[ Sunday 28 August 1983 - Saturday 3 September 1983 ]
[notebook Creation - The Metaphysics of Peace II = CMP II: DB31]
[page 75]
page 802: Much of cosmology is fooling about with mathematics. This solution antedates all mathematics and might be called metaphysical. Nevertheless it appears relevant. A theory of how specific laws came to be must in some way help the determination of what they are. [2014: symmetries]
[page 76]
. . .
Misner page 813; Singularity has infinite curvature and infinite density which occurs at finite proper time.page 815: Horizons: Background radiation puts limits on time when universe was anisotropic.
page 818: Part VII: Gravitational Collapse and Black Holes.
Universe, after period of maximum size, begins to collapse back to nothing, a structureless point, not, you might say, a very intelligent thing to do but something that the Universe in a sense committed itself to doing when it chose a certain mass and laws of gravitation. Or did it? Will it turn out to have just small enough mass to go on expanding forever? Will it be able to stop one day, perhaps with the help of people, and become a stable structure?
. . .
[page 78]
. . .
In the actual Universe first there was singularity and then there was structure. In other words, singularity is a more primitive high energy state which has its own laws for getting itself to a structure. Gravitational collapse is another example of high energy physics going back in time.
Misner page 939: Hawking. Hawking and Ellis
All the possibilities covered in this book are plausible solutions to Einstein's equation. The existence of differential equations puts only general constraints on the general solutions which may come up. [differential equations are a static shell containing dynamic processes.]
page 943: Gravitational waves.
Define a new kind of time called ontotime (from ontogeny). This time is measured not by the ticking of clocks but by the stochastic processes of intelligence and provides an ordering without a metric. The best known example of this ordering is the biological classification of organisms. Using this time one can correlate later periods with greater information per unit energy etc. Greater energy per unit information is to
[page 79]
go back in ontotime. The various singularities which appear in the study of electrons, gravitational singularities etc represent very early periods in ontotime (and can exist now, as these things do in high energy experiments; in other words such experiments represent a step back in ontotime).
One can understand from this ordering how rigidly an idea is constrained to its correct order in time. Before it can come to be, all the prerequisites must be there, and he or she who would propose a new theory must work their way through all the prerequisites (as Newton did) before the final product is there. Thus Einstein was hindered by his lack of knowledge of Riemann, and more specifically, because he was not aware of the Bianchi identities. The problem shows when one is making something - all the prerequisite operations on clay before one can even begin to throw a pot. When all the basic ingredients for a given breakthrough [insight] have been prepared, it is almost inevitable that it will come. . . . Lonergan
[length of insight measured in bits = n; length of search proportional to 2n; Say reduce to subsearches length m. Then number of searches = 2m/n.]
. . .
Misner page 1050: uniqueness of free fall, ie all test particles follow the same trajectories. Gravitation describes these trajectories.
[page 81]
Misner page 1054: experimental evidence for metric comes mainly from elementary particle physics.
The electron, behaving as it does as a possible pointlike particle and relating closely to the photon, has to have some claim to priority in ontotime. Dimensionless constants such as the fine structure constant must be invariant in all systems of units. Fine structure constant looks like one for further study.
page 1061: Constancy of fundamental constants would seem to indicate that they are determined by some sort of digital rather than analogue system, not subject to 'drift', and readily reproducible as electrons, photons etc are created and destroyed.
page 1063: Constancy of many physical constants guaranteed by conservation of energy: appearance of conservation of energy guaranteed by appearance of conservation of constants. Conservation of energy guaranteed by conservation of constants, which must be the consequence of some 'positive' law. . . .
[page 82]
. . .
[page 83]
Physicists working up from practical experiments must meet philosophers coming down from the mystic heights somewhere in the middle, and this meeting must be without a seam; in other words intelligence must reign all the way.
Define complexity C as Chaitin does, and let ontotime be represented by T. Let intelligence be conceived as an operator that maps C(T0) onto C(T1), not continuously, but by a step of insight. The previous structure has two components (Lonergan), the first component determinate or systematic, and the second open to development. Intelligence then inputs prestructures, integrates them and outputs a new structure, except that there is no real input or output. The output becomes part of the intelligence and therefore gives it the power to understand the next step in the process. The Universe must thus be considered as a single intelligence becoming more intelligent as it goes. Can it be proved that the system must be closed? Can all this be explained in less than
[page 84]
a treatise, which must be a closed system as the system is a closed system. In a way the only possible treatise is an isomorphism of Lonergan's book. it is difficult, at this point, to extract meaningful subsets of the whole.
So we must begin with insight; go down to the beginning of the Universe; go up to the end of the Universe. Pull out a few physical laws on the way.
. . .
[page 86]
Misner chapter 43, page 1180: Superspace: Arena for the Dynamics of Geometry.
All systems become more complex. Some of them remain stable and multiply. It takes intelligence to select the stable from the unstable, that is what judgment is. Intelligence is the randomisation process. Lonergan's emergent probability needs reexamination here. Is this meaningful or meaningless? How to decide between all possible formulas in symbolic logic. . . .
Three cases: entropy increases; entropy remains constant; entropy decreases.
page 1181: Says spacetime does not make sense in quantum mechanics. Given precise 3-geometry, one cannot characterise time rate of change. Uncertainty principle forbids. Distinguish formal and intelligent theories. Goedel's theorem is an intelligent discourse on formal theories. Intelligence is the dynamically rising metatheory of all theories.
The Uncertainty principle does not let us give meaning top 'deterministic history of space evolving in time'.
[page 87]
Misner page 1183: that is 4D spacetime geometry simply cannot exist in Quantum mechanics, except in a classical approximation.
Very interesting set of statements here - introduces the idea of superspace.
. . .
It is customary to analyse the findings of physics as though the world were, from the point of view of intelligence, dumb, perhaps deterministic. Quantum mechanics has forced us to think about the interactions of the observed system and the observer. Goedel's theorem has made us think a little about the place of mathematicians in the world of mathematics. What is lacking is a unified approach to these disparate fragments of an overall knowledge of the world and ourselves.
What we seem to have is an enormous amount of evidence pointing in the same direction. What seems to be lacking is a point of departure. The logical place to go from would appear to be a combination of thermodynamics and logic, two things which I hate.
[page 88]
. . .
Misner page 1196: Universe must be closed intellectually as well as spatially - what's the difference? Intelligence is the generative principle, but it depends for its working on the communication of the whole system. The Universe is what we communicate with via, for Einstein, photons.
'Physics is by definition what goes on its eternal way despite all the shadowy changes in the surface appearance of reality.'
page 1197: 'Some day a door will surely open and expose the glittering central mechanism of the world in its beauty and simplicity.' [2014: transfinite network]
'Paradox of gravitational collapse'
[page 89]
Misner Box 44.1 page 1197: 'Uncertainty principle: binding too close to centre of attraction makes zero-point kinetic energy outbalance potential energy; consequent existence of a lowest quantum state; can't radiate because no lower state to drop to.'
Is this so? Don't we need a more fundamental discussion of structure than this?
page 1198: What are the limits of validity of relativity? Coulomb's law holds down to 10-15 cm - a striking example of what Wigner calls 'the unreasonable effectiveness of mathematics in the natural sciences.' Eugene Wigner
page 1201: 3 levels of gravitational collapse: Universe; black holes; fluctuations at Planck distance. Universe continually collapsing and uncollapsing.
page 1202: '44.3 Vacuum fluctuations: their prevalence and ultimate dominance'
'No point is more central than this, that empty space is not empty. It is the seat of the most violent physics.'
What do you mean by empty space?
Clifford's quote: continual communication
[page 90]
Is a particle a geometrodynamic exciton? What else is there out there out of which to build particles but geometry itself. Wormholes - undressed electrons.
Density of field fluctuation energy in vacuum = 1094 grams per cubic centimetre. What does this mean. This is virtual stuff, ie communication in the annihilation region.
page 1203: 'In other words [elementary particles] represent a first order correction to vacuum physics.
Pregeometry The magic building material.
[page 91]
A Spring (Southern Hemisphere) Meditation.
'Scientists seeking the cool light of reason are apt to discover the 'high tensility' of human relationships and thereby miss a major clue in the functioning of the whole system. For what we have is what is durable, the mode of life that has endured the vicissitudes of enormous time, for what the system optimizes on is action, or spunk, or the overall ability get in there and get it, because the ones that get in there and get it are the ones who have got it; and so the ones who last, and are we. But the way in which this game works becomes more and more subtle all the time,and the ultimate trickiness of it all might be beyond the reach of our understanding and might in principle be beyond the understanding of any being no matter how intelligent. But this can not be so because conscious intelligence can remodel itself many times in a lifetime but evolution needs tens of lifetimes to come up with anything new. It is Achilles and the Tortoise , but in fact Achilles could be infront, It could be conscious intelligence which is the leading edge of human development, which is in fact the development of culture and this the culture of being led by the deepest thinkings of the bet available minds. This must be a matter of hope, and eventually of science, which would force us into an optimistic stance with regard to the future of the world, a stance which become conscious would feed on itself and thus bring about its own continuing evolution. Is this good science,
[page 92]
or is it good mathematics, or is it a statement which is still out of reach of current educateddiscourse. Wow good dope high falutin' all this, and does it get anywhere at akk into the reality of the situation? This always must be our contant fearm that we are not connected to what is really happening ourselves, and so we have to invent a god whose very benevolence guarantees that we are in the know, or can get to be in the know. But I think the argument I gave above guarantees that we we are, even tough the realization of this can awaken echoes of hte paranoid reaction which might have produced the Psalms and other agonised writings for people whose mind is being flooded and somewhat fazed by new consciousness, And perhaps the new consciousness continues to grow and it is this which exposes generation after generation of us to the sae angst and leads us to make the same lamentations, although from an ever more conscious viewpoint. And now we hav reached a evl of consciousness where we can admit, and revel in the intelligence of all that we find emergent around ourselves part of the immense pyramid of lesser beings that raised mankind and presumably thousands of other species like us throughout the universe. It is all such a mixed up business this mating, both physically and intellectually, because it is there that we are going to have our
[page 93]
offspring, genes and memes in our own progeny. And that once evolution has become conscious of itself, becomes the conscious target of our striving, both in life and in mating, At least so it seems to me, and I wonder then at the peculiar deviation from the accepted mainstream my particular genesis has placed me and have no choice but to bow down before the weirdness of the randomness of sexual mating. I think I'll submit this as a Time essay. We can't print that, it is too weird for words. That's why you can print it . That's your business, to move people along at the fastest possible rate to the complexities of the future. You think you are a stuck in the mud, a traditionalist, a churchman, You will have nothing to do with new fangled ideas and dangerous modes of thought, it is no good. It is precisely the likes of you that provides the reacion, the baseline, the stability to allow others to push forward. For society must maintain its stability and not stumble in a blind rush to the future, and so like all creative systems, like all the Universe, it has checks and balances, one force meeting another, the age old nation of tension A = B, A is related to B, A is B, A is not B. They are distinct these two statements and not mere rationes, they are so real
[page 94]
that they lie at the basis of all that is. When we can get our minds around that idea and apply it to a brick, we are ready to come to know and love the universe as it really is. It does not help to seeing such an amazing reality as being not just as mind or shit, but as a most amazing manifestation which is one with ourselves and differs only from ourselves in that its intelligence is slower because it has not attained the gift of consciousness which was ours to reach, but in other ways is in some wise identical with us. That warm soft earth that moulds itself to my feet as I walk is very much one with me and I am one with it, and I should respect it and care for it and try to get to know it, because it has made me possible and I stand on it in a very real ontological sense, Without the soil and the sun and the mammals and the air and everything else there would have been no humans. It is almost blinding to see how much of it is devoted to ourselves as the most complex species that came before us might have seen had he been conscious, but we are the first to attain that privilege, and we have been amazed by it, fled from it in religion and obscurantism, and once that was good, as a stabilizer. But as society grows up it can learn to run faster and cast aside some of the fear of stumbling for the exhiliaration
[page 95]
of the race, give up the hard and fast grip on economic necessity which has been needed by governments to survive in the days of tight belts and real famines. We should be able to get the production of our goods done quite efficiently by people who really wish to do that sort of thing. One could go on at very great length elaborating the potential flowering of the guaranteed income society. I stop only to note: it will take time in coming. Many things cannot be changed easily. so the dawn of a properly conscious society may be slow. but it will be sure, and I hope this little essay can give a few people a glimpse of what I think the future holds.
PS I feel that this is marvellous stuff/ But how will I feel when I am not stoned, I feel I have waited a long time to write this.
PPS. I don't want to be your Messiah, and even though I know that these days the job can be very laid back, and need not be fatal. One need not fear too heartily the fate that could befall me in the old days if one was too forward in speaking out strange and worrying words on principle.
Am I so afraid that this is really the ideas that these times need that people will come flocking after me. No. All that they need is there, and they can do it for themselves, and probably very few will see it.
[page 96]
. . .
Anybody who writes but for money is a fool: Johnson Samuel Johnson
Misner page 1203: Most evident shortcoming the the geometrodynamic model is that it fails to supply any completely natural place for spin 1/2 in general and the neutrino in particular. The next few lines are instructive:
'Attempts to find a natural place for spin 1/2 in Einstein's standard geometrodynamics founder because there is no natural way for a change [DIGITAL] in connectivity to take place within the context of classical differential geometry. Still searching for a natural way to describe quantum fluctuations in the connectivity of space.
In many ways, these can be cyclic, not random, little 'DO' loops in the universal computer.
[page 97]
Misner page 1204, box 44.3: 'Unless and until an answer is forthcoming, pure geometrodynamics must be judged deficient as a basis for elementary particle physics.'
Quantisation and uncertainty go together as inherent qualities of a digital system.
page 1204: 'For this muliple connectedness of space at submicroscopic distances, no single feature of nature speaks more powerfully than electric charge. Yet at least as impressive as charge is the presence of spin 1/2 throughout the world of elementary particles.
. . .
[page 98]
'One does not classify the closed orientable 3-manifold of physics completely when one gives its topology, its differential structure and its metric. One must tell which spin structure it has.'
page 1205: 'bucket of dust': Borel set. Borel set - Wikipedia
Wheeler is 73, 63 when he wrote the book. No wonder he knows so much.
He puts quantum mechanics before geometry - Borel set has probability amplitude of becoming assembled. Make Borel set into being vs non-being.
Misner page 1206: On Sakharov's idea: Gravitation is the metric elasticity of space (Box 17.2)
'With the discovery of the positive electron , one came to recognise a little of the life that heat can unfreeze in 'empty' space.' So empty space does not have energy, it has potential structure and the energy must be put in to get at it. [ie potential is negative energy]
page 1207: Study of smeared out 'mas effects' does not reveal detail. One must look to quantum effects (Dalton's ratios, Mendeleyev, photonsm Brownian motion, quantization of spin etc) to get at fine structure.
[page 99]
Simplicity of overall effect reflects simplicity of principle, which may be realised through a complex intervening mechanism.
'The vacuum is animated with the zero point activity of distinct fields and scores of distinct particles, all of which, according to Sakharov, contribute to gravity.'
Misner page 1208: Is not the source of dismay the apparent loss of guidance that one experiences in giving up geometrodynamics - and not only geometrodynamics, but geometry itself.
-note that the Universe works.
Thomas Mann: 'Science never makes an advance until philosophy authorises it'
Bohr: 'A great truth is a truth whose opposite is also a great truth.'
[page 99]
Misner page 1209: [Is pregeometry the] calculus of propositions
. . .
At the beginning, there can be no coding, because there is no context to code and decode. The system requires development of quite a bit of complexity before the necessary coding and decoding can be done , eg DNA.
page 1212: '... bare bones quantum mechanics lends itself in a marvelously natural way to formulation in the language of the calculus of propositions, as witness not least the book of Jauch (1968).' Jauch
page 1214: Reprocessing of Universe.
'The gravitational collapse of a star, or a collection of stars, to a black hole extinguishes all details of the system except mass and charge and angular momentum.
Charge is conserved so net charge is zero. Lines of electromagnetic force begin and end on charge. Yet electromagnetism can give rise to energy. The Universe has zero mass energy, all positive energy being balanced by negative energy. This is the logical outcome of the principle of conservation of energy. Planck's constant h is the basic constant of proportionality between energy and information [entropy]. Creation of a + bit entails creation of a - bit. Energy is conserved by this mechanism. Momentum may be another zone for the creation of yin and yang. Yin = 0, Yang = 1.
[page 101]
Electric charge is another binary, Fine structure constant is something to do with the number of bits required to set up an electric charge.
Misner page 1215: What else can a particle be but a fossil from gravitational collapse.
page 1217: Why is the Universe so big - so that we can be here? No, we are here because it is so big.
Leibniz thought of the Universe as a world of relationships, not a world of machinery. [what is the difference? A machine is a set of realised relationships!]
By the act of understanding, the intelligence becomes what is understood. In other words, it adds to its being an increment equal to the complexity of the new understanding.
To be conserved, a quantity must be algebraically addable, and, we suggest, the net quantity in the Universe is zero. The existence of energy etc can then be explained by the segregation of positive and negative quantities and the conservation in a small area can be calculated. One is tempted to call differentiated energy yin and yang, assign it to bits of dimension h [Planck's constant] (in space time) and say that there is no meaningful distinction between potential and kinetic energy. What this means is that apart from its intelligible structure, the Universe is nothing.
[page 103]
Science and Information Theory, Leon Brillouin - Academic press 1962. First edition 1956. Brillouin
Brillouin page x: Operational definition: Information = reduction in possible states.
'But we are in no position to investigate the process of thought, and we cannot, for a moment, introduce into our theory any element involving the human value of information.'
Hence the need for intelligence: It can distinguish between information of great importance and a piece of news that has no great value for the person who receives it.
page xi: Absolute information. Leo Szilard noticed the similaritybetween information and entropy. Entropy in thermodynamics and information theory - Wikipedia
Following Lonergan, we propose an invariant structure called intelligence. Lonergan
page xii: negentropy
[to Szilard]
[page 105]
Leo Szilard: On the Decrease in Entropy in a Thermodynamic System by the Intervention of Intelligent Beings. Szilard, Leo Szilard (PDF of article)
The violation of the second law is of importance insofar as it might lead to the construction of a perpetual motion machine and thus to the violation of the first law, which is far more basic to the integrity of the deterministic system.
The upshot of statistical mechanics has got a lot to do with counting states. If we consider a set of markers, the statistics of thermodynamics look at them as non-correlated individuals. However, by arranging them in complex codes, intelligence can get far more states for its own use than are available to the thermodynamic system. For a system of N particles with two states and in thermodynamic parlance 2N states. On the other hand, if its particles are used as binary digits, the system has 2N states available for it to play with, in other words
[page 106]
the intelligent states are 2N/N per particle rather than 2.
. . .
Coding - consider the hydrogen atom which has a very large number of states as compared to either an electron or a proton. By combining two particles, one gets a rapid multiplication of states, all of which have their own statistics, to some extent outside the purview of classical thermodynamics.
[page 107]
Shannon's formula, based on Boltzmann's epitaph S = k log W gives a convenient and mathematically tractable way of measuring information.
Then to Khinchin.
Khinchin: Mathematical foundations of information theory. Khinchin.
[definition of Shannon entropy] Entropy (information theory) - Wikipedia
Properties
1. certainty, entropy = 0
2. equirobability yields maximum entropy
3. Independent schemes, entropy adds: H(AB) = H(A) + H(B)
4. Dependent: H(AB) < H(A) + H(B)
Khinchin page 7: - experiment removes uncertainty, yielding information
page 13: Entropy of Markov chains: 3 theorems
page 22: Application to coding theory.
[page 107]
A text may be considered as a simple Markov chain, letters are finite number of states A1, A2 with transition probability matrix pik.
Discovery of optimum coding is equivalent to finding minimum complexity by Chaitin's measure. This will then give some clue to the physical law hiding there. Coding theorems say actual complexity is very much less than apparent complexity, but the Universe, if intelligent, will gradually up its use of symbols to the point where actual coding is as efficient as can be. Maybe. Chaitin.
A lot of what I have to say must relate to these coding theorems, which connect the efficiency of non-redundant systems to redundant systems.
Khinchin page 30: On the fundamental theorems of information theory.
page 36: The uncertainty of a situation cannot be increased as a result of obtaining any additional information.
[page 109]
So what we are saying is:
1. Start with nothing
2. decompose into + and - energy units, size h (planck's constant) -
Energy conserved.
3. These communicate to form structure stable/unstable
4. Stable structures are the basis for further structures.
5. Entropy increases into stable/unstable structures.
6. Stable structures through coding increase intelligible entropy
much faster than physical entropy.
7. Coding theorems say that most of the action is in stable
structures anyway (classical limit - something to do with ergodic
sources)
8. Random process needed to form new structures - thermodynamic
randomisation does not 'see' intelligible structure.
9. Intelligible - being - what is = ground and context for the next
step in intelligibility, which has random probabilities.
Explain
: digital/rounding errors etc
: pestilential presence of life
: route around second law
: bootstrapping of system
: prevalence of mathematics
: driving force of evolution - many more probable states of well
coded system.
Mathematical methods, complexity, randomness
[page 110]
How is only part of it.
Every individual situation has a history and an explanation.
Khinchin page 44: In statistical communication theory the output of every information source is regarded as a random process. Alphabet / finite.
page 46: source considered to be stationary; may also be not stationary (an act of development).
page 51: Borel field
High probability group / low probability group.
E-property holds for any ergodic source. Asymptotic equipartition property - Wikipedia
Khinchin page 75: The channel.
Channel has input alphabet/output alphabet. If input → output is 1-1, then channel is called noiseless, and can be considered as acting as a function. A physical law thus behaves in some ways as a channel, as does a computer.
page 77: Channel with memory.
[page 111]
Khinchin page 90: The culmination of the theory of discrete information is Shannon's theorems on the optimum use to be made of noisy channels by suitably coding the text.
Feinstein's fundamental lemma
page 91: Channel capacity = maximum rate of transmission.
Assume that the universe is a communication channel whose input is its
page 102: Formally any code can be regarded as a kind of channel with the input alphabet A0 and output alphabet A.
Does the E-property mean there must be laws of nature, ie the set of all possible messages in fact constrains itself to a small subset of the possible? Is this simply a consequence of the statistical properties of the alphabet. Look at the Universe as an interlinked series of channels. The alphabets of some are the messages of others. Ie some alphabet goes to make up the set of atoms, which is the alphabet of the set of molecules, which is the alphabet of the set of cells etc etc. The E-property looks like an intelligent thing, and is a consequence of the maximisation of entropy. Let the source be not just ergodic but a Borel set . . .
Back to Brillouin.
Brillouin page 152: Cha[ter 12: Free and bound information
page 153: Uses entropy as a physical rather than mathematical term. 'system naturally evolves toward the average structure of highest probability.'
In other words, if the Universe is intelligent, then intelligent behaviour has the highest probability.' Ie averaging must be the intelligent thing to do. This looks a bit hard to take, on the other hand, minimizing energy mazimizes entropy/energy, which is what we would expect an intlligent thing to do, less labour, more thought. Not the protestant work ethic or the mechanical engineer's dream, though.
page 155: Information considered free in mind, bound in physical system.
[page 113]
partially intelligent.
Brillouin page 155:
'We must, of course, ignore any element of human value. For example, we exclude the case of a scientist collecting data and then discovering a scientific law as the result of study of the data. Our definitions do not apply to such a problem. It is only by excluding the process of thought that we have been able to develop a satisfactory theory of information.'