Notes
[Sunday 8 February 2009 - Saturday 14 February 2009]
[Notebook: DB 65 Symmetric U]
[page 106]
Sunday 8 February 2009
To keep the Trinity or leave it out? [of why-quantized] What Augustine and Aquinas are saying is perfectly consistent with both experience and quantum mechanics: Augustine Aquinas 165 Any system observing itself, diversifies itself. The Father begets the [Son] The qubit begets two bits; I reflect upon myself and slowly bring forth all these words, while personally becoming older and more complex. And credit where credit is due. The psychological model has a long history stretching deep into the past in all cultures that have left us a written history. Hacklin
This process in analogous to Peano's adding 1, or Cantor's generation of the next transfinite number. From a network point of view an oscillator is the simplest computation while the reproduction of a person or the generation of the Son may be modelled by the production of a new transfinite number.
Kauffman Kauffman
Monday 9 February 2009
We are thinking of a communication channel as
[page 107]
an algorithm (represented by a Turing machine which transforms the message emitted by the transmitter into the message received by the receiver. For duplex communication, we require the inverse algorithm that goes the other way. Quantum field theory thinks of the communication of forces in terms of the exchange of particles, so we can think that forces have something to do with particles, algorithms and transformations. From this point of view we can think of every particle as a snippet of software that serves as a subroutine in the overall universal process, so explaining why all electrons etc are identical because they are all the same software. Further, we imagine that point particles are those whose software does not require 3-space for its representation. How do we extend this idea to fermion vs boson, ie antisymmetric and symmetric wavefunction, ie using all the possibilities at a given level of complexity.
Yang-Mills Gauge theory - Wikipedia, Yang-Mills theory - Wikipedia, Mass gap - Wikipedia
Dodd page 87: 'So invariance the the Lagrangian under local gauge transformations requires the existence of the photon: the long range electromagnetic field. A physical explanation of its existence may be thought of as communicating the difference space-dependent conventions defining the phase of the electron wave at different points in space.' Dodd, Coughlan
By carrying energy from place to place that suggests that energy can be localized, ie that the point energy of the initial oscillator has been distributed over 3-space while remaining constant (conserved) in time.
Tuesday 10 February 2009
[page 108]
The physics community has long been receiving free drinks on the strength of the scientific and successes of the second world war. From their point of view it seemed reasonable to develop nuclear weapons before Hitler, but the belief that Hitler was developing weapons suggests, in hindsight, the same sort of politically driven intelligence failure that led us into the invasion and destruction of Iraq. Rose, Ricks
Yang-Mills gauge theory and networks.
From the initial oscillator to spacetime.
C, P and T are our fundamental symmetries, or, we might say, the fundamental breakings of symmetry. Streater and Wightman Clearly the initial oscillator, since it is associated with no counter or no complexification is in a sense reversible in time since it has no time, not has any measurable period, ie there is nothing to compare it to. It is, we might say, pure energy with no structure except two states, p and not-p which succeed one another in 'any' order.
The next symmetry, also not requiring space in the conventional sense, is C, the diversification into 'particles' and anti-particles. The defining characteristic of such particles is that when they meet they 'annihilate' into pure energy, which can then break its symmetry once more into different particles.
Next, P requires some notion of space for its conceptualization and it is formalized as Lorentz Transformations with a negative determinant, at least in 3-space (Streater & Wightman).
Dodd: 'Spontaneous symmetry breaking: Obtaining asymmetric solutions (ie massive W bosons) from a symmetric theory (ie
[page 109]
gauge invariant theory) is common in many branches of physics. . . . How has [does?] this come about? The answer lies in the fact that the symmetric state is not the state of minimum energy, and that in the process of evolving toward the minimum energy state, the system has broken its initial symmetry, page 89. Spontaneous symmetry breaking - Wikipedia, Yoichiro Nambu - Wikipedia
Symmetry (as in the symmetric Universe) presents us with a huge array of possibilities which are represented in our model as permutations which, when implements as algorithms, give us more or less effective ways to achieve a given task. These algorithms, we surmise, compete among themselves and from all being winners are winnowed down to the fittest, thus breaking the initial symmetry,
Dodd, page 89: 'We now want to apply these ideas to particle theory to see if a broken symmetry has anything to do with particle mass.'
The C symmetry must have been broken at a time when the whole Universe was so small (or communication so fast) that it was broken throughout the Universe so (as far as we know) there are not whole regions (galaxies, clusters, etc) in the Universe made of anti-matter.
The symmetry represented by U(1) simply represents the initial oscillator with all its manifestations we now call qubits. Qubit - Wikipedia
We can only get stationary patterns of interference (as in the two slit experiment) if we have stationary relationships of phase which in turn require stationary energies. If we conduct the two slit experiment with 'non-monochromatic' particles their different wavelengths give different interference patterns whose sum is spatially symmetric
[page 110]
and so invisible. Conversely, we can use a glorified 'two slit' ie a diffraction grating, to sort a mixture of wavelengths into different energy bins, as is done in spectroscopy.
Is the initial oscillator the Goldstone boson, undetected because it is ubiquitous? Goldstone boson - Wikipedia In the unbroken symmetry there is just the Goldstone boson whose symmetry is broken in to a Goldstone boson (the kinetic energy) and a massive particle, which corresponds to a particle with kinetic energy.
Goldstone bosons and Higgs particles. Higgs boson - Wikipedia
Gravitation + general covariance leads us to continuity at the fundamental level. So we ask 'is gravity quantized? No, because it deals with pure energy it is foolproof and so incapable of error by pure symmetry. Gravitation treats all possibilities equally.
Selection and spontaneous symmetry breaking?
For the initial oscillator, the formula E = h bar omega products hat the quantum of energy is the energy of the Universe.
Dodd page 15: 'Resolution of [the paradoxical appearance of the photon as both a particle and a wave] requires the introduction of a new entity which reduces to both particle and wave in different circumstances. The entity turns out to be a field. . . . ;
All the information in quantum mechanics is carried by phase which is equivalent to action, ie energy x time = frequency x time = the amount of resource devoted to computation since 1 revolution = 1 execution of a Turing machine.
[page 111]
Dodd page 19: 'Heisenberg's approach is the literal manifestation of Wittgenstein's parting philosophical rejoinder, 'concerning that of which we cannot speak, we must pass over in silence'. Wittgenstein, Ludwig Wittgenstein - SEP We can speak (or write equations) only of what we observe, and so observation is to have pride of place in quantum theory.'
A particle is the superposition of many processes operating at different frequencies, that is the execution of a complex algorithm.
Pauli exclusion principle = particle no cloning: simply put if particles are fully identical there is only one of them not two. Identical particles means the same piece of software executing in different instances.
Churchill page 289: 'Few recognized the difference between winning battles and making lasting conquests. Parliament in its youth was eager for war, improvident in preparation and resentful in paying for it. Churchill
page 295 'The revolt, which to the historian is just a sudden flash of revealing light on medieval conditions among the poorer classes, struck with lasting awe the imagination of its contemporaries. It left a hard core of bitterness among the peasantry, and called forth a vigorous and wasteful resistance from authority. Henceforth a fixed desire for the division of ecclesiastical property was conceived.'
page 295: 'The bishops were instructed to arrest all unlicensed preachers, and the Archbishop himself rapidly became the head of a system of Church discipline, and this, with the active
[page 112]
support of the state in the Lancastrian days, eventually enabled the Church to recover from the attack of the laity.
Churchill page 296: 'By his frontal attack on the Church's absolute authority over men in this world, by his implication of the supremacy of the individual conscience and by his challenge to ecclesiastical dogma, Wyclif had called down upon himself the thunderbolts of repression. But his protest had led to the first of the Oxford Movements.' John Wycliffe - Wikipedia
'Fuller the seventeenth century writer, wrote of Wyclif's preachers: "These men were sentinels against an army of enemies until God sent Luther to relieve them".'
The qubit drives the world. Looking at enough of them with random phases, we see U(1), but at the detailed level, each of them goes its own way with a certain frequency. Circle group - Wikipedia
U (1) is Abelian. Not so more complex groups. Abelian group - Wikipedia We can see what is happening in the construction of chiral molecules which have enough structure to be orthogonal to one another no matter how they are placed in space.
1401 De Haeretico Comburendo Henry IV
Michael Atiya: 4 [Clay Millennium] problems at the interface of geometry and analysis. Clay Millennium Prize - Atiyah
. . .
[page 116]
John Tate: [3 Clay Millennium prize problems} Reformulation of Arithmetic and Geometry Clay Millennium Prize - Tate
. . .
[page 117]
Wednesday 11 February 2009
Hamilton's variational principle: Systems evolve so as to minimize L = T - V. For a computer T = rate of processing, V = capacity of memory. Memory is governed by the Pauli exclusion principle, so, as in an atom, if you want more memory you
[page 118]
must have more electron states each having different potential energies mediated by their relationships to the nucleus [and eachother]
Each new correspondent on a network is a 'perturbation' of the network.
Dodd page 28: 'In the quantum version [of Hamilton's principle] as we are dealing with wavefunctions (or more properly fields) which extend throughout space, we do not deal with the total Lagrangian L directly, but with the Lagrangian density L
This assumes that quantum theory takes place 'in' space. We would prefer to think of pace as emerging in some way from quantum mechanics.
'By minimizing L with respect to the wavefunction [of a free electron] and its time and space derivatives, it is possible to derive Dirac's equation of motion of the electron denoted D Psie
Interaction of photons and electrons:
L0 Psie = L of free electron
L0 A = L of photon
Linteraction ( Psie , A ) = L of interactionso L = L0 Psie + L0 A + Linteraction ( Psie , A )
'This is the top level specification of the fields being described. . . . The variational principle now describes the propagation of the fields in terms of the creation and destruction of the quanta of the fields and by the wavefunctions of the quanta during their existence
[page 119]
(referred to as propagators in this context).
Feynman diagrams and Feynman rules.
Dodd page 29: 'To calculate the probability P of any physical event . . . it is first necessary to select the initial and final states being observed, denoted |i > and <f | respectively, and then to select all the Feynman diagrams which can connect the two. [All possible network connections]. The mathematical expression for the diagram is then worked out: essentially, the wavefunctions of the quanta are multiplied together to give the quantum mechanical amplitude m for the sub-processes. The amplitude for a number of sub-processes may then be added to give the total amplitude M which is then squared to give the required probability of occurrence.'
This setup is linear because there is no 'self' interaction - photons only interact via electrons and vice versa.
The probability of interactions of photons and electrons is low. 'As each new order of diagram contains a new photon line with two vertices the relative magnitude of successive orders is reduced by e2 /h bar c = 1/137. So only he first few subprocesses need be calculated to achieve an acceptable approximation to the exact answer.
page 30: 'Virtual processes' (unobservable processes) made possible by uncertainty principle.
Renormalization: 'In writing down the Feynman diagrams of the sub-processes we find some whose amplitude (product of wavefunctions) appears to be infinite.'
page 31: In 1949 Feynman, Dyson and Tomonaga showed how the
[page 120]
infinite contribution to the perturbation series can be removed by redefining the electron, photon and electric charge to include quantum corrections. [?] When the real electrons, photons and charges appear, the infinite diagrams are included implicitly and should not be recounted. The mathematical proof of the demonstration is known as 'renormalization'. Renormalization - Wikipedia
All sounds like 'ad hocery' to me arising form the need to deal in continuous mathematics which assumes that the quantum of action can be infinitely subdivided as in the 'path integral' method. We would like to think that all processes involve an integral number of quanta and by enforcing this rule we would get rid of a lot of trouble, but how to do it? The heuristic principle here is that when the world was very young and simple (before it even had space) processes had to be simple and they have taken on their complex appearances by being embedded in the complex machinations of higher levels of the system. [thus eg in everyday computations, simple nand gates are hidden in the rendering of complex images]
Dodd page 32: 'All the calculations in quantum field theory follow from the specification of the correct interaction Lagrangian, which is determined by the conservation laws obeyed by the force under study.'
Minimizing Lagrangian means minimizing processing rate (=T ) while maximizing memory (=V ). What does this mean. All memory = all space = all the things that do not change (relatively speaking) with time = carries potential = potential energy. In standard physics we see potential as being carried by a field in space. How do we understand this in a network model?
Even though it looks complex in the expanded Universe, we are inclined to view gravitation as the fundamental force, since it seems to account for the large scale structure of the Universe
[page 121]
and yet be indifferent to structure, since it sees all structures that have energy, even if these structure are 'dark'. Dark energy - Wikipedia So energy couples to itself (very weakly) and we might say that gravitation itself has no memory and so no structure. When we put it into space (or should we say 'when space uses gravitation' we get the inverse square law and Einstein's curved = dynamic space. We might find the essence of gravitation by looking at Einstein's field equations in zero dimensional space.
Equivalence
General covariance
(subject to the constraint of C infinity gaussian
manifold.
General covariance - Wikipedia
We divide the initial oscillator into a collection of secondary oscillators distinguished only by the frequencies (energies).
[The fixed point here is the differential equation which admits as solutions all energies summing to ℵ0, which we might say corresponds to the initial singularity]
. . .
In the absence of space angular and linear momentum are both equal to energy.. The origin of space breaks the symmetry of energy into energy and momentum.
God is the most symmetrical being of all. [Omnino simplex Aquinas 20]
We understand symmetry breaking by the generation of new network layers followed by competition among the peers of the new layer for the resources of the previous layer leading to a set of 'fit' systems like the fundamental particles. QED --> Yang mills.
Since the Universe begins as one and remains one, any breaking of symmetry must be accompanied by a 'symmetry restoring' feature which maintains the unity. This implies communication between the pieces of the broken symmetry which physics calls gauge particles. Gauge boson - Wikipedia
Given our idea that gravitation is not quantized we have not so much a gauge particle as a gauge flow, so we conceive of energy flowing around as a non-viscous conserved (incompressible) quantity subject to some differential equations like dE/dt = 0.
Memory, potential, force, distance, energy
Conjugates: 'god' 'prime matter'.
Google.org Google.org
. . .
Before the advent of spacetime, all local symmetries are global symmetries since global = local.
We might look at the symmetry group as a channel through which information may be sent as U(1) is the channel in electromagnetic communication. So Yang-Mills theories of SU(2) etc are more complex channels.
Space and time symmetries, by being broken, enable us to communicate by various serial and parallel channels, such as this writing.
Lower layers of the network are more physical and more abstract. [Abstract knowledge attempts to model these lower layers through the fog of complexity built upon them]
[page 123]
CONSERVATION = MEMORY [software (which is in fact harder than hardware)]
A symmetry group is a closed world of possibilities = CHANNEL
Actual communications are broken global symmetries = local symmetries.
The covariant derivative, by taking into account local symmetries, enables us to connect the changes in local coordinates to the real changes in a particle as it moves through the coordinate mollusc, taking the 'connection coefficients' from place to place into account. Einstein
Dodd: 'The physical laws governing any process are formulated with a particular origin and a particular coordinate system in mind.'
Not so with networks, in which everything is a relationship (channel) between two points, completely defined by the points without reference to any coordinate system. From a network point of view the 'coordinates' are the languages (protocols, algorithms, particles) used to mediate any communication. Ultimately all messages go through the initial singularity, which is completely symmetrical, ie enjoys general covariance, or equivalently, no protocol.
The birth of the qubit = the procession of the Logos, 'simultaneously' produces both potential and kinetic energy. The kinetic energy lies in the oscillation between the two persons, the potential energy from the simple fact of their distance. In the case of the primordial qubit (the initial oscillator), the gauge particle moving between the two concentrations of energy [the 'Holy Spirit'] is itself energy, and we need to dream up a way to couple this to gravitation. [Einstein has done it?]
[page 124]
We do not wish to upset quantum mechanical calculations, but to put them in a wider context.
We see each layer persisting in the layers above it, so we should expect to see the initial singularity (eternal God the Father) everywhere just as we see the initial oscillator (qubit, Father & Son) everywhere. We may interpret the Trinity as a semi-mythological explanation of the emanation of the world from the divinity. Tantra - Wikipedia
The network is 'self-coordinating'.
So we need to introduce a paragraph into why_quantized about general covariance and the expansion of this from the continuously constrained world of general relativity to the 'Turing general covariance' of the world starting from the qubit and the introduction of the quantum of action which is in effect just the initial singularity, the fundamental arithmetic unit.
Oscillation of energy between the two states of a qubit is the same as oscillation of probability, the total probability remaining constant. We can see this as a parity or space inversion, usually described by a continuous rotation.
Linguistic encoding and decoding are equivalent to a covariant derivative.
. . .
[page 125]
The mathematical continuum makes sense if it can be mapped to a logical continuum, so the idea of a line of discrete points is held together by mapping the discrete points to a real line which is physically (= logically) continuous.
Dodd page 44: '. . . the conservation of electrical charge . . . can be represented by requiring the Lagrangian to remain invariant under arbitrary shifts in the phases of the charged particle wave functions appearing in the Lagrangian.
Ie charge is an algorithm which remains the same while processing all the different messages represented by different phases.
The L is something static that can be written down and so represent an algorithm that can process many different inputs and is symmetric with respect to the inputs. So English speakers are symmetric with respect to the language, since they can process all inputs equally. This symmetry is partly broken when one speaker uses words the other does not know and completely broken when they use two different languages (considered orthogonal to one another).
The layering of the permutation network may be considered in terms of groups and subgroups.
With a computer, we only observe the input (say keyboard) and the output (say screen). All the other operations of the machine are transparent (= virtual)
[page 126]
Dodd page 46: Muon behaves exactly like a heavy electron and decays into an electron in 2 x 10-6 s, so it is not found in ordinary matter.
Can we see a meson as an inefficiently coded electron, achieving the same end with a lot more cycles (energy) [and so selectively disadvantaged].
A language must be symmetrical so that it can express many different ideas with equal facility, ie flatness.
Say it again. A communication channel, ie an algorithm, must be open to all messages obeying the protocol, ie flat or symmetric. So a Turing machine can multiply, add, divide, etc any two rational numbers as long as none of the inputs or outputs exceed 'machine infinity'.
Thursday 12 February 2009
Lagrangian is composed of additive elements. We might assume that L (initial oscillator) = 0, ie the kinetic energy of the Universe is equal to its potential energy, which is equal to the zero energy of the initial oscillator, which does not exist in the sense that it communicates with nothing outside itself. Fact? Fantasy? Meaningless? Convincing? Testable? Consistent?
Interference of two indistinguishable electrons, N 448:262, 233 Neder et al
INTERFERE - RESONATE
[page 127]
't Hooft N448:271 't Hooft Reconciliation of Quantum Mechanics and Special Relativity completed in the Standard model.
't Hooft page 271: '. . . [gauge theories] had been proposed by Chen Ning Yang and Robert Mills who were inspired by the fact that the two basic forces of nature that were well understood, gravity and electromagnetism, were both based on the principle of gauge invariance: that is that symmetry transformations can be performed in one region of spacetime without affecting what happens in another.'
Or does it mean that every local change in explained by a message to or from elsewhere?
Hoddeson et al Rise of the Standard Model Hoddeson
Asymptotic freedom: the strength of reactions reduced at short distances, (instead of blowing up to infinity?)
'Bjorken scaling' Wu-Ki Tung
't Hooft page 272: '. . . theorists had concluded that no quantum field theory would be suitable for the strong force - until the asymptotic freedom of Yank-Mills fields was uncovered.
'This [1970s] model describes the closely related Yang-Mills systems for he three major forces . . . one Higgs field and several matter fields. These matter fields were Dirac fields, describing the four known leptons and the three known quarks (up, down and strange) all of which has half a unit of spin. According to this theory, the Dirac particles cannot interact directly with one another but only by exchanging energy quanta of the Yang-Mills field. The interactions between Yang-Mills and
[page 128]
matter fields are identical for all particle types; only the Higgs fields couples differently to the different matter fields. And only in this was is differentiation brought between the various kinds of particles according to this new insight.'
Discovery of more quarks and leptons gave us the 'standard model'.
't Hooft: page 273: 'Adding neutrino mass terms to the standard model, was, however, only a minor repair and not totally unexpected, although it did add more parameters to the model. The earlier version had 20 fundamentally freely adjustable parameters in it; now the number would need to be increased to at least 26.'
And this for 24 fundamental particles: 12 bosons and 12 fermions. [?] Elementary particle - Wikipedia
page 273: 'By the 1980s it was understood that quantum field theories are perfect frameworks for the detailed modelling of all known particles. Indeed, if we require theories with only a limited number of elementary degrees of freedom, and thus a finite number of freely adjustable parameters, then it must be assumed that all forces are renormalizable. But, for all strong forces, the more stringent conditions of asymptotic freedom is required. The only theories with these desired properties are theories in which Dirac particles interact exclusively with Yang-Mills fields and (where needed) Higgs fields. This is now regarded as the answer to that problem of more than half a century ago - how to reconcile quantum mechanics with special relativity.'
The fact of consistent universal structure points to memory, which in turn points to the 'eternal' initial singularity.
Lederman N 4488:310 Lederman Book 1993 The God Particle Lederman 1
[page 129]
Does the Higgs really give mass to everything?
Lederman page 312: 'By necessity we are now comfortable with the hypothesis that all standard model particles have zero radius and so no [spatial] substructure. [Although they have enough structure to have different identities = quantum numbers].'
This suggests that they are outside space in the same way as the internet is apparently outside space. As I browse files and talk to people around the world, their spatial distances and orientations are irrelevant to me. All I need to know is their [logical] address (which can be mapped to a physical computer somewhere) and their 'content'.
Neder et al 448:333 'For a single particle the interference is between the amplitudes of the particle's wave functions, whereas the interference between two particles is a direct result of quantum exchange statistics. ' Neder et al
What we mean when we say that a particle has mass is that it has a very short range (as a force mediating 'virtual' particle) because it can only borrow a quantum of energy for so long before ut has to give it back and cease to exist. This assumes m = E/c 2.
Many theologians (not me) claim that their source is outside the Universe.
The development of the standard model has not been easy and many of the problems have arisen from the perceived need to take all calculations to the continuum limit. Our task here is to reconcile the discrete network
[page 130]
picture with the continuous picture, and the natural starting point appears to be gravitation, which (although it is not part of the standard model) appears to be naturally continuous. Einstein's key insight when developing the theory of relativity was that coordinates systems (at least as understood by his contemporaries) were not part of nature, but simply convenient forms of addressing the elements of a system under study. What matters in nature is the relationships of the elements to one another. Their relationship to a coordinate system is merely a way of clearly expressing their relationships to one another. This insight is captured by the term 'general covariance' which means that no matter how we choose the coordinates, nature goes its own way. The fixed points in the natural system are events and we may use different coordinate systems to label natural events in any way we like subject to one constraint only, that the transformations between different coordinate systems be smooth and continuous, that is diffeomorphisms, a constraint naturally captured by tensor analysis. Diffeomorphism - Wikipedia Tensor - Wikipedia
Tensors through the mechanism of covariant derivatives and connection coefficients automatically compensate for changing bases, so a tensor equation true in one coordinate system is true in all coordinate systems connected to the first by a diffeomorphism.
The network approach goes one step further, doing away with external coordinate systems altogether, requiring only distinct addresses with no fixed spatial relationships whatever to do their business. All that is needed to send a message is the address of the recipient and the message, and the address is something local to the recipient, rather than global.
[page 131]
By doing away with an ordered coordinate system, communication systems must search their address books to find recipients, but if addresses are hierarchically ordered, the process can be fast.
Standard model does not exist in geometric space but in address space.
Gravitation is in a way the simplest gauge theory because it works in real familiar imaginable space and time. Einstein's insight was to use Gauss and Riemann's ideas to provide an intrinsic addressing system for cosmic dynamics It is also simple because it is blind to all but energy which behaves like a single global conserved flow, just like money, with the added feature that like money, energy attracts energy. The gravitational gauge is energy.
KINETIC energy is ATTRACTIVE
POTENTIAL energy is REPULSIVE, so systems try to move away
from areas of high potential, like the top of the swing of a
pendulum. One is repelled by the tops of hills and attracted by the
valleys, but energy is nevertheless conserved. So the high potential
of the initial singularity repels the Universe into expansion, yet as
soon as it begins to expand the resulting kinetic energy is
attractive.
CURVATURE = POTENTIAL
Curvature restricts communication, flatness encourages it, so we travel more easily over flat surfaces than hilly ones.
[page 132]
Friday 13 February 2009
Quantum gauge theories were inspired by the classical gauge theories, Maxwell's electrodynamics and Einstein's gravitation. Both may be understood using the simplest gauge model of all, the classical harmonic oscillator, embodied in a simple pendulum or weight on a spring. This in turn comes back to Newton's gauge equation F = ma which is enunciated in Newton's three laws which are a more detailed statement of the ancient idea no effect without a cause, where cause is translated force. To this Newton gave mathematical expression.
All of this can be understood in terms of the interplay of potential and kinetic energy mediated by force. In total, energy is conserved, but it may flow from potential to kinetic and back again through the intermediary of a force. Causality tells us that force is acting when we see a change of movement of energy. force is a message.
This concept received its highest classical expression in the general theory of relativity, where gravitation is seen as the intermediary between the shape of space (a potential) and the movement of bodies within it, expressed in Einstein's equations, which deal with a continuum of conserved energy.
The foundation of universal structure is the abstract bifurcation of the initial singularity into a potential and a motion. We identify the potential with memory and the motion with processing, and the principle of causality becomes no
[page 133]
memory changed without process. Ie the communication is the gauge measuring the change of potential.
Maxwell Maxwell
As in mathematics, the discretum comes before the continuum. Since the invention of the continuum it has come to dominate mathematics and hidden much of what the discrete has to tell us. This only began to find its way back into the light of day with the work of Cantor, Frege and co, who saw that even the arguments about the continuum were discrete and logical.
The fate of the Standard Model now hangs upon the Large Hadron Collider. Will is reveal the Higgs boson? Will it reveal new physics?
I smoke to gain insight and hope that in later life, if I lie dying of smoke induced cancer, that I will be able to look back on what I have seen and communicated to the world [and feel] that it was worth it. I hope Einstein felt this.
We may look upon a differential equation as a fixed point of an infinity of dynamic solutions like the vibration of a string and its overtones which would be countably infinite if not suppressed by the stiffness of the string
FLOW - FLUX - FLUXIONS Method of Fluxions - Wikipedia
Change + cause of change = 0. Once we can appreciate the cause of a change, it is as though nothing has
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happened.
