Notes
[Notebook Turkey, DB 55]
[Sunday 30 March 2003 - Saturday 5 April 2003]
[page 193]
Sunday 30 March 2003
Jammer. Jammer.
page 152: There is no conflict between 'mechanical' and 'spiritual'. The common thread is that they may both be predictable, ie (somewhat) deterministic.
"God' explains nothing, in such sentences as "all forces are the work of God".
ESSENCE = how it works ie, {PROGRAM, STRUCTURE }, eg {genome, cell}
[page 194]
NEWTON'S THEOLOGY
A formal system (like the Principia) can only have meaning in a system that can execute it. God is a name for the universal system that can execute all forms. Newton.
When God executed Marxism-Leninism, the result was ultimately murder and collapse.
page 153: Newton, Opticks:
"Whence is it that nature doth nothing in vain [selection] and whence arises all that order and beauty which we see in the world?" q 28, page 369. Newton. Excellent list of questions.
The basic trait of the US government is FEAR brought on by GREED. The US creates enemies by its greed. These enemies induce fear in the US. Inverse Generosity breeds security.
SLOGAN OF THE DAY 'generosity breeds security'
We love it because it is good for us. The church suppresses it because it leads to empowerment and independence. The repression is subtle, through the definition of sin and the managed self policing under the all-seeing eye of God, with the confessional to enable the system to keep track of the thoughts of the people. A cult. A psychic control mechanism.
The ethics of brainwashing the children: a fundamental question for the world. All this comes under RELIGION
Monday 31 March 2003
Theology (god) is the default explanation of everything. How does it work? How god wants it to work.
How do things work: the parts of a system move one another, eg internal combustion engine. Computer is a physical process made isomorphic to a logical process - clock hides gradual (continuous) changes [leaving only the logical steps in view]
Jammer.
page 157: The fact that in any inverse square situation the attractive influence of a sphere can be modelled by a point mass at the centre of the sphere greatly simplifies astronomical calculations. Given that the Universe has to perform these same calculations in working out its future from the past, perhaps we can see some selective pressure moving the system toward the inverse square law as the simplest and most durable solution.
page 158: . . . Newton's concept of force which formed the foundation of the theological interpretation discussed in the last chapter, originated from a reaction to the Cartesian view of geometrized physics which recognized only extension and impenetrability.
We try to get 'arithmetized physics' which recognizes only 'count' ie democratic voting physics. [but what is count? The actual count is defined by the method of counting, rather as a one form reduces a vector to a number.]
page 159: We distinguish between dynamics and kinematics but the difference is relative, and in the end even our dynamic explanations are simply kinematic ones since we can say nothing about the acts, only the essences (static structures) of acts. This does not mean that essence and existence are really distinct, only that the only thing we can communicate to one another is the essence of an act. The act itself is incommunicable (?) [quantum-no cloning?] (Speakable and Unspeakable in Quantum mechanics. Bell. Bell. This is to say that my experience (esse) is incommunicable, but given a
[page 196]
shared language and shared experiences, [we can come close].
genomic - humanic --> general linguistics and the evolution of language. The evolution of languages and structures are parallel and dual. At a given peer level (peer index), the same information is carried in the structure of the language as in the structure of the system [?].
The transfinite lives by mapping itself onto itself. A force is a mapping. [the force of self love]
Leibniz: the purely kinetic point of view, advanced by Descartes, is too one sided for a comprehensive understanding of natural phenomena and must be supplemented by a dynamic [creative] principle.
Function: many --> one. (entropy destroying, integrating)
Transformation: many --> many . . .
God: everything we do not understand.
Integration flattens complex structures for transmission to the other side where they are reconstructed in one of the ways consistently possible for the flattened product and the environment. Protein folding is partly the function of environment and chaperones. Environment is a set of tools which facilitate certain operations - enzymes.
entity - encode - transmit - decode - entity
Entity is called user. Technical terms, entity, peer index.
[page 197]
A message is the physical embodiment of a text. PACKET, PARTICLE.
A packet has an abstract representation of itself (CHECKSUM) which tells the receiver whether it is undamaged or not (at a certain level of probability).
Error correcting layer delivers error free (~ 1/x) data from end to end, eg ATOMS, INTACT PACKETS.
The basic plan is to conceptualize our world in terms made familiar by the theory and engineering of communication and computation. We want a theology delivered on the net that uses (tacitly or explicitly) the net as a model.
Jammer
page 160 Monadology - dynamics.
So we conceive of the Universe as pure act manifest in varying essences. card(act) = ℵ0, card(essence) = aleph(>0).
So in the network everything moves at its own place unless a change is communicated (force)
Core of the Trinity theory: REAL RELATIONS. Aquinas 165.
Eventually you will have to take note of what I am doing because I am using your language (mathematically encoded) to express ideas that you reject such as "Universe is divine", ie Universe is self explanatory, ie its essence is to be.
page 162: gauge theory.
[page 198]
This is it, moving on through the fog looking for clear vision. . . .
page 166: Newton De Principia does not discuss energy.
Every explanation presupposes an invariant, like energy, momentum, action, [metric] c, h, G, k.
Energy = rate of action; more energy, act faster.
IN (INVARIANT) OUT
(LANGUAGE)
(PROTOCOL)
(FORCE)
We seek science for its predictive value.
. . .
Does the Universe need the injection of new forces? Is it running down?
Leibniz: "The same force and vigour remains always in the world, and only passes from one part of matter to another, agreeably to the laws of nature."
page 169: This is a religious conviction [CONVENIENS - Thomas]
"His physics accords and harmonizes with his theology yet without mutual interpenetration. As we have mentioned before,
[page 199]
spiritual principles cannot be employed for physical explanations, nor the converse."
"'agere est character substantiarum'. These words, which he wrote in his Specimen dynamicum, may serve as a motto of dynamic mechanism. The world is a set of dynamic mechanisms adding up to a big dynamic mechanism? system.
mechanism - > deterministic
system -> deterministic, non-deterministic [sensitive to
environment]
page 170: Quod non agit, non existit.
Movement requires contact. FORCE = CONTACT, so action at a distance is meaningless, ie action without action.
PARTICLES have both DEPENDENCE and INDEPENDENCE.
page 171: law of continuity - the Universe is one.
page 179; "Kant steers a middle course between the Cartesians and the Leibnizians in their dispute about the true measure of force . . . "
page 185: Tyndall: "What do we know about an atom from its force? You may imagine a nucleus which may be called a, and surround it by forces which may be called, to my mind the a or nucleus vanishes and the substance consists of the powers m. And indeed what notion can we form of the nucleus independent of its powers . . . "
Schelling: "It is a mere delusion of the phantasy that something, we know not what, remains after we have denuded an object of all the predicates belonging to it/" ie all its operators, languages, translators and transformers.
The relationship of action to text is in a way the relationship of fast to slow? No.Maybe we define text as dead, incapable of self motion. [Text is in the ground state, incapable of action by itself]. We do not open a book and expect it to have changed itself from
[page 200]
last time we read it.
Muhammad spread his religion (to a degree) by conquest. We do not want to go so far but by taking on a .com property we do wish to spread by commercial conquest.
page 196: Mechanistic explanation of gravitation. Computational/communication network explanation of gravitation.
page 200: Third school of thought in the interpretation of force: "those who conceive force either as a primitive and irreducible action, or a purely relational concept, devoid of a separate ontological status and to be defined only operationally [? real relation <==> real operation] can also be traced back to Newton and his immediate commentators."
All this philosophical speculation really adds nothing to the practical consequences of Newton's laws and methods of calculation.
Essence - definition - may be infinitely long [like the definition of the Universe - definitions can be shortened, a la Chaitin, if they have repetitive elements, ie redundancy. The ultimate in compression (zero redundancy) is indistinguishable from a random number. Chaitin. ] The essence of a Turing Machine is its program.
Jammer page 203: "It was soon recognized that the issue involved transcends in its importance the technicalities of mathematics and physics and has a bearing on the evolution of scientific knowledge as a whole."
How it works -> how to do something.
"The interpretation of force, matter and motion became a problem of general philosophic interest.
George Berkeley De Motu (1721) Siris [Chain] (1744). Berkeley.
page 204: Berkeley: "Force, gravity, attraction and similar terms are convenient for the purposes of reasoning and for
[page 201]
computations of motion and of moving bodies, but not for the understanding of the nature of motion itself." De Motu.
"With respect to attraction it is clear that this was not introduced by Newton as a true physical quality, but only as a mathematical hypothesis."
OUR BIG STEP: RELATIONS ARE REAL, FREEDOM IS REAL
. . .
page 204: "Real efficient causes of the motion . . . of bodies do not in any way belong to the field of mechanics or of experimental science, nor can they throw any light on these." Berkeley, De Motu section 41.
Text travels at c with respect to me, and so, for me, is frozen in time on my horizon and acts in some way as my cultural DNA. Here, with this growing text, I am expressing my interaction with my culture.
page 205: All that natural science can supply is an account of the relations among symbols and signs [and these relations could very well be real, that is implemented in the world] but the sign should not be confounded with the vera causa, the real cause of the phenomena. [distinct but isomorphic to the real - implementable.]
[Berkeley was a] hard nosed formalist, forgetting the application of ideas and language. All expressed ideas are elements of a language. A language is the leading edge of a literature, that is language fossilized in text. The language lays down the literature as it moves through time (the literature being theoretically eternal and fixed in time).
RULE OF LAW = RULE OF LITERATURE (TEXT)
[page 202]
interpreted by judges in the light of modern language/culture [+ juries = peers]
page 307: Berkeley: All agents incorporeal (dead). Only texts are corporeal MATTER = TEXT
and so to God = nothing/everything - the all-answer!
'"Force" is a construct of the conceptual scheme of physics and should not be confounded with metaphysical causality" [whatever that means].
page 209: Maupertuis "We speak of forces only to conceal our ignorance"
"The concept of force is but an invention to satisfy our desire for explanation.
Yes, and it is a good invention if it gives us a model whose behaviour is measurably isomorphic to reality. SURVIVAL.
Force: broad applicability; broad definition: an act of communication is a force. Force is communication.
page 210: Maupertuis: "Our attempt to transcend by means of causal ideas the domain of experience is philosophically illegitimate".
But it happens and is productive, so where does that leave your philosophical constraint?
All this talk is an attempt to kick off the old emotional shackles and let pure formalism lead us into the full complexity of nature.
page 211 All this criticism (ie disempowering nature) leads to a bigger and bigger role for god the puppeteer making everything move in harmony by remote control rather than local communication.
Leonhard Euler Mechanica rational mechanics, 'apodictic science', 'necessary truth'. Euler.
[page 203]
. . .
d'Alembert Trait de dynamique
What we are really looking for is efficient methods of applying dynamics to practical problems in engineering.
page 214: Lagrange Mecanique Analytique (1788) Lagrange.
"Reduire la theorie de la mecanique et l'art d'y resoudre les problemes que s'y rapportent a des formules generales dont le simple developpment donne toutes les equations necessaires pour la solution de chaque probleme."
Christie The Secret of Chimneys page 199: "Its a very useful thing sometimes, an idea." Christie.
Language must have both structure and freedom.
page 215 Saint Venant: ". . . whatever problem in terrestrial or celestial mechanics we consider, forces never appear in the data or in the answer to the problem" (? weight)
page 221: :Force as well as mass are thus reduced in Mach's conception of mechanics to purely mathematical expressions relating certain measurements of space and time."
Tuesday 1 April 2003
Jammer page 241: "With the works of Mach, Kirchoff and Hertz, the process of eliminating the concept of force from mechanics completed its logical development."
[page 204]
COURT: an attempt by two views to incline a judge and jury to themselves - FORCE OF EVIDENCE, LAW, ARGUMENT
Compare 'causa' which began as a legal terms (?)
page 243: " . . . has been contended that the concept of potential energy is no less mystical than the concept of force."
ENERGY OF STRUCTURE: The energy spends half its time in the text and half its time in the changing of text - Simple Harmonic Motion. Motion between states of rest is communication between texts.
TEXT ACTION READING (text to processor) WRITING (processor to text)
Reading and writing are the same actions looked at differently - every read is a write.
WRITING is hidden until READ (ie acted upon)(dead law)
. . .
What is going on here is the translation of physical notions into communication notions to eliminate events like war.
"Hertz, J J Thompson and others . . . attempted . . . to reduce the allegedly confused notion of potential energy, again with the aid of concealed masses and their motions, to the concept of kinetic energy complementary to the kinetic energy of visible masses."
We aim to set up a mew conceptual framework whose elements conform more precisely to the reality than the set of words and ideas that found the current dialogue. We can them provide a
[page 205]
set of mappings from the informal language of the world to the formal language of the model.
. . .
What is real? Ideas about this question seem to be strongly correlated with times and places. Here, for the time being, we are concerned with the time line that runs through Ancient Greece, the Roman Empire, medieval Europe to modern Europe and its colonies. This leaves out two thirds of the planet, but we must begin with what we know. The aim is to produce concepts and models of reality that are acceptable to everybody, [ie invariant over human space and time]
Looking at the history of epistemology, we might discern a broad trend running from the proposition 'true reality is invisible' to the proposition 'reality is right here before our eyes'. In more technical terms a move from that rationalist/idealist end of the spectrum to the empiricist/realist point of view. Is the visible Universe a puppet of invisible forces, or is it fully responsible for its own life? Can it explain itself?
An assumption of the idealist view is that the visible Universe cannot explain itself, hence the invocation of invisible 'gods' to make it work. 'God' here means "the explanation of everything we cannot explain" which is a lot and growing.
The idea that the world is not self explanatory depends quite a lot on how we understand the world. Is it order or chaos? Are things going well or are they going badly? Is there a positive force of evil, and other such questions. The hope here is to provide a model of the world that shows that the world can be self explanatory because a) the model is self explanatory; and b) the model appears to map onto the world.
[page 206]
The model we use is a communication network. From a physical point of view, a communication network is a set of physical agents connected by a set of physical lines. The agents provide interfaces to other agents. Depending on how we look at the system, different agents may be designated users or tools.
Potential and kinetic energy simplify the treatment.
"The principle of least action takes the very simple form that with a given quantity of energy, any material system will by its unguided motion go along the path which takes it from one configuration to another in the least possible time. J J Thompson, Applications of Dynamics to Physics and Chemistry.
'Potential" is simply a slightly different encoding of the notion of force. Force becomes the gradient of potential.
Statics is the branch of dynamics where forces are in equilibrium and produce no motion eg engineering structures - civil engineering vs mechanical (dynamic) engineering (including thermo- and hydrodynamics).
page 248: Force <--> energy. Many ways to get the same result distinguished by clarity and convenience.
page 249 Force as a function? Input and output?
page 250: "The concept of force as a purely functional relationship is in full accord with its application in quantum mechanics and nuclear physics".
We can say, in terms of our model, that all English terms point to some relationship which may be a mapping broadly taken, or a function (integration) many --> 1!
Quantum Mechanics is reversible
[page 207]
page 251: "It is of course the correspondence between the mathematical result and the experimental result that justifies the procedure. "
Quantum mechanics can explain itself because it is reversible, ie entropy preserving.
Packet communication: exchange force "Its unconventional character lies rather in the assumption of a continuous exchange of particles which accompanies the interaction and transmits the force - a process that receives its operational justification through Heisenberg's uncertainty principle."
ie non-dissipative = non-thermodynamic communication.
[the big question, answered by Cantor Universe is how does the Universe both increase and conserve entropy?].
The 'quantum mechanism' is hidden from us by size: there is a lower bound to the consciousness (self interaction) of the Universe measured by Planck's constant.
Planck scale: distance at which gravitational energy becomes comparable to the masses bound?
. . .
[page 208}
. . .
Kissinger on young Rumsfield "a skilled fulltime politician-bureaucrat in whom opinion, ability and substance fuse seamlessly" An operator in other words. (We just have to construct the Hilbert space.) Economist, Lexington 29 March 2003, 37.
"He is 'one of us' in a way that Colin Powell could never be. Mr Rumsfield is one of the most conservative members of a conservative club" ibid.
"Mr R, they whisper, is a classic victim of 'Sun King syndrome', a near universal malady among bosses of all sorts that leads them to overestimate their own abilities and underestimate everybody elses."
"Whether Mr R is breaking another one of his rules, and needlessly repeating Mr McNamara's mistakes in Vietnam all those years ago, we shall soon discover."
Wednesday 2 April 2003
Jammer page 254: Mass of virtual particle determines range of force.
FORCE and STATE: different forces cause different changes of state, ie FORCE carries information: PARTICLE - PACKET - FORCE.
[page 209]
Network picture of the Universe is naturally covariant, since we need no coordinate system, just agents and links whose physical position is rather secondary at the network level - though we explain physics also by network. [this is not strictly true - all the physical entities in a network are mapped to logical addresses, which serve as a frame of reference for the physical and vice versa. This mapping is covariant, in that a network will function as well as long as its physical elements have internally consistent logical addresses.]
Jammer page 257: "in relativity the quantity force is not in general codirectional with the acceleration it produces".
"On the grounds of the rejection of the absolute simultaneity of two distant events, special relativity comes to the conclusion that action at a distance has to be excluded as a legitimate physical notion. Forces, in other words, can only be contact forces."
page 258: "Through the principle of equivalence, based on the proportionality of inertial and gravitational mass gravitation reveals itself as merely an inertial force - it is fictitious to the same extent as centrifugal force, for example". (?) [it seems that centrifugal forces are real enough, and generate real pressure/stress!]
geometry of continuum determined by line element.
Solution of a differential equation takes us from local to global (relative)
General relativity assumes only one law of motion:
the variation of the integral of the distance is zero (variational law), ie particle moves on an extreme path.
page 259: "Thus gravitational forces are the outcome of a 'wrong' metric" [so I am 'wrong' when I am attracted to the earth?]
We look to the network model to resolve this sort of problem. But how - each time I think of this it looks easy until I get involved, and then the difficulties show.
[page 210]
A commentary on the ten commandments eg "thou shalt not covet thy neighbour's wife" [Exodus, 20:17 Exodus.] - gender specific assumption of property. Allow autonomy and we have a quantum mechanical situation of binding and loosing.
"Whatever you bind on earth will be bound also in heaven. Matthew 16:19. Matthew. . . . freedom and constraint - very logical, bound and free terms.
Jammer page 250: If the appropriate Riemannian metric had been used, in which the so called gravitational potentials gmn are determined through the field equations by the mass-energy distribution, the trajectory of our projectile would identify itself as the geodesic line in four dimensional spacetime corresponding to the given initial conditions.
page 260: gravity is purely formal. Spacetime is a text which is manipulated by quantum processes?
Geometrodynamics: what makes it go? Expansion/contraction.
Gravitation sees energy alone. There is no need to introduce too much complexity.
261 "[Force] lies now in the functional relationship between the spacetime structure and the mass-energy distribution, via Einstein's field equation. The Board of Trustees of the University of Illinois.
"Once this assumption [irreducibility of field equation] is made the whole mechanics of gravitation consists in the solution of a single system of covariant partial differential equations."
[The tensor formalism determines the communication links between the various equations. So we can describe the gravitational network by at most the interactions of the ten fields carried by the stress energy tensor and the Einstein tensor. ]
PHYSICS: the language of contact.
Why is the Roman Catholic Church tradition so averse to the body? It is a necessary simplification to develop corporate structure that informs the Church. "Body" as a measure confounds the pure hierarchical notion because it makes us all equal animals.
[page 211]
Jammer page 263 ". . . it is essentially the non-linear character of the field equations that made it possible to deduce the dynamical laws from the field equations themselves.
The field equations choose the dynamical law as TEXT specifies MOTION.
To conclude: Force is the mapping from theory to reality, the intuitive connection between the words and the effects cf. the forces of hunger, lust, self defence etc built into our genome.
Yourgrau and Mandelstam: Variational Principles in Dynamics and Quantum Theory. Yourgrau and Mandelstam.
Y&M page 17: Fermat's principle: The variation of the integral of ds/v = 0. v = velocity at any point. ds is an element of the path (ie a real number representing an infinitesimal length.
Variation is zero: ie the difference between the integral taken along the actual path and that taken along a neighbouring path is an infinitesimal quantity of the second order in the distance between the paths, [ie it vanishes more quickly that the distance between the paths as they are brought together]
page 19: Maupertuis (1698-1759) The principle of least action.
essai de cosmologie (1759) ". . . the perfection of the Supreme Being in its Divine Wisdom would be incompatible with anything other than utter simplicity
[page 212]
and minimal expenditure of action." (?) Why not maximum complexity and maximum action?
page 24: Euler and Lagrange Euler (1707-1793)
The principle of least action was first published as an explicit dynamical theorem by Euler in 1744: the variation of the integral of vds = 0.
page 29: "Credit for having first given the correct formulation of the principle of least action for general cases must be attributed to Lagrange 1736-1816."
[a system of interacting particles] moved from one configuration to another in such a way as to make the total action, ie the sum of the actions of the individual particles, stationary as compared with adjacent virtual motions between the same configurations and having the same energy as the actual motion,
. . .
Minimum action to achieve a permutation. Each piece goes to its final state in one move.
A system of interacting particles whose forces are derived from a potential [TEXT]
Force, desire, money: a text can be a force. So the potential that drives a Turing machine is its program.
Force: mathematical side = ordered set; physical side - desire. An ordered set implies a desire.
a book carries a message (force, desire)
PATH = set of configurations.
[page 213]
Y&M page 31:"[Lagrange's proof] confirms that the principle of least action as expressed by Lagrange, together with the law of conservation of energy, is fully equivalent to Newton's laws of motion and may, indeed, be employed as an alternative formulation of the principles of dynamics."
MATTER = POTENTIAL = TEXT
ENERGY = MOTION = CHANGE OF TEXT.
Harmonic oscillator: TEXT changing TEXT
. . . here -> there -> here . . .
PHYSICS = {CONSERVATION OF ENERGY, LEAST ACTION}
Page 33: Equations of Euler and Lagrange.
Lagrange: generalized coordinates, ie any set of variables sufficient in number to define unambiguously the configuration of the system, ie one-one mapping. Transfinite network as a configuration space in habited by Turing machines. Each set whose cardinal number is ℵ0 is big enough to hold one Turing machine and map all its configurations.
Answer to a problem = integration.
page 34: generalized force. . . .
41 Hamilton: generalized momentum.
Hamiltonian function is the energy of the system expressed as a function of the generalized coordinates (eg positions and momenta) . . .
[page 214]
So the foundation of a physical law is a force that has the effect that the law is supposed to have.
Y&M page 44: Hamilton: "The theoretical development of the laws of motion of bodies is of such interest and importance that it has engaged the attention of all the most eminent mathematicians since the invention of dynamics as a mathematical science by Galileo . . . Among the successors of those illustrious men, Lagrange has perhaps done more than any other analyst to give extent and harmony to such deductive researches by showing that the most varied consequences respecting the motions of systems of bodies may be derived from one radical formula; the beauty of the method so suiting the dignity of the results, as to make the great work a sort of scientific poem."
How do we describe the potentials in a computer?
An act either converts potential energy into kinetic energy of kinetic energy into potential energy:
Gun firing: potential to kinetic; leaf growing kinetic to potential?
page 47: Hamilton's principle "a system moves from one configuration to another in such a was that the variation of the integral of the Lagrangian with respect to time between the path taken and a neighbouring path coterminous in space and time with the actual path is zero. . . .
Newton, Einstein and everybody else are circling the collection of observations and symbols and explanations that their predecessors have collected, each trying to see the way forward, to create a set of relationships between the bits and pieces that they have trying to see a little further. At this
[page 215]
point we are playing with matter, spirit, information, communication, error, general relativity and quantum field theory. How do they all fit together. We are thinking in terms of particles and fields that is texts and protocols for the interaction of texts and meanings. Just like an Agatha Christie. But at least there the author knows the answer. Here nobody does.
Thursday 3 April 2003
De Ente et Essentia. Every communication involves two terminals, source and recipient. Even a monologue can be conceived as a person talking to itself.
We begin with the two characters Being and Essence. . . .
Thomas had an absolute foundation in God. We are in god, so we are reduced to relativism. Fixed things control the moving, as the moving change the fixed.
Fixed essence in Plato's Ideas.
Symmetry = fixed relationship.
Epistemology - evolution, sculpture, big bang - Darwin.
The foundation of Christian epistemology is God.
Our central idea is transformation, modelled by permutation. Every instance of a word is unique [the word may have been used often be fore and have an approximate standardized (dictionary) meaning, but it is made unique by the context of its utterance. Nothing in the world happens twice.]
Glossary: noCloning
Once we work down to a fixed set of symbols, we can
[page 216]
begin to do calculations with them, substituting one for another in accordance with the definitions of the symbols eg y = x2, dy.dx = 2x . . .
Yourgrau and Mandelstam:
page 45: extend the principle of least action to generalized coordinate systems, ie how to apply it to the transfinite network, the goal of all our work.Must learn it first.
In generalized coordinates least action principle is written [equation]
where we take r to be a natural number drawn from an index set cardinal ℵ0.
Lagrange introduced generalized coordinates,.
Back to that rather desperate feeling of not having it in me to achieve what I want to achieve, The whole system is just too complex. One must continue, however, to search for easier and clearer paths to the goal.
The duality of generalized coordinates is designed to cover the main classes of interaction, ie p, q may be momentum, - position, energy - time, action - number. Here we reflect our theoretical position by choosing essence - existence and write equations like Hamilton's canonical equations.
. . .
H (Hamiltonian) = T (kinetic energy + V (potential energy) = existence + essence. Constant H +> more existence +> less essence.
[page 217]
H = energy = m. dH/dt = power = dm/dt. (m = mass; assume c (velocity of light) = 1).
Whatever our theory, its inputs and outputs are representations of numbers,
essence = ordered set; existence = operator.
essence2 = essence1 + the sub of operations involving e1 and e2.
If you want to appreciate the importance of encoding for intelligibility, look at the binary version of this file and see if you can make more sense of it than of this text.
Prevent resource based conflict: "Thou shalt not covert thy neighbour's x" But if what is one is very poor and the Neighbour rich? Is this likely?
Let us, as they say, assume a spherical chicken . . .
We build our model using three layers of the transfinite network, peer indices n-1, n and n+1. We can then study its behaviour at the boundaries n=0 (n-1 does not exist) and ℵ0 (n+1 does not exist).
Small world: if I can just get published by Nature, I will link to hundreds of other small worlds. JOURNAL is shortcut or wormhole!
Hilbert oscillator --> Harmonic oscillator.
Peer index n: singly, doubly, nthly ordered sets.
All the dynamics we read about is modelled by natural and reals, what is the advantage of bringing in the transfinite numbers? - layered shape of the Universe.
[page 218]
Emch. Emch.
page 6.: "Newton's originality, at the beginning of the Principia, was mostly in his determination to write down basic axioms from which the theory could proceed deductively by mathematical reasoning, and his ability to extract concise axiomatic statements from the mist of ideas that has accumulated on mechanics . . . "
Quantum theology = quantified theology = physical theology.
page 24: "The canonical procedure by which the Hamilton function H is associated to the Lagrange function L is the Legendre transformation.
Canonical = explicitly coordinate free.
page 35: We learn about the real by contemplation of the impossible.
EXPLANATION - THING/MODEL
FORCE is the intuitive term to use to connect elements of the thing with elements of the model.
Cylinder has zero Gaussian curvature but different topology from the infinite Euclidian plane. Topology describes the way things are connected on a global scale but is unconcerned with lengths, whereas curvature is closely connected with length. General relativity (and the geometry of curved space) require a clear distinction between topology and curvature.
Curved = warped.
"The crucial thing for the warp is not the bulging out but the fact that the distances between neighbouring fibres is no longer consistent with the rules of Euclidian geometry.
[page 219]
The metric therefore depends upon the coordinates we choose as well as the actual geometry of space.
Taxicab metric, ds = |dx| + |dy|. This shows that quadratic metrics, which are the only ones we use in physics, are just a special case. "Geometry" in more generalized metrics is not even "non-Euclidian" in the usual sense, It is totally different. [However, by taking an abstract enough view of geometry, we can arrive at properties common to all metric spaces.]
Hilbert spaces.
Tautology: A smooth surface is one with finite Gaussian curvature at all points.
Leahy: Bad Cosmology
Pressure in the early Universe is the driving force for expansion? No
Cosmic Constant: Leahy blunder
"And in fact the constant was not necessary because it is perfectly possible to include an equivalent term as part of the stress-energy tensor, representing the vacuum value of some quantum field; this is the basis of inflationary cosmology.
"God is slick be he ain't mean' "One could say that Einstein's main achievement in 1905 was to use this positivistic rejection of purely theoretical entities to weld together that mish-mash of ideas . . . into a coherent and well-justified whole.
Newton: We do not have to explain perpetual motion but rather change of motion.
Friday 4 April 2003
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"Curiosity demands that we ask questions, tat we try to put things together and try to understand this multitude of aspects as perhaps resulting from the action of a relatively small number of particles and forces, acting together in an infinite variety of combination" Feynman, 2-1.
In ℵ0 any system less that ℵ0 is modular.
Essence and existence are distinct in subsets of the Universe (broken symmetry), one in the Universe as whole (god)
PHYSICS --> STATISTICAL MECHANICS --> CHEMISTRY
aleph(n) --> statistical mechanics (Kolmogorov's axioms of probability) --> aleph(n+1)
Somewhere here in the transfinite transition we must study the increase in power of permutation over subsetting. Kolmogorov goes from aleph(n) to aleph(n+1) by 'random events' as is made necessary by "Chaitin's Rule" [no system can control a system more complex than itself - requisite variety]. Chaitin. On the other hand, the permutation power in aleph(n+1) allows is to control the random events in aleph(n).
This power comes from the domination of n log n over n log 2. put Stirling's formula in here,. I'm dreaming, but according to the experts, dreaming is part of the job. The other part is realizing the dream by work, not magic or fairies!
Feynman 3-2: "For a time it was believed that the substances that are associated with living things were so marvellous that they could not be made by hand, from inorganic materials.
- So life is a combination of less- or not-lives.
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3-9 "How did it get that way? . . . There is no historical question being studies in the physics of the present time. We do not have a question 'Here are the laws of physics, how did they get that way."
This is coming, see Greene, Smolin, . . .
3-10 See the Universe in a glass of wine. "So let us put it all back together, not forgetting ultimately what it is for. Let is give us one more final pleasure: drink it and forget it all!
4-1 Conservation of energy "That is a most abstract idea because it is a mathematical principle: it says there is a numerical quantity which does not change when something happens.
4-5 Principle of virtual work.
Saturday 5 April 2003
On an orbit from physical dynamics to theological dynamics.
Monists had to deny motion.
Dualists, eg Aristotle.
Galileo inertia.
Newton - calculus, transformation.
The purpose of this article is to construct an explanation (in terms of physical dynamics) of the path from physical to theological dynamics. We mean here by theological dynamics the theory which explains not only
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the motion of material particles but also motions in what is traditionally known as the spiritual or immaterial domain.
We begin with an hypothesis about the existence of the spiritual or immaterial domain. We shall proceed in terms of naive set theory, leaving it till later to tighten things up with an axiomatic approach.
PHYSICAL = PUBLIC
SPIRITUAL = PRIVATE
Feynman I 7-4: "Any great discovery of a new law is useful only if we can take out more than we put in" (profit, productivity).
How do we measure the momentum of the Roman Catholic Church? Then we can calculate how much force and time are needed to turn it around. Then we can use the transfinite reproduction theorem or some such which says that if we can produce an idea so seductive (and therefore powerful) that everyone is attracted by it and assimilates it into their system (plasmid, virus) so that the influence of the RCC evaporates we have turned a ship around with minimal effort, just as the captain of an oil tanker might by gentle pressure on a small wheel.
Amplification and error correction are both exponential/? structure. We can study them in the abstract space of the transfinite network.
This work is all done with the aid of drugs and gorgeous photos, substitutes, in celibacy, for a real mate. But at my age, perhaps, it is good for the world if I forswear mating and pour my energy into a theory of peace. Even if it is a failure, some of its beauties may inspire others to find a path to the same target - THE VISION OF GOD.
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I am an animal and must learn to run myself as an animal, selecting the inputs for the outputs wanted and vice versa.
A good explanation of the world is an interesting tautology = (in the formal world) equality or, more precisely, identity. - how do we distinguish. What we mean is substitutability, the error correcting and creative root of the world.
We explain our model by linking it to the facts.
One beauty of the net is that the commercial and corporate entities are the same effective size as individuals.
One measure of the rate of real progress is the rate of text production, but that does not control for the meaningfulness (entropy) of the text produced. Small world entropy. Watts. Why are small world constructions more efficient? Hierarchy and copying. One proceeds by linking intuition and formalism, trying to see features of the world in features of the formalism. This is the dual mutual sculpting process that explains both the evolution of the world and the evolution of science.
Spirit acts on matter and matter on spirit.
Science works best when there is a bijection between language and reality. So we create phase spaces with enough dimensions to provide every degree of freedom in reality with a degree of freedom in the model: n particles, say, n dimensions.
A significant quantum mechanical problem is the mapping between Hilbert space and 4-space. Veltman. We think of independent degrees of freedom as independent degrees of freedom with no crosstalk. But what happens when we rotate the axes? Then momentum in the . . . x direction can be split between the x, y, and z directions. Nevertheless the reality that space is 4D does not change.
. . .
We can see the complexification of the world as the multiplication of independent channels of communication. . . .
Symmetry = degree of freedom/degree of indifference.
We are indifferent to communication channels which we cannot read and write.
Because communication is relative, it is in a sense coordinate free, but it still depends on protocols to establish the relationship, ie make communication possible, eg the internet protocol.
In many situations there is 'crosstalk' between dimensions. North is north and east is east, but the distinction breaks down at singularities like the poles. Linear independence.
