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vol VII: Notes

2015

Notes

[Sunday 6 September 2015 - Saturday 12 September 2015]

[Notebook: DB 79: Galileo Wins]

[page 65]

Sunday 6 September 2015

Go . . . and beat your crazy head against the sky. Lovin' Spoonful

Always looking for the biggest error to attack. Today's winner is from page 59: depreciation of the natural world.

Eureka Street: How Huge am I?

Dear Tim [Cook], I am an advocate of scientific theology and evidence based religion. Both of these pursuits are closely related to software. First, theology, the traditional theory of everything, tries to reverse engineer the system of the world. Religion, applying theological insights, attempts to establish peaceful and prosperous human communities.

The root of my advocacy is the assumption that the world is divine. on the whole, the intellgentsia have deprecated the world (the flesh and the devil) since time immemorial, assuming that it is not divine. If the world is divine all experience becomes experience of god and the foundation of scientific theology.

My story, so far, is available at naturaltheology.net.

Williams: 'The delicate alchemy of desire and demand is something Apple has proudly perfected. "A lot of times people do not know what they want until you show it to them," Jobs once said, which in retrospect acts as a neat summary for Apple's approach to the phone, tablet, laptop, desktop, music player and watch markets; instead of inventing these markets, it redefined them.

[page 66]

So redefine religion with the insights of information engineering from Cantor through Hilbert, Goedel, Turing and Shannon to the internet and beyond to the human network.

. . . to content and services after hardware perfected.

Monday 7 September 2015

My idea is that because Noether's theorem is established for continuous Lie groups, and a [real] continuum contains no information, continuity establishes a symmetry, that is a situation where nothing happens, for example symmetry with respect to time means energy does not change. It is conserved. Symmetries understood as 'nodes' where nothing happens [fixed points] are to be contrasted with god (and so the universe) which is pure action, where everything happens, by the via negativa not-god = not-action. The boundary on god is nothing, nothing observable, nothing to see 'outside' god. Emmy Noether: Invariant variation problems, Richard Feynman: Symmetry and conservation

Noether:

'What is to follow, therefore, represents a combination of the methods of the formal calculus of variations with those of group theory.'

'By a "group of transformations", familiarly, is meant a system of transformations such that for each transformation, there exists an inverse contained in the system, and such that the composition of any two transformation of the system in turn belongs to the system. '

Ie a group is reversible [a 'coder-decoder' or 'codec'] and this is the group expression of 'nothing happens' ie entropy (action) is conserved. Codec - Wikipedia

[page 69]

Eureka Street: Judicial power and the Pope. George Williams. In my opinion the Catholic Church is on the rocks and the root cause of the problem is the role attributed to the Pope as Vicar of Christ. We read in Canon law that there is no recourse from a papal decision. George Williams

The Link between Noether and the transfinite computer network is in the concepts of groupa and reversibility. This describes the hierarchy of symmetries contained in an event (the algorithms of the layers beneath the event, but the actual concrete event is irreversible. Time has one direction.

The big link here is the equivalence of logical and geometric continuity. In both there are regions of 'nothing happens'. Logical reversibility is an analogue of geometric continuity. The algorithm of light is responsible for its constant value [so this algorithm establishes a definite relationship between space and time]. Algorithms of action, energy and momentum are the symmetries of these quantities, everywhere present in their computation. The words lead me on, as maybe discovery in mathematics and physics where the choice of symbolism is seen to play a role in the discernment of meaning.

Quantum mechanics is a grpup theory, up until the observation, at which point the symmetry is broken, and a boundary is established between past and future. The arrow of time is the probabilistic prediction of quantum theory: every wave function eventually collapses = everything is ultimately observed, a tautology because everything observed is effectively (and empirically) everything.

Noether §6: the group theory of relativity.

'Hilbert enunciates his assertion to the effect that the failure of proper laws of conservation of energy is a characteristic feature

[page 70]

of the "general theory of relativity". In order for this assertion to hold good literally, the term "general relativity" should be taken in a broader sense than usual, and extended to the foregoing groups depending on n arbitrary functions.'

First we must 'see' it, and then go into the engineering details of how to construct the reality envisaged, ie prove it, because if it is proven it exists, at least in a formal sense, and if it has formal reality, it may become a symmetry of reality.

Quantum mechanics, insofar as it is invisible, ie limited to reversible computations, ie computations taking place at constant entropy (fixed bandwidth and memory [time-space].

Symmetry breaking mens establishing meaning, logging on to a network - speciation, defining and occupying a niche.

Tuesday 8 September 2015

Sometimes all this appears to be too good to be true. At other times it seems to be necessary. From an objective point of view, it is a fantasy that appears to have many contacts with reality. I probably rely most on my faith, the subconscious motivation that keeps me working on this on the chance that something will come of it. Not a sure thing, but better than buying lottery tickets.

I am slowly falling in love with the equation symmetry = algorithm = computer (turing machine). Here we get a bit stuck, however, in that we have been saying that geometric continuum is nothing, because it has no marks, but logical continuum depends upon

[page 71]

computation, which is a dance of marks and so cannot be written off as nothing, Are logical and geometric continuity duals, one a point, the other a space?

Maybe we can get out of this problem by pleading that both continua are invisible, geometric continuum becasue it has no marks, algorithimic continum becasue a watched computer never halts.

Wednesday 9 September 2015

Beautiful sunny day somewhat marred by the death of a good friend in an accident on a farm. Funeral Friday.

Sex, a wet continuum. Wets = binds loosely to.

An equation of continuity can apply to discrete entities like atoms, the steady state number of atoms entering a leakproof pipe equals the number leaving it. Same for quanta of action flowing through a computation.

We attribute the value of complex numbers in physics to the periodicity of computation, beginning with the clock frequency and growing as the computation becomes more complex until the period becomes the age of the universe.

How do we apply conservation laws to digital physics? Via quantum mechanics, and equations of continuity which explain conservation: energy flows without creation or destruction. How does probability flow?: given an alphabet ai with probabilities pi which flow (in a dynamic alphabet) to maintain the normalization i pi = 1.

[page 72]

We understand conserved flow and complexification by a system like our blood flow, two trees joined at both roots and branches [leaves]. The plumbing of the Universe. Is this the whole content of Noether's theorem for 'fields'?

Neuenschwander page 107: 'If the functional is extremal, then the Euler-Lagrange equation holds. When the functional is both invariant and extremal, then the Rund-Trautman identity together with the Euler-Lagrange equation gives immediately the Noether conservation law. In the case of our field φ(t, x), the Noether conservation law offers an equation of continuity

μ jμ = 0

where the current jμ stands for [a function of the] generators of a transformation .' Neuenschwander

N page 61: 'Consider transformations described by a continuous parameter that can be varied starting from ε = 0. The identity transformation ε = 0 makes no change whatever. As ε increases, the differences between the original and the new coordinate system becomes larger and larger. Noether's theorem deals only with continuous transformations.'

The digital model of the network trees gives us an additive arithmetic (superpositional) description of conservation. [conservation is local in that every 'bidirectional interaction' involves zero space-time interval, quantum mechanical, prior to space].

The constraint of continuous mathematics adds considerable complexity and difficulty to physics.

Thursday 10 September 2015

[page 73]

Still in trouble with symmetry, although the general drift seems clear, am not yet able to integrate Noether and my would be digital world. The problem seems to revolve around the relationship of the two continuities. Today I have no other demands so I can spend a solid day on it and hope to have an outcome by bedtime.

The formal mathematical view is that motion is relative and it really makes no difference if we think of the physical system as stationary and the reference system (reference body) moving, or keeping the reference system fixed and letting the reality move, as Newton does.

Einstein's general relativity is the first major example of the modern view. All disussion requires duality, we say that a is b or not-b. Einstein used a mathematical manifold to name the events in the world. From the point of view of this naming, every event is unique [and has a unique name or coordinate]. He then imagined all possible continuous motions by describing the relationships between two different namings of the events of the world [one of which is a continuous transformation of the other]. He was able to produce a fixed relationship which governs the continuous transformations between namings which is a set of ten fields described by ten differential equations called the metric. The basic point of all this is that no matter how we look at a set of space-time events, they always have the same metric relationship to one another. How we look at them does not change [them].

Extremal action corresponds to extremal code, ie most or least efficient.

Friday 11 September 2015
Saturday 12 September 2015

phys09Gravitation

Gravitation introduces proper time which is related to proper energy

[page 74]

by the Planck-Einstein relation and modelled by the circle group. Planck-Einstein relation - Wikipedia, Circle group - Wikipedia

The Heuristic structure is built on digital layers, like a network increasing its entropy by one unit with each added layers. We consider gravitation as an algorithm in the energy layer, the second after the primordial layer of action.

Einstein worked in 4D space-time but gravitation predates the existence of space, which arises as 2D fermions, 3D, 4D which is complete be3casue no crossed wires. Each new dimeson of space complxifies the metric, adding 1 + 2 + 3 + 4 = 10 dimensions to the 4D metric, gμν, μ, ν, 0 .. 3.

Misner Thorne and Wheler page 302: ' "Every physical quantity may be describable by a (coordinate free) gemetric object and the laws of physics must all be expressible as gemetric relationships between geometric objects. This view of physics, sometimes known as the "principle of general covariance" pervades twentieth century thinking. But does it have any forcible content?' No/ General covariance does not spearate viable from non-viable theories. Yes? ' "Nature likes theories that are simple when stated in cordinate free geometric language. According to this principle, nature must love general relativity ad it must hate Newtonian theory. Of all the theorires ever concocted by physicists, general relativity has the simplest and most elegant geometric foundation [three axioms: (1) there is a metric; (2) the metric is governed by the Einstein field equation G = 8πT; (3) all special relativistic laws of physics are valid in local Lornetz frames of metric].

The basic measure in general relativity is proper tie whose definition becomes more complex (involving space [= memory]) as the Universe complexifies: energy (T), c (TL-1) (boson), fermion (TL-2), moving fermion TL-3.

Takes four layers to get from God to 4-space. NOP. NOT, NAND, Fermion [that is a space big enough to model a computer].

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Further reading

Books

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

Coulson, Charles A, Valence, Oxford University Press 1985  
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Deutsch, David, The Fabric of Reality: The Science of Parallel Universes - and its Implications, Allen Lane Penguin Press 1997 Jacket: 'Quantum physics, evolution, computation and knowledge - these four strands of scientific theory and philosophy have, until now, remained incomplete explanations of the way the universe works. . . . Oxford scholar DD shows how they are so closely intertwined that we cannot properly understand any one of them without reference to the other three. . . .' 
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Feynman, Richard P, and Robert B Leighton, Matthew Sands, The Feynman Lectures on Physics (volume 3) : Quantum Mechanics, Addison Wesley 1970 Foreword: 'This set of lectures tries to elucidate from the beginning those features of quantum mechanics which are the most basic and the most general. . . . In each instance the ideas are introduced together with a detailed discussion of some specific examples - to try to make the physical ideas as real as possible.' Matthew Sands 
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Neuenschwander, Dwight E, Emmy Noether's Wonderful Theorem, Johns Hopkins University Press 2011 Jacket: A beautiful piece of mathematics, Noether's therem touches on every aspect of physics. Emmy Noether proved her theorem in 1915 and published it in 1918. This profound concept demonstrates the connection between conservation laws and symmetries. For instance, the theorem shows that a system invariant under translations of time, space or rotation will obey the laws of conservation of energy, linear momentum or angular momentum respectively. This exciting result offers a rich unifying principle for all of physics.' 
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Popper, Karl Raimund, Conjectures and Refutations: The Growth of Scientific Knowledge, Routledge and Kegan Paul 1972 Preface: 'The way in which knowledge progresses, and expecially our scientific knowledge, is by unjustified (and unjustifiable) anticipations, by guesses, by tentative solutions to our problems, by conjectures. These conjectures are controlled by criticism; that is, by attempted refutations, which include severely critical tests.' [p viii]  
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Rasmussen, Carl Edward, and Christopher K I Williams, Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning), The MIT Press 2005 Amazon editorial review: 'The book deals with the supervised-learning problem for both regression and classification, and includes detailed algorithms. A wide variety of covariance (kernel) functions are presented and their properties discussed. Model selection is discussed both from a Bayesian and a classical perspective. Many connections to other well-known techniques from machine learning and statistics are discussed, including support-vector machines, neural networks, splines, regularization networks, relevance vector machines and others. Theoretical issues including learning curves and the PAC-Bayesian framework are treated, and several approximation methods for learning with large datasets are discussed. The book contains illustrative examples and exercises, and code and datasets are available on the Web. Appendixes provide mathematical background and a discussion of Gaussian Markov processes.' 
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Taleb, Nassim Nicholas, The Black Swan: The Impact of the Highly Improbable, Random House 2007 Amazon editorial review From Booklist 'In business and government, major money is spent on prediction. Uselessly, according to Taleb, who administers a severe thrashing to MBA- and Nobel Prize-credentialed experts who make their living from economic forecasting. A financial trader and current rebel with a cause, Taleb is mathematically oriented and alludes to statistical concepts that underlie models of prediction, while his expressive energy is expended on roller-coaster passages, bordering on gleeful diatribes, on why experts are wrong. They neglect Taleb's metaphor of "the black swan," whose discovery invalidated the theory that all swans are white. Taleb rides this manifestation of the unpredicted event into a range of phenomena, such as why a book becomes a best-seller or how an entrepreneur becomes a billionaire, taking pit stops with philosophers who have addressed the meaning of the unexpected and confounding. Taleb projects a strong presence here that will tempt outside-the-box thinkers into giving him a look.' Gilbert Taylor Copyright © American Library Association. All rights reserved 
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Links
Circle group - Wikipedia, Circle group - Wikipedia, the free encyclopedia, 'In mathematics, the circle group, denoted by T, is the multiplicative group of all complex numbers with absolute value 1, i.e., the unit circle in the complex plane or simply the unit complex numbers back
Codec - Wikipedia, Codec - Wikipedia, the free encyclopedia, 'A codec is a device or computer program capable of encoding or decoding a digital data stream or signal. Codec is a portmanteau of coder-decoder or, less commonly, compressor-decompressor.' back
Emmy Noether, Invariant Variation Probems (English Translation), M. A. Tavel’s English translation of “Invariante Variation sprobleme,” Nachr. d. K ̈onig. Gesellsch. d. Wiss. zu G ̈ottingen, Math-phys. Klasse , 235–257 (1918), which originally appeared in Transport Theory and Statistical Physics,1 (3), 183–207 (1971). 'The problems in variation here concerned are such as to admit a continuous group (in Lie’s sense); the conclusions that emerge from the corresponding differential equations find their most general expression in the theorems formulated in Section 1 a nd proved in following sections. Concerning these differential equations that arise from pro blems of variation, far more precise statements can be made than about arbitrary differential equ ations admitting of a group, which are the subject of Lie’s researches. What is to follow, there fore, represents a combination of the methods of the formal calculus of variations with those o f Lie’s group theory.' back
George Williams, Disquiet over Heydon's role difficult to dispel, 'This process should be abandoned and replaced with the decision being made by an independent judge. The problem is especially acute when it comes to royal commissioners. They lack the independence of the judiciary, need not be legally trained and as political appointees can be hired and fired by the government at will. The idea that such a person should determine whether they are disqualified from their own job is wrong in principle and runs counter to community expectations of how the legal system should operate.' back
Lovin' Spoonful, Darling Be Home Soon, back
Matt McDonald, Global pressure exposes the limits of Australian foreign policy, 'Even on the government’s own terms – a commitment to national security and the national interest – its foreign policy comes up short. National security requires international co-operation in response to increasingly transnational problems. Until the government understands this reality, its foreign policy will not genuinely serve Australia’s long-term interests. And Australia will certainly not be seen as a credible international player.' back
Michael Bradley, The slippery slope of justifying air strikes in Syria, 'There are two elements to this. First, is it possible to achieve the military aim of permanently degrading or destroying an armed insurgency from the air alone? Secondly, can you destroy an ideology? Both these questions are answered by history. No war has ever been won from the air. Ground forces are always required, one way or the other. A lot of IS fighters have been killed, and maybe eventually it can be fought to enough of a standstill that the remainder give up the cause. The cause will still exist. Our refusal to learn the lessons of past experience guarantees that the seeds of future wars are being sewn by our approach to winning the current one. If IS is the bastard child of Al Qaeda, it's not pleasant to imagine what the grandkids are going to look like.' back
Paul Daley, A dark chapter of history is tied up in the name of the Canning electorate, 'Some of the desert people agreed to help Canning blaze the track and find the water so that as many as 800 stock could be watered at each well, a day’s walk apart. Others were coerced – chained by the neck and fed salt so that maddening thirst would force them to lead Canning and his men to the water. Maltreatment of the black people was endemic.
This week, with the name Canning ringing in my head, I paid a visit to Kaninjaku – stories from the Canning Stock Route, an exhibition at the National Museum of Australia. Kaninjaka, drawn largely from the NMA’s extensive stock route collection, is based on a larger museum exhibition about the Canning track that toured Australia a few years ago.' back
Planck-Einstein relation - Wikipedia, Planck-Einstein relation - Wikipedia, the free encyclopedia, 'The Planck–Einstein relation. . . refers to a formula integral to quantum mechanics, which states that the energy of a photon (E) is proportional to its frequency (ν). E = hν. The constant of proportionality, h, is known as the Planck constant.' back
Remy Davidson, The quantitiative easing experiment if ending in global recession, 'But fear not. Goldman Sachs’ economists have spoken: “Global recession is very unlikely.” Ah, economists. People who are good with numbers, but lack the personality to be accountants.' back
Rhiannon Williams, iphone 6S launch: Apple prepares for life after the iPhone, back
Richard Feynman, Lectures on Physics III,17: Symmetry and Conservation Laws, 'The most beautiful thing of quantum mechanics is that the conservation theorems can, in a sense, be derived from something else, whereas in classical mechanics they are practically the starting points of the laws. . . . In quantum mechanics, however, the conservation laws are very deeply related to the principle of superposition of amplitudes, and to the symmetry of physical systems under various changes. This is the subject of the present chapter. Although we will apply these ideas mostly to the conservation of angular momentum, the essential point is that the theorems about the conservation of all kinds of quantities are—in the quantum mechanics—related to the symmetries of the system.' back
Tim Cook - Wikipedia, Tim Cook - Wikipedia, the free encyclopedia, 'On October 30, 2014, Cook came out as gay in an editorial for Bloomberg Businessweek, stating "I'm proud to be gay, and I consider being gay among the greatest gifts God has given me."[48] Cook also explained that he has been open about his sexuality "for years" and, while many people at Apple were aware of his sexual orientation, he sought to focus on Apple's products and customers rather than his personal life. He ended the article by saying "We pave the sunlit path toward justice together, brick by brick. This is my brick." As a result, Tim Cook became the first openly gay CEO on the Fortune 500 list. back
Wojciech Hubert Zurek, Quantum origin of quantum jumps: breaking of unitary symmetry induced by information transfer and the transition from quantum to classical, 'Submitted on 17 Mar 2007 (v1), last revised 18 Mar 2008 (this version, v3)) "Measurements transfer information about a system to the apparatus, and then further on -- to observers and (often inadvertently) to the environment. I show that even imperfect copying essential in such situations restricts possible unperturbed outcomes to an orthogonal subset of all possible states of the system, thus breaking the unitary symmetry of its Hilbert space implied by the quantum superposition principle. Preferred outcome states emerge as a result. They provide framework for the ``wavepacket collapse'', designating terminal points of quantum jumps, and defining the measured observable by specifying its eigenstates. In quantum Darwinism, they are the progenitors of multiple copies spread throughout the environment -- the fittest quantum states that not only survive decoherence, but subvert it into carrying information about them -- into becoming a witness.' back

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