Limitations of Proofs & Theories, First published by Scribd in 2008

The Worldwide Acclaimed All Rights Reserved to Benjamin Gal-Or, 1968, 1972, 1981, 1983, 1987, 2007, 2008

Cosmology, Physics and Philosophy Benjamin Gal-Or, Vol. 4, Scribd, July 2008 Free, Core Curriculum Course (CCC), 207 pages

What Did van Gogh Imagine When He Painted This Picture?

Apparently he did not think that the field of gravitation has generated all.

Yet, his painting convey the ‘reality’ that all living and non-living systems are embedded in a 'field of brush strokes’, which, by themselves, in their very shape, direction and rhythm, convey the presence of flux, structure, cosmos and universal field of force, which penetrates all things and is at one with land, life, sky and the stars.

The telescope at one end of his beat, And at the other end the microscope, Two instruments of equal hope …

Robert Frost If you can look into the seeds of time, And say which grain will grow and which will not, Speak then to me …

William Shakespeare 1

All Rights Reserved to Benjamin Gal-Or, 1968, 1972, 1981, 1983, 1987, 2007, 2008

Evokes a person heart! Has generated a large number of responses from around the world, some declaring that it has turned them into “GalOrians”. Since the thought presented by this book is so rich, translators of our country should recommend this book with all their intellectual power.

Chinese Academy of Sciences A Master Piece. Any good library must have a copy of this Classical work. The well-known author bases his philosophy on a very sound knowledge of present-day scientific theories.

Indian Journal of Physics This is one of the most beautiful books that I have read.

Outstanding Books List Recommended by Encyclopedia Britannica, Nature, Philosophy of This is a great book, and an exciting book; readable, worth reading and enlightening. Sir Karl Popper We are all Gal-Orians. Foundations of Physics (Editor) Tour de force. A magnificent and sustained piece of work !

Sir A. Cottrell, Cambridge University Chancellor Appeals to scientists of all disciplines who are prepared to open their minds. Shines a welcome light in some dark corners of science.

Sir Karl Popper, in a Foreword, correctly describes it “a great book”.

New Scientist Gal-Or’s “beauty” has always been the object of science, which, he lyrically observes as “a most fundamental aesthetic frame of mind, a longing for the run-away horizons of truth and symmetry that we always M. Wickman, Order Amidst Chaos: try to reach.”

Enlightenment Aesthetics after Post-Modernity I do not know a better modern expression of science, philosophy and classical humanism than that of Gal-Or’s book. Hah-Arretz Daily The works of scientists like Gal-Or, Bohm, and (Noble Prize-Winner) Prigogine provide important resources. Prigogine's formalisms do not really tell us how irreversible change emerges from reversible [mathematics]. (in this Gal-Or is superior). Gal-Or assigns priority instead to general relativity and to gravity which drives the emergence of chemistry, life, and intelligence.

Philosophy of Science, Foundations of Social Progress

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5.3

One must always look beyond earth , the 5.1; 5.3 5.4 solar system , our galaxy and our 5.5 local group of galaxies , while comprehending about the dark-cold, 4.4 expanding-‘voids’-Space-1 that wraps 4.13 all superclusters of galaxies (Diagram below) and assessing its everlasting control on everyday life, and its origin (p.20; p.89).

The “Kingdom of Darkness” [‘voids’ in Figs.

1.1 & 1.2, p.4] illuminates some dark corners of science, and is more important, and interesting, as demonstrated by this book, than all the shining sources combined.

Our universe contains billions of gravity-structured galaxies (e.g., upper picture), each (e.g., right), containing billions of gravity-structured stars. Only Space-1 expands (Diagram & Figs. 1.1; 1.2, p.4). Without its expansion no process in the cosmos, including 4.1 life, is possible (p.9-13, 89). Gravity and Space-1-Expansion generate all chemistry , 4.3 plant and animal behavior (Chapter 6), black holes , time, biological time, brain-mind perceptions (p.12), orientation, written languages, socio-biological concepts [Chapters 5 & 6], gravity-natural-selection and key concepts in the ‘exact & life sciences’ and the ‘humanities’ (Chapters 1 to 8).

Non-expanding Space 3 wraps our galaxy 3

Space 1

Space 2

wraps clusters

DIAGRAM: Space-1-Expansion is the UNSATURABLE SINK for all energy pouring into 4.15 (a), (b), (c) it from all shining sources (p.4). It is composed of adiabatic envelopes 4.13; 5.5 that wrap all clusters and superclusters of galaxies [Fig. 1.2 below]. Gravity and 4.12 4.1;4.2 3.4 Space-1-Expansion generate all structures , chemistry , time-asymmetries , written languages and brain-mind perceptions (Parts A to D). This worldwide acclaimed

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All Rights Reserved to Benjamin Gal-Or, 1968, 1972, 1981, 1983, 1987, 2007, 2008 outlook (p.2) opens new intellectual horizons by crossing frozen disciplines and reassessing afresh key concepts in the ‘exact & life sciences’ and the ‘humanities’.

Fig. 1.1: Space-1 Genesis. Expansion of the previously opaque universe (Chapter 1, p.40) forms the shown expanding, cold ‘voids’ [SPACE-1, (Blue)] and hotter matter emitters of radiation in Spaces 3 & 2 (p.3). Space-1 was formed below 3000K (starting at 3.2 then around 300,000 years post Genesis). Photons, neutrinos and anti-neutrinos escaped from the newly-formed aggregations of nuclei, and were irreversibly absorbed in the newly-formed, unsaturable sink: SPACE-1 [Fig. 1.2 below]. About 2 billion years post Genesis, these gravity-induced, proto-massive-entities, were 4.2 already condensed and heated for nuclear fusion to start. This NASA picture shows that, on a large scale, the early universe was isotropic and homogeneous in terms of distribution of cold ‘voids’, hot matter-structures-emitters and their 4.1 maximum temperatures . There had been no net energy flow across adiabatic 4.15 envelopes in Space-1. [Cf. Fig. 1.2 below]

Fig. 1.2: The largest portrait of the universe [NASA]. The ‘voids’ that compose Space1 (dark-cold spaces observed in between shining filaments or clouds of superclusters), have increased in size (Cf. Fig. 1.1) These ‘voids’ are interconnected in Space-1.

Uniform maximum temperatures, isotropic & homogenous distribution of ‘voids’ & galaxies are preserved (CF. Fig. 1.1). No net flow of energy from one adiabatic 4.15 ‘envelope’ to another exists. These ‘envelopes’ wrap all superclusters. Studying one is similar to the difficult study of the whole universe. As a student, in 1958, I 3.4 discovered the origin of irreversibility & time-asymmetries by examining just one 28 4.3 such envelope (Appendix IV, p. 163). Above 10 K, at black-hole’s gravitational-energy

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All Rights Reserved to Benjamin Gal-Or, 1968, 1972, 1981, 1983, 1987, 2007, 2008 3.1-3.3

density, all fields-forces-interactions in nature are unified with ‘gravitation’ the sole origin of all structures since Genesis. [p.6; Table I & Assertion 1.1, p. 47]

3.3

--

Faust: 'Tis writ: 'in the beginning was the Word!'

I pause, to wonder what is here inferred?

The Word I cannot set supremely high, A new translation I will try.

I read, if by the spirit I am taught, This sense: 'In the beginning was the Thought'.

This opening I need to weigh again, Or sense may suffer from a hasty pen.

Does Thought create, and work, and rule the hour?

'Twere best: 'In the beginning was the Power!'

Yet, while the pen is urged with willing fingers, A sense of doubt and hesitancy lingers.

The spirit come to guide me in my need, I write, 'In the beginning was the Deed!'

Johann Wolfgang von Goethe Faust I. Transl. Philip Wayne (Penguin Classics, London)

SYNOPSIS I ________________________________________

More than ever before the recent discoveries in astronomy and space research have forced us to re-assess many of our fundamental concepts in most branches of science and philosophy. Nevertheless, the Einsteinian relativistic gravity3.3 and quantum physics3.2 remain two different physico-philosophical world outlooks that are in constant conflict with each other3.5.

The fundamental dispute splits physics into at least two unbridgeable systems of thought, each involving far-reaching implications in general science, philosophy and education.

The disputed differences are between Einsteinian gravity physics3.3, 3.5 and quantum physics3.2; 3.5. These may be referred to as Type I Disputes.

Type II disputes is mainly amongst proponents of string theories4.6 to 4.11 , the ‘cosmological constant’2.1 to 2.5; 4.5; 4.16, ‘dark matter’2.1 to 2.5; 4.17, 5

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‘pre-creation physics’, ‘pre-creation universes’ and the origin of irreversibility and time asymmetries in nature3.4; 3.5.

The Central Theme The Central Theme of both this course and world outlook include two Branches: In the ‘Exact & Life Sciences’ & in the ‘Humanities’.

The ‘Exact & Life Sciences’ Branch focuses first on failures to unify the fundamental forces-fields-interactions in nature3.1-3.5, while claiming that the key reasons for these failures are: (i) Attempts to unify fields-forces-interactions by false mixing of symmetric with asymmetric mathematics [Assertion S.1], instead of first unifying time asymmetries around verified general relativistic cosmology and Space-1-Expansion.3.4, 3.5, 4.15 (ii) Above 1028K, at black-hole’s4.3 gravitational-energy density, all fields-forces-interactions in nature3.1-3.3 are united within gravitation3.3 -the sole origin of all structures. [Table I, Chapter 1, p. 40; Assertion 1.1, p.47, Chapters 3 to 8; Footnotes 3.4, 3.5, 4.15, 4.6-4.12 and Volume I]

Assertion S.1 At gravitational-energy density of a massive black-hole4.3, but as a massive ‘white hole’, and above 1028K, all fields-forces-interactions in nature3.1-3.3 are unified in what has evolved to be recognized by us 13.7 billion years later as general relativistic gravitation3.3 -- the sole origin of all time asymmetries3.4 and structures; the starting theory of any attempt to unify physics. [Table I, Chapter 1, p. 40; Assertion 1.1, p.47, Chapters 3 to 8; Footnotes 3.4, 3.5, 4.15, 4.6-4.12 and Volume I]

Irrespective of any mathematical funambulism performed in a proof, or a theory, symmetry is always conserved in the equations.

If one starts with symmetric equations, the result can never be asymmetric. Space and time in fundamental physics are symmetric3.4. So are the laws of fundamental physics, except the 2nd Law of thermodynamics. Similarly, asymmetry is conserved.

Asymmetry can neither result from symmetry, nor vice versa.

(Yet, a Nobel Prize was awarded to I. Prigogine for presenting such a false ‘proof’ in violation of the laws of mathematics. Starting from Ritz wrongly attacking Einstein [1], all subsequent ‘Authorities’ have similarly failed3.4; 3.5; 4.6 'to 4.11. Endless publications in statistical & quantum mechanics rely on false mathematical ‘proofs’ and wrong verbal, pre-mathematical definitions [Chapter 4] that fabricate ‘proven’ origins of time-asymmetry and irreversibility in nature.)

See also Assertion S.3

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Beyond the issue of unifying fundamental physics [Chapter 3], this branch deals with astronomy, astrophysics, and cosmology [Chapter 4], gravityinduced orientation, balancing, socio-biology, biological clocks and some medical treatments. [Chapter 6; This Synopsis] as well as with the limitations of applied mathematics, mathematically-based definitions, statements, theories and computer ‘proofs’ [Chapter 8].

The ‘Humanities’Branch deals with the origins of linguistics [Chapter 6], world history [Appendix V] and a new world outlook ranging from Abrahamic religions [Appendix VI] to a fresh look on faith [Chapter 10, p.119]; from the origin of literature to a fresh view on socio-biology [Chapters 6, p.89 & 10]; from the origin of animal and human physiological structures to education. Nevertheless, this branch begins with gravity-induced physico-philosophical issues that are presented in the opening pages, this Synopsis and the Introduction (p.32). It then proceeds in Chapters 6 [p.89] & 10 [p.119], Appendix V (p.168) and Appendix VI (p.181). Beyond these one may consult Volumes I & II. [Cf. Table of Contents, p.20]

Recent Discoveries

Recent

astronomical discoveries combined with advances in gravitational socio-biology [Chapter 6, p.89 and Refs. 9, 50], have generated a revolution in our understanding of the most critical roles gravity has played from the early cosmos to the origin of life, language and brainmind perception of the world and everyday life.

The new discoveries have triggered a fresh world outlook that illuminates some dark corners of science and causes us to re-assess almost everything that we have so far taken for granted, including the apparent conflict between Genesis via astrophysics, astronomy and modern physics, and Genesis via the Bible. [Chapter 1, p.40; Appendix VI, p.181] In fact, the new discoveries in the remote external world, including those made in bio-satellites and the Hubble Space Telescope, have generated a revolution in our understanding of our external vis-à-vis internal world; a scientific revolution without parallel in the whole recorded history of mankind; a fresh look at nature, which opens up new horizons and generates new needs to reexamine all previous cosmological, biological, behavioral and philosophical convictions.

[Assertions S.2 and S.3]

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At the very core of this ‘external-to-internal’ revolution, we find gravity physics, gravitational-biology, Assertion S.2 gravity-perception, gravity-induced languages, Expanding Space-1 [Diagram, p.3] is gravity-induced socio- composed of expanding ‘voids’ [Fig. 1.2, biology, geo-biological p.4] and adiabatic envelopes 4.15 that are clocks and a new, gravityinterconnected. Chapters 1 to 8 essence of induced, explain and illustrate how all time natural selection in the asymmetries3.4 and irreversibilities in living and non-living nature are originated and caused by worlds [Chapters 2 to 8]. While Space-1-Expansion -- the universal, Einstein's general unsaturable sink4.4.

3.3, 3.5 remains the relativity This new world outlook [Ref. 13; 1958cornerstone of modern 1972] not only helps to unify physics cosmology and astrophysics; the [Assertion S.3], but extends beyond it into indispensable theory for the domains of socio-biology, history understanding most of the the realities of the arts and religions, new discoveries in including the asserted kind of DUALITY between science and astronomy, it is Newtonian gravity (that religion as different manifestations of is included as an one and the same reality.[chapter 10] approximation in General relativity) that affects much of our everyday life. [Chapter 6] Gravity, combined with updated observations in all fields of science, will guide us in structuring this book; starting from the very large cosmological structures and proceeding to the much smaller subatomic systems in which quantum physics still fails to explain the origin of time asymmetries and irreversibility in nature.

Can The Foundations of Science Be Deduced From Relativistic Cosmology?

Although some of the greatest scientists (from Newton to Einstein) studied cosmology and made substantial contributions to it - until recently it had a rejecting speculative image. Indeed, most scientists used to reject its importance, using such arguments as: Why rely on anything based on information that had originated in remote, personally inaccessible regions of space and time? Should not we first

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complete our local physics before we use strange astronomical data to reexamine the very foundations of science?

To begin with it should be stressed that such geocentric, or rather anthropocentric conceptions, are as common today as they had been in the times of Copernicus (who had dethroned the Earth and paid with his life for that), Shapley (who dethroned the Sun, but was not killed), and Baada (who dethroned our Milky Way, and nobody cared anymore). And they make cosmology and astrophysics difficult intellectual subjects, even to intellectually mature persons.

Indeed, astronomy, astrophysics and cosmology - unlike local physics, chemistry, and biology, are observational rather than experimental sciences, since they deal with objects at such great distances as to be beyond the reach of direct, Assertion S.3 man-made experimentation.

Moreover, until recently these observations have been too scarce, and the ratio of speculation to fact too high, for cosmology, astronomy and astrophysics to qualify as "hard sciences."

Recent discoveries in space, however, have transformed the situation by yielding solid new data and drastically circumscribing both speculations and physicophilosophical outlooks and models.

All attempts to unify the fundamental forces-fieldsinteractions in physics3.1 to 3.5 have, so far, failed3.5, 4.6 to 4.11.

Trying to unify fields-forces by false mixing of symmetric with asymmetric mathematics, instead of first unifying time asymmetries3.4 around verified (p.84) general relativistic cosmological asymmetry: Space-1-Expansion.3.4, 3.5, 4.15, is asserted to be the major source of failures to unify quantum physics with gravitation.[Assertion S.1]

This transformation is due largely to NASA’s Hubble Space Telescope, new infrared, radio and X-ray techniques, including the use of gravitational lens to study the ‘dark-age’ epoch of our cosmos when it was 200,000 to 500,000 years old.

The new discoveries of supernovae4.1, quasars4.14 and black holes4.3 in the centers of galaxies4.5, and before, in 1964, the background blackbody radiation4.12, have stimulated new interest in astrophysics, general 9

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relativity, relativistic cosmology, remote planetary systems, the formation of stars, galaxies, clusters and super-clusters of galaxies4.13.

Indeed, of late, we have witnessed a new revival of astronomy, general relativistic cosmology and astrophysics, a renaissance sustained by an almost daily inflow of verified empirical information on the dynamic universe around us.

To deny today the central role of astronomy, cosmology and astrophysics in modern science is to deny the very methodology of science, and to reject a large portion of its empirical evidence. Most important, gravitation3.3 is the most universal, all embracing, fieldforce-interaction in nature. Unlike quantum physics 3.2, it is scale-free, namely, it is not confined, or limited to any scale, as quantum physics is3.2; 3.5.

Gravity Vs. Heart Failure And The Biology of Our Musculoskeletal System The evolution and everyday functioning of our skeleton -- bones, legs, hips, joints, cartilages, ligaments, femurs, tibia, pelvis and muscles [64], has been "in response" to the force and direction of gravity.

Heart Failure vs. Gravity, say, in swollen legs, or flooded lungs cases involves the use of the gravity vector in medical treatments [64].

Nevertheless, the cardinal role gravity plays in the treatment of gravity-induced disorders in human biological systems, perception, health and longevity has been largely overlooked by health providers and bio-medical researchers, partly because the key role of gravity as the universal generator of all bio-structures, physiological forms, locations, disorders, orientation and organization has not yet been well appreciated. [9, 50, Volume I]

Gravity-Induced Socio-Biology & Brain-Mind Perception Gravity penetrates all space and all physical and biological structures. It affects all cells in our body-brain, as well as plant growth and animal and human orientation and behavior in everyday life [Assertion S.1; Parts A & B]. It also controls all ecological systems, while affecting the origin, growth and performance of cells in living organisms.

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We are the ashes of dead stars, the remnants of a supernovae4.1 that had exploded when the universe has already passed more than half of its present age. Except hydrogen and helium, all chemical elements in the cosmos, and in our body, had been originated inside supernovae. The sin of these exploding massive stars was to convert, by nuclear fusion4.2, their light chemical elements, (hydrogen and helium) to heavier ones [oxygen, carbon, nitrogen, etc.], more quickly than do smaller stars, like our sun.

It is always gravitation that plays the central role in the "selection" of the structures to be produced: First in controlling the cosmic expansion of inter-superclusters Space-14.4, then in forcing chemical evolution through a succession of specific reactions in which evolution means the development of complex elements from simple ones, i.e., of oxygen, carbon, nitrogen, silicon, etc. out of the hydrogen and helium in the stars4.1. [Hydrogen and helium make up about 99% of all observable matter in the universe. Hence, we and the planets in the solar system5.1, constitute just a little dirty stain in the vast ‘clean’ universe.]

Gravity is the only 'suitable' force that can build all the elements in the chemical periodic table by successively adding, in the hot interiors of active stars, small increments of mass and electric charge in selected combinations that are controlled by its force4.2. Thus, the building blocks of life had been originated by gravitation, and the entire evolution of life has since been controlled by it. [p.89] Following such cosmological expansion and massive stars explosions4.1, the newly formed chemical elements cool and may combine to form molecules in deep-cold space, which is not entirely ‘empty’. In fact, the first local "aggregates" of matter in the solar system already contained some simple molecules, including some based on carbon.

Again it was gravity that stratified all chemical compounds in ‘horizontal’ layers according to their specific gravity. Indeed, the geological strata of layers of rocks composed of one material, e.g., shale or limestone, lying between rock beds of other materials, have been structured by the "selective force of gravity”.

Life is strongly affected and shaped by gravity. Some specific organelles and nuclei in biological cells are "heavier" than the rest of the cell, and serve as prime gravity-orientators. Such gravity orientators-pointers also allow plants to grow "vertically upward".

Thus, gravity controls the direction of growth in roots, leaves, branches, etc. It also affects the movement of animals [50] in the sense 11

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of giving a common reference for orientation, 'balancing', â&#x20AC;&#x2DC;coordinationâ&#x20AC;&#x2122; 'walking', and space perception.

The response of living organisms to gravity may be initiated by changes in the distribution of pressure on sensitive locations, exerted either by the entire cell content, or by particles (statoliths) heavier or lighter than the surrounding cytoplasm. Gravity perception may also be caused by movements, or reorientation of such particles. Acceleration, by gravity, causes stresses to be set-up in cell membranes, or in the organ as a whole, which, in turn, generates a response vis-Ă -vis the gravity vector.

The Origin of Life and of Primitive Learning Since all plants and animals have evolved under the influence of gravity, their form and structural development are strongly shaped by this pointed force. In turn, they have "learned" to exploit it and even to cope with it - learned in the evolutionary as well as in the ontogenetic sense of the development of the organism.

The sensing devices which plants and animals use for "gravity receptors", "g-perception", "bioperception" ("gravity accelerometers", "gravity-induced biological clocks", etc.) are not yet well understood, even though a voluminous literature has been published on this subject.

But what we already know justifies the central role we expect gravity to play in life origin, control, orientation and adaptive processes. For instance, we know that if a growing higher plant is displaced with respect to the "upright" position, some tens of minutes later it will adapt its growth in such a way as to restore its original orientation in coincidence with the gravity vector. (If it is displaced only briefly and then restored to its original orientation well before the growth response can set in, it still responds to that displacement.) Indirect, gravityinduced orientation-adaptation of an organism may also occur when an organism orients itself by a gradient of density differences, or hydrostatic pressure.

The connection between gravitation and the origin of life, on one hand, and between gravitation and form, adaptive structure, growth rate, growth direction, adaptive behavior, navigation, and adaptive space perception, on the other, must therefore be studied. Indeed, a considerable empirical evidence has been accumulated so far on these 12

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subjects [50, Volume I] by biophysicists, biologists, plant physiologists, botanists, zoologists and neuro-physiologists.

The Origin of Life, Biological Clocks and Innate Perception The origin of temporal behavior in animals can be traced back in time and out to external physical influences. Even “innate patterns" are frequently associated with simple orientation movement in the field of gravity, i.e., as "upward-downward" ordering of biological systems in reaction to gravity. Consequently, gravity and geophysical periodicities emerge as prime sources of ordering, reproduction and simple orientation movements. Animals low on the evolutionary scale have a lesser adaptability to changes in the environment. Consequently, their dependence on heredity-geophysical-gravitational origins is high in proportion to animals high on the evolutionary scale.

Arrows of Time It takes us some measurable time 'to read' a word, a sentence, a page, or a book, and even more so to 'comprehend' its meaning. I term this elapsing time, and its pointed direction, the 'Linguistic Arrow of Time' and maintain further that each word and each sentence, generates an irreversible 'Structural Space-Time Arrow' in our mind and/or a 'Space-Aggregated-Asymmetric-Picture' which points from the writtentyped, form-configuration, or 'beginning', to their 'end' at the ‘right’ for Greek, Latin and English, etc., at the’ left’ for Hebrew and Arabic and ‘down’ for Chinese. Each letter-symbol, each word and each sentence is, therefore, an aggregated, configuration-boundary, gravity-oriented asymmetry on a page-space or on a computer display. Each generates an aggregated, configuration-boundary, gravity-oriented asymmetry in our brain-mind, where it is irreversibly recorded and associated with meaning introduced by education – the force that always controls the fate of nations, religions and civilizations. [Chapter 6, p.89 ]

Gravity-Induced Space-Time Perception Our perception of time, space, symmetry, asymmetry and direction are

similarly controlled by various gravity detectors (Chapter 5, p.89). These include displacement of cell parts, or of portions of multicellular structures, and intercellular structures. Much experimental evidence 13

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collected in spacecraft proves that there is a loss of orientability in growing seeds under weightlessness ['zero gravity']. Animals are no exception. Each of us is 'conscious' of the common "up-down" surroundings, and about "weight" and acceleration [Ref. 51].

We are born with innate gravity-sensors. Gravity-sensors also tell trees how to grow vertically up, even on steep mountainsides. All these are normal external experiences directly controlled by gravity. More specific examples range from inertial changes of the fluid in the vertebrate inner ear to a crystallizing suspension of organic spheres in water. The earth's gravitational field produces an elastic deformation that is readily observed through its asymmetric effect on the evolving crystal structure [Volume I]. These elastic forces play an important part in crystallized virus systems. Hence, the gravitational force provides not only a reference axis, but also a useful biological function that excludes foreign particles, such as antibodies, from a crystal. [Volume I].

Gravity-Induced Biosphere and Life The gravity-induced life envelope of earth, comprising a very thin layer (surface and lower atmosphere), was created by the "selective force of gravity". It is therefore gravitational selection that puts carbon, nitrogen, oxygen, water vapor and lightning at one and the same layer for the generation of the first DNA and the beginning of biological evolution. And it is gravitational selection that protected the early products of this evolution from damaging external radiation by supplying the upper protective layer of ozone. [Volume I] Biological detectors of sound modulation have much to do with sensors for earth gravity; both are special kinds of bio-accelerometers. In other words, gravity, bio-accelerometers and the various ways organisms are affected by vibration are interrelated. [Volume I].

Our Brain-Mind Perception As one reads this sentence, a corresponding aggregated asymmetry is

generated inside his or her brain-mind. To conform with innate [Kantian-like] and external experiences, and to communicate with our society, we introduce 'grammar' - that which keeps universal 'spacetime-order-of actions': What happened first, later, and in a 'universalfuture-tense order-of-things'. What is past for one person must be valid, fixed and confirmed by all else. In short; each word and each sentence, 14

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is equipped with an 'arrow of time' that 'forces order in our speech and life' and always points 'from past to future', and never in reverse.

To Conclude: Gravity generates structures and controls all geological layers and global phenomena ranging from mountain crests, tectonic folds, valleys, village and city structures, transportation systems, oceans and lagoons, to springs, wells, swamps, glaciers and rivers, as well as the ecological-systems connected with them.

Synopsis II

How To Use This Book ________________________________________________________ There is hardly any good reason to select a level prior to reading the first pages, Synopsis I and the 9 Assertions in the Introduction (p. 32).

Level I. This multiple level is composed of a few sub-levels that can be adapted to local cultural-educational needs according to the guidelines presented in the Introduction and Appendix I: Homework and Grading, especially if used in ‘Adult-Education’, or even in a ‘High-School-CCCC’ [Cultural, Core Curriculum Course].

Readers may range from high-school pupils to adults interested in updating and advancing their education by self-help [Assertion IN.3].

Level II: The ‘Undergraduate Level’ is suitable for a two-semester course that includes the use of Volumes I and II [See Table of Contents, p.20).

Comprehending the footnotes is recommended.

The autodidactive methodology [Assertion IN.3] should be used when there is no qualified CCC-Coordinator.

Level III. The Central Theme (p. 6) crosses frozen disciplines in both the ‘exact sciences’ and the ‘humanities’.

For graduate students this level is suitable for a two-semester course that includes selective parts of Volumes I and II, the footnotes and the Appendices provided here.

It is in Volume I where one finds mathematically-based theories, refutations of false ‘proofs’, critique of various ‘established’ theories, derivations of Einstein’s Field Equations [general relativity], quantumstatistical thermodynamics, Quantum Chromo-Dynamic [QCD], higher levels of philosophy and re-assessment of the nature of time, time arrows, linguistics and current studies of brain-mind aggregations-perceptions.

Volume II: Critique of Western Thought, provides six Lectures, mainly in the domain of the ‘humanities’. The autodidactive methodology [self-help] is best used when there is no qualified CCC-Coordinator, or when this book is used by faculty, independent scientists, people of the arts, theists, or dropouts, for themselves.

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The Origin of the Deepest Crisis in Education This broad subject is introduced in the Introduction and in its 9 Assertions.

It traces past educational cultures in order to formulate the aims, scope and foundations of this unified CCC. Pedagogical Features In writing this Volume IV, I continue the effort to simplify and update Volumes I & II and make them more suitable for a wider circle of readers, researchers, faculty and students. For that purpose I include new pedagogical features that help support the integration of this CCC with the new world outlook presented here.

The 1958 Discovery In 1958, by adopting the Einsteinian minority position as a student, I asserted that proponents of quantum statistical and probabilistic thermodynamics smuggle into their thermodynamic theories the result that they wish to prove, without declaring the contraband3.4. Similar charges are aimed today against proponents of string theories4.6 to 4.11.

[Appendix IV],

The Time Paradox To rise to the status of a scientific theory, a candidate must be supported by verifiable observations. Yet, in the actual world, there is a clash between theoretical, time-symmetric fundamental physics, and timeasymmetries observed in nature.3.4 The ‘exact sciences’ can be reduced to physics, and fundamental physics, at high energies, to just three fundamental forces-fields: The electroweak 3.1 , the strong 3.2 and the gravitational 3.3.

Over the last 100 years or so many have tried to develop ‘final’ proofs that would bridge these conflicting worlds of science. All in vain. Theorists select only prediction while ignoring the time-symmetric retrodiction, final conditions, etc.

Fig. 1.2 shows the expanding, cold ‘voids’ between shining superclusters of galaxies [Space-1, Diagram]. Uniform maximum temperatures, isotropic and homogenous distribution of voids/galaxies (on large scales) are preserved (Cf. Fig. 1.1). There is no net flow of energy from one adiabatic ‘envelope’4.15 to another. Such adiabatic configurations wrap superclusters of galaxies.

In 1958 I discovered the origin of irreversibility and time-asymmetries3.4 in nature by examining just one such envelope -- but around a cluster, not superclusters of galaxies [Fig. 1.2], which have been confirmed later – as explained in this book and in Volume I.

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All Rights Reserved to Benjamin Gal-Or, 1968, 1972, 1981, 1983, 1987, 2007, 2008

Being a student, and, later, an un-experienced professor, none wanted to listen to my central theme and non-conventional, general relativistic world outlook.

Most refrained to do that because it was based on general relativity and cosmology, both far beyond their knowledge.

That situation has changed in 1969 during the International Conference on Classical and Relativistic Thermodynamics [Pittsburgh, Ref. 13] that I had organized with the participation of some Nobel-Prize winners.

Worldwide acclaims started slowly after my Science and Nature papers in 1972 and the awarded Gold Medal from The New York Academy of sciences.[Ref. 13]. For more information see Appendix IV. Full worldwide acceptance has been delayed until the 80’s, with the publication of Volume I, and its subsequent editions.

(About Einstein's opposition to probabilistic quantum outlook of the world) Many of us regard this as a tragedy, both for him, as he gropes his way in loneliness, and for us, who miss our leader.

Max Born

You sadist. You make people think.

Ezra Pound

People are born ignorant, not stupid; It is education that makes them stupid.

Ancient Dictum published by Bertrand Russell

Man to the Universe: I Exist !

The Universe to Man: “So what ?”

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All Rights Reserved to Benjamin Gal-Or, 1968, 1972, 1981, 1983, 1987, 2007, 2008

Do most professors take closest to their heart the moneybox?

Priority in Parts A & B is assigned to relativistic as gravity physics3.3 applied to cosmology and to determinism over indeterminism. It is an unpopular thesis in which Einstein had been practically left alone.

To begin with, I visit his world outlook and use it to assess some new developments such as gravitational lens, new supernovae4.1 and string theories 4.6 – 4.11.

String theories are popular but are not science. They cannot even pass Popper’s Putting a Frame Around principle for being part of Does Not Make it a Unified Theory it.

They cannot be [From Am. Sci., Sigma Xi] verified by experiment and thus cannot even rise to the scientific status of being wrong [51, 53]. They justify Einstein’s claim: Quantum theory is not a complete theory.

Eventually realizing that Einstein has been right, armies of theoretical physicists work hard since his death to bridge quantum theories with general

18

All Rights Reserved to Benjamin Gal-Or, 1968, 1972, 1981, 1983, 1987, 2007, 2008

relativity by inventing various kinds, types and brands of unverifiable string theories4.6 – 4.11. All in vain.

The essence of Space-1-expansion [Diagram; Figs. 1.1; 1.2],

and of relativistic gravity cosmology, are not easy to grasp.

I shall therefore assume the position of a tourist guide of a Quantum Physicists Attack Symmetry Virtual Deep-Space Breaking Discovered in Tour [Chapter 7] aimed Quantum Kaonic Systems [CPT Breaking] at discovering the ORIGIN and CAUSE of radiation-energy gradients around stars, galaxies, clusters and superclusters of galaxies4.13; gradients4.13 that generate all irreversible processes in nature, including those that lead to life.

The key mission during the Tour is to search for ‘adiabatic envelopes’4.15 that wrap filaments or clouds of clusters or super-clusters of galaxies. These clusters and superclusters are like islands of non-expanding, gravity-bounded aggregations, in expanding, unsaturable sink. It is to this sink that all ‘solarwind-type’ of radiation-energy in the universe is irreversibly pouring in. Local quasars4.14 and black holes4.3 form additional, local sinks. Their ancestors, the massive gravitational aggregations4.1; 4.2; 4.5; 4.14, also had come into being by Space-1-Expansion. [Diagram p.3; Figs. 1.1; 1.2, p.3]. The universal sink is composed of a large number of interconnected ‘voids’ and adiabatic cells4.15 [Diagram, sites (a), (b), (c,] each imaginary adiabatic envelope ‘encages’ a super-cluster or superclusters of galaxies by no-net-flow of energy across its isotropic and homogeneous, large-scale, geometrical boundaries. [Fig. 1.2, p.4, p.3] During the tour I must cross frozen disciplines and bring home the evidence about the MASTER ARROW OF TIME [Volume I].

Back to earth I re-assess how gravity and Space-1-Expansion-Induced gradients (Diagram, p.3) cause not only all irreversible processes and timeasymmetries, but how they control ‘Gravity Selection’ and orientation that, in turn, control plant and animal behavior, languages and key concepts in the ‘exact sciences’ and the ‘humanities’ 1.1

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All Rights Reserved to Benjamin Gal-Or, 1968, 1972, 1981, 1983, 1987, 2007, 2008

CONTENTS OF THE FOUR VOLUMES Assertion 001 A ‘precise definition’ is often slippery, distorted or misleading. Contrary to intent, it may cause a large error. (Chapter 8, p.106). Nonetheless, we usually assume that we know exactly what we are defining, or talking about, until someone starts wondering, if at all: What is its complete meaning?

Our scientific-educational practice often begins a lesson, or a theory, by defining a symbol, axiom, or an object – the act that a priori erects a ‘fence’ around each: Anything outside that fence is, a priori, lost.

There is no fence outside the cosmos. [S. Hawking and his club (Appendix III, p.160), have claimed that they had invented ‘The Theory of Everything’. Indeed, it -35 accepts no fence for there is no one below their smallest ‘thing’ (10 meter) or outside the biggest one: the Cosmos. Nevertheless, they had to retract from that claim.

4.6-4.11 Moreover, their ‘string theories’ are not scientific [51, 53]. Their smallest scale is more than 15 orders of magnitude below any verification scale of any current --19 and expected -- experimental technique in science (10 meter).

Hence, it is better to begin this course and worldoutlook with key verified facts about the cosmos, and we already possess them. [Cf. Figs. 1.1, 1.2, p.4, and Table I, p.40], We can then work back and forth between these reliable facts and general relativistic cosmology, instead of with microphysics and then proceeding up the scale to explain the overall cosmic facts, for, unlike the strong force3.2 in quantum physics, gravitation3.3 penetrates all, is scale-free and constitutes the greatest macro builder in the universe. Moreover, according to the great Greek philosopher Plato: Everything is connected with everything else.

Therefore, any reliable definition must begin with 'the whole universe', or fail. [Chapter 4, p.70].

Mathematically-based theories that predict a new entity that is verified by independent experimentation, or astronomical observations, is an essential part of verifiable science. Otherewise it is neither complete nor in verified science. (Chapter 8, p.106]

VOLUME I Worldwide Acclaims ……………………………………...……… ii SIR KARL POPPER, Foreword ……………….……………..…. xx SIR ALAN COTTRELL, Foreword ………………….………..... xxi Preface ……………………………………..….……….…..……... xxii Introduction …………..………………………..………………….

1.1 The Revival of Relativistic Cosmology vs. Modified Concepts in Physics and Philosophy …………………...….…

1.1.1 The problem of ordering ……………………...….…

1.1.2 How did it all start? ………………………………...

1.1.3 The first seven stages ……………………………....

2 2 3 5 7 20

All Rights Reserved to Benjamin Gal-Or, 1968, 1972, 1981, 1983, 1987, 2007, 2008

2.2 2.3

2.4 2.5 2.6 2.7 3.1 3.2

1.1.4 The present matter-dominated era ……………………..

2.1 The Einsteinian Methodology: A Preliminary Remark .

The Withdrawal of Philosophy From Physics (and of Physics From Philosophy) …………………………….…...…

The Greatest Ambition of Physics ……………………..…......

2.3.1 Unification of initial-boundary conditions first?

Unification of fields second? …………………...…....

2.3.2 Should unification begin with differential equations? …………………..…….…...…

The Great Physico-Philosophical Gains From The Discovery of the Cosmic Background Radiation ………..

The Expanding Universe ………………………….…….…...

The 1977 “Aether Drift” Discovery ……………..………....….

Verification of Physical Laws by Astronomy and Astrophysics ……………………………………….……….…

Some Tentative Assertions …...……………………..…...…..

The Skeptic’s Outlook .……………………...………..…...…..

11 11 13 16 16 17 19 22 23 24 26 69

PART I: Preliminary Concepts 1.

From Terrestrial Gravitational Structures To Black Holes and Neutrinos in Astrophysics ……...…..

1.1 Gravitation, Asymmetry and Structure ……………….……

1.1.1 A fallacy associated with current theories ……..….

1.1.2 Gravity-induced sedimentary structures …………..

1.2 Stellar Structures and the Hertzsprung-Russel Diagram ….

1.3 Supernovae, Gravitational Collapse, Neutron Stars, Pulsars …………………………………….

1.4 X-Ray Astronomy, Binary X-Ray Systems, and Gravitational Clocks ……………………………………...

1.5 Black Holes …………………………………………….…

1.6 Gas, Dust and the Formation of Stars in Our Galaxy ….…

1.7 How Are Cosmic Distances Measured? …………………

1.8 Neutrino Astronomy and Astrophysics …………………

1.9 The Emergence of Gamma-Ray Astronomy …………….

1.10 Exploration of Extra-Solar Space

By Unmanned Spacecraft ………………………………..

2. From “Conservation” in Classical Physics To Solitons in Particle Physics ………………………..……

2.1 Aim and Scope …………………………………………...

74 80 80 81 88 92 100 106 113 116 130 132 134 136 138 21

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2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13

Limitations of Theory ……………………………………

The General Macroscopic Equation ……………………..

Continuity Equation (Total Mass Conservation) ………...

Conservation of Linear Momentum and Gravity.…………

The Navier-Stokes Equations and Gravity ……………….

Kinetic-Energy Equation and Dissipation Function in Gravitational Fields …………….

First Law of Thermodynamics or Energy Conservation Equation ……………………………………

First Law and Enthalpy …………………………………..

First Law In Terms of Temperature Field ………………..

Entropy Balance Equation ………………………………..

Beyond Classical Physics: Solitons, Antisolitons and Conservation ………………….

Neutrinos and the Powerful Role Conservation Equations Play in Subatomic Processes (Addendum) ……

140 142 146 147 149 152 154 156 157 159 160 163

3.

From General Relativity and Relativistic Cosmology To Gauge Theories ………………………….……………….. 166 3.1 Introduction ……………………………………………….... 167 3.1.1 Einstein’s field equations in general relativity ……….….. 169 3.1.2 Confirmation of Einstein’s Theory of Gravitation ………. 172 3.2 Principles and Formulations of General Relativity and Relativistic Cosmology ………………...…………………… 181 3.3 Observations, The “Age” of the Universe And “Equivalent Local Cells” …………………….……….… 200 3.4 Timekeeping, Accelerated Observers and the Principle Of Equivalence …………………………………… 204 3.5 From General Relativity to Unified Field Theories ………… 205 PART II: From Physics to Philosophical Crossroads and Back

4. The Arrows of Time …………………………………..….…... 214 4.1 Time and The Arrow of Time: The Most Distorted Of All Ideas? ………………………….. 215 4.2 Asymmetry-Symmetry-Space-Time and The Unification of The Laws of Physics …………………… 216 4.3 Methodology, Aim and Scope ……………………………… 217 4.4 Confusing Concepts of Time and Time Asymmetries ……… 219 4.5 The Entropic Arrow of Time ……………………………….. 222 4.6 Causality, Causation and Time Asymmetries ………………. 226 22

All Rights Reserved to Benjamin Gal-Or, 1968, 1972, 1981, 1983, 1987, 2007, 2008

4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18

Causation and Determinism in Relativistic Theories ………………………………………… 227 Cosmological Arrows of Time and Cosmic Time …………. 230 A Few Remarks …………………………………………….. 232 Time-Reversal Invariance and Irreversibility …………….… 236 Microscopic Time Asymmetries in “Elementary Particles” ………………………….……….. 240 The Death of Scale-Based Physics ……………….………… 242 The “Dual” Quantum-Geometrodynamical School and “Superspace” ………………………………….. 243 Tachyons and Causal Violations …………………….……… 246 Macrocausality and Microcausality in Quantum Mechanics … 247 Fading Memory in Classical Physics ……………………….. 247 Doubts As To The Universality of Entropy ………………… 249 Entropy-Free Thermodynamic Arrows of Time ………….…. 250

5. The Crisis In Quantum Physics ………………………….…… 254 5.1 Preliminary Review …………………………………….……. 255 5.1.1 The effect of gravitation and the outside world on quantum physics …………………………..…. 258 5.1.2 The three main schools of thought ………………….… 261 5.2 Einstein’s Objections to the Uncertainty Principle ………….. 262 5.3 The Heresy of a Few Skeptics …………………………….…. 265 5.4 Mythologized Concepts of Quantum Physics …………….…. 265 5.5 The Failure of Classical and Quantal Statistical Mechanics to Deduce Irreversibility and Time Asymmetries ……………………………………………….… 267 5.6 The Emergence of Quantum Chromodynamics And Super-Symmetry ………………………………………... 272 5.6.1 Spatio-Temporal Approach to Quantum Physics …….. 272 5.6.2 From Weinberg-Salam Theory to Quantum Chromodynamics …………………………... 273 5.6.2.1 Conservation laws as symmetry principles; and vice versa …………………………………... 273 5.6.2.2 Global, exact, approximate, isotopic and SU(3) symmetries ………………………..… 274 5.6.2.3 From SU(3) to renormalizable gauge theories ……………………………………….... 276 5.6.2.4 Quark confinement asymptotic freedom in gauge theories ……………………………. 276-1 5.6.2.5 QCD and the search for higher symmetry principles …………………………………… 276-1 23

All Rights Reserved to Benjamin Gal-Or, 1968, 1972, 1981, 1983, 1987, 2007, 2008

5.6.3 From Quantum Field Theories to Super-Symmetry Super-Gravity …………………………………….… 276-3 5.6.3.1 On the limits of super-gravity ‘unified field theories’ ………………………... 276-4 PART III: From Physics to Cosmological Crossroads and Back 6.

Cosmology, Physics and Philosophy …………………….

6.1 Reduction of Thermodynamics to Gravitation ………

6.1.1 Methodology ………………………………….

6.1.2 Dialectical gravitism: Definition of the first problems …………………………………

6.1.3 Gravitation as super-asymmetry ……………..

6.2 The Earliest and Most Universal Asymmetry: Observational Evidence …………………..…………..

6.2.1 Which space expands and which does not? ……

6.3 Gravitation-Asymmetry Principle of Equivalence …..

6.4 Can Intercluster Space Be Saturated With Radiation? .

6.5 Derivation of the Master Asymmetry From Gravitation Theories ………………………….

6.6 Irreversibility in the New Gravitational Cosmological Thermodynamics …………………….

6.7 Origin of Dissipation in Newtonian Fluids ………….

6.8 Terrestrial Thermodynamics …………………………

6.9 Connections With Classical and Continuum Thermodynamics …………………………………….

6.10 Electromagnetic Irreversibility And the Master Asymmetry ……………………...…..

7. Cosmological Origin of Time and Evolution ………………

7.1 Time: The All-Embracing Concept …………………..

7.2 Cosmological Origin of Time ……………………….

7.3 Cosmological Interpretations of Newton’s Laws of Motion …………………………………..….

7.4 Gravitational Origin of Structure and Evolution .……

7.5 Gravitation and the Outflow of Energy Into Un-Saturable Space …………………………………

7.6 Stellar Evolution …………………………………….

7.7 Terrestrial Evolution ………………………………...

7.8 Some Open Questions ………………………………

7.8.1 Microscopic T-Violation and the Master

277 277 277 278 279 279 282 284 287 290 293 297 299 301 303 308 309 310 314 316 322 324 325 326 24

All Rights Reserved to Benjamin Gal-Or, 1968, 1972, 1981, 1983, 1987, 2007, 2008

8.

Asymmetry: A possible Connection? ………..…

327

Black Holes and the Unification of Asymmetries ………

8.1 Introduction ………………………………………..

8.2 Observational Evidence ……………………………

8.3 Schwarzschild Solution and Black Holes ………….

8.4 Black Holes Mechanics and Entropy ………………

8.5 Can Black Holes “Evaporate”? …………………….

8.6 Primordial Black Holes? …………………………...

8.7 Back to the Melting Pot of Unification? …………...

329 330 331 332 340 341 341 341

PART IV: Beyond Present Knowledge 9.

Havahayism – The Science of The Whole …………..…… 348 9.1 The Futile Quest for Final Answers ……………….. 349 9.2 An Example in Havahayism ……………………..…. 350 9.3 From Cosmology to Irreversible Structures and Memory ……………………………………..…. 365 9.4 The Skeptic Outlook ……………………………..…. 415 VOLUME II

Critique of Western Thought Introduction …………………………………………………....

10.

420

A Few Historical Remarks on Time, Mind and Symmetry ………………………………………..…

437

The Philosophy of Time & Change: Some Historical Notions …………………….…………

455

Structuralism and the Divided American Thought: A Short Glossary of Terms ……………………………..

467

13.

Policy and Publicity: A Critique ……………………….

483

14.

Thought-Provoking and Thought-Depressing Quotations ……………………………………………….

495

Critique of Western Methodology ……………………..

530

11.

12.

15.

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All Rights Reserved to Benjamin Gal-Or, 1968, 1972, 1981, 1983, 1987, 2007, 2008

VOLUME III THE FIRST ONLINE DRAFT OF THE FREE CORE CURRICULUM COURSE

Cosmology, Physics and Philosophy Dec. 15, 2007, MSN SCRIBD

1. Introduction ………………………………………..…………… 11 2. From Cosmology to the Foundations of Physics ………..…….. 29 3. Gravity-Induced Brain-Mind Perception Vs. Everyday Life …44 4. How Did It All Start? …………………………………………… 55 5. ‘Gravitational Selection’ Vs. 'Natural Selection' ……….……... 64 6. Condensed World History …………………………………...… 69 7. The Skeptic Outlook ……………………………………….….. 94 8. Beyond Present Knowledge …………………………………… 100 9. CCC Homework ……………………………………………….. 103 References and Further Reading …………………..………….. 122

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All Rights Reserved to Benjamin Gal-Or, 1968, 1972, 1981, 1983, 1987, 2007, 2008

Cosmology, Physics and Philosophy Benjamin Gal-Or,

Vol. IV

[This Vol. 4]

Free, Core Curriculum Course (CCC), MSN SCRIBD, July 2008

Worldwide Acclaims [Part 1] ……………………..………..….....……

2

Illustrated Preface ………………………………………………………

3

Synopsis I ………………….……………………………………….….….

5

Synopsis II: How to Use This Book ………………………….…....

15

Contents Volume I ……………………………………………………..………………...….

Volume II ……..………………………………………………………………....…

Volume III ………………….……………………………………………...…..…..

Volume IV ……………………………………….………………………….….…

20 25 26 27

Worldwide Acclaims [Part 2] ………………… …………..….….…..

29

INTRODUCTION Notes to Readers, Students, Mentors and Professors ….…

32

Knowledge Is One. Its Division is Human Weakness; The Crisis In Education; The Temples of knowledge; Assertions I.1 to I.9

PART A

From General Relativistic Cosmology to Unified Physics 1. How Did It All Start? General Relativistic Cosmology ……….… 40 The New Astrophysical Time; TABLE I, Figs. 1.1 & 1.2 of the Universe

2. How All Life Would End? ………………………………………… 55 Recent discovery: The expansion of Space-1 is accelerating to a cold death of all life

3. The Greatest Ambition of Physics …………………………….... 60 Gravity, Electro-Weak, Quantum Physics; String Theories; Thermodynamics

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All Rights Reserved to Benjamin Gal-Or, 1968, 1972, 1981, 1983, 1987, 2007, 2008

PART B

From Cosmic Structures to Everyday Life and Back 4. Can The Foundations of Science Be Deduced From General Relativistic Cosmology? ……………………. 70 5. The 1958 Discovery of The Origin of Time-Asymmetries & Irreversibility ……………………………...………………………….. 81 PART C

Language, Brain-Mind Perception and Gravity 6. Test Your Mind; Bio-Sociology and Everyday life ……… 89 7. Virtual Deep-Space Expedition To Discover A New World Outlook ………………………………………… 101

PART D The Skeptic Outlook 8. Limitations of Mathematically-Based Theories ………... 105 9. The Biggest Clash between Science and Religion ……… 113 10. Dualities in Science, the Arts and Religions ……….……. 119

APPENDICES I:

Homework and Grading ……………………………………..... 123

II:

List of Nobel-Prize Winners by Country ……….….….…...... 125

III: The Pipa Prize to Stephene Hawking ………………………. 160 IV: Personally-Encountered Instructive Lessons ……………... 163 V: Condensed World History TABLE II …………….………...

168

VI: The Origin of Writing, Time, Religion and Literature … 181 VI: Names & Codes of God in Abrahamic Religions …….….. 191

References

….…………………………………………………..….……. 201

28 Credits & About the Author ………………………………………… 207

All Rights Reserved to Benjamin Gal-Or, 1968, 1972, 1981, 1983, 1987, 2007, 2008

Worldwide Acclaims

CONTINUES FROM PAGE 2

"The Judeo-Christian Tradition” is in accord with Gal-Or’s conclusions states Weisskopf and quotes: "Most astrophysicists, cosmologists and astronomers agree that the biblical account of cosmic evolution, in stressing `a beginning´ and the initial roles of `void,´ `light´ and a `structure-less´ state, may be uncannily close to the verified evidence with which modern science ha already supplied us" V.F. Weisskopf, Scientific American Gal-Or launchs a new spirit of inquiry by his excellent and thought provoking writings. I would recommend awarding a prize and would hope that this would serve to focus attention on a most important subject.

T. Gold, Cornell University One noted scientist [B. Gal-Or], even affirms that the stress placed by Genesis, Chapter one, on ‘beginning’ and the initial roles of ‘void’, ‘light’ and a ‘structure-less’ state, “may be uncannily close to the verified evidence with which modern science has already supplied us.”

Christian Apologetics, Journal A comprehensive explication of a large area of science which the reader may study in many subjects. Highly recommended to the philosopher of science.

Contemporary Philosophy An interesting and original book, easy to read, interesting and fascinating.

Nouvo Cimento This book has a wide-ranging scope. Dr. Gal-Or develops a philosophy of Space Science Reviews science which he calls Havahyism.

Smithsonian/NASA Astrophysics Data Systems A book like this should be in all libraries and in the hands of many astronomers.

Cornelis De Jager, Laboratory for Space Research, Utrecht, The Netherlands, Smithsonian/NASA Astrophysics Data Systems Interesting to read, integrating much of scientific material.

Deutsche Literaturzeitung One of the best books on the totality of the sciences & the universe/ It was one of the favorite books of Sir Karl Popper. It looks at physics and the universe as a totality of the mathematical philosophical understanding. It also combines the physical concept of time with human psychological perception and brain understanding of languages.

Robin (forumhub.com/expr/@202.54.92.222

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All Rights Reserved to Benjamin Gal-Or, 1968, 1972, 1981, 1983, 1987, 2007, 2008

Einstein's time-symmetric tensor was elevated by Gal-Or’s “New Astronomical School of Unified Thermodynamics” to the status of the source of “Master Asymmetry” controlling not only irreversible thermodynamics, but all physical and biological phenomena!

Gal-Or calls “GRAVITISM” (his philosophy) that gravitation is the prime cause of structures, irreversibility, time, geo-chemical and biological evolution -- that the expansion of the universe is the cause of the second law of thermodynamics -- that microscopic physics, and thermodynamics in particular, cannot be understood without reference to cosmology.

He ties “irreversibility” to the “expansion of space itself”, i.e. as far as space is expanding, the contribution of all kinds of radiation in space is weakened “irreversibly” due to the expansion phenomenon itself.

Such loss, or “degradation” of energy in the depth of inter-cluster expanding space, may then be considered as a universal sink for all the radiation flowing out of the material bodies in the expanding universe.

Advancement of Physics, APEIRON I have in the meantime studied your book, with great interest, and made pages of notes on it. I feel as if I had been on numerous walks and talks with you on the great questions, and know that would be great to go on with them!

Who cannot be impressed by your love for the great men of all times and all countries, by your phrase “working back and forth between theory and fact”, by your belief that philosophy is too important to be left to the philosophers, by your concern for where thought and language lie in the scheme of things – and by so much more!

I continue to reflect, again and again, on your central thesis that expansion is the origin of all asymmetry in time. What an ingenious phrase is your, “smuggle irreversibility in without declaring the contraband”!

I regard your book as seeking to accomplish two tasks – and being two books – at the very least.

One is the exposition of your central thesis, with clarity, and careful mustering of every argument pro and con that can lead to testable consequences.

I don’t see how it is possible to do proper justice to a thesis of such importance by mixing it in with the other great task. That is to give students an appreciation of the unity of philosophy and modern physics. You do both tasks far better than I could hope to. I give you my personal thanks for putting the two books into a package that I personally have found most thought-provoking.

John A. Wheeler Institute for Advanced Studies, Princeton

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All Rights Reserved to Benjamin Gal-Or, 1968, 1972, 1981, 1983, 1987, 2007, 2008

Gal-Or's remarkable book [Parts A & B] sees and seizes the world whole.

He emphasizes that all scientists operate under some set of philosophical prejudices, and that failure to acknowledge this is selfdelusion. Furthermore, he argues that a failure to attend to the philosophical base of physics leads to an empty scientism.

His work is challenging on many levels, constituting a review 'with derivations' of general relativity 'as applied to cosmology', thermodynamics, the current state of theoretical particle physics, astrophysics, as well as a summary history of western philosophy, 'especially the philosophies of time and mind' and critiques of western society, the intelligentsia and the relationship between academic science and government.

One 'and perhaps the central' theme explored, is that of the interplay between symmetry and asymmetry. His primary interest is not in the recent progress in the unification of forces in gauge theory, although he finds support in it for his Einsteinian outlook, but is rather time, time's arrow, and the asymmetry between past and future. Around time are accumulated discussions, both mathematical and philosophical, of thermodynamic reversibility, time reversibility, the nature of causality, and the use of advanced and retarded solutions to wave equations.

The second major theme is that of gravity and its overwhelming domination of the actual form of the universe, at all scales. The combination of these themes is not accidental; they are point and counterpoint to his thesis that the time asymmetries are connectable to and perhaps even determined by the master asymmetry given by the gravity of general relativity: the remorseless cosmological expansion.

He argues that only the expansion can provide the unification of time asymmetries.

The expansion provides, among other things, an for radiation, which, in turn, permits the establishment UNSATURABLE SINK of gradients in temperature and density, which provide the basis for the physical process that leads to life.

He also criticizes the sloppy and improper use of the concepts of entropy 'and the related notions in information theory' and quantum indeterminism, especially as covers for an inadequate understanding of temporal asymmetries. Taking an Einsteinian position on the interpretation of quantum mechanics, he looks forward to revitalization of Einstein's quest for a deterministic interpretation of quantum events.

The value of this book lies in the challenging combination of ideas which Gal-Or presents, which goes far beyond what can be sensibly described in a review. [This] work may be too large to digest as a text in these days of the decline of academic institutions "as GalOr describes them", but that will be the loss of both the faculty and the students.

AMERICAL JOURNAL OF PHYSICS

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All Rights Reserved to Benjamin Gal-Or, 1968, 1972, 1981, 1983, 1987, 2007, 2008

Introduction Notes to Readers, Students, Mentors and Professors I.1

The Road to Hell is Paved with Good Intentions

At the beginning of my first professorship position (at the Johns Hopkins University), I was so absorbed in polishing and re-polishing my first lecture that I completely forgot to go to the classroom and teach it.

About 30 minutes past the time, while I was still working hard in repolishing the lecture, a shy student opened the door of my office to politely inform me that 5 minutes ago all students had left the classroom. The whole university laughed.

Years ago, I tried to simplify Volume I and adapt it for easier reading by all readers and by students outside the domains of physics and philosophy. Being a prisoner of the style, quest and mission of Volumes I, it was almost impossible to simplify and abridge the 300 mathematical equations and 520-pages. That draft was therefore abandoned and forgotten.

In December 2007, a shy student informed me that he could not understand the physico-mathematical themes presented in Volume I, and therefore signed-out of the CCC where it was used.

My immediate reaction was to publish, on December 15, 2007, the unfinished draft as a Free, Online Volume III. Six months later this revised version has become this online book. However, it has not yet been polished and re-polished. Anyway, all mistakes are mine.

*

*

*

Until around the mid-Thirties of the previous century, Core CulturalCurriculum Courses (in Europe!) were made as â&#x20AC;&#x2DC;scientificâ&#x20AC;&#x2122; as possible, and science propped up its foundations by turning to philosophy. This attitude was in part motivated by the desire to 32

All Rights Reserved to Benjamin Gal-Or, 1968, 1972, 1981, 1983, 1987, 2007, 2008

appropriate the sciences with the great ‘prestige’ of philosophers, and for the philosopher the fast-growing ‘status’ of science.

Hence, European professors vied with one another in presenting science based on high philosophical grounds, and philosophy as a ‘science among sciences’, or even as the ‘sum of the other sciences’.

Assertion IN.1 Knowledge is One. Its division, a human weakness; its aim, a universal beauty; an aesthetic frame of mind; a longing for the run-away horizons of truth and symmetry that we always try to reach.

Modern physics is a picture of reality; not the house-in-itself.

It is a man-painted picture of Knowledge awaiting to be discoverd.

A ‘PhD’ was then a bona fide Philosophy Doctor, a person of advanced core knowledge and eloquence outside his specialism.

Western education has since withdrawn from the game.

Empty specialism has since gained the highest prestige, especially in the U.S.; no longer do professors need borrow it from philosophy, nor to teach Core Curriculum Courses [CCC].

Assertion IN.2 The origin of our aspirations to advance interconnected thinking is not known.

What we know is that it is not rooted in “well-fenced” traditions and “accepted” disciplinary sciences.

Indeed, contemporary teachers and professors vie with one another in presenting Our educational mission is to fragmented, technical lectures bridge fragmented courses in devoid of interconnected modern curriculum courses, content, for they can no longer with an all-embracing outlook, hope to achieve popularity by and adapt it to face the everinjecting updated core growing needs of narrowing knowledge into what has specialism. gradually become an ever narrower, disciplinary professionalism.

This turn of events has resulted in overvaluation of technical professionalism, empty academicism, absolutation of ever-narrower 33

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disciplines, and the common inclination to reject bona fide core knowledge from the class. A pity. For these trends only push the young into cynicism, nihilism and feelings of emptiness in education and in society at large.

I.2

Interconnected Thinking, Teaching and Research

Although most academic teaching and research must be distributed amongst various departments of a university, there is an objective need to regenerate an old tradition that cannot be associated with any specialism, because the ideas with which it deals are common to all studies, or not involved in any. Accordingly, the selection of interconnected kernels of updated knowledge to be included in this book is based on an interconnected approach to what I consider a much needed, simplified CCC book for all.

Assertion IN.3 The greatest challenge in aquiring updated, verified knowledge and the ability to be intellectually independent, is self-removal of externally-imposed disciplinary borders while working hard, often alone, as an AUTODIDACT.

The Current Crisis in Education is not subsiding. More than ever before it demands answers, reassessments, a neo-philosophy and acts: How to teach mutual interactions instead of linear causality; structured complexity instead of summation of events; structured historical buildup of facts, instead of summation of isolated events.

Modern skepticism is usually the negation of a core, interconnected, educational methodology. Not so with Einstein's skepticism.

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To start with, Einstein advocated the total removal of borders between traditional disciplines.

The current academic crisis, especially in the U.S., may be moderated by using the Einsteinian methodology, at least as properly adapted CCC series provided in high-schools and, on structured higher levels, in undergraduate and graduate schools.

Such a methodology may lead to new, interconnected fertilization between the most promising kernels of fundamental knowledge, and, thus, to the potential to rejuvenate educational methodology by resorting to an old-new world-outlook and practice.

Assertion IN.4 Without a Guiding-Structuring Theme, or at least a Unified World Outlook for gaining an all-embracing, interconnected cultureknowledge that crosses frozen disciplines, any CCC is nothing but a pity encyclopedia displayed by a specialist nominated by “Organizers” as the “CCC-Coordinator”, who remains helpless in teaching the alluring beauty of mathematics, physics, the life sciences, and comparative religions but fails to perceive their profound educational implications to all, as a whole.

Assertion IN.5 Structuring an all-embracing CCC-Outlook is a matter entailing far more ambiguity than the technicalities of the application of any disciplinary course and its “Academic Credit Regulations”.

Assertion IN.6 Students are often discouraged by their professors and mentors from asking fundamental, interdisciplinary questions in class, as a result of which inconsistent, or outright incorrect premises, are given a better chance of perpetuating themselves.

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I.3 Our Temples of Knowledge Literary intellectuals, the ‘humanists’, people of the arts and most educators are currently ignorant of modern advances in the ‘exact sciences’, of their mathematical formulations, experimental, observational and verification methods. They are likely to resort to an a priori, or superficial answers to complex problems whose detailed implications are beyond them.

Similarly, faculty, ‘experts’ and professionals in the “exact sciences”, via their past, evernarrowing, disciplinary education, are currently ignorant of the wide-span knowledge, literature, arts and history that are needed to share their thinking and aspirations with other thinking persons.

Literary intellectuals at one pole – at the other scientists, and as the most representative, the physical scientists.

Between the two a gulf of mutual incomprehension – sometimes (particularly among the young) hostility and dislike, but most of all lack of understanding.

C. P. Snow, The Two Culture Cambridge University Press [33]

Assertion IN.7 Students flood colleges and universities with the hope of finding there the grand outlook of a spacecraft.

Entering our temples of knowledge they settle for that of an eagle, but what they often find is that of a specialist gopher.

The resulting gap can hardly be bridged despite the fact that our globe is currently an interconnected village, internationally linked by what might be expected to bridge old gaps between cultures, languages, religions and educational disciplines.

Nevertheless, the facts are that deep divisions keep deepening and deserts of narrow specialism keep spreading more than ever before. A sad fact. A dark future.

I.4

From General Relativistic Cosmology to Re-Assessing The Foundations of Science, or Vice Versa?

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In selecting knowledge kernels to be included here, I am simultaneously faced with Assertion IN.8 subjectivistic and objectivistic discourses; Large cosmological systems subjectivistic, because all dominate smaller ones, not vice thought is, to some extent, versa. [Assertion 001, p.19] Vindicated ordered by personal bias; by empirical data that span a broad objectivistic, because all range of modern astronomy, rational empirical knowledge astrophysics, physics, biophysics, singles out regularity and socio-biology, history and order ranging from the archeology, this assertion is objectivistic origins of employed here to arrive at some anything in the world, to the new concepts in a fresh world subjectivistic perception of outlook on science, philosophy the individual ‘Here-Now’. and beyond.

Nevertheless, the following issues may also need to be encountered: Should this course be directed from ‘innate’, or ‘a priori ideas’ of subjective human knowledge, to ‘external’ objective concepts? Or vice versa?

Should a bona fide CCC begin by updated, key, verified facts and discoveries and their origins and vindications by modern empirical knowledge? or by unverifiable string 4.6-2.11 that attempt to theories unify all fundamental forcesinteractions in physics? 3.1-3.3

Assertion IN.9 Thanks to the subdivision of knowledge into fragmented ‘disciplines’ and ‘territories’, we often fail to perceive the interconnectedness between ‘selfcentered’, or conflicting outlooks, to judge their collective importance and to estimate their inherent structure, inner logic and ordering.

In trying to overcome this lacuna, I begin this book with cosmology and its distorted image among scientists and laypersons.[Assertion 001, p.19]

Einstein’s failed attempts to unify [deterministic] gravity physics3.3 with [non-deterministic] quantum physics3.2, have played a major role in structuring this book. Both drive the (unpopular) philosophy to rejuvenate and bring closer together interconnected educational methodologies in the ‘humanities’ and the ‘exact sciences’.

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Conclusion: The guiding philosophy and practice of bona fide CCCSeries are too important to be left to the sole care of disciplinary experts.

I.5 Survival of a Civilization and Education Both culture and civilization are precarious. Their survival depends on innovation and inner morality a splendid minority maintains with incalculable effects these have had upon all well being of academia, government and socio-economic of each country at all times. It is therefore pertinent to investigate how, where and when such rare developments occur or are subdued.

The origin of this problem is intimately linked to the noninterconnected moral roles played by some scientists, politicians, large companies lobbyists and law manipulators in our civilization today.

A contemporary lobbyist can only deal with problems by applying those disciplinary methods and non-interconnected moral codes that are familiar to him or her through the non-philosophical (and sometimes anti-intellectual) methods of current education.

The resulting vicious cycle opens unbridgeable gaps between the â&#x20AC;&#x2DC;professionalsâ&#x20AC;&#x2122;, and, gradually, isolates each. It is this separatism that causes declining standards, empty government and the current crisis in education.

Most students today participate in fragmented courses of disciplinary professionalism that leave them with a feeling of inner cultural emptiness in academia. In fact, what they find in the temples of knowledge is bureaucracy, inertia, nihilism, careerism, populism and irresponsibility of the faculty to provide them with what would make them bona fide cultured persons.

Wondering about their lost dream in the temples of knowledge, some promising students ask: Has the Time for Cultured Mentors in Academia Passed?

An ambitious student, who commences his/her studies in the firm belief that much of the fundamental-core knowledge of our 38

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civilization is comprehended by at least most faculty, is extremely perplexed to discover, sooner or later, that the professors are uncertain about the fundamental, interconnected meanings of what they teach in class.

Other, who seek explanations about the world at large in which they live or about the worlds at small that compose the world at large, realize that it entails sub-terrainian links between an undeclared philosophy of fragmented education as adhered to nowadays by most.

That mundane philosophy of education is bound to confront intellectually starving students. Sensing that, the intellectuallystarving students often give up, or blame themselves unnecessarily for their inability to grasp what their mentors dismiss as trivial.

A splendid minority of bright students dare to continue, by themselves, the interminable search, which calls for questioning, reexamination, screening, and at times radical rejection of ‘accepted’, or ‘established doctrines’ that fail to justify themselves through their own logic, consistency, universality and testability.

Int.1

Footnotes presented in this volume are often interconnected. They have been included to detail or illuminate some specific subjects, disputes and issues that are related the Central Theme.

But no footnote can be considered as “Introduction to”, “Review of”, or “History of” the “Disciplinary Domain” it deals with, or refers to.

Without resorting to any mathematical equation, a few footnotes dealing with specific subjects stand about ‘midway’ between mathematically-formulated concepts provided in Volume I, and the abridged-simplified ones adopted here. Reference to them is marked as: […] 1.1, 1.2, …, 2.1, 2.2, …, or as […]AII.1; AII.2, …, namely, located in Chapters 1, 2, … etc., or in Appendix II, etc., respectively.

Int.2

References are minimized for reasons elaborated below. The few provided at book-end are marked as […][1, 2, …] or Ref. 11, etc.. Selection of what to read and what to study, and in what order, depends on the reader’s interests, background and on a qualified CCC-coordinator, if there is one.

Adding extensive bibliography may be confusing or misleading; there is always a temptation to be “in” regarding what has recently attracted popular attention. There are also the ‘name droppers’, the ones who wish to impress others, or put them down, if they have not heard about their last peer-circle annual meeting, or what the ‘name dropper’ had picked up in a party, committee, a club, or the media.

No science is immune to the infection of politics and the corruption of power.

Jacob Bronowski 39

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8 Limitations of Academic Definitions and of Mathematically-Based Theories

8.1 "Provable By Theory" Applied mathematics is the key tool of ‘exact sciences’. It constitutes a special kind of 'intelligent thinking’ that is integrated with its ‘universal grammar' -- a sort of critical thinking which has been partially developed to safeguard our minds from prejudices and inconsistencies. Yet, consistency, by itself, is a two-sided issue, as I shall briefly review next..

A "mathematically-based theory" is considered "consistent" if it never proves a contradiction. In formal logic, both mathematical statements and proofs are written in a symbolic language, whose validity and proofs rest on a theorem that follows from the starting list of axioms.

Such a proof may also be validated by a computer, and such programs are available. A theory is a set of statements, some of which are taken as valid without proof (axioms), and others, the theorems, are taken as valid because they are implied by the axioms. A complete and consistent set of axioms for all mathematics is impossible. "Provable by theory" means "derivable from the axioms and primitive notions of the theory, using logic.”

8.2 Tarski's Indefinability Theorem According to this theorem No sufficiently powerful language is strongly-semantically-self-representational. Namely, arithmetical truth cannot be defined in/by arithmetics.

Accoriding to Smullyan[42], Tarski's Indefinability Theorem is somewhat superior to the famous Gödel's Incompleteness Theorems [Refrs. 33-43], which are more related to mathematics and less to a wide range of philosophical issues and languages. Tarski's theorem is not directly about mathematics but about the inherent limitations of 40

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any formal language that is strongly-semantically-selfrepresentational when it contains predicates and function symbols defining the semantic concepts specific to that language.

8.3 Gödel's Incompleteness Gödel [Refrs. 33-43] has demonstrated that conventional mathematics, which we tend to consider as a supremely logical and consistent system, involves paradoxiacal, self-referential statements about itself, i.e., a conventional mathematical system, say, the mathematics of flat space in the Euclidian geometry -- an ‘absolute stage’ on which Newtonian gravity and physics stands, can be incomplete because one has not discovered all its necessary axioms.

In computer science, for instance, one can never create a complete and consistent finite list of axioms, or even an infinite list. Each time that one adds a statement as an axiom, there will be other correct statements that cannot be proved, even with the new axiom.

Moreover, if the system can prove that it is consistent, it is not. As might have been expected, this idea has been much debated by mathematical philosophers: How can a theory be both correct and unprovable?

Is mathematics a loop of our mind?

Is the mind a self referential loop?

Gödel's first incompleteness theorem shows that any system that allows one to define the natural numbers is necessarily incomplete: it contains statements that are neither provable correct, nor provably false. Some scholars therefore argue that this refutes the logicism of Gottlob Frege and Bertrand Russel, who had aimed to reduce/define the natural numbers in terms of logic. Not all axiom systems satisfy these hypotheses, even when these systems have models that include natural numbers as a subset. For example, there are axiomatizations of ‘flat’ space that do not meet the hypotheses of Gödel's theorems.

Another limitation applies only to systems that are used as their own proof systems. Gödel's theorem has another interpretation in the language of computer science. Theorems are computably enumerable: one can write a computer program that will eventually generate any valid proof. One can then ask if it has the stronger property of being recursive: Can one write a computer program to definitively

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determine if a statement is true or false?

Gödel's theorem says that you cannot. His theorems, however, are confined to sufficiently strong axiomatic systems, i.e., that a theory contains enough arithmetic to carry out the proof of the incompleteness theorem. Some scholars claim that Gödel's incompleteness theorems have provided a deadly blow to David Hilbert’s program towards a universal mathematical formalism.

Nevertheless, the essence of these issues is much more complicated, as shown next.

Undecidable Statements: A statement is neither provable nor refutable. Hence, some scholars resort to the concept "independent". but, that concept is also ambiguous.

Meta-Language: A sufficiently developed language cannot represent its own semantics. Any meta-language includes primitive notions, axioms, and rules absent from an object language. Theorems provable in a meta-language are not provable in the object language.

“Truth”: Some of the aforementioned theorems may presuppose that mathematical "truth" and "falsehood" are well-defined in an absolute sense, rather than relative. If an axiomatic system can be proven to be consistent and complete from within itself, then it is inconsistent.

Minds and Machines: Gödel's incompleteness theorems may also reflect on human intelligence. While Gödel's theorems cannot be applied to humans, since they make mistakes and are, therefore, inconsistent, it may be applied to the domain of science. Sets of expressions are coded as sets of numbers. For various syntactic properties (such as a formula, a sentence, etc.), these sets are computable. And any computable set of numbers can be defined by some arithmetic formula. There are various additional theorems and sub-theorems 34-49. I do not intend to expand on them in these pages, for these pages are mainly written for the general reader, without resorting to any mathematics. We therefore move next to elaborate on some more practical domains in the mined fields of verifiable scientific theories and proofs.

Pure and Applied Mathematics attempt to stay aloof and beyond human emotions and ambitions. It protects one from making mistakes, prior to and aft writing down a single mathematical equation. How 42

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mathematics -- combined with verifiable observations -- help protect the human mind from falling into unverifiable traditional dictums or ‘intuitively’ generating mistkes is demonstrated by the following dramatic event in the history of science; when Einstein had concluded that his [tensorially based8.3] field equations of general relativity3.3, our most universally verified theory of acceleration and gravity, harbors a mistake. To correct that ‘mistake, he forced on these equations a ‘correction number’, called the cosmological constant.

Luckily his tensorial field equations were flawless, despite the fact that a cult of believers in its unverifiable interpretations has evolved during the last 90 years or so, telling us about an imaginative need to leave that artificial constant in Einstain’s field equations.

8.4 Space-Time and Symmetry-Asymmetry The deep essence and the fundamental meaning of curved space-time, symmetry-asymmetry, statistics and probabilities are understood only by a portion of scientists. A much smaller portion, or, in fact, a splendid minority, maintains that probabilities, statistics and quantum postulates provide them with no ‘free will’ [1.11].

8.5 Differential Equations Vs. Observations It is in the unique domain of mathematics that time-symmetry, reversibility and the symmetrical laws of physics serve us as key tools to better understand nature, despite the limitations mentioned above.

And it is only by combining (conceptual, reversible, analytic) timesymmetry with (factual, aggregated, observational) time-asymmetry, or by combining reversible equations with a priori known, factual, initial and boundary conditions, that one may, mathematically, arrive at a reliable world outlook in agreement with observations/experimentations. For more information see Refs. 7, 8.

While symbols and analytical concepts may be symmetric, words and sentences (in order, syntax, phoneme, form, sound modulation or other modes), or ‘useful’ physico-mathematical equations, are basically asymmetric. Mathematics, gravitation, symmetryasymmetry, aggregation, time and meaningful sentences are coupled.

While some minor reservations are justifiable, there is an overwhelming "word of evidence", derived from physics, the languages and the studies of linguistics, cybernetics, information and mathematics, that fortifies this contention.

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8.6 The Popperian Falsification Principle The greatest living philosopher of science in the last century, Sir Karl Popper, has introduced the Falsification Principle about the ability of mankind to establish what is science and what is non-science, in addition to what might be ‘true’ within the domain of a given theory, or a set of ‘facts’, axioms or definitions Scientific theories can be falsified by irrefutable, multiple evidence.

They are, therefore, falsifiable. As to the great dispute in physics between deterministic general relativity3.3 and probablistic quantum theories3.2, Popper strongly disagreed with Niels Bohr’s physicophilosophical interpretations and supported Albert Einstein's realist approach to determinism and scientific theories about the universe and its contents and processes.

Applied mathematics is often used to cross disciplinary borders.

However, some use it as a cover to advance their subjectivistic, unverifiable claims, proofs and ‘theories’. The examples provided in footnotes 3.4 and 3.5 illustrate how -- by a priori selecting only timeasymmetric mathematics, or time-asymmetric mathematical solution that fits with their desired ‘proof’ – they easily fool themselves or others.

‘Pure mathematics’, is often develped for its own sake, without a priori harboring intentional applications, although they may be ‘uncovered’ later.

According to Einstein, when we predict the behavior of a specific or confined set of natural phenomena, we usually mean that we have found a ‘constructive theory’ covering this set. When we find that other sets of phenomena are incompatible with that theory, we tend to either generalize or modify it, or failing that, seek an alternative one.

To this ‘constructive’ category Einstein opposes the so-called “theories of principles” (exemplified, according to Einstein, by thermodynamics and the general theory of relativity), whose point of departure and foundation are not hypothetical constituent, but empirically observed general properties from which mathematical formulae are deduced so as to apply to every case of observation which presents itself. Thus, according to Einstein, the merit of constructive theories lies in their comprehensiveness, adaptability, and clarity for a given set of phenomena, while that of the “theories of 44

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principles” -- in their logical ‘perfection’ and universality and in the vast observational spectrum of their formulation at any scale and time.

Yet, Einstein did not trust some semi-hidden aspects of his own general theory of relativity2.5. Two such events are described next: The failure of statistical mechanics (both classical and quantum) to deduce and explain the origin of irreversibility, time-asymmetries, cosmic and local structuring, generation of order and what is called “entropy growth” -- as well as its philosophical and applicative limitations and lack of large-scale universality -- has been explained in footnotes 2.5, 3.4 and 3.5 as well as in Volume I. Indeed, Einstein had not suspected that his general theory of relativity already incorporates another ‘theory of principle’: Thermodynamics, especially the so-called Second Law of Thermodynamic. Namely, the foundations of thermodynamics are NOT a separate, stand-alone, theory of science; it is NOT fragmented from the rest of physics. It constitutes an integral part of gravity-induced, interconnected, unified physico-philosophical knowledge.

8.1

Scalars are numbers, ‘constants’, or measurable quantities that one can count. They harbor no direction in space, time or space-time. Algebra and calculus belong to this domain, and both constitute boring subjects to most students, and to me. An example is speed.

8.2

Vectors are scalars and other entities that harbor direction in space, time, or space time.

These are frequently used as the ‘first derivatives’ of entities, physical or imaginative, in space, time, space-time or higher dimensions. An example is velocity.

8.3

Tensors There are various types of tensors. This footnote is confined to Einstein’s stress tensor, or metric tensor, which allows anyone to express the same laws of physics, namely, they should be the same for any observer in the universe: Rotating, standing still, moving linearly at constant speed, accelerating, standing on a tiny, or a massive planet, or near a star or a blackhole4.3, i.e., under different gravitational fields (different curved space-times). In Einstein’s General relativity3.3 they express mathematical derivatives in 3 space coordinates and a single time coordinate. Additional dimensions may be used, for instance, in String theories4.6-4.11. Tensors constitute a sort of translators that define that what one observes and measures, say, in a flat space-time, harbors the same FORM in any and all other curved space-time points [observers].

Tensors are, therefore, the reliable translators from one set of coordinates, say, a set used by a rotating observer, to those used, say, by an observer ‘falling’, or fast accelerating into a black hole, or ‘standing’ on the planet Jupiter.

Thus, metric tensors express a theory by resorting to a single universal language. In Einstein’s Filed Equations they can all be arranged on one side of these equations, then equaling zero [invariant] for any observer. We may judge that result as a ‘symmetric invariance’.3.4 8.4

Life Quality and Scientific Progress. Anyone who claims to function without reliance on a philosophy is self-deluded. Life quality, happiness and all scientific progress, advance, stagnate or decline under the domination of a philosophy, whether declared or undeclared.

In Science: To undertake any study in science one must consciously maintain a philosophy and not pretend to avoid it. It is in science that we are guided by two principles: One, empirical, according to which the conclusions drawn from a theory must be confirmed by experience, the other, semi-

45

All Rights Reserved to Benjamin Gal-Or, 1968, 1972, 1981, 1983, 1987, 2007, 2008 logical and semi-aesthetic, according to which the fundamental laws should be as few and as unified as possible and compatible with logic. Bold and adventuresome philosophical speculation is at best self indulgence, a passing culture occurring when anyone speaks a language that is neither accessible to, nor intended for empirical verification and the unity of knowledge. (Assertions IN-1 to IN.9) Empirical and speculative methodologies must seek to comprehend nature, by putting it all together in the service of repeatable verification, exactitude and the unity of human thought. In seeking to comprehend nature we must bear in mind, on one hand, that the greatest snare for creative thought is uncritical acceptance of traditional assumptions, and, on the other, that new philosophies are not necessarily more advanced than old ones.

It is meaningless to ask: What is the world made of? What are things-in-themselves?

Materialism, idealism, positivism, string theories and the like are isolated over-simplifications in a pluralistic science and philosophy. Actual scientific and philosophical works require the simultaneous use of several concepts and methods. This pluralism explains why a given scientific theory can be considered “valid” and yet relative, rather than absolute. All theories teach us only interconnections between different descriptions of one and the same reality; all are nothing but shadows of reality painted with words and symbols. [Chapter 10] We have found a strange footprint on the shores of the unknown. We have devised profound theories, one after another, to account for its origin.

At last, we have succeeded in reconstructing the creature that made the footprint; and lo! It is our own.

Eddington While I extract pleasure from such flowery prose, I cannot agree with the implied conclusion. It is not only ‘our footprint’ that counts. There are other ‘footprints’. One may find them anywhere in nature; ‘on the shores of the unknown’, on the beaches of Florida, or in the fields of facts related to past world times prior to the emergence of life on this planet. And they do not solely belong to man, nor to any ‘quantum-physics observer’.

Man is neither the center of the universe, nor the sole ‘footprint maker’ in it. When we examine the faint radiation that arrives from the depth of space-time; a non-living world space-time that had existed before life emerged -- before any ‘quantum-physics observer’ has been introduced into our science by theorists on this planet, we cannot affect any reality on that far-away emitter of the radiation we observe here-now on earth.

Anthropomorphism and subjectivism would not advance us far away. They can only prevent us from opening gates to new horizons, or block the doors leading to the advancement of updated, verified-unified, single world knowledge.

Readers of these volumes may see that one way in which I have tried to bridge our awareness of interconnections between fragmented disciplines of ALL our knowledge, is to make these unbridgeable disciplines a little easier to comprehend, by anyone, as they are -- under the same roof -- through the use of the most unifying agent in the entire universe: The Gravity-Induced World Outlook.

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References I shall make you love books more than you love mother, and I shall place their excellence before you.

A scribe is the task-must of everyone.

Father to Son in the Middle Kingdom of Egypt (Papurus Saller I)

1. W. Ritz, Phys. Z. 9, 903 (1908); A. Einstein, ibid. 10, 185 (1909); ibid. 10, 323 (1909); A. Friedman, A: Über die Krümmung des Raumes, Z. Phys. 10 377– 386 (1922), (English translation: Gen. Rel. Grav. 31, 1991–2000 (1999)); E. Hubble, A Relation between Distance and Radial Velocity among ExtraGalactic Nebulae, Proceedings of the National Academy of Sciences of the United States of America, Volume 15, Issue 3, pp. 168-173 (1929) 2. E. Schrödinger, Space-Time Structure, Cambridge University Press (1950) 3. C. W. Kilmister, Eddington's search for a fundamental theory. Cambridge Univ. Press (1994) 4. H. F. M.Gönner, On the History of Unified Field Theories. Living Reviews in Relativity (2005) 5. D.J. Schwarz and B. Weinhorst, (An)isotropy of the Hubble diagram: comparing hemispheres", Astronomy & Astrophysics 474: 717–729 (2007) 6. D. L. Wiltshire, Exact Solution to the Averaging Problem in Cosmology, Phys.

Rev. Lett. 99: 251101 (2007).

7. D. Zwillinger, Handbook of Differential Equations (3rd edition), Academic Press, (1997) 8. A. D. Polyanin and V. F. Zaitsev, Handbook of Exact Solutions for Ordinary Differential Equations (2nd edition), Chapman & Hall/CRC Press (2003) 9. J. Tou, et al, Models to Study Gravitational Biology of Mammalian Reproduction, Biology of Reproduction Vol. 67. (2002) 10. S. Perlmutter et al. (The Supernova Cosmology Project) Measurements of Omega and Lambda from 42 high redshift supernovae, Astrophysical J. 517: 565–86 (1999).

11. Adam G. Riess et al. (Supernova Search Team) Observational evidence from supernovae for an accelerating universe and a cosmological constant Astronomical J. 116: 1009–38. (1998); M. Gasperini, et al, The pre-Big Bang Scenario in String Cosmology, Physics Reports, Vol. 373, 1-212 (2003) 12. On HYPATIA: Grand Commentaire, de Théon d'Alexandrie aux 'Tables faciles' de Ptolémée, Livre II, III, Vatican City (1985, 1991); Commentaries de Pappus et de Théon d'Alexandrie sur l'Almageste Tome III. Théon d'Alexandrie, Rome (1943); The calculation of an eclipse of the sun according to Theon of Alexandria, in Proceedings of the International Congress of Mathematicians, 1, 209-219, (1950), Providence (1952); de notre ère (Marinus de Naplouse - un commentaire au 'Petit commentaire' de Théon), Janus 63 (13), 167-184 (1976); Théon d'Alexandrie et les 'Tables faciles' de Ptolémée, Arch. Internat. Hist. Sci. 35, 114-115, 106-123 (1985); 'Commentaire à 47

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l'Almageste' de Théon d'Alexandrie, Antiquité Classique, 56, 201-218 (1987); O. Neugebauer, A history of ancient mathematical astronomy, New York, (1975); A. Khan, Hypatia; Authorhouse, (2001); M. Dzielska and F. Lyra, Hypatia of Alexandria, Revealing Antiquity, No. 8, Kessinger Publishing, (1997); K. Chares, Hypatia: New Foes with an Old Face, Kessinger Publishing (1997); A. Margaret, Hypatia’s Heritage: A history of Women in Science from Antiquity Through the Ninetheenth Century; Hypatia: A Journal of feminist philosophy, Indiana University Press; I. Mueller, L.S. Grinstein & P.J. Campbell Women of Mathematics: A Biobibliographic Sourcebook.

New York: Greenwood Press, (1987); M. M. Mangasarian, The Martyrdom of Hypatia (1915); J. Bregman, Synesius of Cyrene: Philosopher-bishop, University of California Press (1982); A. Fitzgerald, Letter of Synesius of Cyrene to

Hypathia, London (1926); M. Dzielska, Hypatia of Alexandria. Oxford Press (1996); J. J. O'Connor & Edmund F. Robertson Hypatia of Alexandria, MacTutor history of mathematics; M. B. Ogilvie, Women in science: Antiquity through the nineteenth century. MIT Press (1986); Hypatia Physics, culture and sense of duty, Spanish university association that defends science, knowledge, public university and public policies (2006); T L. Heath, A History of Greek Mathematics, Oxford (1921); A. Tihon, and I. Le Livre (eds.), Notes sur l'astronomie grecque au Ve siècle; W. Müller, Das isoperimetrische Problem im Altertum mit einer übersetzung der Abhandlung des Zenodoros nach Theon von Alexandrien, Sudhoffs Arch. 37 39-71 (1953); P. Pingree, An illustrated Greek astronomical manuscript: Commentary of Theon of Alexandria on the 'Handy tables' and scholia and other writings of Ptolemy concerning them; J. Warburg, Courtauld Inst., 45, 185-192 (1982); Recently published Reports by the Department of Mathematics, St. Andrews University in Scotland, UK. 13. B. Gal-Or, [Editor] A Critical Review of the Foundations of Relativistic and Classical Thermodynamics, Pittsburgh, Pa. April 7-8 (1969), Mono Book, (1970); Cosmology, Physics and Philosophy (CPP), Springer Verlag, New York (1981, 1983, 1987 editions); On The Origin of Irreversibility, Science, 176, 11-17 (1972); 178, 119 (1972); Nature 230 (1971); 234, 217 (1971); Entropy, Fallacy, and the Origin of Irreversibility: An Essay on the New Astrophysical Revolutionary School of Thermodynamics. Annal. N.Y. Acad.

Acad. Sci., 196 (A6) 305-325 (1972); Cosmological Origin of Irreversibility, Time and Time-Anisotropies- I, Found. Phys. 6, 407 (1976); 6, 623 (1976); 7, 50 (1977) 14. M. Hadley, The Logic of Quantum Mechanics Derived from Classical General Relativity, Foundations of Physics Letters, 10, No. 1, 43 (1997) 15. I. Prigogine, A. C. Eringen, P. Fong and B. Gal-Or, Panel Discussion, pp.

505-507, “A Critical Review of Thermodynamics”, Proceedings, International Symposium, A Critical Review of the Foundations of Relativistic and Classical Thermodynamics, Pittsburgh, Pa. April 7-8, 1969, Mono Book, (1970) 16. A. Strominger and C. Vafa, Microscopic Origin of Bekenstein-Hawking Entropy, Phys. Lett. B379 1996; J. D. Bekenstein, Black holes and entropy, Phys. Rev. D 7, 2333 (1973); Ph.D. Thesis, Princeton University 1972; S. W. Hawking, Annal. N.Y. Acad. Sci. 224, 268 (1973) 17. M. Sachs, Quantum Mechanics and Gravity, Springer, 2004 48

All Rights Reserved to Benjamin Gal-Or, 1968, 1972, 1981, 1983, 1987, 2007, 2008

18. T. de Chardin, Pierre Teilhard. The Making of a Mind: Letters From a Soldier-Priest 1914-1919. Harper & Row, Publishers (1961) 19. H. de Terra, Memories of Teilhard de Chardin. Harper & Row, Publishers (1962) 20. M. Devitt, Realism & Truth. Princeton University Press (1984) 21. R. Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness. Oxford University Press (1994) 22. H. Reichenbach, The Rise of Scientific Philosophy, University of California Press (1951) 23. C. D. Rollins, Editor. Knowledge and Experience, University of Pittsburgh Press (1966) 24. L.D. Landau and E.M. Lifshitz, Statistical Physics (Addison-Wesley, Reading (1969) 25. A. Pais, Subtle is the Lord: The Science and Life of Albert Einstein Oxford (1982) 26. B. Zwiebach, A First Course in String Theory, Cambridge University Press 2004 27. A.S. Eddington, The Nature of the Physical World, MacMillan, NY, Cambridge (1929), 28. J.A. Wheeler and R.P. Feynman, Rev. Mod. Phys. 17, 157 (1945); 21, 425 (1949) 29. A. Benson, The True Origins of Christianity and the Bible, Prudential, Clovis, CA, 1999 30. P. N. Strearns et al, The Encyclopedia of World History, 6th Edition 31. J. Hartley, Contemporary Physics, Vol. 45 (6) ( 2004) 32. C. P. Snow, The Two Cultures and A Second Look, Cambridge University Press (1964) 33. K. Gödel, Über formal unentscheidbare Sätze der Principia Mathematica und verwandtr Systeme, I. Monatshefte für Mathematik und Physik, 38: 173-98 (1931).

34. J. van Heijenoort, From Frege to Gödel: A Source Book on Mathematical Logic. Harvard University Press: 596-616 (1967).

35. G. Boolos, A New Proof of the Gödel Incompleteness Theorem, in Boolos, G., Logic, Logic, and Logic. Harvard University Press (1998).

36. H. Putnam, Minds and Machines in Sidney Hook, ed., Dimensions of Mind: A Symposium. New York University Press (1960).

37. J. B. Rosser, Extensions of some theorems of Gödel and Church, Journal of Symbolic Logic 1: 87-91 (1936).

38. J. van Heijenoort, Gödel's Theorem in Edwards, Paul, ed., Encyclopedia of Philosophy, Vol. 3. Macmillan: 348-57, (1963).

39. D. Hofstadter, Gödel, Escher, Bach: An Eternal Golden Braid. Vintage Books (1979).

40. R. Rucker, Infinity and the Mind: The Science and Philosophy of the Infinite.

Princeton Univ. Press (1995).

41. R. Smullyan, Godel's Incompleteness Theorems. Oxford Univ. Press (1991).

42. H. Wang, A Logical Journey: From Gödel to Philosophy. MIT Press (1997) 43. S. Peter,. An Introduction to Gödel's Theorems. Cambridge University Press (2007).

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All Rights Reserved to Benjamin Gal-Or, 1968, 1972, 1981, 1983, 1987, 2007, 2008

44. E. J. Masoro and S.N. Austad (eds.): Handbook of the Biology of Aging, Academic Press (2006).

45. J. D., Rowe and R. I. Kahn, Human Ageing: Usual and Successful. Science, 237, 143-149 (1987) 46. F. Philip, Einstein: His Life and Times, Alfred Knopf (1953, 1972) 47. J. E. Lidsey, et al, Physics Reports, Vol. 337, 343-492 (2000) 48. A. Vilenkin, Many Worlds in One: The Search for Other Universes. New York: Hill and Wang, 235 (2006) 49. R. Serway and J. Jewett, Jr., Physics, for Scientists and Engineers, with Modern Physics, 6th Edition, Brooks/Cole, pp 1273-1275 (2004) 50. R. H.Anken, Gravitational Zoology: How Animals Use and Cope with Gravity, Hinrich Rahmann (2001) 51. L. Smolin, The Trouble with Physics: The Rise of String Theory, the Fall of a Science, and What Comes Next. New York: Houghton Mifflin, 392 (2006).

52. B. Gal-Or, Vectored Propulsion, Supermaneuverability and Robot Aircraft, Springer Verlag (1990) 53. P. Woit, Not even wrong: the failure of string theory and the search for unity in physical law, New York: Basic Books (2006) 54. Adam G. Riess et al. (Supernova Search Team) "Observational evidence from supernovae for an accelerating universe and a cosmological constant", Astronomical J. 116: 1009–38 (1998) 55. R. G. Crittenden & Turok N., "Looking for Lambda with the Rees-Sciama Effect", Phys. Rev. Lett., 76, 575 (1966) 56. J. Hogan, "Unseen Universe: Welcome to the dark side", Nature 448 (7151): 240–245 (2007).

57. S. Weinberg, Anthropic bound on the cosmological constant, Physical Review Letters 59 (22): 2607–2610 (1987) 58. J. Polchinski, String Theory, Cambridge University Press (1998) 59. P. Binétruy, Supersymmetry: Theory, Experiment, and Cosmology, Oxford University Press (2007) 60. Dine, Supersymmetry and String Theory: Beyond the Standard Model, Cambridge University Press (2007) 61. M. Gasperini, Elements of String Cosmology, Cambridge University Press (2007) 62. C. Johnson, D-branes, Cambridge University Press (2003) 63. K. Becker, et al, String Theory and M-Theory: A Modern Introduction, Cambridge University Press (2007) 64. M. H. Beers (ed.) MERK Manual of Medical Information, 2nd Home Edition, pp. 15, 138, 300-308 (2003)

Credits Most photographs are acknowledged as due to the general courtesy of NASA’s FREE-TO-THE PUBLIC service, as this volume IV is. Some pictures were taken by the author. Most figures, diagrams and 50

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caricatures are taken from the unabridged VOLUMES I and II [Ref. 13]. The List of Nobel Prize Winners by Country has been provided free by Nobel-Prize Selection Committees and has been reproduced by Wikipedia â&#x20AC;&#x201C; The Free Encyclopedia.

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