vol VII: Notes
2015
Notes
[Sunday 6 September 2015 - Saturday 12 September 2015]
[Notebook: DB 79: Galileo Wins]
[page 65]
Sunday 6 September 2015
Go . . . and beat your crazy head against the sky. Lovin' Spoonful
Always looking for the biggest error to attack. Today's winner is from page 59: depreciation of the natural world.
Eureka Street: How Huge am I?
Dear Tim [Cook], I am an advocate of scientific theology and evidence based religion. Both of these pursuits are closely related to software. First, theology, the traditional theory of everything, tries to reverse engineer the system of the world. Religion, applying theological insights, attempts to establish peaceful and prosperous human communities.
The root of my advocacy is the assumption that the world is divine. on the whole, the intellgentsia have deprecated the world (the flesh and the devil) since time immemorial, assuming that it is not divine. If the world is divine all experience becomes experience of god and the foundation of scientific theology.
My story, so far, is available at naturaltheology.net.
Williams: 'The delicate alchemy of desire and demand is something Apple has proudly perfected. "A lot of times people do not know what they want until you show it to them," Jobs once said, which in retrospect acts as a neat summary for Apple's approach to the phone, tablet, laptop, desktop, music player and watch markets; instead of inventing these markets, it redefined them.
[page 66]
So redefine religion with the insights of information engineering from Cantor through Hilbert, Goedel, Turing and Shannon to the internet and beyond to the human network.
. . . to content and services after hardware perfected.
Monday 7 September 2015
My idea is that because Noether's theorem is established for continuous Lie groups, and a [real] continuum contains no information, continuity establishes a symmetry, that is a situation where nothing happens, for example symmetry with respect to time means energy does not change. It is conserved. Symmetries understood as 'nodes' where nothing happens [fixed points] are to be contrasted with god (and so the universe) which is pure action, where everything happens, by the via negativa not-god = not-action. The boundary on god is nothing, nothing observable, nothing to see 'outside' god. Emmy Noether: Invariant variation problems, Richard Feynman: Symmetry and conservation
Noether:
'What is to follow, therefore, represents a combination of the methods of the formal calculus of variations with those of group theory.'
'By a "group of transformations", familiarly, is meant a system of transformations such that for each transformation, there exists an inverse contained in the system, and such that the composition of any two transformation of the system in turn belongs to the system. '
Ie a group is reversible [a 'coder-decoder' or 'codec'] and this is the group expression of 'nothing happens' ie entropy (action) is conserved. Codec - Wikipedia
[page 69]
Eureka Street: Judicial power and the Pope. George Williams. In my opinion the Catholic Church is on the rocks and the root cause of the problem is the role attributed to the Pope as Vicar of Christ. We read in Canon law that there is no recourse from a papal decision. George Williams
The Link between Noether and the transfinite computer network is in the concepts of groupa and reversibility. This describes the hierarchy of symmetries contained in an event (the algorithms of the layers beneath the event, but the actual concrete event is irreversible. Time has one direction.
The big link here is the equivalence of logical and geometric continuity. In both there are regions of 'nothing happens'. Logical reversibility is an analogue of geometric continuity. The algorithm of light is responsible for its constant value [so this algorithm establishes a definite relationship between space and time]. Algorithms of action, energy and momentum are the symmetries of these quantities, everywhere present in their computation. The words lead me on, as maybe discovery in mathematics and physics where the choice of symbolism is seen to play a role in the discernment of meaning.
Quantum mechanics is a grpup theory, up until the observation, at which point the symmetry is broken, and a boundary is established between past and future. The arrow of time is the probabilistic prediction of quantum theory: every wave function eventually collapses = everything is ultimately observed, a tautology because everything observed is effectively (and empirically) everything.
Noether §6: the group theory of relativity.
'Hilbert enunciates his assertion to the effect that the failure of proper laws of conservation of energy is a characteristic feature
[page 70]
of the "general theory of relativity". In order for this assertion to hold good literally, the term "general relativity" should be taken in a broader sense than usual, and extended to the foregoing groups depending on n arbitrary functions.'
First we must 'see' it, and then go into the engineering details of how to construct the reality envisaged, ie prove it, because if it is proven it exists, at least in a formal sense, and if it has formal reality, it may become a symmetry of reality.
Quantum mechanics, insofar as it is invisible, ie limited to reversible computations, ie computations taking place at constant entropy (fixed bandwidth and memory [time-space].
Symmetry breaking mens establishing meaning, logging on to a network - speciation, defining and occupying a niche.
Tuesday 8 September 2015
Sometimes all this appears to be too good to be true. At other times it seems to be necessary. From an objective point of view, it is a fantasy that appears to have many contacts with reality. I probably rely most on my faith, the subconscious motivation that keeps me working on this on the chance that something will come of it. Not a sure thing, but better than buying lottery tickets.
I am slowly falling in love with the equation symmetry = algorithm = computer (turing machine). Here we get a bit stuck, however, in that we have been saying that geometric continuum is nothing, because it has no marks, but logical continuum depends upon
[page 71]
computation, which is a dance of marks and so cannot be written off as nothing, Are logical and geometric continuity duals, one a point, the other a space?
Maybe we can get out of this problem by pleading that both continua are invisible, geometric continuum becasue it has no marks, algorithimic continum becasue a watched computer never halts.
Wednesday 9 September 2015
Beautiful sunny day somewhat marred by the death of a good friend in an accident on a farm. Funeral Friday.
Sex, a wet continuum. Wets = binds loosely to.
An equation of continuity can apply to discrete entities like atoms, the steady state number of atoms entering a leakproof pipe equals the number leaving it. Same for quanta of action flowing through a computation.
We attribute the value of complex numbers in physics to the periodicity of computation, beginning with the clock frequency and growing as the computation becomes more complex until the period becomes the age of the universe.
How do we apply conservation laws to digital physics? Via quantum mechanics, and equations of continuity which explain conservation: energy flows without creation or destruction. How does probability flow?: given an alphabet ai with probabilities pi which flow (in a dynamic alphabet) to maintain the normalization ∑i pi = 1.
[page 72]
We understand conserved flow and complexification by a system like our blood flow, two trees joined at both roots and branches [leaves]. The plumbing of the Universe. Is this the whole content of Noether's theorem for 'fields'?
Neuenschwander page 107: 'If the functional is extremal, then the Euler-Lagrange equation holds. When the functional is both invariant and extremal, then the Rund-Trautman identity together with the Euler-Lagrange equation gives immediately the Noether conservation law. In the case of our field φ(t, x), the Noether conservation law offers an equation of continuity
∂μ jμ = 0
where the current jμ stands for [a function of the] generators of a transformation .' Neuenschwander
N page 61: 'Consider transformations described by a continuous parameter that can be varied starting from ε = 0. The identity transformation ε = 0 makes no change whatever. As ε increases, the differences between the original and the new coordinate system becomes larger and larger. Noether's theorem deals only with continuous transformations.'
The digital model of the network trees gives us an additive arithmetic (superpositional) description of conservation. [conservation is local in that every 'bidirectional interaction' involves zero space-time interval, quantum mechanical, prior to space].
The constraint of continuous mathematics adds considerable complexity and difficulty to physics.
Thursday 10 September 2015
[page 73]
Still in trouble with symmetry, although the general drift seems clear, am not yet able to integrate Noether and my would be digital world. The problem seems to revolve around the relationship of the two continuities. Today I have no other demands so I can spend a solid day on it and hope to have an outcome by bedtime.
The formal mathematical view is that motion is relative and it really makes no difference if we think of the physical system as stationary and the reference system (reference body) moving, or keeping the reference system fixed and letting the reality move, as Newton does.
Einstein's general relativity is the first major example of the modern view. All disussion requires duality, we say that a is b or not-b. Einstein used a mathematical manifold to name the events in the world. From the point of view of this naming, every event is unique [and has a unique name or coordinate]. He then imagined all possible continuous motions by describing the relationships between two different namings of the events of the world [one of which is a continuous transformation of the other]. He was able to produce a fixed relationship which governs the continuous transformations between namings which is a set of ten fields described by ten differential equations called the metric. The basic point of all this is that no matter how we look at a set of space-time events, they always have the same metric relationship to one another. How we look at them does not change [them].
Extremal action corresponds to extremal code, ie most or least efficient.
Friday 11 September 2015
Saturday 12 September 2015
phys09GravitationGravitation introduces proper time which is related to proper energy
[page 74]
by the Planck-Einstein relation and modelled by the circle group. Planck-Einstein relation - Wikipedia, Circle group - Wikipedia
The Heuristic structure is built on digital layers, like a network increasing its entropy by one unit with each added layers. We consider gravitation as an algorithm in the energy layer, the second after the primordial layer of action.
Einstein worked in 4D space-time but gravitation predates the existence of space, which arises as 2D fermions, 3D, 4D which is complete be3casue no crossed wires. Each new dimeson of space complxifies the metric, adding 1 + 2 + 3 + 4 = 10 dimensions to the 4D metric, gμν, μ, ν, 0 .. 3.
Misner Thorne and Wheler page 302: ' "Every physical quantity may be describable by a (coordinate free) gemetric object and the laws of physics must all be expressible as gemetric relationships between geometric objects. This view of physics, sometimes known as the "principle of general covariance" pervades twentieth century thinking. But does it have any forcible content?' No/ General covariance does not spearate viable from non-viable theories. Yes? ' "Nature likes theories that are simple when stated in cordinate free geometric language. According to this principle, nature must love general relativity ad it must hate Newtonian theory. Of all the theorires ever concocted by physicists, general relativity has the simplest and most elegant geometric foundation [three axioms: (1) there is a metric; (2) the metric is governed by the Einstein field equation G = 8πT; (3) all special relativistic laws of physics are valid in local Lornetz frames of metric].
The basic measure in general relativity is proper tie whose definition becomes more complex (involving space [= memory]) as the Universe complexifies: energy (T), c (TL-1) (boson), fermion (TL-2), moving fermion TL-3.
Takes four layers to get from God to 4-space. NOP. NOT, NAND, Fermion [that is a space big enough to model a computer].
