Natural Theology

I have just published a new Book Cognitive Cosmogenesis: A systematic integration of physics and theology. Please buy a copy to support this work.

Contact us: Click to email

Notes DB 93 Theological Genocide - 2025

Sunday 7 December 2025 - Saturday 13 December 2025

[page 166]

Sunday 7 December 2025
Tweet of the day: Theology is our most important and influential science worldwide but it is based mostly on ancient mythological texts. But the Universe is real, created itself and is here for all of us to see. It is the body of god and reveals the mind of god if we learn to look.

[page 167]

Over two thousand years the Bible has transformed most of the human mental world. The purpose of my book is to do the same, to replace the ancient text imagined by our ancient ancestors with the body of the real god whose truth, spoken to us at every moment of our lives, reveals the real mind of God. Nicholls (2025): Cognitive Cosmogenesis: A systematic integration of physics and theology

Letter to Faraday Institute re Cognitive Cosmogenesis:

The statistical output of our quantum mechanical world as measured in Minkowski space is identical to the output of the communication source A modelled by Shannon’s mathematical theory of communication, a set of characters ai whose probabilities pi add up to 1 and whose entropy in bits is given by Σi pi log2 pi. We may interpret this output as a message, and on the hypothesis that the universe is itself divine we may interpret this output as a message from the divinity analogous to the Bible and other ancient theological texts and thus as a source giving us access to the mind of the divinity and an appropriate source for scientific theology.

I examine this idea in my book Cognitive Cosmogenesis: a systematic integration of physics and theology which was drafted as a PhD thesis and I offer it to you for consideration and possible review. It was published on 5 December by Austin Macauley. I do not have a copy yet, but will post you one if you wish when they send it to me.

John D. Norton: Philosophical significance of General Relativity Theory.

Norton: symmetry is the essential notion for realizing the principle of relativity. It is present in special relativity. It is missing in GR. Can we extend Lorentz covariance to general covariance? No.

‘The geometric structures that make up spacetime are all that is necessary for a theory of gravity. The idea is implemented in general relativity by making special relativity the special case of flat spacetime [diagonal metric, 4 parameters]. General relativity covers the cases where spacetime is no longer flat and more varied gravitational phenomena appear [upper right corner metric, 10 parameters].

John D. Norton (2022_02_07): Philosophical Significance of the General Theory of Relativity

Inertial and accelerated motion remain distinguishable absolutely. Satellite is accelerating but it is [locally] in inertial motion [moving through flat Minkowski spaces].

“The G-field is conditioned and determined by the energy tensor.” What did Einstein tell us? The ten entries in a 4 x 4 matrix are needed to describe the gravitational field in the epoch of the universe when bosons and fermions have come into existence through the bifurcation of zero-energy flat space [primordial, Aquinas–Einstein singularity]. So did gravity arrive with particles bifurcating the zero energy world [the first fruits of quantum mechanics?].

[page 168]

We have to see how this relates to the quantum and logic and maybe at the root we find the not operator, kinetic = not potential, fermion = not boson, kinetic + potential = boson + fermion = 0. But there must be something special in hadrons comprising 2 and 3 quarks.

This is where cognitive theory should come into its own because the renormalization and asymptotic freedom and confinement stories seem a bit weird and we need something new to win the Millennium prize and integrate the quantum and gravity stories. Two years to next book, lust-4-lfe marketed by sex sells, the Sabrina Carpenter book. Carlson, Jaffe & Wiles (2006): The Millennium Prize Problems, Sabrina Carpenter: Manchild

Back to Jaffe and Witton: Fields are a mistake [since spacetime per se does not exist, only particles and their real relationships] because continuity is a mistake, led astray by gravitation which is intrinsically coordinate free [ie zero dimensional topological space described by absolute (“self cancelling”, tensor) differential calculus]. Continuous spacetime does not exist. What is the anti field essay. It comes out of the ten steps and the commentary thereunto: Lust_4_Life.

The 64$ question is how quantum mechanics bifurcates gravitation and how we would like to say that it is the same bifurcation that creates kinetic and potential and also creates bosons and fermions and the reality is all particles and pure mathematical spacetime does not exist in the sense that it is the empty Platonic set of consistency which is a logical thing whose existence is identical to its essence ad both are in effect empty. Making god per se omniscient was a step too far.

Page 130: What does “dA is the gauge covarant deriative of the exterior derivative” mean?

[page 169]

Jaffe and Witten page 131: What does the massless nature of the classical Yang-Mills waves mean? What is the vacuum? Because they mix Hilbert and Minkowski space they lose degrees of freedom that could clean up the mess.

1: Mass gap, every excitation of the vacuum must have energy Δ > 0. Is vacuum Hilbert (no space, time, momentum or energy) or Minkowski: x + t + p + E. Mass gap - Wikipedia

2. Quark confinement, ie binding energy greater than quark mass [the boson is more energetic than the fermion?] Color confinement - Wikipedia

3. Chiral symmetry breaking. Chiral symmetry breaking - Wikipedia

There does not exist a convincing, whether or nat mathematically complete theoretical computation demonstrating any of the three properties in QCD as opposed to a seriously simplified truncation of it. [Jaffee & Witten p 132].

Ie first we have to dream up a plausible structure to hang the maths on.

The false shangri la: a mathematically complete example of a gauge theory in 4D space-time, nor even a precise definition of quantum gauge theory in 4D, BECAUSE quantum theory does not exist in 4D!

page 133: QFT became increasingly central to physics throughout C20: but it is fundamentally mistaken because it restricts QM to Minkowski space. All we really want is naked quantum algorithms to achieve the three points above and we will get them all in the 10 steps (or bust): [they will appear as matrices which superpose certain Hilbert basis vectors to yield the desired result through a self-adjoint operation, ie by superposing them in the right way. Is this how superconductivity works]. Superconductivity - Wikipedia

So Millennium prize to pay for teeth [hopeless dream, but someone has got to do it and I am such an outlier I have a chance].

We are talking about body and soul: the soul is the formal structure activated by the body ≡ energy.

[page 170]

Monday 10 December 2025

Ghostly night of dreams perhaps motivated by worries about the reception of my book. Reassured by dependence on physics rather than ancient theologies concocted by sycophantic theologians to please and justify their powerful masters, and the power of science to cut through fiction. Now feel back on the ground and my gravitatioal divinity is working for me. 9.26 make some $$: BAS got gas sales contract with Origin.

David Shoebridge:senator.shoebridge@aph.gov.au

[list of destinations for review copies of my book]

Nambu Nobel page 58: ‘In quantum theory [spontaneous symmetry breaking, ie no energy involved?] becomes also possible for the entire space-time for the “vacuum” is not void but has many intrinsic degrees of freedom. In this context it may an important role in cosmology. As the universe cools down it may undergo one or more SSB transitiona from states of

[page 171]

higher symmetry to lower ones which change the governing laws of physics. Do I believe this? Of course not, like all field theory it is a tangled mess of Hilbert and Minkowski space. Yachiro Nambu (2008): Nobel Lecture: Spontaneous Symmetry Breaking in Particle Physics: a Case of Cross Fertilization

Tuesday 9 December 2025

Emails to Holy Office and NYT: cultdiv@ccdds.va, editorial@nytimes.com

Re: Cognitive Cosmogenesis: A systematic integration of physics and theology

Your Excellencies

I am a strong believer in the words of Jesus “Love God, Love Your Neighbour. Consequently, in 1963, I entered the Dominican Order in Australia, was solemnly professed and studied the work of Thomas Aquinas for 5 years. I was impressed by the way Aquinas developed Christian Doctrine with the work of Aristotle and was pleased to see that Aquinas’s work is still central to the doctrine of the faith (Canon 252 section 3). During the Second Vatican Ecumenical Council I suggested to my superiors that the Order should begin a study parallel to this work of Aquinas, investigating the possibilities of the hypothesis that the Universe is divine and that close observation of the real universe can provide a foundation for a scientific theology in tune with modern social expectations for the quality of information released by public corporations such as the Roman Church.

Despite my solemn profession I was expelled from the Order, an event which severely upset my mother who was a very staunch Catholic and was shocked that her gift of her oldest son to the Church was rejected. Apparently my vows were annulled by some Vatican paperwork but the Order has failed to release any information to me about the reasons for my treatment. I consider this an abuse of power tantamount to severe intellectual and personal abuse. Hopefully, as the Church brings its sexual abuse of children under control, it will be forced to turn its attention intellectual and spiritual abuse.

In the 60 years since that time, I have written the book mentioned in the subject line above which was launched last Friday 5 December. My book makes a powerful scientific case for theology based on the physical reality of the world rather that on ancient texts composed long before we had any knowledge of the size and magnificence of the Universe.

Here is a very brief summary of my work submitted to the British Faraday Institute for Science and Religion:

The statistical output of our quantum mechanical world as measured in Minkowski space is identical to the output of the communication source A modelled by Shannon’s mathematical theory of communication, a set of characters ai whose probabilities pi add up to 1 and whose entropy in bits is given by Σi pi log2 pi. We may interpret this output as a message, and on the hypothesis that the universe is itself divine we may interpret this output as a message from the divinity analogous to the Bible and other ancient theological texts. We thus have a source giving us access to the mind of the divinity and an appropriate source for scientific theology.

I examine this idea in my book Cognitive Cosmogenesis: a systematic integration of physics and theology which was drafted as a PhD thesis. I offer it to you for consideration and possible review. It was published on 5 December by Austin Macauley.

I hope you will obtain copies of my book, bring it to the attention of the Pontifical Academy of science, and provide a substantial response to my thesis.

One approach is to expose the RCC as a scam based on imperial power rather than truth. Make this a tweet of the day? Another tweet: Today I emailed the Holy office to warn them out my book.

[put them together] . The Roman Catholic Church serves about 18% of the world population as a scam based on imperial power rather than truth. Make this a tweet of the day? Another tweet: Today I emailed the Holy office to warn them out my book. I hope you will obtain copies of my book, bring it to the attention of the Pontifical Academy of science, and provide a substantial response to my thesis.

Email books@theguardian, reviews@the guardian [not done]

Rapa Nui showed that even entrenched mysteries yield to systematic investigation. Carl Lipo (2025_11_27): Drones, physics and rats: Studies show how the people of Rapa Nui made and moved the giant statues – and what caused the island’s deforestation

[page 172]

I feel proud and happy about my ten steps for L4L but I am finding it very hard to write the commentary, the feeling is there but not the words, trying to thread the way through all the confusion embedded in the quantum field theory by mixing Hilbert and Minkowski space. The question how does energy make a quantum form into a particle is analogous to how does a body make a soul into a person. As far as I know, I do not have an immortal soul but the Aquinas–Einstein singularity is in effect exactly that, an eternal structureless existent. We escape the body-soul question by the ancient definition of simplicity that asserts that essence and existence are identical in god and it seems reasonable to take the ancient theological idea over into physics as the first step in fashioning particles by explaining how the form and the body cohabit, ie that energy animates the form to act in the way that the form demands, just as feeding petrol into a stationary internal combustion engine and starting it makes it run as long as the fuel lasts and the forms and tolerances of its parts remain intact. Now I need to go out for a walk (ie do the bins). In my 40 years in Elands I worked for 5 hours a day and thought for the other 12 and this was a good balance.

The components of an engine are the top of a long chain of forces which shape the particles from which they are made from elementary particles through molecules, crystals, and other solid state structures that yield a part which can maintain its form with sufficient precision to interact constructively with all the other parts of the engine to make it work, ie maintain the recurrent cycle of events which we call running, perfectly analogous to the reproductive process in living systems. This we might call green behaviour, not stressing systems beyond their limits so that they can continue to reproduce their designed and designated behaviour.

[page 173]

Things are coming out now. Field theory imagines an ubiquitous superposition of fields which occupy the whole of spacetime, by which they mean Minkowski space. We are not told where these fields came from, presumably put in place by the creator and they are continuous in the calculus sense and do not appear to interact with one another so we cannot see them as elements of Hilbert space. In their relaxed [vacuum??] state they do not represent any particles. The energy to make particles is imagined to arise through uncertainty [vacuous fluctuations?] in other words the vacuum is raised to a higher energy by quantum ‘vibrations’ [presumably creating energy from nothing].

Now I need to check this story against sources of quantum field theory which I take to be Auyang, Weinberg and Zee with a touch of Dirac and Feynman so I can write this out as a succinct and accurate subset of cl4l_05_particles. Another step forward. Then we go back to Hilbert space in the singularity and quantum mechanics as the genetic process that produces the forms (ie vectors, wave functions) that serve as the input to the universe, the basis states generated in the initial singularity by Brouwer’s fixed point theorem and computable functions. Sunny Auyang (1995): How is quantum Field Theory Possible?, Stever Weinberg (1995): The Quantum Theory of Fields Volume I: Foundations , Anthony Zee (2010): Quantum Field Theory in a Nutshell, P A M Dirac (1983): The Principles of Quantum Mechanics (4th ed)

So for the moment back to Jaffe and Witten, looking for a story a bit like the paragraph above.

Jaffe + co: “The most important QFTs are gauge theories.” What is a gauge theory: Wiki: ‘In physics a gauge theory is a type of field theory in which the Lagrangian is invariant under local tranformations from certain Lie Goups’.

A Lie group is a group which is also a differentiable manifold, ie continuous and therefore unreal.

[page 174]

Yang + Mills page 192 ‘gauge change = phase change’. Chen Ning Yang & Robert L. Mills (1954_06_28): Isotopic spin conservation and a generalized gauge invariance

Since Ψ may be defined on x, y, z, and t, the relative phase factor of Ψ at 2 different points is therefore completely arbitrary (because when Hilbert space is independent of Minkowski space, there is no x, y, z, and t, in Hilbert space).

By ditching quantum field theory I have created a sea of troubles for myself but the time will come when the problems are solved and the beautiful clarity of the independence of Hilbert space from Minkowski space will pay for itself in the way that it has already opened the way to a union physics and theology which remains more of a hunch than a proof but the union of quantum mechanics and communication will sort this out. Another possibility verging on the edges of my consciousness is that the non-linearity of Yang-Mills will disappear when we do away with the interference of special relativity. The key is that because Hilbert space has no space and time the Lorentz transformation is necessary to maintain the independence of Hilbert space from Minkowski space because for Hilbert space all the different spacetime points are the same, as the Lorentz transformation shows.

How do we apply the idea to Yang-Mills (after we have already thrown renormalization out the door). We have to get deeper into the boson – fermion distinction as it applies in QCD. I say all this without really knowing what it all means as may be the case when people write poetry and play music — it could be anything, like quantum mechanics,

[page 175]

ie as a wave field quantum mechanics is like music and poetry, it can mean anything when it is tied down [given context] in Minkowski space in the same way as the Church ties down the Bible and music to constrain it to the official interpretation. So apply this to the containment of energy in fundamental particles which is effect the containment of the variety of quantum mechanics as different life forms contain the possibilities of genetic variation.

Wednesday 10 December 2025

VUL offer closes 23/12

What we are seeking are simple clear explanations without too many demanding prerequisites which implement the principles of simplicity and ‘courtroom entropy’ ie explanations of the same complexity as the reality explained [starting from an empty “transcendent” singularity about which nothing can be said besides “it exists”].

Auyang: Page 4: Feynman: ‘We always have a great deal of difficulty in understanding the world view that quantum mechanics represents.’ Hidebound by Minkowski space intellectualism rather than music?

‘The phenomenalist doctrines are espoused by the Copenhagen School that dominates quantum interpretation and are academically influential . . .’.

page 5. Many physicists find that that the chief philosophical issues concern the reality of the microscopic world, the objectivity of quantum theories and the relation of the world to our experiences. Auyang (1995): How is quantum Field Theory Possible?

[page 176]

The ladder of creation [begins with the] empty [but real, physical] reality (singularity) generates [abstract] form which is generates reality which generates force. In this way we accommodate the reality that information is physical and also the source of creation, the form/energy/ bootstrap [every layer creates new forms which attract energy to become a new layer, like the idea [form] of steam engines directs energy into making steam engines]. Thomas Newcomen - Wikipedia

Thursday 11 December 2025

Copy to USCCB - time to fight back against fake news

The specific feature of the Einstein universe is that it is a continuous, compact, convex space with the Minkowski metric. To make this universe possible we have to explain the Minkowski space and we do this with a combination of Hilbert space, quantum mechanics and the formation of a particulate communication network with zero sum bifurcation [which creates fermions and bosons]. The quickest way to see this is with the Einstein Hilbert Lagrangian in that T [fermion] − V [boson] = 0. Einstein-Hilbert action - Wikipedia

This goes in the essay on Justice, sequel to quantocracy.

The fundamental create discovery is the form / reality bootstrap, form, investment. construction = quantum mechanics / [bifurcation of gravitation /] energy. Space is a network of nodes (fermions, spin ½, bosons spin 1) [idea first documented on non-quantum mechanical 2019 honours thesis Prolegomena to scientific theology].

We understand this through the Lagrangian and stationarity — stationary = hermitian [real] = self-adjoint, ie motion is cancelled, fixed point theory [provides a similar answer].

[page 177]

My book [Nicholls 2025] is a positive outcome of childhood intellectual abuse [by the Church]. Nicholls (2025): Cognitive Cosmogenesis: a systematic integration of theology and physics

Quantum intelligence, working in 2D Hilbert space created [the forms of] bosons and fermions, the fundamental network [elements] of the universe. Now I should read my honours thesis again, putting it in [its proper] quantum context. It was the beginning of the network view [which I had harboured since I started to write Welcome to natural theology. [See it in the wayback machine Naturaltheology.net, 2001]

Michael Falk: Michael Falk (2025_12_11): ‘Artificial intelligence’ myths have existed for centuries – from the ancient Greeks to a pope’s chatbot

Reading the Five Books of Moses I see that Yahweh the god of Israel is a greedy stupid old power tripping narcissist like Donald Trump who destroys everything that he touches by cowering before greedy fools. Robert Alter (2004): The Five Books of Moses: A Translation with Commentary

We have to extend the physical ideas of symmetry to people as I have tried to do in quantocracy and must now complete justice. I vaguely see a target but first I must deal with the field theory and this accounts for the agonizingly slow birth of L4L. The interpretation of the physical nature of information and the form energy bootstrap have been significant steps I think, and just need to push on through the ten steps and the commentary. cl4l05_particles is slowly coming into focus and feeding back some enlightenment to cl4l01 → 04.

Friday 12 December 2025

Why am I so optimistic? The overall simplicity of my Ansatz to have Hilbert space on the initial singularity derived from Augustine’s Trinity and Brouwer’s fixed point theorem releasing the full power of quantum mechanical variation and selection. [This is] based on a simple understanding of QM based on de Broglie waves and superposition, eliminating the unphysical ideas of QFT which appear to be derived from the traditional story of an omniscient creator setting the universe on a restricted and deterministic trajectory of development. This plus the energy-form bootstrap opens a clear path to a self creating divine universe. Now to make it stick beyond the advantages mentions in Cognitive Cosmogenesis.

USCCB office of the General Counsel: http:www.usccb.org/ogc/

Hi, I am aware that the Church is slowly responding to its long history of child sexual abuse. My interest is the child intellectual abuse now revealed by scientific assessments of Catholic doctrine.

This doctrine led me to join the Dominican Order since I found masturbation irresistible and the claim that masturbation is a mortal sin clealy make it impossible for me to reach heaven without extreme superogation.

This doctrine is clearly false and blighted half my life from age 5

I have now, aged 81, written a book Cognitive Cosmogenesis: a systematic integration of physics and theology. I point out in meticulous detail that the reality of physical universe replaces the Bible and that Catholic doctrine is egregeously false.

This book is a foundation for legal action against the Church for knowingly propagating false witness, breaching the Decalogue. I am a Christian: I love god, I love my neighbour.

Best wishes,

Jeffrey Nicholls

More detail at www.naturaltheology.net

Tweet: @USCCB: Dear @USCCB Publication on 5 December 2025 of my book Cognitive Cosmogenesis: a systematic integration of physics and theology marks the end of the Roman Catholic Church as you have it. Please read and adjust your doctrine to real science. I love the true God .

A speech is a periodic vector in sound. When I am making as speech I spread a perodic vector over time, a sequence of events, breaking it down into its basis phonemes.

The most difficult point I have to overcome in cl4l05_particles is to explain how all the features of particles and their interactions in Minkowski space create the details of special

[page 179]

relativity when QM contains no space and time. Where do these come from? This difficulty probably explains why it was a lot easier for the creators of traditional quantum theory to simply assume the existence and work from there as we see even in the proponents of axiomatic quantum field theory like Streater and Wightman. Here we run up against Chaitin’s entropic interpretation of Gödel’s incompleteness results suggesting that if the information is not in quantum theory it cannot be in Minkowski space. A central issue which will determine the structure of cl4l05_. Gregory J. Chaitin (1982): Gödel's Theorem and Information

Saturday 15 December 2025

Aquinas’s god is omnipotent in the same way that Hilbert’s formalism is omnipotent, able to be anything that is non self-contradictory. Formalism (philosophy of mathematics) - Wikipedia

There’s nothing about love in the Nicene Creed. It is just a bit of bureaucratic formalism, a law. Love is concrete, form and energy.

Behiel: Dirac equation: Its most interesting feature is its linearity, so we have to get rid of the quadratic elements. So we take the square root and are going to force the square root to be linear.

Matrices can be used to get rid of the cross terms, γμpμ = mc

Dirac equation: [γμμ + mc/ℏ] ψ = 0.

This means that ψ has 4 components – a bispinor with 4 complex numbers at each point in spacetime, spin up and down, electron and positron.

[page 180]

What we have is two coupled spinors at each point in spacetime. Spinors give us double cover in rotation.

Michael Atiyah: No one fully understands spinors, square roots of geometry ,at the core of fundamental physics – in Minkowski space. Goddard (1998); Paul Dirac, The Man and His Work

Are spinors the bases of stable matter – Pauli exclusion. No it is quantum physics and self-adjoint operators.

Behiel: Why do spinors exist in the first place? Rotations in 3D.

Topology, homology, simply connected, homology class: same topology. Simply connected can shrink to a point, winding number, No cut the loop.

Axis angle representation (Gauss?) no Euler.

Spinor is the 2 component complex vector that an SU(2) matrix acts upon, very like qubit and fermion + boson.

Inverse of SU(2) is determinant 1 and inverse is complex conjugate transpose = hermitian = unitary.

How many degrees of freedom does a spinor have? 3, since length of spinor is 1, so we have 4D hyperspace radius 1. Hypersphere is simply connected. Is SU(2) connected to SO(3)? Yes, double cover.

All this stuff has to do with how quantum mechanics in a

[page 181]

qubit produces fermions and bosons which give the backbone of Minkowski space.

Spinors double cover 3D Euclidean space so rotations in 3D can be covered by SU(2). Spinors for each SO(3) orientation are negatives of one another,

Dirac created 4D equation, but perhaps we can take it to 2D, fermion and boson, ψ = a|fermion⟩ + b|boson⟩.

4D space is ‘covered’ by fermions and bosons.

Dirac equation is gorgeous, introducing spinors, antimatter and respecting the linearity of quantum mechanics, but physics still had to develop quantum field theory to deal with relativity and introduce a load of unfounded assumptions that have proven problematic:

Continuity vs uncertainty principle / fields created ad hoc
renormalization
fluctuation and cosmological constant problem
intractability of gravitation
non-linear Yang-Mills and renormalization to explain asymptotic freedom and confinement, a bit bogus and ad hoc
infinite feynman diagrams
no explanation of spacetime / saved by Lgrangian.

[page182]

So I finish the evening mildly depressed because my theoretical dreams are coming true too slowly but the job is going well and we are getting the power of quantum mechanics out into the open with a countable infinity of basis states matching the lengths of DNA strands controlling life forms which are at least as complex as quantum mechanics. There is quantum mechanics beneath all this DNA. The network model is slowly coming alive again running on bosons and fermions and their power of simplicity is keeping me strong.

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

Alter (2004), Robert, The Five Books of Moses, W. W.Norton 2004 ' Through a distinguished career of critical scholarship and translation, Robert Alter has equipped ua to read thr Hebrew Bible as a powerful cohesive work of literature. In this landmark work, Alter's masterly translation and probing commentary combine to give contemporary readers the definitive edition of the Five Books of Moses
Amazon
  back

Auyang (1995), Sunny Y., How is Quantum Field Theory Possible?, Oxford University Press 1995 Jacket: 'Quantum field theory (QFT) combines quantum mechanics with Einstein's special theory of relativity and underlies elementary particle physics. This book presents a philosophical analysis of QFT. It is the first treatise in which the philosophies of space-time, quantum phenomena and particle interactions are encompassed in a unified framework.' 
Amazon
  back

Carlson (2006), James, and Arthur Jaffe & Andrew Wiles, The Millennium Prize Problems, Clay Mathematics Institute and American Mathematical Society 2006
1: The Birch and Swinnerton-Dyer Conjecture: Andrew Wiles
2: The Hodge Conjecture: Pierre Deligne
3: The Existence and Smoothness of the Navier-Stokes Equation: Charles L Fefferman
4: The Poincare Conjecture: John Milnor
5: The P versus NP Problem: Stephen Cook
6: The Riemann Hypothesis: Enrico Bombieri
7: Quantum Yang-Mills Theory: Arthur Jaffe and Edward Whitten 
Amazon
  back

Dirac (1983), P A M, The Principles of Quantum Mechanics (4th ed), Oxford UP/Clarendon 1983 Jacket: '[this] is the standard work in the fundamental principles of quantum mechanics, indispensible both to the advanced student and the mature research worker, who will always find it a fresh source of knowledge and stimulation.' (Nature)  
Amazon
  back

Goddard (1998), Peter , and Stephen Hawking, Abraham Pais, Maurice Jacob, David Olive, and Michael Atiyah, Paul Dirac, The Man and His Work, Cambridge University Press 1998 Jacket: Paul Adrien Maurice Dirac was one of the founders of quantum theory and the aithor of many of its most important subsequent developments. He is numbered alongside Newton, Maxwell, Einstein and Rutherford as one of the greatest physicists of all time. This volume contains four lectures celebrating Dirac's life and work and the text of an address given by Stephen Hawking, which were given on 13 November 1995 on the occasion of the dedication of a plaque to him in Westminster Abbey. In the first lecture, Abraham Pais describes from personal knowledge Dirac's character and his approach to his work. In the second lecture, Maurice Jacob explains not only how and why Dirac was led to introduce the concept of antimatter, but also its central role in modern particle physics and cosmology. In the third lecture, David Olive gives an account of Dirac's work on magnetic monopoles and shows how it has had a profound influence in the development of fundamental physics down to the present day. In the fourth lecture, Sir Michael Atiyah explains the widespread significance of the Dirac equation in mathematics, its roots in algebra and its implications for geometry and topology.' 
Amazon
  back

Nicholls (2025), Jeffrey, Cognitive Cosmogenesis: A systematic integration of physics and theology, Austin Macauley Publishers 12025 ' This book is a personal narrative of those events and a defense of the belief that the universe itself is divine. The central argument is that by embracing this reality and abandoning notions of supernatural deities, humanity can resolve its problems. The universe, it is argued, is self-creating, and a proper understanding of physics leads to a plausible scientific theology. The natural intelligence inherent in the universe, from cellular organization to ecosystems, far surpasses any artificial intelligence. Comprehending this natural order, the author suggests, would make achieving world peace relatively straightforward. The book contends that modern theologians should recognize the physical world, rather than ancient texts, as the foundation for credible theology. It also addresses the historical entanglement of religion and politics, asserting that the model of creation presented herein fundamentally rejects the imperialistic ambitions that have fueled genocidal holy wars.'  
Amazon
  back

Weinberg (1995), Steven, The Quantum Theory of Fields Volume I: Foundations, Cambridge University Press 1995 Jacket: 'After a brief historical outline, the book begins anew with the principles about which we are most certain, relativity and quantum mechanics, and then the properties of particles that follow from these principles. Quantum field theory then emerges from this as a natural consequence. The classic calculations of quantum electrodynamics are presented in a thoroughly modern way, showing the use of path integrals and dimensional regularization. The account of renormalization theory reflects the changes in our view of quantum field theory since the advent of effective field theories. The book's scope extends beyond quantum elelctrodynamics to elementary partricle physics and nuclear physics. It contains much original material, and is peppered with examples and insights drawn from the author's experience as a leader of elementary particle research. Problems are included at the end of each chapter. ' 
Amazon
  back

Zee (2010), Anthony, Quantum Field Theory in a Nutshell, Princeton University Press 2010 ' Since it was first published, Quantum Field Theory in a Nutshell has quickly established itself as the most accessible and comprehensive introduction to this profound and deeply fascinating area of theoretical physics. Now in this fully revised and expanded edition, A. Zee covers the latest advances while providing a solid conceptual foundation for students to build on, making this the most up-to-date and modern textbook on quantum field theory available. This expanded edition features several additional chapters, as well as an entirely new section describing recent developments in quantum field theory such as gravitational waves, the helicity spinor formalism, on-shell gluon scattering, recursion relations for amplitudes with complex momenta, and the hidden connection between Yang-Mills theory and Einstein gravity. Zee also provides added exercises, explanations, and examples, as well as detailed appendices, solutions to selected exercises, and suggestions for further reading.' 
Amazon
  back

Links

Carl Lipo (2025_11_27), Drones, physics and rats: Studies show how the people of Rapa Nui made and moved the giant statues – and what caused the island’s deforestation, 'Rapa Nui, also known as Easter Island, is often portrayed in popular culture as an enigma. The rationale is clear: The tiny, remote island in the Pacific features nearly 1,000 enormous statues – the moai. The magnitude and number of these monuments defy easy explanation.
Since European ships first encountered these stone giants in the 18th century, outsiders have branded the island as fundamentally mysterious, possibly beyond archaeologists’ ability to explain. This characteristic is part of what makes the island famous. Tour operators market the inexplicable. Documentaries promise unsolved puzzles. Popular books ask how “primitive people” could possibly move 70-ton megaliths.
Archaeological researchers have put forward various explanations for the statues, which were made between 1200 and 1700, but there remains no consensus. For decades, experts offered plausible scenarios: powerful chiefs commanding workers, elite-controlled statue quarries, wooden sleds drawn by hundreds of islanders, roller systems, wooden rails and ceremonial pathway markers. Based on authoritative assertions and compelling narratives, these accounts are rarely connected to archaeological evidence.
I’m an archaeologist who has been studying Rapa Nui for more than two decades. In newly published research, my colleagues and I believe we’ve solved the mystery in three essential ways.' back

Chen Ning Yang & Robert L. Mills (1954_06_28), Isotopic spin conservation and a generalized gauge invariance, ' It is pointed out that the usual principle of invariance under isotopic spin rotation is not consistant with the concept of localized fields. The possibility is explored of having invariance under local isotopic spin rotations. This leads to formulating a principle of isotopic gauge invariance and the existence of a b field which has the same relation to the isotopic spin that the electromagnetic field has to the electric charge. The b field satisfies nonlinear differential equations. The quanta of the b field are particles with spin unity, isotopic spin unity, and electric charge ±e or zero.' back

Chiral symmetry breaking - Wikipedia, Chiral symmetry breaking - Wikipedia, the free encyclopedia, ' In particle physics, chiral symmetry breaking generally refers to the dynamical spontaneous breaking of a chiral symmetry associated with massless fermions. This is usually associated with a gauge theory such as quantum chromodynamics, the quantum field theory of the strong interaction, and it also occurs through the Brout-Englert-Higgs mechanism in the electroweak interactions of the standard model. This phenomenon is analogous to magnetization and superconductivity in condensed matter physics. The basic idea was introduced to particle physics by Yoichiro Nambu, in particular, in the Nambu–Jona-Lasinio model, which is a solvable theory of composite bosons that exhibits dynamical spontaneous chiral symmetry when a 4-fermion coupling constant becomes sufficiently large. Nambu was awarded the 2008 Nobel prize in physics "for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics".' back

Color confinement - Wikipedia, Color confinement - Wikipedia - the free encyclopedia, ' There is not yet an analytic proof of color confinement in any non-abelian gauge theory. The phenomenon can be understood qualitatively by noting that the force-carrying gluons of QCD have color charge, unlike the photons of quantum electrodynamics (QED). Whereas the electric field between electrically charged particles decreases rapidly as those particles are separated, the gluon field between a pair of color charges forms a narrow flux tube (or string) between them. Because of this behavior of the gluon field, the strong force between the particles is constant regardless of their separation. back

Dasha Burns (2025_12_12), ‘Nobody Wants to Take Responsibility for the Tragedy That’s Going on Here’, ' To this day, Bill Gates remains a relatively mild-mannered, non-political guy. But he’s also not going to ignore reality.
For the first time in 25 years, the number of child deaths is on track to rise from the previous year, to the tune of an additional 200,000 deaths, according to the Gates Foundation. And it’s not a coincidence, he says, that it’s coming after the Trump administration and other wealthy countries slashed foreign aid at the beginning of the year.
“There were sudden and massive cuts — you just can’t deny that’s led to lots of deaths,” Gates said in an interview with the Conversation.
The Trump administration disputes that notion, of course, but regardless, Gates is still eager to work with them. He said he’s had good conversations with President Donald Trump and Secretary of State Marco Rubio to try to boost funding going forward.
In a wide-ranging conversation, the Microsoft co-founder-turned-philanthropic giant also touched on his decision to pull back on climate funding, the potential job displacement caused by AI and his conversations with Robert F. Kennedy Jr., the vaccine skeptic now running the Department of Health and Human Services.
“Robert Kennedy wrote a book that says I kill millions of children and make billions of dollars on vaccines,” Gates said. “It’s close to correct. I spend billions of dollars to save millions".' back

Dicastery for the Doctrine of the Faith, Dicastery for the Doctrine of the Faith, Profile, back

Dicastery for the Doctrine of the Faith - Wikipedia, Dicastery for the Doctrine of the Faith - Wikipedia, the free encyclopedia, ' The Dicastery for the Doctrine of the Faith (DDF) is a department of the Roman Curia in charge of the religious discipline of the Catholic Church. The Dicastery is the oldest among the departments of the Roman Curia. Its seat is the Palace of the Holy Office in Rome, just outside Vatican City. It was founded to defend the Catholic Church from heresy and is the body responsible for promulgating and defending Catholic doctrine.' back

Einstein-Hilbert action - Wikipedia, Einstein-Hilbert action - Wikipedia, the free encyclopedia, ' The Einstein–Hilbert action (also referred to as Hilbert action) in general relativity is the action that yields the Einstein field equations through the stationary-action principle.' back

Formalism (philosophy of mathematics) - Wikipedia, Formalism (philosophy of mathematics) - Wikipedia, the free encyclopedia, 'In foundations of mathematics, philosophy of mathematics, and philosophy of logic, formalism is a theory that holds that statements of mathematics and logic can be considered to be statements about the consequences of certain string manipulation rules. . . . Formalism stresses axiomatic proofs using theorems, specifically associated with David Hilbert. A formalist is an individual who belongs to the school of formalism, which is a certain mathematical-philosophical doctrine descending from Hilbert.' back

Gregory J. Chaitin (1982), Gödel's Theorem and Information, 'Abstract: Gödel's theorem may be demonstrated using arguments having an information-theoretic flavor. In such an approach it is possible to argue that if a theorem contains more information than a given set of axioms, then it is impossible for the theorem to be derived from the axioms. In contrast with the traditional proof based on the paradox of the liar, this new viewpoint suggests that the incompleteness phenomenon discovered by Gödel is natural and widespread rather than pathological and unusual.'
International Journal of Theoretical Physics 21 (1982), pp. 941-954 back

John D. Norton (2022_02_07), Philosophical Significance of the General Theory of Relativity, ' General relativity appeared in science at a fertile moment philosophically. In the mid 1910s, new, modern traditions were emerging in philosophy of science. The philosophers building this new tradition were especially impressed by Einstein's achievement. They took careful note of the theory and of Einstein's general views on scientific methodology. The influence of Einstein's success with general relativity remains today a popular example and test case for views on the relationship of theory and evidence. At the center of these considerations is a reappraisal of how evidence bears on theory. As we shall see below, there are two sides to the reappraisal. One overturns an older view and the other promotes replacement views. back

Karen Cummings (2025_12_10), Cowbois reimagines Hollywood’s Wild West – with a wonderful queer twist, ' Music and theatre can bring into the world places and stories that exist only in the imagination. Can music and theatre also change hearts and minds?
This question is at the heart of Cowbois, a new music theatre piece written by Charlie Josephine and directed by Kate Gaul.
Cowbois reimagines a Hollywood-esque Wild West where rugged individuality and hyper masculinity are challenged and eventually replaced by joy, freedom and resistance. It dreams forward towards a utopian vision, where hope and desire can be forces for change.
back

Laura Poitras /Praxis Films, Laura Poitras /Praxis Films, ' Praxis Films & Collaborators Laura Poitras Laura Poitras is a filmmaker, journalist and artist. → Yoni Golijov Yoni Golijov is a producer and a socialist organizer. → Brenda Coughlin Brenda Coughlin is an independent producer. → Henrik Moltke Henrik Moltke is a journalist and filmmaker. → Katy Scoggin Katy Scoggin is a fictional and documentary writer-director, cinematographer, and producer. → Contact Praxis Films inquiries: info [at] praxisfilms [dot] org Project inquires: Nick Shumaker Anonymous Content [contact] Press inquiries: U.S. Press Cinetic [contact] International press Claudia Tomassini & Associates [contact] Laura Poitras' PGP Key: 3217 C509 292F C670 76EC D75C 7614 269B DDF7 3B36 Distribution: All the Beauty and the Bloodshed [contact] CITIZENFOUR The Oath My Country, My Country [contact] back

Lie Group - Wikipedia, Lie Group - Wikipedia, the free encyclopedia, 'In mathematics, a Lie group . . . is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure. Lie groups are named after Norwegian mathematician Sophus Lie, who laid the foundations of the theory of continuous transformation groups. Lie groups represent the best-developed theory of continuous symmetry of mathematical objects and structures, which makes them indispensable tools for many parts of contemporary mathematics, as well as for modern theoretical physics. . . . One of the key ideas in the theory of Lie groups is to replace the global object, the group, with its local or linearized version, which Lie himself called its "infinitesimal group" and which has since become known as its Lie algebra.' back

Mass gap - Wikipedia, Mass gap - Wikipedia, the free encyclopedia, ' In quantum field theory, the mass gap is the difference in energy between the lowest energy state, the vacuum, and the next lowest energy state. The energy of the vacuum is zero by definition, and assuming that all energy states can be thought of as particles in plane-waves, the mass gap is the mass of the lightest particle. Since the energies of exact (i.e. nonperturbative) energy eigenstates are spread out and therefore they are not technically eigenstates, a more precise definition is that the mass gap is the greatest lower bound of the energy of any state which is orthogonal to the vacuum.' back

Michael Falk (2025_12_11), ‘Artificial intelligence’ myths have existed for centuries – from the ancient Greeks to a pope’s chatbot, ' It seems the AI hype has turned into an AI bubble. There have been many bubbles before, from the Tulip mania of the 17th century to the derivatives bubble of the 21st century. For many commentators, the most relevant precedent today is the dotcom bubble of the 1990s. Back then, a new technology (the World Wide Web) unleashed a wave of “irrational exuberance”. Investors poured billions into any company with “.com” in the name.
Three decades later, another new technology has unleashed another wave of exuberance. Investors are pouring billions into any company with “AI” in its name. But there is a crucial difference between these two bubbles, which isn’t always recognised. The World Wide Web existed. It was real. General Artificial Intelligence does not exist, and no one knows if or when it ever will.
In February, the CEO of OpenAI, Sam Altman, wrote on his blog that the very latest systems have only just started to “point towards” AI in its “general” sense. OpenAI may market its products as “AIs”, but they are merely statistical data-crunchers, rather than “intelligences” in the sense that human beings are intelligent.
back

Mohana Basu (2025_12_11), Giant 3D map shows almost every building in the world, Scientists have produced the most detailed 3D map of almost all buildings in the world. The map, called GlobalBuildingAtlas, combines satellite imagery and machine learning to generate 3D models for 97% of buildings on Earth. The data set, published in the open-access journal Earth System Science Data on 1 December1, covers 2.75 billion buildings, each mapped with footprints and heights at a spatial resolution of 3 metres by 3 metres. The 3D map opens new possibilities for disaster risk assessment, climate modelling and urban planning, according to study co-author Xiaoxiang Zhu, an Earth observation data scientist at the Technical University of Munich in Germany. It could also help to improve how researchers monitor United Nations (UN) Sustainable Development Goals for cities and communities, Zhu adds. back

Richard Behiel, The Mystery of Spinors, ' In this video, we explore the mystery of spinors! What are these strange, surreal mathematical things? And what role do they play in physical reality? We'll talk about the algebra of SO(3) and SU(2), and the profound physical implications of spinors, particularly as it relates to spin-statistics and the stability of matter! back

Richard Behiel, Dirac Equation: Free Particle at Rest (solution to Dirac Equation), back

Richard Behiel (2023_11_21), Deriving the Dirac Equation, ' In this video, we'll derive the Dirac equation, and see where it comes from!' back

Sabrina Carpenter, Manchild, ' [Chorus] Man-child
Why you always come a-running to me?
Fuck my life
Won't you let an innocent woman be?
Never heard of self-care
Half your brain just ain't there
Man-child
Why you always come a-running, taking all my loving from me?

[Bridge] Oh, I like my boys playing hard to get
And I like my men all incompetent
And I swear they choose me, I'm not choosing them
Amen, hey, men
Oh, I like my boys playing hard to get (Play hard to get)
And I like my men all incompetent (Incompetent)
And I swear they choose me, I'm not choosing them (Not choosing them)
Amen (Amen), hey, men (Hey, men)

[Chorus]
Man-child
Why you always come a-running to me? (Always come a-running to me)
Fuck my life
Won't you let an innocent woman be? (Amen)
[Outro]
Oh, I like my boys playing hard to get (Play hard to get)
And I like my men all incompetent (Incompetent)
And I swear they choose me, I'm not choosing them (Not choosing them)
Amen (Amen), hey, men (Hey, men)' back

Sachi Kitajima Mulkey (2025_12_05), What Scientists Found When a Deep Sea Mining Company Invited Them In, ' Industrial mining of the seabed could reduce the abundance and diversity of tiny animals living in the depths of the Pacific Ocean, a new study found.
The study, published Friday in the journal Nature Ecology and Evolution, was funded by The Metals Company, which is vying to become the first company to conduct commercial mining on the ocean floor.
Researchers from the Natural History Museum in London analyzed samples from the seafloor before and after a mining test and found that the number of worms, minute crustaceans and other small animals in the path of the mining vehicle fell 37 percent. The variety of the creatures also declined by 32 percent.
The data came from the Clarion-Clipperton Zone, an area in the Pacific Ocean between Hawaii and Mexico that is targeted for seabed mining because it is rich with potato-sized nodules that contain nickel, cobalt, copper and manganese. The metals are used in renewable-energy technologies and also have military applications.
The Metals Company has spent some $250 million studying the environmental effects of seabed mining. The dozens of researchers involved had contracts that allowed them to independently analyze and publish their results. This emerging collection of work represents one of the largest and most comprehensive research efforts conducted in the Clarion-Clipper Zone to date. [. . .]
The Metals Company had to rely on independent scientists because it needs data for an eventual environmental impact statement (which regulators require before commercial mining can begin) but Mr. Clarke said there are few commercial contractors with the expertise necessary for studying deep sea ecosystems. The company will continue to fund research while scaling up any commercial operations, he said.
“There’s some papers out there that are based on work that we funded that are not necessarily very useful or complementary to us,” he said. “But that’s because we had this agreement with the academics to get them on board".' back

Superconductivity - Wikipedia, Superconductivity - Wikipedia, the free encyclopedia, ' Superconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic fields are expelled from the material. Any material exhibiting these properties is a superconductor. Unlike an ordinary metallic conductor, whose resistance decreases gradually as its temperature is lowered, even down to near absolute zero, a superconductor has a characteristic critical temperature below which the resistance drops abruptly to zero. An electric current through a loop of superconducting wire can persist indefinitely with no power source.' back

Thomas Newcomen - Wikipedia, Thomas Newcomen - Wikipedia, the free encyclopedia, ' Newcomen's great achievement was his steam engine, developed around 1712; combining the ideas of Thomas Savery and Denis Papin, he created a steam engine for the purpose of lifting water out of a tin mine. It is likely that Newcomen was already acquainted with Savery, whose forebears were merchants in south Devon. Savery also had a post with the Commissioners for Sick and Hurt Seamen, which took him to Dartmouth. Savery had devised a "fire engine", a kind of thermic syphon, in which steam was admitted to an empty container and then condensed. The vacuum thus created was used to suck water from the sump at the bottom of the mine. The "fire engine" was not very effective and could not work beyond a limited depth of around thirty feet.' back

USCCB: General Counsel, USCCB: Office of General Counsel, ' The Office of General Counsel acts as the source of legal advice to the USCCB. OGC also supports the work of diocesan attorneys, State Catholic Conferences, and other national, regional, and local Catholic entities by providing uniform assistance on constitutional, tax (including the administration of the Group Ruling), litigation, and other matters.
OGC attorneys have special expertise in the law of tax exemption, pensions, immigration, education, civil rights, pro-life, intellectual property, and communications. These areas are practiced in the context of church-state relations, and with particular attention to their impact on not-for-profit entities.
OGC participates in rulemaking and other federal agency proceedings on behalf of USCCB, and provides legal support to the USCCB’s Committees and Subcommittees when they speak to matters of public policy and pastoral concern. OGC represents USCCB in litigation as a party or as amicus curiae. OGC supports the various efforts of diocesan counsel, principally through the National Diocesan Attorneys Association.
OGC attorneys also publish scholarly works and engage in public speaking on issues of law and policy.' back

Yachiro Nambu (2008), Nobel Lecture: Spontaneous Symmetry Breaking in Particle Physics: a Case of Cross Fertilization, ' Particle physics is an outgrowth of nuclear physics, which began in the early 1930s with the discovery of the neutron by Chadwick, the invention of the cyclotron by Lawrence, and the ‘invention’ of meson theory by Yukawa. The appearance of an ever increasing array of new particles in the subsequent decades and advances in quantum field theory gradually led to our understanding of the basic laws of nature, culminating in the present standard model. When we faced those new particles, our first attempts were to make sense out of them by finding some regularities in their properties. researchers invoked the symmetry principle to classify them. A symmetry in physics leads to a conservation law. Some conservation laws are exact, like energy and electric charge, but these attempts were based on approximate similarities of masses and interactions. Nevertheless, seeing similarities is a natural and very useful trait of the human mind, the near equality of proton and neutron masses and their interactions led to the concept of isospin Su(2) symmetry. On the other hand, one could also go in the opposite direction, and elevate a symmetry to a more elaborate gauged symmetry. Then symmetry will determine dynamics as well, a most attractive possibility. Thus the beautiful properties of electromagnetism were extended to the Su(2) non-abelian gauge field. But strong interactions are short range. giving a mass to a gauge field destroys gauge invariance.' back

Zvi Bar'el (2025_12_8), Analysis If Trump Embraces Erdogan's Peace Force in Gaza, Israel May Find Itself Sidelined With Hamas Still Armed, ' The 'bromance' alliance between the Turkish and U.S. presidents aids Erdogan's ambition to become the driving force of the Gaza peace plan's next phase and could lead to an arrangement in which Hamas lays down its arms rather than turning them in
The beauty of the public statements given by Tom Barrack, the U.S. special envoy to Syria who also serves as ambassador to Turkey in his spare time, lies in their directness and bluntness.
So it was when he explained to Lebanon that it was a "failed state" and that international expectations that it would be able to disarm Hezbollah were "unreasonable."
So it was this Friday at the Milken Institute Middle East and Africa Summit in Abu Dhabi. In a public conversation with Paul Wallace, Bloomberg's managing editor for the Middle East and North Africa, Barrack didn't mince his words.
"If I were personally advising Netanyahu, I would say that's one of the most brilliant things he could do," Barrack told the audience, adding that he does not think that this "brilliant thing" will happen because of a lack of trust.
The "brilliant thing" Barrack would advise Netanyahu to do is to agree to Turkey's participation in the international stabilization force that is supposed to protect the civilian activity and reconstruction in Gaza that the Trump administration hopes will begin within a few weeks.' back

www.naturaltheology.net is maintained by The Theology Company Proprietary Limited ACN 097 887 075 ABN 74 097 887 075 Copyright 2000-2026 © Jeffrey Nicholls