natural theology

We have just published a new book that summarizes the ideas of this site. Free at Scientific Theology, or, if you wish to support this project, buy at Scientific Theology: A New Vision of God

Contact us: Click to email
vol VII: Notes

2018

Notes

Sunday 16 September 2018 - Saturday 8 September 2018

[Notebook: DB 82: Life and Death]

[page 280]

Sunday 16 September 2018

I have long wondered how to use the transfinite numbers as a scale of entropy. The problem has been that if we take something like a gas and reduce it to a liquid we are thermodynamically reducing its entropy, so from the point of view of the gas I once was out there in the stars but we can take the view that the information carried by a point is equal to the entropy of the space from which it is chosen, so that from this point of view my information content (and reputed entropy) is equal to the entropy of the gas from which I came. Or words to this effect [appropriate to information theory rather than heat engineering].

Some thoughts on representations and their transformations in the mental processing pipeline.

We look for a unique and invertible representation which also gives design for action, being transformed and differently coded as it flows through the pipeline making maximum use of the sensory input to achieve effective action. We may be able to apply a Lagrangian to the relationship between the input and output to be optimized by selective pressures.

[page 281]

Semantic representation carries a dimension of intent, I want to catch this chicken to eat.

We think in terms of an unbroken pipeline from sense to muscle, in football, as in philosophy, watching the play and responding, listening to the lectures and writing. As well as data immediately collected by sensation the processing pipeline has structural constraint and is also affected by memory, habit and experience. There are fixed and variable elements in the process, varying from very stable structures like bones and joints to ephemeral synaptic weights which can change in milliseconds.

Features of philosophical pipeline process from lecture to essay are reflected in literary allusions like the white whale and boiling frogs. Herman Melville: Moby-Dick

We can see social cognitive diseases like murdering witches, refugees and anyone who is different.

Huxley: 'happy making drugs have all the advantages of Christianity and alcohol with none of their defects. Brooker and Daraiseh Keith Brooker and Isra Daraiseh

Causal representation must account for the fact that deception is a very important input to fitness [and places an extra load on mind since the deceiver must maintain two or more representations of the situation in hand].

Everything represents itself and depending on context may represent an infinity of other things.

Monday 17 September
Tuesday 18 September 2018

Faith is an essential prerequisite to science. No hypothesis

[page 282]

gets tested until someone takes the trouble, and some ideas, like the Higgs boson, have taken tens of billions of dollars in salaries and equipment to finally bring to the acid test. If I was being paid to dream up my theologcal dream I might be in for fifty years at $100k or so, say 5 million and it still has a long time to go, although I am hoping to get the philosophy department at Adelaide U to help me, which might speed things up a bit.

Religion motivates enormous developments (cathedrals) and enormous disasters (religious wars). It is necessary to redirect this religious feeling toward the real God.

Wednesday 19 September 2018

Naturalizing morality: we operate in two epistemological spaces, pragmatic survival [business] and scientific rationalism [academia]. The pragmatic space tends to be zero sum, given the fixed foundation of resources upon which the evolutionary system is built, so it gives us the competitive element that lies at the root of rape, plunder, genocide and so on. Scientific rationalism, on the other hand, which principally operates in the realm of religion [and theology] recognises the positive sum that arises from cooperation with one another, with love of God, love of on another and creative elements in general, including technology for greatly increasing the physical substrate available for our species (at the cost of other species), health care and all the technological devices that we have developed to widen our horizons and increase out quality of life.

[page 283]

Polanyi: Tacit dimension: in a layered system, the higher layers impose boundary conditions on the lower layers. Polanyi: The Tacit Dimension

Gatlin: game theory sets the boundary conditions. Gatlin: Information Theory and the Living System

Thursday 20 September 2018

Now that I have reached a comfortable old age and am sitting in my philosophical armchair with my hot water bottle on my knee and a beer by my side I have time to reflect on my rather random walk through life. Earth has changed a lot on the last 75 years, and perhaps the biggest influence was the second world war which not only changed the political map but put science at the forefront of making war, with the effect of making it so destructive as to be useless for its ancient function of increasing the fitness of one community by plundering another. A consequence of this has been the globalization of business which has become in many ways simply plunder by other means. What to do about all this? I have never really had any power or wealth, but I do have the ambition of emphasizing the power of cooperation in the context of a divine world whose real power is the power of networks and cooperation. I have two essays to finish tomorrow, both concerned with the role of evolution. What I am trying to emphasize is not so much the survival of the fittest side of nature red in tooth and claw but the cooperative forces that have led t multicellular creatures and the development of human societies. Here science must overcome divisive ideologies if we are to live in peace.

[page 284]

My contribution to the future, apart from my beautiful children will be, I hope, a comprehensive theological picture of peaceful and sustainable life within God, the heart of my MPhil project. These essays have caused me not a little grief but I can now see the way forward to explaining the power of evolution through cooperation based on shared protocols, ie symmetries. Whether I can make this point in the short space of an essay is a further question.

In a way I am a bit bored because I have said all I want to say and am waiting for something new to turn up in my consciousness. I can control a lot of my conscious content because it is pretty much a cognitive representation of all my sensations at this moment from the warm hot water bottle to the taste of my beer and the pleasing screen on my computer which says my shares just went up $949 [after a few months in the doldrums]. I can make myself conscious of these and millions of other things just by looking and remembering but what really beats the boredom for me and comes loaded with excitement [is new and unexpected insight]. Yesterday I was trying to write about the thermodynamics of evolution, Physical thermodynamics tells us that systems are stable when their entropy is at a maximum and they are in thermal equilibrium. Due to solar radiation, however, the surface of the earth is far from thermal equilibrium, as we see from the rapid changes in weather, some very big like cyclones. Yet life, although far from equilibrium, is stable. I attribute this to error free communication in living networks and yesterday I noticed (perhaps for the first time) the fact that Shannon's theory of communication predicts that completely error free

[page 285]

communication requires that messages be coded in blocks of infinite length which requires codecs of high complexity. The virtuous circle is that complex systems require complex codecs for their stability, something which . . . can be provided by complex [structures], so complexity can bootstrap itself in the way we see in [Teilhard] de Chardin's complexification. That was yesterdays insight, but what is today's? I am still waiting. Tomorrow I will write it up for my evolution essay, and I hope to wake up in the morning with a new idea. Lonergan: Insight: A Study of Human Understanding, Teilhard de Chardin: The Phenomenon of Man

Friday 21 September 2018
Saturday 22 September 2018

Essay are in. The results, from my point of view, are a lottery, but they were a step forward for me, taking a line somewhat different from the source, but I hope clearly expressed. Now what? Ladies in Black, nice tale of happy endings. Ladies in Black (film) - Wikipedia

Gintama, a Saturday night movie - no My Mistress My Mistress - Wikipedia

Movies are not the answer. Everybody has some trouble in their lives, crime, deceit, accident and movies explore al the possibilities, but on the whole they are somewhat formulaic and not a good as reality, but a diversion, entertainment.

So much of life is spent hunting, which may be why we like search engines so much. But it is hard to use a search engine if you do not know what you want.

Copyright:

You may copy this material freely provided only that you quote fairly and provide a link (or reference) to your source.

Further reading

Books

Click on the "Amazon" link below each book entry to see details of a book (and possibly buy it!)

Acemoglu, Daron, and James Robinson, Why Nations Fail: The Origins of Power, Prosperity and Poverty, Crown Business 2012 "Some time ago a little-known Scottish philosopher wrote a book on what makes nations succeed and what makes them fail. The Wealth of Nations is still being read today. With the same perspicacity and with the same broad historical perspective, Daron Acemoglu and James Robinson have retackled this same question for our own times. Two centuries from now our great-great- . . . -great grandchildren will be, similarly, reading Why Nations Fail." —George Akerlof, Nobel laureate in economics, 2001  
Amazon
  back

Casti, John L, Five Golden Rules: Great Theories of 20th-Century Mathematics - and Why They Matter, John Wiley and Sons 1996 Preface: '[this book] is intended to tell the general reader about mathematics by showcasing five of the finest achievements of the mathematician's art in this [20th] century.' p ix. Treats the Minimax theorem (game theory), the Brouwer Fixed-Point theorem (topology), Morse's theorem (singularity theory), the Halting theorem (theory of computation) and the Simplex method (optimisation theory). 
Amazon
  back

Debreu, Gerard, Theory of Value: An Axiomatic Analysis of Economic Equilibrium, Yale University Press 1972 Amazon customer review: 'This is not an easy book. The mathematics are very rigorous, but everything is well defined, and it is self-contained. However, it pays to read this short book. If you want to understand the foundations of the modern economic analysis, this the place to look.' A Customer 
Amazon
  back

Gatlin, Lila L, Information Theory and the Living System, Columbia University Press 1972 Chapter 1: 'Life may be defined operationally as an information processing system -- a structural hierarchy of functioning units -- that has acquired through evolution the ability to store and process the information necessary for its own accurate reproduction. The key word in the definition is information. This definition, like all definitions of life, is relative to the environment. My reference system is the natural environment we find on this planet. However, I do not think that life has ever been defined even operationally in terms of information. This entire book constitutes a first step towar dsuch a definition.' 
Amazon
  back

Heath, Thomas Little, Thirteen Books of Euclid's Elements (volume 1, I-II), Dover 1956 'This is the definitive edition of one of the very greatest classics of all time - the full Euclid, not an abridgement. Utilizing the text established by Heiberg, Sir Thomas Heath encompasses almost 2500 years of mathematical and historical study upon Euclid.' 
Amazon
  back

Heath, Thomas Little, Thirteen Books of Euclid's Elements (volume 2, III-IX), Dover 1956 'This is the definitive edition of one of the very greatest classics of all time - the full Euclid, not an abridgement. Utilizing the text established by Heiberg, Sir Thomas Heath encompasses almost 2500 years of mathematical and historical study upon Euclid.' 
Amazon
  back

Heath, Thomas Little, Thirteen Books of Euclid's Elements (volume 3, X-XIII), Dover 1956 'This is the definitive edition of one of the very greatest classics of all time - the full Euclid, not an abridgement. Utilizing the text established by Heiberg, Sir Thomas Heath encompasses almost 2500 years of mathematical and historical study upon Euclid.' 
Amazon
  back

Lonergan, Bernard J F, Insight: A Study of Human Understanding (Collected Works of Bernard Lonergan : Volume 3), University of Toronto Press 1992 '. . . Bernard Lonergan's masterwork. Its aim is nothing less than insight into insight itself, an understanding of understanding' 
Amazon
  back

Marr, David, Patrick White: A Life, Knopf 1992 Editorial review from Library Journal : 'From Library Journal An admirably readable biography of the Nobel Prize-winning author of Voss , The Tree of Man , and many other books, this work is full of detail on White's family and prosperous background, the events and people in his life, his writing habits, his religious beliefs, his cantankerousness and temper, his causes and doubts, his attraction to the theater, and much more. White helped Marr gain access to people and material, even authorizing him to collect his letters, "the backbone of this book." Marr deals intelligently with important issues (among them, White's rootedness in and dissatisfaction with Australia, his sense of himself as an outsider, his relation to his mother, and, in particular his homosexuality, which White considered central to his novelistic and theatrical ability), avoiding psychoanalytical speculations and other intrusions. White reviewed the book shortly before he died, finding it "so painful he often found himself reading through tears. He did not ask Marr to change a line."' Richard Kuczkowski Copyright 1992 Reed Business Information, Inc. 
Amazon
  back

Melville, Herman, Moby-Dick, Bantam Classics 1981 'First published in 1851, Herman Melville’s masterpiece is, in Elizabeth Hardwick’s words, “the greatest novel in American literature.” The saga of Captain Ahab and his monomaniacal pursuit of the white whale remains a peerless adventure story but one full of mythic grandeur, poetic majesty, and symbolic power. Filtered through the consciousness of the novel’s narrator, Ishmael, Moby-Dick draws us into a universe full of fascinating characters and stories, from the noble cannibal Queequeg to the natural history of whales, while reaching existential depths that excite debate and contemplation to this day. 
Amazon
  back

Newton, Isaac, Philosophiae Naturalis Principia Mathematica , Harvard University Press 1972 One of the most important contributions to human knowledge. First translated from the Latin by Andrew Motte in 1729,  
Amazon
  back

Newton, Isaac, Principia volume II The System of the World, University of California Press 1966 back

Newton, Isaac, and Julia Budenz, I. Bernard Cohen, Anne Whitman (Translators), The Principia : Mathematica: l Principles of Natural Philosophy, University of California Press 1999 This completely new translation, the first in 270 years, is based on the third (1726) edition, the final revised version approved by Newton; it includes extracts from the earlier editions, corrects errors found in earlier versions, and replaces archaic English with contemporary prose and up-to-date mathematical forms. . . . The illuminating Guide to the Principia by I. Bernard Cohen, along with his and Anne Whitman's translation, will make this preeminent work truly accessible for today's scientists, scholars, and students. 
Amazon
  back

Newton, Isaac, Philosophiae Naturalis Principia Mathematica , Harvard University Press 1972 One of the most important contributions to human knowledge. First translated from the Latin by Andrew Motte in 1729,  
Amazon
  back

Polanyi, Michael, and Amaryta Sen (foreword), The Tacit Dimension, University Of Chicago Press 2009 Amazon product description: '“I shall reconsider human knowledge by starting from the fact that we can know more than we can tell,” writes Michael Polanyi, whose work paved the way for the likes of Thomas Kuhn and Karl Popper. The Tacit Dimension argues that tacit knowledge—tradition, inherited practices, implied values, and prejudgments—is a crucial part of scientific knowledge. Back in print for a new generation of students and scholars, this volume challenges the assumption that skepticism, rather than established belief, lies at the heart of scientific discovery.' 
Amazon
  back

Stewart, Ian, Why Beauty is Truth: A History of Symmetry, Basic Books/Perseus 2007 Jacket: ' ... Symmetry has been a key idea for artists, architects and musicians for centuries but within mathematics it remained, until very recently ,an arcane pursuit. In the twentieth century, however, symmetry emerged as central to the most fundamental ideas in physics and cosmology. Why beauty is truth tells its history, from ancient Babylon to twenty-first century physics.' 
Amazon
  back

Teilhard de Chardin, Pierre, The Phenomenon of Man, Collins 1965 Sir Julian Huxley, Introduction: 'We, mankind, contain the possibilities of the earth's immense future, and can realise more and more of them on condition that we increase our knowledge and our love. That, it seems to me, is the distillation of the Phenomenon of Man.'  
Amazon
  back

White, Patrick, and David Marr (Editor), Patrick White Letters, University Of Chicago Press 1996 Amazon book description: '"Letters are the devil, and I always hope that any I have written have been destroyed."—Patrick White Patrick White spent his whole life writing letters. He wanted them all burnt, but thousands survive to reveal him as one of the greatest letter-writers of his time. Patrick White: Letters is an unexpected and final volume of prose by Australia's most acclaimed novelist. Only a few scraps of White's letters have been published before. From the aftermath of the First World War until his death in 1990, letters poured from White's pen: they are shrewd, funny, dramatic, pigheaded, camp, and above all, hauntingly beautiful. He wrote novels to sway a hostile world, but letters were for friends.' 
Amazon
  back

Links

Agnieszka Pikulicka-Wilczewska , Deserted Aral Sea hosts electro gig with environmental twist, ' Uzbekistan was until recently one of the world's most isolated countries. Under President Shavkat Mirziyoyev, it has been gradually opening up. The Stihia festival, with avant-garde sounds and ambient techno played by DJs from Berlin, Georgia, Russia and Uzbekistan, was part of the new vision. The location was not accidental. The ship graveyard, littered with the skeletons of vessels rusting away in the sand, is what remains of the mighty Aral Sea.' back

Anthea Lacchia, 558m-year-old fossils identifed as oldest known animal, 'A fossilised lifeform that existed 558m years ago has been identified as the oldest known animal, according to new research. The findings confirm that animals existed at least 20m years before the so-called Cambrian explosion of animal life, which took place about 540m years ago and saw the emergence of modern-looking animals such as snails, bivalves and arthropods.' back

Brouwer fixed point theorem - Wikipedia, Brouwer fixed point theorem - Wikipedia, the free encyclopedia, 'Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after Luitzen Brouwer. It states that for any continuous function f with certain properties there is a point x0 such that f(x0) = x0. The simplest form of Brouwer's theorem is for continuous functions f from a disk D to itself. A more general form is for continuous functions from a convex compact subset K of Euclidean space to itself. back

Candida Moss, Was Council of Nicaea Church Just Found Under a Lake?, ' In the past week, scientists announced the discovery of ancient Roman ruins underneath the surface of the lake in Iznik, Turkey. But this was not just any archaeological discovery. They have may have chanced upon the ancient Basilica of the city of Nicaea (now Iznik), one of Christianity's most historic sites and the place where the Church made its first official statement about the relationship between Jesus and God.' back

Catharine McGregor, Morrison's bid for religious freedom looks like legislated homophobia, 'Earlier this week, my colleague Tony Walker made a plea for a more civil, respectful public debate uncluttered by the slogans, epithets and abuse that are the currency of the culture wars. As he observed, "political correctness", "identity politics" and "virtue signalling" are now mere terms of abuse. One could compile a book of such arid labels and insults which have become a substitute for argument. Their primary purpose now is to situate those who deploy them on the political spectrum.' back

Eugene Wigner, The Unreasonable Effectiveness of Mathematics in the Natural Sciences, 'The first point is that the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it. Second, it is just this uncanny usefulness of mathematical concepts that raises the question of the uniqueness of our physical theories.' back

Galois theory - Wikipedia, Galois theory - Wikipedia, the free encyclopedia, 'In mathematics, more specifically in abstract algebra, Galois theory, named after Évariste Galois, provides a connection between field theory and group theory. Using Galois theory, certain problems in field theory can be reduced to group theory, which is in some sense simpler and better understood. Originally Galois used permutation groups to describe how the various roots of a given polynomial equation are related to each other. The modern approach to Galois theory, developed by Richard Dedekind, Leopold Kronecker and Emil Artin, among others, involves studying automorphisms of field extensions.' back

Hannah Hoag, Europe's Triumphs and Troubles Are Written In Swiss Ice, ' Sandra Brügger, a climate scientist at the Institute of Plant Sciences and the Oeschger Centre for Climate Change Research at the University of Bern, developed a technique to study the pollen, fungal spores, charcoal and soot locked in an ice core drilled from this Swiss glacier. She is aiming to disentangle the ways extreme weather, innovation, crop failures and pollution have shaped Europe since 1050, when Macbeth ruled Scotland.' back

Harrison Smith, Freddie Oversteegen, Dutch fighter who killed Nazis thrugh seduction, dies at 92, ' When she rode her bicycle down the streets of Haarlem in North Holland, firearms hidden in a basket, Nazi officials rarely stopped to question her. When she walked through the woods, serving as a lookout or seductively leading her SS target to a secluded place, there was little indication that she carried a handgun and was preparing an execution.' back

Homeomorphism - Wikipedia, Homeomorphism - Wikipedia, the free encyclopedia, 'In the mathematical field of topology, a homeomorphism or topological isomorphism (from the Greek words (homoios) = similar and (morph) = shape = form (. . . ) is a bicontinuous function between two topological spaces. Homeomorphisms are the isomorphisms in the category of topological spaces — that is, they are the mappings which preserve all the topological properties of a given space. Two spaces with a homeomorphism between them are called homeomorphic, and from a topological viewpoint they are the same.' back

Justin Chang, Review: Keira Knightley illuminates a writer's awakening in the schrewd, witty "Colette", ' The history of the arts, among other zones of human accomplishment, is full of mediocre men who have taken credit for the accomplishments of extraordinary women. . . . Here to prove the point — and also to complicate it, in unexpected and pleasurable ways — is “Colette,” a witty, spirited portrait of the great French writer and libertine during the early Belle Époque years of her career. It recounts the tempestuous, convention-defying marriage of Colette (Keira Knightley, very good) and Henry Gauthier-Villars (Dominic West, ditto), better known by his nom de plume, Willy, a self-styled impresario of the publishing world who nurtured, exploited and ultimately betrayed his wife’s writing talent.' back

Keith Brooker and Isra Daraiseh, Guide to the classics: Donald Trumps's Brave New World and Aldous Huxley's dystopian vision, ' A year-and-a-half into the presidency of Donald Trump, some see this administration as the stuff of dystopian nightmares. Trump’s apparent disrespect for truth is suspiciously similar to the manipulation of history in George Orwell’s Nineteen Eighty-four. The crass, three-ring-circus texture of the current crowd in Washington recalls the degraded America depicted in Mike Judge’s 2006 cinematic farce Idiocracy. However, the English writer Aldous Huxley’s 1932 classic Brave New World might provide the best dystopian gloss on our contemporary predicament. ' back

Ladies in Black (film) - Wikipedia, Ladies in Black (film) - Wikipedia, the free encyclopedia, ' Neil Young of the Hollywood Reporter said of the film, "Ladies in Black quietly but effectively points out the seldom-stressed positives of immigration and integration, and thus deserves attention far beyond its own native shores". Australian film critic David Stratton, writing for The Australian, wrote "Ladies in Black may be seen mistakenly as lightweight or slight; it isn't. It brims with subtext and nuance and at the same time succeeds in being a thoroughly enjoyable entertainment." ' back

Lloyd Strickland, Four centuries of trying to prove God's existence, 'Whether God exists or not is one of the most important philosophical questions there is. And the tradition of trying to establish God’s existence involving evidence is a long one, with a golden age during the 17th and 18th centuries – the early modern period. ' back

My Mistress - Wikipedia, My Mistress - Wikipedia, the free encyclopedia, ' A sixteen-year-old boy discovers his father's suicide. Distraught, he goes searching for ways to numb the pain. He then meets a mysterious woman who turns out to be a dominatrix and finds solace in her arms.' back

Paul Daley, 'Wholesale massacre': Carl Feilberg exposed the ugly truth of the Australian frontier, 'During his short life Danish-born Carl Feilberg risked more than any other Australian journalist or author to expose the brutality against Indigenous people on the ultra-violent Queensland colonial frontier of the late 19th century. He wrote millions of words provoking the conscience of townspeople, frontiersman and politicians in Australia and Britain. His writings about colonial violence against Aboriginal people impacted federation and regional geopolitics, and enhanced understanding of frontier war for generations of progressive Australian historians.' back

Perron-Frobenius theorem - Wikipedia, Perron-Frobenius theorem - Wikipedia, the free encyclopedia, 'In linear algebra, the Perron–Frobenius theorem, proved by Oskar Perron (1907) and Georg Frobenius (1912), asserts that a real square matrix with positive entries has a unique largest real eigenvalue and that the corresponding eigenvector has strictly positive components, and also asserts a similar statement for certain classes of nonnegative matrices. This theorem has important applications to probability theory (ergodicity of Markov chains); to the theory of dynamical systems (subshifts of finite type); to economics (Leontief's input-output model); to demography (Leslie population age distribution model)[2] to mathematical background of the Internet search engines and even to ranking of football teams.' back

Schauder fixed point theorem - Wikipedia, Schauder fixed point theorem - Wikipedia, the free encyclopedia, 'The Schauder fixed point theorem is an extension of the Brouwer fixed point theorem to topological vector spaces, which may be of infinite dimension. It asserts that if K is a convex subset of a topological vector space V and T is a continuous mapping of K into itself so that T(K) is contained in a compact subset of K , then T has a fixed point.' back

Sperner's lemma - Wikipedia, Sperner's lemma - Wikipediam the free encyclopedia, 'In mathematics, Sperner's lemma is a combinatorial analog of the Brouwer fixed point theorem, which follows from it. Sperner's lemma states that every Sperner coloring (described below) of a triangulation of an n-dimensional simplex contains a cell colored with a complete set of colors. The initial result of this kind was proved by Emanuel Sperner, in relation with proofs of invariance of domain. Sperner colorings have been used for effective computation of fixed points, in root-finding algorithms, and are applied in fair division (cake cutting) algorithms. Unfortunately it is now believed to be an intractable computational problem to find a Brouwer fixed point or equivalently a Sperner coloring even in the plane, in the general case. The problem is PPAD-Complete, a complexity class invented by Papadimitriou.' back

Wiles' proof of Fermat's Last Theorem - Wikipedia, Wiles' proof of Fermat's Last Theorem - Wikipedia, the free encyclopedia, 'Andrew Wiles' proof of Fermat's Last Theorem is a proof of the modularity theorem for semistable elliptic curves released by Andrew Wiles, which, together with Ribet's theorem, provides a proof for Fermat's Last Theorem. Both Fermat's Last Theorem and the Modularity Theorem were almost universally considered inaccessible to proof by contemporaneous mathematicians, seen as virtually impossible to prove using current knowledge.' back

www.naturaltheology.net is maintained by The Theology Company Proprietary Limited ACN 097 887 075 ABN 74 097 887 075 Copyright 2000-2020 © Jeffrey Nicholls