A Taboo Kind of Retirement Apology 12th November 2009

Many thanks to everyone for my retirement party and for a great life experience! Enclosed, in return, is my farewell present to you all. In the emerging tradition of lightning electronic publication, this is an illustrated research version of my 'trick-or-treat' (see later) speech, with live links to the current ground-breaking developments mentioned, and my research works, including Sexual Paradox and my live research overviews on the origins of life, the evolutionary tree of life and the conscious brain.

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If we're talking mathematics, why do we have 52 weeks in a year, why are there 7 days in a week, and yet there are 12 months in a year?

Coincidentally with todays date, I had 12 points for this 'apology' and I thought, there's one taboo kind of point that maybe I shouldn't talk about that might bring everything undone. But, why the 13, and why the 12, and why is 13 unlucky? [Since this is also the Eve of a Friday 13th]. This has to do with our book "Sexual Paradox", that David Gauld just drew attention to.

Left: A taboo kind of point (click to enlarge): To avoid all NZ psilocybes being deemed ad-hoc as prohibited species by the DSIR, I classified the local species jointly with Gaston Guzman, the world's leader on Psilocybe taxonomy, (Mycological Research 1991 95/4 507-508, Mycotaxon 1993 XLVI 161-70) resulting in discovery of my own 'native' species Ps. aucklandii. Center Left: European Venus of Laussel has a horn with 13 notches linking the moon, fertility and the menstrual 28 day period. Center Right: Chris Knight's sex-strike theory linking the moon, ovulation, sex and hunting from "Sexual Paradox". It was said in the 19th century that the last of the southern Bushmen were driven to cattle stealing, because their women folk said "No meat - No Sex". Right: Fulton's cave rock drawing of girls menarche (c1000BC). Inset !Kung Bushmen celebrate the same ritual of first menstruation, believed to be so powerful that to set eyes on her will destroy a hunter's prowess.

It's an idea that is mathematical, because it's about self-organized criticality and the idea is that human super-intelligence has come about because the two human sexes have vastly different reproductive investments and because each sex is running while standing still, they have to court one another in such a way that only the most 'intelligent' genes survive. [The prisoners' dilemma places this strategy as self-organized criticality onto a cusp bifurcation point.] That's what the thesis of "Sexual Paradox" is about and it has something to do with chaos theory and self-organized criticality, so it is mathematical, but it comes back to the 12 and 13.

What you find happened is that basically the female menstrual period is driven by the moon. It's a lunar cycle and is what you might call a sinusoidally-kicked rotator. The heart is also like this. The heart is supposed to have a periodic rhythm, but it's actually chaotic [a pacemaker-kicked oscillator] - James brought this up when I gave my colloquium talk - the only time you really have an ordered process is when the heart is having a heart attack, and then it's death! The 13, I think, is caused by the week being invented because women had a knowledge of time before men did and they timed everything according to their own menstrual periods, which have an average of every 28 days [13x28=364] when the lunar cycle is actually 29.53 days [12.36 cycles per year], and then there was a kind of male rebellion and we have [12 months], 12 angry men, the amphictyony and the 12 tribes of Israel. So 12 repressed 13 and the number 13 became unlucky.

What I would like to do is look back at what Bill Barton said [about protecting academic principles], which is a question of - 2 things. So I'll reduce the 12 and 13 to 2!

In Praise of Academic Freedom

One of them is this serious question about what is academic freedom and I'm retiring today because of a dispute about my Amazonian leave and that goes back a long way because when I first got employed by the university in 1969 and then in 1976 after seven years - the sabbatical notion - I got my leave granted and nobody asked any questions and I was given my ticket to go round the world - nobody said "What are you going to do"? Nobody said "You have to justify where you're going to go", and I was interested in "What is consciousness?"

You're all looking here at me and what you're actually having is a subjective conscious impression of being at a party - it could be a dream - you're probably don't think it's a dream because there's various tests of reality we can make that it's not a dream, but dreams can be very convincing - and so what I did was went to India and I tried to get an understanding - India has a philosophical idea that mind is finer than matter and the description of reality starts from subjective consciousness and it's got a deep long-standing tradition, so I wandered around India as a sadhu and it’s about the last thing that you could possibly imagine a mathematician having a valid place for being but nobody asked any questions because it was the concept of academic freedom and the concept of sabbatical leave.

So I then went to England and I interviewed Nobel prize winners and I did a scientific quest about molecular biology and the origin of life. John brought up why didn't I get my PhD and you know, congratulations to Eamonn for getting and FRS. I'm sorry that James has had to put on three parties - why did you put on a party for me - why didn't you just take me to the elephant house [where the Department Christmas party is being held] - I think that a serious miscarriage of justice happened about what sabbaticals are and I think that was the right way to go and I'm still standing here with a "Quantum Mind" T-shirt because in 2003 I went to an academic conference about this relationship between the brain, how the brain develops subjective consciousness, what its there to do, how it fits into the scientific description of reality - it's still the biggest abyss facing science. We don't know the answer to this one, we don't even know how to devise a description of reality which is starting to formulate scratching at the edges.

Now I didn't do a 'Mickey Finn' to the University by going there, but there's a rationale and why it all happened, which was that I grew up in a medical family and I grew up driving to accidents with people killed on motorbikes, people screaming "My baby - my baby", going to other places where someone had had a heart attack, going through the delivery wards and all the new babies, so it was like life and death and I got this feeling that you couldn't really survive in the world unless you were a doctor, but then I went to the university a year early and I hadn't done biology in school and I ended up missing out on getting medical intermediate and then I tried to do physics. Then at Victoria there were a lot of nuclear physicists and some of them died of leukemia because they had far too much radioactive substances in their laboratories. At stage three, I became incredibly depressed when I took nuclear physics which is really a doomed science its not really part of the picture, apart from a few nuclear establishments - the Large Hadron Collider doesn't need to do nuclear physics, we've got beyond that and I ended up, by default, graduating in Mathematics.

In Defence of the Pursuit of Knowledge

Having done that, I went to Warwick and then I realized: "Wait a minute, mathematics is something really, really special, because mathematics is the keyboard of reality!" All the scientific descriptions of reality are couched in mathematics, so if you want to understand the relationship between the weak force and the colour force, you've got a chance if you are a mathematician. You've got a chance if you are a physicist, but you've only got a chance with physics, so to speak, [but maths works for all the sciences] so what I tried to do was use this opportunity that happened, kind of accidentally, or as a consequence of my family origins, to take my mathematical experience and say: What's my duty to the pursuit of knowledge? And my duty to the pursuit of knowledge is to say "What are the most serious questions facing humanity in terms of understanding?" And then I would say: We don't know how life began. And this is all tied up with religious ideas, and it's tied up with mistaken ideas about quantum physics, because [some people] think that the only way you'll get interesting molecules is like a green cheese by random accidents, with ball and stick molecules, but that's not a realistic model. Later on along came chaos theory and non-linear dynamics and it filled in a lot of those pictures, but I didn't have those pictures at the beginning, so I looked at the origins of life, I looked at how does the brain generate consciousness, and took those on as challenges [documenting the main theses in my 1978 paper "Unified Field Theories and the Origin of Life", which John Butcher just drew attention to]. Now if you're in a mathematics department, that's going to run the risk that you are going to make speculative investigations and they won't necessarily generate you a doctorate. They won't necessarily generate you a paper in Nature because you don't have the data to justify the thesis.

Figures from the two breakthrough discoveries on origins of life (Click to enlarge). Left: Sutherland's new direct routes of synthesis of RNA nucleotides from primitive precursors. Center: Genetic analysis shows the last common ancestor of life came before DNA replication in the latter RNA era. Right: The last common ancestor was not a cell, as the genes for cell walls are different in bacteria and archaea, but has a viable long term non-equilibrium generative interface in environments where organic molecules can be concentrated by factors of up to 1010 bringing concentrations to biological levels, and reaching the point where fatty acids form membranes, in micropores in the carbonate towers forming over olivine - acid seawater 'lost cities' ocean floor vents.

So the critical issue of the second question is: Was the thesis false? Was this pipe dreaming? And what has turned out 40 years later? Because I was employed in 1969, and it's now 2009, so yes it's 300 years if you like [as James jokingly suggested] and the answers are very interesting, because for 30 years at least it looked like the origin of life was unsolvable, insoluble, and that nobody knew how to make RNA, and then in 2009 two papers were suddenly published and one of them showed that from absolutely primitive molecules you can actually get RNA nucleotides by a completely different route from those that anyone had imagined you don't get the sugars and the bases and the phosphates separately and then try and put them together - they won't fit together, they won't make RNA but there's another kind of chemical reaction and if you put the phosphate into the chemical reaction it all comes together. [The second research breakthrough concerns a unique phase interface in the form of undersea vents (not the black smokers, but milder chemical garden Lost City vents from the reaction of cosmologically abundant olivine with acidic primal ocean sea water) which show how prebiotic chemicals could be concentrated to cellular levels over whole geological time scales and form membranes and the RNA era] and what I did was say - there's a thesis and the thesis says that the origin of life is a cosmological process - it's part of how the laws of nature work - it's part of the non-linearities of the way the forces of nature have split symmetry and what I would say is that, as of 2009, it looks like that thesis is valid and the conjecture was true.

Evidence for genetic symbiosis became clear only after the Human Genome Project results were published (click to enlarge). History of human mobile DNA elements covering some 250 million years of evolution showing continuing germ-line coexistence of some 100,000 reverse transcribing LINE-1 elements, a subpopulation of which remain highly active, and their transcriptional 'piggy-backing' 900,000 Alu SINES.

Now there was another thing that I put into that 1978 paper and that was there is some sort of very deep symbiosis between viral genetics and cellular genetics and when the human genome project came out, it turns out there are things called LINE1 elements that go right back to the slime mould and they're involved in interactive processes, they're involved in certain kinds of medical conditions because of their mutations, they generate themselves when sperms are being made and eggs are being made, and they're an integral part of how the modular nature of the genome arising in humanity has come about , so that was also a true conjecture. [This goes as far as a dependence of mammals on retroviral cell-budding syncytin genes to enable the placental membrane. Viral particles on the placenta were noted in the 1978 paper.]

Left: Evidence for instabilites at the quantum or molecular level being able to influence brain states (click to enlarge). Top: Evidence for complex system coupling between the molecular and global levels. Stochastic activation of single ion channels in hippocampal cells (a) leads to activation of the cells (c). Activation of such individual cells can in turn lead to formation of global excitations as a result of stochastic resonance (d). Individuals cells are also capable of issuing action potentials in synchronization with peaks in the eeg (e). Bottom: Influence of chandelier cells in amplification. Single pre-synaptic pyramidal action potential leads to multiple post-synaptic excitations. Structure of chandelier or axon-axonal cells with dendrites (blue) and axons (red). Right: Quantum analogue of the kicked top using an ultra-cold cesium atom kicked by both a laser pulse and a magnetic field. In figure 9b is shown the classical dynamical phase space of the kicked top showing domains of order where there is periodic motion and complementary regions of chaos where there is sensitive dependence on initial conditions as a result of horseshoe stretching and folding. In the quantum system (second row) in the ordered region (left), the linear entropy of the system is reduced and there is no quantum entanglement between the orbital and nuclear spin of the atom. However in the chaotic region (right) there is no such dip, as the orbital and nuclear spins have become entangled as a result of the chaotic perturbations of the quantum top's motion.

The third thing is about consciousness, and going away to India and so on, and what I want to say is that there are some new results that I found were very fascinating. [I am interested in a model where sensitive dependence on initial conditions in transitions at the edge of chaos in global brain dynamics leads to sensitivity to quantum processes, opening the can-of-worms of quantum uncertainty and 'free-will'. This is also consistent with the similarity between wave front coherence as distinguishing attended signal from noise in brain dynamics and wavefront coherence, as the fundamental measure of Planck's constant of the quantum.] Until recently it looked like chaos was suppressed by at least closed quantum systems - then about a month ago there was a paper that came out about the kicked top and it was suspending a Caesium atom in a vacuum and them firing a laser at it and also putting it in a magnetic field and throwing it into a chaotic state and then what happened was the quantum system entered a deeper state of entanglement [with the nucleus], so we have a very very big question here about quantum entanglement, quantum chaos, the amplification of [the 'butterfly effect' of] classical chaos and "What is the brain doing when you have the 'eureka' phenomenon of saying 'aha' and you [at first] don't have the pieces of the puzzle fitting and then the solution suddenly appears?" We suddenly go through some sort of intuitive process [a transition from space-filling chaos to order] and arrive at the answer.

In Appreciation of Collegiality

So what I would say is that thank you to John Butcher for appointing me, and that was a very foolish thing to do, and I would like to thank George Seber for not firing me when student fired darts in PLT2 when suddenly in the middle of the lecture they started firing whole pieces of the Herald newspaper and the whole floor was littered with darts that big and Ron Keam came in and complained to Physics and George Seber came into the class and castigated me and castigated the class.

I want to say that I repaired that situation because there was a lecturer called Arnold Hart who was a very sincere lecturer, he worked very, very hard, but he had a tremendous amount of trouble supervising the engineering students and there was an era that was the first era that we had student evaluations and now we can say this is a political exercise in expediency, we can take a good view of it and say it's a democratic process, but the first student evaluations were an absolute safety valve for the engineers to vent their wrath on Arnold Hart and suddenly Arnold Hart took ill after reading the student evaluations and he took ill and said "I just can't seen to get up out of bed" and then passed away. So I was commissioned with the task of going into MLT1 and taking over the engineering students, so having had these darts launched at me and seeming to be too loose and a hippie dropout lecturer and not keeping the covenant of discipline, I walked into MLT1 and it was absolute bedlam - the students were shouting at the tops of their voices no one was looking at the front of the theatre at all - I can't remember if there was a microphone, but I think I grabbed the microphone and said "You killed the last lecturer!" and they all stopped dead in their tracks and there was not a sound in the theatre.

Images from the Amazon field study phase of my millennial sabbatical, disputes over which led ultimately to my retirement. Centre: NOAA sattelite coverage of the same period showing extensive fires. Almost the entire area today is in agribusiness. The second phase of this sabbatical led to a twelve day workshop at The Academy of Jerusalem, above the main souk in the Old City, leading discussions on the biodiversity paradigm of the Tree of Life with liberal rabbis and others. A conservation strategy also followed by E. O. Wilson author of "Sociobiology" amd "The Future of Life". It was the formal invitation from The Academy of Jerusalem which resulted in my being awarded an extension to my original short-leave granted for the biodiveristy impact study into long leave through to the millennium. Therefore all aspects of this leave program were bona fide. In addition to the Amazon biodiveristy impact study I did interviews on conservation strategies with major world NGOs, including Friends of the Earth, Greenpeace, and the Nature Conservancy. These issues are of pivotal importance to the future of humanity and the diversity of life. I consider this leave to have been highly effective and that it was contrary to academic principles that my subsequent leave application was denied by the then Dean Dick Bellamy and that my ensuing appeal, headed by Raewyn Dalziel, was unsuccessful.

And I'd like to thank David Gauld, because Bob Mann was one of the most cantankerous lecturers in the university, but I had a very close liaison with him because I went out to the Coromandel, where we have got land and I realized that so much of the habitat of biodiversity is getting destroyed so we really should do something at university that students coming through in a science degree should also have an opportunity in their degree to see what the impact of the sciences they are studying are, so I went around the university and somebody said to go and see Bob Mann, and I ended up striking up a relationship with Bob Mann and we devised a course called environmental studies 200 and it became a functioning course.

But Bob had run into some serious problems because he had had a masters student doing a project and he had given them a grade of A and it's a funny echo - What is coincidence?, What is fate? I noticed that David Bryant mentioned a few days ago in an e-mail about somebody getting a paper in Nature, and in passing mentioned that it was pain to the animals that figured, so Bob Mann gave an A grade to this M.Sc. student, who complained about the unnecessary pain to the animals in this experimental paradigm.

Now at the time the professor of Biochemistry had a wife who was also a biochemist and what happened was the professor took the grading, took it to his wife and his wife crossed out the A and gave it a D and then gave it back to Bob and then Bob took it to - whatever - whatever - I don't know, I've never been through disciplinary committee, or the disputes tribunal or any such thing, but the end result was that the professor of Biochemistry resigned and moved overseas, Bob moved to continuing education on a five year contract, and a new professor of Biochemistry was appointed who would not have Bob in his department over his dead body.

So then his contract ran out and Bob had been doing talk back radio and the current Vice Chancellor was Colin Maiden, who was think big, so we had Motonui and we had Bill Birch and we had the massive plan to burn up the natural gas of New Zealand to make it into petrol, which as we know was a financial failure, and Bob Mann was drawing attention to that, but Colin Maiden didn't like it, so he said cancel environmental studies and fire Bob Mann [who had been lecturing the course], and so I thought you know, Bob can go, but environmental studies can't go. So I went down to the student quad and got a desk and I started collecting student signatures [to save both Bob and the course] and I got about 2,500 signatures and took it to the registry and said "There!" Then Colin rang up David and said "Have you got any smut on Chris King?" "Of course!" No - thankfully David declined.

Circular panorama of the land in the Coromandel. A communally owned conservation reserve (click to enlarge).

I'm going to stop here with my "two points", but I've been very grateful to everyone in the Department I've been with, it's been an absolutely enjoyable and creative journey being and working here, it's been a very good department to work for and work with. It's been very collegial and congenial and in terms of the heads of department Marston Conder and George Seber and David Gauld and Ivan Reilly as the Director of the School and James Sneyd and Bill Barton, I think the Department's been extremely well-served by heads, even though they have had different styles, they have served the collegial interests and I think it's something to do with mathematics and the magic of mathematics that we carry most of what we do, like I used to say that we carry everything we do in our heads so we don't have to work from 9 to 5 in a chemistry lab. Now I'm rather reluctantly saying that at least 60% of what I do is in my laptop, but there's still something very special about mathematics that it is something that is part of our psyche and something that we do as a process of thought and it seems to have engendered for the Department over a long period a very beneficent toward the people that have struggled to teach and do research in the era of PBRFs and so on.

Okay two points, that's enough!

Actually - trick or treat - I covered virtually all of my 13 points, except for 2 about the future. Here they are:

The first is that we have had the fortune to live in a transitional generation and that scientific knowledge of the universe is going through a cumulative S curve and we have already, even with the standard model of physics, come close to the theory of everything, and given the human genome project and molecular biology, discovered perhaps more than half of what there is conceptually to discover, so in future there may not be so many new discoveries to make. We are going to have to be more creative with our lives and spend time caring for the living environment, loving one another, making music and telling engaging stories round the camp fire. This goes also for the institutional mentality. I have preserved an independence from being just an academic because I have many strings to my bow, from the conservation community, through music to the cosncious and sexual quests and travel to far-flung wildernesses. There is a big risk in any institution of becoming 'ring-wraiths' of academia. Don't let it happen!

My world music compositions involve a variety of Western and Eastern stringed instruments.

The second is that mathematics is a classical discipline going through a social evolution, involving a degree of attrition, as human populations pass a lot of their more mechanical numerical reasoning on to calculators and computers. Although mathematicians may hold it sacred, to a certain extent mathematics runs the risk of becoming an artifact of the history of ideas, unless it can regenerate itself from the fertile ground beneath its rigorous foundations, as our ideas of the universe evolve. Its classical foundation, based on point elements and infinite limits, is in a degree of conflict with the quantum view of the universe, in which wave and particle aspects are complementary, so that the inconsistencies we find between relativistic and quantum descriptions of the universe may have their source ultimately in the fact that our mathematics is at root classical and may need a fundamental revision of its premises to bring our reasoning into line with how the universe actually works.

One last thing, one of these coincidences, I just noticed this thing in the newspaper, about time and space and coincidence, and here we have "Retirement winds back the years say scientists" - they say that when people retire they actually feel and act and biologically are ten years younger - this was the right day to see this! I'm not retiring to go out to pasture and it's the creative process that allows more free time to do those nefarious things.

James Sneyd: Thank you Chris. I would like to end by emphasizing two things. The first is that your work, particularly in mathematical biology Chris was ahead of its time and this has in fact been proved by things like the Santa Fe Institute, for instance which have taken up a lot of your ideas. So I don't think you need to feel that in any way that your ideas have been ignored, because they certainly haven't. [James is right in the sense that the Santa Fe Institute was not founded until 1984, ironically also as a result of a falling out with nuclear physics paradigm at Los Alamos].

The second thing I wanted to say is that I want to emphasize what Bill said - that you have kept true to certain ideals, which many other people have not. I think you should feel proud of that as well.

Dhushara.com My Media, Publishing and Research Web Site

MATHS 745 Chaos, Fractals and Bifurcations Course Materials Semester 1 2009

Post-retirement Research

  1. Save the Outer Link: An Urban Transport Review 2019
  2. The Complexity Dynamics of Magic Cubes and Twisty Puzzles 2019
  3. The Intrigues and Delights of Kleinian and Quasi-Fuchsian Limit Sets 2019 Mathematical Intelligencer doi:10.1007/s00283-018-09856-6 Preprint
  4. Kleinian and Quasi-Fuchsian Limit Sets: An Open Source Toolbox 2018 This article presents a full development of the research into Kleinian and quasi-Fuchsian limit sets described in the work Indra's Pearls, with a complete functioning depth first search algorithm in both generic native C and in Matlab, with the C version encapsulated into a Mac app DFS Viewer, for depicting virtually all quasi-Fuchsian and Kleinian limit sets.
  5. An Intrepid Tour of the Complex Fractal World 2016 using Dark Heart 2.0 Complex Viewer Package for Mac.
    Exploring chaos through a new integrated package depicting the fractal dynamics of virtually every complex function from simple quadratics,
    through polynomials, rational and transcendental functions to Riemann zeta and cutting edge zeta and L-functions.
  6. The Physics and Computational Exploration of Zeta and L-functions 2016 This article presents a spectrum of 4-D global portraits of a diversity of zeta and L-functions, using currently devised numerical methods and explores the implications of these functions in enriching the understanding of diverse areas in physics, from thermodynamics, and phase transitions, through quantum chaos to cosmology. The Riemann hypothesis is explored from both sides of the divide, comparing cases where the hypothesis remains unproven, such as the Riemann zeta function, with cases where it has been proven true, such as Selberg zeta functions.
  7. Holy War Against Science: 2016 Evolution versus Intelligent Design. Explains why the evolutionary tree of life is correct while creationism and ID is a religious deception, and shows how nature can give us a superior spiritual view of the universe and life within it.
  8. The Resplendence Codex 2015 This article investigates how the quest for apocalypse compromises our ability to care for the natural diversity and viability of the planet in resplendence and how a change of paradigm could solve this.
  9. Religion, Politics, Sexual Reproduction and the Future of Human Society This article provides an in depth investigation of the causes and solutions of the serious long-term instabilites facing human society including climate change,resource depletion habitat destriction and over-population in terms of fertility, and the effects of religion and politics on human ability to deal with future change.
  10. The Hyperactive Resting Brain on MEG A two minute MEG profile of a subject in the resting state from the Human Connectome Project generated using wavelet transforms to show interactions between alpha, beta and gamma oscillations suggesting wave coherence processing as occurs in quantum processes.
  11. Taming Riemann's Tiger: Jan 2015 Has a young Indian i-Phone Programmer Solved the Most Challenging Enigma in Mathematics?
  12. Chronicles of Insomnia and the Magic Bullet's Poisoned ChaliceDec 2014 How to get a good night's sleep and persuade a quarter of women in the US to take drugs.
  13. Nature, Violence, Consciousness, Sexuality and World ReligionOct 2014 This article is an unveiling expose of the lethal fallacies that underly the religious traditions which between them are followed by a majority of people on this planet, and which between them constitute one of the most principal threats to the future survival of humanity.
  14. Space, Time and ConsciousnessFeb 2014 This paper presents a potential mechanism for the conscious brain to anticipate impending opportunities and threats to survival through massively parallel weak quantum measurement (MPWQM) induced by the combined effects of edge of chaos sensitivity and phase coherence sampling of brain states. It concludes that the underpinnings of this process emerged in single-celled eucaryotes.
  15. Sex, Genes, Politics and Company Law: Can Capitalist Democracy coexist with Human Survival? Aug 2013 This article investigates whether electoral democracy and corporate activity, lacking any real genetic stability and prone to winner-take-all exploitation, particularly of natural resources; able to change from a shark to a tiger by a simple act of recapitalization; and often short-lived in a predatory merry-go-round of relentless takeover and corporate cannibalism; driven only by the profit imperative and the vagaries of the free market, can provide any basis for long-term economic and ecological sustainability. We also examine how both capitalism and democracy are manifestly social products of the male gender to the exclusion of the immortal sex men live their lives to fertilize, unearth the inevitable Machiavellian strategies of deceit that coexist in any climax society and seek the keys to an ecological completion of the economic quest for a life of natural abundance.
  16. The Cosmology of Conscious Mental States May 2013 We explore the diversity of mental states, and examine to what extent these are both a product of specific known brain processes and yet may access a complementary aspect of existence to the cosmology of the physical universe and its natural biosystems, potentially giving mental states an existential cosmological status.
  17. Stripping God Naked: The Cosmology of Unveiling Jan 2013 An overview of the evolution of human sexual and religious concepts common to our founding cultures and their implications for world crisis today. (to appear Sci. God J. 2013).
  18. Culture Out of Africa Jan 2013 New edition of our chapter from Sexual Paradox: Complementarity, Reproductive Conflict and Human Emergence to include current research on genetic evolution of founding human peoples along with cross-cultural investigations of diverse Bushman, Hottentot, Pygmy, and Nilotic peoples.
  19. Entheogens, the Conscious Brain and Existential Reality June 2012 A 'state of the art' research overview of what is currently known about how entheogens, including the classic psychedelics, affect the brain and transform conscious experience through their altered receptor dynamics, and to explore their implications for understanding the conscious brain and its relationship to existential reality, and their potential utility in our cultural maturation and understanding of the place of sentient life in the universe.
  20. Riemann Zeta Viewer 1.7 Sept 2012 Lion compatible version, extended to include fourth degree L-functions, and Mellin transform methods for Dirichlet, modular form, and elliptic curve L-functions.
  21. The Tree of Life: Tangled Roots and Sexy Shoots: Tracing the genetic pathway from the first eucaryotes to Homo sapiens Jan 2009-Jun 2012 A fully referenced research review to overview progress in unraveling the details of the Tree of Life, from life's first occurrence in the hypothetical RNA-era, to humanity's own emergence and diversification, through migration and intermarriage, using research diagrams and brief discussion of the current state of the art, as of the beginning of 2009. DNA Decypher Journal 1
  22. CA2D for Mac Jan 2012 Open souce cellular automata application including diverse systems, from simulations scarring of the wave function in quantum chaos to the prisoners' dilemma in evolutionary modeling.
  23. A Dynamical Key to the Riemann Hypothesis May 2011 This note sets out a dynamical basis for the non-trivial zeros of the Riemann zeta function being on the critical line x = 1⁄2. It does not prove the Riemann Hypothesis (RH), but it does give a dynamical explanation for why zeta and the Dirichlet L-functions do have their non-trivial zeros on the critical line and why other closely related functions do not. It suggests RH is an additional unprovable postulate of the number system, similar to the axiom of choice, associated with the limiting behavior of the primes as n tends to infinity
  24. Fractal Geography of the Zeta Function Mar 2011 http://arxiv.org/abs/1103.5274 The quadratic Mandelbrot set has been referred to as the most complex and beautiful object in mathematics and the Riemann Zeta function takes the prize for the most complicated and enigmatic function. Here we elucidate the spectrum of Mandelbrot and Julia sets of Zeta, to unearth the geography of its chaotic and fractal diversities, combining these two extremes into one intrepid journey into the deepest abyss of complex function space.
  25. Cosmological Foundations of Consciousness Jan 2011 Journal of Cosmology (Overview) This paper explores the cosmological basis of consciousness and subjective experience from cosmic symmetry breaking through biogenesis, and eucaryote emergence, to the human brain.
  26. Cutting Through the Enigma of Consciousness November 2010 Exploring the dimensions of subjective consciousness and the ultimate theory of everything.
  27. Cosmology of Sexual Paradox and the Fall August 2010 This is the article that came out of our talk in Jerusalem, while on our chaotic 90-day orbit of the planet. It is an in-depth and wide ranging review supported by cosmological science and human cultural and genetic history with significant implications for utopian patriarchal religions and the future of humanity.

Research Papers to Retirement

  1. The Ising Model of Spin Interactions as an Oracle of Self-Organized Criticality, Fractal Mode-Locking and Power Law Statistics in Neurodynamics Aug 2009 This short report highlights properties of fractality and self-organized criticality in the Ising model of ferromagnetism and how these ideas can be applied using wavelet transforms to comparisons with the study of self-organized criticality in neurodynamics. Matlab programs are provided to freely replicate the results.
  2. Exploring Quantum and Classical Chaos in the Stadium Billiard 9 July 2009 This paper explores quantum and classical chaos in the stadium billiard using Matlab simulations to investigate the behavior of wave functions in the stadium and the corresponding classical orbits believed to underlie wave function scarring.
  3. Experimental Observations on the Riemann Hypothesis, and the Collatz Conjecture 22 May 2009 This paper seeks to explore whether the Riemann hypothesis falls into a class of putatively unprovable mathematical conjectures, which arise as a result of unpredictable irregularity. It also seeks to provide an experimental basis to discover some of the mathematical enigmas surrounding these conjectures, by providing Matlab and C programs which the reader can use to explore and better understand these systems.
  4. Exploding the Dark Heart of Chaos 8th March 2009 This paper, with its associated graphical software and movies, is an investigation of the universality of the cardioid at the centre of the cyclone of chaotic discrete dynamics, the quadratic 'heart' forming the main body of the classic Mandelbrot set. Using techniques investigating and exploring the continuity, bifurcations and explosions in its related Julia sets, we demonstrate its universality across a wide spread of analytic functions of a complex variable, extending from the classical quadratic, through higher polynomials and rational functions, to transcendental functions and their compositions. The approach leads to some interesting and provocative results, including decoding satellite periodicities, and multiple critical point analysis, leading to layered Mandelbrot sets, and intriguing issues of critical point sensitivity in the irregular structures in the Mariana trenches of the more complex functions.
  5. The Tree of Life: Tangled Roots and Sexy Shoots: Tracing the genetic pathway from the first eucaryotes to Homo sapiens Chris King Jan 2009 This article is a fully referenced research review to overview progress in unraveling the details of the Tree of Life, from life's first occurrence in the hypothetical RNA-era, to humanity's own emergence and diversification, through migration and intermarriage, using research diagrams and brief discussion of the current state of the art, as of the beginning of 2009.
  6. The Central Enigma of Consciousness Nature Precedings 5 November 2008 The nature and physical basis of consciousness remains the central enigma of the scientific description of reality in the third millennium. This paper seeks to examine the phenomenal nature of subjective consciousness and elucidate a possible biophysical basis for its existence, in terms of a form of quantum anticipation based on entangled states driven by chaotic sensitivity of global brain dynamics during decision-making processes. Evidence is presented for the evolutionary emergence of chaotic excitation as a universal sense organ in the founding eucaryotes, which then became used in a context-sensitive manner by complex central nervous systems, leading to the dynamical brain.
  7. Why the Universe is Fractal 2008 Review of fractal processes in cosmology and the genesis of biological complexity.
  8. Sensory Transduction and Subjective Experience: Expression of eight genes in three senses suggests a radical model of consciousness PDF Original Preprint 14 Jan 2007, revised 21 June 2007 Nature Precedings 1 Jan 2008, Activitas Nervosa Superior 2009; 51:1,45-50. Recent research into the mouse genome and whole genome mapping of the mouse brain has made possible direct investigation of the brain expression of unusual genes. A search of the Allen Brain Atlas database for encephalopsin, otocadherin, espin, otoferlin and stomatin-like protein 3 has provided genetic evidence for widespread specific expression in the brain of five genes ostensibly specific to sensory transduction, in vision, hearing and touch. A novel biophysical model is proposed for the biophysical function of their proteins, in generating the internal model of experiential reality.
  9. The 'Core' Concept and the Mathematical Mind Preprint 4th Feb 2007 Pure mathematics is often seen as an 'inverted pyramid', in which algebra and analysis stand at the focal point, without which students could not possibly have a firm grounding for graduate studies. This paper examines a variety of evidence from brain studies of mathematical cognition, from mathematics in early child development, from studies of the gatherer-hunter mind, from a variety of puzzles, games and other human activities, from theories emerging from physical cosmology, and from burgeoning mathematical resources on the internet that suggest, to the contrary, that mathematics is more akin to a maze than a focally-based hierarchy, that topology, geometry and dynamics are fundamental to the human mathematical mind, and that an exclusive focus on algebra and analysis may rather explain an increasing rift between modern mathematics and the 'real world' of the human population.
  10. Quantum Cosmology and the Hard Problem of the Conscious Brain 2006 in "The Emerging Physics of Consciousness" Springer (Ed.) Jack Tuszynski 407-456. The conscious brain poses the most serious unsolved problem for science at the beginning of the third millennium. Not only is the whole basis of subjective conscious experience lacking adequate physical explanation, but the relationship between causality and intentionally willed action remains equally obscure. We explore a model resolving major features of the so-called 'hard problem in consciousness research' through cosmic subject-object complementarity. The model combines transactional quantum theory, with chaotic and fractal dynamics as a basis for a direct relationship between phase coherence in global brain states and anticipatory boundary conditions in quantum systems, complementing these with key features of conscious perception, and intentional will. The aim is to discover unusual physical properties of excitable cells which may form a basis for the evolutionary selection of subjective consciousness, because the physics involved in its emergence permits anticipatory choices which strongly favour survival.
  11. Cosmic Symmetry-breaking, Bifurcation, Fractality and Biogenesis 2004 Neuroquantology 3 149-185 PDF.
  12. Sexual Paradox: Complementarity, Reproductive Conflict and Human Emergence 2004 450pp http://www.sexualparadox.org A treatise on the paradoxical nature of cosmic complementarity and the strategic relationship between the sexes in biological evolution and human cultural emergence. "Sexual Paradox" unveils the subterranean realities underlying our cultural future. It is a book about sexual paradox, the nemesis of our pretensions, yet the genesis of our living destinies. It demonstrates that sexual paradox is at the core of all descriptions of reality, lurking in the quantum realm and in the relationship between body and mind as much as in our hormone-steeped bodies and rising pulses. It presents the idea of sexual paradox as a cosmic principle spanning the widest realms, from physics, through biology to our social futures.
  13. Chaos Quantum-transactions and Consciousness - A Biophysical Model of the Intentional Mind 2003 Neuroquantology 1 129-148. PDF
  14. Biocosmology 2000, 2002 http://www.dhushara.com PDF An investigation of biogenesis and biological evolution, as the interactive culmination of cosmic symmetry-breaking, in generating fractal complexity, from molcular complexes, through cell organelles, to tissues, and ultimately the generation of subjective consciousness.
  15. The Codex of the Tree of Life 1999, 2006 http://www.dhushara.com
  16. Genesis of Eden - Diversity Encyclopedia 1998-2003, with additions to 2009 CD publication
  17. Quantum Mechanics, Chaos and the Conscious Brain. - 1997 J. Mind and Behavior 18/2 155-170.
  18. Fractal Neurodynamics and Quantum Chaos : Resolving the Mind-Brain Paradox through Novel Biophysics - 1996 Advances in Consciousness Research The Secret Symmetry : Fractals of Brain Mind and Consciousness (eds.) E. Mac Cormack and M. Stamenov, John Betjamin.
  19. Further observations on the genus Psilocybe in New Zealand - 1993 Mycotaxon XLVI 161-709
  20. Modular Transposition and the Structure of Eucaryote Regulatory Evolution - 1992 Genetica 86 127-142
  21. Wind and Solar Hybrids for getting a high quality continuous electricity supply - 1991 Solar Progress 12(3,4) 4-9
  22. A New Species of Psilocybe of Section Zapatecorum from New Zealand. - 1991 Mycological Res. 95/4 507-508
  23. Fractal and Chaotic Dynamics in Nervous Systems - 1991 Progress in Neurobiology 36 279-308
  24. Did Membrane Electrochemistry Precede Translation? - 1990 Origins of Life & Evolution of the Biosphere 20 15-25
  25. Dual-Time Supercausality - 1989 Physics Essays 2/2 128-151
  26. A Model for Transposon-Mediated Eucaryote Regulatory Evolution - 1985 J. Theor. Biol. 114 447
  27. A Design for a Smoothly Generating Power System that uses both Wind and Solar Power - 1983 N.Z. Jour. Tech., 1
  28. A Model for the Development of Genetic Translation - 1982 Origins of Life, 12 405-417
  29. Unified Field Theories and the Origin of Life - 1978 Ak. Univ. Math. Reps.