vol VII: Notes
2015
Notes
[Sunday 30 August 2015 - Saturday 5 September 2015]
[Notebook: DB 79: Galileo Wins]
[page 50]
Sunday 30 August 2015
Pitch: On distinguishing true salvation from false salvation. (On Visible Salvation).
Salvation is a widespread notion in theological and religious tradition. It ay be achieving an eternity of bliss with the divinity after death, or it may simply mean having a peaceful and prosperous life. The opposite of salvation, damnation, may take the form of an eternity of excruciating pain in Hell to the failure or get the chosen lolly.
Traditionally religions offer the means of salvation. At one end of the spectrum we have purely spiritual means like prayer and fasting, and at the other engineering operations like building sewers or an effective government information processing system.
Here we look at salvation from the perspective of survival.
Trapped by the binding of unfulfilled desire..
We may think of a Turing machine as an algorithm, or as an instance of an algorithm addressed by a particular input or (as in the universal Turing machine) an algorithm for loading an algorithm to be executed in multiple instances.
Each algorithm is a symmetry or metric binding output to input.
Opportet distinguere [one should distinguish] holds for the world as well as for its intellectuals, and the goals of the intellectuals should (?) be to
[page 51]
track the world.
Universals are real, we call them symmetry, and they trace the history of the establishment of fixed points in the system.
We are looking for self sustaining (self reproducing) systems, those capable of attracting the nutrients for growth.
Monday 31 August 2015
A network has to furnish both privacy and publicity. private protocols use encryption to prevent intercepted messages from being deciphered. The number of possible encryptions is so great that everyone can have their own, a one-to-one correspondence. Publicity, on the other hand, requires plain language deigned to give some message maximum impact, ie maximum audience of people likely to do something, like sort their rubbish. Messages must be encoded in a way that couples to our 'psychology'.
Gravitation, content free messages, no addressing. These features are added onto the flow of four-momentum that is provided by the space-time in which we exist.
Gravitation is expressed as continuous differential equations that represent the average occurrences (probabilities) of various events The events themselves, as in quantum mechanics, are discrete like the reception of a particle.
Maybe the particles of gravitation are Higgs bosons (spinless bosons).
Speciation: subdivision of protocols.
[page 53]
Field: algorithm written in space-time, ie a computation (like multiplication).
Gravitation: mtaphysics, the integral heuristic structure of being Gravitation / energy. The conservation of energy is achieved by closed flows of energy through leakproof pipes, ie pipes that conserve probability, normalize the Universe. Prime matter = clock.
Tuesday 1 September 2015
God = initial singularity = initial symmetry.
Evolution of fixed points breaks symmetries. Each layer not only breaks the symmetries of the layer beneath it but creates new symmetries to be exploited by the layer above it and so on.
Let us guess that gravitation introduced one dimensional space and breaks the symmetry of time from simply a sequence of identical events to an ordered sequence of before and after made possible by the existence of memory.
Borders are artificial creations. Charter of human right guarantees us all access to everywhere provided only we are not impairing the rights of others [entering their private space uninvited?].
Complexification - symmetry breaking.
2D space-time can accommodate spin [the singlet state?].
Political evil entered the world when Moses went up the mountain, spoke to God and came back down telling everybody
[page 54]
that he spoke with the authority of God and would kill anyone who disputed his authority. He went on to slay many over the incident of the Golden Calf. Exodus 32
Spin is a symmetry, broken by various values ±½, ±1 etc. This links closely to computation as action, pysically embodied logic.
Symmetry and universals Symmetry - Wikipedia, Problem of universals - Wikipedia
Gauge invariance: the mathematics expresses symmetry, ie algorithm which gives a distinct answer for each set of input. F = m.a. m.a - constant gives us symmetry (indistinguishability) in force.
Ever since I first saw the Blues Brothers I have realized I am on a mission from God, The mission is to reveal the true God which has been hidden in plain sight by the spin doctors of Catholicism and the other major Christian religions. Dan Akroyd
Wednesday 2 September 2015
Layered network seems to provide natural explanation for law / symmetry / universals. This sort of thing bolsters my faith in the network model. I need this because the incredible complexity of the Standard Model defeats me. Nevertheless I have faith thay any computation of value in the standard model is computable, that is leds to a testable result. The network, limited in its power by the bounds on computability can manage this. What we are looking for are the algorithms that make the universe behave as it does. Taking a cue from Turing and recursive function theory, I am working on the idea that all computations can be realized by a suitable
[page 55]
switching among a space-time community of nand gates. Such a structure is capable of executing any computable function. Computability theory - Wikipedia, Sheffer stroke - Wikipedia
We embrace quantum information theory and accept it as the invisible explanation / computation of the universe. An algorithm is a symmetry coupling a set of inputs, say m and a, to yield a set of outputs we will call F. The machine computes F = ma This computation is verified if it is found to be consistent with measured values of F, M and a and we find this to be so in the space of Newtonian physics. Relativity requires that we redefine m. So a Turing machine as an algorithm is a symmetry, and a particular instance of that algorithm [is a fixed point in the symmetry]. Richard Feynman
The complexity of big programs is beyond comprehension if faced 'head on', but becomes manageable by breaking the overall process into orthogonal units which can communicate with one another to provide a system capable of meeting all the demands of the task to be automated.
So we begin with no-operation, then go to not, and and the other logical primitives. How are these represented, stored and brought into communication with one another?
passage of time — rotation of vector — complex multiplication
state at a moment — superposition of basis states — complex addition.
The game is to couple the recursive complexification of the universal network with the observed layers we see in the structure of the world.
We might say the foundation of mathematical theology
[page 56]
is mathematical metaphysics, which traces the evolution or development of mathematics from simple axiom systems like logic and set theory.
A mathematical statement owes its meaning to the milieu in which it exists, which is the mathematical community, extended in both space and time. History of mathematics. We begin with things with no actual meaning, a set of points and some axioms and build things upo from there, like Euclid. If we were a God deciding to have fixed points, (or being required by consistency to have fixed points) where would we start? History of Mathematics - WikipediaOne requirement of the starting point is that it has a future. We are here because our starting point led to us, Some pople think this points to a very precise tuning of the initial state of the universe which must have been done by a creator outside the universe, Others think everything is possible that does not involve contradiction, since contradictions are dead ends beyond which progress must take a random jump for one option or another, From the point of view of the clock driving the world, the fundamental logical operation is not. There are an infinity of dualities that can model the connective not, male is not female, one is not two and so on: not = orthogonality, nothing in common, Movement north is independent of movement east
Two extremes: live completely for one-self; live completely for others. They are always superposed, as Adam Smith suggested, although controlling the hidden hand is important. Invisible hand - Wikipedia
Thursday 3 September 2015
We are seeking a union of heaven and earth that will
[page 57]
bring meaning to our earthly lives.
Catholicism: The symmetry that underlies global diversity. Entropy is maximized when we have symmetry because everything becomes equally possible, giving the culling (selection) process the maximum range to choose from and it will select for a finite number of species, fixed points in the genetic continuum. The weed makes the sentence appear brilliant, although it will fade into the background as I continue [almost weightlessly] along my generalized (transfinite) geodesic. Geodesic - Wikipedia
4-space describes the simplest symmetry for a physical computing machine: a clock and three dimensions of wiring, so there are no crossed wires and so confused signals. The diron again. [search site]
Symmetry breeds complexity by not-caring, not controlling, and the higher layers explore the complexity for stable species (forms).
Higher layers must curate lower layers to ensure their own survival, and so everybody has a vested interest in keeping space-time as a perfect abstract model of a communication system, giving orthogonal adresses / communication channels and a clock to synchronize everything, ie keep it in the correct phase relationships within the superposition. We look after the space that looks after us, or should so so.
Probability is conserved because action is conserved [conservation demands that every creation is mirrored by an annihilation ?].There are only so many acts to go around, and if one is happening others are not, so the probability of a source a emitting the letter ai, plus the probability of emitting some aj ≠ i is 1. Probability of p and [or] not-p is 1.
[page 58]
A fundamental error of Christianity is denial of death and a huge legend that has been constructed (The History of Salvation) to rationalize this denial.
God = unconscious = invisible process, the continuum that underlies the discrete observations which appear here as sentences and paragraphs. Although these notes are made at random, they have a certain coherence due to the arising from the same subconsious dynamism.
Friday 4 September
The Catholic business plan: bring its doctrine into conformity with science. The Catholic Church has been a resounding success, beginning in the first century ce with a few dozen workers, now become a global enterprise with as many clients as facebook. But it has fallen out of step with [many] of its potential users.
The written intellectual history of the Church begins with the prologue to the Gospel of John and continued to develop vigorously until the fourth century when it became the official religion of the Roman Empire and codified its beliefs. Much of this work was done against a background of Platonic metaphysics, which maintains that real reality is outside this world.
The next big development in theology, metaphysics and science coincided with the beginnings of the university system and the assimilation of Aristotle into Medieval Europe.The result was the work of Saint Thomas, whose writings remain (officially) central top Catholic theology (canon 252). Aquinas produced his synthesis by merging Catholic dogma and
[page 59]
Aristotelian metaphysics. In particular, Aristotle produced the notion of potency and act, and used it to argue for the existence of a first unmoved mover. This argument was taken over to the letter in Thomas' first proof for the existence of God, which remains a tacit foundation for the Catholic Faith. Code of Canon Law: 252
One may see Bernard Lonergan as the Aristotle of the twentieth century trying to move Aristotle and Thomas' ideas from the physical to the psychological world. In his book Insight he interprets the Scholastic potency and act as the ability to understand and actual understanding, indicated by the act of insight. Instead of motion in space we have motion in mind. Lonergan then goes on to use this idea to argue for the existence of a transcendental world beyond human ken, the traditional Catholic position. Although Aristotle probably thought the first mover is part of the universal system, Catholic theology places God outside the World. Lonergan: Insight: A Study of Human Understanding
This position has never received universal assent and its position is significantly weakened by the development of quantum information theory. Lonergan was right: reality is psychological, where by psychological we mean an information processing system. He was wrong, however, to consider the universe as a puppet of a transcendental power. The transfinite psychology of the universe is sufficient to embrace our traditional notions of God. Richard P. Feynman: Simulating Physics with Computers
It seems that the intelligentsia have deprecated the material world since time immemorial This may be an attempt by the wealthy to demarcate themselves from the poor, the peasants, the miners and the tradespeople who did dirty jobs. So Aristotle and Thomas both thought of matter as potential, something that required an existing actuality to bring it into being. Now we know that matter is alive, the source of action, in fact performing all the roles of the creator.
[page 60]
A source can only emit one letter at a time, in a serial stream. Nevertheless is draws from a 'parallel' [or 'superposed'] set of letters, its alphabet, choosing letters at random or according to some algorithm or set of algorithms that give meaning to the serial stream and maybe influence its probability structure [with maximum entropy coding, probability structure will remain flat = random].
Two features of the world revealed by quantum information theory explain its divine power. First, quantum operations have the computing power of a universal turing machine, the mathematical upper limit of computability. Second, memory in quantum computation is described by state vectors in Hilbert spaces of finite or infinite dimension, This formal universe has infinite memory. Like God, there is nothing doable it cannot do.
. . .
Bring green religion back into politics.
Negotiation: opposed forces seeking an equipotential surface (symmetry) within which they can communicate (no crossed wires).
Quantum observation is formally identical to insight, differing only in complexity.
We transfer the analytical notion of limit into the network world through the notion of recursion. As we approach zero by recursive selection of epsilons and deltas in analysis, so we approach the concrete world by recursively adding layers of complexity as we localize our abstract theories.
[page 61]
This work is beginning to feel more like a job to me and less like an impossible fantasy. It now seems possible so see a realistic goal to be achieved by the psychological and theological approach to the universe, most generally the cybernetic approach, based on the fact that control is possible in some maps of human space.
. . .
Neuenschwander page xi: 'As perhaps the central organizing principle of postintroductory physics, Noether's theorem deserves to be more widely known among physics students . . . This book attempts to fulfill that need. Neuenschwander
Morrison, N page 1: 'For Leibniz, symmetry is related to the indiscernability of differences.
N, page 3: 'Rotating [a cylinder] and not being able to tell that it has been rotated captures the sssence of what we mean here by symmetry.'
page 4: 'The existence of invariance reveals an underlying symmetry.
'' "Invariant" means that a quantity's numerical value is not altered by a coordinate transformation. "Conserved", in contrast, means that within a given coordinate system the quantity does not change throughout a process. . . . Noether's theorem relates conservation to invariance and thus to symmetry.
'. . . what invariant quantities lead us to conservation laws? . . . These quantities are called functionals. In the functional we have a powerful concept that puts almost all of physics into a common language. Everything
[page 62]
wonderful I am going to relate here comes through these functionals.'
Neuenschwander page 5: Functional = definite integral.
page 15: 'Generally a "functional" is a mapping from a well defined set of functions to the real numbers.'
Saturday 5 September
Wikipedia: Noether's theorem. 'Euler-Lagrange d/dt (∂L/∂q̇k) = ∂L/∂q.
Thus if one of the coordinates , say qk, does not appear in the Lagrangian, the right hand side of the equation is zero and the left hand side requires that d/dt (∂L/∂q̇k) = d pk /dt = 0, where the momentum pk = ∂L/∂q̇k is conserved through the motion.The absence of the ignorable coordinate qk from the Lagrangian implies that the Lagrangian is unaffected by changes or transformations of qk; the Lagrangian is invariant and is said to exhibit symmetry under such transformations. This is the seed idea generalized in Noether's theorem'. Noether's theorem - Wikipedia
How do we carry Noether's results in infinite dimensional continuous manifolds to the transfinite computer network? Maybe because in the 'digital to the core' approach, conservation of action is guaranteed by the 'collapse of the wavefunction', ie all the continuous discussion
[page 63]
boils down to a series of quantum events, each measured by the quantum of action, the same quantum of action, in effect, flowing along the whole sequence of atomic events in the computation, finally appearing observably at the end of the invisible computation or flow. In quantum mechanics the collapse of the ψ is understood to be a discontinuous event at the conclusion of a continuous and invisible process. Here, however, we see the whole process as stepwise, and the observation a step is no different than any of the others, it just happens to be observed. In general we claim that action is conserved by the treelike splitting of large events into small ones [differentiation] and the inverse process (integration) of seeing a sequence of small events as one larger event, all of whose cardinals are the number of quanta of action involved in the event (set) we are considering.
We express space as a function of time: ∫t dt = ½t2. Tick of time to tick of space.
Functional is a mapping from a set of functions (instances of an algorithm) to the real numbers. An algorithm may have a stationary point, at which small changes in the input make minimal change to the output, ie it must be nonlinear.
Extremal: most efficient algorithm / least efficient algorithm.
Least efficient algorithm works simply with beans, and no position significant notation, ie identical particles, no ordering.
Space-time gives addresses (distinguishability) to otherwise indistinguishable (symmetric) particles. So all identical humans can be named by giving them an address, which may be a spacetime structure or may be simply a serial number (1D parameter), or even a symbol which itself has no natural order.
[page 64]
The fact that in gravitation one maximizes rather than minimizes the action sugests that gravitation works in bean counter mode with no meaning or ordering.
Neuenschwander page 37: 'Hamilton's principle and Newton's second law are equivalent—but only for classical mechanics.
I am in a sea of complexity, like the woodheap at Ferrers St, slowly sorting and assembling the pieces of wood to make a wall, as one makes walls with random pieces of stone.
N page 43: 'The world line of a freely falling particle would be that for which the elapsed proper time between two events was maximized, making the world line a geodesic in space-time.
Hamilton's principle selects for extremal algorithms, either the most or the least efficient. N page 47.
page 47: Why K - U? a) equipartition K = U
page 48; b) Proper time from A to B maximized.
page 61: Speed of light is frame independent so length and time become frame dependent.
page 61: 'Consider tranformations decribed by a continuous parameter ε that can be varied starting from ε = 0. The identity transformation ε = 0 makes no change whatsoever. As ε increases from zero the diffference between the original and the new coordinate system becomes larger and larger. Noether's theorem deals only with continuous transformations.
page 52: Metric converts coordinate displacements to distances.
