Notes
[Notebook: DB 61 Warm]
[Sunday 22 July 2007 - Saturday 28 July 2007]
[page 109]
Sunday 22 July 2007
Einstein revisited the notion of simultaneity in a world
[page 110]
where communication through space entails delay. He assumed this delay to be measured by a physical constant, c, the velocity of light. c is the constant resulting from dividing the distance travelled by photon by the time it takes. It is about 300 000 kilometres per second. PDG - U of California, NIST
Distant events in the past may therefore appear simultaneous with events in the observer's present. Furthermore, each observer is surrounded by a horizon beyond which no further information can be obtained by a light based message.
This phenomenon [applies] to all forms of communication. If the receiver is moving sway faster than the message, there is no change of communication. This is the plight of football players trying to chase down a ball that is moving faster than they are.
The velocity of light is the fundamental constant in massless particles. All massive particles move at less than the velocity [of light]. Light particles can be accelerated to near the velocity of light, but on the whole the more massive a particle, the slower is goes. We must be speaking locally here, because at cosmological distances the relative motion between massive particles like galaxies can move apart at the velocity of light.
Horizon volume = [k]c3 [or maybe c4 in spacetime]
We need a symbol for [the maximum local velocity of massive particles, c. [Bold face] not because we are moving faster than c which is unobservable, but because they are heavier than massless.
[page 111]
An idea has been enshrined in a symbol. Now we can imagine human horizons ranging from the solipsist to the caring and engaged global citizen. We want to supplement goodwill by developing effective algorithms for peacemaking.
PEACE <--> POWER SHARING <--> MAXIMUM ENTROPY (STABILITY)
Maximizing human entropy by a) equality/justice; and b)scientific coupling to environment (= god)./
A system is isolated by its horizon. Two way communication and equilibration can only take place within the horizon, at the level say of self, family, village/tribe, city, nation, world etc.
The horizon is not a function of distance but of relative velocity, as we would expect in a dynamic Universe. In the expanding Universe, for instance, the horizon occurs when things are receding at c. When we come to deal with any other c, the situation is similar. There comes a distance at which events are no longer relevant to a given individual, which we might call the horizon of interest. We might say that all events within an individual's horizon of interest have a bearing on the fitness and survival of the individual.
Horizon is a function of distance and rate of expansion, ie the ratio of the actual velocity v to the local value of c.
[page 112]
The mathematical representation of curved space used by Einstein depends on the fact that the 'shape' of the space can be defined by a metric function that varies from point to point in spacetime. This metric function can be converted, using the constraints inherent in differential geometry, into the Riemann curvature tensor, another operator existing at every point in spacetime that allows us to measure the rate of change of velocity between neighbouring geodesics, relative acceleration of objects in free fall. If this rate is zero, the pace is flat and all inertial frames move with constant velocity relative to one another.
spin 1: photon 2 degrees of freedom
spin 2 graviton -
spin 3 too hard to talk about. But spin is just a set of degrees of
freedom and so if I have many degrees of freedom I have much spin.
Entropy = count of degrees of freedom = degrees of freedom per particle x number of particles.
Why do we find different particles at different energy scales? Does more fundamental = higher energy? What if the photon is the simplest particle, infinite energy range, fixed velocity.
We see life as a local process of stepping through spacetime, so what what is the life of the photon? It has no rest frame, since its velocity in the same in every inertial frame, the constant of nature that governs
[page 113]
causality in communication.
We try to relate gravitation to the network model via the interpretation of 'gravitational' (= spacetime ) parameters into information theoretic parameters. So we have a little table
Spacetime
Information theory
mass
internal processing rate
momentum
memory
energy
processing rate
Spacetime has evolved as the optimal tradeoff between processing rate and memory. An ordered lookup table requires logwordlength(n) operations to pick one element. To calculate a computable element might take a lot longer [more operations], but use much less memory. So we need to devise an algorithm that gives us the Minkowski metric. The Lorentz transformation follows 'apodictically' from the Minkowski metric. [via the invariance of the interval
Minimum action or stationary action is a function of the Lagrangian L = KE - PE. Potential energy is the energy associated with momentum, kinetic energy is associated with action so L = action/sec - [velocity x] action/metre ?
We examine the effects of finite communication velocity as a function of
1. the distance between sources
2. the relative (constant) velocity of sources [special relativity]
3. the relative acceleration of sources [general relativity] (ie the effect of their communication on one another - correlation, closeness.
[page 114]
ANIMATION = KINETIC [abstract]
REALITY = DYNAMIC [concrete]
Let us think of spacetime as tissue - look at the photos of planets and nebulae. NASA, Hans-Thomas Janka
Landecker page xi: 'A tissue is evidently an enduring thing. Its functional and structural conditions become modified from moment to moment. time s really the fourth dimension of living organisms. It enters as a part into the constitution of tissue. Cell colonies, or organs, are events which progressively unfold themselves. They must be studies like history,' Alexis Carroll. Landecker, Alexis Carrel - Wikipedia
Landecker page 1: 'technologies of living substance' of which religion is one, the culturing of humans in a certain society.
Tissue culture: human culture. Religion seeks to become an ideal human culture medium, a milieu humaine.
The hypothesis is that gravitation represents properties of the universal network itself rather than any particular message that may be sent. These properties are captured by the theories of relativity and quantum mechanics, the 'hardware' or physical layer of the Universe,
We begin with a simple translation table (page 113) then turn to quantum mechanics. Quantum mechanics is scale invariant. it does not mind how many possible inputs or outcomes thee are for an event, as long as they are all normalized to 1.
[page 115]
I see the site (naturaltheology.net) as a condensation nucleus for a wiki. By gradual accretion of detail, the original sed becomes just one of the many points in a newly created space.
Continuous functions describe flows that are too complex to resolve. The most basic of these flows is the flow of probability. A probability current of ℵ0 flows through the Universe all the time. This figure is all that is set by the initial singularity, that it [is] an entity from the moment time began and it is ubiquitous, consistent with the classical model of god. Aquinas 39
The initial singularity is a potential plurality because although it is just marking time in an invisible way (like the invisible phase in quantum mechanics) we can add a space (a counter) to generate an affine parameter which is time, an ordered set of numbers each of which (except the first or smallest) has a before and an after. One of our most basic perceptions in that you cannot go back in time, now forward. Time implies action, implies creation and annihilation implies birth and death. The old timers who dreamt up the idea of marketing immortality has to get rid of the whole shebang, and so invented a contradictory world of timeless activity, the vision of God, beatitude. Aquinas 608
Tuesday 24 July 2007
Whereas general relativity is modelled in a differentiable manifold, quantum mechanics works in a much bigger space, function space. Function space
[page 116]
like all the spaces used in mathematics and physics may be thought of as a data structure. Each event [pair of events] in spacetime is associated with a metric, a set of connection coefficients and a curvature tensor. The number of dimensions in the space tell us something about the complexity of the objects in that space. The points in 4-space are in fact differential equations telling s how things change as we move from point to point in the space.
Quantum mechanics is worked out in Hilbert space, a function space with certain properties that correspond in the long run to the conservation of the probability currents running through the Universe. All available information about the state of a quantum system can be encoded in a vector in a suitable Hilbert space. Hilbert space range from two dimensions sufficient to describe two state systems like spin 2 particles, up to countable, uncountable or even larger numbers of dimensions, depending on the cardinality of the domain of the function to be represented.
An observation of a quantum system us represented in the formalism as an operator with certain eigenvectors. The actual observation will yield any one of these vectors. The operator contains information about the probabilities of the observed system appearing in one of the eigenvectors, represented by eigenvalues ?
The measurement operator establishes a basis for the observation: Feynman Stern Gerlach. Feynman So my eye contains a frame of reference against which photons are observed,
[page 117]
The religion of a group of people is embodied in their administration and public service.
Network = data structure with distributed processing. Data structure determines how we find a list of data - random search or planned lookup.
Wednesday 25 July 2007
Human affairs have a quantum sort of uncertainty - Agatha Elephants. Christie This is an argument for scale invariance, ie the uncertainty principle acts at all scales and gives scale at all scales, eg the scale of the hydrogen atom.
The world is normalized to one in space, that is in mathematics, but normalized to ℵ0 in spacetime, because time gives us a lot of ordered slices of space.
The uncertainty principle relates to capital through borrowing and lending. What we are calculating is the probability that certain particle exchanges will take place, that is the probabilities of certain messages being exchanged.
All the elements to a superposition can be solutions to the same differential equation. ei omega t = cost omega t + i sin omega t, omega t = 1 + 2 n pi.
Planck's equation gives us the shape of the superposition, the energy in each eigenvalue/eigenfunction.
A book (or any message) is a transformation, which we model by permutation [and which is emitted by the mind of one person to operate on the mind of another person] There are a few steps missing here!
[page 118]
The model is a message. A message is a model. A model is a transformation. In linear algebra transformations are represented by matrices, IN - ROWS; OUT - COLUMNS or vice versa.
At the initial singularity all words mean the same thing.
Feature of quantum mechanics: Lo, Popescu and Spiller. Lo, Popescu and Spiller
. . .
In classical physics [action] has the dimension of energy.time, ie ML2T-1, the same as angular momentum. In the fully quantized world we say that action is a set of operations whose cardinal is a pure number and whose ordinal [is] a sequence of sub-actions. Quite often the order of subroutines determines the effect of the whole routine. So we see in the operations of cookery and quantum computation.
Another statement of the network hypothesis is that the whole universal process may be modelled as a network of quantum computation.
We approach quantum mechanics through the window of quantum computation and quantum information. Nielsen and Chuang
I have a house full of books and have spent thirty or forty years trying to absorb their content. Now, like Poirot,
[page 119]
I am relying on (my network of) little grey cells to come up with a consistent integration of all this information with my experience of life to come up with a consistent picture of the nature of god.
Mathematics is physical. It works right thee with the marks on paper. We employ meaning to cut down the necessary number of marks, so that mathematicians routinely write finite articles about infinite sets and prove things about these sets, like the theorems of differentiable manifolds and function spaces (computable manifolds).
The essence of mathematics is that a set of infinite cardinality may be represented in a space of the same cardinal number of dimensions. So we speak of geometric objects or groups which may be infinite spaces in themselves, and so with me, and infinite point in an infinite dimensional (human) space.
ENTROPY <==> MEANING. The 'amount of meaning' in an event is its cardinal, and places it somewhere in the transfinite hierarchy of meaning. The unreachable 'god' stands a the topless top of this hierarchy, Cantor's 'Absolute', a mathematically impossible entity that effectively bounds mathematics and any mathematical (ie symbolic ie abstract) representation of the Universe. Hallett, Absolute infinite - Wikipedia
Agatha Christie is my methodological Bible. Although each example is contrived as a detective story, each tale carries the lessons of science, that even small facts can be significant, that a consistent constellation of all the facts (ie messages from the situation) may define a unique answer (which may be a set of answers). We use facts to constrain and narrow down the space of possibilities, Requisite variety, like wrestling, getting a hold that immobilizes the opponent.
[page 120]
The opposite of love creating an environment that maximizes the lover's entropy.
A theory of everything constraints the Universe to one point, the set of all consistent sets, which we know to be non-existent. Already we have an uncertainty principle, manifested in the equality of entropy and information.
ENTROPY = a property of a SPACE
INFORMATION = a property of a POINT in a space
Lord have mercy on us: a pious hope for an easy run through the vicissitudes of life.
Is this work? Not yet in the sense of income, but yes in the sense of maintenance and capitalization. Building an intellectual property as I would build a house.
The time is coming to bring in some cub-contractors.
Reference the whole glossary to Wikipedia via links file.
Propositional calculus is digital and definite, complete and computable. Propositional Calculus - Wikipedia The trouble starts when we introduce quantification to give us predicate calculus: not 'A = B', but 'there exist and A, B such that A = B' versus 'for all A, B, A = B'. One proposition is expanded to a countable number of propositions. The number of quantifiers beings in powers of countable numbers. We model this in Hilbert space, each quantified occupying a dimension and the overlap integral deciding how many of the A's actually do equal the B's.
[page 121]
PROPOSITIONAL CALCULUS = the mathematical theory of classical computing.
Thursday 26 July 2007
9.25 The snake in the fridge is just waking up.
Elephants page 142: 'It is difficult to be sure. Very difficult. I've not been sure of it in the years that have passed since then, and there are quite a lot. ' Christie
Mathematics is an application of logic. We therefore imagine that logic is logically prior to mathematics and constrains the channels in which mathematics may flow.
Probability current, density operator.
These ideas are a blessing, a small step along the way, which seems to have so many steps.
To control a system is to bring it to a desired state or sequence of states, a point or sequence of points in state space.
Relativity and quantum mechanics work mathematically without ,meaning, as is appropriate to the physical layer. Meaning is added by the higher layers that use the physical, culminating in god, the ultimate user.
DUST NOTATION (CUISENAIRE) (ROMAN)
PLACE VALUE NOTATION (ABACUS) (ARABIC)
[page 122]
'Arouse interest'
We seek a consistent theological picture on which to proceed.
Requisite variety and the solution of equations. One polynomial can replace many linear equations, ie encode the same solutions as a set of linear equations.
Mapping by annihilation; mapping with creation and annihilation allows different structures to come into existence, destroying the old ones but preserving some symmetries, action, energy, momentum, all network things.
Religion is a public good whose means of production has traditionally been philanthropic, voluntary and not for profit. The actual mode of production is not to important, however, as the actual intellectual content of the religion which forms the foundation for its ethical directions. So is The Theology Company to be not for profit or commercial? My inclination has always been toward eventual public listing since this involves close public scrutiny with potential for very rapid growth.
A letter to . . . , my broker, on raising money for The Theology Company and its websites, the debt to be serviced by advertising income and other streams to be dreamt up by the packaging and marketing divisions.
Google, eg
[page 123]
The core is lots of traffic
1 000 unique visitors yields $5 per month in revenue
10 6 $5000 per month = a living
1010 $50M OK = a power.
What is the difference between missionary and marketing culture? The missionaries believe in their product, and some will die for it, whereas the average marketer will very wisely steer clear of anything injurious to their health.
The Theology Company makes no comparisons with or gives adverse publicity to other religions, nor does it raze their churches, smash their images [or] lay their countryside waste. This is a corporate position because personally I am a bit crooked on the Roman Catholic Church because it seems to me it should know better. But I have accepted that if there is anything better, I should get on with producing and marketing it.
A public company in which everyone can share. Voting power attached to individuals rather than shares. Maybe not possible, and repulsive to big investors.
A big enough company listed in all the markets would assume some sort of calming role in the financial vacuum (if Quantum field theory is to be believed).
[page 124]
. . .
All the product is available n the internet. We can set up thing such as the 'natural religion catechism'.
Core asymptote: zero footprint, where zero = human metabolism = materialistic dream guiding practical reality, the point at infinity.
Zero footprint on earth; zero footprint on eachother. We interpret zero as measure zero, as in the alphabet has measure zero in the space of words.
. . .
Classical religion - Imperial religion
New religion - Natural religion.
Soldiers are 'physical missionaries' sent to gain control of physical stocks in the same was that spiritual missionaries hope to control human minds and wills, ie hearts.
[page 125]
Control of desire.
. . .
To develop and market an intellectual property to be nicknames 'intellectual divinity'
Religion has long been too sacred to talk about, like sex once was. By commercializing and publicizing it we take it out of the realm of the sacred into financial probity, product value, safety and effectiveness, occupational health and safety.
Friday 27 July 2007
Every point p in the network is at the root of a tree whose leaves are every other point within the horizon of p.
A New Theology
A communication remains virtual until the addressee has replied (the loan is paid off?)
Requisite variety: the alphabet cannot control the word, but the word can control the alphabet, thereby increasing its own entropy.
[page 126]
TENSOR PRODUCTION
What is the next thing in my life: proper time (vs relative [communicated] time)
physXXCausality: c and the 'light cone' (communication cone).
An equation is a symmetry: it stays the same as the values of its variables change. As is a proof.
Why is the world quantized? And why can't we predict exact outcomes? Dense coding is indistinguishable from noise. Chaitin
