vol VII: Notes
2012
Notes
[Sunday 23 September 2012 - Saturday 29 September 2012]
[Notebook: DB 73 Spring2012]
[page 60]
Sunday 23 September 2012
The trinity is an ancient clue to the creation of the world. Father begets son and theiur bond is the spirit: two fermions and a boson.
position significant notation couples meaning, order and mapping.Complex numbers describe unobservable processes that lie hidden in the relationships between reals. Stewart, pp 59, 60
Our highest levels of ingenuity lie in the personal problems of ourselves and others, family, friends, and the general population, that is politics. So the order of technological analysis after the synthesis of theology begins with politics, the harmonious organization of effective societies, that is societies delivering increased fitness to all their members, inclusive rather than extractive. Acemoglu and Robinson. Acemoglu & Robinson
[page 61]
4. The mathematical community is a network
The mathematical theory of networks is built on Cantor's transfinite numbers, via the mathematical theories of communication and computation.Communication and function space <--> computation.
Cantor Universe is a recursive function space, each higher cardinal being the sets of all functions on sets of the cardinal before it. Adding one becomes equivalent to adding all possibilities.
Error correction by increasing the length of the signals is the fundamental constitutive fact of the Universe . . .
Let zero hour be 6 am and then the hours beginning with 0 are night, beginning with 1 day.
The beauty of writing for Communications in Pure and Applied Mathematics is that the mathematics can be taken for granted.
The digitization bootstrap makes communication error free and computation deterministic. The set of Turing machines (cardinal ℵ0) is the determinitic backbone of the Universe, bones, not muscles, and muscles are made of {dynamic, static}, ie fixed points inserted 'by hand' or by evolution / creation.5. Symmetry is nothing
Electron a sends a message to electron b via photon c. Feynman QED. Feynman
Capture that thought, a mapping of myself onto myself via
[page 62]
the complex software layers of my life to the ultimate hardware, the Classical God, initial singularity. Both initial singularity and god are products of the same line of thought: how do we understand the all powerful nothingness at the root of creation, the yoni from which creation Yoni - Wikipedia
Cantor Universe is a big enough playground for anybody, How do we cut it down to size - optimization = stationary action, a point of some equilibrium / linearity.
Shannon's Communication in the presence of noise is an analogue proof that digitization is necessary for error free communication. Claude Shannon
Acemoglu page 97: 1348 Ralph of Shrewsbury, bishop of Bath: '"Almighty God uses thunder, lightening and other blows which issue from his throne to scourge the sons whom he wishes to redeem. Accordingly, since a catastrophic pestilence from the East has arrived in a neighbouring kingdom, it is very much feared that, unless we pray devoutly and incessantly, a similar pestilence will stretch its poisonous branches into this realm, and strike down and consume its inhabitants. Therefore we must all come before the presence of the Lord in confession, reciting psalms."'
Gravitation = primordial entanglement.
Monday 24 September 2012
Index: The Roman Catholic Church serves here as our example of an
page 63]
elite, extractive, dysfunctional religion because I know it so well. You may draw similar conclusions about an extractive political system near you. I draw support for this picture from Acemoglu and Robinson.
The sun shines and I go on and the pump too, that waters my garden. One can easily imagine that an inclusive global society is both necessary and sufficient to see us through all the technological challenges that face us in the process of adapting to peaceful, sustainable life on a changing Earth.
Message is static and endures through space and time,. The sources and sinks of messages are dynamic systems that change from moment to moment, Messages are observable fixed points arising from and feeding into unobservable complex dynamics.
It is an everyday experience, starting with a idea plan, entering a phase of dynamic and often uncertain construction heavily influenced by events in the real world and finishing with a clear conclusion, cake, building, baby, a new complex fixed point (message) broadcast to the world,. This project began with the simple idea that the Universe is divine and after it reaches a publishable state will help build a new human world.
The local god of natural religion may be called Gaia, the Earth, driven by the Sun God whose origins go back to the beginning of the Universe, the Wide (non local) god. Wild, ie the Universe is Wild.
Wild = {action, fixed point} [={action}]
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Employ the Gruen mob to develop and propagate the idea.
Free enterprise = free search for fitness. But the organization must be such that no one is left behind, which is likely to happen in the elite vs masses scenario.
Mathematical community is a relatively peaceful, coherent and inclusive world where the elite, by publication, can pull the less elite along after them as the mathematical discoveries percolate through society to the beginnings of childhood education.
The beauty of being a greenie is that all [an adequate amount of] the scientific information is in place on on the way and one need only draw conclusions from this and advocate policy on the basis of these conclusions. Conditions in theology and religion, however, are much more primitive because it has yet to embrace scientific methodology, so there is little science upon which to form policy within the ancient religions, it must be brought in from outside, starting , like genesis, from the outside.
What we need first is a radical change in the politics of theology, making it into a science orthogonal to politics. In the beginning is politics. In the end is work (or not-work), heaven or hell.
We are inclined to associate maximum entropy with maximum chaos but Cantor shows that maximum entropy
[page 65]
comes with maximum order, a situation exploited by Shannon. Maximum order is the source of maximum entropy, some guess that stable points in the dynamics are stable because they have maximum entropy. So the entropy of the natural numbers exceeds the entropy of the continuum and creation follows Shannon's proof (see page 62 supra).
The theological elite are not interested in thus work becaiuse it undermines most of their raison d'etre: who needs a theological elite if God is here and now for all to see?
Tuesday 25 September 2012
Stewart page 180: Maxwell: 'In those days it was assumed that waves had to be in something.' Not so with probability waves, which simply record the frequencies of certain events which occur between the agents of the event, eg a 'collision' of two particles.
Half life works because each event is comprises of smaller events which also have half lives (frequencies) ie at the quantum level (isolated systems) there is no clock stepping out equal intervals at the end of which come event occurs, This randomness is overcome when a means for synchronizing (ordering) events emerges.
Life: how do we organize (order) the rather random behaviour of elementary events?
Unitarity reflects the fact that a quantum system is a source inthe sense of communication theory, with
[page 66]
a certain alphabet of events (eigenvalues) with a certain probability structure normalized to 1.
Stewart page 208: Schrödinger: 'His equations might be continuous but many features of their solutions would be discrete - including the energy levels.'
The discreteness enters through the back door, through the independent degrees of freedom of the Hilbert space. The continuity is present in the allocation of probabilities to the various dimensions of the Hilbert space, the basis states identified by the eigenvalue equation, an orthogonal subset of the states described by the Schrödinger equation. Structure arises rom structure, so the constraining box and the constrained structure arise 'simultaneously', that is what an event is, a structure meeting an isomorphic constraint, the 'collapse' of dual spaces.
Dirac in Steward page 213: 'The commutator of two quantum matrices is equal to the Poisson bracket of the corresponding classical variables multiplied by the constant ih/2π Poisson bracket - Wikipedia
Wednesday 26 September 2012
Rule of law = human symmetry. Acemoglu page 306.Science is part of the judiciary, observing reality and judging whether the parliament and the executive are steering the ship of state on the optimum course, well away from reefs and other hazards.
For power engineers, entropy is the enemy. But God is
[page 67]
not a power engineer but a thinker and a communicator and both are improved by the wise use of entropy.
One notices a strong but largely unconscious correlation between mood and the probability of realizing a particular dream which may be anything from pure happiness to getting a big beam successfully raised into position,. Often dreams (like flying)appear at first sight impossible and it is only by building a lot of anciliary technology (like trusses and high power/weight motors) that it becomes possible. My continuing source of pleasure is the hypothesis that the Universe is divine is gradually appearing to be consistent within itself and with the data, the root of a new scientific theology.
The elite have historically used the promise of pain to force their slaves to suffer the pains of inferiority. Catholicism and other religions have supported this practice by declaring pain a redemptive experience rather than admit its true nature, which is to tell us when things are going wrong.
The internet with its cloak of anonymity has allowed many of the otherwise hidden mental states in the community to be revealed. We learn a lot when an alpha male trying to shift the blame for rape compares women who are not completely veiled to raw meat, attracting flies, something which mere macho males cannot resist taking. Taj El-Din Hilaly - Wikipedia
Politically one wishes to overthrow the current theological elite and replace them with citizen scientists whose specific role is divining what is going on in any situation.
[page 68]
Free speech: are Allah and Mohammed so weak that they cannot stand a bit of criticism? I live in a country where free speech is well maintained. I am a baptized Catholic and an ex cleric who has come over the years to see the Roman Catholic Church as a rather evil empire and in Australia I have no fear of saying this. The Church in the arrogance of its infallible power does not concern itself with minnows like me. The State is indifferent to what I say about the Church. The Church, if I did become noisy enough to become noticed might try to shut me down through the courts, but it is not going to be able to behead me of just cut off my hands so that I cannot write any more.
etc . . .
Acemoglue & Robinson page 372: 'Nations fail today because the extractive economic institutions do not create the incentives needed for people to save, invest and innovate. Extractive political institutions support these economic institutions by cementing the power of those who benefit from the extraction. Extractive political and economic institutions, though their details vary under different circumstances, are always at the root of this failure.'
Quantum mechanics is purely time based. Its closest analogue is music, a complex serial stream. Space and memory are emergent. This time is not the time of a regular clock, but a series of events at random intervals spaced like radioactive decay of an infinite position of half lives.
[page 69]
Love - symmetry Politics, Economics, Religion, CultureThursday 27 September 2012
Acemoglu & Robinson: 'What is crucial is that growth under extractive institutions will not be sustained, for two key reasons. First sustained economic growth requires innovation and innovation cannot be decoupled from creative destruction, which replaces the old with the new in the economic realm and also destabilizes established power relations in politics. Because elites dominating extractive institutions fear creative destruction they will resist is and any growth that geminates under extractive institutions will be ultimately short lived. Second the ability of those who dominate extractive institutions to benefit greatly at the expense of the rest of society implies that political power under extractive institutions is highly coveted, making many groups and individuals fight to obtain it. As a consequence there will be powerful forces pushing societies under extractive institutions towards political instability.
page 456: Progress when the underdogs begin to organize.
Gamma functions make permutations into a continuum. Gamma function - Wikipedia
What Cantor had invented we now call function theory, The points in space no longer have postion but no magnitude, ther position represents a magnitude, possibly a vast magnitude, as the the space of mathematicians.
A&R page 462: '"If we do not control the television we do not do anything."' General Bello, Peru
[page 70]
Acemoglu & Robinson page 462: '"To uphold the leadership of the Party in political reform, three principles must be followed: that the Party controls the armed forces; the Party control cadres; and the Party controls the news."'
The sections of Development are superposed, so that we can talk about the politics of science, love, theology and so on. In practice they are superposed in a network was with each node experiencing them in a time division multiplexed way, that is the multiplexing of one undivided attention to a wide variety of different tasks.
Index: theological spring, let a million flowers bloom, and then cut off their heads.
Theology, politics and economics are all in the long run matters of life and death.
The world begins as 1 and by complexification generates the scalars 2, 3, . . . each of which in practice corresponds to a degree of freedom. The electron is spin up or spin down, but the probabilities of these states form a continuum when the electron is embedded in a larger system. From a software point of view there is only one electron, the electron algorithm instantiated in an infinity of different environments.
A network of mathematicians. We know from biological studies that a mathematician is an enormously complex network of molecules and cells and tissues all controlled by a central nervous system comprising many
[page 71]
billions of neurons and perhaps trillions of connections. We presume that the central nervous system is the physical substrate of mind. And we know that mathematics is a product of collaborating minds which communicate by physical means such as speech and writing. Here we concentrate on the written mathematical literature that connects mathematicians across time and space. Each mathematician is a potential source or recipient of a mathematical text, which is written in a symbolic language common to mathematicians throughout the world.
While we may consider the space of mathematical minds to be continuous, the mathematical literature is discrete.
We may guess that somewhere in Cantor's transfinite function space is a structure complex enough to be placed into correspondence with the internal processes of a working mathematician.
Friday 28 September 2012
Cordero et al Bacteria Science 337:1228 Cordero et al
The model outlined above is based on the Platonic interpretation of the relevant mathematics, which assumes that ℵ0 is a really big number corresponding to a fully resolved set of all natural numbers. But we assume that the real world is not Platonic in this sense, but is instead governed by Landauer's hypothesis that information is physical. This idea introduces a relativity of transfinity, induced by the low resolution (uncertainty) in real physical systems.
[page 72]
x. From Plato to Landauer
We can now discuss the modern quantum mechanical representation of the procession of the word postulated by the ancients.
This paper is part of a project to reintroduce theology to the spectrum of sciences, a position it lost about the time of Galileo when theologians refused to widen their data collection beyond their own writings and those of their predecessors. Theology is the study of God, traditionally everthing, so that theology is the traditional theory of everything, There seems to be a feeling among physicists that a theory of everything ids limited to an understanding of the alphabet of atomic (structureless, point) particles upon which the Universe is built. Such a theory does not directly address either the genesis of the universal system itself or its subsequent evolution to populations like ourselves that pursue conscious science as a community activity. Science, in the sense of effective knowledge of the environment, is present at all levels of the Universe. Theology might expand this point of view while remaining firmly founded on observable data. This is tantamount to shifting the focus of theology from the traditional invisible, mysterious and other god that is widely spoken of outside the sciences to the Universe itself. The present hypothesis is that the Universe is divine. A mathematical model of God requires a very large structure. I have long thought that Cantor's transfinite Universe is such a structure and the ubiquity of function theory and group theory in physics has reinforced this view. Fixed point theory and Landauer's hypothesis have opened as path to understand the evolution
[page 73]
of fixed points (ie creation) within one entity so simple that its essence is to exist (Aquinas ref)
We cannot represent the Platonic world except by imagination and meaning. Let N be the set of natural numbers {0, 1, 2, , , , n . . . }
Real - complex real . . .
How do mathematicians identify new fixed points: by using proofs to move from what is known into the unknown which can be explored in imagination. We get a greatly simplified version in histories of mathematics which emphasize the major steps forward and ignore all the petty domestic details of the lives of mathematicians who did the work.
Each symbol represents a computation, it is dynamic, it does something. A symmetry does nothing.
BINDING - MAPPING - CREATING.
Creation remains the same pure act but increases the number of stationary points. Einstein on specific heats. Pais pp 389-401
Feynman III 8-6 'The main problem in the study of fundamental particles today is to discover what are the correct representations for the description of nature.
An inverse opnion of many layers.
Feynman III 8-7 How states change with time,
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The classical God is one quantum of action. How does it plit into discrete, independent quanta of action like the father and the son? Observation of self, the photon going through two slits interferes with itelf. Let is interfere with one another.
Virtual: Feynman 10-6: 'a "virtual exchange" means that the phenomenon involves a quantum mechanical iterference between an exchanged state and a non-exchanged state.'
Saturday 29 September 2012
Stationary states of understanding emerge form the mental whirl, and can be written down, like this, transmitted to others, and understood by them to represent a feature of their own internal processes.
From symmetry to creation. For Aquinas actus purus implies omnino simplicitas, but this is not so, given the stationary points of action which subdivide it into acts, with continuous symmetries (ie nothing observable) between them. Insights (= fixed points) come 'out of nowhere', ie the vast unobserved process of a central neural networks.
Now weld my exhaust - error correction, maintaining my vehicle as a stable fixed point which determines its function as a legal and effective means of transport.
There is a creative advantage in poverty. If I had managed to toes the line (as the Church holds that i could without any constraint on my humanity) I would
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now be a senior cleric with all my needs paid for by the faithful, including all the transport I needed to do my job. But this was not to be, and I sit here in the hills scamming along like any other poor revolutionary building up my forces to descend upon the plains and show them there is another way of looking at life. First, however, my model is being tested against the experiences of my life without the blindness necessary to conform to an ancient militaristic organization.
Species / niche are duals rather like vector / form in MTW, dual spaces, dual vectors, with same entropy and mirrored structures, the species having a response to every variation of the niche if it is to survive [niche = independent variable] In Quatum field theory the species / niche duality is particle / field. The field is the niche in which particles live, and we may think of the field itself being a result of the particles, 'bootstrap of emergence'.
Emergence = more complex dynamics = more fixed points, [= increased entropy] = new codecs . New ways of communicating.
Simple souls, carefully nurtured in a closed scholastic academia cannot be expected to go too far astray, and if they do they will not get work and will have to turn to something else, like driving taxis.
Mathematicians / mathematical literature - general covariance, the gravitation that holds any community together, a direct consequence of communication symmetric with respect to the meaning of the communication.
Christianity is a meliorist dream based on the old notion of
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the underdogs begging favours from the elite. That model has proven a failure worldwide, not least by the behaviour of the Christian elite taxing the faithful. Now we know that the underdogs must organize for themselves if they are not to be subject to one extractive elite after another.
One may see the Catholic Church as a new field for the priestly elite to cultivate.
Development: Love / Judgement. What does not suit God does not work, like a badly soldered joint, a lie in court and so on. Actions imbued with love of god are likely to be judged good because by love of God we take all God's desires into account and so do a perfect job of soldering the pipes,. Judgement is invariant with respect to complexity, seeing only error relative to a certain desired outcome. Judgement works from moment to moment, not just on the last day, and it is up to us to define our society in a way which makes errors costly to those who make them and easy to detect. The social immune system, social security.
Deighton Sinker page 69: 'Only ignorance is invincible'. Deighton
A sure way to wealth is manipulating people, salespersonship, payment, blarney, reasonableness, violence are all means to get people to do what we want. Some people manage this a lot better than others, Patriotism; faith; deceit. In every trade there is a complex superposition of interests.
