Notes
[Notebook: DB 60 Spotlights]
[Sunday 15 April 2007 - Saturday 21 April 2007]
[page 191]
Sunday 15 April 2007
Can all universal activity be comprehended under the rubric of error correction? We move when we are uncomfortable and it is torture to be restrained (or contorted). Unfortunately 'error' is a pejorativish term, but it is the best. Can also
[page 192]
say 'feedback'.
'From big bang to to tender caress'
Increase in complexity is matched by decrease in energy per bit. With current technology (hard drives, a change of state costs x Joule. In DNA, a change of state costs y. On the other hand, nuclear and quark changes of state are accompanied by z J.
No action can be fully reviewed or fully predicted.
'Cook dinner' is a superposition of algorithms which change depending on what's for dinner, who is coming. Although these algorithms are complex they may be broken down into discrete steps, as we find in recipe books. Do dishes. Change angular momentum.
Proposition: that the transfinite network represents the bounds (and lack of bounds) on imagination.
Potential: changing structure takes energy.
Event: electron changes orbit; photon emitted/absorbed.
Monday 16 April 2007
Tuesday 17 April 2007
Vector - covariant derivative. Here the fact that the differentiation (derivation) explicitly involved comparison of two points reveals more clearly the discrete space
[page 194]
assumptions that underlie the 'passage to the limit' which gives us the continuous functions of mathematical physics (and all the rest of mathematics - is there any 'rest' ie mathematical theorems that are not implemented in the Universe? Maybe not).
The general tendency here is to move in the opposite direction, wondering how a Universe that begins as a structureless point (described by the properties of the classical god) ends up, as here, wondering about itself and how it came to e through me and countless others. We begin by describing the space of possibility: potency. [we describe this in Platonic terms, but when physically implemented, these Platonic structures carry energy]
I'm trying to revolutionize theology and after much to-ing and fro-ing I am quite prepared to admit it. This is (I feel) because I have spent so many years turning the thing over from all sides that I have sufficient confidence to risk making a fool of myself by publication. Publication also requires a lot of effort that can only be 'justified' if the probability of payoff is sufficient.
Hobson page 92: 'The coordinates with which one labels points in a manifold are entirely arbitrary. Hobson
This is Einstein's assumption that there is a reality (the point) whose existence is independent of its relationships to other points. Such a point is an unobservable abstraction, since to observe it we have to 'break' this independence, ie in some way 'bind' to the point in question, and then, as quantum mechanics tells us what we observe depends upon a superposition of the states of the 'observer' and the 'observed. In reality this relationship is
[page 194]
symmetrical. The symmetry is broken at a higher peer level (lower energy) by the fact that the particle physics is coupled to a system, something complex, that gives meaning to defined physical events like the laying down of this string of ink and spaces.
The independence of points an coordinates is the independence of physical and logical memory and process.
Hobson page 92: '. . . at any point P on the surface, one can say that, for example, the air temperature has a particular value or that the wind has a certain speed in a particular direction. These respectively scalar and vector physical quantities do not depend on which coordinates are used to label points in the surface.'
Physicists describe physical fields by equations. Metaphysicians describe logical space by proofs, that is executions of Turing machines or communications which we treat as permutations in the active sense, as in the sentence 'this permutation turns that permutation into that one (abc) changes abc to bca, etc.
Entropy may be conserved in logical space, but not necessarily energy and momentum SPIN? ENTROPY
Our basic explanatory duality may be the distinction between physical and logical space which we might say are generally covariant to one another.
The transfinite network is a logical space built on the physical
[page 195]
space described by quantum mechanics and relativity.
The bodies upon which we exist are continually changing at the physical layer while remaining relatively stable in the logical layer.
Physics places engineering constraints in the implementation of logic, just as economics placed constraints on human reproductive behaviour (a logical ie metaphysical process)
Hobson page 93: 'we can define a tensor t as a linear map from some number of vectors to real numbers.' Reducing a complex system to a simple countable (observable) system. We may think of messages as pinholes through which large systems (like myself) communicate their internal states. My internal states are vastly more complex than this writing. Nevertheless this writing does constrain your mental states as you read it and consciously or unconsciously think about it.
Tensor is linear map, like quantum mechanics also linear. The forces are non-linear, curved, dynamic, creative.
DYNAMIC = able to enter a currently unoccupied state.
The Platonic world is a space of unoccupied states. In physics a subset of these states is occupied and our quest is to decide on the nature of these states (a formal structure) and their occupation rates and transition rates.
'a tensor must give the same real number independently of the reference system in which the vector components are calculated.' ie the
[page 196]
tensor must 'know' about the coordinate system in order to transform it away.
Linearity (and physics) are based on the cardinals of certain set which are often 'normalized' to q by measurement theory. Logical space, however, depends on order as well as number.
page 94: 'The components of a tensor in a particular basis set specify the action of the tensor on other vectors in terms of their components. ie TENSOR REPRESENTS BASIS
Wrestling: voluntary submission
Boxing: involuntary submission.
OPERATOR<==> METRIC (QUANTUM MECHANICS <==> GENERAL RELATIVITY)
The operator tells us how much two amplitudes overlap, from which we compute the probability of transition which as a measure of formal or logical distance.
OPERATOR - OVERLAP - METRIC
. . .
Indices index memory locations in which certain
[page 197]
values or functions may be stored.
Hobson page 114: 'As we shall see, the notion of orthonormal sets of basis vectors at any point in spacetime is of fundamental importance for our description of observers.
Natural culture is not so normative as institutionalized religious culture, since it is open to all options consistent with the fitness and social responsibility of its practitioners.
Wednesday 18 April 2007
INSIGHT = finding a 'natural' (simple) basis for observation. In effect the observer rotates itself until things look simple like walking around a plantation until one see the rows of plants. (Hobson page 129).
page 131: [In Cartesian coordinates} 'it is much easier to disentangle the physical effects from artifacts of the coordinate system.' This statement implicitly accepts the 'local realist' position which may itself be an artifact of 4-space applied to quantum logical events.
What does the mathematics mean? That certain equations hold, ie certain things (to which we have chosen to assign different symbols) are the same, ie we have given different meanings to the same physical reality, eg
motivated by different methods of measurement, eg rods and clocks.
[page 198]
Mechanics deals in three dimensions, Mass, Length and Time. The constants c and h enable us, in the relativistic quantum model, to express all of these in terms of one of them, Here we choose time because 'proper time' seems to be the simplest of the invariants. [fit = harmony in proper time]
Veltman xi: 'It must be added that there exists, strictly speaking, no sound starting point for dealing with non-perturbative situations.' The network gives us a way to unify these two approaches. As the Feynman diagram suggests, the nature and probability of a given state are coupled more or less strongly to the space of 'nearby states',which ultimately involves the whole Universe, rather weakly, through gravitation. This is just a network, and my state depends to a degree on my communication with the states around me, the brilliant sunshine, the beautiful people, work, etc. From a non-perturbative point of view, the computations in the network performed by Turing machines are deterministic and digitally exact, subject to no perturbation. Veltman
page xi: '. . . given that one believes Feynman diagrams, path integrals may be considered a very valuable tool to understand properties of these diagrams. They are justified by the result, not by their definition. They are mathematical tools.' Their success means they couple to reality just as my pipe wrench couples to pipe, so Feynman diagrams tell us something about reality, just as pipe wrenches tell us something about pipe.
To get something to work we have to devise a suitable mechanism, [eg] a physical engine to implement the conversion of thermal to mechanical energy.
[page 199]
Thursday 19 April 2007
Veltman page 17: 'What we are doing here is of course quite horrible. . . . This plague, having to abandon Lorentz invariance in order to define the formalism, seems common to all approaches to quantum field theory. One always needs some kind of grid.'
This problem may arise purely from the desire to 'pass to the limit' from a discrete formalism (little boxes etc) to a continuous formalism. Our proposal is to [utilize] physically discrete entities in constructing a formal mechanism that imitates the behaviour of the world.
The mapping from the mechanism to our world is founded on Landauer's hypothesis that all information is represented physically. This gives us a coupling between the logical world and the physical world. it is a very loose coupling, based simply on the existence of discrete, unique and identifiable entities (which we call symbols) in both realms, logical and physical. The first constraint on our modelling is that the logical and physical realms are part of the same Universe. This investigation i as much part of the universal process as star formation or death.
Veltman Page 17: 'The final results, the Feynman rules, do not suffer from this breaking of Lorentz invariance. We will, by necessity, ignore this difficult issue.
All arithmetic equations in physics are normalizations, eg Hobson page 138 'partial dmu jmu = 0 ==> j is conserved (normalized to some value)
[page 200]
Goodwill ('professionalism' covers everything: we want to do it right , so we are prepared to make the investment necessary to correct errors in our code as they become apparent. This can happen, of course, only if the effort is well capitalized.
Warming up to do something : excitement vs laziness
. . .
The energy with which you observe is equal to the energy that you see, and the same goes for momentum, complexity etc etc, but all is quantized (pixellated).
[page 1]
Dirac's delta is a logical symbol that need not necessarily be represented by a Euclidian point in 4-space.
Veltman page 21: 'To every Lorentz transformation or more generally, a Poincare transformation, corresponds a transformation in Hilbert space.
Does this statement couple the network (Lorentz) too tightly to the messages transmitted through the network (Hilbert)?
Veltman page 21: Under translation, the state |p> goes over into the state
which shows explicitly how transformation of vectors in Hilbert space differs from what happens in ordinary space. Note that the vector |p> just gets a phase factor, in other words it stays normalized and represents, physically speaking, the same state.'
So states are not in spacetime? ie indifferent to spacetime location, ie indifferent to address in the network.
POTENTIAL ENERGY = FIXED (CONTROLLED)
KINETIC ENERGY = VARIABLE (UNCONTROLLED)
Hobson page 149: 'Einstein's proposal was that gravity should no longer be regarded as a force in the conventional sense, but rather as a manifestation of the curvature of spacetime,
[page 2]
this curvature being induced by the presence of matter. This is the central idea underpinning the general theory of relativity.
Since gravitation is its own source, curvature is its own source, so even empty space is curved.
page 150: 'The world line of a particle in a freely falling non-rotating laboratory occupying a small region of spacetime, the laws o physics are those of special relativity.
Quantum mechanics is independent of spacetime?
The real frames of reference in the description of the Universe are those that interact by communication. We may set up arbitrary frames to study an event but the natural frame is the superposition of the frames of the interacting particles.
Blocks of land are connected to the body politic by bonds of paperwork, and they move with respect to their owners by rewriting documents.
Friday 20 April 2007
All phenomena are observed by an observer, a tautology if ever there was one. Every observation is a manifestation
[page 3]
of god to itself, a communication between two persons of the transfinity.
The key to ancient cosmology was the transformation needed to map a cosmological explanation of the motions of the heavens with the actual heaven we observe.
Classical physics thinks it can look at events. Quantum physicists are involved in the events they observe.
Hobson 'Free from any external forces, the observer's world line traces out a geodesic in r spacetime.' From a quantum mechanical point of view, this situation cannot be realized because observation == force, ie exchange of particles (messages)
We suppose that gravitation describes the network hardware with which we observe the messages, ie [the network] 'turned off'. But how is a network its own source? Natural election selects for sources that is entities that work for their own survival. The power of error correction acts as a ratchet leading to better defined ad more complex systems. 'Better definition' and complexity are both measured by cardinals: the number of pixels on the screen., the number of bits of memory.
Each layer of the network uses processes in the layer below it as elements of its alphabet.
Hobson page 158: 'The solution to our mathematical problem of finding a coordinate independent way of defining the curvature of spacetime will lead us to the field equations of
[page 4]
gravity.
page 161: A line cannot be intrinsically curved.
General relativity represents a nearest neighbour (contact) network where ? Or maybe the appearance of connection coefficients suggests the opposite. The definition of the covariant derivative depends on passage to the limit. We can loosen the concept in network space, by considering a set of 'connections' sufficient to join any two points n the network. This 'coefficient' comprises an address and a protocol. There is an overall protocol to describe addressing, a prerequisite for universality.
In general relativity the line element is the message. From this message we try to reconstruct the space from which this line element 'emanates', ie the source of the line element. A network is a set of 'line elements' (messages) distributed in space and time and addressed by their connections with one another.
