The General Theory Of The World In a Nutshell
From Quantum Waves to the Linguistic Connection:
A Supertheory Unifies Knowledge and Generates a Theory of the World
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Western science began about 2,600 years ago when the first scientists - the Greeks of Miletas - Thales, Anaximander and Anaximenes - rejected the myths of their day and assumed, instead, that the world was lawful, causal or nonmiraculous. They specifically assumed that everything in the world results from motion differentiating a conserved primordial substance.
Two questions arise. First, is this principle powerful enough so that a proper theory of the world can be deduced from it, as ordinary geometry can be deduced from Euclid's five axioms? If so, The Hellene's Lawfulness Principle would be far more than a principle, it would be the Axiom of the World. Second, it has long been debated whether such a thing as a theory of knowledge exists, which might organize a comprehensive theory of the world.
When these matters are formulated mathematically, a theory of knowledge is obtained which acts like a World Program. It constructs, by rote, a general theory of the world and all subordinate theories, from quantum and relativity theory to sociology and grammar. Moreover, everything follows from the Hellenic Lawfulness Principle, which, therefore, is the World Axiom. What makes such a sweeping organization of the world possible is the startling finding that a lawful world must be a certain kind of system which evolves simply by exploring all the ways the motion of a primordial substance can build all possible structures, as though the world results from a bang on a drumhead which runs through its possible motions.
In addition, language is, itself, a system which evolves in the same way, that is, by combining and relating in all possible ways certain elementary words representing substance and motion. Using an unfamiliar word, we can say that the world is a Double Combinatorial System, once physical and once linguistic. We will outline this theory of the world in two parts to obtain: 1. A theory of knowledge and 2. A general theory of the world. We will see that the two theories are fully verified, for their multitude of detailed predictions are born out.
Reduction and Deduction
Compression of a world theory into an axiom is analogous to compressing the physical world into a single quantum particle at the time of the Big-Crunch. Theory reduction and physical reduction are analogous abstract and concrete Big-Crunches, respectively. Conversely, abstract expansion from the world axiom to a world theory is analogous to the physical expansion of the world from the Big-Bang to the ensuing evolution. Consequently, there are two Big-Bangs - and Big-Crunches - one abstract or linguistic and one concrete or physical, one deductive and one physical.
Members of the literary culture often refer derisively to reduction as 'reductionism'. To be sure, there is plenty of flawed reduction. But to exclude it altogether is to exclude reasoning, since the inverse of reduction is expansion or deduction. It is often overlooked that "The whole is equal to the sum of its parts plus their relations". If a biochemist reduces a living cell to its molecules, he will recover the living cell, provided he combines the molecules in their correct relations, both internal - the shape - and external. Otherwise, the world would be miraculous and mankind could prove God's existence experimentally.
Lawfulness and Simplicity
A lawful world is also foundationally simple. Arbitrary complexity would mean unlawfulness. Among other things, simplicity means that no given structure can be admitted into a lawful world, for that complexity would then have to be analyzed. This would lead to either an endless series of analyses or to the admission of miracles. Instead, a lawful physical world must be derived entirely from combinations of inherently stable wave systems in a structureless primordial substance. Like a vibrating drumhead, motion in a lawful world must drive all possible wave systems in a primordial substance to form all possible stable structures permitted by the attributes of the primordial substance and motion. These attributes are specified by World Constants. (As used here, the term 'world' is synonymous with 'universe', with a small 'u', meaning the knowable, lawful, causal and nonmiraculous.Κ 'Universe', with capital 'U', refers to the 'world' plus an indeterminable unlawful exterior).
The Language-Physics Connection
Stability in physical systems ultimately arises for the same reason that musical waves have a fundamental frequency and reinforcing harmonic multiples. If two wave trains are in-phase, they add or reinforce each other. Otherwise, they cancel and disappear. The result of this selective elimination and reinforcement is quantization and the formation of stable discrete harmonic wave systems. Consequently, stabilization and quantization of structures are related aspects of wave motion.
Just as the physical world builds up entirely as a hierarchy of quantized wave elements producing stable concrete structures, so language, which is used to represent the world, is built from analogous discrete word elements producing a hierarchy of stable abstract structures.
Enter Leibniz
A system which evolves simply by filling its possibilities - and doing so discretely - was first called combinatorial by G.W. Leibniz, the 18th century German scientist and contemporary of Newton. The motto of such a system is: Everything that can happen will and everything that does happen must. Only a combinatorial system, that is, one consisting only of motion and substance in its discrete or quantized form, can meet lawfulness and simplicity requirements. Since the combinatorial principle generates both the physical and linguistic worlds and is the only system consistent with the Lawfulness Principle, we will conclude that this Principle is actually the World Axiom. Accordingly, the world can properly be called a Combinatorial or Leibnizian-Hellenic System.
Allegorically, a lawful world can be viewed as a Cosmic Symphony produced by the pizzicato pluck of the Big-Crunch on a three-dimensional violin string. Mankind emerges trying to sing the accompaniment. The world has also been usefully compared to a computer. But the world computer generates an internal metacomputer - mankind. The bigger question is how does this come about and what is the hardware of these two computers? Also, what is their software, that is, their programs and underlying logic?
Enter Euler and Combinatorial Programs
Using Leibniz' terminology, the waves being combined are called combinatees and the motion doing the combining is called the combinator. Equations describing all the configurations such systems can enter into are called generators. The 18th century Swiss mathematician Leonhard Euler first developed such generators. In particular, he developed one for vibrating strings. In a spectacular development, modern physicists have found that this equation reproduces, in great detail, the complex substructure of the world - the elementary particles - described by quantum theory. This string equation also meets the conditions of Einstein's relativity theory. Consequently, Euler's formula provides the basis for quantum gravity - the ultimate foundational science of physics
Some experts think all this work is bringing physics to its mature, final stage, just as classical quantum theory gave a complete theoretical description of chemistry. But the logic behind the string equation - and the world - has been obscure. The answer: Euler's string generator is a combinatorial equation and the world is a combinatorial system.
More On The Language-Physics Connection
It turns out that language is also a combinatorial system. We will see that language uses unit words - nouns and conjunctions - which are analogs of the physical concepts of substance and motion forming the elementary particles. Just as motion is the physical combinator of waves acting as physical combinatees, so conjunctions are the linguistic combinators of nouns acting as linguistic combinatees. Language also has a combinatorial generator analogous to Euler's string equation. And this produces all possible stable abstract structures just as the string equation produces all possible stable physical structures. Thus, the world fills its combinatorial possibility set, both abstract and concrete.
Vortices, Fields and Matter
Theory and experiment show that physical motion drives the primordial substance into an extended array of ring vortices, like smoke rings. This is called the minimum energy configuration. Disturbances of this vortex array can then produce only two possible classes of motion:
1. Standing wave deformations of the vortices and
2. Propagating waves transmitted over the vortex array.
Deformations of the standing vortices constitute matter particles. These induce related propagating waves which constitute the field particles. In turn, the field particles deform and destabilize the matter particles. This causes them to move with respect to each other, usually combining. Therefore, the matter particles are the quantized combinatees and the field particles are the quantized combinators.
A vortex ring can be deformed and vibrate in four different ways - rim undulations, rim constrictions, ring-breaking and composites. It is not yet certain which motions induce which physical effects. But, to be explicit, assume that these four standing wave properties constitute, in order, the matter properties called mass 'charge', electric charge and strong and weak nuclear charges. There can then be only four corresponding types of propagating wave motion or field types. Gravitons induced by mass carry the force of gravity. Photons induced by electric charge carry the electromagnetic force. Gluons or 'strongons' induced by the strong charge in quarks carry the strong nuclear force. And 'weakons', that is, vector bosons, carry the weak nuclear force.
The elementary particles, both matter and field - standing and traveling waves - are the true atoms of the world. They have no internal structure, only wave motion. At last, some six dynamic levels beneath everyday experience, we come to the end of the onion skin structures of the world. Such a finite completion is required of a lawful world, for it cannot have infinities, e.g., infinite substructures.
Frictionless superfluid liquid helium provides a remarkable physical model of this world system. When energized it also forms vortex arrays and these exhibit many quantum features.
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The Four Evolutionary Paths of the World
Broad examination of the evolutionary trends of the world studied by various sciences shows that general evolution proceeds along four paths, each dominated by one of the four forces while the other three play secondary roles. Unfortunately, specialists have fragmented the terminology. It can be unified around the terms 'physics' and 'chemistry'. In a lawful world, everything is a branch of physics. Therefore, one can refer to ordinary physics and chemistry as nonadaptive physics. Biology is adaptive physics. Sociopsychology is sentient physics. Grammar and logic are representational physics. These are materialized in the form of neural chemistry and computers.
The four evolutionary paths can be unified around the term 'chemistry'. They are then expressions of (1) strong nuclear chemistry, (2) weak nuclear chemistry, (3) gravitational or cosmological chemistry and (4) the usual electromagnetic chemistry.
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The First And Second Evolutionary Paths:
The Nuclear Forces And Nuclear Chemistry
Along the first evolutionary path, the strong nuclear force binds elementary particles together. In particular, the strong nuclear force combines quarks to form nucleons such as protons and neutrons. These are combined further to form atomic nuclei by a variation of the strong force called mesons. These nuclei can be so large they constitute neutron stars, although these are obtained by gravitational collapse along the third evolutionary path. This is an example of force interactions, nuclear and gravitational. Along the second evolutionary path, the weak nuclear force produces a series of reactions called Beta-decay.
The theory of elementary particles has recently graduated from classical, point-particle mechanics, with no interior, to the spatially extended string-vortex wave mechanics mentioned above. Advanced taxonomies, based on group theory - the mathematics of symmetry - can now classify and predict the dozens of elementary particles. The best known of these is the classification of quarks by the eight-fold way.
The strong nuclear force compresses multiple positive electric charges within quarks against their repulsive energy. Like a loaded spring, cocked by the nuclear force, this electrical compression can be released as nuclear energy with conversion of mass into energy according to E = Mc2. This conversion is the transformation of the standing vortex wave motions of matter particles, Mc2, into the traveling wave motions of field particles, E, where c2 is the factor taking into account the internal rotational and vibrational energy of matter not present in field particles.
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The Third Evolutionary Path:
Gravitational Chemistry and the Cosmological Reaction
The gravitational force controls the cosmological reaction sequence and the destiny of the world. This could as well be called cosmological or gravitational chemistry. It produces an aggregating, build-up or formation reaction sequence followed by a collapse sequence or what the chemist would call a condensation series. This build-up, followed by a collapse phase, suggests a cyclical history for the world.
The aggregating sequential reaction starts with the Big-Flash of the Big-Bang. This is observed today as the uniform background radiation. The elementary particles congeal out of this Big-Flash and then combine to form the light-weight chemical element, hydrogen. Hydrogen further combines with itself to form the gravitational reaction sequence of cosmic dust, planetoids, planets, solar ignition, galaxies and galactic structures. The resulting firmament is like so much floc precipitating out in a test tube.
When solar burn out occurs, gravitational collapse produces supernovae explosions emitting the heavy elements. These contribute to the build-up phase but end in a sequence of condensed dwarfs, pulsars, neutron stars (giant atomic nuclei) and a series of black holes of solar, galactic and cosmic dimensions. The cosmic black hole - the 'cosmon' - results from total collapse of the universe. This is the Big-Crunch. Most of these reaction products have been observed, although, for obvious reasons, the cosmic black hole can only be inferred.
As the world constants of motion reach the elastic limits of the constants of substance, the Big-Crunch is followed by the Big-Bounce. In turn, this leads to the Big Bang and re-expansion of the universe. In an autonomous, internally nonmiraculous or lawful world, only this cosmic recycling can supply the mass-energy for the next cycle. Theories of entropic heat death and endless inflation are miraculous, for they require special creation of the world, which defies the lawfulness assumption.
Conservation and relativity theory require that time be finite over each cosmic cycle while the number of cycles must be unlimited if the world is to be lawful. To sustain this perpetual motion, the motion must be of the second or frictionless kind and the primordial substance must be a superfluid, that is, net frictionless like the liquid helium model. At the time of each Big-Crunch, occurring about every 1011 years, entropyless gravity resets the world to zero entropy or perfect order. This is a cold death, not the heat death of the chemist. The system then bounces and re-expands. Altogether, this is called the oscillatory Big-Bang theory of the world.
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The Fourth Evolutionary Path:
The Electromagnetic Force: Adaptive Chemistry and Much More
In the multiplicity of cosmological environments, some, such as our planet, exhibit a balance of forces permitting the electromagnetic force to realize its great intricacy. With a few exceptions, buried deep in the nucleus, the forces up to this point have all been single valued or scalar forces (measured by a scale). Their controlling law is Energy or Action Minimization. This can only produce nonadaptive or nonlearning physics and chemistry, although there can be elements of self-organization as seen in the physical structures of the world, from atoms and compounds to solar objects and vortices. Nevertheless, such systems run 'downhill' producing increasing disorder until the Big-Crunch resets the world. But the fourth and final force, namely, the electromagnetic force, is a two-component or vector force - electric and magnetic. These forces lie at right angles to each other. They also operate at energy levels humans normally experience, for we are creatures of the electromagnetic force.
These right-angled forces produce spatially directed chemical bonds. This accounts for the complex structures and energetics of the chemistry underlying adaptive physics or biology. In turn, biology leads to neurobiology which leads to sentient socio- psychology and language. Each of these stages introduces a new controlling law along this, the fourth and final evolutionary path. While the life systems are less abstract than the others, they are far more intricate. In fact, they are like Rube Goldberg systems. The next Table lists the four systems comprising nature and the controlling laws which distinguish and govern them.
SystemΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚ Controlling Law
I. Nonadaptive physics and chemistry:ΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚ The Energy law
II. Adaptive (learning) physics or biology:ΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚΚ The Survival law
III. Sentient (conscious) physics or psychology and sociology:ΚΚΚΚΚΚ The Happiness law
IV. Representational physics or grammar, including math-logic:ΚΚΚΚ The Information Gain law
Adaptive Physics or Biology: The First Learning System. Polymerization of certain monomers into long chains, followed by complementary pairing of the chains, constitutes the DNA double helix. When a DNA pair untwists, zipper-like, each half picks up more monomers and duplicates in geometric progression. For the usual thermal and related reasons, the sequence of monomers occasionally varies or mutates. The resulting variation plus duplication leads to self-organizing evolution under a new controlling law: Competitive Survival Maximization. This drives the electromagnetic system along the self-organizing path of adaptive physics or bio-evolution.
Amino acid side groups on DNA co-polymerize under the direction of the DNA monomer sequence. This produces selected proteins capable of enzymatically regulating every possible chemical reaction. This triple ability to self-duplicate, vary and direct protein production defines the gene. When the gene directs the production of lipids, these spontaneously form enveloping molecular membranes. With this, the biological cell emerges to enter into its vast combinatorial possibilities. This is the first adaptive or learning system. It is inter-generational, not individual.
The logic of bioevolution is that of a game of 20 Questions. Every monomer sequence rejected by the environmental judge eliminates all subcases and, so, quickly optimizes survival.
Hot deep sea vents supply iron sulfide catalytic surfaces and key metabolic steps transforming nonadaptive to adaptive chemistry, bioenergetics and life. Simple organic compounds modeling DNA have now been discovered which undergo Darwinian evolution in the test tube.
Multicellular organisms evolve when cells secrete and adhere to a common spherical membrane, the basal lamina. Under topological transformations these 'tissue cells' combine to form the organs of metazoa. The organs specialize to perform the same metabolic functions required by the cell and its organelles. Organisms in colonies similarly specialize. Thus, DNA, gonads, as well as queen and consort are analogs. The underlying cell differentiation is regulated by a DNA cascade called epigenesis. Genes activate arrays of new genes at each successive cell division.
Insentient Neurobiology: The Second Learning System. The ubiquitous electrochemical signal of cell membranes appears early, involved in the fertilization process. Some cells exploit these signals by combining in all possible ways to form all possible signaling networks. Excitatory and inhibitory activity play the role of ON-OFF switching in computers. By varying their connections and excitatory and inhibitory activity, neural nets come to embody every possible logical operation. But early circuit architecture is only capable of pairwise or Pavolvian conditioned learning resulting in insentient, second level learning or adaptivity. It is personal or intra-generational.
Internal body functions and external environments can now be mapped into this brain circuitry. This provides the set of motivating instincts in lower animals. Feedback leads to the purposive, goal-seeking behavior of these organisms. Up to the level of the opossum, they are largely insentient biorobots. They are insentient because they are largely unconscious, use only conditioned learning and can only maximize survival.
Sentient Physics and Mankind: The Third Learning System A few genetic mutations cause grid-like neuronal growth which converts the Pavlovian circuitry into Steinbuch learnmatrix architecture. These superparallel circuits have been shown, both mathematically and by computer simulation, to act holographically. Along with fused logic and memory operating in real time, consciousness or self-awareness results. When the instincts of lower animals are mapped into consciousness, consciousness becomes sentient. That is, it becomes caring or goal-seeking in higher animals, especially mankind.
The set of unconscious instincts then becomes the set of conscious interests with accompanying subjective emotions and mood. This produces a new, subjective controlling law driving this new, sentient system along yet another trajectory, namely, fulfillment or Happiness Maximization. Mankind results. Like everything else, this is subject to constraints, in this case, internal genetic constraints and external environmental opportunities.
At this point, the computer embodying the subjective controlling law is brought on-board, within mankind. This makes him the first complete system. In contrast, lower animals are incomplete systems, for their controlling law of survival maximization is located off-board in the environment. When all this is expressed mathematically, as a certain hamiltonian function discussed below, we obtain a proper formal theory of mankind - a mature psychology.
The Steinbuch matrix computer is the self-programming, creative successor to the externally programmed noncreative von Neumann computer of today. Intelligence lies in matrix hardware, not in the software programming of von Neumann computers. Von Neumann himself knew better but many experts contend otherwise. The software programming for mankind is the theory of knowledge and the world program discussed here.
Sociopsychology and the Fourth Learning System Finally, to gain the additional happiness (and survival) of the social multiplier, individuals combine and permute in all possible environments to form all possible groupings or institutions covering the set of all possible interests and emotions resulting in all possible societies. Societies provide the fourth and final learning system - the interpersonal learning system of sentient education and culture.
Representational Physics: Language and its Theory: Combinatorial Grammar Continuing along the electromagnetic combinatorial path, language emerges via the Steinbuch learnmatrix to represent, map or model the world symbolically.
Language turns out to be another combinatorial routine paralleling physical combinatorics. It also uses discrete or 'quantized' basic words called nouns which correspond to physical combinatees, that is, substance or matter particles plus conjunctions which correspond to physical combinators, that is, motion or field particles. Language also has an abstract combinatorial generator analogous to Euler's physical string generator. And this abstract generator generates stable abstract structures analogous to the stable physical structures generated by Euler's string generator. In fact, grammar and physics are homologous sciences. Grammar is just abstract physics or physics unconstrained by world constants. This defines what we mean by abstract. Conversely, physics is grammar constrained by world constants. Hence, it is concrete. We may say that the world constants materialize, transform or map grammar into physics.
The controlling law governing this new system - the abstract, representational or linguistic system - is the Information Gain. This is the difference between the size of theorems deduced from axioms and the size of the axioms themselves. This can be measured in bits, words or even dollars. For example, take the difference in cost to send, by telegram, Euclid's entire geometry textbook from NY to LA minus the cost to send his five axioms, from which the entire textbook can be deduced by rules included in the axioms.
One seeks to maximize this information gain by making the axioms as small as possible and the theorems derived from them as large as possible. The grammar teacher says: Children, be as informative but as concise as possible.
As a combinatorial system, the foundations of language, like the foundations of physics, have two primary components, combinator and combinatee. Hence, we call this combinatorial grammar. In physics, we have seen that the combinator was motion or field particles which combine substance or matter particles as the combinatees. In combinatorial grammar, the corresponding linguistic combinator and combinatee are the two primary parts of speech or word types, namely, the combinator word type or conjunction - and verbs derived from them - and the combinatee word type called nouns and their defining sets of adjectives. In the abstract, the nouns and adjectives are called sets and elements.
The traditional grammarian calls the first word type the noun. The universal noun is the word 'thing', that is, anything or everything. It is the analog of physical substance or standing matter particles and is formally denoted by bold X. But nouns can be reduced to or defined by lists of adjectives of quantity and quality. For example, the person 'Jim' is uniquely specified by his height, weight, age, parentage, schooling, blood type and so on. Accordingly, one could use a nounless language but for its awkwardness. But this demonstrates how far one can reduce the abstract world to its foundations.
The second or combinator word type is the conjunction in the form of the universal Boolean conjunction, NOR. NOR is a combination of NOT plus OR (this is inclusive OR, i.e., A OR B OR BOTH). NOT takes combinatee-things apart and OR puts them together. Hence, they are the linguistic analogs of translational field particles. These take physical combinatees or matter particles apart - and also put them together.
NOR is also the analog of ON-OFF switching in computers and of corresponding excitatory and inhibitory activity in neural systems. Summarizing, language and physics have the same foundational combinatorial structure. Both use basic combinators acting on basic combinatees.
The only attributes are those of quantity and quality. These are modifiers of the combinatees and combinators in both physical and linguistic domains, although grammar has no constants - on pain of loosing its generality and becoming physics.
Every number can be generated combinatorially by applying NOR - or its mathematical equivalent, +/-, to the universal number one (1). For example, zero is given by "one minus one equals zero (1 - 1 = 0)." Similarly, all qualities can be generated combinatorially by NOR applied to the universal dimensions of the world, mass, length and time, MLT. For example, energy is ML2T-2. Consequently, a thought, emotion or mood is a space-time, LT, distribution of energy in the form of signals in nerve nets.
Collecting terms and adding the constraint conditions, c, we get what can be variously called the Combinatorial, Thought-processing, Leibnizian or Logical Alphabet:Κ <1, MLT; X, NOR;c>.
Because this Logical Alphabet contains the basic concepts of universal logic, it is capable of thought-processing, carried out below. This goes far beyond the mere word-processing of today's ordinary alphabet, which is essentially phonetic hieroglyphics.
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Linguistic Symmetries
These results expose remarkable linguistic symmetries. They are analogous to those of physics, where they express the conservation law and organize the elementary particles. Combinatee and combinator have dualistic symmetry, for one cannot have one without the other. Quantity and quality are also duals for, again, one cannot have one without the other, except in artificial analyses like mathematics and dimensional analysis. Quantity, 1, and quality, MLT, are applied symmetrically to combinatees, giving adjectives, and also to combinators giving adverbs, noting that prepositions and verbs are derived from conjunctions, although irrelational verbs come from nouns. To expose the underlying symmetry, we could as well call adjectives adcombinatees and adverbs adcombinators.
Euler Again: If we now let NOR operate combinatorially over the terms of the Logical Alphabet, including NOR itself, we get the abstract or linguistic Euler generator. We recall that the Euler string equation generated Universal Physics and its chain of concrete structures and sciences. Similarly, the abstract Euler generator generates, by rote, Universal Grammar with all its word types, sentence-equation types, abstract structures and abstract sciences. This includes the whole of mathematics, logic and geometry as well as probability and game theory. Since verbs are products of nouns and conjunctions, we could have a verbless as well as a nounless language. All these are just linguistic combinatorial routines, analogous to the physical combinatorial routines. We conclude that the world is a double combinatorial routine, abstract and concrete.
Stability Conditions: Abstract and Concrete Stability conditions are central to structure, both abstract and concrete. The familiar physical bond strength provides one aspect of stability. Let us define a universal bond strength measured by a change of the controlling law of a domain upon separating the objects of that domain. In physics and chemistry, this is measured by how much energy is required to separate two particles or atoms. Correspondingly, the abstract bond strength is measured by the change of the information gain on separating an element from its set. This measures the importance of the element to the set.
Stability also involves variations of the bond strength called activation barriers. They permit structural changes to occur within a preserved system the bonds of which remain intact. For example, an engine remains an engine even when its pistons rotate. Similarly, mathematicians impose closure on a set of numbers. This permits the numbers to rotate or permute, like numerical pistons, without changing the set or overall system structure. This closure condition, plus abstract bonding, produces stable abstract structures. Physical stability ultimately rests on constructive wave interference. In more advanced physical systems, the activation role is played successively in biology, psychology and sociology by instinct, habit and tradition. The stable algebraic structures of universal algebra, based on closure, underlie all of mathematics and are combinatorial in origin.
The Universal Hamiltonian System Structure
There is also a stable universal abstract system and theory structure called the hamiltonian. This is a combination of three equations derived from Newton's theory of gravity. They give the possibility, necessity and constraints of every system. For example, they correspond to the detective's method, motive and opportunity, respectively.
Newton gave mankind his first complete discourse in a defined domain - the domain of linear gravitational theory. Transformed into hamiltonian form, all mature physical theories are hamiltonians. As early workers had hoped, the hamiltonian is found to organize all systems and their theories in standard format, from relativity and quantum theory to sociology and grammar. And all systems are ultimately formed alike by combinatorics. The hamiltonian can be used to produce missing theories, by rote, in biology, psychology, sociology and grammar. Even Deming's theory of business practice is a hamiltonian. The theories of economics and democracy, put in hamiltonian form, greatly simplify these subjects and, in this form, they can challenge the feeble political and economic theories - and theories of knowledge - put forth dogmatically by Marx and others.
The hamiltonian is so powerful that the variational hamiltonian, which takes the mean and variance of every term in the hamiltonian, generates everything from the set of observed personality types and mental disorders to the classes of institutions.
The final states of nature's four systems are called, respectively, equilibrium, immortality, nirvana/utopia and completion. The hamiltonian is called system, theory, story grammar and complete discourse by the engineer, scientist, grammarian and logician, respectively. These synonyms reflect the different perspectives of these fields. System refers to the engineer's fact of the object world, out there. Theory refers to the scientist's statement about the system. Story grammar refers to the universals of the scientist's theories. Complete discourse refers to the universals of theory minus all attributes of number and dimension, as required by logic.
Referring back to sociology, we noted earlier that individuals of all personality types combine and permute in all possible environments to form all possible groupings or institutions covering the set of all possible instincts and interests producing all possible societies. But individuals, institutions and environments are all hamiltonians. Consequently, society is a triple hamiltonian. It must be evaluated over all variations of every term in each hamiltonian plus all their interactions. Theoretical sociology was long sought, with little success, by Parsons, Merton and others using the natural language method of the literary culture. But it can only be developed by the formal mathematical language of the scientific culture.
Grammar and Physics are Homologous Sciences
We see that grammar and physics turn out to be homologous sciences. Grammar is the abstract or constant unconstrained physics of all lawful worlds. Physics is the concrete or constant constrained grammar of a particular world. Physics is the materialization or transformation of grammar by the world constants. This Linguistic-Physical Homology explains the mystery of why "Mathematics is so unreasonably effective in the physical sciences" (Wigner). It also explains why language is so easy for children to learn: Language structure parallels physical structure and both are combinatorial hamiltonian systems which can be transformed into each other.
Universal Profits, Benefits and Costs. The next Table shows how the controlling law or necessity part of the hamiltonian can cover all four systems of nature by using a generalized form of the economist's concept of profit. This equals the difference between generalized benefit (return, output) and generalized cost (investment, input).
System: Profit = Benefit (Return) Minus Cost (Investment)
Physics: Min. Energy = Kinetic energy minus Potential energy
Biology: Max. Survival No. = No. Born minus No. Dead
Psychology: Max. Happiness = Interest/emotion return minus Interest/emotion cost
Abstract: Max. Info. Gain = Theorems in bits minus Axioms in bits
Therefore, there is the energy profit of nonadaptive physics; the life profit of survival in biology or adaptive physics; the sentient profit of happiness in sociopsychology; and the linguistic or intellectual profit of information gain in the abstract sciences. Each is the difference of a benefit and a cost characteristic of its domain. This exhausts combinatorial evolution along the electromagnetic path.
The Unifying Theory of Knowledge. This story of the world contains a supertheory or unifying theory of knowledge also called metatheory, the science of science and the strategy of the scientific method. It starts from the Hellenic Lawfulness Principle taken as the world axiom. From it, we deduced the universal combinatorial system formation principle of Leibniz as the only system which can meet the lawfulness condition, including its simplicity requirement. Once a system is formed, the hamiltonian supplies the universal system operating principle. The Linguistic Principle then shows how language and physics are related as analogous combinatorial systems. Finally, completion criteria exist but are not treated here. This is an axiomatic theory of knowledge, since these four principles - formation, operating, linguistic and completion - follow from the world axiom and hold for all four systems of nature as well as organizing world theory.
This unifying theory of knowledge converts the several Special Theories of Evolution - physical, biological, sociopsychological and linguistic - into the General Theory of Evolution using common terminology and structures. This is an explicit, unified theory of everything. It provides science unification based on the underlying logic of the world.
The Limits of Knowledge: Knowing What Cannot Be Known - And Why. There are inherent limits to knowledge in a lawful world. For example, by definition, in a lawful world, one cannot discover unlawfulness, i.e., metaphysics, miracles or God. All such claims are unverified and result from either faulty observation or faulty logic. More generally, knowledge boundaries can be divided into internal and external indeterminacy principles. The internal indeterminacies include those of Heisenberg (position and momentum), Einstein (absolute space-time) and Godel (incompleteness).
The external or metaphysical indeterminacy principle states that unlawfulness external to the knowable world can neither be proven nor disproven. Not even the existence or nonexistence of an external world can be established, because our world is involuted or turned in on itself in space and time by the force of gravity as a condition of lawfulness. The ancients wisely referred to this intricacy as Deus Absconditus - the absconding, hidden or nonexisting God of a lawful or autonomous world.
The History of General Combinatorics
Thales et al, the first Western scientists, about 600 BC, initiated modern science by proposing that everything in the world results from motion differentiating a conserved primordial substance of given attributes of quantity and quality (fixed by the world constants of substance and motion). Thus, quantity and quality of substance and motion constrained by a conservation law are the five basic concepts.
Aristotle (and later Bertrand Russell) substituted thing and relation for substance and motion as the irreducible concepts. But this is also a switch from the object domain of physics to the linguistic codomain of grammar. That is, we refer to physical substance and physical motion with quantity and quality attributes fixed by world constants of substance and motion and to linguistic things and relations with quantity and quality attributes specified by adjectives. The first pair is constrained by world constants, the second pair is being treated as variables unconstrained by world constants. This is the underlying difference between physics and grammar.
These two pairs are rendered operational by using Leibniz's concepts of combinatees and combinators. Thus, substance and motion are physical combinatee and combinator, respectively, while thing and relation-formers are operational linguistic combinatee and combinator, respectively. Note that it is not thing and relation but thing and relation-forming conjunctions, which are operational.
Modern physics shows that a certain correction is now required, for motion underlies all reality. What we perceive as substance or matter is a certain type of motion in an underlying primordial substance, namely, the standing wave motion of matter particles characterized as half-integer spin fermions. We specifically view this substance or matter as the result of various vibratory motions within ring vortices in an extended vortex lattice filling space. The different motions - ring undulations, constrictions, ring breaking and their combinations - constitute the matter properties of mass, electric and nuclear charges.
Another type of distributed motion racing through the lattice is induced by these standing modes of motion. This second type of motion is called field. For each matter property, there is a corresponding field type: the force of gravity is carried by gravitons, the electromagnetic force is carried by photons and the strong and weak nuclear forces field are carried by gluons and vector bosons, respectively. Thus, we can now relate substance and motion to fermions and bosons, that is, to matter and field particles. And these elementary particles - fermions and bosons - which have no deeper structure but consist only of waves, are the physical combinatees and combinators, respectively.
We then reduce the linguistic 'thing' to a universal noun denoted by bold X having quantity and quality attributes denoted by strings of adjectives, xn. In the abstract, these are called sets and elements (of sets).
Finally, we reduce 'relation', that is, in operational terms, the relation-forming conjunctions to the universal Boolean operators, NOR = NOT + (inclusive) OR (or -/+ and cut/join). From these all other irrelational conjunctions (e.g., AND) and relational conjunctions such as EQUIVALENCE, INCLUDES and IS IN (equals, is greater and less than) and all functions can be derived. Thus, we now relate things to X (xn) and relation-formers to NOR, which are the linguistic or abstract combinatees and combinators, respectively.
Therefore, looking across both the concrete physical domain and the abstract linguistic codomain, we can relate fermions to nouns and bosons to the conjunctions NOR, with attributes specified by world constants in the concrete case and by more abstract adjectives in the abstract case. Specifically, all quantities as numbers can be generated by applying NOR (or 1/+) to the universal number one (1) - a version of Peano's Postulates - and all qualiities can be generated by applying NOR to the universal dimensions, MLT (from Newton's Principia). So, we now have the logical, Leibnizian or combinatorial alphabet for thought-proce: <1, MLT; X, NOR; constraints, c>.
The concept of the function, f, was first developed by Laplace and Euler. Y = f(X) (or, using state terminology, X = f(U)) is a relation, f, between X and Y which is specified for many values of X and Y. It contains the physics of a system, especially in the vector differential equation form: dX/dt = f (X0, U), called the Equation of State.
The related combinatorial generating function or generator, G(X) = Y, means "Take all combinations and permutation of the objects, X, to get the resultants, Y"). Therefore, G is the same thing as NOR(NOR). In ordinary linguistic grammar, this is the sentence, XRY, i.e., "X has the relation, R, to Y". In mathematics, it is the equation (or inequation) and X and Y are called operands and R is the operator or function.
In the physical domain, the analogous generator, which generates the set of elementary particles, is a vortex variant (still under development) of Euler's vibrating string equation with dual channel amplitude solution, A(s, t).
There are extensive symmetries and supersymmetries in both the physical and linguistic domains. In the physical domain, we have seen that the logic of vortex lattices requires that for every fermion, there must be, as observed, a boson. That is, for every physical combinatee, there is a physical combinator. In addition, all the conservation laws can be expressed as various space and time symmetries.
In the linguistic codomain, there is corresponding symmetry between combinatees and combinators, in the sense that one cannot have one without the other, as one cannot have a quantity attribute without a quality attribute. Moreover, every combinatee and combinator has a quantity and a quality. At the first relational level called the sentence (that which makes sense), there is the base sentential symmetry XRY. Of course, for purposes of analysis, the quality attribute is eliminated in pure mathematics (quantimetrics) and the quantity attribute is eliminated in dimensional analysis (qualimetrics) and both are eliminated in pure logic.
With this, we have set up the proper combinatorial foundations of the world, both concrete and abstract, and traced out the history of their development over nearly 3,000 years.
Leibniz is often cited as the last generalist. He certainly was among the greatest. However, Helmholtz and Comte are often cited as generalists of a later era. Moreover, all these were pre-theoretical or relative generalists. They more or less encompassed the knowledge of their day but had no idea where the boundaries of knowledge lay, although Leibniz understood the underlying logic of the world - the bottom boundary. Today, science can begin to move on from its specialty paralysis to embark on the Age of Theoretical (Absolute) Generalism. With this, the limits of knowledge will also be exposed.
Comments
Creationists and others who wish to contest this theory must attack the whole of unified nature and do so mathematically. Nothing else warrants consideration.
Since a supertheory unifies knowledge and organizes a verified axiomatic theory of everything, we conclude that we live in a combinatorial or Leibnizian-Hellenic world. Because the Hellenic Lawfulness Principle initiated science about 3,000 years ago, and since everything can be deduced from it, this Principle turns out to be the World Axiom. Therewith, generalist science returns full circle to its Hellenic roots. Euclid's axiomatic geometry is expanded to world axiomatics and the Conservation Law - the first law of thermodynamics - becomes embedded in the larger concept of lawfulness.
The theory of knowledge is equivalent to the strategy of the scientific method. Consequently, the scientific method - and world theory - can now be taught explicitly. This provides a true, deductive or axiomatic core education. In turn, this makes possible a common culture and the transition from today's high-tech societies to truly modernized high-think societies, no longer "drowning in information while starving for knowledge".
In spite of the nay-sayers, science will now play a far more central role in general education and society than in the past. Previous analyzers of the role of science have erroneously assumed that today's immature specialty sciences and their fragmented languages constitute the final stage of science. They have, therefore, missed the brilliant future ahead for mature generalist science using mankind's mature, final language. This can now provide comprehensive understanding based on the General Theory of Evolution which unifies quantum gravity, cosmology, bioevolution and proper theories of mankind, economics, politics, society and language. This foretells the coming Age of Generalism - the Third Enlightenment. The Common Culture becomes possible.
Nearly 3,000 years ago, Thales and his compatriots, the first scientists, got the foundations of the world and of science right. Their Hellenic Lawfulness Principle is the Axiom of the World from which everything follows. It is "The Primordial Word which says the whole world at once", as Newton's hamiltonian is the Final Word and Leibniz' combinatorics is the Logic of the World.