Notes
[Notebook: TURKEY DB 55]
[page 224]
[Sunday 6 April 2003 - Saturday 12 April 2003]
Sunday 6 April 2003
we need to be able to apply the action principle to the
[page 225]
transfinite transition one --> many. First try to understand it intuitively , then mathematize it. Alphabet and language evolve in harmony, and then break free from one another. So increasing the complexity of the language we learn to use old words to say new things.
The transfinite transition is a bearing, a degree of freedom. Peace will come to earth when we distinguish our biological needs at the animal/physical level ℵ(<n) from our spiritual and ideological; needs ℵ(>n) (a human peer group assumed to be ℵ(n)?)
We understand the spiritual by formalizing the physical and extrapolating the formalism.
Let us suppose (how many times has this been said before) that the role of dynamics is to describe moving systems in stationary text. This effort which is visible from the beginning of recorded history has always been bedevilled by the idea expressed in the ancient phrase 'The Tao that can be spoken is not the true Tao'. [to overcome this we think of the true Tao as the superposition of all speakables]
In order to establish as broad a base as possible for the tower we wish top build, we begin our history with Parmenides, whose extant fragments suggest that he denied that dynamics is meaningful because motion is illusory. Parmenides. Inspired by a goddess, Parmenides takes a strong . . .
Feynman 14-2
"Everything we have just said is contained in the formula work = the integral of force times distance." Feynman. It is very well to say that this is a marvellous formula but it is another think to understand what it means or what its consequences are.
Measurement = self awareness = communication of the world with itself.
[page 226]
Monday 7 April 2003
An operator solves a problem and emits an observable solution.
All writing is an attempt to express internal states in a static text. Some writings are so important that we call them discoveries, but all are revelations. Newton, by studying the works of his predecessors created within himself a state which after suitable evolution he was able to describe in the Principia, so setting parts of the world off in a new direction. Newton, Westfall. Ie Principia was (and is) the embodiment of a force.
Sexuality is one of the many components of the 'social force vector' operating on any human particle in social space at any time.
Feynman 15-3
a) "substituting the Lorentz transformation into Maxwell's equations leaves the form of the equations unchanged. "
b) "How do we change Newton's laws so that they remain unchanged at high velocity? . . . As it turns out, the only requirement is that the mass in Newton's equations must be replaces by m = mo/ square root (1 - v2/ c2).
So if mass is a measure of energy and energy is a measure of temporal complexity, we see that anything moving from my point of view looks more complex the faster it goes. Since momentum also increases with mass and velocity, we see the spatial complexity increasing too. This is crude, but let us suppose that the mass has a visible structure which we take as a proxy for the complexity of the mass. This structure, while changing its shape, does not change as a representation of a certain amount of information, but it does change its mass, so making the statement above somewhat problematic. So how do we
[page 227]
reconcile these two definitions of complexity. By invoking the transfinite distinction cause by the transfinite transformation. Einstein's law holds at the physical peer level, but not at the peer level of gross structure on a massive body. What is changing is the relationship between a symbol (structure) an its physical embodiment, so that more mass energy is required to represent a certain symbol when it is in relative motion than when it is not. But we would like physics top be true at every level, but perhaps we must drop that and say that mathematics holds at every peer level , but the 'forces' implementing the mathematics change. Here we have fog, but as always enough fascinating glimpses to drive me on. There is no doubt that glimpses are far more attractive in a way than full frontal confrontation, perhaps (for some reason of fitness) we enjoy the chase more than the kill. But kill I must if I am to capture the beast in the text I hope will contribute to the peace of the world.
Feynman 15-15 It appeared that nature was in a conspiracy to thwart the measurement of the velocity of the ether wind.
"It was ultimately recognizes, as Poincare pointed out, that a complete conspiracy is itself a law of nature. Poincare then proposed that thee is such a law of nature, that it is not possible to discover any ether wind by any experiment; that is there is no way to determine an absolute velocity."
ie there is nothing observable corresponding to Newton's absolute system of coordinates.
Instead of seeing quantum mechanics as the explanation of quantum information theory, let us now see quantum information theory as an explanation of quantum mechanics. The formalism remains the same but the social interface changes with this change of point of view (transformation)
[page 228]
Change of point of view = transformation. Special relativity shows us how to change our point of view from comoving to moving with relative velocity in some inertial frame. GR takes us from one inertial frame to another (which is by definition relatively accelerated, otherwise it would be the same inertial frame.
lengths shorten, time increases.
In each layer of the transfinite network there are more symbols so more possible structures which may be expressed as 'laws'. A law can be characterized not only by its content but by how long it lasts. In a good democracy, bad laws last only a short time and perfect laws, once established, last as long as the environment in which they work.
All measurements are effectively rational numbers, so all possible measurements are encompassed by the set of natural numbers N. This is true not just for human observers, but for all 'observations' (real relationships) made by one entity on another. The use of continuous functions to model observables is thus somewhat overkill. This is in fact why we can only observe eigenvalues of operators and the continuum appears as one point to a natural number, even though the points may in theory be measured by different reals all corresponding to the same n.
What if we start taking positive and negative square roots in special relativity ie allow right angled triangles to have negative hypotenuses? (which demands that the hypotenuse be a vector? are the integers (+ - naturals) vectors rather than scalars?)
Feynman 15-6 'Light clock' - a beautiful thing!
Len Deighton Hope. Deighton.
Tuesday 8 April 2003
Wednesday 9 April 2003
[page 229]
Nature Commentary, Ruedi Aebersold p 115. Aebersold.
Browsing mode -learn the genomic/proteomic language and then study how cells speak it in order to compose new sentences ourselves.
eg a) discover all single nucleotide polymorphisms b) "scoring" associates various patterns of SNPs with corresponding phenotypes.
Detrimental effects of sanctions on human altruism. Fehr & Rockenbach
'In fact much of the economic backwardness in the world can plausibly be explained by a lack of mutual confidence inhibiting cooperation in the production and exchange of goods and services.'
". . . even in modern societies the overwhelming majority of all social and economic exchanges are not based on complete and legally enforceable contract, but on implicit agreements and social norms lacking explicitly specified sanctions for non compliance.
Prevailing models are based on strict self-interest.
"The axiom of self interested behaviour implies that the only remedy for compliance problems is in the provision of sufficient rewards or sanctions. Yet if these incentive for cooperation undermine altruistic behaviour the remedy may do more harm that good because is aggravates the compliance problem. Influential social scientists have hypothesized that economic incentives might undermine altruism but so far it has been impossible to provide compelling evidence from
[page 230]
field studies.
A game, played by 238 students at the U of Bonn.
". . . as our experiments indicate, sanctions intended to deter non-cooperation may backfire because they undermine altruistic cooperation. Whereas altruistically motivated sanctions for the benefit of the group ["public good"] enhance cooperative behaviour, sanctions that are imposed to enforce an unfair distribution of resources have the opposite effect. This is in contrast to prevailing approaches in economics, biology and behavioural ecology, which predict cooperation-enhancing effects of sanctions regardless of the moral legitimacy or purpose of each sanction."
MORAL (relative to peer index n) is an output of peer index (n+1), ie altruism is an outcome of a spiritual (more complex than individual) analysis of the group/. Maybe a product of entanglement.
Feynman
20-3 3 Dimensions. Feynman 1.
"Why is torque a vector? It is a miracle of good luck that we can associate a single axis with a plane and therefore we can associate a vector with the torque; it is a special property of three dimensional space. In two dimensions, the torque is an ordinary scalar, and there need be no direction associated with it. [there us no direction available to consistently associate with it, since the two available dimensions are taken up with the lever arm and the line of force] In three dimensions it is a vector. If we had four dimensions, we would be in great difficulty, because (if we had time, for example, as the fourth dimensions), we would not only have planes like xy, yz and zx, we would also have tx, ty and tx planes. There would be six of them, and one cannot represent six quantities in one vector in four dimensions."
[page 231]
In other words, 'controlled communication' through transmission of angular momentum (action) by a torque would not be possible because the torque message does not have sufficient variety to fully constrain the change in angular momentum. This condition may have a selective advantage in that the duals (message = essence and entity = being) are able to control one another. This might be the peer condition, equal countable complexity cf duals, leads to deterministic (controlled) communication. So I make DNA, DNA makes my children and so generation after generation (or tick after tick of the {generational} clock).
So we take time as the fundamental unit of process, and a sequence of times as the most abstract representation of the Universe. A sequence of equal pulses has a frequency measured by its energy (energy measurement is as accurate as the identity of the pulses) but we may sample such a sequence at any desired frequency by looking for every nth pulse. We can imagine a Turing machine doing this acting efficiently as a frequency divider, performing any task that takes the number of steps we wish to use as a divisor. So a 917 step process would deliver an output (signal, pulse) at every 917 step of its own clock.
Thinking like this, a set of unique individuals card (ℵ0 could deliver a new permutation of itself in ℵ0 steps, thereby acting as a divide by ℵ0
Feynman page 20-4: Vector product 'cross product' is non-commutative.
polar vectors have a direction imposed by arbitrary convention.
Being and essence are duals. What we mean by duals is that the carry the same information carried in two different ways which can be transformed from one to another by an operation like differentiation, etc.
[page 232]
ie gradient of a potential -> force vector. Same information, different form.
axial or pseudo-vectors (torque T and angular momentum L) have just one cross product in their definition.
Feynman page 20-6: "We may now claim to understand the precession of gyroscopes, and indeed we do mathematically. [given inputs, we can compute output]. However, this is a mathematical thing, which in a sense appears as a 'miracle'. It will turn out as we go on to more advanced work, thee are circumstances in which the mathematics will produce results which no one has really been able to understand it in any really direct fashion. An example is the Dirac equation which appears in a very simple and beautiful form, but whose consequences are hard to understand. In our particular case, the precession of a top looks like some kind of a miracle involving angles and circles and twists and right hand screws. What we should try to do is to understand it in a more physical way.
21-1: The harmonic oscillator.
'. . . a strange thing occurs again and again: the equations which appear in different fields of physics, and in every other science, are almost exactly the same, so that many phenomena have analogs in different fields.
harmonic oscillator <--> differential equation - linear differential equations with constant coefficients
[page 233]
Simple harmonic motion
Feynman page 21-2: 'If we multiply a solution of this equation by a constant, it is again a solution.' ie scale invariant - linear differential equations to not see the size (energy, amplitude) etc of the motion x, but only its frequency.
Driven oscillator grows to infinity (in the absence of losses) if the driving frequency is equal to the natural frequency, and not otherwise.
Call this TEMPORAL CONSISTENCY, the root form (of C) in a Universe whose fundamental dimension is time, ie count of repetition.
The most abstract parametrization of the Universe is the number of ticks (counts) since t0.
page 22-1 '. . . in theoretical physics we discover that all our laws can be written in mathematical form; and that this has a certain simplicity and beauty about it.
Australian Catholic University: It all comes down to whether you attach any real importance to your theology. If it is not important, an unverified rationalist approach is ok, but if theology is a matter of life and death, rigid quality control is required, and we must use scientific method.
page 22-2 continuity - ordering
page 22-3 abstraction and generalization (mental and physical)
[page 234]
'One cannot say, for instance, that -2 time 5 really means add five together successively -2 times [ = subtract five successively 2 times - action, like time, is a strictly positive count]
'Onward! The great plan is to continue the process of generalization; whenever we find a problem we cannot solve, we extend our realm of numbers.
NUMBERS = PARTS. There is some relationship between the parts (elements) we have and the (dynamic) structures they we can build. The Universe needs a set of parts that spans all possible structures, including the discreteness of its parts.
22-4 Dedekind.
22-7
page 22-10: sin and cos are algebraic functions which show us how to compute the metric structure of Euclidian space. Does algebra come before geometry? In a computational sense, yes!
23-2: differentiation of an exponential brings down the coefficient of the exponential as a multiplier:
'(Differentiation is now as easy as multiplication! The idea of using exponentials in linear differential equations is almost as great as the invention of the logarithm, in which multiplication is replaced by addition. Here differentiation is replaced by multiplication)'
23-4 low friction = high q = sharp resonance.
page 23-7: 'The difficulties of science are to a large extent the difficulties of notations, the units and all the other artificialities which are invented by man, not by nature.'
page 23-9 Mossbauer q = 1010.
25-4: Impulse - Green's function.
[page 235]
Feynman page 26-3 'The real glory of science is that one can find a way of thinking such that the law [symmetry] is evident'.
First axiom: time is of the essence. Least time.
page 26-6:' The importance of a powerful principle is that it predicts new things.'
What is the cause of self destruction? The same as demolition in the building trade, Knocking down the old to get the resources necessary to build something new (site, materials, energy, design). A new design needs a new physical structure somewhere because
Axiom 2: All information is coded physically.
This website is encoded physically in my computer and in bits and pieces all round the web. All these pieces are linked together by the common web address on their path.
PATH <--> DATA. The path points to the data so that we can take the data as the 'meaning' of the path. If every datum is 1 bit, then we can say that all the meaning in the world is encoded in the pathways of various bits which may be two state physical systems like electrons.
DATA and ADDRESSING are DUALS.
page 27-1: 'The most advanced and abstract theory of geometric optics was worked out by Hamilton, and it turns out that this has very important applications in mechanics.' Hamilton.
Thursday 10 April 2003
Friday 11 April 2003
Third axiom: action is of the essence - stationary action
[page 236]
William Rowan Hamilton (1833) On a general method of expressing the paths of light and of the planets by the coefficients of a characteristic function.
'From this law, then, which may perhaps be named the LAW OF STATIONARY ACTION, it seems that we may most fitly and with best hope set out, in the synthetic or deductive process, and in search of a mathematical method.'
'. . . from this law . . . I deduced . . . another connected and coextensive principle which may be called by analogy, the LAW OF VARYING ACTION.
Fermat: least time - applies to light but not to massive particles? Least action is more generally applicable.
'Maupertuis gave the name of action to the product of space and velocity, or rather to the sum of all such products for the various elements of any motion; conceiving that the more space had been traversed and the less time it had been traversed in, the more action may be considered to have been expended . . . '
Euler - action = integral v ds is stationary,
STATIONARY = CONSISTENT (IN PHASE)
One dimension in which I fail in my attempt to understand mathematical arguments is in 'attention span', where after a while, the 'load' of following the argument becomes too great and I drop it, quite analogous to carrying something heavy up a hill, at least form the point of view of experience. Here we are moving a force through a distance using a supply of energy which eventually runs out.
There seems to be a correlation between progress in the development of the natural religion project and enthusiasm to work on it. This is to be expected, and suits the principle of stationary action, that the greatest progress is made when things are in phase, and vice versa. The payoff is perceived productivity - is it better to be working on this or digging holes? Of course digging holes
[page 237]
is part of the mix, since it not only earns money, but keeps me fit for the decades of work that still seem necessary before the project develops a life of its won.
Giving USA
Minimum action - work
maximum action - play
Physics minimizes action at a given peer level. Metaphysics shows us how to use order to minimize action below what can be achieved by physics(?) Basically, by choosing certain orderings out of all the possibilities, we can increase the speed (frequency) of certain events by a huge factor.
So a catalyst (an element of aleph(n=1) is a structure (ordered set) that speeds up a certain event in ℵ0.
DARK MATTER = non-halting Turing Machines.
A window on dark energy.
Is something new arising amid all the demolition? It would be nice. The modelling seems to be coming along nicely, but is most difficult in physics, mainly perhaps because it is so hard to get behind the instinctive interface to the world and see how it all works.
Maybe we could write an article around the cosmology confirmed by the Wilkinson Anisotropy probe, of weave it into theological dynamics. C L Bennett et al.
One feature of theological dynamics is that it can explain the enormous inertia of institutions like the RCC, an inertia which may in fact be much greater than the sum of the inertia of its constituent people.
Multiplication/division of 'effective inertia' ['dressed mass']
[page 238]
What is the unit of inertia. It is the same as mass. The heavier you get the harder you are to get moving. But (see Mossbauer) one can get mass by being fixed to a massive object.
To achieve a given overall change, a certain number of quantum changes (quantum events) are required. Cunning design (ie productivity maximizing design) minimizes the number of quantum events needed to achieve a given change.
The ratio of energy to angular momentum. The energy of the orbits in an atom varies as 1/n2, but it takes one quantum of action to go from one orbit to the one with the next highest angular momentum. As n --> infinity, the change 1/(n+1)2 - 1/n2 approaches zero, ie the frequency of the photon emitted or absorbed goes to zero when the electron reaches the continuum.
Is the network view a 'unified field theory"! Yes if we can discover an isomorphism between 'network' and 'field'.
Saturday 12 April 2003
Lost it while writing the date.
Christianity: find out who is guilty and punish them, with the aid of God, the all seeing police person.
Alternative: harm reduction/welfare, with the integrity of memory taking second place. [part of the Christian problem might be the belief that their system is divinely ordained perfection, so anyone swimming against it must be a sinner.]
