Notes
[Sunday 9 August 2009 - Saturday 15 August 2009]
[Notebook: DB 67: jciii]
[page 90]
Sunday 9 August 2009
Peter Sutton The Politics of Suffering page 212 quoting Mary Darkie; 'Reconciliation is about getting to know each person individually. It means letting go of old ideas that all white skinned people are the same or all black skinned people are the same. All people are different; they may have the same skin colour, but inside each person is unique. Its whats inside each person that is important. I sometimes think we live in a crazy world that we always have to divide people into separate groups. [kinship?]
'Reconciliation also means letting go of anger and blaming. I had to let go of these things in order to get to know people as they really are. We cannot forget the past but letting go of anger and hurt allows us to move forward.' Sutton
We do not ask how the initial singularity came into being any more than Christians search for the origin of God, but accept it as a fact, to some extent justified by subsequent events.
Misner, Thorne & Wheeler: 'Any forward step in human knowledge is truly creative in this sense: that theory, concepts law and method of measurement--forever inseparable--are born into the world in union.
Annihilation
Formal structure = stable = equilibrium = maximum entropy [stationary action].
[page 91]
The simplest representation of any quantity (log n) of entropy is simply a set of units with cardinal n. The logarithm is conventional and simplifies entropy calculations, but the untransformed entropy is simply a number.
ORDERED = BONDED
RANDOM = UNBOUND = FREE UNCORRELATED
Nothing happens without funding. Funding is measured in quanta of action (processing cycles) or some function thereof.
Exponential increase in count = linear increase in logarithm [log exp n = n]
Peers can be different [see Sutton above]. All that is required for peerdom is equal power so that all trades are fair.
Increase entropy by adding a symbol vs increase in entropy by producing ordered strings of symbols. Entropy varies linearly with the length of the string of symbols measured because the exponential increase in cardinality is balanced by the logarithmic reduction in the length of the representative string.
Monday 10 August 2009
Whereas Maxwell's demon is the (failed) servant of a power engineer trying to overcome the increase of entropy with time, Shannon's demon works for communication engineers by increasing the entropy of communication spaces and so the information carried by points in these spaces. Since engineers are inclined to look down on increasing entropy and see it as an evil, they see no reason to explains its
[page 92]
increase. Nevertheless it needs explanation, and this explanation, as Cantor saw, lies in order.
Permutational gearing: the ultimate size of the Cantor Universe depends on the size (entropy] of the space of [distinct symbols] upon which it is built.
The morning is the harvest of the night, yielding, with the help of caffein, nicotine and cannabinol new points in textual space such as this. As we define a point, so we define a space, and from a formal point of view this is just as true in mathematical fantasies as in physical realities. The information content of the above sentence [and this one] is measured by the entropy of the space in which it exists [which may be different for different readers], which is in turn the product of the entropies of each word in it.
Although they are static on paper, words are fixed points in the dynamics of the world which, in effect, connects the words by logical continuity / meaning / mapping.
Tomi Ungerer Moon Man Ungerer
There is perpetual motion in the reversible world described by quantum mechanics, but not in the irreversible world of quantum field theory, where particles are created and annihilated.
Why quantized is a foundation for theology, since we are trying to rephrase the first part of Genesis, explaining how the world came to be. Genesis
Because we are working in a non-constructive way
[page 93]
we ultimately find that the explanation of creation is that there is no explanation except the tautology that if Cantor's theorem were not true the formal world would be self-contradictory and so not exist, which simply means that Cantor's theorem and all other theorems of mathematics did not exist in the formal mathematical sense of being self-contradictory.
Irreversibility is obvious. From an abstract point of view a memory location can be in a superposition of states, even though when it is observed it will be found to be in a particular state. From a concrete point of view therefore, we can say that every memory is always in some state (since this is the definition of state) and that when we change the state of a memory we erase the old state while writing the new, an irreversible step.
This picture only works if every memory location is unique, a property constructed into the symmetric network.
ABSTRACTION = SUPERPOSITION
CONCRETION = MESSAGING
There can be no chaos without order, since it is order that creates the cardinal number of distinct events that are the elements of the chaos.
Are we there yet?: the end of every motion is a fixed point, a new state of memory.
LINEAR = INTERACTION FREE = REVERSIBLE
Energy --> particle = motion --> stationary point.
[page 94]
This is what happens. At each tick of the clock the system calls 'all change' and at the end of the tick the machine has settled down to a new static state which can be read out ('dumped').
Since the world is concrete, every memory is in a fixed state and they are all unique, so that there are as many states as memory locations, hence the utility of permutation as a formal framework to describe the dynamics of the Universe. No cloning theorem.
Peskin & Schroeder page 781: '. . . the theory of elementary particles--like other areas of physics that depend on the quantum fluctuations of continua--still holds deep mysteries, and quantum field theory remains the principal tool for the exploration of these questions.' Peskin & Schroeder
Lewis Allegory of Love page 64: '. . . [Augustine] comments on the fact--to him apparently quite remarkable--that Ambrose, when reading to himself, read silently. You could see his eyes moving but you could hear nothing. In such a passage ones has the solemn privilege of being present at the birth of a new world.' Lewis
If we think in probabilistic terms we can make the cardinals of the relative transfinite numbers continuous and let the resolution of a set of cardinal 0 < x be 1 / (x = 1) (ie 1 when x = 1, 1/ℵ0 when x = ℵ0 etc.)
Creation: Shannon's demon might be explained more explicitly. Better to start vague. Like any effort to resolve a new picture of the world, this one is strongly out of focus but I believe that some of the blurs I see might materialize into a theory of the world capable of embracing everything.[page 95]
Lewis page 67: 'If there is any safe generalization in literary history it is this: that the desire for a certain kind of product does not necessarily beget the power to produce it, while it does tend to beget the illusion that is has been produced.' So the history of the motor vehicle, but the desire for effortless ecologically sound transport is still moving toward fulfilment more than a hundred years after cars began to multiply.
Lewis, page 72: 'Here, as in all other military metaphors, whether of the Christian or the pagan moralists, we are reminded of the lasting impression which the discipline and circumstance of the legions made upon all the nations of the empire.' Roman legion - Wikipedia
Prudentius, Psychomachia 906: War rages, horrid war Even in our bones; our double nature sounds like armed discord.
'Fervent bella horrida, fervent
Ossibus inclusa fremit et discordibus armis
Non simplex natura hominis.' Lewis page 72
Eliminate war by effective global religion.
Ancient literature is our path to ancient psychology.
Literary criticism is part of theology, the development of the human mind as it is recorded through time by contemporary writers.
Lewis page 83: 'The gods must be, as it were, disinfected of belief; the last taint of the sacrifice and of the urgent practical interest, the selfish prayer, must be washed away from them, before that other divinity can come to light in the poetic imagination* [which includes the scientific imagination and formalism to remove the moralism].
[pager 96]
Evolutionary selection goes for efficient algorithms and efficient data structures, like indexing, so that data can be quickly found. Evolution / least action. Evolution - Wikipedia Principle of least action - Wikipedia
*'For poetry to spread its wings fully, there must be besides the believed religion, a marvellous that knows itself as myth.' Work and play.
Theological Studies The theological implications of 'Why quantized?'
The world is divine means the world has sufficient physical resources to be a true one to one scale image of the physical layer of the divinity.
Tuesday 11 August 2009
Submit why_q [Why do we observe a quantized Universe?] to Science
The aim of religion is to keep God happy in the hope that God will reciprocate by keeping us happy. This definition shows us the way to corruption in religion. How do we know what God likes? A lot of people through the ages have set themselves up as God's spokesperson. One of the most prominent on earth is the Pope. Pope - Wikipedia
I have submitted. Will my submission be accepted? This is the question in all situations where an agent wishes to initiate conversation with another agent (or 'source', agent is a better term).
Wednesday 12 August 2009
[page 97]
Lewis, page 113: '[The allegorical method] was not simply a better or worse way of telling a story. On the contrary, it was originally forces into existence by a profound moral revolution occurring in the latter days of paganism. For reasons of which we know nothing at all . . . men's gaze was turned inward.*'
Jaynes The Origin of Consciousness, ie the origin of reflection. Jaynes
Augustine: God's reflection is the word of God. Augustine
Quantum mechanics: The Hilbert space of communication is the product space of the communicants, even if it is me looking at myself. Zurek
*'But the age, so turned, sees not a compact 'character' of modern fiction, but the contending forces which cannot be described at all except by allegory. Hence the development of allegory, to supply the sublime element in literature, to paint the inner world, followed inevitably.'
We consciously observe, in thought and action, stationary points in our own minds, as we observe them in the world around us.
Stationary software guides computational dynamics. The dynamic possibilities guide the design of the software. [design = evolution]
Why_q opens the way to the proposition that human intelligence is nothing special in the Universe and allows us to understand better my old position that the collapse of the wave function (to a stationary eigenvalue) is isomorphic (up to a complexity) with the human act of insight which (in Lonergan's picture) leads to a stationary proposition like the definition of a circle. [The quantum axiom that an immediately repeated observation yields the same result points to the stationarity of messages] Zurek
The Trinity is the fundamental network unit, two nodes and a link (or two links and a node) [fermions are outside time, bosons are outside space]
[page 98]
When we click on the address we evoke the file, that is the data at that address, like ringing a doorbell. A beauty of the network is that it is intuitively clear because we are network creates ourselves.
Something has escaped me. It did not remain stationary long enough for me to get a good look. Here it comes . . .
A Turing machine is a logical continuum and we may think of the path of a photon through the symmetric network as a logical space. The photon machine starts when the photon is emitted from a certain state and halts when the photon is absorbed, transmitting its state to the absorber. Because the photon has no rest mass, it has no rest energy and so no process in its own frame, so the message delivered is the message given with no in flight evolution, so we may think of the photon machine as a Turing machine born halted.
Is gravitation quantized?
On the photon
One cannot talk to a photon. it annihilates as soon as it speaks. Since one cannot talk to it is hears no noise and so cannot degrade., although in a macroscopic flow of photons as in a radio signal, the thing may degenerate by spatial dispersion and the absorption of some and the emission of others into the channel.
Thursday 13 August 2009
Quantum entanglement and communication.
[page 99]
Shannon's strategy for defeating error is to encode the output of an information source into blocks. By making the messages longer (the points in message space) one simultaneously makes the communication space larger, and in fact the number of possible messages and the size of the message space grows exponentially with the length of the message, just as the number of numbers that can be represented by an Arabic numeral grows (to be contrasted with the growth of Roman numerals).
The error proofness of a code depends on the Hamming distance between the codes, since we imagine that error enters (in the first approximation) symbol by symbol and that the result of error is to substitute one symbol for another. If as in numeration, we use every possible string of coded symbols, the Hamming distance between code words taken pairwise will often be one. For the encoding to be of any use we must choose a set of code words whose pairwise Hamming ditances are significantly greater than one. If the symbol error rate is rs we need to choose a Hamming distance hd such that rs exp hd is sufficiently small to satisfy our error specification.
In order to increase the distance between code words, Shannon's strategy is to employ the spare entropy in natural messages which results from the skewed probability distribution of symbols, words, sentences etc. Since entropy is maximized when symbols are equiprobable, the transformation of a space of non-equiprobable
[page 100]
symbols into a space of equiprobable symbols we make the entropy of the code space (for a given number of symbols) greater than the entropy of the source space [herein lies the power of democracy, making people 'equiprobable']. This means that the code space has a higher cardinal number than the source space and so can accommodate all the sequences of symbols in the source space into a subset of the same length sequences of symbols in the code space. The words in the code space can then be distributed so that their pairwise Hamming distance is greater than one by a factor depending on the ratio of the source entropy to the code entropy.
This is in effect to select a subset of words in code space which looks like a correlation. This 'non-classical' correlation we guess to be identical to the correlation induced by entanglement. Prove this. At this point we might be forced to introduce a bit of mathematical symbolism but I will try to resist as it is hard to type.
The measurement of entanglement.
Lo, Popescu & Spiller page 30: 'Here we treat entanglement as a resource that allows is to teleport quantum states and construct unbreakable codes, a resource that we can extract, purify, distribute and consume. Lo, Popescu & Spiller
RESOURCE = FORM = SYMBOL = WORD (WORD = {SYMBOL}).
'The states of the subsystem do not determine the state of the system'. [This is the foundation of communication, making it necessary, since I cannot work out the state of both of us from my own state].
[page 101]
A form is identical to the initial singularity, that is isolated and static, ie invariant through time. So energy is a resource because it is conserved and 'isolated' in that it is to be found indifferently in all states.
ACTION - CHANGE OF FORM = CHANGE OF MEMORY STATE
Thought this Shannon/entanglement idea was new to me, but I find I have annotated Lo 'product state - E-theorem', showing the idea was there vaguely which I read the book, ordered 21 May 1999. It is reassuring that this idea seems to have come to the surface again in a more developed context, since I have gone from 'Hilbert oscillator' top 'transfinite symmetric network', something which we see as a set of memories working on themselves to create for us the world we experience.
Evangelism is marketing. Evangelism - Wikipedia Jesus, Mohammed, Confucius, all great salesmen. And a lot of it depended on their product being better than anything else in the market place, since it has produced monopolies in certain markets that look like cultural colonization, and it is certain that everywhere the missionaries went the sword was sure to follow. Evangelize them until you are powerful enough to cut them up. Is this cynical? Not in terms of error correction, where it is good to examine the consequences of the worst failure of the system we are designing, a crash, a war, any 'accident' ie unintended consequence of our actions.
From our formal point of view accident = error = contradiction.
[page 102]
Trying to see the most salient elements of Christianity: from a great distance we may see it as an evolution of the concept of law through the Old Testament and the Roman Empire. In the Empire law = will enforced by the sword. In Christianity, they replace the will of the Emperor with the will of God which is a to significant extent more global, more abstract, more embracing and a foundation for the further development of a body of dogma which was believed to represent the nature and will of God so God's actions were made more transparent. We wish to continue this trend by saying that there is no mystery in God, it is our lives, which are subject to certain constraints which we consider arise from the theory of communication, including the constraint of entanglement which we guess to be an error free state which gains this status by occupying only an infinitesimal subset of the points in the formal message space.
When building, especially when lifting heavy things to great heights proceed step by step to that we can stop at any step when the conditions for the next step are not fulfilled. Lonergan: virtually unconditioned. Lonergan
Friday 14 August 2009
Christianity is greedy in the sense that it seeks infinite bliss as the reward for obeying a finite set of prescriptions [too good to be true].
'Feynman's Rule': 'Independent paths add; sequential paths multiply. The addition is a vector addition represented by complex numbers. So we imagine Turing processes operating independently,
[page 103]
with independent clock frequency and phasing interrupting one another in a reversible process, so that sometimes they helped one another, sometimes hindered, and maybe we would get the 'two slit' result. This is add independents. Multiply look at the Argand diagram; the advancing phase represents the passage of time.
REVERSIBLE = RANDOM WALK, since directions in time are equiprobable. When we introduce irreversibility we introduce directions in time, since prior states are erased. This is in effect the definition of prior. Erasure is made necessary because memory is limited (countable) so that infinite processes must recycle memory as the Universe recycles atoms into different structures.
IRREVERSIBLE = ORDERED SET
Maxwells' demon does something irreversible to complete her task. Logically the irreversibility is in the erasure since the past is no longer there but has been converted into the present by a logical (discrete, not continuous) step. On this view, consistent with quantum field theory, motion is the creation and annihilation of particles; at our scale this is the same as birth and death. The process of coming to life requires the reproduction of all the complexities of a mature human encoded in the genetic and somatic codes of a fertilized egg. This embryogenesis is an irreversible process, but different cells stop at different levels of differentiation, beginning with the egg whose relative entropy is zero (log(1 state)) which divides to give entropy 1 (log 2) and so on. Here the human microscosm is a model of the universal macrocosm following the same path from entropy zero.
[page 104]
A Turing machine, considered as a complete set of logically connected states from go to halt looks like a superposition of waves if we abstract from the actual states and watch instead just the rate of action without differentiating what is done. This is physics. When we add meaning to processes, differentiate them, we must move into the metaphysical world of the evolution of memory, the state of the world.
The most general way to approach the world is to identify and count its state. The identification is a formal matter. The count counts how many times a particular state is executed.
STATE = EXECUTABLE EXECUTING (E = h / tau, tau = clock pulse width = 1/nu, nu = clock frequency).
So every quantum state is a reversible process 'in itself'. The fun starts when they start communicating with their own children. Writing sentences like this sitting in the sun (before I go to work) is heaven enough for me. As it has been freed from the burden of the church my life has become happier.
Size and frequency are inverse measures of information/ entropy. My problem is, 'is all this totally idiosyncratic' of 'has it general application'. Only by putting it in the public domain and inviting comment can I answer this question. So far the website has harvested little feedback, a conversation every year or so, but it also serves as a public source that might eventually attract attention. Currently rated circa 2 millionth in the world.
Formally, the websites are my children which will eventually become dynamic when 'reader feedback' begins to influence them.
[page 105]
The nature of the world is shaped by reader feedback. As the environment reads you, so shall you survive, richer or poorer.
The search for mathematical expression of theology is an attempt at both verification and globalization, since we all speak the same mathematics and the flaws in our models become more evident the more precisely (ie 1 to 1 correspondence) we express them. This is the power of formalism, to model and predict reality by expressing the same relationship between the input and output as we find in the world. So the bane of my life, plastering, getting a smooth surface with minimal sanding, a repulsive activity.
The fact that I am still alive gives me some confidence in myself, and consideration of my evolutionary history gives me more. I am a state (a process) in a tree of processes rooted in the initial singularity and branching transfinitely to the present moment.
TRANSFINITE GAP = LOGICAL TRANSFORMATION
The repeated execution of the same Turing machine is some sort of gain for the Universe.
TURING MACHINE = CAPITAL (a FORM)
The fundamental method of dealing with eror in many domains is to retry. The situation here is relatively NP - the agent cannnot compute and control itself beyond a certain point. When the shot is fired and misses the bullseye the agent may form a hypothesis about why it missed and shoot again. And so on ad infinitum and possibly
[page 106]
the olympics!
ENTANGLEMENT - MEANING
The meaning of a point depends on the space in which it is measured. As the initial singularity reproduces itself it gives itself a larger space and so more meaning.
STATISTICS - CARDINAL
ALGORITHMS - ORDINAL
Saturday 15 August 2009
Feast of the Assumption of the Blessed Virgin: another symbol of wishful thinking. Assumption of Mary - Wikipedia
ENTANGLEMENT - TAXATION
Removing variety in level n to increase variety in level n + 1, since error correction applied in n is exponentially rewarded in n + 1. From this point of view, the system is optimized by keeping the variety of n down since this will exponentially increase the variety of n = 1. Then we set
POPULARITY = STATE COUNTING
When I first started to learn science a heavy emphasis was placed on the impersonality of it all. We are to be led by data, not the
[page 107]
personalities of our colleagues, contemporaries and forbears. Now we admit the personalities while keeping the epistemological ethic.
The root of the religion is the epistemological ethic. Hence the Roman Catholic Church belief that it is the possession of 'The Truth'. John Paul II
Truth cannot contradict truth? Formally this is true, but what about the real world where things are killing each other. Rust never sleeps. Rust Never Sleeps - Wikipedia Death is a consequence of error - the system no longer goes through the necessary subprocesses to keep the main process going which is life, symbolized by the interval tau (little tau)
From life = process we derive tau = {tau}, a big life is a set of coupled little lives.
Nielsen & Chuang Entanglement page 573. Nielsen & Chuang
'. . . given that Alice and Bob [personifications, sources] share an entangled pure state |psi>, into what other types of entanglement |phi> may they transform |psi>, given LOCC (local operations, classical communication)?
FORMALISM = ZERO ENERGY STATE (possibility, superposition)
This is a log of my own states reduced to writing. Whether this log is of interest to you is out of my control, but if you do take an interest in it it means we do have something in common which is revealed in communication terms by the entropy of our joint state [being] less than the maximum predicted by the tensor product of our individual states.
[page 108]
Personification goes from personifying Alice and Bob as operators to personifying them as human persons. As human persons, the variety of interaction is much greater but the concept of being operators vis a vis one another remains useful.
The bottleneck is classical communication. I cannot get into your head nor you mine except via some 'body language', ie encoding our feelings into states of the body which can be read by another body.
Classical communication is a concrete realization of an infinite superpositions of states. Local processes use a lot more bandwidth than communication between local processes. We presume the Universe some how optimizes the distribution of processing. So we see gravitation shortening channels of heavy traffic.
Bell: (|00> + |11>) / sqrt (2)All we are saying is that |0> and |1> are orthogonal. The symbols 0 and 1 are labels not quantities
CARDINAL = QUANTITY [physical]
ORDINAL = LABEL (mapping, correspondence etc etc [logical])
Majorization: 'Majorization is an ordering on d-dimensional real vectors intended to capture the notion that one vector is more or less disordered than another.' Nielsen & Chuang
Where is the constraint in quantum mechanics: in the assumption of continuity, the deterministic evolution of a wave equation seen
[page 109] <>/p>
as a superposition of a (countable?) sequence of frequencies / wavelengths (durations)?
Khinchin page 13 Entropy of Markov Chains Khinchin
By definition the entropy of Markov chains is constant. We are looking for a system that increases entropy.
Khinchin page 23: 'It goes without saying [tautologically] that the rules of coding must guarantee that the original text can be uniquely reconstructed from the coded text, which requires in particular that different sequences of the uncoded text must be coded differently.'
Khinchin page 25: 'Theorem 4 'If the entropy of a given text is H, then the greatest lower bound of the compression coefficient mu for all possible codes is H / log m, where m is the number of different symbols of the text. (assuming that text and code have the same cardinal of alphabet = number of letters).
Khinchin page 32: 'In this paper I attempt to give a complete detailed proof of both these Shannon theorems [ ], assuming any ergodic source and any stationary channel with finite memory.
'Stationary channel with finite memory' = (reversible?) Turing machine.
H(AB) < H(A) + H(B) implies correlation (communication) (Khinchin page 36)
We might say that entanglement is established by encodings more complex than the simple one-one correspondence between source and code,
[page 110]
ie arising from computations more complex than lookup tables.
Uncertainty: why am I reluctant to check my email for correspondence from Science? Like my father waking me with exam results in 1959?
A particular (as opposed to universal) Turing machine is a channel or constrain operating between its initial state and its final state.
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