natural theology > notes > 16 september 2007

Notes

[Notebook: DB 61 Warm]

[Sunday 16 September 2007 - Saturday 22 September 2007]

[page 196]

Sunday 16 September 2007

Cantor sees a set as a 'collection into a whole' of 'objects of our thought or our intuition.' If we consider our observable environment to comprise ℵ₀ events (we can always find one more), there are ℵ₁ ways of selecting subsets of these events and ordering them. What science seeks to do is to select out of these possible

[page 197]

orders the ones that are actually realized, and give the observed connections and orderings.

Since sets are indifferent to size we can use them to construct structures of any size.

Monday 17 September 2007

Replace the billiard ball paradigm with the network paradigm. This implies replacing cardinal continuity with logical continuity.

The endgame. : finally breaking free of the apologetic scaffolding of my opposition to Christianity and moving toward a freestanding picture of the divine world. An interpretation of the standard model need make no mention of theology, dealing only with universal Turing machines in a network.

1. Map network to quantum mechanics = function space
2. add special relativity <- why quantized
3. Add general relativity <- bandwidth, energy
4. Add meaning (unary --> binary) optimization and Lagrangian + scale invariance.

Tuesday 18 September 2007

Universe is inherently dynamic (unlike text) so physics requires a time dimension. The introduction of space 'breaks the symmetry' of the time dimension, so [creating] many different proper times (mine, yours, etc) which are 'spatially' separated.

Peacock page 3: '[Special relativity] is an elaboration of the intuitive point of view that the properties of empty [? inertial] space

[page 198]

should be the same throughout the Universe.' Peacock In fact there is no 'empty space', space and the 'content of space; are divisible in thought but not in reality. Lonergan

Peacock page 4: 'Despite the mathematical complexity that can result, general relativity is at ear a highly intuitive theory: the way in which everyday experience can be generalized to deduce the large scale structure of the Universe is one of the most magical parts of physics.'

The relativistic 'interval' dx is an 'infinitesimal' and so a mathematical artifact. In reality (let us say) there must be some 'unit' of distance which in information terms is something like Hamming distance.

Things are simple in the rest frame

"the only valid physical laws are those that equate two quantities that transform in the same way under an arbitrary change of coordinates, ie physics abstracts from meaning. Peacock page 4.

Gravitation only becomes observable when some other force exists to push us off our geodesic.

Einstein: inertial force gravitational force.

page 7: 'the important aspects of gravitation are not so much to do with first-order effects as second order tidal forces.: these cannot be transformed away and are the true signature of gravitating mass.'

GENERAL COVARIANCE - ABSTRACTION FROM MEANING

[page 199]

INCONSISTENCY = ERROR

THE UNIVERSE IS CONSISTENT = ERROR FREE

The big issue for me is finding the optimum balance between freedom and control. I think this optimum is enshrined in the physical world and is captured by the stationarity of the Lagrangian. We might imagine that these stationary points are moved to new eigenvalues by the discovery and propagation of algorithms.

Sci 24/Aug/2007 page 1040 'Trusting the adversary's intentions is critical to negotiations, which have no chance unless both sides believe in the other's willingness to recognize its existential concerns. Atran, AxelRod and Davis

From a simplification point of view, the initial state of the Universe might have obeys Bose statistics and we could say that un the initial singularity all the energy f the Universe is concentrated in one state of frequency E_u / h.

Kreyszig page 2: in calculus we study functions defined on the real lie. R. Kreyszig

{AXIOM} = alphabet of a process.

Metric continuity vs logical continuity.

Violence occurs in incomplete spaces when the point to which people want to converge is not available to them, eg free love in the Roman Catholic Church.

[page 200]

TO DB 62 INTERPRETATION

Wednesday 19 September 2007

[DB 62 Interpretation]

[Page 1]

Thursday 20 September 2007

COMMUNICATION --> CORRELATION

The degree to which two states are correlated is measured by the inner (dot) product.

Just like the ancient models of the world proposed by Moses, Plato, Aristotle and Aquinas, the standard model is invisible to use and has been constructed to explain the phenomena of life like good years and bad years, victory and defeat, our own origins, the nature of sunlight an everything else. This is pure speculation (except in the case of Moses and the other prophets who claim to have direct information form the Maker and Controller of the world - not admissible evidence to many). Speculation justified by the fact that it seems to work. Genesis, Plato, Aristotle, Aquinas

You can say what you like to the internet, but if you don't transmit it in Internet Protocol, no one will receive it.

Kreyszig page 49: 'A mapping from a normed space X into a a normed space is called an operator. A mapping from X into R or C is called a functional. Kreyszig

'It is basic that the set of all bounded linear operators from a given normed space X into a given normed space Y can be made into a normed space which is denoted B(X, Y).

COMPLEXIFICATION

[page 2]

We can consider the historical complexification of mathematics as model for the complexification of the Universe.

Operators on finite dimensional normed spaces can be represented by matrices, which are a form of parallel processing, since given two matrices in memory of side n, n² machines can be assigned to fill in the elements of the product matrix. Otherwise we have nested do loops.

Kreyszig page 50: a vector space is an additive Abelian group.

h bar = RESOLUTION LIMIT of the world.

We make a vector space into a metric space by introducing a norm which measures the length of vectors, the metric induced by the norm. Kreyszig page 59 The metric tells us nothing about their direction, which is the operative parameter in quantum mechanics. Direction is captured by the inner product.

The vast range of possibilities in Hilbert space is not all exploited by nature. In nature, the transformation of states in controlled by an 'equation of motion'.

Friday 21 September 2007

Quantum mechanical measurement: the measurement basis us decided by the measurer, and the result will be an element of the spectrum of the measurement operator.

[page 3]

In analysis points are defined by sequences which are generally generated by some operator that transforms term(n) of the sequence into term (n+1). This technique is used in the continuum, but discrete results can be determined by finite arithmetic computations: F = ma.

Saturday 22 September 2007

Related sites

Concordat Watch

Revealing Vatican attempts to propagate its religion by international treaty

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Kreyszig, Erwin, Introductory Functional Analysis with Applications, John Wiley and Sons 1989 Amazon: 'Kreyszig's "Introductory Functional Analysis with Applications", provides a great introduction to topics in real and functional analysis. This book is part of the Wiley Classics Library and is extremely well written, with plenty of examples to illustrate important concepts. It can provide you with a solid base in these subjects, before one takes on the likes of Rudin and Royden. I had purchased a copy of this book, when I was taking a graduate course on real analysis and can only strongly recommend it to anyone else.' Krishnan S. Kartik
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Lonergan, Bernard J, and Michael G Shields, Grederick E Crow (Editors), The Ontological and Psychological Constitution of Christ, University of Toronto 2002 Amazon Book Description 'Bernard Lonergan's De constitutione Christi was written to accompany a course being taught in Latin at the Gregorian University, Rome during the 1950s and 60s. This little-known treatise, volume seven in the series, is presented in English translation, accompanied by the original Latin text. Here, Lonergan tackles the metaphysical and psychological questions raised by the unique makeup of Christ, who is both fully human and fully divine, according to traditional Christian theology. His analysis falls into two parts: ontological and psychological. In dealing with the ontology of the incarnate Word, Lonergan explores the notion of person, and in doing so provides an interesting treatment of the existential question of personal authenticity raised by Kierkegaard and treated by Lonergan under the heading of Existez. Moving into his psychological analysis, he argues that consciousness is not a matter of introspection, a perception of oneself as object, but rather an awareness of oneself as subject. He then applies this understanding to the self-awareness of Christ, with particular reference to the question of Christ's knowledge of himself as both human and divine. This book is a foundational text in critical areas of contemporary theology; however, it was never widely circulated and has remained effectively unknown to contemporary scholars. With this translation the work will finally be made accessible'
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Peacock, John A, Cosmological Physics, Cambridge University Press 1999 Nature Book Review: 'The intermingling of observational detail and fundamental theory has made cosmology an exceptionally rich, exciting and controversial science. Students in the field — whether observers or particle theorists — are expected to be acquainted with matters ranging from the Supernova Ia distance scale, Big Bang nucleosynthesis theory, scale-free quantum fluctuations during inflation, the galaxy two-point correlation function, particle theory candidates for the dark matter, and the star formation history of the Universe. Several general science books, conference proceedings and specialized monographs have addressed these issues. Peacock's Cosmological Physics ambitiously fills the void for introducing students with a strong undergraduate background in physics to the entire world of current physical cosmology. The majestic sweep of his discussion of this vast terrain is awesome, and is bound to capture the imagination of most students.' Ray Carlberg, Nature 399:322
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Papers

Atran, Scott, Robert Axelrod, Richard Davis, "Sacred Barriers to Conflict Resolution", Science, 371, 5841, 24 August 2007, page 1039-1040. 'Our research team has measured emotional outrage and propensity for violence in reaponse to peace deals involving compromises over issues integral to Israeli-Palestinian conflict with Israei settlers, Palestinian refugees, and Hamas versus non-Hamas students. Our proposed compromises were exchaning land for peace, sovereignty over Jerusalem, the right of Palestinian refugees to return to their former lands and homes inside Israel, and recognition of the validity of the adversary's own sacred values. We found that the use of material incentives to promote the peaceful resolutiuon of political and cultural conflicts may backfire when adversaries treat contested issues as sacred values. Symbolc concessions of no apparent material benefit may be the key in helping to solve seemingly intractable conflicts.'. back

Frey, Bruno S, Alois Stutzer, "What Can Economists Learn from Happiness Research? ", Journal of Economic Literature, 40, 2, June 2002, page . Abstract: 'In recent years, there has been a steadily increasing interest on the part of economists in happiness research. We argue that reported subjective well-being is a satisfactory empirical approximation to individual utility and that happiness research is able to contribute important insights for economics. We report how the economic variables income, unemployment and inflation affect happiness as well as how institutional factors, in particular the type of democracy and the extent of government decentralization, systematically influence how satisfied individuals are with their life. We discuss some of the consequences for economic policy and for economic theory.' . back

Links

AEAWeb Journal of Economic Literature Editor's Note: 'The Journal's purpose is to help economists keep up with the ever-increasing volume of economics research. This goal is effected by publishing survey articles and essays, book reviews, and an extensive bibliographic guide to the contents of current economics periodicals.' back

Genesis Genesis, from the Holy Bible, King James Version from the Electronic Text Center, University of Virginia Library back

Plato The Internet Classics Archive | Works by Plato Apology Translated by Benjamin Jowett Charmides, or Temperance Written 380 B.C.E Translated by Benjamin Jowett Cratylus Written 360 B.C.E Translated by Benjamin Jowett Critias Written 360 B.C.E Translated by Benjamin Jowett Crito Written 360 B.C.E Translated by Benjamin Jowett Euthydemus Written 380 B.C.E Translated by Benjamin Jowett Euthyphro Written 380 B.C.E Translated by Benjamin Jowett Gorgias Written 380 B.C.E Translated by Benjamin Jowett Ion Written 380 B.C.E Translated by Benjamin Jowett Laches, or Courage Written 380 B.C.E Translated by Benjamin Jowett Laws Written 360 B.C.E Translated by Benjamin Jowett Lysis, or Friendship Written 380 B.C.E Translated by Benjamin Jowett Meno Written 380 B.C.E Translated by Benjamin Jowett Parmenides Written 370 B.C.E Translated by Benjamin Jowett Phaedo Written 360 B.C.E Translated by Benjamin Jowett Phaedrus Written 360 B.C.E Translated by Benjamin Jowett Philebus Written 360 B.C.E Translated by Benjamin Jowett Protagoras Written 380 B.C.E Translated by Benjamin Jowett The Republic Written 360 B.C.E Translated by Benjamin Jowett The Seventh Letter Written 360 B.C.E Translated by J. Harward Sophist Written 360 B.C.E Translated by Benjamin Jowett Statesman Written 360 B.C.E Translated by Benjamin Jowett Symposium Written 360 B.C.E Translated by Benjamin Jowett Theaetetus Written 360 B.C.E Translated by Benjamin Jowett Timaeus Written 360 B.C.E Translated by Benjamin Jowett back