Notes
[Notebook: DB 60 Spotlights]
[Sunday 25 March 2007 - Saturday 31 March 2007]
[page 136]
Sunday 25 March 2007
Natural secrecy - no cloning
N446:257 Lardelli 'grain consumption now exceeds production'. Lardelli
Cavalier-Smith (same ref) ' 'Organisms are not mere assemblages of genes, whether inherited vertically or laterally, but cells (or integrated assemblies of cells)
[page 137]
in which there is a mutualistic cooperation of genomes, membranes, skeletons and catalysts that together make a physically and functionally coherent unit capable of reproduction and evolution.' Cavalier-Smith
Since Aristotle invented the syllogism we have made considerable extensions to abstract logic and realized that it can be implemented not just with written sentences, but with electrons, DNA and anything else whatever that can be used as a vehicle for discrete information. Amos
Adami reviewing Amos: 'all physical systems can be viewed as performing computations.' Adami
Buzsaki Rhythms of the Brain. Buzsaki
We know that all the signalling in the brain is discrete yet we observe periodic functions in its overall behaviour. Can it be the same in quantum mechanics?
'The interaction and interference of multiple brain rhythms often gives rise to the appearance of noise in an electroencephalogram. This noise is the most complex type known to physics and reflects a metastable state between the predictable behaviour of oscillators and the unpredictability of chaos.' Buzsaki Nature 446:267.
. . .
'. . . [Einstein Podolsky and Rosen, EPR] did not use the world "paradox". They were with the man in the street on this business. For
[page 138]
them these correlations simply showed that quantum theorists had been hasty in dismissing the reality of the microscopic world. In particular, Jordan was wrong in supposing that nothing was real or fixed in that world before observation. For after observing only one particle, the results of subsequently observing the other (possibly at a very remote place) is immediately predictable. Could it be that the first observation somehow fixes what was unfixed, makes real what was unreal, not only for the near particle, but also for the remote one. For EPR this would be an unthinkable 'spooky action at a distance'. To avoid such action at a distance they have to attribute to the space-time regions in question real properties in advance of observation, correlated properties which predetermine the outcomes of these particular observations. Since these real properties, fixed in advance of observation, are not contained in the quantum formalism, that formalism for EPR, is incomplete. It may be correct, as far as it goes, but the usual quantum formalism cannot be the whole story'. Bell
[the formalism explains this correlation by entanglement? ]
Perhaps the problem lies in the low variety forced on the quantum formalism by the requirement of continuity.
I can weld without any real knowledge of metallurgy. The necessary properties are built-in to the materials I use an I just have to juxtapose everything properly while feeding in chemical or electrical energy. What is built into quantum systems? Nothing (or everything). They simply obey a certain logic which gives us the Universe we have out of all the different ones we might have
[page 139]
had, and perhaps find some relationship between actuality ad possibility, mediated by control.
Ground: When I first began to thing of religious and political problems through the cybernetic lenses of variety (entropy) and control. All based on the general survivalist idea that if we all run in different directions they can only catch a few of us - safety, and control, lie in numbers, properly deployed, The stables human network of all is a 'small world' or 'scale free' network embracing all humanity, an eventually the whole planet an Universe. Some difficult questions lie ahead of us.
Bell, page 150: 'The following argument will not mention particles, nor indeed fields, nor any particular picture of what goes on at a microscopic level. Nor will it involve any use of the words 'quantum mechanical system' which can have an unfortunate effect on the discussion. The difficulty is not created by any such picture or any such terminology. It is created by the predictions about the correlations in the visible outputs between certain conceivable experimental set-ups.
The thought experiment . . . designed to find [that] the joint conditional probability distribution P(A,B | a,b) does not split into a product of independent factors
[page 140]
'Amazingly, the unitarity constraint is the only constraint on quantum gates. Any unitary matrix specifies a valid quantum gate', Nielsen ie so long as the sum of the probabilities = 1.
So unitarity must explain locally inexplicable quantum correlations, the only constraint available.
General relativity and quantum mechanics both represent the effect of control n the transfinite network.
RANDOM = INCOMPRESSIBLE . . . Chaitin
'Using this definition of randomness, Chaitin demonstrated the surprising fact that although most integers are random (incompressible), only finitely many of them can be proved random, within a given consistent axiomatic system. A form of Gödel's famous incompleteness theorem, this result implies in particular that in a system whose axioms and rules can be described in n bits it is not possible;e to prove the randomness of any integer ,much longer than n bits.' Gardner
. . .
d'Espagnat The Quantum Theory and Reality d'Espagnat
Does 'logical continuity' exclude action at a distance? So allowing 'action at a distance' and 'logical continuity'
[page 141]
Logical continuity: All men are mortal; Socrates is a man; therefore Socrates in mortal.
Of course we cannot say all men are mortal until we see Socrates die.
classically inexplicable two-valuedness
classically inexplicable correlation
d'Espagnat; 'a theory is expected , , , also to provide some understanding of the physical events that are presumed to underlie the observed results.'
'Even if quantum mechanics is considered to be no more than a set of rules, it is still in conflict with the view of the world that most people would consider obvious or natural.' 1. Realism; 2. Inductive inference; 3. spacelike separation = local realistic theories of nature.
Local realism falls down in 'experiments . . . concerned with correlations between distant events and the causes of these correlations.'
The velocity of light is a coding delay. If something is sent completely uncoded, it could travel instantaneously?
'Whenever a consistent correlation between . . . events is said to be understood, or to have nothing mysterious about it, the explanation offered is always some link of causality.'
[formally causality implies implication]
Meaningless communications, the physical foundation of the Universe, do not need to be encoded or made discrete because all are acceptable and the concept of error is absent. No
[page 142]
state can be called erroneous. This is he vacuum.
Quantum mechanics violates the Bell inequality. Peter Rogers
Correlation comes from communication at any time before the measurement. Measuring instruments may introduce correlations by constraining the variety of what is measured.
Inductive inference is an application of continuity = symmetry.
I go round and round rattling the walls of my cage like a trapped philosopher. Each sentence in these notes is a rattle. It is fides quaerens intellectum: I know the Universe is divine but I have still to complete the road from physics to God.
What you see is what you are; what you are is what you see, 50/50 insight.,
d'Espagnat page 131: 'Hidden parameter theories and local realistic theories in general, lace limits on the extent to which certain distant events can be correlated; quantum mechanics, in contradistinction, predicts that under some circumstances the limit will be exceeded. Hence is should be possible, at least in principle, to devise an experimental test that will discern between these two theories,'
Monday 26 March 2007
Entanglement - correlation - control
[page 143]
The first thing we have to do is stop cracks, that is catastrophic failures, that is failures that propagate at high velocity,.when all the peasants rise simultaneously. All cracks are caused by self propagating stress concentrations, so crack prevention comes down to reducing stress concentrations, that is distributing stresses throughout the part to avoid local concentrations. In metalwork we do this by rounding corners, minimizing the use of brittle materials, and so on. This is tantamount to increasing the entropy of the set of local stresses.
If we consider this set,m we can see that many events could not care less about stress concentration - it is only the ones that are teeing the load that know about it and can communicate their stress to their neighbours [by strain] and get them to take up some of the load. The atoms in solid materials can do this by altering bond lengths and the slipping of crystals and so on.
In human societies we generally find a tendency for the 'ruling set' to offload stress from their lives onto the ruled classes, so making their lives easier and more magnificent while the underlings paid taxes or risked their lives.
We want to model this so as to understand stress concentration and relief in our general system, the transfinite network, and to apply them to problems in our own self-management. We might define stress as uncongenial control, what is felt by a system which is moved out of its comfort zone by forces outside its control.
[page 144]
The 'comfort zone' is surrounded and protected by the 'margin of safety', which preempts as many foreseeable errors as possible.
A very basic control in the Universe is represented by the quantum mechanical model of entanglement, a source of non-local correlations in the Universe. . . .
What I want now is for the transfinite Universe to give me a combinatorial argument (a la Boltzmann) for the existence of entanglement n the Universe.
A theory tells us how to apply arithmetic to a given situation.
STRESS - ERROR The higher the stress the faster the bonds break.
What I am looking for is a discrete logical explanation of quantum mechanics which applies at all scales of complexity. Is this possible? Should it be possible? But perhaps thee is a continuous underlay where error correction and so discreteness is not required?
Most games have an umpire or referee who has to stop them and restart them when situations arise where the game cannot continue
[page 145]
like ball out of bounds or a penalizable infringement of the rules. Other things (like the Universe) go on forever because they never reach an untenable position.
Communication -= force - acceleration
By differentiating a movement we learn the movement of the movement and we can go on doing this recursively. With some functions (finite polynomials) this eventually leads to a constant, but infinite power series can be infinitely differentiable. We can differentiate the Universe back to the constant initial singularity. This coincides with a feature of the classical go, whose eternity was equivalent to a rate of change of zero.
Le Carre Naive page 283: 'To make wanting the justification for everything.' le Carre
A particle out of place wants to go back to its place.
WANT = ERROR
le Carre page 329: 'The truth is you', she whispered. 'Not what you say. You'.
The particle is the message and the message may be true.
Tuesday 27 March 2007
STRESS = ENERGY
Back to an old idea - inconsistency leads to action.
[page 146]
Entanglement makes the Universe into a 'small world' 'scale free' network.
Inconsistency leads to action. But why? Inconsistency is related to discomfort, ie a high level of parameters out of bounds, and so the system must act to fix things lest they get worse. Conscious ones like us can work this out, but what about the unconscious Universe? Let us say that consciousness = feedback (awareness of self). This feedback has a time constant. When we are dealing with rapid onset errors, this may be (for me) hundredths of a second. On the other hand evolution is also adaptive feedback with a time constant measured in generations. If we measure in 'generations' all processes may be normalized to one another, so we may identify loops in the Universe ranging from ℵ0 cycles per second to 1/ℵ0
MODELLING AND mate choice
genotype -- phenotype --> selection/non-selection
This is a system that can build structure from chaos. What does not repeat is under represented, while those things that go on generation after generation become over represented. This is linear growth. In addition, we have positive and negative exponential growth, which is achieved by copying the organizing algorithm so that each individual has a private copy.
[page 147]
So events to some extent control their consequences, and so multiply like us.
A death spiral: using biomass produced with the help of fossil fuel to replace fossil fuel.
The first task for a model of the Universe is to explain the big bang. Taken as a whole, the big bang has brought the Universe we now experience (through sex, drugs, music, telescopes etc) from the initial singularity believed to have no structure. Aquinas 20
We encounter here a basic duality: there is no need for error correcting codes unless error is possible and error is only possible when the set of possible sentences has been partitioned into correct or erroneous by the needs of some structure. One the other hand, error correcting codes are only possible if there is software to transform the input strings into the output strings. Everything can be packed into a string with a suitable algorithm, ie a suitable ordered set. So we imagine codes and structures bootstrapping one anther into existence. But how? Here is the hub of creation: everything no matter how complex is possible in the chaos but some of these promote their own survival, thus changing the probability structure of the chaos.
What does it mean that uncoded transmission move instantaneously, minimally coded transmission move at the speed of light and 'massively' coed transmission (like me)
[page 148]
at various lesser velocities. Nevertheless we can understand the structure imposed on the Universe by this slow movement in exactly the same was as we understand the structure imposed by the velocity of light. The boundary lies between finite and infinite, and this is the paradigm for boundaries between various finite values of velocity or anything else. The economy, for instance, or the global environment, is a big complex thing with a lot of inertia (ie old structure take work to change) and so its time constant is long, as long as it takes to heat up the oceans at about 5W (greenhouse extra) per square metre,
Quantum error correction = the bootstrap toward precision. Let us assume that this is why eigenvalues are so sharp, because there is a very efficient control system which increases the perfection of the control the longer we observe. Because every observation if a count, and the longer one counts the more precisely we will be able to define any pattern we find in the counting,
Wednesday 28 March 2007
The big bang. We usually see bangs in terms of destruction, the endless carnage wrought by those whose only channel of communication with their fellow people [is bombing]. The cosmological big bang was a constructive explosion. What we see when we look back, is the generation of layer after layer of new structure in the Universe as it expands from the 'initial singularity' predicted by the general theory of relativity.
There us a scale where gravity conquers all.
[page 149]
Meaning what? It is the only structure. The simplest structure can be represented y a bit. We can imagine simpler structures gradually fading to nothing as their entropy approaches zero. On the other hand a structural gain, no matter how small repeated enough leads to gain, as we learn from the formula e = (1 + 1/n)n. Something which we guess remains true for n = aleph(n), a larger cardinal. Ie e is invariant with respect to the cardinal of the set on which it is computed.
Grow = become more frequent (relative to the average of everybody)
Can the instantaneous channel carry any information and so be responsible for the violation of the Bell inequalities caused by quantum entanglement? The instantaneous channel is effectively pure noise and no signal, so we would not expect it to tell us much.
Nielsen: 'one shared EPR [Einstein Podolsky Rosen] pair together with two classical bits of communication . . . is at least equal to one qubit of communication.
Or maybe this noise acts as a one time pad making communication possible if both terminals know the code.
Maybe to do something religious you have to be a bit mad. Love conquers all; gravity conquers all. Either way a lot of details get overlooked when one is on a crusade. My crusade is really for myself, but having solved my problem, it would be nice to pass the algorithm on if one things that it will build a more peaceful and secure world. We
[page 150]
maximize entropy by minimizing arbitrary control in all its forms.
The transfinite network is our vacuum, not what is but what is possible. What is actual is the 'normalized' transfinite network which is a point in the potential which is moving around in the vacuum, appearing at different points.
WANT stabilizes us, but too much kills us, as well as too little.
In the Platonic mathematical world the whole of the transfinite network exists simultaneously, the natural numbers upon which it is founded being duplicated a transfinite number of times to represent all the permutations of permutations of . . .
Thursday 29 March 2007
Quantum mechanics uses continuous mathematics to calculate the probabilities of discrete events. It also uses continuous mathematics to calculate the values of various fixed parameters of the Universe like the eigenvalues of an operator which are the solutions of an eigenvalue equation. We can measure such eigenvalues by some sort of apparatus (like s spectrometer) and counting frequencies of the events made visible by the apparatus, and so we have confidence that they are real and that the eigenvalue equation somehow reflects a mechanism that cuts down all the possible products of a matrix and a vector to just those which do not
[page 151]
change the direction of the vector, but only its length, which we ultimately interpret as a probability. So we can say that the structure of the world manifests itself in the nature and frequency of various events, an interplay of form and function.
Maxwell's classical equations are continuous and deterministic up to constants of integration. (is 'continuous and deterministic' a contradiction?) From the quantum point of view we interpret them as predictions of the probabilities of certain events, and we can say the same for Einstein's field equations. Because quantum events are so small and the Universe so large, this interpretation has no practical consequences except when gravitational fields are so great that we must couple gravitational and quantum formalism to get a reliable model of the phenomena.
Continuous mathematics arises when we use geometric analogies to take discrete mathematics to the limit, sum to integral. In this process we tend to overlook the identities of the individual points although the set theoretical development of mathematics takes every point into account, or at least devises processes which are believed to work no matter how finely we divide the geometric line by mapping it to numbers of unlimited closeness.
This is the Platonic world, with unlimited resources, and so no competition for resources. The observable world, on the other hand, is 'normalized' by the requirement that reliable communication must be quantized.
Hobson page 148: '. . . the trajectory through space
[page 152]
of a particle in a gravitational field is independent of the nature of the particle.' Hobson All particle move the same way just as a communication network is indifferent to the content of the messages it transmits (and in the limit, to the size )length) of messages).
Further, no particle falling freely in a gravitational field feels any force (constraint) from that field. If we define Universe as 'subject to no constraint', we can imagine a Universe as something falling freely in its own gravitational field.
Hilbert space is flat, in that the metric in the dot product is 1, and the basis vectors form an orthonormal set.
Keep flicking back and forth between the human condition (in particular mine, and ultimately all people with an exponentially decreasing level of involvement as their distance from me increases). Gravitation is indifferent to the nature of the particles it effects: as far as we know it treats planets, people and electrons in exactly the same way, in other worlds it is a symmetry joining all levels of complexity in the Universe. Whether you are a lumps of rock or a cloud of gas or a preternaturally sensitive poet, gravity treats you the same.
And hat does it do? Special relativity arises from the transmission delay necessary for the construction of packets according to some error detecting and correcting protocol.
[page 153]
There is no more data in the continuum that twice its highest frequency x k, a constant to be determined. If this is so, the idea that there is an infinite amount of information in a qubit because it can occupy any point on a continuum needs modification. It all depends how squiggly our continuum is. Sampling Theorem, Shannon, Nyquist. Wikipedia
Special relativity operate in flat pseudo-Euclidian space. In this space we find observers moving inertially, that is without acceleration = constant relative velocity. Einstein saw that this was insufficient to describe the real Universe in which particles accelerate. Further he saw that one could approximate the accelerated world with a sufficiently large number of flat spaces to describe the outline of the curved space arising from accelerated motion.
The space of general relativity can be approximated to any degree of precision by a manifold of flat spaces whose relative positions are defined by certain 'connection coefficients' that enter into the covariant derivative. Potential 4 x 4 x 4 = 64 of them.
Connection coefficients are connected to the metric so the same information can be encoded in both. But the metric has a maximum of 16 coefficients which 'modulate' the product of two vectors dx at a point x.
Despite its ubiquity, gravitation nevertheless has structure which can be encoded in the Riemann curvature tensor. This tensor has potentially 256 independent components, but in reality symmetries reduce it
[page 154]
to 20 independent components. [error defeating redundancy?]
. . .
I am engaged. On the one hand it seems impossible to fulfill my dream, to give a clear proof that god and the Universe are one; on the other, I am committed to this path and want to follow it as far as I can go, while having logged some of what I have seen on the way,
Hobson page 170: 'For example the world line of the centre of mass of a rigid body in free fall is a timelike geodesic, but this is not true of the other parts of the object, which are constrained to move along curves parallel to the centre of mass rather than along neighbouring geodesics.'
The problem is to run a consistent set of databases. When different parts of the same system are not synchronized errors are possible and their probability some function of how far things are being pushed off their geodesics.
Let us interpret the transfinite network in the light of the general theory of relativity. We argue that gravitation is the property of the network itself, and is indifferent to the actual meaning of the messages being conveys, although it does take notes of their size (mass/energy). In this respect it is like a laissez-fair network administrator who measures everybody by bandwidth and storage and
[page 155]
charges accordingly, probably on some sort of logarithmic scale, so constant increments of money increase the computing power available exponentially. [Moore's law Jon Stokes]
We want to make the transfinite network into the field equations of general relativity. There can be no doubt that this is possible given the potential power of an instance of the transfinite network.
A process cannot evolve without memory, that is fixed (and variable/fixable) structure. A Turing machine relies heavily on memory to contains its algorithms and variables.
The emplacement of gravitation (fixation) is the first visible step in the 'big differentiation'.
Hobson 176: 'Maxwell's equations relate the electromagnetic field F at any point to its source, the 4-current density at that event. Einstein's equations relate spacetime curvature to its source, the energy-momentum of matter. As we shall see, the analogy goes further. In any given coordinate system, Maxwell's equations are second order partial differential equations for the components Fmn of the electromagnetic field tensor (or equivalently, for the components Am of the electromagnetic potential). We shall find that Einstein's equations are also a set of second order differential equations, but instead for the metric coefficients gmn of spacetime.
[page 156]
How do we constrain the enormous variety of he transfinite network to gravitation? Does quantum mechanics come first?
Fides quaerens intellectum: first the dream (eg the principle of equivalence) and then the detail (Riemann geometry). The Aristotle idea that we work from generalities to particulars. This is true of design where we begin with the dream: get people to the moon and back and then work out the details right down to the logical bits.
Feynman: 'Let us make recommendations to ensure NASA officials deal in a world of reality, understanding technological weaknesses and imperfections well enough to be actively trying to eliminate them.' Feynman
'For successful technology, reality must take precedence over public relations, for Nature [God] cannot be fooled. Page 236-237.
Degrees of freedom have an energy spectrum which determines their rate of occupation.
Feynman page 242: "It shows that the imagination of nature is far greater than the imagination of man.'
page 244: 'So what is this mind of ours: what are these atoms with consciousness. Last week's potatoes! They now can remember what was going on in my mind a year ago - a mind which has long
[page 157]
been replaced.' [is this general covariance again?]
Hobson page 187: 'We can therefore view the cosmological constant as a universal constant that fixes the energy density of the vacuum
page 187: 'How can we calculate the energy directly of the vacuum? This is one of the major unsolved problems of physics. The simplest calculation involves the summing of the quantum mechanical zero-point energies of all the fields known in Nature. This gives an answer about 120 orders of magnitude higher than the upper limits on lambda set by cosmological observation. This is probably the worst theoretical prediction in the history of physics!
Friday 30 March 2007
Hobson 189: 'the gravitational field itself carries energy momentum and therefore acts as its own source, whereas electromagnetic field carries no charge and so cannot act as its own source. '
[the Universe acts as its own source]
charge = rate of communication = strength of interaction
Saturday 31 March 2007
Feynman on spin" The management thought the shuttle had a failure rate of 10-5. The engineers
[page 158]
thought more like 10-2, 1000 times more frequent. Feynman op. cit. One sees similar statistics in decision to invade Iraq.
General relativity is the theory of the network. Quantum mechanics is the theory of encoding the messages that are transmitted don this network.
Jesus said love everybody. We want to expand on this by drawing a relationship between love and justice. We think of justice in terms of stress distribution and define a just society where the stress of survival is equally (or reasonably with respect to ability) distributed, bringing about a state of maximum entropy and stability.
Communication: correlation + creation. By establishing definite basis states common to two entities, we open the door to a far larger space of permutations of this alphabet.
Quantum mechanics shows us how to adjust probabilities so that desirable things happen more often. Prudence does the same in the world of human affairs.
Beautiful thoughts (relationships of terms) flit through my mind too quickly to write down., but at least I can be assured that they are in me somewhere, somehow.
The temperature of the initial singularity must be 0 because a) it has no parts and b) it cannot move because it is already everywhere there is.
[page 159]
Feynman: Science: a long history of learning how not to fool ourselves.
Much of Christianity is shaped by fear of death and overcoming that fear, perhaps by bogus means like the promise of heaven.
