Notes
[Notebook: DB 60 Spotlights]
[Sunday 26 November 2006 - Saturday 2 December 2006]
Sunday 26 November 2006
Monday 27 November 2006
[page 36]
Tuesday 28 November 2006
Oozing ahead at somewhere between a plate tectonic and a fundamental particle velocity. Now we want to explain wave mechanics in terms of recursive function theory in a network where processes are communicating with one another, but actual communication (resulting in an 'observation'), ie the emission and absorption of a particle, can only take place when all conditions are met. [this is equivalent to 'contact is established'] Quantum mechanics uses a very straightforward algorithm to
[page 37]
compute the probabilities of events. Can we reproduce this algorithm by a mechanistic arrangement of Turing machines with delay. Seems quite likely.
If we put someone at the top of the tree or they put themselves there we are bound to get a corrupt system because the top dog is in a position to avoid, squash or misrepresent reviews of its actions because it has sovereign power, ie control of sufficient military power to kill members of the loyal or disloyal opposition.
We therefore need a topless system, or more specifically a system with an abstract top often called god. God judges the powerful as well as the weak. The path to becoming a dictator thereby requires taking control of god as well, so ruling by divine right and justifying it by claiming to be the only authentic channel to God, and pronouncing one's personal plans through the persona of god.
God exists independently of any ruler religious of secular, however, and so is open to observation and verification by all. Given a scientific theology,. we can sift the spurious claims about god from the genuine ones, and so place the governance of our societies on a sound realistic footing. All bullshit, spin and other sectarian views of the truth must be identified and deprecated if we are to manage our fitness realistically.
Now we ask, when is a function computable? Look to quantum mechanics for clues, in the eigenvalue equation
[page 38]
X = x psi, where X is a complex matrix, x is a [complex] scalar and psi is a vector. Stationary states are represented by eigenvectors of the relevant energy matrix. In other words, we have a considerable compression of data when we express it in terms of a diagonal metric, and this compression allows (or is tantamount to) computability. It is an act of knowledge, a compression of complexity from ℵ1 to ℵ0, or more generally aleph(n) to aleph(n-1).
The quantum field theory interface problem. Quantum mechanics explains (gives meaning to, connects) our observations all of which are in the 4-dimensional graphic user interface, and all of which are counts of the events observed in a certain basis defined by the instrument, eye, ear, telescope, microscope, line of questioning etc. Question sets up a basis in which the answer is coded. [general covariance = the truth is independent of the language of the question.]
From the point of view of algorithmic information theory, a mathematical continuum contains very little information and is therefore quite a tight constraint [eg in general relativity].
Wednesday 29 November 2006
Einstein page 114: 'Only when the continuum is a Euclidian one is it possible to associate the coordinates x1 . . . x4 with the points of the continuum so that we have simply ds2 = dx12 + . . . '.
The compression from Gauss to Descartes is analogous to the compression in the eigenvalue equation.
[page 39]
The idea of Gaussian coordinates leads us to the notion of 'Gaussian wiring' which explains why space is 3D, so all points can be joined simultaneously [contacted] without any wires having to cross.
The beautiful fit between the large scale structure of the Universe and Riemann's geometry [ie Einstein's general theory of relativity, which we prefer to call the general theory of invariance] is matched or exceeded by the fit between complex linear vector spaces and the small scale structure of the Universe [ie quantum mechanics. which over the last century has turned out to fit the world perfectly]. Both are examples of the 'unreasonable effectiveness of mathematics in the natural sciences' noted by Wigner. Wigner page 222
The explanation, I think, is simple. Mathematics is a symbolic system and the [observed] Universe is a symbolic system. An event, as understood by quantum mechanics, is a symbol, that is a definite and separate addressable thing which may be used with a suitable code to convey meaning, like these letters. Symbols can be both static (static in their own reference frame like the shape W) and dynamic (in their global reference frame). As I write and you read these symbols one after another, each effectively comes to life and dies out of your perception as your eye (like my pen) moves along each line and down the page.
Mathematically, there is no difference between the way elementary particles talk and people talk, and in fact elementary particle talk forms the physical layer for people talk, which is mostly an exchange of photons [light particles, when we look at each other or use electronic communications] and phonons [particles of force, as when we touch, speak and hear] and heavier particles like pheremones and genes.
Adultery: another form of communication
Thursday 30 November 2006
Friday 1 December 2006
'Higher order mapping' Bargmann Nature 444:295 Bargmann 'peer layer or group'
[page 40]
Washing and error correction: if each wash removes 90% of the dirt, we can quickly achieve infinitesimal levels of dirt by repeated washing.
gene flow -
Attitude needs to be founded on knowledge, but with a bluff element designed to minimize expenditure in the attainment of the goal (scare them into submission rather than conquest, diplomacy vs war)
The brain is not 'grey matter' but a dense and complex computational network and the same can be said for all matter, which is in no way passive as the ancients thought.
We want network explanations for a) Minkowski metric; and b) relativity and spin.
a) makes coincidence possible in spacetime, so all communication results from contact.
b) Dirac's equation?
Evolution: We proceed from general covariance and the abstract theory of networks to the concrete world by evolution by natural selection - self perpetuating structures propagate in spacetime, the others don't.
Although we talk about wave particle duality, empirically thee is no such thing. We observe only particles.
[page 41]
The waves are part of the abstract model although no-one can deny their utility as a bridge between the classical notion of continuum and the particle nature of experience.
What we have been talking about is a metaphysics in the words of one prominent Catholic theologian Bernard Lonergan: 'Now let us say that explicit metaphysics is the conception, affirmation and implementation of the integral heuristic structure of proportionate being.' Lonergan page 416
'A heuristic structure, then, is the notion of an unknown content [unheard gossip], and it is determined by anticipating the type of act through which the unknown would become known [a few beers and conversation at the shop] A heuristic structure is an ordered set of heuristic notions [the symmetric Universe]. Finally, an integrated heuristic structure is the ordered set of all heuristic notions [which does not exist]. Lonergan page 417
What he means is when we look around what do we expect to see? A puppet show worked by God seems to be the position of the Church. here we propose a vast network of 'personalities' all chattering away together, a transfinite extension of the trinitarian threesome developed by the jejune minds of Platonic modellers.
Given the network heuristic, we now come to fill in the details. Everywhere we look we see things talking to us (and we only see the ones that do talk to us). We begin with our basic conversation which keeps us glued to the earth. Why is this so? [general covariance means that at some level everything can talk to everything, so the Universe is one]
Our metaphysics tells us that whatever gravitation is, it is a language, form or process that constrains the way the whole system fits together. To find that form, we begin with the axiom that in the model of god proposed here, god is not capable of intelligent design, by which I
[page 42]
understand deterministic progress into the future along preordained paths.
We cannot 'prove' the axiom but can suggest a cybernetic argument that makes it look plausible. The world we see is the world that communicates with us. Ultimately this communication is a set of quantum events (like the reception of a photon in my eye) which are processed through layer after layer of network to bring us to see what we see. How is this network structures? What we observe is finite but the possibilities of the world are transfinite. There is therefore something constraining the transfinite world to make it appear finite. A constraint that reduces the cardinality of the formal system.
This constraint is that the Universe began as a simple undifferentiated point (the initial singularity) whose properties were analyzed by ancient theologians everywhere. The Universe has remained forever one (because there is nothing outside to fragment it) and so we can assign to it an entropy of 0, 1 state.
Now let us guess that this force for unity and control (the Bose force) is opposed by the Cantor force [Fermi force] for transfinite differentiation. The equilibrium point of these forces is the point of least action, that is the point of most efficient software. In this way we begin to exert selective pressure on the Turing machines that inhabit the computable network.
[page 43]
In the competition for computing resources, inefficient algorithms are selected against.
One could say, of Einstein's relativity, that it is the most efficient algorithm to give a consistent Universe wide communication protocol, which is the software expression of a singularity which has diversified into four-space. Why do we live in this spacetime and not the one of infinite dimension?
Where we see stability in a dynamic system we suspect the existence of control. Central to control theory is the principle of requisite variety. Ashby, Chaitin In our Universe the space of physical messages available for control is finite, whereas the possibilities are infinite and not therefore controllable. We may express the principle of requisite variety in terms of physical bandwidth, which, through quantum mechanics, is equivalent to energy.
In a network we measure bandwidth in bits per second. If the bandwidth of the controller is greater than the controllee, deterministic control is possible. Now, we may ask, has the present sufficient bandwidth to control the future?
Now, is the bandwidth of the future greater than the bandwidth of the past. The principle of conservation of energy says no. Bandwidth is conserved. This principle appears in quantum mechanics as the conservation of probability, that is the conservation of the rate of events.
[page 44]
From a cardinal point of view, quantum mechanics is not creative. Creativity enters the world with quantum field theory, the theory of the creation and annihilation of particles. Quantum field theory is generally considered to apply only in the microscopic domain. Here we shall use our idea of invariance with respect to complexity to extend it to transfinite domains.
The greatest feature of this model, to my mind, is its lack of esotericity. Basically, it seems, the Universe runs on gossip. The intensity of this gossip is measured by the sheer size of the Universe. We know al about gossip, its strengths and subtleties and innuendoes, all of which give us insight into conversations between atoms or cells or nations. In each case we use the network paradigm to transform the subject of our inquiry [into our own frame of reference] and then [ask] how we would behave in the circumstances. In other words we use our metaphysics to extend the personal and anthropomorphic view to the whole Universe.
Corruption and inefficient algorithms hinder creativity; on the other hand superior efficiency carries with it the moral hazard of overdoing things. In other words, power corrupts, reducing the fitness of the powerful until they are swept away by new systems that grow toward corruption in their own terms. Now if this cycle is slow and deep, high levels of corruption are needed to spark collapse and the collapse may be painful, whereas a fast shallow society (approaching
[page 45]
a democratic continuum) will correct errors at a much smaller level and so steer a course more closely approaching a geodesic in the space of states.
[. . . text moved to page 41]
The Christian view of creation is not creation. Nothing new came into reality, jut a copy of a Universe that has existed forever in the mind of god.
One thing leads to another: the chain of Turing machines.
Saturday 2 December 2006
