Notes
[Notebook: DB 60 Spotlights]
[Sunday 7 January 2007 - Saturday 13 January 2007]
[page 68]
Sunday 7 January 2007
Thorne, Black Holes, Membrane Paradigm. MacDonald
3+1 view of gravitation, ie slices of 4-space parametrized by time is equivalent to a computation process parametrized by system clock or program counter. Depending on how far away in the network we are looking at a given system we will see its clock operating in its own proper time (very close) or slower (distant).
[page 69]
Physical Theology to Theological Studies or Zygon.
We can say that Lonergan has failed to understand
the exploit the . . . full power of his account of his
'schemes of recursion'. So we can cast them in the language of the
computable manifold and then use them first to explain the translation
that Lonergan himself has made from the Summa (and related
works) to Insight (and related works), in other words how the
mind of Aquinas was transformed into the mind of Lonergan, as
revealed by their lives and works. This translation is NP
(Nondeterministic Polynomial). Lonergan found the text of Insight by
a non-computable process of search in the space of all possible
n letter blocks guided by the search constrained (terms) he
had assimilated from Aquinas. These words themselves are the result
of similar searches made by myself, guided by all the inputs I have
received since birth. The reception of this input (which came to me
at the physical level in the form of fundamental particles) has been
guided by my structure which has been created by recursive processes
stretching back to the initial singularity, which we model as the
classical god.
The protein codes [genes] are the physical layer of the genotype. These physical elements are regulated by layer after layer of control which we are beginning to find among what was once considered 'junk DNA', so powerful is the reductionist instinct. We long ago learnt that protein activity was partly controlled by the rate of transcription of various genes.
[page 70]
These words are precious to me because it has taken so long to find them, and they capture a feeling that I seem to have had (unexpressed) for a long time. . . .
Was the Third Reich analogous to a black hole, sallowing Germany (the cultural entity) and largely destroying it before it evaporated under the impetus of the Allied reconquest and then coalesced into the Germany we have today?
Rowling: Half Blood Prince. Rowling
The continuum contains no information. But from the point of view of any observer, there is no continuum. All information comes in discrete chunks, ie quanta.
Selective pressure works only on the phenotype, that is on the countable communications. It is therefore P (?), ie capable of being modelled by a countable set (ordered set, network) of Turing machines.
We model a set of permutations as a network and each distinct permutation is a distinct [closed] path through the network.
We do not observe ideas, but only their phenotypes ie (eg) the texts (sequences) in which they are encoded.
[page 71]
A model is a program, an algorithm, a set of instructions for getting from a to b, (eg INGREDIENTS --> CAKE). Alexander
FORCE: When elements with complementary structures meet things happen. When elements with non-complementary structures meet, nothing happens. They cannot communicate.
Monday 8 January 2007
IDEALISM = FORMALISM (see Plato)
We may divide particles into two classes: those with internal states that can be changed without killing or even harming them, like us and atoms; and those which are annihilated b any change of internal state and become something else. These are truly fundamental (massless) particles. Massive particles have internal processes, which means they have variable memory locations within them, such as the state of an atom or the state of a mind.
MIND <==> MASS (This is exactly the opposite of the scholastic view that mind is immaterial and so massless).
Materia prima: nec quid nec quale nec quantum, nec aliquid eorum quibus ens determinatur. Something indefinite ++ infinite.
Forma prima == not materia prima, ie a determination, something definite = finite, bounded, countable.
[page 72]
There is only one materia prima (in each peer level) since it can be anything that can be represented by permutations at that peer level (BOSONIC)
Form, on the other hand, is definitely one thing, and so we need to aleph(n) forms to exhaust all the potential at peer level f(n). f(n) (?)
We begin with the one. Somehow 1 has ℵ0 possibilities, ie 1s of different cardinal. So what peer levels have we? 1, finite, countably infinite . . . ; let us call these 1, 2, 3 . . . . The cardinal of peer level 3 is aleph(0, peer level 4 ℵ1 and so on. Peer level 2 is a finite natural number, n, and pl 1 is 1.
Commentary on Insight.
Continuity: short history distinguishing between geometrical and logical. Then a discussion of empirical residue from the point of view of this distinction. Read more Lonergan about mathematics; find my old notes from readings of Lonergan. Hilbert on continuity: More on logic, logical continuity, proof and Turing machine.
If a proof is sound, there is logical continuity between premisses and conclusion. This is the 'deterministic' proof which can be executed by a Turing machine.
But can a Turing machine execute a reductio ad absurdum? Here we have logical confinement rather than continuity. We relate the two by saying that a set of propositions held together by logical confinement is continuous in a non-deterministic way. [ate the eigenvalues of a quantum mechanical operator continuous in this way?]
[page 73]
Non-deterministic continuity = unity of God. A bag of consistency [superposition of states]. Or at least of not-inconsistency, leaving room for plenty of uncertainty.
Life is what you make it, at least to some degree; the other part of life is those things that are out of your control. But the idea is to be ready for anything, so that you can stay on course [a prudent insurer foresees all possible insured losses and makes provision for them].
These notes are notes of introspection, me reading out my own mind, and as Lonergan would say, trying to appropriate my own metaphysics. My advantage over Lonergan is a certain understanding of formal theory a la Cohen on the continuum hypothesis and the fact that it is independent of set theory. The proof of independence is achieved by generating a logical continuum that shows that set theory has nothing to tell us about the cardinal of the continuum because set theory is independent of cardinality, a set may have any number of elements and the theory still holds, blind to number. As we might expect from the principle of requisite variety, we cannot expect a finite discrete system, which is what set theory is in the hands of mathematicians, to be able to tell us about the continuum modelled as a transfinite system. On the other hand, logical continua can tell us about logical continua because we can confine our arguments (and the mind of the Universe can confine its arguments) to equivalent sets.
So requisite variety breaks a symmetry in set theory and makes the symbols >, <, and = significant.
Set theory is the application of logic to . . . certain
[page 74]
structures, sets defined by their membership, and the members of sets defined by their order. By applying arithmetic to ordered sets we get vector algebra, addition of vectors, multiplication by a scalar, inner and outer products, etc.
Rowling page 477: 'Voldemort himself created his worst enemy, just as tyrants everywhere do! Do you have any idea how much tyrants fear the people they oppress? All of them realize that one day, amongst their many victims, there is sure to be one who rises against them and strikes back.'
Tuesday 9 January 2007
The search for absolute foundations is quite natural as a basis for security. The only absolute we can rely on is consistency, and this itself is only manifest when we make an observation. The issue is confused, of course by life and death. Inconsistency is equivalnt to death, consistency carrries with it the possibility of birth and complete consistency (bonum ex integra) requires birth (?). All that is observable is consistent (we do not see the dead) Observable consistency is equivalent to proof.
Religion compries a hope based on faith which leads to charity. The desire for charity (which engenders security) motivates the search for faiths (ie communicable beliefs) which engender hope. A faith is equivalent to a plan - the only way we have a hope of erecting structure x is for all of us to cooperate in plan y which we believe will bring about structure x, which we further believe will increase our securities. Plans, like going to war, which
[page 75]
manifestly decrease security are to be avoided. We winnow goo9d plans from bad by modelling. Modelling has a number of cources of error which include lack of detail, lack of adequate search for failure modes, and self interest on the part of the promoters of a scheme.
. . .
The Christian asumption of immortality is unphysical, insofar as given a finite supply of physical resources (symbols) birth implies death.
Wigner page 201: . . . quantum mechanics slaims to apply to all situations and to give all meaningful predictions.
