Notes
[Notebook: Transfinite field theory DB 56]
[Sunday 30 May 2004 - Saturday 5 June 2004]
[page 97]
Sunday 30 May 2004
The physicists view: mathematics is an essential part of the language, but we need not worry too much about the logical perfection of our arguments because we are going to check the results against reality anyway. The important thing is to communicate and test the idea.
RESONANCE = error free communication. So low Q = loss of energy = loss of coherence = 'error' (decoherence) [-2 degrees, biro sluggish]
Heaven on earth is possible if a) we accept that death is inevitable and act to optimize our time of death and b) we exploit the spare entropy (headroom) in the Universe to eliminate the errors which we experience as pain and suffering. This 'elimination' is work, and it can be achieved if we exploit the spare capacity for work in the human population. Much of human energy is wasted due to the poor systemic structure in which many people are embedded. Some make useless things, others have no way to act to help themselves.
The 'full success' of metaphysics is to a achieve a unification of the Universe at all scales of space, time and complexity [momentum, energy, action].
Complex numbers are a feature of matrix mechanics necessary for the equations to have solution, ie points at which various equalities hold.
Our discussion of the human peer level is founded on the notion of individual sovereignty. This holds in all peer groups, the creation and annihilation operators operate between peer levels, aleph(m-1), aleph(n), aleph(n+1).
[page 98]
The rotten core of the doctrine of original sin runs right through Insight. Lonergan It has its value, however, in the restatements of old truths upon which we can build, ignoring the rot until we have built a new system that does not need original sin to motivate it.
Lonergan page 259: 'The needed higher viewpoint [to fight the 'social surd'] is the discovery, the logical expansion and the recognition of the principle that intelligence contains its own immanent norms, and that these norms are equipped with sanctions which man does not have to invent or impose.'
We reject empirical residue and make the identification intelligence == nature, so that natural theology is intelligent theology.
Monday 31 May 2004
Tuesday 1 June 2004
What I do is read lots of books and get vague understandings of what they are saying, and then combine and permute these ideas to try to come up with a linked string that leads from A to B. The process, I feel, is probably analogous to the progress of any other particles from some A to some B. So my day consists of reading, thinking and writing interspersed with the practical chores necessary to keep my part of the show on the road.
We can devise a metric for noetic space or any other space in the form of a Hamming distance between permutations. The maximum is the length of the permutation, the minimum is two (swap a pair). What is the distribution? Find out.
FUNCTION expresses RELATIONSHIP
DICTATORSHIP - minimal feedback due to the low bandwidth of the dictator.
[page 99]
Wednesday 2 June 2004
God is the great motivator in Aristotle and Thomas. The outer unmoved heaven drove the rest, as both 'efficient' and 'final' cause. It drove the actual movements of earth, water, air and fire that constitute the world. It also drove the aspirations of the sentient beings on earth by being their 'final' cause. This structure is good since the whole notions of design and planning are driven by a vision of a better whatever.
What does motivate the Universe? We see that it conserves energy. When we model energy by the Hamiltonian function in quantum mechanics, energy appears in little packets that we can imagine (Feynman) as little arrows spinning at a certain rate. This visual model contains the same information as the expression phi = exp (i h E). The little arrows go round as time goes by because they have energy. The total number of revolutions (ie integrated over time) is the action E.t or dE.dt, the energy parcel multiplied by a duration.
GERLACH: 'No experiment is so dumb that it should not be tried'.
Thursday 3 June 2004
The search engine theorem: the narrower the search term, the more the results. A theory of everything is a search term that yields the whole Universe.
On modifying expectations by modifying the wave function: "Mechanotransduction . . . ' N 429:83, 6 May 2004, Tschumperlin et al
'Search term' = search structure. There will come a
[page 100]
there will come a time when people interested in anatomy can plug in a sample picture and get all its nearest neighbours displayed on their screen. At the other end of the spectrum, each of us is our own search term in the game of love.
Searching the transfinite network is the same as finding our way around it.
. . .
If this is a theory of everything, it must account for the existence of the searcher as well as the search term. We can understand the network, but we cannot see inside the users. So, in a sense, each peer payers of the transfinite network finds itself nested between two black boxes, one too complex for it to comprehend and the other too small and fast for it to see.
The metaphysical question is what sort of space do we live in. The first bit of data we have in the search for an answer seems to be the sort of idea that Descartes had, cogito ergo sum. Some might say that the unthought life does not exist, or exits only for itself. When reflection enters, so does generation, and the system reflects itself generation after generation, a sequence of events growing out of one another like plant . . . seed . . . plant . . . .
Atomic beads on strings of light. Searching is the basic survival mechanism, searching for the physical objects that fulfill our needs,.
John Maynard Smith, Obit. Eors Szathnary and Peter Hammerstein
Inappropriate behaviour: permutations rejected by the system, or not stationary states,
[page 101]
In the ℵ1 permutations of ℵ0, each element of ℵ0 appears ℵ1 times.
Error is self correcting, since it leads eventually to the death of the erroneous entity.
A basic assumption: two particles with one address are one particle. Perhaps an addressing gauge comes in here, so that if two identical particles try to have the same address, they automatically change one another in an identifiable way. We might distinguish fermions and bosons and the splitting of degenerate states in this way.
The idea is the inverse of the empirical residue which says . . . 'identical particles at the same address' and 'identical particles at different addresses' have no meaningful difference.
Addresses: The Cantor Universe is n addressing system.
Occupants: Ultimately addresses define occupants.
Friday 4 June 2004
Saturday 5 June 2004
Big bang vs continuous creation, an old argument that seems to have been resolved in favour of the bang, but quantum field theory tells us that we are a seething mass of creation and annihilation.
N429:129 13 May 2004 Entanglement. Bouwmeester The whole world is one entangled state; what varies is the strength of the coupling between all the various states. These couplings are al less that 1 (== identity) and can be transfinitely small (1/aleph(n) in our model.
One beauty of the transfinite network is that it is also scale invariant in the 'vagueness' of its operations, ie 2 ℵ0 it equivalent to ℵ0aleph(o), which
[page 102]
tells us that in exponential processes, the size of the basis carries no weight compared to the number of generations.
As we sit here drinking and looking around the model for good bits (wormholes), fits and so on, we are inclined not to be too critical. This seems reasonable in the early stages while the thing is still a baby. Eventually, if it is any good, it will survive without parental care.
To make a loop (Lonergan 'scheme of recurrence' Lonergan page 141 sqq) we need a cycle of Turing machines each one taking the output of another as its input - this is a network - which can be represented by cycles of permutation == groups. So we interpret the transfinite network (tn) as an algebra of transfinite matrices.
Thinking of the transfinite network in terms of information theory, we see that the complex symbols available in sets of cardinal aleph(n) is transfinitely more error proof that the complexity available at aleph(n-1).
The abuse of notation throughout the discussion so far is to let the symbol aleph(n) stand for the whole complex of cardinal and ordinal numbers of cardinal aleph(n)
The added precision is adequate to define (resolve) the new cardinal number of distinct entities. The resolution grows exponentially faster that the number of elements, so paving the way for the next level of elemental complexity.
COMPLEXITY <--> RESOLUTION Walther N 429:158
All communication is force: only those entities feel a given force which can decode it. The found physical forces are the four basic communication channels.
