Notes
[Notebook: DB 59 Draughts]
[Sunday 3 September 2006 - Saturday 9 September 2006]
[page 147]
Sunday 3 September 2006
Relativity of locality Wigner, Symmetries page 51. Wigner
The type in the boxes is symmetrical (all the same - each symbol) The symmetry is broken when it is set into text.
'Massive" = 'Internal process'. Insofar as a letter is static (invariant) it has no mass and so can travel at the local 'speed of light'.
Deighton: London: Individuals vis-a-vis organizations. Deighton
[page 148]
All communication is confined to two points whose distance apart while communicating is zero. A 'broadcast' is a set of one-one correspondences.
All communication takes place at zero (logical distance) which we take to be bidirectional implication.
The execution of a Turing machine requires a quantum of action. The smallest Turing machine (ie the one that carries us the least difference) is the identity operation. The machine reads a square, erases it (if you like) and then writes the same thing as it read. Two of these can be coupled in opposite phase to make a unitary system,
Rate of action = frequency = energy.
. . .
Logical implications overlap so that the distance between them is less than zero. How much overlap? We can make this calculation with gravitational coupling. Gravitation applies to al particles, even those with no internal structure (dark matter?), and since these particles have no internal structure, if they overlap they must totally overlap (?).
[page 149]
Quantum mechanics all works on phase, which takes us quickly to frequency, energy, momentum etc. Gravitation encompasses the whole symmetric network, every point being its own 'rest frame' and in contact with the others by logical operations to which we attribute logical continuity.
The classical continuum does not allow points to overlap, but sets of points may. In other words, the points in the classical like (names by the real numbers) do not touch.
We measure overlap by comparing phase through the inner product.
[von Neumann} showed us the cardinal (integral) transition between continuous and discrete space, so unifying the two versions of quantum mechanics by showing that they led to the same results. von Neumann Heisenberg's ansatz again.
We would hope to map the symmetric network to quantum mechanics in a similar way. Aleph(0) different Turing machines, but no limit to the distinct number of instances of a particular one. PARTICLE = TURING MACHINE. Motivation electron, meson, tau. (Family of three).
So let us construct a Turing machine version of Dirac's equation:
We are all so happy when something 'works' = comes out right (like childbirth).
[page 150]
Angle (phase) = degree of overlap which runs from -1 through 0 to +1. I overlap completely with myself 1. I antioverlap with my environment (not - me) In between is 0.
There seems to be no reason why we cannot substitute the Turing model for the harmonic model except that the harmonic model is supported by three centuries of tradition and a vast literature, whereas it is hard to see how to apply the Turing model. Press on.
Monday 4 September 2006
Tuesday 5 September 2006
In quantum mechanics the 'overlap integral' (scalar product of two vectors) gives the probability amplitude that when we measure one vector a we get the other b, ie it tells us the degree to which a implies b. There is no implication between orthogonal vectors, and identity between a vector and itself. The classical 'measurement' of a vector gives us a probability |amplitude|2of a given event a --> b.
Wednesday 6 September 2006
Einstein introduced a new way of measuring distance, showing that we must consider spacetime together, giving us a new concept of 0 distance.
Quantum mechanics introduced a new way of computing probabilities and showed us that we must take interactions (past and future) into our
[page 151]
accounts. Greenies introduced a new way of accounting for our actions, showing that we must take all causes and consequences into account.
My internal state (happiness, sadness) maps to my external state (rich, poor) via a set of expectations.
Religion and politics: Quality control begins with measurement, since if we cannot measure things we cannot control them. Measurement always requires some discrete unit (even if it is the last significant decimal place). Some things like sheep are naturally countable and quantum mechanics tells us that everything in the Universe [is countable].
The fundamental principle of quantum mechanics is that everything we see is countable. Although quantum mechanics has a lot of continuous formalism in it, the name of the game has been to get the continuous formalism to come up with isolated (discrete) points like the eigenvalues of an operator, which exist independently of the basis (language) in which they are expressed.
The relative state formalism of quantum mechanics fits naturally with the symmetrical network, since a change at one point can be inferred from a change at another of the two points are in communication, ie in contact.
We can relate all our emotions to action. I am depressed when I cannot conceive an action which will achieve what I want (or need), elated (like in love) when I can see my way to overcoming death by reproduction.
[page 152]
Thursday 7 September 2006
Rigid = 1 inertial frame = no relative velocity. A truss remains rigid as long as every one of its elements maintains its position relative to the others.
Riemann in Jammer page 181: 'The basis of metrical determination must be sought outside the manifold in the binding forces which act upon it'. Jammer
The 'logical metric' has values 0, 1. Either it is logical or it is not because predicate calculus is complete. No question remains unanswered.
Bound and unbound. Unbound terms, like pronouns, are 'symmetrical' because they may be mapped to many different 'meanings'.
