Notes
[Sunday 26 October 2008 - Saturday 1 November 2008]
[Notebook: DB 64 Gravitation]
[page 137]
Sunday 26 October 2008
We may think of quantum mechanics in terms of neural networks, and see a Hamiltonian matrix as a way of representing the synaptic weights of connections between different neurons.
Neural homeostasis might be equivalent to normalization in quantum circuits. Nature 455:912 Ramocki and Zogbi. Ramocki and Zogbi
The advent of quantum mechanics was preceded by a growing list of discrepancies between experimental observations and classical theory. (Park Park) A similar situation exists today with the failure of local realism, our inability to quantize gravitation, the existence of 'dark' matter and energy and the need to explain the evolution of intelligence without invoking god.
Park:
1. Wave/particle nature of light
2. Infinity in black body radiation
3. Stability of the atom
Since Hij = Hji*, diagonal terms must be real and off diagonal terms complex conjugates of their mirror images. If the off diagonal terms are 0, there is no probability of a transition between various states Hii, although they may have different energies which add up to the total energy of the system.
Feynman Quantum Mechanics Chapter 8: Feynman
Quantum amplitudes are in perpetual motion represented by the complex exponential exp(-i/h Et ), but the probability remains constant since the absolute square of this amplitude is 1. The difference in phase between two amplitudes, however, can have real effect on probabilities. Brandt and Dahmen
Monday 27 October 2008
The full Cantorian function space embraces everything that can be represented symbolically which is tantamount to everything which is tantamount to everything that can happen for a communicating entity. Every experience is a message, so the space of all messages and the space of all experiences are coterminous (or co-non-terminous).
Most religions and religious ideas have been developed by ruling class workers like the Buddha and the Pope who have promoted a system leading to their (corporate) benefit.
One wants to be a condensation nucleus, the archetype of a widespread phase change, like Jesus.
The key to survival is that every day, every moment, you gain more than you lose [although savings enable one to weather times of loss].
Religion: the art of life : the technology of peace.
There comes a time when things go from formal to real, from saying to doing, ie to financing and action. We see the details better in big deals, but the structure of the deal is universal.
[page 139]
Collapse of the wave function = encoding for transmission.
My idle youth is over. I must get my shit together and pass it on.
The basic task is mapping life to quantum mechanics. Why do we want to do this? Because it is a good idea. Quantum mechanics works very well in the physical realm, but it is also indifferent to complexity, and so we would expect it to work very well in every realm, and we use the network model to demonstrate this.
Mathematically, quantum mechanics meant moving from classical arithmetic space to quantum function space.
Veltman page 33: 'A vector in Hilbert space represents a physical state. What is a physical state? A physical state is simply a possible physical situation [a symbol] with particles moving here and there, with collisions, with dogs chasing cats, with people living and dying, with all kinds of things happening. Often people make the mistake of identifying a physical state with the situation as a given moment, a picture from a movie. But that is not what we call a physical state, The situation at some moment may be seen as boundary conditions: if one knows the situation at some moment, and one knows the laws of nature, then in principle we can deduce the rest. ' Veltman
No. Reduction always fans out into an infinity of
[page 140]
possibilities. [Veltman's story may be true for an unobserved system, but without observation, we will never know!]
Tuesday 28 October 2008
Rushdie Satanic Rushdie, Salman Rushdie - Wikipedia
The Roman Catholic Church is part of my past and has served as a fixed jumping off point, a brand X, for the path I have taken.
[Quantum mechanics axiom] 6. Repeated measurements [with the same operator/apparatus] give the same result. Because a measurement is a message, a form outside time, to which time is invisible and irrelevant, and so remains stable, to be the same when repeated. Insofar as quantum systems are mapping onto themselves (via differentiation) there must be fixed points (Brouwer). Brouwer fixed point theorem - Wikipedia
Formally all the bits in a computer are identical, and physically thee is not much difference between them. What gives them meaning [and differentiation] is their space-time position in the computing process. Somewhere in the machinery of the Pentagon is a single bit whose two states are press the button for nuclear war and do not press ... .
Wednesday 29 October 2008
Rushdie page 49: 'A man who sets out to make himself is taking on the creators role according to one way of seeing things, he's unnatural, a blasphemer, an abomination of abominations. From another angle you se pathos in him, heroism in his struggle, in his willingness to risk; not all mutants survive. Or consider him sociopolitically: most
[page 141]
migrants learn, and can become disguises. Our own false descriptions to counter the falsehoods invented about us, concealing for reasons of security our secret selves.
page 52: '. . . the confining myth of authenticity . . . '
The initial singularity is the ultimate hardware, a zero (spatial) dimensional point which nevertheless carries energy and grows a la trinity. The Universe is a fully dressed natural line, mapping time to structure.
New Yorker 27 October/2008 Pierpont pp 66-73, page 33 Brando: 'In America we are unable to approach such refinement [to present Shakespeare or classical drama of any kind satisfactorily]. We simply do not have the style, the regard for language or the cultural disposition.' Pierpont
The basic problem with the US is immaturity, maybe. Best illustrated by the weird things they believe, mostly variations on the Christian theme of revelations to a particular individual who makes a career out of selling them to the rest of the population.
Hamlet III:2 'Let your discretion be your tutor. Suit the action to the word, the word to the action, with this special observance, that you o'erstep not the modesty of nature: for anything so o'erdone is from the purpose of playing, whose end, both at the first and now, was and is to hold, as 'twere the mirror up to nature.' Shakespeare
Thursday 30 October 2008
General relativity describes the dynamics of space, time and energy.
[page 142]
Special relativity describes a static space with a fixed metric represented by etaij = diag(-1, 1, 1, 1). General relativity has a dynamic metric represented by Einstein's field equations G = T, where G describes the kinematics of space-time and T the disposition of energy in space.
Einstein's description is formal and kinematic, based on Gaussian curvature (as developed by Riemann) and continuous mathematics. The 'continuity constraint' is a sign of measure theory which moans in turn that we are dealing with cardinal rather than ordinal numbers, although as the space becomes more complex, we have more (ordinal) degrees of freedom, each of which is computed by cardinal arithmetic.
distance = f(energy). Part of Einstein's genius was to find (but not explain?) the exact relationship. In particular, distance is a function of 4-space, not 3-space. Here we begin with a very direct relationship between distance and energy, embodies in the photon, which obeys the relationships E = h bar nu, p = h bar k = h/lambda, nu is time, lambda is space.
The principle of equivalence means that we can transform a local gravitational field to 0, so that local space becomes flat and rigid, by falling freely.
Weinberg page 70: '. . . it is precisely the very strong assumption that the Principle of Equivalence applies to gravitational fields that will lead us . . . to Einstein's field equations of gravitation. Weinberg
INERTIAL = NOT COMMUNICATING
[page 143]
We assume that gravitation is the ur-communication, the most primitive symbol operating in a protocol where error is impossible and so coding is unnecessary. Then we proceed to build the Universe out of this assumption.
First, the nothing like properties of gravitation mean that it can exist happily in an initial singularity with no spacetime size, ie every observer in a more complex space sees it travelling at the (observer's) 'velocity of light' (and remember thus may be the speed of a sailing ship).
Our dynamical principle is like set theory where the elements of the sets are 'snippets of code' which can be assembled to achieve various tasks. We have watched the evolution of computing from the binary logic level through higher and higher levels of language until we come to languages like Ruby and beyond, to online shops written in Ruby, and on to all applications. So we will say spacetime is an application of gravitation, just as we say Photoshop is an application of propositional calculus. Photoshop itself obeys propositional calculus and maybe here we see a clue to the 'non-linearity' (self reference, recursiveness) of gravitation that gives us al all times (including the initial singularity) a closed curved Universe. Intuitively, we live inside rather than outside the initial singularity.
Lines of thought formally (but not linguistically) isomorphic to this have been abroad for a long time amidst mystics, theologians, and philosophers, which Einstein certainly was.
PROPER TIME is our first foundation My proper time is the sequence of my experience.
[page 144]
At the level of complexity we are currently investigating an anthropomorphic or solipsist approach is reasonable, since we are simply talking about encoding and decoding messages. From the point of view of a coding system, the messages come from infinity, are processed and dispatched back to infinity, the infinity being the mind of the users who are the spaces that give 'user-meaning' to the messages. The coder only has to deal with 'coder meaning' using coder protocol. The coder meaning may be many layers below the user meaning.
PEER MEANING is encoded using the protocols of the peer group. These protocols are abstract insofar as they stay the same (or are invariant) no matter what the sequence of symbols passed to them for transmission.
Physical review.
Every person must work from their own point of view. Religion is the set of transformations of one human point of view into another so that we can see things from another point of view and so form networks of cooperation (a tautology - no cooperation, no network)
Weinberg page 26: 'The fundamental property that defines Lorentz transformations is that they leave invariant the 'proper time d tau defined by
The dx's change with direction, 0, 1, 2, 3. Direction = degree of freedom.
[page 145]
The propagation of light is described by d tau = 0. This formally expressed the fundamental property of the initial singularity from which we construct our Universe.
Fortune favours the prepared mind because little pieces of the jigsaw have already found tentative positions so the cardinality of the problem is reduced, making a final solution more probable.
The initial singularity is massless. Time and energy come into existence together, and then space-time and mass. Special relativity tells us that if proper time is invariant, E = mc2.
Weinberg page 39: '. . . if two tensors with the same upper and lower indices are equal in one coordinate system, then they are equal in any other coordinate system related to the first by a Lorentz transformation.
ie they are invariant with repsect to space-time encoding.
A conservative (scalar) network without storage must conserve current. Such a network may deal in (say) energy or probability. When we introduce storage, currents are no longer necessarily conserved, but the total quantity of 'fluid' is. Space is somewhere one can staore mass, the ralation between energy currents and stored mass is E = mc2.
Weinberg page 73: The metric is the gravitational potential whose derivatives determine the field of affine connections F l mn. Another example of form (shape of space) controlling dynamics.
[page 146]
Weinberg page 249: '. . . the theory of gravitational radiation provides a crucial link between general relativity and the microscopic frontier of physics.'
'. . . it is the radiative soluions of Einstein's equations that will lead here to the concept of a particle of gravitational radiation, the graviton. '
Is there only one graviton? Only 1 electron? Gravitons, electrons ans al the other particles are formally identical, differing only in their spacetime points of birth and death, their genealogy in effect.
page 252: '. . . it is only possible to attach a precise meaning to the concept of an elementary particle when it is far away from all other particles and for gravitons this corresponds to a weak field solution of the field equations.
We are not trying to change any well established physical theory here, only to give it a new interpretation which is nevertheless consistent with observation.
Isolated quantum system described by vectors in Hilbert space. Isolated and energyless space-time system described by Minkowski space. Both Hilbert (unitary) and Minkowsli (Lorentz) spaces have their characteristic transformations.
We think of everything as a process with some fixed points (invariant with respect to time) which we call memory
. . .
Basically, one must regulate one's speed by the data available to maintain an acceptable level of certainty
[page 147]
(security). It is dangerous to go faster than the data permits
So we have the principle of total self interest which leads to the principle of total cooperation, since energy spent in cooperation contributes exponentially to the growth of the system.
The principal difficulty is to see through the mytho-poetic interpretation of the human condition to tje realities of the human condition, and to devise ways to improve ourselves subject to these constraints.
Perhaps the world is ruled by good taste, but it must be realistically guided by good taste. Which is?
Maximize entropy because this is going with the flow. But entropy has a cost so we must do a cost benefit analysis of high entropy vs low entropy freedom vs dictatorship.
The network can accomodate unlimited growth, since it is based on protocols which can be implemented anywhere.
General covariance means anyone can communicate with anyone, ie a universal protocol.
The basic key to success is to be out there with a superior product. Superior marketing may outweigh a product disadvantage, but it is in some ways unfair.
