vol VII: Notes
2012
Notes
[Sunday 15 July 2012 - Saturday 21 July 2012]
[Notebook: DB 72 Energaia]
[page 130]
Sunday 15 July 2012
Some principles:
1 There is nothing outside the Universe, it is unique and self sufficient.
2 All observable phenomena at all scales are discrete events
3 The only constraint is local consistency
4 It started very simple and complexified
5 The system is intelligent enough to make us [by itself, see 1]
6 The Universe has maximum size and complexity, since [it is] unbounded.
7 The only complete representation of reality is reality itself
8 Knowledge is made possible by symmetry
TOPOLOGY - PIPEWORK (Pascal's principle, conservation)
Metric is irrelevant in topology, where one imagines smooth expansion and contraction of continua within topological boundaries.Polya & Latta page 75: 'Differentiation is the most important analytic operation that we can perform on real functions. . . . A complex function of a complex variable is equivalent to a pair of rreal functions of real variables; only if the pair is exceptionally well assorted can we differentiate the complex function.' Polya & Latta
The fact that photons (unlike particles with rest mass) lose energy as the Universe expands suggests that they are not 'independent' particles, but are in some way mapped onto spacetime and lose energy as space 'expands'. This can be explained by the principle of equivalence in, for instance, the rocket thought experiment.
Polya page 90: ',. . . a differentiable complex function of a complex variable is represented by a sourceless and irrotational field.' [maybe just like the baby Universe]
[page 131]
What does the inexorable progression of the proper time at the velocity of light mean in computing terms? [proper time is maximised in the frame at which the event is at rest]
Business runs government vs government runs business: Japan / China. US = Japan.
'Both the real and imaginary parts of a differentiable complex function satisfy Laplace's equation.' page 96. Laplace's equation - Wikipedia
Satisfaction = beatitude. Aquinas 608
Monday 16 July 2012
All we have to do is imitate the outcome of the eigenvalue equation which tells us the frequency and structure of events via the eigenvalue and the corresponding eigenfunction.
More complex means a more constrained (orthogonal) alphabet which founds an exponential (n!) increase in the complexity of the next layer. This complexity is cut down by selection, It may be that inn the fully concrete system everything is effectively random (maximum entropy) and the only complete representation of reality is reality itself.
What is the information of a conservation law? Nothing, because the only information is carried by change. To read a static page is to make it dynamic - relative motion, We might assume that all motion is a logical process.
Complex functions are the equivalent of two coupled real
[page 132]
functions, the coupling represented by the Cauchy-Rieman equations. Cauchy-Riemann equations - WikipediaVelocity is an angle, the relationship between two dimensions, distance and time. [so connect to phase?]
Mappings a different way of saying the same thing so reality repeats itself in many different ways by mapping onto itself.
Tuesday 17 July 2012
All the continuous functions of physics begin with discrete approximations and take the limit. Insofar as the limit gives an exact version of the actual function, we might assume that the discrete 'approximation' in fact described the situation exactly in the region of low cardinal numbrt.
Spacelike separation is equivalent to orthogonality, no communication, no overlap.
The continuum is nothing and can carry no information. The quantum computers are making the same mistake as the mystical theologians who whing that an omnino simplex God can make and know every event in the Universe [with no internal structure to map to such events]. A mystery, of no help to us.
The size of the quantum of action has not changed but we might see that the Universe started off as just one wuantum of action which has multiplied up to the current number which is a measure of the entropy of the Universe. Energy is conserved by[page 133]
decreasing the frequency of the multiplying actions, There are ℵ0 distinct actions (angels, computers, Turing machines) but there may be any number of instances of each.
Action is invariant but not necessarily conserved.
Energy is conserved, but is not invariant, depending on relative velocites of frames.
Writing is my new sex. Sorry to feel the sex going, really, but there seem to be drugs for it if necessary.
My life is one complex quantum of action with a huge number of stationary points.
INFORMATION = OBSERVABLE CHANGE
The entropy of the digital world is greater than the entropy of the continuous world and so the continuous world does not have the variety to model the real world in which every experience is a discrete event, a change of state. The states (wave functions) are not observable, but their changes are
Superpostion: The superposition of meanings and nuances in a word describe a sort of Feynman diagram or network on which each possible meaning is stored in a 'neuron', and coupled to the word in question by links of greater or less strength (frequency of communication). The quantum
[page 134]
mechanical view of superposition is unphysical because there is no way continuous functions can represent all the information stored in the superposition. This concept is an artefact of the fact that the superposition is the set of solutions to a differential equation, a wave equation that holds for an infinity of waves of different frequencies, each 'stored' in a dimension of Hilbert spaceDIMENSION = DEGREE OF FREEDOM = MEMORY
The Hilbert pace is the memory, the operators the computers. A measurement is an operation with an outcome, the event we call measurement, the emission of information by the observee, its reception by the observer, represented, we find, by an amplitude and its conjugate.
The physical interpretation of complex numbers. The physical embodiment of complex numbers.
Landau Information is physical: an item of information is a physical event. In the gossip world, the biggest physical events are a and b are now lovers, or a and b have split up.
Wednesday 18 July 2012
Every day I feel that I am circling around the problem and seeing more small features, that i hope will eventually coalesce into a comprehensive dual of reality and enable me to communicate
[page 135]
effectively with my environment. In the long run if the world is φ, my theory is φ* and their product will be an actionable model of the world, an observation.
Looking for salvation beyond the Planck Scale, keeping to the tradition of mystery. Greene: The Elegant Universe
Office workers only have to deal with the complexities of their own kind, fieldworkers have to deal with everything nature can come up with, and managers mediate between the two.
h is the physical infinitesimal. Quantum of action = 1 transfinite bit of information, a trabit, tranbit (cf bit, qubit, maybe tit. binary digit, transfit, trit, [trait]).
Qubit considered to contain an infinite quantity of information because the coefficients a are b and complex (and so continuous) numbers in |q> = a|0> + b|1>, |a|2 + |b|2 = 1.
Planck's constant is invariant with respect to complexity.
The task of science is to map the world by establishing correspondences between events in the world and events in a model of the world. We choose to model the world using the transfinite numbers, each of which can be mapped onto the fixed points of the system of interest. If, during a modelling exercise, we find that we do not have enough numbers to create a one to one correspondence between the model and the world, we can always use the resources that we have to move to the next transfinite number and test that. Does all this mean anything?[page 136]
Quid est hoc quod est esse. Did little Thomas really ask his nursemaid that? Is it a legend that I have heard? Is it a legend that I made up?
In the real world religions have to compete for their capital, which is adherents. We want a church of believers, like the church of scientists who arrive at their ideas not by democratic process but by trying to track the world, which includes human decision processes.
In natural religion our guidance comes not from on high but from the minutiae of experience.
Decision making in a Turing machine is deterministic [not really a decision?].
We must reform the Roman Catholic Church so that it can peacefully cohabit with all the other churches in the world. A generally covariant (completely symmetrical with respect to people) church.
MTW page 130: 'Spacetime contains a flowing "river" of 4-momentum. Each particle carries its 4-momentum vector with it along its world line .. . quantified by the stress energy tensor T
Thursday 19 July 2012
We see many events as continuous 'within' themselves but they are nevertheless a discrete object in their totality, like a raindrop. When we examine an event more closely, however, we see that it comprises many sub events, each with the same properties of continuity and discreteness. We may apply
[page 137]
this idea to the whole Universe, which we take to be a definite entity whose 'interior space' is continuous, Going in the opposite direction, we see that the smallest possible event is measured by the quantum of action, and such an event has no 'observable interior'. but can only be treated and understood as an irreducible unit. It is here that we would like to introduce logical continuity, the interior of a quantum of action being modelled by a Turing Machine whose interior is invisible because it is a deterministic process that cannot be interrupted by observation but must go though until it is complete when it emits an observable event.Science 336:1615 'Unlike human brains today's computers deal with processing and memory separately. Data are constantly moved around resulting in a speed and power "bottleneck".'
Just about all dynamic activities come down to timing, hit or kick the ball at the right moment, operation of computers, etc. Memory takes the criticality out of timing, as building a house each step has a stable endpoint (like each step in a Turing Machine). But maybe the Lagrangian method tells us there is a balance between memory and processing, 'saved' time and 'real' time. In the case of relativity, proper time is maximized in the frame where there is no motion.
Here we see something like a Lagrangian, (time)² - (space)² where we can relate (time)² to kinetic energy and (space)² to potential energy (Inteval)² = (time)² - (space)² so time increases the interval, whereas increasing space reduced the interval.
[page 138]
Since a network needs addresses (coordinates) to work in the first place, we no not need to provide an 'outside' coordinate system as is done in physics.
So we want to explore the idea that the Universe is like a digital computer network, not necessarily binary. In fact we allow numbers to transfinite bases. I am still in the forest and every time I try to plot a logical course through the snippets I have I have got lost, but hope one day to complete the circuit. Lonergan, emergent probability [schemes of recurrence]
The general method of creation is to increase resolution by error correction and to increase error correction by exploring the increased resolution rising from ordering.
Zygon: generalized ecumenism <--> general covariance <--> general relativity.
Communication with God: 'I will give you the keys to the kingdom of heaven; whatever you bind on earth shall be bound in heaven; whatever you loose on earth shall be considered loosed in heaven.' Matthew 16:19 Pius IX - Vatican I
Should be the other way around, with heaven, not God, calling the shots. The Popes, like the Caesars, have arrogated divinity to themselves when they should have left it to the Universe. It is the two year old mentality, placing themselves at the centre of the world.
Christianity is a childlike religion, claiming God for a Father and placing themselves in the centre of the world.
[page 139]
Misner, Thorne & Wheeler: Tangent space is outside the manifold so Einstein not so much disposed of bodies of reference as changed them to suit the hypothesis of general covariance. page 205. Network, on the other hand (we think) is its own 'coordinate' basis.Local = something it takes an action to get out of. Locations are deparated by actions, ML2T-1.
I feel that my thought processes are very slow, especially since it has taken me half a lifetime to get this far, but I can take heart from the observation that it took the Universe about 8 billion years to make the Earth and another four billion to come up with my species and me. God thinks slowly but in exceedingly fine detail.
Nothing can stop in 4-space? What about the null geodesic? [Maybe everything has proper time, even a photon, except that its 'rate' of proper time is zero. In everything else time marches on, and the speed of time is the fundamental invariant in the Universe, related to c?]
In logical continuity it is the operator that joins two points (the operation) and we visualize these operations as steps in a computation which the continuous paradigm signified by equations, eg F = ma. The operations act as the overlapping links in Aristotle's chain like definition of continuity: those things are continuous whose ends overlap. In quantum mechanics the logical connection between two states is measured by the 'overlap integral', a Venn diagramish idea.
Writing, talking to myself via a special code (writing). Reading back over the past one sees the meandering intersection of developing concepts, all of which are coupled in my mind and become conscious enough to remember and write,
[page 140]
every now and then, Writing is my version of the creation of a particle, a book which exists outside time and can be localized at many different points of space and time, via the internet. This may all end up n the net to last forever, if the necessary services are bought.
An operation represent a set of eigenfunctions that can operate on the input to give the output, a set of computers, ie a set of routines or procedures. Eigenfunctions can be shared when the sharers share bases.
The attempt to connect quantum mechanics and computation has blurred both for me, trying to get them so far out of focus tht they merge. The difficulty with quantum mechanics, as with ancient theologies, is that the 'works' that drive the phenomena are invisible and so must be conjectured through examination of the phenomena. What we see is that time is continuous and inexorable, whereas space is broken up into all sorts of things encased in some sort of nothing, the tabula rasa that Aristotle imagined in the newborn. Tabula rasa - Wikipedia
Quantum computation takes the simple route of discovering operations in 2D Hilbert space that mimic the logical functions, This works, but there is a resolution problem introduced by the Born rule,. We may set the wave function up to give us an exact result, but this 'exact' result is a superposition of possibilities which is only realized in many trials. How do we get deterministic computers to do this? By choosing and executing routines at random times, that is random phases relative to one another so as to create a time ordered permutation of outcomes.
[page 141]
We cannot see inside a quantum of action, yet we imagine it to be a continuous and differentiable process, hence the canonical method and Feynman's path integral, but why don't we just say that every cycle of a 'wave' is an event, a real particle is produced, transmitted and initiates another cycle. The output of one process establishes a memory state which is input to the next step, and we model this by logical elements sending messages to one another in step with a clock [or at random, as we see with particle 'decays']. The complexity of the message transmitted from one processor to another is a measure of the complexity of the particle transmitted. All this is really about the transmission of me from birth to death, I m s complex particle created incrementally by an evolutionary process which requites memory, like writing, DNA is a string of letter carrying a lot of information. Path integral formulation - Wikipedia
All the mathematics of physics might come from simply adding quanta of action together [with no reference to their 'meaning' that is the actual Turing machine that each represents].
The continuous approach works to beautifully that it seems stupid to go digital. But communication theory tells is that only a discrete Universe with orthogonal states can communicate without error, and so be stable. The 'collapse of the wavefunction' is demanded by error free communication. Wojciech Hubert Zurek
The digital thing is really a revolt against the Platonic conception of information as spiritual and replacing it with the notion that information is physical and the Universe begins with zero information and entropy and grows as we can see.
[page 142]
Is the finite velocity of light the constraint out of which the whole of the Universe is built. dividing the structure into spacelike and timelike relationships.The output of a tensor is a number. Tensor - Wikipedia
Force - Will Will (philosophy) - Wikipedia, Volition (psychology) - Wikipedia
Differential forms and exterior caluclus Misner, Thorne & Wheeler 90 sqq.
Should I stay or should I go, To stay means shut up, toe the line, and reap the benefits of solidarity; to go, free thought and economic uncertainty. My first big decision, to stick to my feelings in the order of preachers so I was asked to go left me poor but happy. Now I am a pensioner and I can continue my subsidized monastic career. Order of Preachers
Potential puts the tension into space, so a particle orbiting the sun follows a line between centrifugal force and gravitational attraction, the geodesic.
Reference frame = language / metric = meaning
Why do matrices work so well in physics? The dot product at the heart of matrix multiplication establishes the conservation of quantities that are shared additively between the dimensions (additive = linear) [in other words the point to a conserved quantity that is prior to and underlies independent degrees of freedom (dimensions)]
Friday 20 July 2012
[page 143]
Saturday 21 July 2012
Gödel and Turing: coding, computers recursion.Useful features of the transfinite tree:
1. Its tree topology
2. Recursive growth
3. Transarency (network)
4. Stationarity
A programmed computation is essentially communication between myriad atomic actions (logical functions), each represented by [the leaves] of the tree communicating with one another through the branches. One can count the depth that one must go down from the leaves to find the common node of any pair of leaves [this measures the distance between them].
Leaf level operations are the concrete reality of the world advancing through time. The concrete world is a spacelike slice.
COMPUTER ≡ NETWORK = superposition of trees.
We take the tree as a means of giving an address to every leaf by a genetic process of descent.
The world is configurable.
Cantor symmetry - conservation of energy.How big is transfinite? The application of continuous mathematics to physics is a one size fits all model that is somewhat incompatible with a world that grows in complexity from zero.
[page 144]
SYMMETRY = SIMPLICITYOmnino simplex = omnino symmetrix.
We construct a static picture of the Universe with the transfinite numbers imagines as a layered tree, the topm,ost layer (the leaves) being quanta of action.
The meaning of each leaf arises from the leaves it is coupled to through the branches. The cardinal of any branch is the number of leaves it carries,. The process of a branch is the sum of all the leaf processes. General covariance means that the leaves may be addressed by an entirely different tree. This is painful because it does not seem to coalesce into a consistent picture but it might be part of the story. The trouble seems to be that the transfinite numbers are not generated by branching, like a binary tree, but by permutation [think of each permutation as a branch from the junction represented by the signals to be permuted]., What we have to realize is how the leaf processes are organized to give the root process, how all the individual quanta of action involved in my life work together to make me a big quantum of action, 100 watts in 100 kilograms for 100 years (in round numbers).
The spacelike surface of action lies between past and future.
Each newborn idea looks beautiful but soon wrinkles with age and turns out not to be the panacea that is first appeared to be, a bit like romance really.
Signal (physical) carries message (logical)
