vol VII: Notes
2012
Notes
[Sunday 24 June 2012 - Saturday 30 June 2012]
[Notebook: DB 72 Energaia]
Sunday 24 June 2012
[page 52]
Since we develop continuous formalism by starting with a discrete formalism and then taking the limit, we have no problem losing the limiting step and keeping its logical precursor. The continuous paradigm puts great weight on differentiation and integration which consider all 'infinitesimals' to obey the rules of arithmetic. In the logical regime we abandon continuity except as an expression of logical contact and consider (in the case of integration) not the addition of a large number of increments whose size is determined by the function to be integrates, but a sequence of discrete processes that lead from one state to another via a sequence of intermediate states so we see the execution of a computer as the discrete 'analogue' of analytical integration.
. . .
Relativity of transfinity: the 'Platonic limit' envisaged by Cantor.
[page 53]
Jordan, Lee and Preskill (page 1132) write: 'In addition to establishing a new quantum speedup our results lead the way toward a quantum algorithm for simulating the Standard Model oe particle physics, which has new features (not exhibited by φ4 theory) such as chiral fermions and gauge interactions. Such an algorithm would establish that, except for quantum gravity effects, the standard quantum circuit model suffices to capture completely the computational power of our Universe.' Jordan, Lee & Preskill
At a huge cost in possibly unnecessary complexity, 10 000 to simulate to a 'state error' ε ≈ 1%, in a system which in the real world actually runs on 1 'gate'.
The appearance of this article is serendipitous in that it seems to emphasise again how far continuous mathematics is from explaining the world. As Noether proves, continuous symmetries define the fixed points of the world where nothing happens. The similarity to null vectors seems suggestive. Outcomes in the observed world (which is the only world we have to explain) are all guided by classical logic and quantum logic may be a misguided effort to connect the before and after states with a continuous function which is not possible because there is no entropy to build the information contained in the operation.
Continuous processes are reversible? Occur at constant entropy 'marks' being neither created nor destroyed. As Aquinas notes, human beatitude comprises the vision of God which in discrete language is a series of insights, collapses of the wave function, spiritual (mental) orgasms. Since this process is all in the imagination, insight need not be true to the world to be
[page 54]
pleasurable.
Given memory as in a Turing machine time is no longer of the essence, phase can stop still and wait for some other process to come into the correct relationship to do something (as when the clock triggers a read or write on the memory).Monday 25 June 2012
The undertainty on the 'uncertainty principle' results from uncoltrolled phases in computation.
What does the pseudo-Euclidean (Riemannian) metric mean? ds2 = dt2 - ds2? Proper time is maximized when distance is zero or minimized. In order to get to the football on time (ie ds = 0) we have to start early by an amount t = s/v. Spatial motion takes time [away from proper time], and the shortest possible time is at c. In my local system, if I am travelling at c relative to distant galaxies, they see my proper time as zero, whereas I see it as normal.
Saudi: Ethiopian Christians in gaol for praying in private home. . . . Asia News/Agencies
There is no smooth functin which converts Rn to Rn+1, which is a necessary device for increasing the number of degrees of freedom (entropy), a process we call creation, same universal dynamics, greater number of stationary points.Hobson page 50: 'The full equations of general relativity do not constrain the global topology of the spacetime manifold. Hobson, Efstathiou & Lasenby
[page 55]
We understand by analysis and synthesis [which are made possible by the nature of the world]. The purpose of analysis is to determine the 'alphabet' (basis states) of the set of phenomena of interest. Given the basis states, we can then use them to synthesize phenomena which (hopefully) match observed phenomena. Phenomenon = message from God.
Our epistmological principle is that every event that we observe is a message from God (which inlcudes our conspecifics) and so has some sort of theological interpretation. The 'basis state' of God is consistency, often not easy to see, but satisfying when we understand how events could be fitted together.
CONSISTENCY = SYMMETRY (No gaps)
Calculus works in the continuum where intervals have a measure expressed as a sum of effectively meaningless 'infinitesimals', is identical units [points].
A computer is a channel, a codec.
Reversible computations are built on two terminal devices.
Tuesday 26 June 2012
Bede is always very preoccupied, like many of his contemporaries, about the date of Easter which may seem to us almost irrelevant but was then a sign of unity, compliance and solidarity in the Church -- if you are not with us you are against us, see page 294 and Book V chapter 21. Bede
One can imagine that much of Bede's hagiography would have been believed by the nuns who taught me. The fundamental evidence for Christianity in Bede's mind seems to have been the miracles
[page 56]
Worked by holy men.
The tonsure was also a big issue - Book V Chapter 21.
Bede page 323: Comet in 729, also 678 (page 327)
Cover: Bede sharpening his quill.
We are still in many ways under the spell of the Christian mysteries that formed the background of Bede's life and work. In many ways we still worship a false God. By evangelism, the Theology Company hopes to reveal the true God.
Hobson page 121: '. . . the equation of motion of a photon implies that its 4-momentum, >i>p and hence its 4-wavevector k is constant along its worldline.' That is the photon is a representation of the continuum or contact between its source and its destination, proper interval τ = 0.
Each of the four dimensions of spacetime has an individual existence and can be represented by a vector, which vectors may be added and combines in various other ways to describe, for instance, the behaviour of electromagnetism described by Maxwell's equations. This is to say that the mathematical symbols in a book like Hobson all flt into a 1-1 correspondence with features of the real world. What we seek to understand is the mechanism behind this mathematical correspondence, and we might expect to see clues in the way we build up set theory from the empty set ∅ along the lines of Jech. So we might hope to see the axioms (alphabet) of the world = God!. The
[page 57]
big leap is to see that God is not a profound mystery beyond human ken but the everyday reality of our lives of which we have sufficient understanding to survive and increase our population and resource consumption in a dangerously efficient manner.
We religiously repeat the dogmas that (in classical mechanics) the frame of reference is completely arbitrary and has no bearing on the real relationships between the real events that we are framing. This is a good heuristic principle and gives us the theories of relativity, but it does not really apply when we get into the network to see what is really happening. Locally, every particle imposes some form of reference on what is sees, decoding the messages is receives according to its own codec (nature, experience), so we understand that animals may see their prey very well but be oblivious to the rest of the world, and so with us. The one track mind tends top see what it wants [or ids made] to see. The situation is formalized in quantum mechanics where an interaction can only take place if the interagents share a codec, that is an orthogonal basis [and an algorithm for encoding and decoding to and from this basis].
A consequence of the network model is that the abstract becomes real and is the lower layers that serve as the symmetries which are broken to give us the concrete Universe of experience.
Relatiovity works mainly with space-time but we like to thibk that energy-momentum is more fundamental and work from this toeard a network metric which will ultimately prove consistent with a space-time metric. The spacetime interval is invariant as the 4=momentum interval is invariant.
Let us assume that the transfinite numbers represent
[page 58]
solutions to the wave function (state function) of the Universe [ie fixed points].
Physics in general has no need for any numbers greater than the cardinal of the continuum, which we assume to be ℵ1. By invoking numbers greater than ℵ1 we open the field for a much more complex view of the Universe. Furthermore we no longer think of continuity in terms of cardinality but in logical terms, where a continuum is equivalent to a sequence of NOPs.
Wednesday 27 June 2012
Some heuristic principles:
1. The action associated with a complete computation is nh
2. An unmodulated continuum cannot represent information.
3. A Turing machine is a lagical continuum.
4. We expect and observe the universal network to be layered like a finite technological network.
5. Since the Universe begins with a singularity, we expect the lower layers of the universal network to be simple.
6. The Universe is inherently dynamic anf the fixed points that we observe (particles, messages) are part of the dynamics.
8. h is the practical infinitesimal in the Universe.
9. The only constraint on God / Universe is consistency.
10. Time and space are emergent processes representing layers 1 and 3 where the initial singularity of pure act is layer [0].
11. The Universe is quantized because it is an error free
[page 59]
network of communication.
12. Symmetry is nothing and things 'come into existence' be sending messages which are broken instances of come symmetry.
13. The dynamical 'gaps' between the fixed points are continua that change nothing from fixed point to fixed point, but the interaction of the fixed points themselves is logical. In practical computers we use the clock to 'hide' the transitions between logical states.
14. Velocity of light corresponds to the simplest algorithm in the Universe in a 2D world.
15. Coordinates give meaning to entities, breaking the underlying symmetry as in a computer where every NAND operation is the same and yet each has a unique address in the overall process of which it is part [takes its data from unique addresses and stores the result in a unique address]. All quanta of action are identical and so isomorphic to the initial singularity.
16. We seek a symmetry that defines the foundation of the human mind and all other creative processes, ie their common element.
17. Our equivalence principle - the Universe is suffused with creative intelligence.
Thursday 28 June 2012
Why do events follow statistical 'laws' like the absolute squares of amplitudes? What is the mechanism behind this appearance? So far we have relied on continuous mathematics to guide the search for this mechanism and we have had considerable success from Newton's celestial mechanics through Maxwell's equations for electromagnetism to the Standard Model but this model does have problems and limitations. The question is can we build an equivalent of better model using digital logic as exemplified by modern computers? The idea of the theory of probability is to explore the symmetries of the quantity we call randomness.
[page 60]
Randomness is founded in symmetry, that is indeterminism or unobservabiity.
Two faces of randomness: 1 is a symmetry, like random outcomes of tossing a fair die. 2 is maximum entropy, like the ideally coded signal using the alphabet of symbols equiprobably. We all this with the theory of measure. Kolmogorov: Foundations of the Theory of probability
Make up your mind. Everything revolves around the interplay of indeterminism and determinism, when to hang loose and when to act decisively.
We are haunted by indecision, will sometimes opt for a random decision (the toss of a coin) when there are no other grounds to decide.
Quantum mechanics conserves the current of probability. How is this done? By normalization.
Shannon enables us to design the ideal characteristics of an error free information source. How well does the Universe reach this bound? Perhaps the Lagrangian tells us.
Equalize potential and kinetic energy, that is memory and its inverse, transformation.
There are ℵ1 functions of the set of natural numbers onto itself, but only ℵ0 Turing machines,. What does this mean? Only an infinitesimal fraction of all possible functions can be deterministically realized.
[page 61]
Maybe the soul of a society is its public intellectuals, opinion writers, judges, professors, authors, poets, architects, engineers, and so on who purport to control social development, both spiritual and material. These people represent in effect symmetries of the body politic since they owe their publicity to the fact that many people take notice of them, they are celebrities.
Potential --> field --> action (force)
Coordinates related to some reference body (ie computer, brain) give meaning to events,. General relativity abstracts from such meaning by treating all coordinate systems as equivalent member of a symmetry or set of identical particles. (Bose-Einstein condensate). So gravitation gives us the interaction common to al particles regardless of meaning and the constraints imposed by that meaning, eg a bricklayers foes not have the constraints of a bishop.
Everywhere we look the laws of physica are the laws of intelligence.
Hobson page 150: 'If gravity is to be regarded as a manifestation of the curvature of spacetime itself and not as the action of some 4-force f defined on the manifold, then the equations of motion of a particle moving only under the influence of gravity must be that of a "free" particle in curved spacetime, ie
dp / dτ = 0where p is the particle's 4-momentum and τ is the
[page 62]
proper time measured along the particle's world line. Thus the world line of a particle freely falling under gravity is a geodesic in the curved spacetime.
Maybe Christianity marks the beginning of an obsession with cleanliness which has led to the population explosion.
There is a null vector corresponding to every velocity, not just c
Insofar as religion is the source of politics (since it sets the environment that determines what is politically acceptable) evidence based religion is the first step toward evidence based politics and hope of saving the world.
Why did the people go for Jesus? Because he was trying to save them from a disaster, 'Our Saviour', but what was the disaster? The 'Original Sin' explanation seems rather thin and late to be such a strong motivation. Maybe, we see from Bede, that the real danger was invading 'pagans' intent on plundering the wealth that Christianity has amassed through good government inherited from the Roman Empire.
How to save the world? I am slowly working my way into the prophet business : invent a forthcoming disaster and market a solution.
Friday 29 June 2012
Symmetry with respect to complexity built into the model
[page 63]
with Cantor's theorem.
Peskin and Schroeder. Peskin & Schroeder An Introduction to Quantum Field Theory
Action occurs in quanta h and any mathematical process that requires integration of a continuous action is unphysical, ie continuous phase is metaphysical.
Extremal Lagrangian corresponds to the cardinal of the computation process needed to achieve the transformation being considered, ie the motion from a to b. This is easy.
Continuum [a, b] establishes the equality or identity of a and b, since the continuum carries no information and so does not differentiate them.
Differentiate = to make different, ie by changing a symbol in the ordered set representing the differentiated entities. To have communication we need first to make a symmetry (carrier) and then break it (modulate it).
The various Feynman diagrams each represent a modulation of the phase of the overall event, from which we very simply compute a probability which can be compared by simple counting to the outcomes of experiments with counters. In our experiments we prepare the input particles and measure the outputs with various counters arranged geometrically around the interaction zone. CERN - LHC
We are giving computer network interpretation of the standard quantum field theory.
To every velocity corresponds a null geodesic, that is to every ratio of distance and time.
[page 64]
The overall design of natural religion is fairly clear. What we need to do now is to use the design to attract the capital necessary to build it.
The creative nature of the Universe is reflected in the fact that anything, no matter how simple, has a countably infinite array of inputs and an uncountably infinite set of outputs. From a simple fuck comes a family. Similarity with Feynman diagrams.
All the mathematical shenanigans of classical and quantum mechanics come down to conservation of energy and conservation of phase, since phase is measured in units of h = 2π, the ratio of circumference to radius in flat space.
Maximize proper time is to minimize action because one is moving purely through time and is stationary in space, ie following a geodesic through spacetime, sitting still, minimizing action.
Thermodynamics and error correction. Mechanical energy is perfect, zero entropy, one state, the boson. The heat engine partitions the energy of the hot source into one component with the same entropy as the hot coure but at the temperature of the cold source, and another component with zero entropy.
Quantum field theory brings with it entropy change not possible in reversible quantum mechanics.
We can put the ℵ0 Turing machines into correspondence with the natural numbers,
1. Derive a few properties of the transfinite symmetric network and
[page 65]
2. show that these fit quantum field theory and
3. The network of human relationships.
Photon is like the graviton but represents a 2D dynamic space rather than 4D, whereas electromagnetism has two charges and gravity only 1. Forces are bosons, can be packaged in bulk in a single state. And fermions? They maintain their individual distance from creation to annihilation. This theory is based on the notion that two fermions cannot be in the same state and to be at the same point in space is to be in the same stare, it is spatial location that gives meaning to states.
Gravitation does not need quantum mechanics to specify the large scale structure of spacetime.
Aquinas steadily prunes the tree of theological possibilities per sic et non.
Processors (nodes) and memories (communication links) are like dual vectors and both contain the same information and are united by some metric yet to be thought out, probably entropy. So the hot and cold reservoirs of a heat engine might be thought of as a processor and a memory, the reading ad writing being through the mechanical (deterministic channel).
All quanta of action are the same and all are isomorphic to the initial singularity. What distinguishes them is their position in the Universal process.
the IS, το ον, a mnemonic.
Theology is the study of God. The question of the existence or non-existence of God is from a methodological point of
[page 66]
view [little different] from the question that exercised our forefathers at the beginning of the twentieth century. Are atoms real?
From military to civil, a phase change from top down to bottom up, duals of one another that control society, one by violence, the other by consensus.
Peskin & Schroeder page 10 '. . . "quantize it" that is, reintepret the dynamical variables as operators that obey canonical commutation relations.' From numbers to sets of numbers.
Gravitation arises from the symmetry that all processes go through the initial singularity.
Saturday 30 June 2012
Peskin & Schroeder makes QFT seem very complex, making it very difficult to see how to build the world up from nothing,. The fact that continuous functions do not appear to carry any information helps, and we have to identify situations where there appears to be an actual computational operation like NOT, AND, etc.
A two input / one output device can be deterministic, whereas one input / two outputs (a fan out) can be underdetermined and therefore someone random in its output states.
We have a similar problem with the complexity of gravitation, but here too continuity and the ability of the network to ber its own reference body may clear the path as is the idea that the space-time dimensions are emergent. What we
[page 67]
really seek to explain is why things appear as they do, and this is an interaction of mater which does the dance, and the photons, which we use to see it.
The shape of traditional theology is to some extent explained by the problems which it has to solve: where do we come from? Where are we going? Why is there evil, death, war, disease, starvation etc. Is there any meaning in this chaotic world? The powerful anthropomorphic Gods of the so called 'primitive' theologies and religions provide working answers to these questions, but these answers have lost a lot of their credibility in the scientific milieu, so theology and religion are due for a major reconceptualization and overhaul. We can discount much of the fictional hypotheses that inform Christianity, while preserving the empirical and rational input that has come from the thousands of years of intellectual development that lie behind the Christian picture.
All the data that we can write down comes in the form of the differential equations that have been found so far to govern the evolution of the world system (Newton's "System of the World') which we like to call the system of the Universe or the Divine nature.
Jaynes: Christianity is a fusion of the 'moral consciousness' of the Hebrews with the 'rational consciousness' of the Ancient Greeks, drawn mainly from Plato, Aristotle and their successors. Jaynes: The Origin of Consciousness
Aristotle, having become the establishment, can be seen to havestood in the way of the development of modern science. On the other hand, modern science might never have come to be without the Aristotelian feeling that the World has a
[page 68]
settled nature of its own which we can understand through science and exploit through art. Christianity is a mass of contradictions arising from the difficult interface between morality and nature (which can be quite violent and irrational). We have a similar dilemma in modern times coming to terms with the fact that the world is quantized, and coherence in a quantum system is maintained by logical operations. So we build the world with set theory, the Cantor Universe. Universe (mathematics) - Wikipedia
Hobson page 158: 'Covariant differentiation is clearly a generalization of partial differentiation.' Really. More a generalization of ordinary differentiation where f(x + δx) - f(x) is the connection which is expressed in the infinitesimal changes of reciprocal spaces connected by a metric.
We can add orthogonal quantities linearly so there is no overlap.
The metric and the connection carry the same information? [one is 16 quantities, the other 64?]
'Let us consider some arbitrary vector field defined on a manifold with covariant components va [continuous and differentiable, of course, so not completely arbitrary]. The covariant derivative of va is given by
∇bva = ∂bva - Γdabvd
No curvature without vectors. Differentiation imagines things happening by an infinity of infinitesimal steps. This is ok in the Platonic world but cannot be in the real world where the minimum step is h So let us conceive of each step in the Universal process as a logical operation such as we find in our digital computers.
[page 69]
The curvature of space is a second differential, ie a process whose input is a similar process (maybe itself), which processes generate the complexity of the curvature tensor with four indices from vectors with one index.
Here we are trying to look at the general theory not as a forest of indices but a continuous process that might be reconceived digitally, beginning with NOP, which parametrizes a continuum or symmetry.
Curvature tensor defined in terms of the metric tensor gab and its first and second derivatives. A derivative is a ratio, like velocity.
A mind like a beehive, little neurons collecting honey which I decant into this notebook every now and then.
Lagrangian only sees first derivatives.
0D = no ordering, no distinction, just action a la Deus thomisticus.
Hobson page 159: 'a general mathematical device that is often used in reducing the algebraic burden of tensor manipulations.'
Haidt (The Righteous Mind New Yorker 25 June 2012 p 31): 'once group loyalties are engaged, you can't change people's minds by utterly refuting their arguments. Thinking is mostly just rationalization, mostly just a search for supporting evidence.' Haidt: The Righteous Mind: Why Good People Are Divided by Politics and Religion
Motivated reasoning (Kahan) 'When a person is conforming their assessment of information to some interest or goal that is independent of accuracy.'
[page 70]
Political parties tend to act as thought police to keep their constituents in line (Roman Catholic Church, Communist Part of China).
Wyden (New Yorker page 33): 'To bring about bipartisanship its going to be necessary to win something people con see and understand. That's why I think tax reform is as huge opportunity for the economy and the cause of building coalitions.'
Love makes the world go round, ie no individual within the Universe is stable by itself but need inputs and outputs to maintain its existence.
We assume the existence of a map between the real numbers and the natural like, following Descartes, and from a practical modelling point of view, it has been extremely useful.
Haidt : all partisanship is built on an underlying symmetry. Although it is broken by partisans, it remains in place as the space (set of coordinates) that gives meaning to the partisan positions.
Stress comes from trying to practice abstract virtues like poverty, chastity and obedience that are a large extent alien to human nature and are a consequence of the lack of correspondence between Christianity and reality. Christianity, based on faith and hope in a loving parent which will make everything right in the end. The insight of natural religion is that we have to be our own loving parent and look after ourselves on the only foundation possible, agree among ourselves what is to be done on the basis of a scientific understanding of our environment.
[page 71]
Continuum and discretum are duals, linked by Cantor's theorem (ℵn --> ℵn+1) and Shannon's theorem (ℵn+1 --> ℵn) as guessed so long ago in the transfinite oscillator, which creates and annihilates. An Essay on the Divinity of Money
Contradictions are hidden behind uncertainties which are represented by probabilities based on continua and measure theory. Once things become clearly defined (orthogonal) deterministic processing becomes possible leading to certainty, the 'conversion' of entropy (a symmetry or continuum, a pure number) into information, a fixed point that can be written down like ll this information derived from the combinatorial continuum inside my head.
Inflation and flatness. One wonders why the Universe is so spread out, instead of being a compact organism like an amoeba. Nevertheless, we imagine a lot of empty pace inside the atoms of the amoeba. Why do we have space -- to distinguish events. Why do we have events? Love makes the world go round, but it is the Cantor symmetry : we must become more complex because it is inconsistent not to.
Feynman diagram taken to a sufficient number of orders would embrace the whole Universe?
Sending informaiton in packets that can take a lot of damage before they become confused.
Stable structures are the result of the discovery of error free codes which we see in operation behind the formalism of qwuantum mechanics.
[page 72]
Augustine was among the first to mingle the Hebrew ideas of personality and the Greek ideas of Divinity in his theory of the Trinity.
The probability is the dot product of to phases?
The empty set carries no quality other than existence and so can serve to model the initial singularity which, like God, from our point of view just is. We have no idea where it came from.
We can bathe an atom in light and sooner or later it will absorb or emit a photon.
Quantum mechanics works purely in the time domain so all depends upon relative phases in the superposition of solutions to a wave equation (state equation).
A Hamiltonian matrix defines a network and the traffic on the various channels in the network.
Every now and then something materializes out of the mist (like this statement).
Gravitation is the foundation of creation because it can be its own source. It may in some way represent the fundamental driving force of the Universe, pure act (they say).
Here we propose a digital alternative to the harmonic paradigm.
Turing machine = closed chain of inference.
[page 73]
Network machine, on the other hand, can be interrupted and sent off on a different trajectory [collision?]
Digitization makes it possible to conduct deterministic calculations with relatively diffuse definitions [eg voltages] of 0 and 1, the only requirement being that they do not overlap, orthogonality.
The Cantor Universe contains a discrete scale of complexity which can be represented in a Universe of identifiable objects, ie numbers, since every number is unique, there is only one one, but many instances of one,
We take God as shorthand for everything and see theology as the traditional theory of everything which has lost some of its influence with the rise of empirical science.
