vol VII: Notes
2012
Notes
[Sunday 12 August 2012 - Saturday 18 August 2012]
[Notebook: DB 73 Spring2012]
[page 1]
Sunday 12 August 2012
I am reading a lot and writing a lot of notes but making very little progress on the articles for Zygon [From physics to theology] and Science [Why is the Universe quantified?]. Why? Something subconscious. My network is apparently moving toward something as yet unknown which is in some sense blocking its way. What is needed, it seems, is a new symmetry to walk along to get from here to there. In physics each such symmetry is expressed as an equation,
[page 19]
ultimately a set of conditions both executed by the same cardinal number of 'plancks', ie operations measured by Planck's constant, which we arbitrarily set to 1. Since the dimensions of h in our world are ML2T-1, we need to multiply by something (anti-h) which has the dimensions M-1L-2T, = 1/p.x = 1/E.t. We see this in all our complex quantum mechanical exponents. Our hypothesis is that the fundamental structure of the Universe is represented by real arithmetic (set theory) and that the next step in complexity leads is to complex arithmetics, which involved multi-component quantities cardinal 2. Then we move to Hilbert spaces and transfinite cardinals.
Memory = zero energy. According to Newton;s first law it costs nothing to remember something, since memory is symmetry with respect to time. Landauer, however, shows that erasure costs kT. What is the relationship between the quantum of action and Boltzann's constant, hν / kT, relating the sizes of two sets of symbols, those following hν and those following kT
Pais page 272 'Lande's formula in fact demonstrates excellently how, in the days of the old quantum theory, gifted physicists were able to make important progress without quite knowing that they were doing., The formula seemed mighty peculiar, but it worked. What was going on? Pais: Inward Bound
The basic question; understand the dynamics. What is going on? Why is x crying, etc.
Pais page 272: All closed shells have zero angular momentum.
page 21]
The elemental atoms are a series of insights, ways of putting elements together, basically following the lego-like algorithm that all fixed ponts are the nodes of standing waves, that is the output of computational processes.
Pais page 277: George Uhlenbeck: "'It was then that it occurred to me that since (as I had learned) each quantum number corresponds to a degree of freedom of the electron, the fourth quantum number must mean that the electron has an additional degree of freedom -- in other words the electron must be rotating".' So breaking its perfectly spherical symmetry by acquiring an axis of spin, the angular momentum vector, two state 'up' and 'down'. [Magnetically, electron is a 1D object]
page 280: Bose Einstein and Fermi Dirac statistics depend upon the 'permutation symmetries of many-particle wave functions.'
Where is the Hilbert space -- just 'where' the particle appear and disappear.
Pais page 281: Boltzmann statistics: Particle identical but distinguished by space-time positions (coordinates). [many bosons can have the same coordinates, ie they are not distinguished by coordinates, they are 'obnoxious' (immune) to space.
Pais page 283: Einstein: the ways of counting (BE, FD) '"express indirectly a certain hypothesis on a mutual influence of the molecules which is of quite a mysterious nature". That influence is, of course, the particle correlations implied by the restriction to symmetric [and anti-symmetric] wave functions.'
So the unobservable wave function affects the observable statistics. What are to to make of this 'old mystery of quantum mechanics' (Feynman)? This might be the bit I am
[page 22]
looking for, the invisible deterministic process, rendered indeterminate because the halted state of a computer is much less complex that the computation. [or because quantum mechanics is not coupled to space, so that events quantum events are mapped randomly onto space-time.]
What is going on behind the scenes? Something arithmetical? logical? Mysterious divine activity? At least something consistent and therefore incomputable and incomplete?
The classical God is not creative insofar as everything already exists within Him, he is just executive, realizing an eternal plan.
All the information is said to be in the state vector, a multicomponent quantity, each component of which we may imagine to be a computable number, representing a maximum of ℵ0 bits of information (or entropy). We might think of each dimension of Hilbert space as a particle in a gas with a certain energy, the total energy of the particles being constant.
What we are looking for is what 'meaning' to give to the mathematics, what physical meaning, ie what is the correspondence between the mathematics and the observations, the operator we call the observable. The best way to map from network to physics might be Dirac's transformation theory, from which we derive a network model of Dirac's equation and the scalar wave equation. Dirac equation - Wikipedia, Wave equation - Wikipedia
Virtual particles: unobservable halts of the computation. Mathematically we do not associate time with a Turing
[page 23]
machine, all we require is an ordered set of operations, the final state of each being the initial state of the next (overlapping continuity) ands the stationary states may last for a very long time without interrupting the logical continuity of the process. So a stationary point (the terminally halted machine) is made of intermediate fixed points (the intermediate halts of the machine). A real computer has two phases, dynamic and halted which are mapped to two phases of the clock: all change; observe; all change etc. So we may think of the world as a superposition of dynamics and fixed points.
Tomonaga page 44: 'Finding the quantum mechanically allowed values of a physical quantity is reduced to finding the eigenvalues of the linear operator expressing that physical quantity; in doing this calculation, depending on what kind of orthogonal coordinate is taken in this abstract linear space, the formalism of matrix mechanics or that of wave mechanics emerges.
I keep putting off trying to understand physics to a later date in the hope that one day physics and theology will come clear to me in the light of one another,. This seems to be happening already, but I am spending a lot of time wondering about quantum mechanics these days, the theory of the procession of the Son from the Father. break a symmetry, you have two identical pieces one of which is not the other, the definition of Father and Son is the initial symmetry is the God of the Old Testament.
My mind is full of algorithms, how to do things. Each algorithm comes with a long list of possible errors and how to deal with them compiles over a long life of practical
[page 24]
work (the roof I went on today was so rusted I would have fallen through had I ventured away from the battens beneath the iron). In the more abstract zone the same thing holds. My big project is to make a working model of a divine Universe that shows how to understand my life, and hope that the human symmetries so exposed facilitate the transfers of the model from me to everybody.
Christianity is centred on evil, guilt, pain, punishment, sacrifice death and many of the other downsides of life, blaming them all on the human tendency to evil and using guilt as a political tool to manipulate us into supporting the Christian position, from which many gain an income.
Can agree with Thomas that seeing God can be blissful, but can also be painful and or/frustrating because many things are hard to see and do, a problem that we might like to solve by magic but must be content with work.
What would make people think my story is true? That it be consistent both within itself and with common experience, We wish to connect issues such as freedom, bonding, and force across the spectrum of complexity from physics to theology.
Requisite variety suggests that an adequate vision of God can be achieved through love of (interaction with) a peer.
Philokalia : weird behaviour caused by a weird understanding of reality. flesh evil, etc. Palmer
[page 25]
Neither I nor the Universe in general can do something unless it works, ie unless we have an effective algorithm, ie look at the tree and the environment, decide which was it is to fall, cut the hinge, etc. Good success? Probably, with experience.
Pais page 311: '. . . early in 1925 a study of Compton scattering in a cloud chamber demonstrated that energy and momentum conservation do hold in individual events'. Deterministic eigenfunctions.
Wine is an elelment of my environment.
Theology = theory of human society, derived from a a theory of the human environment. The need for low entropy energy drives us all.
My address is my content. That is all there is to me. We normally discriminate between address and content, but we can add these to give complete information which we might see as constant, so that more comprehensive addressing corresponds to less content per address, and vice versa. So one might give the full transfinite address of a binary operation, or the binary address of a trtansfinite operation, for the smae total information (entropy).
ENTROPY - SYMMETRY
INFORMATION - BOKEN SYMMETRY
[page 26]
The meaning of these words can be judged in the whole context of the english language, and in the more local context of everything I have written down for later (and other) reference.Quantum mechanics is a generator of space an infinitesimal (time) relative to the structure of space [space does not see time because they are orthogonal].
Pais page 314 Pauli: "'When I was young I believed myself to be a revolutionary . . . [but] I was a classicist, not a revolutionary".'
Maybe we can say that a revolutionary demolishes with no new construction in mind, whereas a classicist envisages a new world built on the old [and an orderly transition between them?]
Let us guess that the amplitude is private, unobservable.
Pais page 333: 'The quantum number [n] of an oscillator is equal to the number of quanta with the corresponding [ν]. . . . this simple yet quite extraordinary remark opened the door to quantum field theory.'
What input next, or sleep?
Pais Subtle page 417 n: Einstein to Infeld: '"I tend more and more to the opinion that one cannot come further with a continuum theory".' Yes, no information in continuum more than in the differential equation and initial/final conditions,. All the information the wave function carries is the difference between states which solve it. Pais
[page 27]
Pais, Inward page 468: Einstein quotes Lessing '"the aspiration to truth is more precious than its assured possession".' Maybe, maybe not, knowing how to grow food seems better than aspiring to be well fed, an a true theology is worth more than hoping for heaven. Charles Fishman
Monday 13 August 2012
There seems to be little hope of replacing the quantum mechanics of amplitudes with anything discrete and logical, so we must accet it and concentrate our wonder on the 'reduction' of the wave packet from a comlex superposition in an infinite dimensional space to a real particle in 4-space with a world lihe of its own [maybe two reductions, complex to real, and symmetrical superposition to broken symmetry].
Pais page 329: 'It is not a weakness but a strength of quantum mechanics that it ineluctably leaves the time and direction of certain elementary processes to chance.' Because it is the layer below space-time and knows nothing of it, it is symmetrical with respect to space and time, like blind justice.
See how a lens picks an image out of a sea of radiation.
The direction of spin only has meaning in a magnetic field.
Dirac in Schwinger (Dirac, Folk and Podolsky) 'the equations of Dirac's theory . . . are obviously relativistically invariant . . . . The obvious relativistic invariance is achieved by the introduction of a separate time for each particle.' Schwinger
Which implies the existence of distance. Obviously.
[page 28]
Now we are looking for a theory of principle. General relativity begins with special relativity and the principle of equivalence,. The principle of special relativity is that the nature of the world is the same for all weightless observers, including the velocity of light whose constant universal value lies at the root of all relativistic phenomena. General relativity - Wikipedia
The principle here is that human creativity and the creativity of the Universe are isomorphic if we disregard the complexity of the systems involved. We are looking for the transformation which takes us unchanged from on God to an infinity of faces of God. Basically we are looking for a theory of creation and annihilation as the theological extension of quantum field theory, We want an unbroken chain from physics to theology.
Is this possible. Yes, because quantum mechanics is symmstrical with respect to the cardinal of the Hilbert space we happen to be using,. We assume here that this cardinality continues into the transfinite numbers. Dirac's delata has already carried us over from spaces of countable dimensions to spaces whose dimension is the first cardinal of the continuum, ℵ1.
What difference does it make if we transform the wave functions and then apply the reduction, or reduce the wave function and then apply the Lorentz transformation? How do we Lorentz transform a complex number? Do we in fact just transforms the domain of the complex numbers but leave the functions the same so that in φ = eit, we transform t, not φ
[page 29]
A puzzle. I will have to get of my high metaphysical horse and examine this at ground level, trying to understand exactly what is going on with mathematical physics. Although our mathematics of quantum mechanics deals in continuous and differentiable transformations, these transformations are represented by distinct fixed symbols of mathematical communication, spoken and written. So we have the same situation in the mathematics community as in the world at large, many dynamic particles whose communication are embodied as fixed points in the world, the mathematical literature, and its dual in the minds of mathematicians. Any theory of the world is an explanation of the fixed points of the world, the nature of particles, orbits, energy levels and all other sorts of data which we feed to our imaginations to generate picture of what might be going on behind the scenes.
Both traditional theology and physics assume that there is some invisible process behind the phenomena,. Quantum mechanics tells is that there is a very loose coupling between the hidden process and observed events. But is this really so? The hidden process may be as random as the observed process. Why have a perfectly Platonic and deterministic wave function only to give is a distribution of the possible outcomes of a given situation? The hopes for quantum computation is that there is a lot more information in the continuous wave function than in the particles that appear on observation (reduction).
Schwinger (1956) (page xvii) 'Yet the real significance of the work of the past decade lies in the recognition of the ultimate problems facing electrodynamics, the problems of conceptual consistency and physical completeness.'
[page 30]
Canonically conjugate = product has dimensions of action (E, t; p, x; action, number; etc)
Tuesday 14 August 2012
Why is the world quantized? We propose here that the world is quantized because is is an error resisting communication network, and Shannon;s mathematical theory of communication shows that the signals used for error free communication must be independent, orthogonal or quantized, separated by 'gaps' like the natural numbers [to prevent confusion].
The following discussion is based on a model we will call a transfinite computer network. Reduced to a slogan, this network mapped into experience suggests that we live in Cantor's paradise.Thomas Jech
As well as explaining the data, a satisfactory model of the Universe must also explain current models of the Universe (as general relativity explains Newtonian physics), the standard model and general relativity. W will turn to this question after we have developed some properties of the model.
First, we all live in Cantor's paradise, atoms and us, and we are connected by a symmetry we call Cantor symmetry,. This explains quantization at all scales. Symmetry with respect to complexity. Both quantum mechanics and general relativity have this symmetry.
For our purposes we will generate the Universe by permutation,
[page 31]
although any exponentiating (creative growth) process will do.
Cantor's theorem is invariant with respect to complexity because set theory is invariant with respect to complexity [so Jech (supra) calls it the theory of the infinite, carrying us from finite to infinite].
The transfinite computer network is the intersection of Cantor's paradise with the mathematical theories of representation (Gödel), computation (Turing) and communication (Shannon).
We build the model and then ask the question - Parmenides and fixed points,. Quantum mechanics gives us a lot of fixed points, but it does not say what cannot be said but leaves it open.
We might somewhat simplify the search for a theory of everything by recognising that the set of eigenfunctions is only countably infinite, and since they are expressed as complex exponentials, tat there is only a countable number of exponents (processes which when repeated go somewhere).
Landauer and the relativity of transfinity.
Fixed point theorems eliminate the need for an alien God.
Fixed points are the nodes of the Universal network, stationary states [or are they the messages, not the nodes?].
Network potential: how much am I influenced by my environment. The only other person interested has no intererest
[page 32]
in the technical details, only in the implied political program for improving the human condition based on a clearer understanding of our relationship to our divine environment.
Transfinite arithmetic has a built in uncertainty principle , a fuzziness that neverthe less contains definite steps. a bit like the real numbers, where we approach the symmetry of all infinitesimals by a process, ε - δ.
Observation, stimulating something, tickling the baby, accelerating the proton, shining a light on an atom, etc.
Reflection: photons emittd / photons absorbed (or total photons. Linear, x, 1-x, non-linear x/(1-x), different expressions of the same fact, one capable of expressing all states, the other running into trouble with perfect reflection (x = 1).
Omnes 156: Both data and model can be expressed as a matrix, observe i get j, a transition represented by an operator. Omnes
Omnes: Bohr: 'The reduction of the wave function is then the sine qua non of experimental semantics.'
Ie we observe a halted computation. The contents of memory are messages halted computations.
[page 33]
Perfect memory stays as it is until another act of computation changes it.
Symmetry with respect to complexity --> equivalence principle universal intelligence = human intelligence.
1. Assumption, transfinite computer network
2. Consequences / constraints; Gödel, Turing, Shannon
A proof is the execution of a Turing machine, Writing the software for such a machine (discovering and documenting) may not be easy, but once it is done it is done for all to see and use.
Google advertising tends to the status quo, since we are served ads related to previously revealed interests found in the binning and statistical analysis of our clicking (keyboard or mouse).
Turing wrote the software for the Universal Turing machine which can be programmed to execute any computable function.
Representation, requisite variety, Gödel numbering.
Mathematics uses Platonist fantasy software (formalism) whereas the world is physically embodied information with local limitations on resolution - the uncertainty principle. A quantum away is orthogonal.
As I write there is a superposition of concepts in my mind feeding into the written particle I produce, nuancing it this way and that like the interactions of a
[page 34]
Feynman diagram to polish the final sentence to this, what it is, a certain stationary state a certain 'distance' from other stationary states - A hamming distance if we just look at the symbols [which we consider to be orthogonal to one another]
We go forward step by step, sometimes halting for a long time at a given step while working out what to do next and how to do it safely.
Pais Inward page 347: 'How could Dirac's relativistic wave equation be so successful yet so paradoxical?'
Wednesday 15 August 2012
Pais page 350: 'The simple problem of the scattering of a photon on an electron is no longer a two-body problem. It is an infinitely many body problem.
As we see each step in the computation as the realization of a particle (signal) which enter the next step of the computation, but is bot observable so we call it a virtual particle, not a complex state but a real state, the complex particles corresponding to nodes in a standing wave, each adding its effect to the overall process and illustrated by Feynman diagrams. (?)
Pais page 362: Heisenberg 1935: '"We know that everything is wrong, but in order to know the direction in which we should depart from what prevails we must know the consequences of the prevailing formalism much better than we do."'
[page 35]
Is this all there is? Much more damaging than the God delusion is the heaven and eternal life delusion, drawn from the God delusion by the premises that this is just for us to show off the glory of God, and the parallel assumption that God loves us and has our best wishes at heart. The root of the cure lies in a new model of God based on a realistic understanding of our experiences of life in the world. This in practical terms, is secular religion, the ancient and evolving art of both getting along together anf eliminating our enemies to improve our overall quality of life, in evolution, fitness.
An enormous amount of good theology was thrown away by the reformers, working under the 'good old days' delusion.
Quantum theory tells us the probability of various events. The problem is to work from the observed probabilities to the logical structure of the process that yields these probabilities. The theory has evolved to predict the probabilities quite precisely, and at the heart of it appear to be the Feynman diagrams, a network concepts.
Pais page 464: 'Beginning with O(α2) one finds in the guts of the radiative corrections contributions from all species of charged particles in the physical world. As one would expect in a network world, as the Feynman diagrams suggest.'
Thursday 16 August 2012
Pais 292: von Neumann: Five fundamental covariants of Dirac theory φbar O φ: O = 1, scalar; O = γμ 4-vector;
[page 36]
O = σμν, tensor; σμν = i/2[γμ, γν]; O = γ5γμ, pseudo 4-vector; O = γ5, pseudoscalar. γ5 = γ1γ2γ3γ4.
The explosion into complexity that came with Dirac's equation and its complexities, codified in Feynman diagrams and rules is a definite sign of network topology. The more energy we put into an event, the more communication (interaction) results, we may say the ripples spread further when we throw in a bigger rock. In network terms, many more channels are activated when an event is assessed as important, as with things going viral on the internet. As energy rises the overall process becomes more complex, but the atomic processes remain the same, they just run faster,
I am happy when I have a feasible plan for whatever, lifting a beam, getting to a football match, a party, etc.
Quark Gluon Plasma: Science.
Viurtual particles are undetectable if they are both a particle and a complete set of states, ie a one state entity, the differential equation itself.
Time is the universal parameter, so we express dynamics as d(whatever) / dt,or, if we go into detail (eg 4D), ∂.
Special relativity is based on the symmetry of space and time, so Dirac set about getting a first order equation in both space and time by replacing the need for a second differentiation by the γ matrices which, in the tiny
[page 37]
digital world of spin are a set of cardinal 4 made out of the Pauli matrices (also cardinal 4), σ0 = I.
Particle detector measures traffic arising from an event.
A principle: Quantum mechanics exists prior to space (it is the hardware of space) and so special relativity does not apply. Non local - spooky action at a distance - so QM is non-local, so we can expect its local projections to be somewhat random.
Noughts and crosses machine. Donald Mitchie - Wikipedia
Pais page 586 Heisenberg: "'The particle spectrum can be understood only if the underlying dynamics of matter is known. Dynamics is the central problem".'
The formal expression of all causal (deterministic) dynamics is Turing machines.
Renormalization and the fuzziness of transfinite numbers.
Friday 17 August 2012
Pais page 393: 'Goldstone theorem according to which spontaneous symmetry breaking of any continuous symmetry G is accompanied by the appearance of one or more species of massless particles, Goldstone bosons.
[page 38]
be small. News of the death of a child can be a very biog shock and change one's trajectory very significantly.
Reading Pais and comparable histories, I feel that I am at an impossibly large distance from the Standard Model and that the gap between the transfinite computer network and the standard model is uncrossable. However, many of these things are one one big insight away so it is worth keeping on the track, especially in the light of our equivalence principle: my mind is isomorphic to the mind of the Universe and the transfinite computer network shoes how they fit together, me a subnet inside the universal net.
Pais page 624 Pogo (?) 'we are faced with insurmountable opportunities.' Pogo (comic strip) - Wikipedia
page 626: What is past is prologue, 'you ain't heard nothing yet'.
[page 39]
and more states come to exist in the Universe, so we associate maximum energy with maximum simplicity and see complexity growing as energy levels come down as we find in the electronic structure of atoms, molecules, cells and so on. How do we reconcile these two pictures?
Most particles have a natural (rest) mass and any attempt to increase their mass and energy without limit leads to the birth of new particles once again sharing the energy. Sop we imagine the initial process of particle generation to have proceeded quickly at the beginning. We see a particle as a message, so this was tantamount to rapid growth of the network and we are inclined to see the formal drivers of the process as a combination of [Brouwer,] Shannon, Turing, Gödel and Cantor. These theorems are stationary points in the dynamics of the mathematics community and highlight the fundamental bootstrap - the fixed points of dynamics in effect create the conditions to prove their own existence.
The psychological equivalence principle is very old and goes back to the first written scientific texts we possess, Parmenides and Heraclitus and their successors to the present day. Say all this often enough and it becomes credible, the text becomes a node representing the stationary points in my mental dynamics.
Saturday 18 August 2012
What we seek, in music, physics and industry in general is harmonious action, and quantum mechanics is a description of this, as is a Turing machine which has no dynamics of its own, it is purely formal, moved by assumed and unseen forces.
[page 40]
From a mathematical point of view all our discussion of continua is carried out in discrete symbols, to which we might say the continuum itself contributes nothing, since is is an unbroken symmetry [and cannot talk about itself].
One can have a meaningless order, that is a natural order (like the natural numbers) which is not coupled to anything else, an abstract order.
My subconscious nucleus acts in its own time.
Zee: the uncertainty in energy plus the equivalence of mass and energy is held to account for the ephemeral creation and annihilation of massive particles This is neat and generally accepted, but is it true? Is it maybe an artefact of the way we map the quatum of action into space-time / momentum-energy? Zee
Dirac page vii: 'The important things in the world appear as the invariants (or more generally the nearly invariants, or quantities with simple transformation properties) of these transformations.' Fixed points of mappings. [this looks like a Platonic point of view, giving form preference to action.] Dirac
'The growth in the use of transformation theory, as applied first in relativity and later to quantum theory, is the essence of the new method in theoretical physics.'
Bohr, Nature 116:845 (1925) 'From these results it seems to follow that, in the general problem of quantum theory, one is faced not with a modification of the mechanical and electrodynamics theories describable in terms of the
[pager 41]
usual physical concepts, but with the essential failure of the pictures in space and time on which the description of natural phenomena has hitherto been based.' Because quantum mechanics precedes the emergence of space.
Weyl page xxi: 'Two groups, the group of rotations in three dimensional space and the permutation group play here the principal role . . . ' Weyl
'The investigation of groups first became a connected and complete theory in the theory of the representation of groups by linear transformations .. . '
h is the natural limit of resolution, just as 1 is the limit of resolution in counting discrete objects.
Dirac page 10: 'Thus all particles camn be made to exhibit interference effects and all wave motion has its energy in the form of quanta.'
'one may . . . extend the meaning of the word 'picture' to include any way of looking at the fundamental laws which makes their self consistency obvious.' Network picture.
Dirac page 11: 'A state of a system may be defined as an undistrbed motionwhich is restricted by as many conditions or data as are theoretically possible without mutual inteference or contradiction.'
ie the fullness of being is a complete set of states.
page 12 'disturbance accompanying observation'. Zurek: two systems must express themselves in a common basis. Wojciech Hubert Zurek
[page 42]
Dirac: 'Only in the special cases where the probability of some result is unity as the result of the experiment deterministic.'
Reduction of wave function = breaking symmetry.
HARDWARE = SYMMETRY
SOFTWARE = BROKEN SYMMETRY
Natural morality: what you do is part of what God does. Like the Pope, we are all God's agents. What we do need is to fit in with the rest of God, ie, in the old language, do what God wants. We generalize the monarchy, just as quantum mechanics generalizes the classical.
The Pope has lost overt power but kept the web of forces which enable it to control a large proportion of global mental structure.
Exponential growth is our friend when we are young and few, an enemy later on if not controlled.
From an algorithmic point of view the scientific ideal is to produce a text which ius a complete and consistent representation of the world, and from which the behaviour of the world can be predicted given various starting conditions.
The real digital content of Dirac's equation lies in its form and particularly in the γ matrices which couple the dimensions of four space to one another, rather like the Lorentz transformations so we might look at the
Λγ.
FQXi comes around again. There is an implicit assumption in physics that the Universe is an artefact of some pre-existent agent which set the Universe going in a particular initial state that has led to our current [state]. This assumption is part of the Christian heritage of those nations that have historically dome the lion's share of physical research, not least in the search for increased military power for the apparently noble task of Christianizing the world. The founder of Christianity instructed his student to go forth and preach the Gospel to all Nations, and they have been very successful, as we can see,. The Christian interpretation of the first chapters of the Book of Genesis iss that the world was created by a pre-existent God who made it the way it is (or at least the way it was until human disobedience led God to cripple his creation with death, pain and work).
Dirac page 35: 'The set of eigenvalues of a real dynamical variable are just the possible results of measurements of that dynamical variable and the calculation of eigenvalues is for this reason an important problem.'
page 38: 'A physical constant in quantum mechanics may . . . be looked upon either as an observable with a single eigenvalue or as a mere number.'
Polanyi page 25: Commitment to a hypothesis: 'The discoverer is filled with a compelling sense of responsibility for the pursuit of a hidden truth, which demands his services for revealing it.' Polanyi
