natural theology

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vol III Development:

Chapter 3: Cybernetics

page 6: Systems

We may see the physical world as set of events like the sun rising and setting, people being born and dying and so on. Although these events often appear separate and distinct we can see that many of them are connected. We will define a system as a network of connected events. System - Wikipedia

Larger events are constructed from smaller events. Because the quantum of action is so small, most the events that we can perceive comprise a huge number of quanta of action. The life of a person weighing 50 kilograms and living for 80 years comprises some 2 x 1050 quanta of action. Planck constant - Wikipedia

Most of our technology is built around coupling various motions to create systems to do some job. The pistons, valves, crankshaft, gearboxes, wheels and suspension of motor vehicles plus the computers that control them are all designed and coupled to make a transport machine.

The particles and couplings of the natural world have evolved since the time when the Universe was a formless unit of pure action. On this site we like to model the system of the world as a computer network. At the lowest physical level, the messages in this network are the fundamental particles and the computers are the processes that are executed when particles are created, annihilated and interact. Particle Data Group. Lawrence Berkeley National Laboratory

Gravitation and the structure of the Universe

As far as we know, every event in the universe communicates with every other event through gravitation. Since a gravitational communication is itself an event, gravity interacts with itself, which leads to complex mathematical expressions for gravitational kinematics. Gravity unites the whole system of the Universe and appears to determine the overall structure of the Universe. We guess that gravity reflects the unity of the initial singularity and defines the lowest physical layer of the universal network. Gravitation - Wikipedia, Hawking & Ellis: The Large Scale Structure of Space-Time

Layering is a feature of engineered networks. Communications beween two users of the network bore down through the software layers until they are encoded as signals in the physical layer. The physical layer carries the signal to the receiver where it is decoded and passed up through layers of software to the other user. We can imagine a similar situation in the network model of the Universe. The proceses in the universal network bore down to gravitation, so that gravitation is involved in every interaction. Insofar as the Universe is divine and the initial singularity within which it emerges is identical to the classical God, we can say that the every message in the Universe passes through God. Tanenbaum; Computer Networks

Transformation

In general, the role of a system is to transform an input into an output. I am a system whose fundamental input is food and my outputs are the many varied manifestations of human life. Smaller systems, like an oven are similar, taking in energy, putting out heat for cooking.

We see the large scale structure of the Universe through gravitation and through light. We will return to the details of gravitation in the Chapter on Physics. Here we see it as an instance of a system.

The relationship of light to space-time is described by the special theory of relativity, which is based on the notion that the laws of nature, including the velocity of light are identical for all unaccelerated observers. Special relativity - Wikipedia

To honour this constraint, communication between observers moving at different velocities requires a transformation known as the Lorentz transformation, which we may think of as an algorithm for transforming what I see when I look at something moving to what I would see if it was at rest. The Lorentz transformation honours the constancy of the velocity of light and establishes that the observed space-time distance between two events is the the same for all unaccelerated observers. Lorentz transformation - Wikipedia

The Lorentz transformation operates between observers in inertial motion. Einstein wished to identify the transformation between accelerated observers. His result is the general theory of relativity which is an algorithm for transforming the laws of nature between any two observers regardless of their state of motion. General relativity - Wikipedia

To achieve this generality, Einstein found that he had to abandon the notion of a fixed frame of reference which has been an essential tool for physicists since the time of Newton. Instead he used Gaussian coordinates and the notion that events only influence one another when they are in contact, that is when their local coordinates are identical.

We are quite familiar with this idea in everyday life. We do not navigate around the house using some abstract frame of reference, but by reference to all the things we can touch like doors, walls, cupboards and floors. Like the special Lorentz transformation, the general transformation preserves space-time distances but now the transformation between moving observers has become a function of the energy density of the neighbourhood rather than being constant throughout the Universe.

The 'big bang'

The initial system broke up into a vast number of subsystems in the course of the creation of the current Universe. We and the Solar system are examples of these systems which range in size from point particles like electrons to clusters of galaxies and beyond.

This process was accompanied by the emergence of three new interactions or communication channels, the strong interaction, the weak interaction and the electromagnetic interaction The strong and weak interactions have very short ranges and so are confined to the construction of small systems like atomic nuclei. Electromagnetism is similar to gravitation in having a potentially infinite range. It is the physical foundation of all the physical and biological systems of everyday interest to us. Strong interaction - Wikipedia, Weak interaction - Wikipedia, Electromagnetism - Wikipedia

Quantum mechanics

A system comprises two general classes of components which we often call hardware and software. The general idea is that the hardware is relatively permanent, the software can change. The software can change because the hardware has variable elements, like memory units, whose state can change independently of the overall structure of the hardware. Computer hardware - Wikipedia, Software - Wikipedia

The hardware and software embody the algorithm that the system executes, and represent the 'personality' of the system. The execution requires that the the system has symmetries, that is changeable elements or memories that can represent the state of the system at each point in its process. The symmetries are properties of the hardware which maintains the structure of its moving parts while they move relative to one another like the pistons, connecting rods and crankshaft of an internal combustion engine. Algorithm - Wikipedia

General relativity is built round one fixed point, the interval between two events, which remains unchanged no matter what state of motion we are in when we observe the interval.

Classical theories assume that we can stand back and look at things without becoming involved. Quantum mechanics, on the other hand, sees an observation as a conversation involving both the observed system and the observer. We have a similar trait. We respond to being 'looked at'.

Quantum mechanics is essentially the study of time, frequency or phase, that is of energy. Quantum mechanical states are represented by vectors in a Hilbert space. Each dimension of this space is represented by a basis vector with a particular energy or rate of change of phase. The relationship between energy and rate of change of phase is given by the Planck-Einstein equation, E = ℏν. We can represent a continuous spectrum of energy in a Hilbert space with an uncountable number of dimensions. When not observed, the quantum system is believed to evolve deterministically according to the continuous 'wave equation'. The overall phase of such a system is the linear sum of all its constituent phases.

Observation interrupts this process, and selects certain state vectors out of the unobserved superposition. The observer is itself a quantum system and the act of observation interrupts it too. What we find for an observation to take place is that both observer and observed must select the same orthogonal (independent) subset of state vectors to communicate. The quantum formalism shows us that these vectors are fixed points in the evolution of both systems. The quantum formalism shows us how to compute these fixed points. They are the eigenfunctions of the operator representing the observer. Different observers may observe different features of the observed system. Wojciech Hubert Zurek: Quantum origin of quantum jumps . . .

The system of the world

We are modelling the observable world as the fixed points in the dynamics of an underlying dynamic system, variously called God, Brahman, the initial singularity or the vacuum. The name is not important. Brahman - Wikipedia

Science has often run up against inconsistencies in its attempts to understand the world. These are solved by new models. Einsteins's special relativity, for instance, reconciled the movement of inertial frames with the constant velocity of light seen by an observer at rest in an inertial frame, regardless of the observers velocity relative to the source of the light.

We expect to overome such difficulties. Here we understand the reason for this to be the fact that the underlying dynamic system is a seamless whole like the God described by Thomas. The events we observe are stationary points in this dynamic system, and are constrained by the unity of that system to be consistent with one another. Our task is to see that consistency. Aquinas 13: Does God exist?

(revised 12 January 2019)

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Further reading

Books

Click on the "Amazon" link below each book entry to see details of a book (and possibly buy it!)

Hawking, Steven W, and G F R Ellis, The Large Scale Structure of Space-Time, Cambridge UP 1975 Preface: Einstein's General Theory of Relativity . . . leads to two remarkable predictions about the universe: first that the final fate of massive stars is to collapse behind an event horizon to form a 'black hole' which will contain a singularity; and secondly that there is a singularity in our past which constitutes, in some sense, a beginning to our universe. Our discussion is principally aimed at developing these two results.' 
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Tanenbaum, Andrew S, Computer Networks, Prentice Hall International 1996 Preface: 'The key to designing a computer network was first enunciated by Julius Caesar: Divide and Conquer. The idea is to design a network as a sequence of layers, or abstract machines, each one based upon the previous one. . . . This book uses a model in which networks are divided into seven layers. The structure of the book follows the structure of the model to a considerable extent.'  
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Links

Algorithm - Wikipedia, Algorithm - Wikipedia, the free encyclopedia, An algorithm is an effective method that can be expressed within a finite amount of space and time[1] and in a well-defined formal language[2] for calculating a function.[3] Starting from an initial state and initial input (perhaps empty),[4] the instructions describe a computation that, when executed, proceeds through a finite[5] number of well-defined successive states, eventually producing "output"[6] and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input' back

Aquinas 13, Summa: I 2 3: Does God exist?, I answer that the existence of God can be proved in five ways. The first and more manifest way is the argument from motion. . . . The second way is from the nature of the efficient cause. . . . The third way is taken from possibility and necessity . . . The fourth way is taken from the gradation to be found in things. . . . The fifth way is taken from the governance of the world. back

Brahman - Wikipedia, Brahman - Wikipedia, the free encyclopedia, 'Brahman (/Sanskrit: ब्रह्मन्) is a spiritual concept in Hinduism, and it connotes the highest Universal, the Ultimate Reality in the universe. It is, in major schools of Hindu philosophy, the material, efficient, formal and final cause of all that exists.[ It is the pervasive, genderless, infinite, eternal truth and bliss which does not change, yet is the cause of all changes.[ Brahman as a metaphysical concept is the single binding unity behind the diversity in all that exists in the universe.' back

Computer hardware - Wikipedia, Computer hardware - Wikipedia, the free encyclopedia, 'Computer hardware is the collection of physical elements that comprise a computer system.' back

Density matrix - Wikipedia, Density matrix - Wikipedia, the free encyclopedia, 'A density matrix is a matrix that describes a quantum system in a mixed state, a statistical ensemble of several quantum states. This should be contrasted with a single state vector that describes a quantum system in a pure state. The density matrix is the quantum-mechanical analogue to a phase-space probability measure (probability distribution of position and momentum) in classical statistical mechanics.' back

Electromagnetism - Wikipedia, Electromagnetism - Wikipedia, the free encyclopedia, 'Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles. The electromagnetic force usually exhibits electromagnetic fields such as electric fields, magnetic fields and light, and is one of the four fundamental interactions (commonly called forces) in nature.' back

General relativity - Wikipedia, General relativity - Wikipedia, the free encyclopedia, 'General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics. General relativity generalises special relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime. In particular, the curvature of spacetime is directly related to the four-momentum (mass-energy and linear momentum) of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of partial differential equations.' back

Gravitation - Wikipedia, Gravitation - Wikipedia, the free encyclopedia, 'Gravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped. Gravitation causes dispersed matter to coalesce, and coalesced matter to remain intact, thus accounting for the existence of the Earth, the Sun, and most of the macroscopic objects in the universe.' back

Lorentz transformation - Wikipedia, Lorentz transformation - Wikipedia, the free encyclopedia, 'In physics, the Lorentz transformation or Lorentz-Fitzgerald transformation describes how, according to the theory of special relativity, two observers' varying measurements of space and time can be converted into each other's frames of reference. It is named after the Dutch physicist Hendrik Lorentz. It reflects the surprising fact that observers moving at different velocities may measure different distances, elapsed times, and even different orderings of events.' back

Markus Possel, The elevator, the rocket and gravity, the equivalence principle, 'Einstein's first step towards that theory was the realization that, even in a gravitational field, there are reference frames in which gravity is nearly absent; in consequence, physics is governed by the laws of gravity-free special relativity - at least to a certain approximation, and only if one confines any observations to a sufficiently small region of space and time. This follows from what Einstein formulated as his equivalence principle which, in turn, is inspired by the consequences of free fall.' back

Mass - Wikipedia, Mass - Wikipedia, the free encyclopedia, 'In physics, mass is a property of a physical body which determines the strength of its mutual gravitational attraction to other bodies, its resistance to being accelerated by a force, and in the theory of relativity gives the mass–energy content of a system. The SI unit of mass is the kilogram (kg).' back

Particle Data Group. Lawrence Berkeley National Laboratory, The Particle Adventure, The Particle Data Group of Lawrence Berkeley National Laboratory presents an award winning interactive tour of quarks, neutrinos, antimatter, extra dimensions, dark matter, accelerators and particle detectors. back

Planck constant - Wikipedia, Planck constant - Wikipedia, the free encyclopedia, ' Since energy and mass are equivalent, the Planck constant also relates mass to frequency. By 2017, the Planck constant had been measured with sufficient accuracy in terms of the SI base units, that it was central to replacing the metal cylinder, called the International Prototype of the Kilogram (IPK), that had defined the kilogram since 1889. . . . For this new definition of the kilogram, the Planck constant, as defined by the ISO standard, was set to 6.626 070 150 × 10-34 J⋅s exactly. ' back

Quantum state - Wikipedia, Quantum state - Wikipedia, the free encyclopedia, 'In quantum physics, quantum state refers to the state of a quantum system. A quantum state can be either pure or mixed. A pure quantum state is represented by a vector, called a state vector, in a Hilbert space. . . . A mixed quantum state corresponds to a probabilistic mixture of pure states; however, different distributions of pure states can generate equivalent (i.e., physically indistinguishable) mixed states. Mixed states are described by so-called density matrices.' back

Software - Wikipedia, Software - Wikipedia, the free encyclopedia, 'Computer software, or just software, is a collection of computer programs and related data that provides the instructions for telling a computer what to do and how to do it. Software refers to one or more computer programs and data held in the storage of the computer for some purposes. In other words, software is a set of programs, procedures, algorithms and its documentation concerned with the operation of a data processing system.' back

Special relativity - Wikipedia, Special relativity - Wikipedia, the free encyclopedia, 'Special relativity . . . is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein (after the considerable and independent contributions of Hendrik Lorentz, Henri Poincaré and others) in the paper "On the Electrodynamics of Moving Bodies". It generalizes Galileo's principle of relativity—that all uniform motion is relative, and that there is no absolute and well-defined state of rest (no privileged reference frames)—from mechanics to all the laws of physics, including both the laws of mechanics and of electrodynamics, whatever they may be. Special relativity incorporates the principle that the speed of light is the same for all inertial observers regardless of the state of motion of the source.' back

State-space representation - Wikipedia, State-space representation - Wikipedia, the free encyclopedia, 'In control engineering, a state-space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations. "State space" refers to the space whose axes are the state variables. The state of the system can be represented as a vector within that space.' back

Strong interaction - Wikipedia, Strong interaction - Wikipedia, the free encyclopedia, 'The strong nuclear force holds most ordinary matter together because it confines quarks into hadron particles such as the proton and neutron. In addition, the strong force binds neutrons and protons to create atomic nuclei. Most of the mass of a common proton or neutron is the result of the strong force field energy; the individual quarks provide only about 1% of the mass of a proton.' back

System - Wikipedia, System - Wikipedia, the free encyclopedia, 'A system is a set of interacting or interdependent components forming an integrated whole.' back

Time dilation - Wikipedia, Time dilation - Wikipedia, the free encyclopedia, 'In the theory of relativity, time dilation is a difference of elapsed time between two events as measured by observers either moving relative to each other or differently situated from a gravitational mass or masses. An accurate clock at rest with respect to one observer may be measured to tick at a different rate when compared to a second observer's own equally accurate clocks. This effect arises neither from technical aspects of the clocks nor from the fact that signals need time to propagate, but from the nature of spacetime itself.' back

Weak interaction - Wikipedia, Weak interaction - Wikipedia, the free encyclopedia, 'In particle physics, the weak interaction (the weak force or weak nuclear force) is one of the four known fundamental interactions of nature, alongside the strong interaction, electromagnetism, and gravitation. The weak interaction is responsible for radioactive decay, which plays an essential role in nuclear fission.' back

Wojciech Hubert Zurek, Quantum origin of quantum jumps: breaking of unitary symmetry induced by information transfer and the transition from quantum to classical, 'Submitted on 17 Mar 2007 (v1), last revised 18 Mar 2008 (this version, v3)) "Measurements transfer information about a system to the apparatus, and then further on -- to observers and (often inadvertently) to the environment. I show that even imperfect copying essential in such situations restricts possible unperturbed outcomes to an orthogonal subset of all possible states of the system, thus breaking the unitary symmetry of its Hilbert space implied by the quantum superposition principle. Preferred outcome states emerge as a result. They provide framework for the ``wavepacket collapse'', designating terminal points of quantum jumps, and defining the measured observable by specifying its eigenstates. In quantum Darwinism, they are the progenitors of multiple copies spread throughout the environment -- the fittest quantum states that not only survive decoherence, but subvert it into carrying information about them -- into becoming a witness.' back

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