Notes
[Notebook: DB 59 Draughts]
[Sunday 1 October 2006 - Saturday 7 October 2006]
[page 191]
Sunday 1 October 2006
Sometimes the model seems too simple and easy (compared, for instance, to quantum mechanics) and makes me suspicious. But, given that the Universe began (in the model) as an unstructured point (or pure act, omnino simplex ) this is to be expected, and since the present contains the past, we expect each point in the Universe to reflect the simplicity from which it was born.
Quivering with life. Every message is a fluctuation, but not necessarily random. As Chaitin noted, fully dense coding and pure noise are indistinguishable. Chaitin, Shannon
COMPUTABLE = OBSERVABLE
Logical confinement = computability?
Logical confinement = consistency. But more thing are consistent than are provable - this is the meaning of incompleteness. Gödel Inconsistent = not-provable. But between inconsistent and possible is the vast space of possibility which is winnowed not so much by logic as by fitness.
ie what can be proved from the axioms of Lego only puts very light constraints on the consistent structures that can be built from Lego.
[page 192]
We may see the flow of history as continuous but when we talk and write about it we see it as a sequence of events, wars, the coming and going of princes, inventions, disasters, births, marriages and deaths. Since earliest times there have been atomists who extrapolated this observation to the smallest scale and they were generally right, although the atom in the Universe is not so much a thing as an event.
Lonergan is sort of onto this idea when he sees being as what is perceived by intelligence and asserted by judgment, ie esse est percipi/percipere. (to be is to be perceived / to perceive)
The fitness approach to existence implies that everything we observe justified its existence on some way by being a functioning art of a coherent whole. Thus we can examine every gene and protein in living bodies on the assumption that it has some role which explains its existence. At the extreme, we have god, the ultimate user, which just exists. God is a constituent of every point in the Universe [and vice versa]. Then we have the evolution of more and more complex processes that rely on effective cultural communication for their survival.
Each character in a string is a degree of differentiation from every other possible string of the same length.
Monday 2 October 2006
Feynman: The exclusion principle '. . . almost all the peculiarities of the material world hinge on this wonderful fact.' III page 4-33. Feynman
[page 193]
INSIGHT = DECODING
What we want to say is that creation is the result of love and vice-versa. How do we model this? Contact.
Tuesday 3 October 2006
Are the problems solved at the quantum mechanical level of computation P or not-P. Quantum mechanics seems to be inherently linear, and so we might suspect that it solves problems in polynomial time with an exponent of 1.
Non-deterministic Turing machine 'guesses' an answer ad then checks it.
Hopcroft Scientific American May 1984 page 80: 'Ordinary experience suggests it is easier to verify a solution that it is to find it in the first place. Nevertheless, no one has been able to prove that the problems solvable in polynomial time with a non-deterministic machine - the class of problems designated NP - are intrinsically any more difficult that the problems in the class P. Whether or not the class P is distinct from the class NP, which is called the P - NP problem, has become one of the major open questions in mathematics.' Hopcroft
The 'degree of inference' is measured by the overlap 'interval'. 100% overlap = apodictic syllogism: a, a --> b, therefore b.
Wednesday 4 October 2006
Unitarity guarantees that the probabilities of possible outcomes of one event add up to q, but this does not mean that
[page 194]
entropy is conserved and the outcome is reversibles of the number of outcomes exceeds the number of incomes, eg if both incomes and outcomes are equiprobable among themselves and their numbers are i and o, we have Hi = log i, Ho = log o, log o > log i.
Santayana writes: 'When all the data of immediate [sic] experience and all the constructions of thought have . . . been purified and reduced [sic again] to what they are intrinsically [sic 3], that is to eternal essences [formalism?], by a sort of counterblast the sense of existence, of action, of ambushed reality everywhere about us, become all the clearer and more imperious. This assurance of the not-given [the perennial philosophy Huxley Huxley] is involved in action, in expectation [what does this data mean] in fear, hope or want: I call it animal faith. The object of this faith is the substantial energetic thing encountered in action, whatever this thing may be in itself; by moving, devouring, [being], or transforming this thing I assure myself of its existence; and at the same time my respect for it becomes enlightened and proportionate to its definite powers. Edman page 19. Santayana
The miracle is that complex entities can manipulate this system to ensure their own survival for thousands, millions, or for some three billion year old bacteria reproducing hourly = 3E9 x 9000 = 3E13 generations. . . .
SOURCE = ENTITY I think source is the preferred more general term. In a way, the entity is the explanation of the behaviour of the source. Communication
[page 195]
theory deals with general sources with certain statistical properties, basically an alphabet emitted at random with stationary letter frequencies. In real life, of course, evolution changes the frequency of the event.
In the symmetric Universe, sources exchange messages which are parts (subsets) of themselves. A basic rule of conservation suggests that at the countable peer level the cardinals of the two elements of the exchange must be equivalent. Why? One cannot build a meaningful network without protocol and the simplest cardinal protocol is arithmetic which works on a conserved flow (with or without storage) exactly like first order ie subsidized banking (linear banking (linear banking, ie 0 interest rate, 0 fees). Banking must go non-linear to make a living and so expand. The users find it pays to pay the bank a certain amount for its services. Of course bankers want to maximize profits, but they are always at risk from hungrier players.
We create by making new things, that is by reorganizing stuff. This is a straightforward idea implemented in activities like doing the dishes and building bridges. As Aristotle noted, activity requires matter and form. A bridge is a lot of steel and concrete put together in a carefully developed form. From that people tried to imagine beings that were pure form, containing no matter. This effort seems partly motivated by the idea that matter is low and dirty, something for slaves to attend to while their masters observed due form.
The interest does not arise from the money but from the employment of the formal capital structure which the money has paid for.
[page 196]
So even though the calculation of interest is a simple exercise in cardinal arithmetic, the actual generation of the profit is a complex ordering of reality, an ordinal. And so we come to second, third, nth order banking.
Quantum mechanics is linear. Non linearity arises when linear systems communicate in non-linear ways by stimulating or inhibiting one another. In quantum mechanics this occurs by linear addition of amplitudes. In computational mechanics order becomes important and we can compress computations using efficient algorithms that yield an advantage over pure linearity. Calculations embody polynomials. 136 = 1 E 3 + 3 E 1 + 6 E 0, etc.
To DB 60, 'Spotlights'
[page 1]
Joyce: 'Ineluctable modality of the visible: at least that if no more, thought through my eyes. Signatures of all things I am here to read, seaspawn and seawrack, the nearing tide, that rusty boot.' Ulysses page 31 3:1-3 Joyce
Joyce greatly increases the entropy of language by opening up permutations conventionally closed. In Finnegan's Wake a very high proportion of the words are new and pregnant coinages. Joyce
Gödel numbering takes from aleph(n) to aleph(n+1)
The possible electronic states of a living thing is a vast number but as far as we can tell from observing living sources they are real. As simple a source as an atom has a locally transfinite set of states. The notion of superposition is that all these states are occupied to some degree, ie as a fraction of total occupancy, a cardinal measure. The total occupancy o the set of states available to a 'single source' is 1. There are ℵ0 single sources in the local (observable) Universe.
Thursday 5 October 2006
'[Riemann asserts] . . . that space in itself is nothing more than a three-dimensional manifold devoid of all form; it acquires definite for only through the advent of the material content filling it and determining its
[page 2]
metric relations'. Space . . . page 98. Weyl
The shape of space is a function of the communications occurring within it.
Weyl page 101: 'As, according to Riemann, the conception "congruence" leads to no metrical system at all, not even to the general metrical system of Riemann which is governed by a quadratic differential form, we see that "the inner ground of the metric relations" must indeed be sought elsewhere. Einstein affirms that it is to be found in the "binding forces" of Gravitation. In Einstein's theory the coefficients gik of the metrical groundform play the same part as does gravitational potential in newton's theory of gravitation.
Friday 6 October 2006
The symmetric Universe and the computable manifold seem to fit together quite well. The SU is he configuration space for the CM, and the CM 'explains' how the system moves from one configuration to another through the action of a computable function, more colloquially, by computation.
MOTION == COMPUTATION
Classical motion is held to be continuous and is restricted by the requirements of continuity. Computational
[page 3]
motion is discrete and capable of exploring the whole symmetric function space, subject to the 'conservation of symbols', ie the 'conservation of events' ie the 'conservation of action, ie that the Universe is 'actus purus'.
The world communicated directly with itself without necessarily establishing any frame of reference except consistency ('love') or inconsistency ('hate') on contact. Physicists, psychologists etc like to reduce the world to scalars (eg mass, intelligence) by establishing and integrating over frames of reference eg 'IQ tests".
The main problem (visible to me) with the CM is the non-reversibility of Turing machines due to erasure which seems to be a consequence of Landauer's ideas. Landauer
How do we overcome this? Can we make Turing machines into a group? Insofar as hey implement arithmetic using the integers and addition, all is well, but trouble starts when we introduce division by zero.
How do we make the symmetric Universe + computable manifold behave like general relativity + quantum mechanics? If this could be done we would have a marketable product!
Saturday 7 October 2006
Compare the computable manifold to the differentiable manifold. A suitable metric is the number of binary operations (symbol swaps) to get from one point to another. Let us assume that the world is made of many instances of the initial singularity, ie of the classical god. Then what? The Initial singularity has one state (it is). We need two states to begin talking.
[page 4]
Although continuous mathematics greatly simplifies many things, we are stuck with the fact that al physical observations are rational numbers of the form count/count, integer/integer. The nearest thing to the infinitesimal required for continuity is the quantum of action which produces a quantum of change or a quantum of motion in a Lego like manner. Quantum mechanics postulates an invisible continuous complex process behind this quantized change which we would like to represent by certain configurations in the configuration space of the computable manifold.
To overcome the reversibility problem we might invent the symmetrical Turing machine which we hope has the same power as a Turing Machine and will turn out to be compatible with quantum mechanics, the symmetric network and general relativity.
General covariance means that there is no a priori correlation between logical and physical addresses in the Universe, but correlations evolve by establishing self perpetuating cycles. A processor that can predict and go straight to the next item of its input (like a builder with all tools and materials at hand) can work a lot faster than one that must perform a search at every step along the way (like continually losing my pencil).
How does a Turing machine work in a world that allows only permutation and is layered in complexity?
The standard Turing machine, when set in motion, performs a sequence of operations whose overall effect is to
[page 5]
produce a decimal representation of a computable number. It has a finite program, a finite set of internal states and a countably infinite memory (tape).
We do not talk of 'erasure' but only of reading and writing to the memory. We can make the discussion simple by giving up the Turing machine metaphor and talk instead in terms of modern networked computers. Here we visualize computations as network operations - two 1's converging on a nand gate spawn a zero (logically) but what happens physically. Here we must learn from quantum mechanics.
Riemann, building on Descartes and Gauss, completed the distinction between logical space (systems of reference) and physical space (what 'actually happens') independently of our interpretation. Einstein then found constraints on the [continuous] mapping of logical and physical space (which for practical purposes are both conceived as 'formal structures') which we interpret as the foundations of effective communication and gravitation.
The network computation process within a cell conserves symbols (?) but it is not necessarily reversible, or processes that go one was naturally may be reversed by supplying energy.
Landauer's hypothesis is that there is a physical space corresponding to every logical space.
How does computable manifold explain the Minkowski metric signature? Is it just a fact of life? [arising directly from delay in communication].
