Sunday 3 March 2024 - Saturday 9 March y 2024
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The business: cognitive creation theory
Heijenoort page vi: 'The great epoch in the history of logic did open in 1879 when Gottlob Frege's Begriffschrift was published. This book freed logic from its artificial connection to mathematics but at the same tine proposed a deeper interrelation between the two sciences. Jean van Heijenoort (1999): From Frege to Gödel: A Source Book in Mathematical Logic 1879 - 1931.
Atiyah page 113: '. . . the geometrical significance of spinors is still very
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mysterious. unlike differential forms which are related to areas and volumes, spinors have no such simple explanation. They appear out of some slick algebra [Dirac equation?], but he geometrical meaning is obscure as illustrated by the global obstruction referred to above. (page 112). Spinor - Wikipedia
page 112: 'Because of the double covering in going to the spinor group there is a potential global obstruction to defining spinor fields (and hence the Dirac operator). When the obstruction vanishes we call the manifold a spinor manifold.'
From my poin of view spirors are not geometrical but logical, consistent with the idea that the quantum of action is a logical operator which is implemented as the simultaneous discovery of a hermitian matrix [operator] and the [associated] spectrum [of eigenvalues] which I understand in psychological terms of thinking of something to say (ie do) ie a list of fixed points [an alphabet] that can be strung together into a sentence, a house or a baby. The idea of making them into a field is something of an abortion. Dirac found that his equation predicted discrete [spin ½] particles. As I have kept saying, continuous fields carry no information. Making particles into fields adds nothing but mathematical fiction to reality.
' In mathematical terms, spinors are described by a double valued projective representation of the rotation group SO(3).' Here we use 3 space to define spinors but perhaps they logically define 3-space
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and so give us the correlation we seek between Hilbert and Minkowski spaces. What does the double covering mean (belt trick puzzle)? Anti-twister mechanism - Wikipedia
[Wikipedia] ' Spinors do not appear at this level of description of a physical system, when one is concerned only with the properties of a single isolated rotation of the coordinates. Rather, spinors appear when we imagine that instead of a single rotation, the coordinate system is gradually (continuously) rotated between some initial and some final configuration. For any of the familiar and intuitive ("tensorial") quantities associated with the system the transformation does not depend on the precise details of how the coordinates arrived at their final configuration. Spinors, on the other hand, are constructed in such a way that it makes them sensitive to how the gradual rotation of the coordinates arrived there. They exhibit path dependence. It turns out that for any final configuratio of the coordinates there are actually two ("topologically")
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inequivalent gradual (continuous) rotations of the coordinates that result in the same configuration. This ambiguity is called the homotopy class of the gradua rotation . . .. This distinguishes them from vectors and tensors, none of which feel the class.'
So we like to think that a spinor is a logical rather than a spatial entity [kinematic not dynamic ??].
We are trying to see quantum mechanics as a logical cognitive theory rather than a theory about events in continuous space. The question since the beginning has been the meaning. The irst plank was laid by Einstein who interpreted Planck's quanta as photons and we want to go along like that, seeing particles with enough entropy to define the Universe and avoiding the infinite degrees of freedom in 19th century space. The principle here is that information is physical: Principle 15: An unmodulated continuum carries no information. The basic issue is revelation: how information is encoded and transmitted. So new book introduction front_05_introduction: Revelation.
The output of quantum mechanics is a probability amplitude fir the emission of a certain symbol, and like a communication source the sum of these probabilities is normalized to 1.
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So we can happily accept that quantum mechanics is the theory of communication of the quantum world (the mind of god) with the visible world the body of god. This is really all we want, and we may put it in the introductory summary' Revelation - world of god: Catholic Church making its money by marketing the word of god,which is all a scam and should be banned by ASIC on the grounds of false communication. This is the case, to be built on the works of the second Vatican Council.
Short term memory with brain and quantum mechanics: narrow band working circuit. Be simple, be direct. cc_gravitation done; cc18_fixed_points complete.
cc19_network; what does this page add? love and conversation.
We start this with abstract computer networks and then broaden to all the physical networks around the globe, ocean, atmosphere.
Moments of despair at what I lost to the church but the only thing to do is to continue with the task of replacing it with something better. I am very fortunate to have gone into the monastery and gained an inside view of the good and the bad aspects of the church. A struggle for understanding and
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a failure that has destroyed billions of lives by taking the imprial rather tha the humane line, creating a system of false belief by violence. Cosmic cosmology is a work of my own redemption.
Shannon's idea is quantum mechanical, the longer you look at a periodic signal, a sequence of characters or action E = hf the more precisely you can read it:
Actually, two signals can be reliably distinguished if they differ by only a small amount, provided this difference is sustained over a long period of time. Each sample of the received signal then gives a small amount of statistical information concerning the transmitted signal; in combination, these statistical indications result in near certainty. Claude Shannon (1949): Communication in the Presence of Noise
We see this in the role of the clock in a computer [which provides a certain time intervals for signals to settle down before they are read by the next step in the process]. In the life of the Universe a signal may be rad with absolute precision: Δ E . Δ t ≈ Δ p . Δx ≈ ℏ.
What is the point of a network? Reproduction. First we list the properties of networks, and then the consequences.
Blankanieves: A fairy tale with a wicked witch who dies, a princess who lies forever? Good and evil. Blancanieves - Wikipedia
Are we getting more political? The battle is against delusion and top down management, chain reactions (gravitation). Better to stay with the science which has built the world so far, so the network page remains politically neutral. properties and consequences, Malthusianism and chain reaction.
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My tendency to take extreme positions on spec tends to paint myself into a corner, but it helps to get closer to whatever I sam seeking, and the paint will dry. What does this mean? Yesterday's reprocessing of cc18_fixed-points feels good now I am seeking the same feeling of cc19_network. This is a bit old hat since the network model has been with me a long time, well before my honours thesis. It has to be beautiful by bedtime. Overall I still think I am on a good thing: quantum mechanics as conversation + symmetry with respect to complexity does the whole job. Where does network fit in? Proves both these points, communication and complexity. As Cantor says we can replace anything, no matter how complex, with a serial stream, as in genetics and ordinary human telephone calls based on the Tacit Dimension ie the packaging, the context of love and familiarity.
The most interesting [new] thing about networks is the spinor (Dirac) ARI Watch. ARI Watch: Dirac string trick
Slow week on the notebook. A bit of revision cc17 - cc21 abs clarifying all the way with removing continuous field from the picture and reinforcing the digital view of the symmetry with complexity vis logical network structure. Now to cc21_matter_spirit in the network
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Dear random brain: give me an idea to chew on over the lang weekend. Monday is Adelaide cup day. Raving rules.
cc22_cosmic_theology. What is the point of this: one quantum [initial singularity] to whole Universe.
[Current outline]
1. From Galileo to Einstein.
2. Is naked gravitation divine?
3. Matter ≡ spirit; phyeics ≡ theology; particle ≡ God [Thales]
4. Meeting: Science and evolution
5: Lust for life: Faith, hope, charity
6. Bootstrspping: kinematic to dynamic
7. quantum conversation: action to Universe.
Looks good, but where is the bit about angels, Minkowski space and the principle of individuation which takes us transfinite?
Putting Cantor into action [starting with the empty set ∅]. To really [physically] construct Cantor's proof we require ℵ1 copies of each of the ℵ0 natural numbers, or, as we have called them, angels. [This is easy in formal mathematics, not so easy in physical mathematics] We achieve this by distributing them through space. As we learn from the Shield of the Trinity, the only way the trinity can avoid logical contradiction is by each of the person occupying their own point in space, by being physically, not just kinematically orthogonal to each other. This the the modern expression of Aquinas and Augustine's idea that what is accidental in created things is substantial in God. Aquinas, Summa I, 50, 4: Is every angel a different species?