Notes

Sunday 13 March 2022 - Saturday 20 March 2022

[Notebook: DB 88: Salvation]

[page 29]

Sunday 13 March 2022

Needham's study of the origin of scientific terms in China, their oracle bone and more modern forms may give us some feeling for how the universe began to express itself back near the beginning of time and space. Vol II, §13, pp 218 sqq. Joseph Needham (1956): Science and Civilisation in China (Volume 2) History of Scientific Thought

page 291: Relationship of Leibniz to Chinese thought through Chinese translations and dispatches.

page 292; Leibniz tried to explain what it would be like to be an atom.

[page 30]

Needham page 294; 'One of the ironies of history is that the Jesuits were proud of introducing to China the correct doctrine of the four elements—just half a century before Europe gave it up forever.'

page 396: 'One of the most interesting points of the subject to which this book is devoted is the question why modern scientific and technology did not spontaneously develop in East Asia.'

page 430: 'But it must be rememberd that out of the morass of magic grew the flowers of true knowledge of Nature—as in magnetism, pharmacy, chemistry and medicine itself. I would therefore venture to say that Tantrism represents one of the fields of research in which interesting discoveries in the history of science in Asia are most likely to be made.

page 431; 'one of the preconditions absolutely necessary for the development of science is acceptance of Nature, not turning away from her. If the scientist passes the beauty by, it is only because he is entranced by the mechanism. But other-worldly rejection of the world seems to be formally and psychologically incompatible with the development of science.'

Monday 14 March 2022

A long and complex dream about fitting an outlet to the bottom of a rainwater tank in the Ellenborough valley may years ago when my client was much younger than she is now. Success was elusive, but eventually I became conscious enough to realize it was a dream and the problem went away.

The network page of cosmic cosmology grew to long so it have broken it into 3, the first dealing with conventional networks in all forms from water and transport reticulation to international diplomacy; the second expanding the abstract idea of a computer network into the transfinite domain; and the third exploring a similar idea in the domain of quantum mechanics to explore the creative power of the universal mind.

Insofar as acceleration is a consequence of the curvature of spacetime, every time I touch the accelerator or the brake in my car or go around a corner, I am establishing local curvature in my enveloping Minkowski space.

[page 31]

Formal mathematics from an Aristotelian point of view. [. . . ] one of his criticisms of Plato's world of forms [was that they could not move themselves so] he moved to invent the unmoved mover to move Plato's forms to action. In the modern world we have two ways to bring formal mathematics alive, in the mind of a mathematician, or in some energized physical representation such as a computer or a machine. As Aristotle realized, what makes the world work is action, and the Catholic Church, through the work of Thomas Aquinas, recognizes God as pure action, the source of all action and the repeated action we call energy.

Aristotle (continuity) Computers are logically continuous by Aristotelian sharing [of "ends in common"]. Point set continuity is a myth only realized by the logical continuity in mathematicians' minds. Noether's theorem states that [this definition of] continuity is equivalent to doing nothing, a no-op, nop [whereas logical continuity involves action]. Aristotle (continuity): Physics, V, iii, Noether's theorem - Wikipedia

Trust yourself. It makes no sense to create a continuum out of a set of isolated points but Cantor made great contributions to mathematics by making infinite objects finite and tractable by putting them inboxes. This is the foundation of bureaucratic government. I am an infinite being. I sit on the bureaucrats' desk in a folder with certain identification marks which couple it to me and my fate is managed by applying legislated algorithms to the contents of the folder. The core of Cantor's discovery is the idea of one=to-one correspondence between infinite sets by dealing with their elements pairwise so long as they can be uniquely identified,

Cantor used this [packaging] to create transfinite numbers which are interesting but possibly useless. We can now separate them from their formulation on a misunderstanding of continuity by establishing correspondence between numbers and computation which brings us back to Aristotelian logical continuity so that we can have continuity without the messiness of [infinity]. A computation after all is simply a determinate sequence of logical operations. Turing showed how we can package computations into subroutines or logical subsets that accept some input and produce some output and act as components to build bigger computations. He found that the cardinal of the set of subroutines [aka turing machines] has the same [value] as the set of natural numbers. Algorithm - Wikipedia

Given this discovery we can repeat Cantor's proof using computations as elements of a power set and conclude that all the possible subroutines in this set is bigger than the set of natural numbers, which is the size of the set of computations. The beauty of this power set, however, is that its subsets are logically continuous snippets of code which can be assembled into computations which are bigger than the set of all computations and this is achieved as Cantor achieved it without increasing the

[page 32]

size of the set of the natural numbers by using them again and again in the subsets. So we can increase the computing power of the universe not by denying the truth of Turing's theorem but by using the same subroutines again and again in different combinations and permutations and following Cantor we can continue this process of complexification recursively ad infinitum. This is how the internet has grown from the first computer, massive but relatively powerless eighty years ago, to the internet which embraces billions of routines many of them repeated trillions of times per second around the globe.

Now a computation is a string of actions, and to determine a given string we need to memory to store the software which we wish to use. This is the role of space, the memory of the world.

All this is good, but it is a classical picture. We must now turn to quantum theory to learn how the operations of classical computation are executed. That is the next page.

Our task is to make the fantasies of mathematicians real enough to make mathematicians.

It is easy for a formalist mathematician to dream up any number of points and squash them in a corner with a Bolzano-Weierstrasse theorem, but how does this apply to a baby universe? If it just created points, idem numero it would get nowhere. They have to be differentiated, that is orthogonal. So we must go to the beginning of this essay and take a close look at the non-cloning theorem which we have already used in the pasges on the creation of Hilbert space and the meaurmenet problem. With the help of superposition and the invisibility theorem we will see how the universe constructs the snippets of code which constitute the foundation of the universe. This looks to us as momentum, strings of waves in space, but in fact every cycle of a wave must be orthogonal to all the rest otherwise is would not be a wave. Becasue of the invisibility theorem we cannot see all this detail, but it must be there otherwise the system would not work. Bolzano-Weierstrass theorem - Wikipedia

A fundamental particle is like a cell. Cells carry a spectrum of signalling molecules in their membranes which reveal much about their internal state. The equivalent with fundamental particles is spin and momentum. Cell signalling - Wikipedia

Tuesday 15 March 2022

[page 33]

Wednesday 16 March 2022

Now we turn to computation in Hilbert space. Nielsen & Chuang (2000): Quantum Computation and Quantum Information

Thursday 17 March 2022

Dreaming impossible dreams as usual and consequently making no progress with cc18_trans_hilbert. The idea here is that if we are to believe Wilczek it took months of supercomputing to compute the life of a proton whereas the real quantum mechanical proton can do this in microscopic times and therefore whatever algorithm it is using is, let us say 10³⁰ times faster than whatever the supercomputer is using. Since quantum theory lies at the origin of the univere it is here that we should look for the source of universal creativity. The question for this page is what is so special about quantum theory that explains this? Spmewhere is here we need to say something about the heuristic of simplcity and logical confinement. Since the proton is apparntly eternal, like the electron, we could like to think of these particles as the baclbone of the universe and the processes involving quarks and gluons as 'necessary' [tautological] , ie it would be inconsistent for them to fail.

Tonight going to see the Bangarra Dance Theatre and be inspired by indigenous metaphysics. Bangarra Dance Theatre: Wudjang; Not the Past

What I would like to think is that the proton is a group whose internal structure is self sustaining because of the fact that all possible exits are physically closed, unlike the mathematical fiat which just defines that there is no way out.

Friday 18 March 2022

We may think of the primordial Hilbert space as a bit like of world of angels, immaterial and guaranteed orthogonality by each one being a different species [difference is the key to existence].

Many Worlds quantum Mechanics Everett & De Witt. Bryce de Witt (1973): The Many-Worlds Interpretation of Quantum Mechanics

Application of heuristic of simplicity: since the initial universe is very simple, a simple minded approach should be sufficient to understand it. This might be sufficient to remove intellectual tours de force like string theory from consideration. cc20_gravitation.

Saturday 19 March 2022

Being a greenie, handing out how to votes. I have been silenced by the war, and faced, as I was, by the reality of evil

[page 34]

represented by the Viet Nam war. I began to identify the problem in some lectures I gave on 2BOB Radio Taree in 1987. The problem is lack of headspace. Our mental environment deviates severely from our genetic makeup [history]. At the bottom we can all, in the right conditions, reproduce ourselves. We might say that the fundamental biological statement which we can say about ourselves, and ever other species, is that we are interfertile. We can look at this mathematically and see that it defines a space, a space in which every element has a material relationship with every element that it can enter into contact with. When we think about peace we will arrive when we become intercultural, It does not mean we have have no culture. it is that every culture would be on a geodesic, freely floating through space according to a complex version of the first law [guided by the curvature of the space in which they move]. Here we are led by Georg Cantor into the transfinite realm where we find the tools to eliminate war by creating a transfinite headspace, that is a theology. That was 35 years ago, and the transfinite numbers and Cantor's theological dreams. Jeffrey Nicholls (1987): A theory of Peace

Einstein showed us how to do this with the calculus of real numbers which is a subset of the calculus made possible by using complex numbers assembled into complex matrices. A matrix sf a model of a communication network that tells us how much traffic is flowing through the links between the elements of the matrix. A matrix is a representation of Cantor's idea that the transfinite cardinal and ordinal numbers can represent anything representable. From a practical point of view this is a definition of representability. If you want to know what is representable, look at the transfinite numbers.

And if this idea of representation has any validity we should be able to observe it at work in the world that physics studies. The key observation here is not how fundamental particles are interacting with one another in various situation as violent as we can make

[page 35]

them. The key to Cantor's idea is that there is no limit to the things that can be represented as a mathematical object.

The quotation from Kuhlman at the head of cc18_transfinite_hilbert:

In conclusion one has to recall that one reason why the ontological interpretation of [Quantum Field Theory] is so difficult is the fact that it is exceptionally unclear which parts of the formalism should be taken to represent anything physical in the first place. And it looks as if that problem will persist for quite some time. Meinard Kuhlmann (Stanford Encyclopedia of Philosophy): Quantum Field Theory

Kuhlman is talking about quantum field theory and points out that it has representation problems. The experimenters identify object (particles) which seem to exist at the interface between real and unreal, or should I say complex and imaginary. W devise this space, which we call a field theory, to try to find the fixed points in their behaviour, things like charge, mass, velcocity and so on.

The probem of representation goes deeper than the fiield theory. We find it in the representation of quantum mechanics itself, which is the substance of the measurement problem. What are we to make of this amazing space that mathematics has opened up to us taking us past the four dimensional world of relativity to the infinite dimensional world of quantum mechanics? We dream that quantum mechanics deals with a space defined by something like the principe of general covariance that gives the key to relativity. This theory is considered to be deterministic and computable and we are devising more and more devices to observe the theoretically predicted phenomena. Measurement problem - Wikipedia

The purpose of this page is to describe the quantum analogue of the general theory of relativity in terms of it being the invisible and fully symmetrical definition of transfinite space This space is mapped onto the Hilbert space which looks like the transfinite version of the natural numbers. Mathematician can dream up sets of many things but I think the basic point about some possible structure becoming real stands at the boundary between [us and] the quantum world where things happen.

How to we do it? Map the natural numbers onto Turing machines. These two sets are equinumerous, but they start at zero and gradually grow by an imagined structure of reproduction which puts quite strong constraints between mathematically imagined structures in Hilbert space and things that are being scientifically observed, in order to discern the true nature of reality, Traditionally this is the discourse they call theology, and there is now a considerable literature in quantum theology, to which it is my desire to add the deep coupling between sex (genes) and art (minds).

[page 36]

The closest thing to being right is to be exactly wrong because change one bit and the story will be exactly right. One of the wildest speculations to gain considerable attention is the many worlds theory. This theory, as fare as I understand it, that instead of a wave function collapsing to one eigenvector and eigenvalues, every element of the superposition becomes actual in some other of the many world, a new one of which may be formed at every quantum event. Since the rate of events is energy, and we have a rough idea of the energy of the universe, we would calculate that new universes are being created at the rate of energy of the universe / Planck's constant (universes per second), ie 10⁵⁰ kilograms (mass) × 10 (conversion factor from kilograms to quanta per second) = 10⁹⁰, new universes, per second, a little far fetched [and remember that every event in these new universes is itself creating new universes at a similar rate].

My interpretation of quantum mechanics might sound like a deus ex machina. but our whole creation story narrated in quantum mechanics seems to be no weirder than any of the others and it pays to stick close to true mathematical, cybernetic, physical and metaphysical principles. Philosophers may argue forever, but science has worked hard to develop practical understanding about how the world works and my guess is that the creative force is a combination of action, Cantor's theory and the no-cloning theorem.

The network protocol built into all networked computers have two functions, inverses of one another, The first is to break down the complex multidimemsional structures in the computer which are to be transmitted to a serial string of bits to be delivered to a piece of hardware like a wire, an optic fibre or a wireless link. The second function, decoding, is to apply algorithms to this string of bits which can convert it back into the moving pictures, games and complex accounting functions [that it came from].

We have two spaces to talk about these things, the real solid 4D world in which we act and the Hilbert spaces where quantum mechanics resides. The real world is built on the quantum world. The quantum world entered the theological world [of angels] that since they have no diversified material substrate but they are pure spirits and the only way to differentiate them is that they should each be a single species. This is basically identical to a Hilbert space where each basis vector is an angel and communications between angels must initiate certain protocol that give them a name in the network. In other words sources which wish to communicate must share a language and the simplest possible language is a string of bits: it has two words, 0 and 1 which come in two varieties classical and quantum. Classical bits are yes / no decisions. Quantum bits, on the other hand are a spectrum of maybe's and the role of quantum mechanics is to understand what these maybes may be and the frequency of their occurrence.

[page 37]

Feynman and others realized that one could do computations with the operators of quantum mechanics. If we could control these things it would open a vast new space of computational power, but it turns out that sufficient control to realize this goal is hard to achieve. Richard Feynman (2007): Feynman Lecture of On Computation, chapter 6

This rather uncontrollable situation we call the vacuum, to which we attach some rather wonderful and somewhat self-contradictory properties, particularity that the vacuum is written in real numbers and so problems of the infinite arise. The answer to this problem is in effect digitized by being contained in the first transfinite cardinal degree of complexity which is also asymmetry, to be broken (ie applied) by the nest layer up.

We have coupled natural numbers to turing machines, and now we couple the set of Turing machines to the set of basis states of a Hilbert space analogy of the natural numbers which can be encoded as a spectrum of frequencies or energies, but whole domain is the set Turing machines and these machines may be connected together into a network by codecs that couple machines together, fundamentally the binary code. I repeat myself a lot. This the beginning of polishing now that I have ground a digital surface of the right shape.

In the end everything is a nested networks of languages made possible by individuals and systems which are multilingual, speaking in 2+ languages.

All translations between languages have to implement the transfinite version f general covariance which ives in Lie groups.

So I am saying that when we look at the world we often see unmodulated frequencies of recurrence, but what is recurring is not simply a phase but a cycle of processing [like a human lifetime], that is the execution of a [network of] turing machines.

Is it true that in the quantum world we can measure interactions in energy but are bind to the processes that are occurring in the periodic transfinite domain, coming to the point that [what] we identify [as] a communication channel [in fact a computer], whose task it is to be reversible, to carry information in two directions.

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Further reading

Books

de Witt (1973), Bryce S. , and Neill Graham, Hugh Everett III, J. A. Wheeler, L. N. Cooper, D. van Vechten, N. Graham (contributors and editors), The Many-Worlds Interpretation of Quantum Mechanics, Princeton UP 1973 Jacket: 'A novel interpretation of quantum mechanics, first proposed in brief form by Hugh Everett in 1957, forms the nucleus around which this book is developed. The volume contains Dr Everett's short paper from 1957, "'Relative State' Formulation of Quantum Mechanics", and a far longer exposition of his interpretation, entitled "The Theory of the Universal Wave Function", never before published. In addition, other papers by De Witt, Graham and Cooper and van Vechtem provide further dicussion of the same theme. Together they constitute virtually the entire world output of scholarly commentary on the Everett interpretation.'  Amazon   back

Nielsen (2000), Michael A, and Isaac L Chuang, Quantum Computation and Quantum Information, Cambridge University Press 2000 Review: A rigorous, comprehensive text on quantum information is timely. The study of quantum information and computation represents a particularly direct route to understanding quantum mechanics. Unlike the traditional route to quantum mechanics via Schroedinger's equation and the hydrogen atom, the study of quantum information requires no calculus, merely a knowledge of complex numbers and matrix multiplication. In addition, quantum information processing gives direct access to the traditionally advanced topics of measurement of quantum systems and decoherence.' Seth Lloyd, Department of Quantum Mechanical Engineering, MIT, Nature 6876: vol 416 page 19, 7 March 2002.  Amazon   back

Links

Algorithm - Wikipedia, Algorithm - Wikipedia, the free encyclopedia, ' As an effective method, an algorithm can be expressed within a finite amount of space and time, and in a well-defined formal language for calculating a function. Starting from an initial state and initial input (perhaps empty), the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states, eventually producing "output" and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input.' back

Aristotle (continuity), Physics V, iii, 'A thing that is in succession and touches is 'contiguous'. The 'continuous' is a subdivision of the contiguous: things are called continuous when the touching limits of each become one and the same and are, as the word implies, contained in each other: continuity is impossible if these extremities are two. This definition makes it plain that continuity belongs to things that naturally in virtue of their mutual contact form a unity. And in whatever way that which holds them together is one, so too will the whole be one, e.g. by a rivet or glue or contact or organic union. ' 227a10 sqq back

Bolzano-Weierstrass theorem - Wikipedia, Bolzano-Weierstrass theorem - Wikipedia, the free encyclopedia, 'In mathematics, specifically in real analysis, the Bolzano–Weierstrass theorem, named after Bernard Bolzano and Karl Weierstrass, is a fundamental result about convergence in a finite-dimensional Euclidean space Rn. The theorem states that each bounded sequence in Rn has a convergent subsequence. An equivalent formulation is that a subset of Rn is sequentially compact if and only if it is closed and bounded.' back

Cell signalling - Wikipedia, Cell signalling - Wikipedia, the free encyclopedia, ' In biology, cell signaling . . . or cell communication is the ability of a cell to receive, process, and transmit signals with its environment and with itself. Cell signaling is a fundamental property of all cellular life in prokaryotes and eukaryotes. Signals that originate from outside a cell (or extracellular signals) can be physical agents like mechanical pressure, voltage, temperature, light, or chemical signals (e.g., small molecules, peptides, or gas).' back

Hive (film) - Wikipedia, Hive (film) - Wikipedia, the free encyclopedia, ' Hive (Albanian: Zgjoi) is a 2021 Albanian-Kosovan drama film written and directed by Blerta Basholli in her directorial debut. The film stars Yllka Gashi, Çun Lajçi and Aurita Agushi. . . . The movie is based on the true story of a woman, Fahrije, who goes against misogynistic societal expectations to become an entrepreneur after her husband went missing during the 1998-1999 Kosovo War. She starts selling her own ajvar and honey, recruiting other women in the process. back

Jacqueline Peel & Rebekkah Markey-Towler, Today’s disappointing federal court decision undoes 20 years of climate litigation progress in Australia, ' The good news: climate science remains undisputed In the original case, the judge made landmark rulings about the dangers of climate change, marking a significant moment in Australian climate litigation. He found one million of today’s Australian children are expected to be hospitalised due to heat stress, they’ll experience substantial economic loss, and when they grow up the Great Barrier Reef and most eucalypt forests won’t exist. According to the judge, this harm was “reasonably foreseeable”. This is important from a legal point of view, as courts have previously considered climate change to be speculative, and a future problem. . . . The federal court found all the minister’s criticisms on the evidence of climate change were unfounded and all of the primary judge’s findings were appropriate to be made.' back

Lorena Allam, Attempted Aboriginal massacres took place as recently as 1981, historian says, ' Attempts at the mass killing of Aboriginal people were still being made as recently as 1981, according to a historian who has spent the past four years researching colonial violence in the Northern Territory. Dr Robyn Smith, who has worked on the University of Newcastle’s colonial frontier massacres map project, says she has also found attempts at massacres in the 1930s and 40s. . . . The 1981 mass poisoning was reported at the time, but remains unsolved. An Aboriginal man and an Aboriginal woman died and 14 others were admitted to hospital, six of them seriously ill, after unwittingly sharing a poisoned bottle of sherry that had been deliberately left on the grounds of the John Flynn memorial church in Alice Springs.' back

Measurement problem - Wikipedia, Measurement problem - Wikipedia, the free encyclopedia, 'The measurement problem in quantum mechanics is the problem of how (or whether) wave function collapse occurs. The inability to observe this process directly has given rise to different interpretations of quantum mechanics, and poses a key set of questions that each interpretation must answer. The wave function in quantum mechanics evolves deterministically according to the Schrödinger equation as a linear superposition of different states, but actual measurements always find the physical system in a definite state. Any future evolution is based on the state the system was discovered to be in when the measurement was made, meaning that the measurement "did something" to the system that is not obviously a consequence of Schrödinger evolution.' 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

Noether's theorem - Wikipedia, Noether's theorem - Wikipedia, the free encyclopedia, 'Noether's (first) theorem states that any differentiable symmetry of the action of a physical system has a corresponding conservation law. The theorem was proved by German mathematician Emmy Noether in 1915 and published in 1918. The action of a physical system is the integral over time of a Lagrangian function (which may or may not be an integral over space of a Lagrangian density function), from which the system's behavior can be determined by the principle of least action.' back

Sasha Grishin, NGV’s Queer advances a beautiful and challenging reading of the queer gaze in art, ' Many exhibitions claim to be a landmark show, but few live up to the hype. This one exceeds the hype. Queer is a beautiful, strange, hard-hitting and challenging exhibition where the central concept is like liquid mercury that, on hitting a hard surface, instantly scatters into innumerable droplets – each perfect in itself. More specifically, it is an examination of art history through a “queer lens”, art that spans millennia and that is drawn from the fabulously rich collections of the National Gallery of Victoria. The exhibition is not anchored in any specific medium but ranges over many art forms through more than 400 artworks occupying five gallery spaces.' back

Somdeep Sen, Why is India standing with Putin’s Russia?, ' India’s approach to the situation in Ukraine is hardly surprising or atypical. Since the establishment of diplomatic ties following India’s independence in 1947, relations between Moscow and New Delhi have been shaped by a “high degree of political and strategic trust”. Across the years, Russia and India routinely took similar stances and supported each other on contentious international issues.' back

Stephen Hawking (2002), What's the Total Energy In the Universe?, ' Stephen Hawking explains the concept of negative energy in his book The Theory of Everything (New Millennium 2002): "Two pieces of matter that are close to each other have less [positive] energy than the same two pieces a long way apart, because you have to expend energy to separate them against the gravitational force that is pulling them together," . . . Since it takes positive energy to separate the two pieces of matter, gravity must be using negative energy to pull them together. Thus, "the gravitational field has negative energy. In the case of a universe that is approximately uniform in space, one can show that this negative gravitational energy exactly cancels the positive energy represented by the matter. So the total energy of the universe is zero".' back