vol VII: Notes
1999
Notes
[Sunday 30 May 1999 - Saturday 5 June 1999]
[Notebook BOOK 4/5/94 DB 50]
Sunday 30 May 1999
Monday 31 May 1999
Tuesday 1 June 1999
[page 329]
Wednesday 2 June 1999
Keep boring in. The publication of the rough sketch of development must contain a clear statement of what is new
a) the Universe is divine
b) this involves no inconsistency
c) scientific theology is possible
d) religions based on scientific theology can move us individually and collectively closer to heaven on earth
. . .
[page 330]
Every person's home is prima facie a black box to the general population and so it should be / the division between public lives and private lives.
POLITICS is the study of our public life.
I strongly resent police intrusion into my home but I know and I knew that I was powerless to prevent it (if only because they outnumbered me 10 to 1, were armed and in communication through their helicopter with much greater forces). I also know that I am keen on stamping out violence of all sorts, from domestic violence to the official violence of state organs. This century has seen an unprecedented number of people murdered by states, the end is not in sight, and there are some big hurdles ahead of us.
The rules of politics are developed and sanctioned by religion.
Methodology: The method of closure. We check our navigation by moving between
[page 331]
known points. For a long time there has been a dichotomy in method. The notion that we are a spiritual soul paced in a material world. Instead we can see ourselves as one within the world, thereby opening up a closure and a cosmological principle. The theory of everything that I propose derives from formal theory, taking the view that the world is asymptotic to god.
Our theology and a physics must therefore be mutually consistent.
Realizations of the permutation group.
Hardware limitation on communication.
We take Newton's position. We do not care what the hardware is, we just produce a model of it. Hardware of the Universe is modelled by littleOmega(0).
Public life: a) my political relationship with the church. b) church censorship by sacking.
Once a priest a priest forever, but has to have faculties. CANON LAW.
[page 332]
The major error is the political enforcement of a belief system.
Power is the power to move one another, that is to exert force on one another.
The study of public life is in itself a public (and so political) act. I am publishing to exert a force on you. To move you toward my point of view, which I happen to think would be very helpful if we all shared it.
Politics mediate between public and private personae. In private we are all equal. My experience of myself is just as meaningful to me as your experience of yourself is to you.
This equality need not hold in the public forum. Indeed historical and current affairs demonstrate relentlessly that some people believe that they have a right to kill or injure others to enhance their own existence.
[page 333]
But take the first person out of this, as is common in scientific writing.
The Memoirs of Richard Nixon MacMillan Australia 1978
naive and tricky, maybe not smart enough to see how transparent all his ploys were, though the people appear to have loved it.
page 851: Watergate breaks
page 855: did Nixon stand against the Liberal flight from reality that led them to mob him. Was it his part in the Viet Nam war, or that his old time politician personality offended the chattering (?) classes who did not have to deal with political reality. Nixon
POLITICS Motive/credibility
CREDIBILITY = f(truth, power)
vs HYPOCRISY Jesus was a political killing that has reverberated to this day.
[page 334]
space (momentum), time (energy) and count (action) are all examples of Cantor symmetry.
Action is primitive, mapping differently to space (spatial frequency) and time (time frequency)
velocity = λ.ν [wavelength.frequency]
Gradient which moves us to heaven is that which leads to minimum action, maximum probability.
De Maupertuis/Aquinas/Lagrange/FeynmanYourgrau & Mandelstam
Perhaps in theology we should leave the first person in, since I am bearing witness to an internal state addressed by I, or we just leave the I out because everybody knows to put it in.
[page 335]
Insight: solving a problem means explaining it away, that is finding an algorithm (as Archimedes did) for removing the problem. A funnel solves the problem of getting liquid into a bottle. One may attempt to pour a thin stream but this is subject to frequent error.
So the content of the insight maybe considered the inverse of the problem ie I = P-1, where both I and P may be considered elements of symmetric group.
Now consider an event as the solution of a problem, that is something happening that did not happen before.
Aleph(1) is the agent intellect for aleph(0) etc.
Time is an exponential, like the transfinite numbers.
We start the model with the permutation group.
[page 336]
Thursday 3 June 1999
Function used to represent Insight. Range and domain may be finite or transfinite, but on general many -> 1
Potentially understood = file.application.
Actually understood when loaded into the application.
To fix ideas, consider birth of QM. Kirchoff to Planck. E(ν, T) = f(ν, T) Kuhn
Fundamental requirement for communication is common language.
FUNCTION is a MACHINE in the abstract mathematical sense (ref to Turing)
Machine infinity, machine epsilon. Machines allow us to tame infinity and zero.
[page 337]
Does the world contain empirical residue. Since empirical residue is by definition observable, that is a scientific question. So we can attack it with scientific method. MTW write ... . This seems to be perfectly in harmony.
Bright idea (heuristic structure) Einstein principle of equivalence. Many years and a lot of help from his friends to finally embody this idea in the language of differential geometry to arrive at a theory to be tested.
Lonergan expresses his ideas in plain english. For scientific purposes, we need something more precise. Following Lonergan and Einstein, want to express Lonergan's insight into insight in the language of information processing.
We begin by letting an act of insight correspond to a mathematical function, so that the class of all insights is the same as the class of all functions. A function is a mapping, and we understand mappings through ordered sets.. Georg Cantor ( ), the founder of set theory, defined a set as the collection into a whole . . . Cantor
This is a bit vague, and the modern approach
[page 338]
. . .
Correspondence = mapping. The mapping between to sets is itself a set containing all the correspondences between the mapped sets.
The general idea of mapping allows many-one and one-many.
Function restrains to many-one.
Function can be executed by a machine. One way to design such a machine is a look-up table. The other way is a rule of some sort.
One is one. Two plus expands into the transfinite (because the passage of time does not add things, it multiplies them.
The sets that fit Cantor's definition are sometimes too big to be true and lead to trouble, like the set of all sets that are not members of themselves. This leads to a distinction between set and class.
[339]
There's a job to be done here (now that we think we know how to do it (the space race, the nuclear race)).
The duality of the model lies in the relationship between occupied and not occupied states. Although the name state sounds static, it means state of motion. For a state of motion to be occupied, it means something is actually moving in a particular way. So thee are as huge number of states of motion for the earth around the sun, and we are in one of them.
We can model the physical world by the integers, giving us a model with cardinal number aleph(0)
The rest is easy,
Back to cardinal arithmetic.
permutations/subsets = n!/2n. What happens as n grows? Top row each new n multiplies current value by n. On the bottom row, each new n
[page 340]
multiples the existing value by 2, so the fraction grows by n/2 for each application of n, ie d/dn n!/2n = n. Somewhere in here we can cook up Bose-Einstein and Fermi-Dirac statistics. Fermions stack up like a binary number (ie position dependent notation = Arabic numerals vs position independent = roman numerals (almost) pebbles (definitely)
Centrelink is a computer programmed to implement social security legislation. Legislation may either specify special treatment for each individual (lookup table) or it may apply rules.
There is no doubt that the eigenvalues of states are fixed numbers. As measurements and calculations become more precise, they will approach these values.
[page 341]
But statistical fluctuations on the occupancy of these precisely defined states are what gives us our actual readings. Statistics/probability arise from superposition.
Field theory - energy and particles are interchangeables. Note that the energy is always carried as a state of particles. In an interaction energy is conserved to that the sum of the energies of the initial states is equal to the sum of the energies of the
We can count: events; cycles in space; cycles in time = periods.
At least I feel that I am getting into the upper abstract air where it all makes sense because confusing detail is omitted.
Jech: My set theoretical bible. Amazon search system can lead you to more recent titles on the same subject. Jech
[page 342]
Model Insight.inverse insight
Model for II is the same as the model for I. Each insight is both forward and reverse, rejecting irrelevant details by seeing how the relevant details work together to give the overall effect.
Model for physics - countable - BEING - occupied states are a set subset of class of all states.
Model for intelligibility = duality
Gravitation STRESS/ENERGY - CURVATURE [communication]
My Set theoretical Bible is Jech: I believe, I do not understand.
The way the police, politicians and lawyers run the law is enough to turn us into a mob of petty criminals for our own protection.
[page 343]
Understand: Physical - MIND - Physical
The action of the mind in the world. Cybernetic loop vs cybernetic chain, vs ordered set.
Time exponentiates space. Phase ei θ, eit.
Read Feynman's QED again. Feynman How do normalization problems relate to those little arrows?
What is the metaphysical meaning of complex numbers? to close the group we have to give up order. The elements of a group need not be ordered, simply gi . gj --> gk an element of G
Identity + dualities (A, A-1)
Representing a group by matrices.
Matrix operates on a vector. This is possible because the elements of both matrix and vector are numbers and functions.
Friday 4 June 1999
. . .
Theory vs reality - every point is meaningful. Extend model to deal with the whole Universe.
Path integral approach and selection for meaningfulness - structure down to Planck length.
. . .
WORK From evolutionary point of view most important work is establishing and maintaining an optimal level of dominance, and this remains true in most hierarchical organisations - Nixon.
work = fighting
[Page 345]
We assume that the physical world evolves fast enough to keep itself very close to equilibrium = definite structure,
Eigenfunction and eigenvectors are evolutionary fixations out of the space of possible functions.
QM, group theory, etc etc all best expressed (in a calculable form) by matrices ie MATRIX OPERATOR operates in PARALLEL on ELEMENTS of a vector.
ie
MATRIX is a general device for transforming between ordered sets of the same cardinal number?
Eigenvalue + function have smaller cardinal than matrix. Finding eigenfunction = knowing
So do we use matrix algebra to describe insight?
Big plan: express insight in the formalism of quantum mechanics
Higman: Higman
[page 346]
Least action = using eigenvectors as a basis.
So we can talk about the basis of a language.
When I get back from Adelaide I am going into the religion business.
R&D
Production
Sales - Quote 'we are all individuals'
Speakable and unspeakable in human affairs.
Rule of law = speakable
Freedom = unspeakable
Freedom = f(speakable) [the physics of battle]
Consistency builds/inconsistency destroys: yin and yang/ Shiva and Shakti?
Consistency is generated at the maximum rate in local processes. This beats the NP problem raised by the growth of permutations.
[page 347]
SPEAKABLE = EIGENBASIS = STATIONARY = INVARIANT (in magnitude?) (in direction)
Human experience as a vector, and vector rotating in aleph dimensional Hilbert (?) space
Transfinite Hilbert space. Can the elements of a Hilbert space be permuted? So we must exist in the same sort of quantum space as electrons, just a bit more complex. This is Cantor symmetry - invariant with respect to complexity.
Is this all close to madness, or the emergence of a clear picture of the dynamics of human interaction? Then we want to examine the dynamics to see how to get away from violence.
VIOLENCE = COMPLEXITY-1
Maximizing the entropy of society by a correct balance between individual and group. The public discourse is the communication between individuals that binds them into a group. So we are looking for the boundary of nested black boxes. My public persona is only a small proportion of what is
[page 348]
going on in me. The boundary between the internal and internal forums. The determination of guilt and innocence. From my point of view, what I am prepared to give to the group and what I can get back from it. Can this be expressed in the language of bonding
BOND TO REACH LOWER ENERGY STATE
NOT-BOND TO MAXIMISE ENTROPY(?)
Maximum entropy arises a some f(bond, not-bond)
This sort of thinking is necessary for peace, getting insight into the constraints on social structure.
Temperature. Social security is the coolant. Competition need not be on such a strident key. We are being driven by the evolution of corporate forces beyond our control, and we must preserve our individual integrity by drawing a line beyond which corporate intrusion is inadmissible - Englishperson's home is his castle etc. Religion has to show the way. We are all individuals (chant together). Both are
[page 349]
. . .
So where is the external/internal boundary?
Rule of law/habeas corpus/human rights/
POLITICS - local theory => human rights
In a population of n, maximum entropy is when GNP is GNP/n per person. But how do we measure this product?
An evolutionary development of human rights.
Culture is {means of communication}. POLITICS uses culture to maintain the unity of the body politic and determine what is to be done as a collective.
Free movement of capital = key to economic optimization (?). Where to invest in maintaining social structures eg the cement industry.
[page 350]
Can we find a cybernetic answer to the boundary between the black boxes? This boundary is where the information exchange between the black boxes is most efficient. Object oriented programming. This is in effect a convention in pointer arithmetic (?)
Taxation Representation
No taxation without representation, that is, deciding how the money is to be spent.
This could all turn ugly if it is interpreted as a call to fascism (because mathematics involved) rather than a call to heaven.
Is there work in heaven? YES
Arriving at satisfactory enterprise agreements. Governments tend to side with organisations because it is easier. Try LOCAL RELAXATION, deal only with people, and ignore organisations. Organisations have no countervailing power against individuals except failure to thrive and hence the sack.
[page 351]
All of this is background to a political position. O to have known my position by inheritance as Richard Nixon did (?) Probably no. I am quite happy with my position now, although it will take a bit of effort to follow the path I have chosen - easier than working for a living however.
. . .
The inside of the black box is the processor, (represented by a set of matrices). The visible features of the black box are the eigenvalues of non-observable eigenvectors and eigenfunctions.
This is what quantum mechanics sees. One cannot be compelled to speak but can be induced to speak. State must maximize carrot, minimize stick, since effects of stick are unpredictable. Too much repression leads to revolt.
Localize reward for effort as much as possible (quick gratification) by delocalizing it as much as possible.
[page 352]
Cashflow - distribution (capillaries) ( individuals)
- concentration (arteries) (corporations)
By definition, cashflow through a corporation exceeds private cashflow of participants (because thee are shareholders to be paid)
Shareholders give a bunch of people (board) their money on the understanding that their investment will return a profit through earnings and capital gains.
By studying my self I conclude that the world is foolproof, that is heaven is a lot bigger (and therefore more attractive) than hell.
What we have is a mathematical way of conceiving spirit and matter as parts of a continuum rather than absolutely separated. Duality -> linkage
1. Finite nature of the Universe.
2. Infinite nature of possibility
[page 353]
[Natural religion] does not need new ritual. It simply accepts local ritual and puts a new slant: we are all divine; our environment is divine; love and working together, caring for everybody is the way to go. OUTGROUPS == CORRUPTION.
VALUE FOR MONEY
No hypothesis can be made about these data because their probability does not differ from chance. But what about Chaitin's theorem? Chaitin
Back to the general geodesic, the minimum action path of an object through its dual space.
Cybernetic realization of geodesic: feeling no force = no visible feedback (control algorithm is so perfect that control signal is imperceptible. MTW p 5. Misner, Thorne & Wheeler
. . .
The explanatory duality PARTICLE/SPACE
[page 354]
Particle shapes space
Space guides particle
Space is the whole language. Particle = local expression (state) in that language)
MTW p 13: The field has everywhere a clear cut value and goes about its deterministic dynamic evolution willy-nilly and continuously, infinitesimal test particle or no test particles. Similarly with the geometry of space.
All materials are equally weightless in an inertial environment. Particle coupled to the same inertial frame.
Unconscious = inertial
Eigenvalues are orthogonal (independent of one another) = degrees of freedom.
. . .
[page 355]
Each of us has a genealogy stretching back through billions of generations to the big bang. That is our community.
I would just like to broaden the definition of scripture to all human experience not the infinitesimal fraction that is recorded in the books and traditions of the various religions. This requires a constant broadening of . . .
All my experience is experience of the divinity.
My life is a dance of quantum states.
My approach to Lonergan is based on the insight that inverse insight is not possible? What we have instead is insight into . . .
I realize I am not so much interested in Lonergan per se as in building a mathematical model of noetic space which was inspired by Insight.
[page 356]
In the Dominicans I was deeply impressed by Thomas but found it impossible to believe that people thought it still current. I was confronted by people who genuinely believed that Aristotle's Physics gave us more insight into reality that the theories of relativity and quantum mechanics. I argued against their position vigorously, being a loudmouthed country bumpkin, and am consequently now a civilian rather than a priest.
This was too much for my tiny mind.
This was a big setback, but hardened me in the position that we can and must improve on Thomas if we are to survive.
I made a few heuristic decisions. First of all, that god is not other than the Universe.
We do what is best for ourselves, whatever spins we try to put on it. Not cynical but wonderful. Sometimes it is best to go alone. Sometimes it is best to seek company.
I wish to record a patter of insights.
[page 357]
The output of insight is a model = algorithm
All possible inputs/all possible outputs - to intellect.
The foundation of this model is set theory.
Rewriting the ideas I got from insight in terms of set theory, and linking this to quantum mechanics.
PHYSICS - God's plumbing
. . .
The set of all subsets of a given permutation (order is preserved within the subsets?) Or can the set 'permute through' a given non overlapping set of subsets (overlapping = covering)
Looking back the problem was the lack of distinction between real and abstract machines. Is the brain a computer? In the silicon sense no. In the mathematical sense, yes.
[page 358]
A mathematical model of noetic space. We begin with observable communications between minds - writing.
LITERATURE = frozen representation of noetic space.
If you cannot freeze it and transmit is you are speechless. Very low key.
Restate Insight in mathematical language.
MTW Everything that goes on in spacetime has its geometric description.
Felix Klein: Erlanger program.
Geometric objects exist independently of frames of reference. Their internal structure is determined by reference to themselves.
The sun shines on the just and the unjust.
We need [more than one] mathematical ways to express complexity.
[page 359]
. . .
Hardware = fastware = narrow ware = serial ware
Software = slow = wide = parallel
I am the (relatively) quiet pleasure of existence.
Physics: that hardware layer of the Universe.
