, a defense which has a suspiciously nihilist feel about it:

Atheism has no doctrines. It does not demand that a person do anything, or refrain from doing anything, on the basis of his unbelief. Consequently, to know that someone is an atheist is to know almost nothing about him—apart from the fact that he does not accept the unwarranted claims of any religion.

Myers response is a plea against a Nihilist interpretation of atheism:

Religion is primitive and lacking in any tools to address deep injustices and correct errors in its formulation. I am all in favor of tearing it down and replacing it with…what? According to Harris, nothing. Atheism has nothing constructive or productive to replace the bad system most people are limping along under — rip it all out and apparently, brute reason can then be trusted to evolve something better.

Never mind that the same atheists who adore the irresponsibility of the idea that their beliefs impose no demands on them are also the same atheists who so detest equality that they spit on feminism;

Reason is not enough. Reason can show you the best way to achieve a goal, but if your goal is mass murder, or denigration of women, or the perpetuation of an oppressive hierarchy, it’ll help you do that, too. We need purpose and value and meaning as well, and if a prominent Leader of atheism is saying that atheism doesn’t do that, that’s a declaration that atheism is bankrupt, and has failed totally. It has become a Great Nothing.

That’s not my atheism, though. I argue that the absence of gods gives greater prominence to the interdependence of the human community, and adds greater weight and urgency to the importance of empathy and equality and all those human values — but if atheism is now a label that allows us to nonchalantly disavow responsibility for the actions of those within our own group, perhaps it’s time to disband the whole idea of an atheist community.

But then it’s also clear that my vision of what atheism ought to be is a minority view. The majority are doing their damnedest to confirm the poor opinion the believers have of us.

It would be wrong to say that atheism always leads to nihilism - after all Myers is probably humanist in sentiment and is looking for meaning and morality - but atheism does, as I have said before, teeter dangerously on the brink of nihilism and anti-foundationalism. Calibrating the moral compass and charting a purposeful course through life is ever the challenge of atheism.  The above is evidence of this challenge.

Pluto

(Click to enlarge)

Some brief off-the-top-of-my-head thoughts on this image of Pluto.

After all the talk about Pluto's surface having a surprising dearth of cratering I realized on looking at the above image that scientists were talking in relative terms; the picture actually shows Pluto to be quite pock marked with craters - however, a lot less so than that of the Moon and other planets, but probably much more so than the Earth. Ergo, Pluto's surface is older than that of the Earth which, of course, is subject to high levels of largely atmospheric based erosion and change. In fact the crater density of Pluto may be comparable to that of the Lunar Mare.  (See the hi-res picture of Pluto on the web site below)

 Pluto has a thin atmosphere as this picture shows:

Pluto's size, along with its inclined and eccentric orbit may be evidence that it is a captured Kuiper belt object; perhaps an outcome of the long term gravitational chaos of the Solar System. If the once very frozen Pluto was relatively recently captured into its current orbit then its solar constant would change. Such orbital change could conceivably result in the low boiling point of some of Pluto's surface compounds just being passed, consequently creating an atmosphere and in turn starting off a slow erosion cycle. This may explain Pluto's relatively "young" surface. But remember; in Solar System terms half a billion years is "young"!

Anyway, be all that as it may, we had better wait and see what the experts say. One thing is clear: Given the number of unknowns there is plenty of theoretical scope to explain the appearance of Pluto!

For more pictures of Pluto see:

http://photojournal.jpl.nasa.gov/targetFamily/Pluto

The Thinknet Project Part 2: Theoretical Underpinnings

The second paper on my Thinknet project is now available here. Below I reproduce the introduction.

1.      Introduction

In part 1 of this series I described the general idea of an association network as based on some of the ideas of Edward de Bono’s book The Mechanism of Mind. In this part I develop the theme a little further by giving it some mathematical backbone.

By August 91 I had written up an association network program on an Amiga 500. I had some vague notion about the tokens of the network being linked by some kind of probability weighting. Up until that time the Thinknet project was very software driven: I wanted to get out a system that did something regardless of whether or not I really understood what it was doing; much of it was an accumulation of several seat-of-the-pants decisions.  I had guessed that the tokens of the network were linked by some probability but I didn’t really have any clear idea as to the theoretical underpinning of this probability. Initially all I did was to code in a universal linking probability factor that represented the fact that although token A would lead to or imply token B it wouldn’t do so with absolute certainty. But it was obvious that using a one size fits all probability was far from satisfactory. During one of our many family beach chalet holidays (10 August to 17 August 1991. Hemsby, Norfolk) I sat on the sand looking out to sea pondering what the underlying theoretical model should be and by early September I had the model up and running.

The model was based on a very simple idea;  in fact the idea was essentially that of a literal interpretation of the Venn diagram. In this model the points on the Venn diagram are thought of as concrete items which can be collected together in various classes according to the properties those items have:  In the Venn notation we draw a circle round a set of points on the diagram to represent a class of items, each of which have some selected property. If we draw two circles based on two classes each defined by their particular property then we can then represent the relationship between these two classes by the extent of the overlap, if any,  between the two classes; an idea familiar to anyone who has seen a Venn diagram

This very literal interpretation of the Venn diagram using items and their respective properties to form classes of items gives us a very concrete model of set theory which immediately circumvents Russell’s paradox. It does this by distinguishing sharply between classes and the items of which they are composed in a similar way that Von Neumann’s version of axiomatic set theory makes a distinction between classes which are not elements and classes which are elements (where my items = elements). 

***

Relevant Links.

The Thinknet project is really part of my Melencolia I series. The links relating to this series are below:

http://quantumnonlinearity.blogspot.co.uk/2014/01/melencolia-i-and-great-plan.html

http://quantumnonlinearity.blogspot.co.uk/2014/06/the-melencolia-i-manifesto-part-2.html

http://quantumnonlinearity.blogspot.co.uk/2014/08/melencolia-i-part-3-sharpening-focus.html

http://quantumnonlinearity.blogspot.co.uk/2014/11/melencolia-i-part-4-generating.html

http://quantumnonlinearity.blogspot.co.uk/2014/12/melencolia-i-part-5-creating-information.html

Also relevant are these links:

http://quantumnonlinearity.blogspot.co.uk/2015/05/algorithms-searches-dualism-and.html

http://quantumnonlinearity.blogspot.co.uk/2015/05/algorithms-searches-dualism-and_12.html

http://quantumnonlinearity.blogspot.co.uk/2015/06/algorithms-searches-dualism-and.html

http://quantumnonlinearity.blogspot.co.uk/2015/06/algorithms-searches-dualism-and_13.html

http://quantumnonlinearity.blogspot.co.uk/2013/02/dembski-im-not-denying-evolutionary.html

http://quantumnonlinearity.blogspot.co.uk/2013/04/theology-and-north-american-id-part-1.html

http://quantumnonlinearity.blogspot.co.uk/2013/06/theology-and-north-american-id-part-2.html

How to Build a Seaworthy Wooden Vessel

The Gotherborg at  Gt. Yarmouth quay

The Gotheborg, the world's largest operational wooden ship, was berthed Great Yarmouth quay at the weekend for the maritime festival and I went to see her. The Gotheborg is in fact a Swedish built replica of a ship of the same name which sailed in the mid eighteenth century. Visitors were charged a reasonable fee to look round her.... and fascinating it was too. Because the vessel is a working boat it conveys that authentic, grimy and untidy ambiance of a going concern; in contrast to the prim scrubbed clean museum piece that HMS Victory has become. The Gotheborg has very much the touch and feel of the real thing and brings the visitor a bit closer to just what it was like to live and work on one of these wooden sailing ships. So, congratulations to the Swedes on their excellent work.

I took some photos of the interior and two of them can be seen below. The first picture is a general view of the gun deck.

This second picture shows us one of the gun portals. with wooden walls around 18 inch thick:

.....So that's how you make an authentic sea going wooden ship! But you don't make it like this:

I doubt this would last five minutes on the high sea, let alone a year

OK, OK, I know that Answers in Genesis's Ark mock up is all about facade, because the real deal would be far too expensive. But for AiG "facade" is very much the name of their game: From their tame academics who produce no young earthist papers for mainstream academia, through the liberal use of the omphalus hypothesis in their cosmology,  to the thin walls of this so-called “Ark”; if it's a choice of style over content, style wins out every-time. The whole AiG outfit revolves round the maintenance of a PR charade; Verdict? Must try harder to bring greater authenticity to the ministry!

Relevant Links:

http://quantumnonlinearity.blogspot.co.uk/2015/06/garden-shed-technology.html

http://quantumnonlinearity.blogspot.co.uk/2011/02/beyond-our-ken-on-mature-creation-part.html

http://quantumnonlinearity.blogspot.co.uk/2013/10/mangling-science-continuing-our-diet-of.html

Kent Hovind Defends Science Against Flat Earther Infestation (Yes, really!)

"The Cultural Logic of Late Fundamentalism"

i.e Fundamentalism is sick, sick, sick!

And now for some light relief.

Disclaimer: Caution, you are now entering Poe's Law zone.

Here's an ostensibly pro-flat earth video by an ostensibly Christian fundamentalist attacking Kent Hovind's defense of established science's heliocentric/spherical Earth solar system. Knock me over with a feather; I found myself rooting for poor old Kent even though he himself is a quite extreme fundie!  But don't ask me whether or not Kent was being spoofed or whether the video is a parody! To  be frank I can't be absolutely sure! However, if people are to be believed there seems to be a fairly recent resurgence of Flat Earth beliefs among Christian Fundamentalists; hence my above recycling of a phrase by Jameson!

Fundamentalist Kent Hovind gets a pasting from fundamentalists even more extreme than himself! But for a change Kent comes up  smelling of roses! (Just! *²)

Here are some other videos on the Flat Earth Conspiracy:

https://www.youtube.com/watch?v=IYYj_h_i5wo

https://www.youtube.com/watch?v=cU0-ASniLvE

Clearly, we are in Poe's law territory here! However, it is true that genuine flat earthers and geocentrics have existed and still exist today. See for example the following two comments below as they appear in the comment thread of the video and which as far as I can tell don't look like spoofs.... although don't quote me!

A Geocentric Commenter:

Some may argue that it not important for salvation if the earth is round or flat and that may be so. for me personally i feel as king David did who says at

  Psalm 8:3-5 New International Version (NIV)

3 When I consider your heavens, the work of your fingers, the moon and the stars, which you have set in place, 4 what is mankind that you are mindful of them, human beings that you care for them? 5 You have made them a little lower than the angels and crowned them with glory and honor.

That the creation of the sun and moon and stars reveals gods love for humans in that they were created for us and this gives us dignity and honor as gods children. we have been robbed of our dignity and honor and birthright as children of our God by the false teaching that the sun is the center and everything exists by chance. we have a conscience that draws us to our heavenly father they take this away and they gave us CONscience. the heavens is our crown of dignity and honor from our creator and father Jehovah.

A Flat Earth Commenter:

Kent I must say, until you do the research and you do the science, You have no more claim to it being a sphere than those same scientist have for claiming the earth is millions of years old. No Kent you have not been in space to see for yourself. All you have is NASA (*But see footnote), and your Ship Sail explanation has been "proven wrong" long ago. But the science being brought today by a preponderance of Science Evidences prove the Earth is Exactly as God said. It's Flat, It's fixed within outer-space "not moving" and all the other stuff moves around earth. Kent You have to use the same "dogmatic" stance that you throw at Dinosaurs and the Planet being Billions of years old. If you want to "Believe it's a Sphere that's your own Religion" Just like you tell all those who say they want to believe in Billions of years and Dinosaurs... I wish to believe as God said it was. FLAT... But It seems strange to me that today you seem to be so worried what others will think. Kent you said you believe God, but it seems more clear you only believe in some of the things God says... hmm strange

The implications for Christian fundamentalism in general are grave: As the above suggests Christian fundamentalists, whether they are flat earthers, geocentricists, young earthers, blood mooners, failed prognosticators or promulgators of conspiracy theorism, all have a distinctive and recognisable commonality in as much as they use a Biblical literalist epistemic. As the video shows the fundamentalist epistemic can be turned against itself in an ironic twist; the video exposes not only the inconsistencies between different fundamentalist groups but also within a ministry like that of Kent Hovind. One thing is clear; there are many shades of fundies out there who are firmly and (over) confidently asserting all sorts of mutually contradictory things and yet they all claim their opinions have divine authority based either on the Bible or the gnostic touch of God; quite often both!

One's first impressions may be that flat earthism and young earthism are scientific questions, but such bizarre claims have more to do with group psychology and sociology than they do science: One can study flat earth theory and young earthism from the point of view of science gone astray, but that is less than half the story; the other and probably more important half is to do with the sociology of belief and group identification. There does, however, seem to be a logical progression here: In fundamentalism's alienation and marginalization from the academic mainstream and from culture in general, it is an easy emotional step to reject modern cosmological science in its entirety; from its inception with Copernicus, through Galileo, Kepler, Newton, and so on to the enlightenment etc, to the fundamentalist it all feels like a conspiracy to defraud them of the faith. Since modern science also owes much to prototypical Greek thinking a further logical step for fundamentalists is the rejection of the (pagan) Ptolemaic cosmos.

Biblical texts written prior to the sixth century BC are likely to have come out of a culture that had no conception of a spherical Earth and this is evidenced by the Bible in as much as there is no mention of a spherical Earth in pre-sixth century Biblical texts; if anything, as the Christian flat earthers point out, the Biblical metaphors hint at a belief in a flat earth. As fundamentalist marginalization and subsequent detachment from social identification continues apace, social fetters suppressing fundamentalist contrariness against the marginalizers are loosed. It is no surprise, then, as disaffected fundies immerse themselves in what they wrongly think to be the self-contained and self-interpreting universe of the Bible they regress to a pre-sixth century BC cosmology in an act of protest and cultural vandalism.

That flat earthism is able get a social purchase even today is not only evidence of certain kinds of social trend but also a sign that the perverse assumptions and special pleading of dogmatic  "presuppositionalism" will always find an intellectual loop hole: This is because in the final analysis very little is directly observable. Our "direct observations" are embedded in a huge mountain of theoretical narrative by which they are synthesized into a comprehensible whole; a perverse and contrary person is always able to eventually find some other bizarre narrative which joins at least some of the dots of observation. A fine example of this is young earthism's omphalos hypothesis whereby any observed state of affairs can simply be explained as the way God made it. Fundamentalism's omphalos tradition has been given new impetus by Jason Lisle's ASC cosmological model. See also John Byl.

It's worrying that a nation such as the USA, on whose prosperity, strength and wisdom the West as a whole very much depends, should be the epicenter of these daft goings on; perhaps it's something to do with that great American independent-can-do spirit which, it seems, has a downside as well as an upside, just as the great German aptitude for collective discipline once showed us its downside. As for the British they tend to lazily maintain the status quo until there's either a threat to their business interests or a threat of an alien evasion. All very stereotypical no doubt, but when you're writing a paragraph of one-liners that attempt to sum up the situation what else can you say?

See also these links:

http://quantumnonlinearity.blogspot.co.uk/2013/12/the-ultimate-conspiracy-theory.html

http://quantumnonlinearity.blogspot.co.uk/2010/07/problems-in-young-earth-creationism_15.html

http://viewsnewsandpews.blogspot.co.uk/2010/11/fundamentalist-argument-clinic-part-1.html

http://viewsnewsandpews.blogspot.co.uk/2011/01/fundamentalist-argument-clinic-part-2.html

http://viewsnewsandpews.blogspot.co.uk/2011/02/fundamentalist-argument-clinic-part-3.html

http://viewsnewsandpews.blogspot.co.uk/2011/03/fundamentalist-argument-clinic-part-4.html

Footnotes:
* ....and the Russian, Chinese, European and Japanese space agencies....and you'd better add numerous private aerospace companies who must be in on the conspiracy as well!
*2  ..although Kent does get himself into a twist over whether the Earth is at the centre of the Universe.

Appendix I : High Structure Tilt

In the Kent Hovind video an argument for a flat earth was offered which I haven't seen before: The argument is that structures over the horizon and yet whose height means they nevertheless stand above the horizon should appear to tilt away from the observer if the Earth is round. But no quantification of this effect was advanced and no proof of whether it would actually be apparent was offered. Take the example they showed of sky scrapers viewed across what they said was 20 miles of sea. The angle these objects would tilt away from the local zenith is given by the equation:

360 x 20/24901 = 0.289 degrees.

Where 24901 = circumference of the Earth.

Now try looking at a tall object in front of you tilted at about 1/3 of a  degree away from you and see if you can see the tilt.

The flat earth clown (I'm not at all sure this man is serious!) who advanced this fallacious argument can be seen in the video below. Many criticisms can be made of his "science", a "science" which involves no quantification and measurement. But to spend too much time on this rubbish is time ill spent as far as I'm concerned. However, this video is evidence of the (recent) link between Christian fundamentalism and flat earth conspiracy theorism.

Flat earthers: Making a mockery of Christianity

Appendix II : Depressed Horizon

Some fundamentalists maintain that the horizon isn't depressed as it should be if the earth was round. In contrast I maintain that it is quite easy to see this depression.

In 2004 whilst holidaying on the Isle of Wight in the UK I stood about 500 feet up on Tennyson Down with my son Stuart looking across to St Catherine's Point  which stands at nearly 800 feet. One would expect, then, that a flat earth horizon at infinity would intersect St Catherine;s Point at well over half it's height, i.e. at the 500 foot mark. We remarked at the time that this was very noticeably not the case - the horizon, as demarcated by the sea, was much lower than this, and I took this to be evidence of the Earth's curvature. What we actually saw was this (A sketch I made shortly afterwards):

View from Tennyson Down looking across to St Catherine's point. In this view the nautical horizon is visibly depressed below the horizontal

Later on I scribbled down some pencil calculations on file paper and these can be seen here. It was these calculations that enabled me to arrive at the figure of 150 feet for the actual height the nautical horizon intersected the land of St Catherine's Point. Although I didn't have any equipment to take measurements, the visual impression was consistent with the theory.

The Thinknet Project: Footnote 2: Incomputability and the Biological Mind

 (Click to enlarge)

The above is a scan taken from Roger Penrose’s book “Shadows of the Mind”.  In this book he claims to have found a mathematical example based on The Halting Theorem proving human beings are capable of grasping otherwise incomputable truths. The pages above contain the core of his argument.

Penrose starts by defining C_q(n) – this notation represents the q^th computation acting on a single number n. Penrose then considers an algorithm A(q,n) which takes two parameters q and n, where, as I’ve already said, q designates the q^th computation and n is the input parameter for this computation. The algorithm A(q,n) is stipulated to be soundly devised in such a way as to halt if C_q(n) does not stop.  However, as Penrose goes on to show this sweeping stipulation entails a contradiction that not only demonstrates the limits of algorithmics (as per the well-established Turing halting theorem) but also the ability of the human mind to transcend algorithmic limitations (a conclusion that is highly controversial).

In order to show this Penrose considers A(n,n): If A works correctly (which we assume it does) then A(n.n) will halt if the n^th computation, when seeded with number n, does not halt.  Penrose then argues that A(n,n) is a computation that depends on just one number, and therefore it must be one of the C_q.  So let’s suppose that A(n,n) is the computation C_k.  That is:

A(n,n) = C_k(n).

Now n is a variable so let us put n = k.   Hence:

A(k,k) = C_k(k).

This latter expression clearly entails a contradiction: For if we insist that A(k, k) will halt if  C_k(k) does not halt, then because C_k(k) is actually the same as A(k,k),  A(k,k) must halt if A(k, k) doesn’t halt!  One way of resolving this contradiction is to relax the original stipulation that A(q,n)  is an algorithm which successfully determines in all cases that Cq(n) will not halt; thus we conclude that C_k(k) is one of those algorithms on which A(q,n) is unable to deliver a result: In other words A(k, k) will not halt when it is applied to C_k(k). The obvious corollary is that because A(k, k) is actually the same as C_k(k) then this means that C_k(k) does not halt either.

The foregoing is a version of Turing’s famous halting theorem; namely, that there exists no general algorithm that can solve the halting problem. However, just over on the next page from the above scan (i.e page 76) Penrose takes things a little further. He concludes that because we, as humans, can see that C_k(k) doesn’t stop whereas A(k, k) is unable to ascertain this then:

…. since from the knowledge of A and of its soundness, we can actually construct the computation Ck(k) that we can see does not ever stop, we deduce that A cannot be a formalisation of the procedures available to mathematicians for ascertaining that computations do not stop, no matter what A is. Hence: Human mathematicians are not using a knowably sound algorithm in order to ascertain mathematical truth

Penrose goes on to propose that the human mind isn't using a computable function at all.

Firstly, before considering whether Penrose is right or wrong let me ask this question: Is this good news or bad news? I think it depends on your interests. If you have a belief in the mystical superiority of the human mind over computers it will suit you down to the ground. If you don’t have a stake in algorithmic AI then you’re probably not too bothered. But if you do have a large stake in algorithmic AI it’s probably all a bit upsetting because it means there is little point in attempting to understand human levels of intelligence in algorithmic terms, even if those terms involve new (computable) physics: For according to Penrose the biological mind reaches into the algorithmically unreachable realm of incomputability. In passing let me just say that for myself I’ve always been rather drawn to a position similar to that of John Searle: That is, the human mind (and probably other minds with a similar biological ontology like cats and dogs etc.) possesses the irreducible first person perspective we call consciousness; but this view in and of itself doesn’t necessarily deny that a passable algorithmic simulation of the mind (i.e., as seen by the third person) could be created if we had sufficient understanding of the algorithmic formal structure of the brain. I have to confess that through my Thinknet Project I do have a bit of stake in algorithmic AI.

But vested interests apart is Penrose right or wrong in his conclusion?

One way of thinking about this contradiction that Penrose uses to derive his version of the halting theorem is to imagine that algorithm A is a system reified on some kind of mechanical ontology, like a computer.  The system puts up a flag when it finds an algorithm with a particular property P; in this case P = doesn’t halt. But there is an obvious problem when A tries to do this for itself: When this happens, in the very act of trying to flag property P algorithm A then violates property P! In effect when A attempts to flag P it's just like one of those sentences that tries to talk about itself in a contradictory way e.g. “This sentence is false”. This kind of conceptual feedback loop opens up the liability of contradiction; that is, in talking about itself A invalidates the very self-properties it is trying to describe.  The way round this internal contradiction is to assume that A cannot have certain items of knowledge about itself; therefore we conclude that A is unable to flag the kind of self-properties that lead to contradiction. This in as an example of the general Gödellian conclusion that for a system like A there exists a class of conclusions about itself that it cannot formally ascertain without contradiction.

But seemingly, as Penrose has shown, this result doesn’t prevent us knowing, for instance, things about A that A can’t know about itself; like, for example, whether or not it stops on certain inputs. Does this mean then that human thinking is non-algorithmic as Penrose concludes?  I suggest no; and I say this because before we start proposing that humans have access to incomputable mathematical truths there is potentially a less esoteric solution to Penrose’s conundrum as I shall now try to explain:

Penrose’s conclusion doesn’t necessarily follow because, I submit, it simply means that the human algorithmic system, let’s call it H, is reified on an ontology beyond and outside of A. That H can flag properties in A without getting itself into the kind of contradictory loop which is raised when A starts talking about itself is, I propose, a result of H running on a different ontology and is not necessarily down to some incomputable power of H. The flags that H raises about the properties of A are not reified on the medium of A’s ontology and therefore conflicts cannot arise whereby A, in the very act of flagging knowledge about itself, has the effect of negating that knowledge. Because H is ontologically other than A flags raised in H can in no way effect the properties of A.

In fact in discussing his conclusion Penrose actually shows some awareness of the out-sidedness of H and considers the case where us human outsiders can think of ways of creating an algorithm that is able to determine that C_k(k) doesn’t stop.

A computer could be programmed to follow through precisely the argument that I have given here. Could it not itself, therefore, arrive at any conclusion that I have myself reached?  It is certainly true that it is a computational process to find the particular calculation C_k(k), given algorithm A. In fact this can be exhibited quite explicitly…… Although the procedure for obtaining C_k(k) from A can be put into the form of a computation, this computation is not part of the procedures contained in A. It cannot be, because A is not capable of ascertaining the truth of C_k(k)….

This is an admission that there are algorithmic ontologies beyond A that can talk about A without facing the contradictions that circumscribe A when it tries to talk about itself. So before resorting to exotic ideas about the incomputable it may be that the more prosaic reason of a distinction of ontology explains why humans apparently know more than A; in fact this is what I am going to propose. This proposal, of course, doesn’t do away with the ultimate applicability of Godel’s and Turing’s conclusions because we simply find that these conclusions bite us humans too when we start to think about ourselves. For although it seems possible to create an algorithm that could embody our own understanding about A Penrose goes on to use what I refer to as the “superset trick” to show that contradictions ultimately must arise when any self-knowledge is sort for, human or otherwise. To this end Penrose envisages a robot that has been given information about the procedure for obtaining C_k(k) (My underlining):

Of course we could tell our robot that C_k(k) indeed does not stop, but if the robot were to accept this fact, it would have to modify its own rules by adjoining this truth to the ones it already ‘knows’. We could imagine going further than this and telling our robot, in some appropriate way, that the general computational procedure  for obtaining C_k(k) from A is also something it should ‘know’ as a way of obtaining new truths from old. Anything that is well defined and computational could be added to the robot’s store of ‘knowledge’. But we now have a new ‘A’, and the Gödel argument would apply to this, instead of the old ‘A’.  That is to say, we should have been using this new ‘A’ all along instead of the old ‘A’, since it is cheating  to change  our ‘A’ in the middle of the argument…..It is cheating to introduce another truth judging computational procedure not contained in A after  we have settled  on A as representing  this totality.

What I think Penrose is trying to say here is that any attempt to change A in order to circumvent the limits on the way A can talk about itself simply creates a new A which when applied to itself is either liable to the same old contradictions or must forever be forbidden certain kinds of self-knowledge. The “superset trick” that I referred to entails subsuming all such possible changes into a “super A” and Penrose rightly tells us that ultimately Turing’s halting theorem will bite this superset A.

But cheating is exactly what we can do if we are something other than the algorithmic system that is A and it is this ontological otherness which, I submit, is giving an apparent, albeit spurious, impression that our minds somehow transcend Godellian and Turing restrictions. We are ontologically distinct from Penrose’s robot and therefore we appear to be able to violate Godel and Turing; but this is true only when we are talking about an object that is other than ourselves. This distinction of ontology won’t rescue us when we start talking about ourselves; for ultimately Turing’s and Godel’s superset based conclusions will also bite when it comes to human self-knowledge: Ergo, when we talk about our own ontology there are certain things we cannot know without raising a contradiction. If these contradictions are not to arise with human self-knowing Turing and Godel incomputability must also apply to human ontology. In summary, then, the scenario considered by Penrose is not proof that human mental life has available to it incomputable knowledge; a better explanation in my view, is that Godel and Turing only apply when distinct ontologies attempt to self-know.

***

However, having said all that I must repeat and extend what I said in the the first part of this footnote: Human mental life is likely to be a non-linear process, thereby giving it a chaotic potential which could make it sensitive to what may be the incomputable patterns of quantum fluctuations. As I said in the first part, this non-linearity arises because thinking updates the memories on the thinking surface which in turn affects thinking, thereby effectively giving us a feedback loop with non-linear potential. But in his book “The Mechanism of Mind” Edward De Bono also identifies another way in which the mind may be non-linear in operation: He considers a model where one thinking surface has its activity projected as input onto another thinking surface which in turn has its thinking activity fed-back to the first surface. This scenario resembles the case where a video camera sends its output to a screen, a screen which is being videoed by the self-same camera. The feedback in both cases is likely to result in a chaotic pattern of evolution, an evolution sensitive to very minor fluctuations. This fairly prosaic way of postulating an incomputable cognitive process doesn’t even ask for new physics; although it does assume that quantum leaping is a literal process and a process that has incomputability at its heart.

So my conclusion is that whilst I don’t think Penrose has successfully shown that the mind is incomputable in his sense, mind nevertheless is potentially a means of delivering incomputable patterns to our world as a result of its sensitive feedback loops.

Penrose on Consciousness

Relevant links:

Thinknet series so far:

http://quantumnonlinearity.blogspot.co.uk/2015/07/the-thinknet-project-part-1.html

http://quantumnonlinearity.blogspot.co.uk/2015/08/the-thinknet-project-footnote.html

Melencolia I series

http://quantumnonlinearity.blogspot.co.uk/2014/01/melencolia-i-and-great-plan.html

http://quantumnonlinearity.blogspot.co.uk/2014/06/the-melencolia-i-manifesto-part-2.html

http://quantumnonlinearity.blogspot.co.uk/2014/08/melencolia-i-part-3-sharpening-focus.html

http://quantumnonlinearity.blogspot.co.uk/2014/11/melencolia-i-part-4-generating.html

http://quantumnonlinearity.blogspot.co.uk/2014/12/melencolia-i-part-5-creating-information.html

The Joe Felsenstein series

http://quantumnonlinearity.blogspot.co.uk/2015/05/algorithms-searches-dualism-and.html

http://quantumnonlinearity.blogspot.co.uk/2015/05/algorithms-searches-dualism-and_12.html

http://quantumnonlinearity.blogspot.co.uk/2015/06/algorithms-searches-dualism-and.html

http://quantumnonlinearity.blogspot.co.uk/2015/06/algorithms-searches-dualism-and_13.html