Notes
[Notebook: TURKEY DB55]
[Sunday 4 may 2003 - Saturday 10 May 2003]
[page 294]
Sunday 4 May 2003
Talking to B of my religious dream that this set of ideas attracts
sufficient income to propagate themselves and grow
[page 295]
to the benefit of myself and my friends and (secondarily)
everybody.
PT Our product is religion, ie physical theology.
Any religion fails unless is is strictly ecumenical and recognizes
[that] all other bona fide religion (ie not 'cults') have an equal
right to exist, so that human religious society may be a
superposition of consistent scientifically acceptable religions, ie
religions consistent with themselves and their environment. We guess
that all such religions have the same entropy and can be transformed
into one another by a transformation akin to the transformation of
language we call translation.
All physical measurements are discrete and countable (quantum) but
the range of meanings (models) that may be ascribed to these
measurements is uncountable (ℵ1.
Since we are looking for the broadest possible point of view we do
not restrict the idea of general covariance simply to the coordinate
system which a particular scientist maybe using to examine a
particular particle or event at a particular moment, but rather
expand it to all events and particles, each of which has a proper
frame of reference or point of view through which it relates the
Universe to itself. The general covariance of science is designed to
be large enough to capture all the covariance of the events that
constitute the Universe. In other words, the Turing machine
representing a given particle at a given point remains the same
regardless of the coordinates in which it is fed its input and into
which it is designed to encode its output.
Tomonaga: Tomonaga
Translators preface: page viii 'The existence of spin and the
statistics associated with it is the most subtle and ingenious design
of Nature - without it the whole Universe
[page 296]
would collapse.' Takeshi Oka
Tomonaga page x: '. . . the statistics [of fermions and bosons] are
obtained from the requirements of relativity and the covariance of
physical quantities.'
page xi: 'the rules of spin and statistics are applicable also to
composite particles.'
Monday 5 May 2003
We may use general covariance to describe human freedom (as it
describes the freedom of other particles). At the coarsest and most
abstract level (transfinite oscillator) entities are described by
cardinal numbers that represent their rate of action (energy,
4-momentum). Covariance suggests that the permutations of the natural
numbers (ie of the set of ordinal numbers constructed from the
natural numbers) . . . are the reference frame for the entity we call
ℵ0. All represent the same being from different points
of view - one permutation, one point of view. Transformations within
a given peer index give different interpretations of the same entity.
Transitions to different peer indices represent a complexification or
abstraction. We can give meaning and context to events in a given
peer index by choosing a large transfinite space as our Universe, eg
aleph(n), and consider ℵ0 in the context of aleph(n), ℵ1
in the context of aleph(n-1) and so on, so that there is a certain
conservation law in operation. As usual, very vague, but just keep
transforming the idea into words until something beautiful appears.
Dreamt about this a lot last night. We see the natural numbers as
a natural frame of reference for the Universe, since a countable
number of events can be placed into one-to-one correspondence with
the natural numbers, and different orderings of events correspond to
different orderings of the natural numbers. This gives us a natural
transition to the next transfinite number ℵ1 which represents
all possible orderings of the events in the Universe, in a way all
possible meanings that can be given to the universal process.
US/UK Act of (Religious)
Toleration, 1689. Noel S
McFerran
[page 297]
Tuesday 6 May 2003
We go straight from the structure of the transfinite network to
the axiomatic theory of probability and evolutionary process, through
which organisms act to increase their probability of survival.
Covariance allows for localization, requiring in order to make a
coherent whole, that there exist a transformation from one locality
to the next. In special relativity, locality means relative velocity.
In general relativity, locality means relative acceleration, which is
turn decided by the distribution of energy in and around the
locality.
From probability theory we go to quantum theory, quantum
information theory, which tells us how the Turing machines that run
the world are connected together and communicate via eigenvalues
encoded and decoded by eigenfunction.
Finally it would be nice of general relativity truly was the
theory of God and so continuous in the sense of having a cardinal
number greater than all cardinal numbers. Here we could revive the
concept of generalized geodesic as the path of our individual lives
coming together at conception, like a star, and falling apart again
in old age, to become the material for the next generation.
Wednesday 7 May 2003
We define God as an entity capable of executing all possible
operations, and we begin with the idea that possible operation in
physics is equivalent to can be done by a halting Turing machine in
mathematics.
Deutsch proposes (perhaps) that our Universe us
[page 298]
just one Turing machine and all the
other possible Universes are all the other possible states of this
machine which are not accessible to us in our Universe. Deutsch
Instead the network model puts all ℵ0 halting Turing
machines together on a network that can solve the ℵ1 possible
Turing machines that do not halt. [?]
Versatility (the total versatility of God, able to do ℵ0
things at once) is measured by entropy. So as God learns from doing
ℵ0 things at once how to do ℵ1 things at once is the
process of creativity. Creation changes the meaning of 'at once' by
creating processes by creating processes that live for any period
between the frequency corresponding to the energy of the Universe and
the total age of the Universe, which increases monotonically forever.
It appears that the age of the Universe is going to increase
monotonically forever. The identity mapping on the set of natural
numbers, It is natural to assume that the total number and variety of
quanta of action in the Universe taken from the beginning to the end,
ie any chosen upper bound, is ℵ0.
Why do people who deal in money make so much more money than those
dealing in drugs or machines or attitudes to life? Possibly has a lot
to do with the 'semantic' value of the currency they are dealing in
and its ready transportability, coupled with the fact that where they
work, the gearing to the real world is relatively high.
TRANSFINITE GEARING
The principle of infinitism. The rules of infinity govern the
finite because the Universe is infinite, and yet it generates
(relatively) finite structures.
Is there anything more to love than strong physical affection and
no games.
[page 299]
From the point of view of physics, every quantum of action is
unique, with an address in space and time and an essence of its own.
The uniqueness is projected onto the variety of action by the
distinction of places and times. So it was not just an act of love,
but a particular act of love between particular actors at a
particular (proper) place and time. The structure of action is
projected on the structure of space and time so that each act is a
distinctly addressed event whose meaning is only fully resolved by
considering its relationships to every other event in the Universe
[within its past light cone].
Two ways to look at the Universe a) individuals, b) relationships.
The same information is in both, described (in physics) as particles
and fields.
Human relationships so transparent to us are massively magnified
(from our point of view) versions of what goes on at every other peer
level in the Universe.
Whether you are a divine artist or a block of concrete, gravity
sees the same thing, a set of energy x.
In the quantum world, the continuum is approximated by events
which, as a consequence, tend to fade into one another with the
passage of time as the ripples from each event move further through
the continuum to influence all the other events in their causal cone.
(at c, causal cone = light cone] In general, however, the space
velocity of information is not a single constant, so that the casual
structure of the human world has a degree of freedom (absent?) from
the physical world. NO, the physical world admits velocities less
than c!
God can do ℵ0 things at once by spacetime division
multiplexing. The Lorentz transformations show us the invariance in
the allocation
[page 300]
of processes to space and time even though, from our point of
view, entities travelling at c have a time velocity of zero
corresponding to the space velocity of c. From the point of view of a
moving particle (process) space is one dimensional, like the tape of
a Turing machine which is read and written to (communicated with) by
the processor following protocols which are themselves written on the
tape, but may be loaded into the memory of the Turing machine.
machine in state si
read tape symbol
moves, erases, writes according to state and symbol
enters state sj.
Do we see the world as a banking system, combating fluctuations
with large numbers so as to create more money and allow growth and
transfer of value (meaning).
General covariance is good and works in physics but what about
more complex levels? Is a particular point of view enshrined in a
choice of reference frame, an inherent part of the structure of the
world. My nature defines my relationship to many aspects of the
physical and chemical world as I seek to meet needs for a certain
range of temperature, pressure and chemical input.
Moral hazard: a set of incentives for a part of a system which
tend to encourage action detrimental to the whole system.
Do we need nature? The answer is obviously yes, and it is hard to
imagine any sane and well informed person imagining that we could
live without sunlight, air, water, soil, food and all the other more
obvious natural inputs to our lives. We need nature for raw material
for sure, but our needs are deeper. Do we need trees as well as wood,
wilderness as well as open cut mines? Here we encounter differences
of opinion on how much we can safely destroy natural assets in our
pursuit of wealth. Here we argue strongly that we need not just
material nature, but the wilderness and complexity of nature as well,
[page 301]
and the more we can conserve, understand and live wilderness, the
happier and more stable our lives can be.
COVARIANCE = ABSTRACTION
BINDING = NON-COVARIANCE (choose a mapping, language and stick to
it.)
Consider 'position independent computer code' ie relative
addressing.
Covariant roots are to be found in concrete realities.
Human language ability (ie hardware) is covariant with respect to
the millions of different human languages that may have existed over
the last few million years. Other non-linguistic signalling ('body
language') is more closely bound (and so, we are inclined to think,
more closely bonded to internal states, ie 'true') We can, however,
learn to control these signals and the best bred 'Englishperson'
might be considered devoid of bound body language, see Agatha (?)
One gets a feeling for something by calculating (imagining) it and
then trying it. So we must do with the Lagrangian and economy of
action.
CALCULATION = abstract version of reality: stones = sheep.
Once more a forgotten thing. Distracted by lighting the fire,
paying the bills etc - maintaining the inputs that keep the show on
the road.
The physical applies at every point in the Universe, like God. It
is God [but not all of God]
Lonergan was grasping for general metaphysical covariance but
slightly missed the connection, due perhaps to the inertia of the
institution he was bonded to,
[page 302]
. . .
Here it has come back: the world is so lively because it is a
competition of exponentials. Any edge, no matter how small, can
become infinitely big if it can be grown exponentially.
Real exponents grow without limit (and eventually destroy their
environment and collapse); leading to complex exponentials which are
cyclic and reflect the reality that there are physical bounds on an
real exponential growth. The fact that complex exponentials seem
essential to quantum mechanics (but think of Wigner), and that it is
linear, seems to show that the wisdom of evolution (in very high
frequency systems) has selected the physics of the world we inhabit
to the optimum line (generalized geodesic) through the space of
possibility. This is so because a total unconstrained entity like the
Universe is free to explore the total space of possibility. That part
of the space of possibility which is consistent is invariant with
respect to time and appears to physicists as the conservation of
energy, the fundamental revelation (?) of physical theology. [?]
The transfinite network gives us an hierarchy of covariance and
bondings, each bonding (like the creation of the human mind) serving
as an alphabet for the creation of a space of even greater entropy,
in which certain points are selected to be given reality (or to take
reality) and the rest remaining as a set of possibilities within
which we find actual events following certain causes. The space of
human animal possibilities is open to be explored by each one of us,
and in the imaginative world, is the stuff of sitcoms.
The marketing root of physical theology is the expression of lust
tempered by human rights. The more lusty we can become while
maintaining truth and consistency, the better chance we have of
recruiting 'believers'. It seems safe to
[page 303]
ask people to believe you if you genuinely believe yourself. There
are, however, (as the transfinite network shows) many levels of
belief. There are, however, beliefs which are fully compatible with
the physical world and we might count these as safe? The basic
problem, as in child sexual abuse and all other forms of human
exploitation, is a misuse (corruption) of power. One person dominates
another for their own benefit. Historical (and present) examples of
this are endless. Some feel that the answer to this is 'full
disclosure' but we have to recognize that there is no sense in
reading a tree its rights, we simply have to respect them. And the
same thing with children and all others who are in a relation of
immaturity and ignorance (like people who have not grown up in modern
rich and technologically and educationally advanced societies.) that
smart agents must respect true protocol, which is not to take
advantage of ignorance, as the sovereign power does which claims that
ignorance of the law (no matter how complex and inconsistent) id no
excuse.
The power of exponentiation means that the most attractive thing
on earth is reproductive potential, whether in people, seeds,
business deals or whatever. These dreams must be tempered by the law
of reversion to the norm.
Phrases with impact: Our Holy Mindfucker the Church,
Thursday 8 May 2003
Friday 9 May 2003
Saturday 10 May 2003
|
Related sites
Concordat Watch Revealing Vatican attempts to propagate its religion by international treaty
Copyright:
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Further reading
Books
Click on the "Amazon" link below to see details of a book (and possibly buy it!)
Augustine, Saint, and Edmond Hill (Introduction, translation and notes), and John E Rotelle (editor), The Trinity, New City Press 1991 Written 399 - 419: De Trinitate is a radical restatement, defence and development of the Christian doctrine of the Trinity. Augistine's book has served as a foundation for most subsequent work, particularly that of Thomas Aquinas.
Amazon
back |
Beale, R, and T Jackson, Neural Computing: An Introduction, Adam Hilger 1991 Jacket: '... starts from basics and goes on to cover all the most important approaches to the subject. ... The capabilities, advantages and disadvantages of each model are discussed as are possible applications of each. The relationship of the models developed to the brain and its functions are also explored.'
Amazon
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Canon Law Society of America, Holy See, Code of Canon Law: Latin-English Edition, Canon Law Society of America 1984 Pope John Paul XXXIII announced his decision to reform the existing corpus of canonical legislation on 25 January 1959. Pope John Paul II ordered the promulgation of the revised Code of Canon law on the same day in 1983. The latin text is definitive. This English translation has been approved by the Canonical Affairs Committee of the [US] National Conference of Catholic Bishops in October 1983.
Amazon
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| Denzinger, Henricus, and Adolphus Schoenmetzer, Enchiridion Symbolorum, Definitionum et Declarationum de Rebus Fidei et Morum, Herder 1963 Introduction: 'Dubium non est quin praeter s. Scripturam cuique theologo summe desiderandus sit etiam liber manualis quo contineantur edicta Magisterii ecclesiastici eaque saltem maioris momenti, et quo ope variorim indicum quaerenti aperiantur eorum materiae.' (3)
'There is no doubt that in addition to holy Scripture, every theologian also needs a handbook which contains at least the more important edicts of the Magisterium of the Church, indexed in a way which makes them easy to find.'back |
Deutsch, David, The Fabric of Reality: The Science of Parallel Universes - and its Implications, Allen Lane Penguin Press 1997 Jacket: 'Quantum physics, evolution, computation and knowledge - these four strands of scientific theory and philosophy have, until now, remained incomplete explanations of the way the Universe works. ... Oxford scholar DD shows how they are so closely intertwined that we cannot properly understand any one of them without reference to the other three. ...'
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Feynman, Richard P , and Albert P Hibbs, Quantum Mechanics and Path Integrals, McGraw Hill 1965 Preface: 'The fundamental physical and mathematical concepts which underlie the path integral approach were first developed by R P Feynman in the course of his graduate studies at Princeton, ... . These early inquiries were involved with the problem of the infinte self-energy of the electron. In working on that problem, a "least action" principle was discovered [which] could deal succesfully with the infinity arising in the application of classical electrodynamics.' As described in this book. Feynam, inspired by Dirac, went on the develop this insight into a fruitful source of solutions to many quantum mechanical problems.
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Genesis, and Alexander Jones (editor), in The Jerusalem Bible, Darton Longman and Todd 1966 'In the beginning God created the heavens and the earth. Now the earth was a formless void, there was darkness over the deep, and God's spirit hovered over the water.' (I, 1-2)
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Hornblower, Simon, and Anthony Spawforth (editors), The Oxford Classical Dictionary, Oxford University Press 1996 Jacket: 'The ultimate reference work on the classical world. . . . Over 6 200 entries illuminate every facet of life in ancient times to provide a gold-mine of factual information and a host of fascinating thematic entries. Most entries give plentiful and detailed references to ancient sources and all but the shortest of entries have extensive cross-references and are followed by full bibliographies.'
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Isaiah, and (Alexander Jones, Editor), in The Jerusalem Bible, Darton Longman and Todd 1966 Introduction to the Prophets: 'The prophet Isaiah was born about 756 B.C. In the year of king Uzziah's death, 740, he received his prophetic vision while in the Temple of Jerusalem. His mission was to proclaim the fall of Israel and Judah, the punishment of the nation's infidelity. ... The prominent part played by Isaiah in his country's affairs made him a national figure, but he was also a poet of genius. Brilliance of style and freshness of imagery make his work pre-eminent in the literature of the Bible; he wrote a conciae, majestic and harmonious prose unsurpassed by any of the biblical writers who were to follow him.'
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Khinchin, A I, Mathematical Foundations of Information Theory (translated by P A Silvermann and M D Friedman), Dover 1957 Jacket: 'The first comprehensive introduction to information theory, this book places the work begun by Shannon and continued by McMillan, Feinstein and Khinchin on a rigorous mathematical basis. For the first time, mathematicians, statisticians, physicists, cyberneticists and communications engineers are offered a lucid, comprehensive introduction to this rapidly growing field.'
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Matthew, and Alexander Jones (editor), in The Jerusalem Bible, Darton Longman and Todd 1966 Introduction to the Synoptic Gospels: '[Matthew is] a dramatic account in seven acts of the coming of the kingdom of heaven. 1. The preparation of the kingdom in the person of the child-Messiah. ... 2. the formal proclamation of the charter of the Kingdom ... i.e. the Sermon on the Mount ... 3. The preaching of the kingdom by missionaries ... 4. The obstacles that the kingdom will meet from men ... 5. Its embryonic existence ... 6. The crisis ... which is to prepare the way for the definitive coming of the kingdom ... 7. The coming itself ... through the Passion and resurrection.' (12)
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Psalms, The Jerusalem Bible, Darton Longman and Todd 1966 Introduction to the Psalms: 'The Pslter is Israel's hymn-book. The Temple, as we know, had its cantors from the beginning, though they are not mentioned until after the Exile. . . . The Psalter was tghe hymn-book of the Temple and the synagogue before it was adopted by the Christian Church.' page 7820
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Robinson, John Arthur Thomas, Honest to God, Westminster John Knox Press 1963 Jacket: 'Bishop Robinson's work, Honest to God, for all its seeming radicalism, was a work of preservation. The task he set for himself . . . was to address this question: How is one to assure the survival of belief in God in a world where such belief is increasingly rejected, not so much because it is incredible as becasuse those who articulate the belief often make it seem incredible. This book is in the form of a via negative, historically a highly respectable enterprise. . . . It was not so much the 'radicalism' of the book that disturbed the readers, it was the honesty.' Joseph William Goetz, The Christian Century
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Tomonaga, Sin-itiro, The Story of Spin, University of Chicago Press 1997 Jacket: 'The Story of Spin, as told by Sin-itiro Tomonaga and lovingly translated by Takeshi Oka, is a brilliant and witty account of the development of modern quantum theory, which takes electron spin as a pivotal concept. Reading these twelve lectures on the fundamental aspects of physics is a joyful experience that is rare indeed.' Laurie Brown, Northwestern University.
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Papers
| Clauset, Aaron, Cristopher Moore, M E J Newman, "Hierarchical structure and the prediction of missing lings in networks", Nature, 453, 7191, 1 May 2008, page 98 - 101. Abstract: 'Networks have in recent years emerged as an invaluable tool for describing and quantifying complex systems in many branches of science. Recent studies suggest that networks often exhibit hierarchical organization, in which vertices divide into groups that further subdivide into groups of groups, and so forth over multiple scales. In many cases the groups are found to correspond to known functional units, such as ecological niches in food webs, modules in biochemical networks (protein interaction networks, metabolic networks or genetic regulatory networks) or communities in social networks Here we present a general technique for inferring hierarchical structure from network data and show that the existence of hierarchy can simultaneously explain and quantitatively reproduce many commonly observed topological properties of networks, such as right-skewed degree distributions, high clustering coefficients and short path lengths. We further show that knowledge of hierarchical structure can be used to predict missing connections in partly known networks with high accuracy, and for more general network structures than competing techniques. Taken together, our results suggest that hierarchy is a central organizing principle of complex networks, capable of offering insight into many network phenomena.'. back |
| Dirac, P A M, "The Lagrangian in Quantum Mechanics", Physikalische Zeitschrift der Sowjetunion, 3, 1, 1933, page 64-72. 'Quantum mechanics was built up on a foundation of analogy with the Hamiltonian theory of classical mechanics. . . . there is an alternative formulation of classical dynamics provided by the Lagrangian. This requires one to work in terms of coordinates and velocities instead of coordinates and momenta. The two formulations are, of course, closely related, but there are reasons for believing that the Lagrangian one is the more fundamental.' Reprinted in Julian Schwinger (editor), Selected Papers on Quantum Electrodynamics, Dover, New York, 1958.. back |
| Hamilton, Douglas P, Harald Kruger, "The sculpting of Jupiter's gossamer rings by its shadow", Nature, 453, 7191, 1 May 2008, page 72 - 75. Abstract: 'Dust near Jupiter is produced when interplanetary impactors collide energetically with small inner moons, and is organized into a main ring, an inner halo, and two fainter and more distant gossamer rings. Most of these structures are constrained by the orbits of the moons Adrastea, Metis, Amalthea and Thebe, but a faint outward protrusion called the Thebe extension behaves differently and has eluded understanding. Here we report on dust impacts detected during the Galileo spacecraft's traversal of the outer ring region: we find a gap in the rings interior to Thebe's orbit, grains on highly inclined paths, and a strong excess of submicrometre-sized dust just inside Amalthea's orbit. We present detailed modelling that shows that the passage of ring particles through Jupiter's shadow creates the Thebe extension and fully accounts for these Galileo results. Dust grains alternately charge and discharge when traversing shadow boundaries, allowing the planet's powerful magnetic field to excite orbital eccentricities and, when conditions are right, inclinations as well.'. back |
| Rosenblatt, Frank, "The Perceptron: A Probabilistic Model for Information Storage and Organization in the Brain,", Cornell Aeronautical Laboratory, Psychological Review, 65, 6, 1958, page 386 - 408. 'Frank Rosenblatt invented the perceptron in 1957 at the Cornell Aeronautical Laboratory in an attempt to understand human memory, learning, and cognitive processes. On 23 June 1960, he demonstrated the Mark I Perceptron, the first machine that could "learn" to recognize and identify optical patterns.' (From Perceptrons:
An Associative Learning Network
by
Michele D. Estebon http://ei.cs.vt.edu/~history/Perceptrons.Estebon.html#3). back |
| Saville, Margot, "Welcome on Board", The Sydney Morning Herald: Good Weekend, , , 3 May 2008, page 23 - 28. 'Even when [women] are placed in a senior role, they often get paid less than the nearest man. In January the Equal Opportunity for Women in the Workplace Agency (EOWA) released a report that examined the pay structure of the five most highly paid executives in Austrlia's 200 largest (stockmarket-listed) companies. Only 80 out of those 1136 positions (7 per cent) were held by women, and when a female became chief financial officer or chief operating officer, she earned half the wage of her male equivalent, while female CEOs earned two-thirds. Even in human resources positions, where women are more common, the pay gap was still 43%.'. back |
| Shermer, Michael, "JAMA and the Mountebank", Nature, 451, , 7 February 2008, page 628-629. Review of Charlatan: America's Most Dangerous Huckster, The Man Who Pursued Him and the Age of Flim Flam, by Pope Brook. '. . . faith in anecdotes can make us easy to exploit. Any medical huckster promising that A will cure B has only to advertise a handful of successful testimonials. Enter John R. Brinkley, one of the most notorious medical quacks of the first half of the twentieth century, and his nemesis Morris Fishbein, the quackbusting editor of the Journal of the American Medical Association (JAMA). Their long struggle throughout the 1920s and 1930s, wonderfully retold in a gripping narrative by Pope Brock, brings to life this tension between folk and scientific medicine.'. back |
| Tour, James M, Tao He, "The fourth element", Nature, 453, 7191, 1 May 2008, page 42-43. 'Almost four decades since its existence was first proposed, a fourth basic circuit element joins the canonical three. The 'memristor' might herald a step-change in the march toward ever more powerful circuitry.'. back |
Links
| Cantor's theorem - Wikipedia Cantor's theorem - Wikipedia, the free encyclopedia 'In elementary set theory, Cantor's theorem states that the power set (set of all subsets) of any set A has a strictly greater cardinality than that of A. Cantor's theorem is obvious for finite sets, but surprisingly it holds true for infinite sets as well. In particular, the power set of a countably infinite set is uncountably infinite. The theorem is named for Georg Cantor, who first stated and proved it.' back |
| Catalyst Knowledge: The Bottom Line 'THE BOTTOM LINE: CORPORATE PERFORMANCE AND WOMEN'S REPRESENTATION ON BOARDS
Women Board Directors (WBD) Align With Strong Performance at Fortune 500 Companies1
Financial measures excel where women serve'
back |
| Gödel's incompleteness theorems - Wikipedia Gödel's incompleteness theorems - Wikipedia, the free encyclopedia 'In mathematical logic, Gödel's incompleteness theorems, proved by Kurt Gödel in 1931, are two theorems stating inherent limitations of all but the most trivial formal systems for arithmetic of mathematical interest..' back |
| Joseph-Louis Lagrange - Wikipedia Joseph-Louis Lagrange - Wikipedia, the free encyclopedia 'Joseph-Louis Lagrange, comte de l'Empire (January 25, 1736 – April 10, 1813; b. Turin, baptised in the name of Giuseppe Lodovico Lagrangia) was an Italian mathematician and astronomer who made important contributions to all fields of analysis and number theory and to classical and celestial mechanics as arguably the greatest mathematician of the 18th century.' back |
| Marist Brothers - Wikipedia Marist Brothers - Wikipedia, the free encyclopedia 'The Marist Brothers are a Catholic religious order of brothers and affiliated lay people. The order was founded in France, at La Valla near Lyon in 1817 by Saint Marcellin Champagnat, a young French priest of the Society of Mary (Marist Fathers).
Worldwide, there are more than 4500 brothers working in 77 countries on 5 continents. They directly share their mission and spirituality with more than 40,000 laypeople, and together educate close to 500,000 children and young people in schools, and minister to the spiritual and material wellbeing of countless others.' back |
| Nazareth - Wikipedia Nazareth - Wikipedia, the free encyclopedia 'Nazareth . . . is the capital and largest city in the North District of Israel. It also serves as an Arab capital for Israel's Arab citizens who make up the vast majority of the population there.[2] In the New Testament, the city is described as the childhood home of Jesus, and as such is a center of Christian pilgrimage, with many shrines commemorating biblical associations.' back |
| Noel S McFerran Toleration Act, 1689 'Forasmuch as some ease to scrupulous consciences in the exercise of religion may be an effectual means to unite their Majesties Protestant subjects in interest and affection: ... ' back |
| Occam's Razor - Wikipedia Occam's Razor - Wikipedia, the free encyclopedia 'Occam's razor (sometimes spelled Ockham's razor) is a principle attributed to the 14th-century English logician and Franciscan friar William of Ockham. The principle states that the explanation of any phenomenon should make as few assumptions as possible, eliminating those that make no difference in the observable predictions of the explanatory hypothesis or theory. The principle is often expressed in Latin as the lex parsimoniae ("law of parsimony" or "law of succinctness"): "entia non sunt multiplicanda praeter necessitatem", or "entities should not be multiplied beyond necessity". . . . Originally a tenet of the reductionist philosophy of nominalism, it is more often taken today as a heuristic maxim (rule of thumb) that advises economy, parsimony, or simplicity, often or especially in scientific theories.' back |
| Perceptron - Wikipedia Perceptron - Wikipedia, the free encyclopedianotesm05d04 'The perceptron is a type of artificial neural network invented in 1957 at the Cornell Aeronautical Laboratory by Frank Rosenblatt. It can be seen as the simplest kind of feedforward neural network: a linear classifier.' back |
| Reality-based community - Wikipedia Reality-based community - Wikipedia, the free encyclopedia 'The source of the term is a quotation in an October 17, 2004, New York Times Magazine article by writer Ron Suskind, quoting an unnamed aide to George W. Bush:
The aide said that guys like me were "in what we call the reality-based community," which he defined as people who "believe that solutions emerge from your judicious study of discernible reality." ... "That's not the way the world really works anymore," he continued. "We're an empire now, and when we act, we create our own reality. And while you're studying that reality—judiciously, as you will—we'll act again, creating other new realities, which you can study too, and that's how things will sort out. We're history's actors…and you, all of you, will be left to just study what we do.' back |
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