natural theology

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Notes

Sunday 30 April - Saturday 6 May 2023

[Notebook: DB 89: Cognitive Cosmogenesis]

[page 21]

Sunday 30 April 2023

Meaning and framing. Most of the theological stuff I have written in the last 60 years emphasizes my difference from the standard model of god, pointing out that the real god is the world, not someone in the sky. Here I am swimming againt the tide and it may be time to turn around and frame my view as the standard indigenous view, really just normal science, as we can see by looking. So the New Theology essay should be retitled the renewal of the Old Theology or something like this, go with the Rainbow Serpent and the indigenous politics of small scale and relative peace. Rainbow Serpent - Wikipedia

[page 22]

An exciting time? A boring time? Looks too easy. May be meaningless to most people, but must be tried. Tomorrow, at the library I will write it and see what it looks / sounds / feels like. The compressed version of cosmic cosmogenesis. A short but important tale of salvation, freedom and peace.

David Attenborough Flying Monsters: I am so impressed by what people do and am always feeling that I am a lazy and slap-dash old bugger who must up my act enormously to produce anything of comparable quality. David Attenborough (2011): Flying Monsters

Flight, a remarkable advance in the history of life, rather like the invention of the null geodesic.

Monday 1 May 2023

On the physiology of romance. From an evolutionary point of view, mating is the most important activity in life, and it has strong physiological implications stretching into all realms of life from fighting to discovery. Jerome O'Rorke OP, late Provincial of the Dominican Order in Australia, used to judge the vocations of his novices by keeping track of their weights, weight loss, for him, being a measure of failing commitment. Personally, he was massive.

[page 23]

6. The theory of the Trinity: From triplicity to infinity
7. The creation of Hilbert space:
8. Evolution I: Random Variation

Currently up to here, to be continued (and no doubt modified).

9. Evolution II: Quantum mechanical selection

Attenborough: Flying Monsters 54.30: Quetzalcoatlus Quetzalcoatlus - Wikipedia, going back to the indigenous beginning, beginning An Old Theolpgy 1 May 2023.

Loro part II: 'Altruism is the best way to be selfish'. Loro (film) - Wikipedia

Name change: No longer A New Theology. Now An Old Theology. [Predating the rise of imperialism] going back to the indigenous beginning [AOT 1 May 2023].

Tuesday 2 May 2023
Confusion reigns, but there is a light on the horizon defining a possible direction. The notion that the old theology rules is a win for the evolution of feeling and the direction of evolution which despite the evils associated with it has persistently operated for the increase in comlexity and higher entropy while tending to reduce energy intensity and nurture peace and wellbeing despite the frequency of violent outbreaks (as in Ukraine, Syria, Sudan . . .) that frequently make the news. I remain hopeful even though disasters are prevalent in the news. This is in

[page 24]

effect the error correcting function of bad news, prompting correction when we are off course.

The stress and anxiety I feel when writing seems closely analogous to an evolutionary process. I have a vague idea of what I want to say: in this case superposition of Hilbert space is a random process, uncontrolled by the initial singularity which provides input for the process of quantum mechanical selection. All this makes sense to me in a sentence or two, but the real problem lies in producing an account of the divine procession of Hilbert space which provides the framework for this variation, which is the subject of the quantum mechanical process of discovering stationary eigenvalues which are the output of observation. Nathan Brownlowe: Has a mathematician solved the ‘invariant subspace problem’? And what does that even mean?

It seems easy to write things out at length as I have done with cognitive cosmology, which occupies about 5MBytes, say half a million words.

So many ideas have come to me over the last few weeks that I am having trouble sorting them out, particularly the zero sum bifurcation of quanta of action into potential and kinetic energy, into energy and time and into momentum and distance, and the role of gravitational potential in the zero sum universe making kinetic particles real. This and my romantic and domestic problems are making my life very full and energetic.

[page 25]

Time to leave the whole Christian story out of it and just write a straight quantum mechanical essay about a universe beginning from a quantum of action which multiplies to give the entropy of the universe — Hilbert space, Minkowski space / gravitation, and cast off all other paraphenalia, the [ancient theologica] scaffolding that has got me this far.

Christianity has been a crutch for me, as it was for Newton, but now I have to break free and do it on my own. The big picture is to start with Hilbert space and then work to Minkowski and gravitation via conservation of energy and the zero energy universe. What we want is a theory of everything based on action and the Lagrangian going through Hilbert space via Fourier to Turing network. Keep all my good ideas and throw away my history.

So I have come to a Thomas Aquinas all is straw day. I have to work out what I really have to offer. Basically theology and physics unntainted by imperialism, ie theology as a science in the only universe, a theory of everything from mathematics and physics to politics and human culture. Moesy Pittounikos: Guardian: Ethical Conundrums

Wednesday 3 May 2023

Science, evidence and proof: Charles Darwin.

Cognitive cosmogensis. New Site

[page 26]

Evolution and the problem of evil - Introduction.

The world's biggest mistake: blaming the victim. The theft of the Great Southern Land.

Quantum mechanics is a theory of evolution. Hilbert generation of basis states and superpositions = variations; quantum operators discovery of fixed points, ie solutions to polynomials = selection. Selection is a cross between a motion and a thing, a point in a moving system that does not move, a fixed point demonstrating that there is no radical difference between motion and stillness [Galilean invariance].

Logical confinement = consistency. [God is logically confined.] The quantum god, pure action, is a compact, convex, continuous entity which can be populated with fixed points which are the orthogonal basis states of a Hilbert space, symmetrical with respect to complexity, with all the spaces fomally identical apart from the number of dimensions (basis vectors).

Thursday 4 May 2023

The core of the new essay is praise of the value of truth and science, adding that indigenous knowledge guided by thousands of years of experience and tradition counts as science even if it does not exactly conform to the current canons of science. The fundamental notion here is that science and evolution both tend toward survival by conforming to local reality.

[page 27]

If a structureless initial singularity is to build a universe some sort of omnipotence, evolution (variation and selection) is necessary. The quantum approach suggested here seems as good as any. The variety comes from both the number of basis states and the superposition of these states. All superpositions are normalized by adjusting the weights of the individual bases so that the sum of their absolute values (probabilities) always remains one, so that the superposed vector represents the statistics of a communication source and the Shannon entropy tells us how much information is carried by each symbol. The mathematical expression of these ideas is very succinct, but requires some decoding.

Friday 5 May 2023

Hilbert's angels are mathematical ideals with the same properties as vectors in Hilbert space, the agents that make the initial singularity work. [They can cooperate (by superposition) to perform more complex tasks.]

We may apply fixed point theory to the initial singularirty.

The coup de gras? or tour de force, or something like that is the creation of Minkowski space and gravitation. Given these we can hand the story over to physicists and evolutionists. Hilbert on the infinite. Cantor on the infinite. David Hilbert (1925): On the infinite, Transfinite numbers - Wikipedia

So far we have been working in the realm of mathematical

[page 28]

ideals and quantum mechanics. Now we can turn to classical reality, gravitation and Minkowski space. Ths transition solves all the problems of quantum field theory outlined by Kuhlman and is based on the zero energy universe. On the one hand, the vision is clear, but in terms of writing it out it remains rather obscure, but I need to make the effort to complete the journey I began 60 years ago. Meinard Kuhlmann: Quantum Field Theory

Saturday 6 May 2023

Why is it so hard to workout something so simple? Like the invention of the wheel. What is unknown is a mystery, something on the other side of the barrier [crossed by] insight. Now I have applied fixed point theory and established the creation of the basis vectors of a Hilbert space in the quantum initial singularity. A modern version of the Trinity. These basis vectors are in a sense quanta of action, both static and dynamic since they are fixed points in an environment of perpetual motion, sharing both motion and stillness. The Schrödinger equation describes the evolution of this sytem and the size of the Hamiltonian operator grows with the size of the Hilbert space. Next step is to contrast quantum observation with Einstein's general covariance and expain the interpersonal nature of quantum interaction against the backdrop of the generally covariant nature of potential and

[page 29]

gravitation in the initial singularity. Then we turn to the emergence of Minkowski space, energy, momentum and massive particles through the intermediary of massless bsons. Looks lovely, just have to find the words and am sorely tempted by the analogy of the trinity, angels, variation and selection in the selection of the features of the universe [attracted by potential increases in entropy, the final cause revisited]. Like the wheel, it is all just around the corner but not here yet, like music it just requires the hand of Fourier to transform it into speech [the role of the vocalist], that is executable code, the Turing "vacuum". These few sentences have, as usual, cured my morning despair and got me ready for my first coffee and corn flakes and begin the fight with the machine to put it into publishable form.

Meanwhile, back on Earth read the news, a catalogue of killing. Like music, my story feels good and it can probably be built with a few old chords, like fixed point theory that I have been using since I first pounded the cloister trying to understand the Trinity, but it is clear that a few more steps are still required and the hard bit is that I still do not know which ones they are.

My ultimate aim is to replace religious imperialism with human symmetry, which reminds me that I have not had much to say about symmetry and symmetry breaking lately. The next step is to break ψ into space and time. ψ is the newx [,unknown].

[page 30]

The oldest fixed point in my career of lust: insight and orgasm. Quanta of action, dynamic fixed points, the fundamental ideal symmetry, to be broken in the emergence of Minkowski into potential and kinetic energy, the massless kinetic energy of the photon and (?) the massive potential energy of gravitation. Aside: [classical] gravitation only sees real energy, solving the cosmological constant problem which is a problem of ideal mathematics?

I am slowly trying to make a transition from builder to artrist, from technician to feeler (aesthete), a change reflected in my decision (page 21) to call my efforts Old Theology rather than New Theology and recognize the damage done to theology and religion by the imperial forces that have taken them over for political rather that cultural selective advantage. At the same time I have been moving to understand that evolution and scientific method are closely related as consistency driven processes whose core has become for me the union of physics and theology which lies behind my latest effort to cast theology as a theory of everything that goes far beyond fundamental particles.

Every quantum system is a communication source, a complete system of events with a certain [normalized] probability distribution.

[page 31]

The initial singularity represented by gravitation is a one dimensional unmodulated drone [pure sound energy] (maybe). Tomorrow we bifurcate the quantum of action to make gravitation [potential] and real Minkowski space with particles, energy and momentum, splitting the quantum [symmetry] into potential and actual (kinetic) energy around the zero energy zero action universe — these pieces will all fit together eventually.

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Ceylan Yeginsu,Rebecca Ruiz& Nimet Kirac, His Cousin Promised a Quake-Proof Building. Then the Walls Crumbled., ' In a functioning system, there would be no ambiguity about who had approved a project. But Turkey’s system is built on ambiguity. The Erdogan government has, for decades, weakened independent, expert construction oversight and fought proposals to toughen standards. Turkey’s chamber of civil engineers, for example, has argued for years that experienced engineers are stretched too thin to adequately supervise construction projects. The group has called for every project to get a dedicated engineer. That idea, which could have slowed down construction, went nowhere. The Erdogan government sued the group in 2015, blocking it from issuing its own, stricter certifications for engineers. Lawmakers also privatized the building inspection process, sidelining Turkey’s engineering and architectural union. And while the government in 2019 eliminated a rule allowing contractors to pick their inspectors, mayors still hold power to push past potential issues.' back

David Attenborough (2011), Flying Monsters 3D, ' 220 million years ago, as dinosaurs were beginning their domination of Earth, another group of reptiles was about to make an extraordinary leap. Pterosaurs were taking control of the skies. The story of how and why these mysterious creatures took to the air is more fantastical than any fiction. In Flying Monsters, Sir David Attenborough sets out to uncover the truth about the enigmatic pterosaurs whose wingspans of up to 40 feet were equal to that of a modern day jet plane. The central question and of the greatest mysteries in paleontology is how and why did pterosaurs fly. How did creatures the size of giraffes defy gravity and soar through prehistoric skies? Attenborough starts to unravel one of science’s more enduring mysteries, discovering that the marvel of pterosaur flight has evolutionary echoes that resonate even today.' back

David Hilbert (1925), On the Infinite, ' We encounter a completely different and quite unique conception of the notion of infinity in the important and fruitful method of ideal elements. The method of ideal elements is used even in elementary plane geometry. The points and straight lines of the plane originally are real, actually existent objects. One of the axioms that hold for them is the axiom of connection: one and only one straight line passes through two points. It follows from this axiom that two straight lines intersect at most at one point. There is no theorem that two straight lines always intersect at some point, however, for the two straight lines might well be parallel. Still we know that by introducing ideal elements, viz., infinitely long lines and points at infinity, we can make the theorem that two straight lines always intersect at one and only one point come out universally true. These ideal "infinite" elements have the advantage of making the system of connection laws as simple and perspicuous as possible. Another example of the use of ideal elements are the familiar complex-imaginary magnitudes of algebra which serve to simplify theorems about the existence and number of the roots of an equation..' back

Jana Norman, The Sacred Balance: blending Western science with Indigenous knowledges, David Suzuki’s influential book has been updated for this moment, ' In his introduction, he looks back at the “many victories” achieved by the environmental movement, including land protections, conservation efforts and preventative measures such as successful blocking of dam projects that would have damaged ecosystems irrevocably. But he notes that, no matter how many wins we celebrated, new threats arose: protected land nibbled away, mining and logging allowed in parks, halted projects renewed and environmental legislation overturned. The science is in, he writes: the consequences of human activity are clear and the threats to our survival are a stark reality. What matters now is that “we shift from anthropocentrism to ecocentrism” and “reformulate” our legal, economic and political systems. Cross-cultural collaboration incorporating wisdom “passed through generations of Indigenous Peoples worldwide” plays a crucial role in getting us onto this “different path”. ' back

Joseph Stepansky - Al Jazeera, The US ‘war on terror’, 20 years after ‘mission accomplished’, ' Washington, DC – Two decades ago, on May 1, 2003, then-US President George W Bush declared “major combat operations in Iraq have ended” in a speech aboard the USS Abraham Lincoln, with a banner behind him proclaiming “mission accomplished”. The theatrical event, coming just 43 days after the United States had launched a ground invasion of Iraq, was meant to declare the beginning of the end of one of the main prongs of Washington’s so-dubbed post-September 11, 2001 “global war on terror” (GWOT). But far from ending operations, the US would send more troops to Iraq – peaking at about 168,000 forces in 2007, with no evidence the country had been involved in 2001’s 9/11 attacks on New York City and Washington, DC. The US would also further expand its GWOT, carrying out what analysts say was an undeterminable amount of strikes and military operations – sometimes through partner forces – against those deemed threats to the US in more than 20 countries across the world.' back

Kit McFarlane, Richard II by William Shakespeare: why ‘the divine right of kings’ (still) matters, ' The concept of “divine right” may seem like an obsolete concept, but it still resonates today when we consider those people whose power, wealth or status seem to elevate them above the rules governing others in society. Social, economic and political systems can also seem to be largely immune from individual questioning and dissent. In 2014, the late Ursula LeGuin made one of these connections plain: We live in capitalism, its power seems inescapable – but then, so did the divine right of kings. Any human power can be resisted and changed by human beings. Resistance and change often begin in art. Very often in our art, the art of words. Shakespeare reminds us we don’t have to think about power in an absolute way. He highlights the tension between absolute power and human limitations. As Greenblatt argues, Shakespeare throws “a garish light on an unnerving fact: even those in the innermost circles of power very often have no idea what is about to happen”. back

Kowlessar, Nainggul, Wesley & Moffat, Remarkable new tech has revealed the ancient landscape of Arnhem Land that greeted Australia’s First Peoples, 'Our work used a technique called electrical resistivity tomography. This is when we pass an electrical current through the ground to measure the nature of the sediments and rocks beneath the surface. This method can map more than 50 metres below the surface, and because it doesn’t involve digging or drilling, we could work right up to existing archaeological sites. Electrical resistivity tomography equipment used to image the subsurface of the floodplains near Red Lily Lagoon, Arnhem Land. Ian Moffat We combined this data with aerial mapping of the modern landscape undertaken with a drone and an airborne laser. This allows us to compare the subsurface results to the contemporary land surface and get a good understanding for just how much change has occurred up to the present day. While geophysics techniques like these are often used to find and map archaeological sites, we instead focused on reconstructing the ancient landscape itself. Knowing how landscapes have changed provides important context for understanding choices people may have made about where to live, what to eat and how to move around.' back

Ky;ie Knott, How religious groups are fighting climate change, and one man who is helping direct their substantial assets into beneficial projects , ' But one section of society often left out of the conversation is faith and religion, a valuable under-tapped resource considering that 84 per cent of the world’s population identifies with a religious group. That is changing, says Martin Palmer, a British theologian, author, broadcaster and environmentalist. ‘Some people ignore what I’m saying’: youth climate fears need to be heard. Palmer is chief executive of FaithInvest, a UK-based global non-profit that helps religious institutions “move their finances into projects that benefit both people and the planet”. “Faith groups are increasingly taking action on the climate and ecological crises,” says Palmer via Zoom from Britain. “Faiths think of future generations – and they think about the right use of your money".' back

LiYuan, Why China’s Censors Are Deleting Videos About Poverty, ' China says it is a socialist country that aims to promote common prosperity. In 2021, its top leader, Xi Jinping, declared “a comprehensive victory in the battle against poverty.” Yet many people remain poor or live just above the poverty line. With the country’s economic prospects dimming and the people’s increasing anxiety about their future, poverty has become a taboo subject that can draw ire from the government. In March, the Cyberspace Administration of China, the country’s internet regulator, announced that it would crack down on anyone who publishes videos or posts that “deliberately manipulate sadness, incite polarization, create harmful information that damages the image of the Party and the government, and disrupts economic and social development.” It bans sad videos of old people, disabled people and children. Behind the ban is a government eager to keep all talk about China positive. The Communist Party brags about how many people it lifted out of poverty in the past four decades, while refusing to mention how it had thrown the entire nation into abject poverty under Mao Zedong.' back

Loro (film) - Wikipedia, Loro (film) - Wikipedia, the free encclopedia, ' Act 2 Ennio Doris, an entrepreneur and an old friend of Berlusconi, boasts of his wealth, praising at the same time the entrepreneurial genius of Berlusconi, who is more concerned that he has lost the elections by only 25,000 votes. Ennio suggests Berlusconi to pass six senators to his side in order to bring down the centre-left government.' back

Meinard Kuhlmann (Stanford Encyclopedia of Philosophy), Quantum Field Theory, ' Quantum Field Theory (QFT) is the mathematical and conceptual framework for contemporary elementary particle physics. In a rather informal sense QFT is the extension of quantum mechanics (QM), dealing with particles, over to fields, i.e. systems with an infinite number of degrees of freedom. (See the entry on quantum mechanics.) In the last few years QFT has become a more widely discussed topic in philosophy of science, with questions ranging from methodology and semantics to ontology. QFT taken seriously in its metaphysical implications seems to give a picture of the world which is at variance with central classical conceptions of particles and fields, and even with some features of QM.' back

Melissa Fyfe, Get cliterate: how a Melbourne doctor is redefining female sexuality, ' You can trace Professor Helen O'Connell's discovery of the full clitoris – and the rewriting of the world's anatomy texts – to two books: one that angered her and another that inspired. The first book, Last's Anatomy, she couldn't seem to escape. The 1985 edition was the set text for her surgical exam and – to her "utter disbelief" as a classic overachiever – she failed the test three times. She calls this the "ridiculous book"; it had almost no mention of the clitoris, and certainly no illustrations, yet there were two pages on the penis. To top it off, aspects of female genitals were described as a "failure" of male genital formation (O'Connell still has the book, the word "failure" underlined in blue pen). "I knew at some point," she says, "that I was going to have to tackle that." She came across the second book – a University of Melbourne social scientist showed it to her – a few months after finally passing her surgical exam, in 1989. It was called A New View of a Woman's Body and was published by the US Federation of Feminist Women's Health Centres. It's full of detailed drawings of vulvas. For the clitoris chapter, the female researchers took off their pants and compared themselves with illustrations in respected anatomy texts. Then they masturbated, observed each other and took notes of the many parts of the internal and external clitoris that were changed by, or contributed to, sexual pleasure or orgasm. Young Helen O'Connell, aged 27, found it "really cool" and the women's observations – though not scientific – "valid".' back

Michelle Langley, Who owned this Stone Age jewellery? New forensic tools offer an unprecedented answer, This new method of ancient DNA extraction provides a more direct way of determining who used specific items in everyday life. The method can only be used for artefacts made from bone or tooth as these materials are porous and can soak up human DNA from repeated contact with bodily fluids (sweat, blood, saliva). Luckily, the bones and teeth of animals (and sometimes humans) were widely used throughout the past to create everyday tools, sacred items, and personal adornment. These osseous artefacts were held in the hand or worn against the body for extended periods, resulting in sweat and other fluids soaking into their surfaces over time. As a result, the artefact records the genetic information of the wearer. Through experimentation with different techniques, Essel and her team found a way to recover that DNA record in a form that is intact enough to be read.' back

Moesy Pittounikos, Guardian: Ethical Conundrums, ' In pondering the silence of St Aquinas, Aldous Huxley argued that the great theologian experienced a fall-on mystical experience and this is why he fell silent and never wrote another word. After seeing the 'clear light', St Aquinas is said to have denounced his entire body of writing; the writing which subsequently went on to fuel Catholic philosophy, as being mere 'chaff' or 'straw'! Is this the proof that God works in mysterious ways?' back

Nathan Brownlowe, Has a mathematician solved the ‘invariant subspace problem’? And what does that even mean?, ' So that’s an invariant subspace. The invariant subspace problem is a little more complicated: it is about spaces with an infinite number of dimensions, and it asks whether every linear operator (the equivalent of a matrix) in those spaces must have an invariant subspace. More precisely (hold onto your hat): the invariant subspace problem asks whether every bounded linear operator T on a complex Banach space X admits a non-trivial invariant subspace M of X, in the sense that there is a subspace M ≠ {0}, X of X such that T(M) is contained back in M. Stated in this way, the invariant subspace problem was posed during the middle of last century, and eluded all attempts at a solution.' back

New York Times Editorial Board, Biden Can Close the Extrajudicial Prison at Guantánamo, ' President Biden said at the outset of his administration that he would seek to have the detention center closed, and he directed the Defense Department to study how best to do so. But at the rate these cases are moving, resolving them could take several more years. Mr. Biden wisely avoided the kind of highly public pledges to close down the prison that President Barack Obama made and could not keep. But to achieve the goal of finally ending the extrajudicial detention of prisoners at Guantánamo — and its disgraceful violations of fundamental human rights and abandonment of the right to due process — requires more of Mr. Biden. Clearing out the remaining prisoners requires cutting through a tangle of laws, policies, procedures and bureaucratic secrecy. These are not simple tasks, but they are well within the power of the White House to accomplish if the process is given a far higher priority. Mr. Biden can use his authority to order the Departments of Defense, Justice and State, the intelligence agencies and other agencies involved to coordinate their efforts and direct their resources to make it happen, as quickly as possible.' back

Poonam Muttreja, Why China got population control wrong; India got it right, ' Half a century ago, India and China stood at a similar point. Their fertility rates – at 5.6 and 5.5 children per woman – were neck and neck and way more than what is regarded as replacement level fertility of 2.1, at which the population stabilises. They also faced similar social and developmental challenges as they sought to build their nations after suffering the devastation of long colonial and imperial humiliations and war. However, their journeys towards population control took vastly different routes, shaped by vastly different policies and approaches. Today, as India’s population passes China’s amid a mix of hope and apprehensions about its implications, it’s important to recall those journeys so societies and policymakers draw the right lessons from them.' back

Quetzalcoatlus - Wikipedia, Quetzalcoatlus - Wikipedia, the free encyclopedia, ' Quetzalcoatlus is a genus of pterosaur known from the Late Cretaceous period of North America (Maastrichtian stage); its members were among the largest known flying animals of all time. Quetzalcoatlus is a member of the Azhdarchidae, a family of advanced toothless pterosaurs with unusually long, stiffened necks. Its name comes from the Aztec feathered serpent god Quetzalcoatl, the feathered serpent. The type species is Q. northropi, named by Douglas Lawson in 1975; the genus also includes the smaller species Q. lawsoni, which was known for many years as an unnamed species before being named by Brian Andres and Wann Langston Jr. (posthumously) in 2021.' back

Rainbow Serpent - Wikipedia, Rainbow Serpent - Wikipedia, the free encyclopedia, ' The Rainbow Serpent or Rainbow Snake is a common deity often seen as the creator God] known by numerous names in different Australian Aboriginal languages by the many different Aboriginal peoples. It is a common motif in the art and religion of many Aboriginal Australian peoples. Much like the archetypal mother goddess, the Rainbow Serpent creates land and diversity for the Aboriginal people, but when disturbed can bring great chaos. . . .. Not all of the myths in this family describe the ancestral being as a snake. Of those that do, not all of them draw a connection with a rainbow. However, a link with water or rain is typical. When the rainbow is seen in the sky, it is said to be the Rainbow Serpent moving from one waterhole to another, and this divine concept explained why some waterholes never dried up when drought struck.' back

Transfinite numbers - Wikipedia, Transfinite numbers - Wikipedia, the free encyclopedia, 'Transfinite numbers are cardinal numbers or ordinal numbers that are larger than all finite numbers, yet not necessarily absolutely infinite. The term transfinite was coined by Georg Cantor, who wished to avoid some of the implications of the word infinite in connection with these objects, which were nevertheless not finite. Few contemporary workers share these qualms; it is now accepted usage to refer to transfinite cardinals and ordinals as "infinite". However, the term "transfinite" also remains in use.' back

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