Ground-0 Axioms vs. First Principles and Second Law: From the Geometry of Light and Logic of Photon to Mind-Light-Matter Unity-AI&QI

Wen-Ran Zhang, Member, IEEE

Abstract—Without the geometry of light and logic of photon,observer-observability forms a paradox in modern science, truthequilibrium finds no unification, and mind-light-matter unity is unreachable in spacetime. Subsequently, quantum mechanics has been shrouded with mysteries preventing itself from reaching definable causality for a general purpose analytical quantum computing paradigm. Ground-0 Axioms are introduced as an equilibrium-based, dynamic, bipolar set-theoretic unification of the first principles of science and the second law of thermodynamics. Related literatures are critically reviewed to justify the self-evident nature of Ground-0 Axioms. A historical misinterpretation by the founding fathers of quantum mechanics is identified and corrected. That disproves spacetime geometries(including but not limited to Euclidean and Hilbert spaces) as the geometries of light and truth-based logics (including but not limited to bra-ket quantum logic) as the logics of photon. Backed with logically definable causality and Dirac 3-polarizer experiment, bipolar quantum geometry (BQG) and bipolar dynamic logic (BDL) are identified as the geometry of light and the logic of photon, respectively, and wave-particle complementarity is shown less fundamental than bipolar complementarity.As a result, Ground-0 Axioms lead to a geometrical and logical illumination of the quantum and classical worlds as well as the physical and mental worlds. With logical resolutions to the EPR and Schr?dinger’s cat paradoxes, an analytical quantum computing paradigm named quantum intelligence (QI) is introduced. It is shown that QI makes mind-light-matter unity and quantum-digital compatibility logically reachable for quantumneuro-fuzzy AI-machinery with groundbreaking applications. It is contended that Ground-0 Axioms open a new era of science and philosophy—the era of mind-light-matter unity in which humanlevel white-box AI&QI is logically prompted to join Einstein’s grand unification to foster major scientific advances.

I. INTRODUCTION

EVERYTHING needs light to be observable as something.But the geometry of light and logic of photon has so far been a mystery hindering scientific advances. While first principles are acclaimed self-evident origins of knowledge,understanding, and thoughts in spacetime, not deducible from other principles, all first principles assert truth as a basis, and none of them can reach logically definable causality and mind-matter unity. Therefore, modern science leaves room for further scientific unification beyond spacetime and truth-based logical thinking. Ground-0 Axioms are introduced in this work with a critical review of related literatures for correcting misconceptions, identifying the geometry of light and logic of photon, and illuminating mind-matter unity for artificial intelligence (AI) and quantum intelligence (QI).

Two fundamental first principles are the first principle of thought and the first cause principle. The first principle of thought was proposed by Plato (428/427 or 424/423-348/347 BC) but formulated by George Boole (1815-1864) [1]. It consists of the laws of identity (A = A), no contradiction(A∧ ?A), and excluded middle (P∨?P). The first cause principle was proposed by Plato’s student Aristotle (384-322 BC). The principle claims that any effect must have a cause,and the first cause is the prime mover or God who moves but unmoved.

Stated verbally by Aristotle, the first cause principle never reached a logical form since Ancient Greek times.Nevertheless, it laid the cornerstone for Aristotelian science—the origin of modern science. The principle tells us that effect with a non-religious cause, logical or experimental,is science; effect with a religious cause is religion. For instance, mind-matter unity is deemed an unsolved scientific problem because it is believed an effect with a non-religious cause. If it were believed a gift from God, that would be religion. Thus, without logical definability, the first cause principle is partially science and partially religion.

Theophrastus (371-287 BC)—another student of Plato and colleague/successor of Aristotle —invented modus ponens(MP) —a basic inference rule or a first principle for logical deduction. MP states that if A is true, A implies B, then B is true. But if A is false, A implies B, B may also be true. MP is not qualified to be a rule of causation due to its lack of causeeffect relation even though it has been the genetic rule of its kind for logical deduction in truth-based analytical reasoning for thousands of years.

As a paramount law of modern science for existence, life,and information, the second law of thermodynamics can be regarded as another first principle. The law is often credited to French scientist Sadi Carnot (1796-1832) who is recognized as the father of thermodynamics [2]. It is expressed later in different ways by authors in physics, engineering, information science and cryptography—a reflection of its developmental status. It asserts that isolated systems spontaneously evolve towards thermodynamic equilibrium—the state with maximum entropy, the total entropy of an isolated system can never decrease and is constant if and only if all processes are reversible. In plain language, the law asserts that any closed system tends to reach a spontaneous equilibrium state. It sets up a static equilibrium condition for modern science but stopped short of going beyond truth in spacetime to identify the geometry of light and logic of photon for open dynamic systems to reach definable causality and spacetime emergence.

Historically, logically definable causality has been deemed impossible (cf. [3], [4]). Without definable causality, mindmatter unity and human-level AI [5] has been logically unreachable. It is noted (cf. [3], [4]) that 1) David Hume—18th century Scottish philosopher and founder of empiricism challenged Aristotle’s causality principle and claimed it empirical, irreducible to pure regularity; 2) Bertrand Russell—a founder of analytic philosophy deemed the law of causality as a relic of a bygone age; 3) Niels Bohr—father figure of quantum mechanics asserted that a causal description of a quantum process cannot be attained and quantum mechanics has to content itself with particle-wave complementary descriptions [6].

As a minority opinion, however, Einstein predicted that causality is definable. It is pointed out (cf. [3], [4]) that Einstein virtually wrestled with definable causality for his whole academic career and never wavered on finding definable causality for his grand unification. He stated [7]:“Development of Western science is based on two great achievements: the invention of the formal logical system (in Euclidean geometry) by the Greek philosophers, and the discovery of the possibility to find out causal relationships by systematic experiment (during the Renaissance). In my opinion one has not to be astonished that the Chinese sages have not made those steps. The astonishing thing is that those discoveries were made at all.”

Einstein’s words got two different interpretations. Given by the majority of the scientific community, the first reaffirmed the greatness of the discoveries in Euclidean geometry by claiming experimental causality as the norm of scientific discoveries and logically definable causality impossible.Given by the minority, the second found it astonishing that“those discoveries were made at all.” Besides Einstein himself perhaps few ventured to take the second interpretation seriously. It is, however, fully corroborated by Einstein’s firm and often misjudged stance on quantum theory. Namely, he asserted that physics constitutes a logical system of thought[8], [9] and, without causality for quantum non-locality, he refused to accept quantum mechanics as a complete theory.That led to the so-far unsettled Einstein-Bohr debate of the 20th century with the tit for tat: “God does not play dice with the universe” vs. “Stop telling God what to do with his dice.”

Now, without definable causality and mind-light-matter unity for a white-box brain model, modern science in spacetime is faced with an observer-observability paradox;general relativity [10] and quantum theory find no grand unification; quantum mechanics has been plagued with paradoxes for a century. It is typical for some quantum physicists to admit (cf. [11, p319]) that “They learn it, and they can carry out its arguments and calculations as well as anyone. But they do not believe it.”

Consequently, originated from being-centered and truthbased Aristotelian science and developed from the formal system in Euclidian geometry, modern science embraced spacetime as its geometrical/logical bases. While Einstein gave a constant for the speed of light in the classical world, quantum entanglement has been observed as an instant effect in the quantum world of Hilbert space. But quantum mechanics so far failed to find a geometrical and logical basis for logically definable causality and mind-light-matter unity; the Einstein-Bohr debate finds no settlement. Few considered the fact that spacetime is not necessarily the geometry of light, and truthbased logic in spacetime is not necessarily the logic of photon in the quantum world, even though light illuminates the classical world in spacetime.

More than 23 centuries elapsed from Aristotle’s syllogistic(or classical) logic to Boolean logic (BL) [1] and fuzzy logic(FL) [12], [13]. Following the first principle of thought all the logical systems are truth-based. But American philosopher Richard Rorty asserted that “Truth cannot be out there—cannot exist independently of the human mind” [14].Subsequently, while BL led to AI, and FL enabled the development of fuzzy AI systems (cf. [15] and [16])especially neuro-fuzzy systems (cf. [17]-[24]), without definable causality quantum computing has not been able to enter AI as an analytical basis to enable mind-light-matter unity for quantum-neuro-fuzzy human-level AI .

Is there a unifying geometrical and logical system for logically definable causality as Einstein predicted? What is the geometry of light and logic of photon that can unify the classical and the quantum worlds? Could it be an inconvenient truth that truth cannot be out there, but equilibrium can?

Unexpectedly, bipolar crisp/fuzzy sets lead to a set-theoretic analytical quantum computing paradigm named quantum intelligence or QI —a natural and fundamental genre of intelligence underpinning biological intelligence and AI [3],[4], [25]-[46]. While AI has been truth-based, bipolar dynamic logic (BDL), bipolar dynamic fuzzy logic (BDFL),and bipolar quantum linear algebra (BQLA) [3], [4], [25]-[30]are equilibrium-based generalizations of BL, FL, and linear algebra (LA), respectively [3], [4], [31]-[46]. With bipolarity and logically definable causality, the concept of quasiequilibrium in thermodynamics becomes extendable to settheoretic bipolar dynamic equilibrium (BDE) or fuzzy equilibrium [3], [4]. Since absolute closeness with perfect equilibrium is practically impossible or unnecessary, all beings in the quantum and the classical worlds as well as the universe itself can be represented as bounded but open input-output(I/O) bipolar fuzzy equilibria—balanced or unbalanced (-, +)bipolar fuzzy sets with bipolar crisp set as a special case.

Thus, as formal extensions to BL/FL/LA, respectively,BDL/BDFL/BQLA opened the door from static truth-based reasoning to dynamic, equilibrium-based, analytical, set-theoretic, causal inference and compution. Consequently, the truth-based first principles and the second law can be unified to a dynamic equilibrium-based paradigm under Ground-0 Axioms—an integral set of related axioms where “Ground-0”stands for “the very beginning.”

The self-evident property of Ground-0 Axioms are justified in this work. The identification of the geometry of light and logic of photon disqualifies spacetime geometries and truthbased logics for the two critical roles. It is shown that Ground-0 axioms lead to information conservation, part-whole unification, and logically definable causality—a path from neural ensemble formation to cognition and human-level AI [5].

While the first principles and the second law are truth-based and originally invented for the classical world, the geometry of light and logic of photon are to illuminate the quantum and the classical worlds as well as the physical and the mental worlds. It is shown that QI can logically resolve major paradoxes plaguing quantum mechanics for a century and leads to equilibrium-based mind-light-matter unity and analytical quantum-neuro-fuzzy AI machinery. A survey on different applications of the equilibrium-based paradigm is presented. Short and long term research topics are identified.An assessment is made on the scientific impact of Ground-0 Axioms. A discussion on scientific unification is presented on some major issues in science and philosophy.

This paper is organized into seven sections. Section II introduces bipolar quantum geometry (BQG), bipolar dynamic logic (BDL), and bipolar dynamic fuzzy logic (BDFL) as a foundation for Ground-0 Axioms. Section III presents Ground-0 Axioms. Section IV presents a critical review on related literatures. Historical misinterpretations are identified and corrected; spacetime geometries and truth-based logics are disproven as the geometries of light and logics of photon;BQG and BDL are identified and justified as the geometry of light and the logic of photon, respectively. Section V outlines the usefulness of the equilibrium-based paradigm in computational psychiatry, decision making, physics, cognitive neuroscience, business intelligence, cryptography, and cosmology. Section VI presents a discussion on scientific unification. Section VII draws a few conclusions. (Abbreviations in Table I are used in this work.)

II. BIPOLAR QUANTUM GEOMETRY AND BIPOLAR DYNAMIC LOGIC

While truth-based logical reasoning has dominated human thinking since Ancient Greek times, bipolar crisp and fuzzy sets mark the dawn of an equilibrium-based paradigm. In this section, bipolar crisp sets, bipolar fuzzy sets, BQG, BDL,BDFL, and BQLA [3], [25]-[29] are introduced as an equilibrium-based set-theoretic, geometrical, and logical paradigm.

A. Bipolar Quantum Geometry

While the universe is background independent that canexpand or shrink, Euclidean, Hilbert, or spacetime geometry is background dependent and less fundamental models. Fig.1 shows a background independent BQG with bipolar interaction and complementarity for spacetime emergence [3].BQG satisfies the conditions of complete background independence (extended from [3], [38]-[43]):

TABLE IFOUR CATEGORIES OF ABBREVIATIONS

1) It is shape-free, quadrant irrelevant, and spacetime transcendent (e.g., U-shaped magnet is bipolar; import-export balance has no shape; equilibrium transcends spacetime).

2) It supports bipolar logical deduction and ontological reduction as well as quantum emergence and submergence.

3) It is ubiquitous, can be anywhere for everything consisting of particle-antiparticle or input-output energy/information (e.g., Photon can be anywhere).

Fig.1. YinYang bipolar quantum geometry (Adapted from [3], [38]):(a) Magnitude model; (b) and (c) Background independent property.

In BQG bipolar quantum agents (BQAs) can emerge/submerge that lead to spacetime emergence/submergence and make bipolar quantum superposition/entanglement equilibrium-based, set-theoretic, and paradox-free. On the other hand, spacetime emergence and submergence provide a basis for logically definable causality, information conservation,and unification of the quantum and classical worlds.

B. Bipolar Sets and Bipolar Dynamic Logic

Assuming an equilibrium-based universe, BQG provides the geometrical basis for bipolar set, logic, and algebra. Fig.2 presents the ontological basis of the mathematical abstraction for bipolar interaction, equilibrium, and entanglement where B1, BF, and B∞in Fig.2(c) are 4-valued (crisp), real valued(fuzzy), and algebraic valued bipolar lattices, respectively.

Fig.2. Bipolar ontology (adapted from [3], [26]): (a) Multipolar equilibrium deconstructed to bipolar equilibria; (b) Bipolar interaction and entanglement; (c) Hasse diagrams of bipolar lattices.

Bipolar lattices B1= {-1, 0}×{0, +1}, BF= [-1, 0]×[0, +1],and B∞= [-∞, 0]×[0, +∞] lead to BDL, BDFL, and BQLA,respectively, for applications in the quantum as well as the classical worlds [3], [4]. Fig.3 presents BDL as a formal system in zero-order (propositional) and first order (predicate)forms. Truth tables of eight bipolar operators (&, ⊕, ? , ?,&-, ⊕-, ?-, ?－) of BDL are given in Table II for reference by engineers as well as scientists. BDL has been extended to BDFL with equilibrium-based revealing of truths.

The equilibrium-based mathematical abstraction assumes bipolar dynamic equilibria (BDEs) or BQAs as its ontological basis. Fundamental BDEs/BQAs include but are not limited to electron (-1, 0), positron (0, +1), particle-antiparticle superposition (-1, 0)⊕(0, +1) = (-1, +1), annihilation (-1, 0)&(0, +1) = (0, 0). Notably, photon is its own antiparticle. As a BQA/BDE photon may change polarity due to bipolar interaction. It is shown later that photon as a BQA provides a logically definable interpretation to quantum superposition and leads to an analytical extension of quantum mechanics to QI [3], [4], [34]-[37].

Originated from bipolar crisp/fuzzy sets [25]-[28] BDL and BDFL are qualified to be dynamic generalizations of BL and FL, respectively. Notably, L. A. Zadeh—founder of FL [12]recognized [13] bipolar fuzzy set theory. The recognition rescued the new theory from concerted abuses with renaming,shallow copying, distortion, sophistry, and plagiarism (cf. [4]).

Fig.3. BDL (adapted from [3], [4]): (a) Basic operations (extended to BDFL, ?(x, y), (u, v)∈B1 or BF, |x| is used for explicit bipolarity); (b)Equilibrium-based laws; (c) Equilibrium-based vs truth-based axiomatization of BDL; (d) Equilibrium-based revealing of truth (extended to BDFL).

TABLE II TRUTH TABLES OF EIGHT BDL OPERATORS(ADAPTED FROM [3])

Mathematically, the bipolar mathematical abstraction [3],[4] consists of bipolar sets, bipolar fuzzy sets, BDL, BDFL,bipolar crisp/fuzzy relations, equilibrium relations, bipolar universal modus ponens (BUMP), BQLA, and bipolar quantum cellular automata (BQCA). Different applications of the theory have been reported in physics [38], [39], [43],quantum biology [3], [40], [42], quantum information science[3], [35], [41], [44], [45], cognitive neuroscience [3], [35],[36], [46], computational psychiatry [3], [32], [33], quantumneuro-fuzzy systems [4], [34], [35], [37], cryptography and security [34], [37], [47], [48], business intelligence and decision [3], [25], [27], [30], [49]-[51].

A comparison of BDL/BDFL/BQLA with classical systems reveals a number of fundamental distinctions [4] such as:

1) BDL is an equilibrium-based bipolar dynamic generalization of BL; BDFL is a generalization of FL and a realvalued extension of BDL. BL and FL as truth-based extensions to classical logic carry no physical semantics; BDL and BDFL as equilibrium-based systems assume both logical and physical semantics that may exist inside or outside human mind as a unification of the first principles and second law.

2) BDL/BDFL leads to bipolar quantum linear algebra BQLA — an algebraic extension or a bipolar dynamic generalization of linear algebra or LA for equilibrium-based modeling and information conservational computing/cryptography (ICC).

3) Without bipolarity, BL, FL, and LA are inadequate for bipolar equilibrium-based representation, interaction, and complementarity. Without a shred of dynamics, truth cannot form causal sets. With bipolarity, the quantum lattices B1, BF,and B∞provide a set-theoretic basis for BQA emergence/submergence with logically definable causality.

4) The bipolar theory is testable. While the search for ether,monads, monopoles, and strings failed to find concrete results,I/O bipolarity and dipoles are observed everywhere in both the quantum and classical worlds. Thus, BDL in BQG qualifies to be a unique formal system — the only one with logically definable causality where “physics constitutes a logical system of thought” [9].

Evidently, without truth, equilibrium cannot be identified;without equilibrium, truth cannot be revealed. Equilibriumbased generalization can be deemed as holistic truth subsuming the generalized. The generalization provides a necessary condition for the unification of the first principles of science and the second law of thermodynamics where the truth-based foundation can serve for a proof of equilibriumbased self-consistency. The two can be used together as long as equilibrium and truth conditions are not violated with the following clarifications:

1) Is Bipolarity Fuzziness? No. BDL is a formal crisp logic;BDFL is fuzzy. Is bipolar fuzzy set fuzzy? Yes. However,fuzzy sets are truth-based and do not satisfy the law of excluded middle where NOT(0.5) = 0.5. As an equilibriumbased generalization of fuzzy sets, bipolar fuzzy sets do not compromise the law. For instance, (-0.5, +0.5) can characterize a unitary I/O balance in half capacity without uncertainty but bipolar true. Logically, NOT(-1, +1) = (0, 0)satisfies the law of excluded middle. Physically, the remaining capacity NOT(-0.5, +0.5) = (-0.5, +0.5) reaches part-whole unification—a subtle but fundamentally critical step toward an equilibrium-based, dynamic, and set-theoretic unification of the first principles and second law with definable causality.

2) Is Bipolar Fuzzy Set Intuitionistic Fuzzy Set [52]? No. In intuitionistic fuzzy set, if both sides are the same we have a true-false contradiction or indetermination that does not satisfy the law of excluded middle such as (0.5, 0.5). If the two poles are equal in absolute values in bipolar fuzzy set we have a unitary bipolar equilibrium such as (-0.5, +0.5).

3) Is BDL/BDFL Multivalued Logic? Precisely, while multivalued logics are faced with the multiple-truths dilemma,BDL/BDFL extends interval-valued linguistic fuzzy sets from the bivalent space [0, 1] to the space [-1, 0]×[0, +1] for paradox-free equilibrium-based bipolar unitarity.

4) Is BDL Dialectics? No. While metaphysics is beingcentered and truth-based, dialectics is contradiction-centered and truth-based, BDL is a harmony-centered and equilibriumbased formal system (Fig.3(b)) that reveals truth [3], [4], [38].

5) Is Bipolar Dynamic Equilibrium Nash Equilibrium [53],[54]? While Nobel Laureate John Nash was the first to bring the concept of equilibrium into game theory and economics,Nash equilibrium as a mathematical formulation does not go beyond the first principles and the second law.

6) Is the Bipolar Quantum Lattice B1the Same as Aristotle Square of Composition? The answer is that Aristotle never went beyond “being qua being.”

7) Is BDL/BDFL Philosophical Logic? Actually,BDL/BDFL as an equilibrium-based system is both logical and physical. Truth, on the other hand, bears no physical semantics.

III. GROUND-0 AXIOMS

A. What is There?

The first principles are criticized in modern days for different reasons. For instances, para-consistency gave up the law of no contradiction, fuzzy logic relaxed the condition of excluded middle, and empiricism denied logically definable causality. Truth-based reasoning has, however, dominated philosophy and science since their beginnings. Indeed, even a probability factor p or a fuzzy number μ characterizes partial truth. If someone were not for truth-based reasoning, he/she might be called a liar.

American philosopher Richard Rorty (1931-2007) asserted[14, p5], however, that “Truth cannot be out there—cannot exist independently of the human mind—because sentences cannot so exist, or be out there. The world is out there, but descriptions of the world are not. Only descriptions of the world can be true or false. The world on its own—unaided by the describing activities of humans—cannot.”

Rorty was courageous to tell the inconvenient truth of truthbased limitation for the first time in the history of science philosophy. If truth cannot be out there, Aristotle’s “being qua being” metaphysics would be missing its essence, and the basic concept of being and truth have to be reexamined.Fundamentally, Rorty’s observation justified the search for a different path for modern science to advance beyond truthbased reasoning to unify the physical and mental worlds.

B. Let There Be Light

Realists may argue that the first principle of thought would be violated without truth being first. The counterargument is that, following Aristotle’s “being qua being” metaphysics, the ultimate Being or the prime mover who reveals all beings is unreachable, and causality is logically undefinable in truthbased terms. We have to answer the critical questions: Can the first principles be related to the equilibrium condition of the second law? Is logically definable causality possible? Can energy/information be conserved? Is part-whole unification possible? Is mind-light-matter unity possible?

It is well-known that the quantum world is unbounded in spacetime due to quantum non-locality but can be bounded in terms of equilibrium-based information conservation and partwhole unification that is beyond the first principles and the second law. Logically, without I/O bipolarity, truth-based logic cannot be used to define bipolar quantum superposition/entanglement as a dynamic equilibrium, and the law of identity (A = A) cannot remain valid because A cannot be identical to A if it is quantum entangled with B and constantly changing such as a tree in photosynthesis cannot be itself in quantum terms, like Heraclites river. But no first principle or second law addresses such barriers between classical and quantum worlds as well as mental and physical worlds. It is observed [55, p44] that realism may be a tempting viewpoint in modern physics but a difficult one to defend, and individual objects may not have an independent existence but exist as part of an ensemble of many.

From another perspective, truth-based reasoning relies on observability. But there is no clear spacetime boundary to observe in the quantum world due to quantum non-locality.So, truth-based thinking is the origin of major successes in science and also the source of major confusions. Without the geometry of light and logic of photon for equilibrium-based causality and mind-light-matter unity, no first principle can satisfy the second law of thermodynamics because everything is in a flux in quantum terms.

Basically, “truth cannot be out there” but dynamic equilibrium can. For instance, humans used to believe that the more horsepower the better for certain type of vehicle. But the truth is that the more fuel efficient the better. Who revealed the truth? Fundamentally, the global equilibrium did it. On the other hand, “all men are mortal” as a first principle cannot be deduced from other truths, however, it has to be deducible from Nature’s equilibrium unless biological life as effect had no natural cause.

It can be further argued that it is wrong to deny God as the prime mover. This seems a tough argument but has an easy answer. An atheist answer could be as simple as “Science is not religion.” A believer’s answer [38] could be: “As the prime mover God certainly can ordain harmony into the universe through equilibrium. Therefore, God should be elevated to the heaven above harmony/equilibrium as well as being/truth. Otherwise, being/truth would be denying the divine supremacy and subjecting God to equilibrium and harmony such as mental equilibrium and nature-human harmony.”

Consequently, without logically definable causality, the first principles of science and the equilibrium condition of the second law of thermodynamics form a geometrically and logically “untouchable” paradox in modern science with many unanswered questions such as

1) If truth cannot be out there, what is there? Can we have truth without dynamic equilibrium?

2) Can the static, closed equilibrium condition of the second law be extended to open, dynamic equilibrium?

3) If space is expanding (or shrinking), how could the first principles in spacetime be truthful in quantum terms?

4) If particle-antiparticle bipolarity is the only property that can survive a big bang and a blackhole [56], should bipolar dynamic equilibrium instead of truth be the essence of being?

5) Without bipolarity how could the mind be in a state of equilibrium, harmony, or bipolar disorder?

6) How can the first principles and the second law be unified?

7) How can the quantum and classical worlds be unified?

8) How can the physical and mental worlds be unified?

9) If the first principles and second law are paramount in truth-based terms, what is paramount in equilibrium-based terms?

10) Without the geometry of light and the logic of photon how could science reach mind-light-matter unity to overcome the observer-observability paradox?

Ground-0 Axioms are for these questions.

Ground-0Axioms:

AxiomA: Truth cannot be out there existing independently of the human mind, but equilibrium can. Equilibrium or quasiequilibrium is ubiquitous. Everything in the universe including the universe itself is a dynamic equilibrium with equilibrium, non-equilibrium or quasi-equilibrium state(s).

Axiom B: Truths are regulated and revealed by dynamic equilibrium. Without equilibrium there would be no spacetime and no being. Without mental equilibrium, there would be no mind, no truth, and no equilibrium-based reasoning.

Axiom C: Energy/information I/O bipolarity is the most fundamental form of polarity; bipolar dynamic equilibrium or BDE is the most fundamental type of equilibrium; bipolar interaction is the origin of cause and effect, change and adaptivity, disorder and stability, randomness and rationality,cognition and intelligence in the quantum and classical worlds as well as the physical and mental worlds. Any multidimensional equilibrium consists of a set of BDEs.

AxiomD: A bounded but not necessarily isolated or closed system tends to reach a dynamic set-theoretic bipolar quasi or fuzzy equilibrium within a set of BDEs with global I/O energy/information conservation and part-whole unification.

Axiom E: Quantum superposition and entanglement are fundamentally BDEs; bipolar causality is the most fundamental and logically definable causality for equilibriumbased revealing of beings and truths; bipolar complementarity is the most fundamental complementarity.

AxiomF: The first principles of science and the second law of thermodynamics must be unified with logically definable causality such that science is distinguishable from religion in equilibrium-based terms.

Axiom G: Without the geometry of light and logic of photon, any observation in spacetime is relative truth limited by the observer-observability paradox of science. To reveal truth in the most fundamental way, the geometry of light and logic of photon have to be bipolar equilibrium-based.

AxiomH: The geometry of light and logic of photon must be identified to illuminate the quantum and classical worlds as well as the physical and mental worlds such that neural ensemble formation and cognition can be unified with logically definable causality and mind-light-matter unity.

Based on bipolar crisp and fuzzy sets, Equations (1a)-(1d)show a connotation of Ground-0 Axioms. (1a) shows that the axioms form a super set of truth-based and equilibrium-based laws; (1b) shows that the equilibrium-based universe consists of the quantum and classical worlds as well as the mental and physical worlds; (1c) shows that any world is fundamentally a set of dynamic equilibria; (1d) shows that any equilibrium is fundamentally a set of BDEs. Thus, Ground-0 Axioms provide an equilibrium-based set-theoretic generalization of the first principles and second law.

IV. THE GEOMETRY OF LIGHT AND LOGIC OF PHOTON

A. Two Critical Questions

It is an historical fact that the first principles and the second law so far failed to provide logically definable causality in spacetime geometries. As a result, quantum mechanics remains primarily an empirical paradigm plagued by philosophical mysteries and logical paradoxes among which the EPR paradox [57] and Schr?dinger’s Cat [58] are wellknown. These paradoxes prevent quantum computing from becoming a general purpose analytical computing paradigm.

Ground-0 Axioms assert that the geometry of light and logic of photon must be identified to illuminate the classical and the quantum worlds as well as the physical and mental worlds with mind-light-matter unity and logically definable causality for resolving the observer-observability paradox. Then, to justify Ground-0 Axioms as self-evident, we are faced with two critical questions:

1) What is the geometry of light? Should it be spacetime geometry, standard bra-ket quantum geometry, or BQG?

2) What is the logic of photon? Should it be Boolean logic,bra-ket quantum logic, or BDL?

B. Historical Misconceptions

Without bipolarity, Paul Dirac introduced the unique quantum concept of superposition and indeterminacy with his well-known 3-polarizer experiment—an experiment performed in high school physics labs nowadays using polarized photons [59] (Figs. 4(a)-(d) and (2)). Dirac stated [59, p11]:“There remains an overall criticism that one may make to the whole scheme, namely, that in departing from the determinacy of the classical theory a great complication is introduced into the description of Nature, which is a highly undesirable feature. This complication is undeniable, but it is offset by a great simplification, provided by the general principle of superposition of states, which we shall now go on to consider.” Einstein commented [8]: “Dirac, to whom, in my opinion, we owe the most perfect exposition, logically, of this theory, rightly points out that it would probably be difficult,for example, to give a theoretical description of a photon such as would give enough information to enable one to decide whether it will pass a polarizer placed (obliquely) in its way or not.”

Fig.4. Dirac 3-polarizer experiment (http://creativecommons.org/licenses/by/3.0/).

Using complex number coefficients that represent probability amplitudes, a diagonally polarized photon is represented by Dirac as a superposition of vertical v and horizontal h states in Hilbert vector space ((2), Fig.4(a)) that led to the Dirac bra-ket standard notation in quantum mechanics. Even though Hilbert vector space has infinite number of dimensions, it lacks direct bipolarity, definable causality, and complete background-independence as shown with BDL in BQG (Fig.1). Without a logical exposition,Einstein and Schr?dinger latter attacked the idea of quantum superposition and argued that it would apply to macroscopic world like a cat being alive and dead. This has been referred to as Schr?dinger’s Cat paradox [58]—an extension of the EPR paradox [57] on quantum entanglement. The paradoxes have shrouded quantum mechanics like a cloud and prevented quantum computing from advancing to a general purpose analytical paradigm.

After nearly a century, the scientific community seems to have forgotten that science is still awaiting a logical exposition of Dirac 3-polarizer experiment. Without it, the geometry of light and the logic of photon could not be identified, the observer-observability paradox would remain intact. Ironically, such a geometry/logic has been deemed by many as an unbelievable fairytale—a disruption to science. It can be observed, however, that spacetime geometries(including but are not limited to Euclidian and Hilbert spaces)are not the geometries of light, and truth-based logics(including but are not limited to Boolean logic and bra-ket quantum logic) are not the logics of photon because they denied the bipolar nature of photon—an elementary particle that is its own antiparticle. Subsequently, no logical exposition to Dirac 3-polarizer experiment is widely accepted in science.

C. Conceptual Correction

Despite the social and philosophical barriers, for the first time, BDL in BQG provides a formal logical exposition [40],[41] of Dirac 3-polarizer experiment. The exposition states that a photon will pass the three polarizers with a polarity flip if the two operators &-and & in BDL take effects in a sequence (See (3a) and (3b)) regardless of any quantum uncertainty [60]. On the other hand, a photon may pass some of the polarizers but not all three of them if the two operators & and& in BDL take effects in a sequence (See (3c) and (3d)). The two possibilities lead to the notion of bipolar probability vs.real-imaginary probability as depicted in Fig.5—a conceptualization of the geometry of Light and logic of photon

Logic of polarized photon passing:

D. Demystification

A comparison of the bipolar interpretation with bra-ket quantum mechanics further confirms that bipolar complementarity is the most fundamental complementarity which logically supports the emergence/submergence of quantum superposition and entanglement [43]. The real and imaginary dimensions in Hilbert vector space, however, do not support background independent bipolar coexistence, interaction,emergence and submergence in logical forms. It is wellknown that negative charge and positive charge flow in opposite directions in electrical current which by convention takes the opposite direction of electron flow. Although light beam is different from electric current, photon superposition should be backed with a unifying bipolar geometrical and logical basis for quantum electronics, bio-photonics, and bioelectronics.

Fig.5. Two different interpretations of quantum superposition (adapted from [40], [41]). (a) Quantum mechanical interpretation without bipolarity and logically definable causality; (b) Equilibrium-based logical interpretation with bipolar probability and definable causality.

Without BQG and BDL, the founding fathers of quantum mechanics once overlooked the bipolar nature of a photon.That is understandable because bipolar sets, BQG, and BDL did not appear in science until a century later. Now, photon can be its own antiparticle with bipolar interaction—a step forward toward logically definable causality and mind-lightmatter unity. With BDL in BQG, quantum superposition in Dirac bra-ket notation (2) can be simplified to bipolar quantum superposition in logical and algebraic forms as shown in (4)—a basis for analytical quantum computing with QI.

Superposition or emergence in logical form (Fusion):

Annihilation (Change to heat):

With bipolarity, the Copenhagen interpretation of quantum mechanics is logically demystified with a formal system.Since the theory is supported by the same historically wellknown observations on Dirac 3-polarizer experiment without changing the absolute values, BQG and BDL as the geometry of light and logic of photon are vindicated; Schr?dinger’s Cat Paradox is logically resolved.

E. Logical Linearity & Physical Nonlinearity

It is observed [43] that due to equilibrium-based bipolar dynamic coexistence and interaction rather than truth-based unipolar AND/OR scaling operations, BDL/BDFL/BQLA presents a unification of logical linearity and physical nonlinearity. With bipolarity, not only can an operator be used for 0-1 linear scaling in absolute values, it can also be used for non-linear dynamic interaction in a bipolar quantum lattice(Fig.2). For instance, bipolar annihilation (-1, 0)&(0, +1) =(0, 0) or superposition (-1, 0)⊕(0, +1) = (-1, +1) cannot be defined and visualized with truth values. Mathematically,Bipolar operators are linear or bilinear in terms of absolute values, and such linearity provides a basis for the soundness of a formal equilibrium-based system that can be proven within itself as truth is revealed from equilibrium [43], [61].Physically it has nonlinear dynamics embedded inherently as the universe is fundamentally a BDE.

It may be argued that linearity/non-linearity is determined by mathematical property but not by physical property. This argument does not hold because it attempts to force truthbased unipolar mathematical abstraction upon a bipolar dynamic equilibrium-based generalization to deny Einstein’s prediction that “physics constitutes a logical system of thought” [9] where logical linearity and physical non-linearity must be unified in the same equilibrium-based universe.

Fig.6 illustrates the necessity of bipolarity. Fig.6(a) shows that an atom is bipolar but cannot be bivalent; Fig.6(b) shows that bipolar dynamic interaction causes spacetime emergence in the background independent BQG that is fundamentally different from any spacetime geometry including Hilbert vector space or the bra-ket quantum geometry as shown in Fig.6(c).One provides causes with bipolar interaction and logically definable causality; another shows effects without logically definable causality. In another words, bipolar interaction and quantum entanglement leads to spacetime emergence. The space and time dimensions, however, are not bipolar interactive and cannot be quantum entangled to provide causality.

It is noted [35], [43] that, as the most fundamental example of the materialization of energy, electron-positron pair production is accurately described by Feynman in his QED theory. He called it “The Strange Theory of Light and Matter”[62], [63]. One problem is that proton consists of quarks [64]in the standard model and does not contain a positron as proposed by Dirac [65]. This brought up the question whether β+and β-decay is part of Nature’s “encryption” mechanism to conceal a positron in a proton to prevent its annihilation with an electron—a logical interpretation of matter-antimatter asymmetry. Feynman noted [66] that the “encryption” idea was suggested by John Wheeler in 1940. In terms of absolute energy/information conservation, the hidden positron hypothesis is a valid theory that supports BQG and BDL/BDFL with bipolar logical linearity and physical nonlinearity for programing the mind and decrypting the universe with a bipolar quantum-neuro-fuzzy associative memory model [35] and a G-CPT theory of quantum emergence and submergence [43].

Fig.6. Spacetime emergence in BQG.

F. Spacetime Emergence With Logically Definable Causality

Spacetime emergence in BQG (Fig.6) posits that bipolar dynamic interaction is the cause for spacetime. Defined in BQG, BUMP in BDL and BDFL makes quantum causality logically definable (see (5a) and (5b)) [3], [4]. BUMP is ubiquitous because everything in the universe including the universe itself is fundamentally a BDE of particle-antiparticle pairs or action-reaction forces, and all BDEs are quantum entangled BQAs.

While MP does not provide logically definable causality due to its lack of cause-effect, BUMP in BDL/BDFL states that,for all BDE functions ?, φ, ψ, and χ, crisp or fuzzy, IF (? ?φ)& (ψ ?χ), Then, we have the bipolar interactive cause-effect process (? *ψ) ?(φ *χ) or in the form of bipolar quantum entanglement, [(? ? φ)&(ψ ?χ)] ? [(? *ψ) ? (φ *χ)] where one event causes another. ?a, b, c, d, we have

Bipolar logical deduction:

In (5), a(t1, p1), b(t1, p2), c(t2, p3), d(t2, p4) are BQAs where k(t, p) stands for “agent k at time t and space p” (tx, ty, px, and pycan be the same or different points in time and space). An agent without time and space is assumed at any time t and space p.

With the emergence of spacetime from bipolar interaction in BQG [38], [39], BUMP qualifies BDL/BDFL as a completely background independent causal logic. Since all previous logical systems in spacetime geometries failed to provide logically definable causality for quantum entanglement to resolve the EPR paradox [57], and to give a logical exposition of Dirac 3-polarizer experiment to resolve Schr?dinger’s Cat paradox [58], BQG and BDL/BDFL are vindicated as the geometry of light and logic of photon—a justification of Ground-0 Axioms in overcoming the observer-observability paradox where absolute values are less fundamental than BDEs/BQAs. With logicaly definable causality, BDL provides a minimal but most general axiomatization of quantum physics and computational neuroscience [3], [4], [67].

It could be argued that what Einstein sought was definable causality in truth-based terms, not in equilibrium-based terms.The counterargument is that, without physical and mental equilibrium, truth cannot be revealed. Equilibrium as holistic truth provides a unification of the quantum and classical worlds as well as the physical and mental worlds where limited truths in spacetime are revealed by dynamic equilibria with bipolar interaction and logically definable causality. The revealing is backed by the formal proof that, after 2300 years since the invention of MP by Theophrastus as the only generic inference rule of its kind, MP is now derivable from BUMP(Fig.3(d))—the justification of QI as an analytical quantum computing paradigm toward mind-light-matter unity and human-level AI.

G. Questions and Answers

Why is equilibrium-based revealing of truths impossible with the standard Dirac bra-ket quantum logic in Hilbert space? And why is wave-particle complementarity not most fundamental? Evidently, Hilbert vector space does not support strict bipolarity for bipolar interaction and logically definable causality even if the same absolute values in BQG are used.Similarly, wave-particle complementarity of the Copenhagen interpretation — the foundation of quantum mechanics is shown less fundamental than the bipolar interpretation — a breakthrough vindicated by the two simple observations: 1)Wave-particle complementarity principle asserts that opposites are complementary but particle and wave are not (-, +)bipolar opposites; 2) photon is its own antiparticle with direct bipolarity that is missing in Dirac ket-notation and Bohr’s wave-particle interpretation. This tells why Niels Bohr asserted that a causal description of a quantum process could not be attained, and quantum mechanics has to content itself with particle-wave complementarity description [6], but Einstein refused to accept quantum mechanics as a complete theory [8], [9], [57].

How could bipolar complementarity or bipolar quantum entanglement be most fundamental? Why does BQG only have two dimensions? Since any multipolar system must be necessarily a composition of BDEs, the logic of photon in the geometry of light has to be most fundamental. Two dimensions enable BQG to reach complete background independence with geometrical and logical unification of quantum superposition and entanglement.

V. TOWARD MIND-LIGHT-MATTER UNITY AND ANALYTICAL QUANTUM-NEURO-FUZZY AI

In this section we present a survey on related applications focused on mind-light-matter unity and analytical quantumneuro-fuzzy AI machinery in computing and information sciences as well as in physics and cognitive neuroscience.

A. Computational Psychiatry for Mental Health

The equilibrium-based paradigm finds many applications,one of them is in computational psychiatry. The fifth edition of Diagnostic and Statistical Manual (DSM-5) [68] produced by the American Psychiatric Association (APA) and the 10th version of the International Classification of Disease (ICD-10) [69] produced by the World Health Organization codify psychiatric diagnoses which are delineated by specific criteria for the timing, co-occurrence and severity of symptoms. The linkage of mental disorders to their biological origins are,however, largely unknown. Arguably, medical treatment of a bipolar disorder (BPD) should target at recovery to a normal mental equilibrium state, but that is not geometrically and logically characterized in DSM-5 and ICD-10. Equilibriumbased computational psychiatry is to tackle this unsolved mental health problem [31]-[33] (see Fig.7).

In clinical psychiatry, BPDs typically show polarity swings.Fig.7(a) presents a 5-state spectrum that has been used to support mood polarity swings (cf. [32]). The spectrum model,however, cannot accommodate the properties of BPDs with bipolar coexistence for medical interaction. A geometrical transformation is shown in Figs. 7(b) and 7(c) that converts the 5-state spectrum to bipolar crisp/fuzzy sets in BQG and enables equilibrium-based, set-theoretic, logically definable causal reasoning on BPDs and other neurobiological disorders that used to be deemed illogical [32], [33]. Thus, the geometry of light and logic of photon can combine neural biological and psychiatric data mining together with knowledge visualization. It makes computational psychiatry possible with a generic equilibrium-based quantum-neuro-fuzzy AI testbed for cognitive neural science and computational psychopharmacology — a frontier of medical science and AI.

B. Bipolar Cognitive Mapping for Dynamic Organizational Modeling and Equilibrium-Based Decision Analysis

While BL and FL find BDL and BDFL as equilibriumbased generalizations, equivalence relations and similarity relations find equilibrium relations and fuzzy equilibrium relations as generalizations, respectively, which are bipolar transitive, symmetrical, and reflexive [3], [27], [30], [70],[71]. The relational models lead to applications in cognitive mapping, dynamic organization modeling, and equilibriumbased multiagent decision analysis [3], [27], [30], [49]—a formal development of earlier cognitive-map-based decision support systems [72]-[75].

Fig.7. A geometrical and logical transformation of bipolar disorder classification to BQG for computational psychiatry (adapted from [32]).

Fig.8 shows an example application of fuzzy equilibrium relations. Fig.8(a) shows a bipolar fuzzy cognitive map(BFCM) in graphical form among a set of political entities(countries or regions) shortly after the cold war of the last century. Fig.8(b) shows the fuzzy equilibrium relation of the BFCM in matrix form. The relation can be clustered into different coalition sets, conflict sets, and harmony sets based on different competition-cooperation (-, +) criteria for focus generation, strategic decision support, and global regulation[3, Ch. 11]. Fig.8(c) shows some clusters in BQG from the perspective of the US. Fig.8(d) shows the bipolar transitive paths for each bipolar relationship in the BFCM graph or matrix.

The transitive paths as strongest bipolar interactive chains provide foci of attentions which can be linked to the ground truths—the available data/knowledge of an expert system for dynamic organizational modeling and equilibrium-based decision analysis [49]. For instance, decision analysis can be performed by questioning a BFCM-based decision support system [49]: “If a cooperation or competition link is strengthened or weakened, what would be the ripple effects?”“What is the most effective way to achieve global harmony and stability?” Of course, a BFCM can be updated to provide decision support for the new question: “What would be the bipolar relational effect if US-China are economically decoupled?”

While a BFCM is holistic, intuitive, and useful, the relational model lacks mathematical depth. It has been extended to an algebraic model with BQLA for quantumneuro-fuzzy AI, information-conservational supercomputing,cryptography, and quantum intelligence machinery [3], [4],[34], [35].

C. Bipolar Quantum Cellular Automata—A Cellular Transformation of Bipolar Fuzzy Sets to QI-Machinery

Fig.8. Bipolar cognitive mapping of international relations (adapted from [3]).

BQLA as a bipolar algebraic model leads to BQCA—a cellular transformation of bipolar fuzzy sets to quantum intelligence machinery [3], [4], [34], [35]. Equations (6a)-(6c)provide the elementary equations for the transformation of bipolar quantum superposition to an entangled BQCA where E(t) is a bipolar column vector and M(t) a BQLG matrix at time t. ?(x, y), (u, v) ∈ B∞= [-∞, 0]×[0, +∞], we have

Bipolar multiplication:

Bipolar addition:

Fig.9. BQCA unification of matter and antimatter (Adapted from [38]).

Bipolar quantum cellular automaton (BQCA):

Let |εcol|M(t) stand for “the energy/information of each column of BQLG matrix M(t)”, we have (7a)-(7c) [3], [4],[34], [35]

Energy/Information conservation:

Energy/Information regeneration:

Energy/Information degeneration:

Equations (7a)-(7c) define a BQCA with energy/information conservation, regeneration (or growing), and degeneration(or aging), respectively, based on I/O bipolar interactions. If degeneration and regeneration form a symmetry, information conservation remains intact as a global law. Notably, partwhole unification used to be impossible with classical set theory due to the “set of all sets” dilemma or the barber paradox. Part-whole unification is a natural consequence of equilibrium-based information conservation among a bipolar fuzzy set.

Equilibrium-based BQCA is logical where a BQLG can regulate BQAs for energy/information conserving, regenerating or degenerating with or without oscillation [34], [35],[40]-[44]. Unlike paradox-prone quantum mechanics, BQLG bridges a gap between neuronal wiring/firing and cognition to enable neural ensembles to be logically/algebraically entangled such that the mind can have freewill with equilibrium-based regulation and cognition. Freewill in the meantime finds its ceilings in energy/information conservation.

It might be argued again that without bipolarity the absolute energy/information can also be conserved. The counterargument is that without bipolar dynamic equilibrium-based interaction, logically definable causality, part-whole unity,and quantum entanglement (5) would be impossible (Fig.6).

D. From Matter-Antimatter Unification to Quantum Bio-Economics and Quantum Biophysics

With BQCA, matter and antimatter are unified to a bipolar atomic model [39]. Fig.9 presents a simulation of the BQCA interpretation for different applications. Fig.9(a) shows that matter and antimatter atoms can be unified to a BQCA; Fig.9(b) simulates energy/information conservation and rebalancing of a BQCA in a dynamic equilibrium wave form(7a) that finds applications in quantum bioeconomics for economic rebalancing and in biophysics for modeling biological equilibrium [3], [40]-[42], [49]; Fig.9(c) simulates energy/information increase of a BQCA leading to nuclear fission or exploration (7b) that finds applications in quantum bioeconomics for modeling economic growth or overheating and in biophysics for modeling biological growth [3],[40]-[42], [49]; Fig.9(d) simulates energy/information decrease of a BQCA leading to nuclear decay (7c) that finds similar applications in quantum bioeconomics for modeling recession or collapse and in biophysics for modeling aging[3], [40]-[42], [49]. It is contended that the bipolar atomic theory has opened an Eastern road [39] toward quantum gravity to reveal the ubiquitous effects of quantum entanglement [61]. Notably, it is so far the only formal theory backed with logically definable causality and observable utility in logical, physical, biological, social, and mental worlds in line with Einstein’s prediction that “Physics constitutes a logical system of thought” [9].

E. Analytical Quantum-Neuro-Fuzzy AI Machinery for Information Conservational Computing and Cryptography

Fig.10. Information-conservational bipolar quantum-fuzzy cognitive mapping (Adapted from [34]).

The law of energy/information conservation [34] asserts that any active quantum-neural-fuzzy associative memory C can be normalized to an information conservational bipolar quantum-fuzzy cognitive map (BQFCM) or a BQLG with(8) such that (7a) is true (QNFAM) [35], [76]. A QNFAM of three international trading partners in an import-export network is shown in Fig.10 together with its normalization to BQFCM/BQLG M(t). The normalization is column-linear but matrix-nonlinear (Note: The import-export numbers are based on published 2014 trade data in million Euros.).

Bipolar normalization:

Information conservation leads to information conservational computing/cryptography (ICC). A major advantage of ICC-based QI over paradox-prone quantum computing lies in its quantum-digital compatible, equilibrium-based high precision collective computing. Fig.11(a) shows a quantumdigital compatible QI architecture that has been prototyped in C++ and Java languages to produce the data in Fig.11(b) and the scaled wave form in Fig.11(c) among three entangled neural ensembles (US-China-EU) for equilibrium-based business intelligence and cryptography [34]-[37]. Each iteration of ICC conserves the absolute total energy/information 3030750 in million Euros —the 2014 import-export grand total—with part-whole unification (see Fig.11(b)).

QI as an analytical extension to AI can be deemed an equilibrium-based unification of the quantum and classical worlds. The significance of the extension lies in its logically definable causality and ICC for holistic top-down and bottomup reasoning vs. truth-based bottom-up only reasoning without definable causality and ICC. While the equilibriumbased formal system has enabled QI with ICC, it finds unique applications where subtotals or binary code segments can be summed up to a grand total big in value but short in form for quantum superposition, entanglement, information hiding,equilibrium-based rebalancing, business intelligence, and cryptography [34]-[37].

Although QI is intuitive for business intelligence where equilibrium-based rebalancing of I/O, spending-gain, or import-export bipolarity are always involved, a puzzling question is how bipolar dynamic equilibrium can be applicable in cryptography that has been always focused on binary code instead of bipolar dynamic equilibrium. The answer is somewhat dramatic but a natural one. Since the geometry of light and logic of photon has revealed the equilibrium-based dynamic nature of the quantum world, QI can be reached through equilibrium-based quantum rebalancing with quantum-digital compatible ICC technology for collective high-precision supercomputing, such as with 30, 300, 3000, 3 million, or more quantum-neuro-fuzzy ensembles instead of only three of them as illustrated in Fig.10 or 11. The cryptography idea leads to the concept of “programming the mind and decrypting the universe” [35] as outlined in next section.

Fig.11. QI machinery for ICC (Adapted from [34]).

F. Programming the Mind and Decrypting the Universe

It is noted in [35] that, while cognition is defined as the mental process of acquiring knowledge/understanding through thought, experience, and the senses for intelligence, quantum cognition (QC) is referred to as the underpinning quantum process of mental activity for QI. QC&QI asserts that neuronal activation, deactivation, ensemble formation, and metabolism are fundamentally bipolar quantum-cellular energy/information regeneration and degeneration with or without oscillation under global energy/information conservation at certain levels [35].

With the equilibrium-based paradigm, neuroscience and cosmology germane unexpected well because they both belong to the same equilibrium-based paradigm and faced with the same ultimate challenge—mind-light-matter unity with logically definable causality, information conservation,and part-whole unification. System neuroscience aims to understand how neuronal circuitry produces the cognitive functions of the brain. But it is still not clear how complex memories are made and how concepts, ideas, and feelings are translated into languages [77, p333]. Quantum cosmology is to reveal the quantum nature of the cosmos for programming the universe [78], but it is seemingly an impossible task without mind-light-matter unity.

It is argued that the brain is neither an electrical machine nor a digital computer but a cognitive system of entangled BQAs for QC&QI [35]. Traditionally, however, the transformation of ionic flow to electronics signals from one neuron to another incurs a loss of equilibrium-based information due to depolarization. Therefore, in order to program the universe, we need to program the mind with QC&QI [35] and bipolarity as a unifying quantum basis for both neuroscience and cosmology.

For instance, ICC-based quantum cryptography can be extended to quantum cosmology. Given 3030750 = 1048549 +998213 + 983988, the subtotals can be concatenated to 1048549998213983988. The concatenation can represent the energy/information distributed in the classical world as well as in the computer world where 3030750 × 34.5970% = 1048549;3030750 × 32.9362% = 998213; 3030750 × 32.4668% =983988 (Fig.11). In this way, the energy/information of a universe or binary code string in a long concatenated form can be segmented, bonded, and encrypted to a grand total much shorter than the concatenation and decrypted with ICC to a set of bipolar dynamic equilibria by a BQCA —a case of programming the mind and decrypting the universe with analytical quantum-neuro-fuzzy cryptography that bridges the quantum and classical worlds [35]. As a collective highprecision computing technology ICC finds applications in quantum cosmology as well as in business intelligence and cryptography.

Fundamentally, logically definable causality makes logical representation of the outside world possible within a neural map in the mind for mind-light-matter unity and equilibriumbased revealing of truths. It is self-evident that the dynamic equilibrium of negative-positive energy/information is a precondition for the globally stable state of the universe that brings the classical and the quantum worlds together with particle-antiparticle, action-reaction, and I/O bipolarity.Otherwise, the universe would be completely stochastic, and the mind would be in total disorder. This line of research has led to the theory of YinYang bipolar relativity [3], G-CPT symmetry [43], QI [34], [35], the geometry of light and logic of photon [40]-[43].

G. From Neural Ensemble Formation to Cognition

As one of the ultimate challenges in science, mind-matter(or mind-body) unification has been philosophically and logically an impasse since Ancient Greek times. It is argued in[46] that, if mind activity can be detected with light in a diagnostic process, and a blind person can also perceive a world through physical contact, biophotonics and/or bioelectronics has to be a bridge for mind-matter unification. Thus,without light, mind-matter interaction cannot be revealed.This argument leads to the equilibrium-based geometrical and logical theory of mind-light-matter unity [36], [46] that can be regarded a unification of the classical and the quantum worlds as well as the physical and mental worlds under Ground-0 Axioms.

It is well-known that, the brain consists of billions of cells called neurons interconnected to form ensembles for the coordination and control of all physical and mental aspects of life. The nucleus of the cell body is structured like an atom but much larger in size and much more complex where I/O bipolarity is essential. Thus, mind-light-matter unity can be logically pictured with an equilibrium-based world of bipolar crisp or fuzzy sets where light bridges or illuminates mind and matter with the geometry of light and logic of photon.

A 3-layer architecture is presented in [46] with a geometrical and logical basis for mind-light-matter unity.With complete background-independence, the geometry of light and logic of photon frees the mind from spacetime limitation and enables ubiquitous equilibrium-based revealing of truths with logically definable causality. The three layers include an outer layer, a middle layer, and an inner layer. The outer layer is the universe; the middle layer is the body layer;the inner layer is the mind layer. Since all layers consists of equilibrium-based bipolar crisp or fuzzy sets with logically definable causality, mind-light-matter unity becomes logically achievable.

Mind-light-matter unity with logically definable causality paved the way from neural ensemble formation to cognition[36]. Fig.12 shows such a logical path. Fig.12(a) shows the bipolar logical/algebraic nature of neural ensemble formation;Fig.12(b) shows a bipolar entangled (Ω) neural map of apple with neural ensembles for color, shape, taste, and vocabulary,respectively; Fig.12(c) shows a bipolar entangled (Ω) neural map of a human agent with neural ensembles for different functionalities including sensory, vocal, mental, and physical aspects.

Fig.12. A logical path from neural ensemble formation to cognition(Adapted from [36]).

While the boxes of Fig.12 used to be black-boxes, now they are analytical or logical white-boxes. With logically definable causality for quantum entanglement, different neural ensembles can all be coordinated by the mind for concurrent functionalities as well as sequential ones depending on whether the coordination is bipolar deductive or entangled.For instance, an apple in the tree can trigger the logic of photon in the visual system of a person to tell his mind “it is an apple,” the person may say the word “apple”, may sense its shape, color, and taste, and may physically walk to get it.This leads to the notion of white-box brain model.

VI. ON SCIENTIFIC UNIFICATION

A. Floor-Roof Theory of Modern Science

Notably, Western science denied (-, +) bipolarity in math and logic since Ancient Greek times [3], [49]. While the Ancient Greek philosophy laid the truth-based foundation or the floor of science, without logically definable causality, the roof of science has been undefined which is described in [36],[79] as the Dao or the Way —an unsolved multifaceted problem persists in science. In neuroscience, the problem is assumed a mind-matter unification problem. In physics, it is construed as the grand unification. In philosophy, it is regarded as the Being that reveals all beings. In the Book of Change (or Yijing), it is designated the Yin and Yang of Nature. In quantum information science, it is assumed the missing laws of physics for programming the universe [78]. In cognitive informatics, it is defined as the logic of QI [35],[36], [79]. The origin of the problem is traced to logically definable causality without which modern science is metaphorically pictured as a magnificent building missing its roof for equilibrium and harmony [4], [36], [79].

The geometry of light and logic of photon leads to the floorroof theory as portrayed in Fig.13. Founded on being and truth the floor includes but is not limited to BL, FL, LA,spacetime geometry and truth-based laws such as the first principles and the second law that provide a truth-based scientific basis for science and AI without logically definable causality. Based on bipolar dynamic equilibrium and harmony the roof includes but is not limited to BDL, BDFL, BQLA,equilibrium-based geometry and laws with logically definable causality and mind-light-matter unity for QI such as Ground-0 Axioms that illuminate the “floor” with the geometry of light and the logic of photon. Originated from a mythical story the floor-roof theory has evolved to a mind-light-matter unity paradigm of AI&QI. Fig.13(a) shows the metaphorical separation of neural ensemble formation and cognition like the Cowherd and the Weaver Girl separated by the Milky Way.Fig.13(b) portrays the logical reunion of the two sides like a metaphorical bridge built on the Milky Way through bipolar quantum entanglement—a logical ladder from the floor to the roof. Fig.13(c) shows the previous computer models of brain,mind, and cognition with truths but no equilibrium-based revealing and logical feedback for mental development. Fig.13(d)presents an analytical AI&QI architecture of brain, mind, and cognition with truth, equilibrium, and definable causal feedback for mental development.

It would be hard if not impossible to give a complete assessment on the potential impact of Ground-0 Axioms as they add an equilibrium-based analytical arm to quantum theory that is still widely open for further exploration.Focused on mind-light-matter unity, the floor-roof theory provides a rich set of short and long term research topics in AI&QI as well as in biophysics and quantum physics.Although without definable causality any scientific theory is widely deemed incomplete, with logically definable causality a scientific theory may still be incomplete. This is because causality opens a door to a new world that may have new doors to be opened. Thus, the equilibrium-based paradigm in general is dynamic, set-theoretic, and fundamentally openended.

B. Research Topics on Mind-Light-Matter Unity AI&QI

Short and Medium Term Research Topics: The integration of equilibrium-based QI with earlier or newly developed neuro-fuzzy AI systems (cf. [15]-[24], [80]-[83]) can be a major research topic in short and medium terms. For instance,such a system in social science should be applicable for assessing the impact of economic decoupling; it should also be applicable in enhancing the equilibrium and stability of robot locomotion and vehicle navigation in control and automation.

Long Term Research Topics: Equilibrium-based bipolar dynamic revealing of truths with logically definable causality as a central topic in science and philosophy has far-reaching impact in technology and engineering. As a generalization of truth-based reasoning, equilibrium-based reasoning can be applied in all scientific areas where equilibrium is central.Two major applications are bipolar quantum computation and communication. An ultimate challenge is to integrate QI into existing neuro-fuzzy brain models and AI systems (cf.[15]-[24], [80]-[83]) to enable physical and social robots to gain human-level AI through machine learning and QI.

C. Bipolar Quantum Logic Gates

Bipolar quantum logic design constitutes a major challenge faced by QI. Fig.14 shows a conceptual design of a bipolar qubit register based on the logic in Table II. Bipolar qubit as a key for BQLG extends 2-state (01) unipolar Bloch Sphere to a 4-state bipolar qubit register for equilibrium-based bipolar interaction, computing, and communication [3], [44], [79](Note: In theory, a holographic extension is possible [3]).Even though QI is quantum-digital compatible, the design and engineering of BQLGs for quantum entanglement and causal circuitry is central for the development and manufacturing of quantum-neuro-fuzzy AI machinery toward mind-light-matter unity human-level AI. Thus, BQLGs are expected to revolutionize quantum computing/communication and lead to quantum-digital compatible high precision super quantum computers for different applications in all fields of science,technology, and engineering especially if bipolar quantum superposition, entanglement, and teleportation are realized.

D. On Science and Art

Fig.13. Floor-roof theory of science (Extended from [4], [36]): (a) Science without roof; (b) Science with roof; (c) Mind with truth but no equilibrium; (d)Mind-light-mater unity with truth and equilibrium.

This paper might be deemed more like an essay rather than a scientific report. A major objection could be that the floorroof theory does not seem to be science but arts. Actually, the comment is partially correct, floor and roof are indeed partially arts and partially science. However, as Einstein predicted that, at the high level of scientific unification,“science and art tend to coalesce in esthetics, plasticity, and form.” That is why the word YinYang has a position in science as well as in art. There is nothing wrong with that as long as the theory is logical with sufficient experimental observations or “sense experiences” to back it up. In this case,the floor-roof theory can host logically definable causality for a resolution to the EPR non-locality paradox on quantum entanglement—the No. 1 paradox in quantum theory and for a bipolar resolution to the death-alive Schr?dinger cat dualism paradox —No. 2 paradox in quantum theory. Since both quantum phenomena have been repeatedly observed in quantum mechanics, the “sense experiences” are, arguably,sufficient.

E. On Fuzziness and Precision

Notably, Ground-0 Axioms are largely based on the extension of quasi-equilibrium to set-theoretic bipolar fuzzy equilibrium. A question naturally arises from fuzziness and precision: Do they contradict each other? Although this work has to stay focused on the analytical quantum-digital compatible aspect and not to indulge in the technical details of dealing with quantum noises and error-correction, bipolar fuzzy equilibrium does lead to the theory of ICC for collective precision [34], [35], [37].

Fig.14. A 4-quantum state conceptual design of bipolar qubit register for BQLGs (Extended from [3], [79]).

First, fuzziness is a concept that extends logical bivalency for characterizing real world imprecision in information. Since bivalency is largely an approximation, FL is more precise than BL for logical reasoning [84] except at the most fundamental level such as the photon level. FL, however, does not satisfy the law of excluded middle. For instance, the fuzzy number 0.5 is both true and false—an uncertainty factor.

Extending fuzzy sets to bipolar fuzzy sets, bipolar quantum lattices lead to equilibrium-based ICC [34], [35], [37]. While divide-and-conquer strategy has been traditionally used for breaking down a task into sub-functions simple enough for a collective solution, ICC extends the divide-and-conquer strategy for breaking down a high precision requirement to a set of lower precision requirements for equilibrium-based,distributed, collective precision. The key is distributed nonlinear normalization of a BQLG matrix for ICC [34], [35],[37] (Fig.11).

How could that be possible? Theoretically, it is because“physics constitutes a logical system of thought.” Backed with the geometry of light and logic of photon where dynamic equilibrium is a natural and logical basis for bipolar interactive adaptivity to stability with information conservation, part-whole unification, and observability in biophotonics and bioelectronics terms. In the physical world,however, the laws of excluded middle, no contradiction, and logically definable causality come to play an essential role—a key extension from truth-based unipolar fuzzy sets to equilibrium-based bipolar fuzzy sets for the unification of quantum and classical as well as mental and physical worlds.

While fuzziness extends bivalency, bipolar fuzziness extends equilibrium and quasi-equilibrium. For instance, the fuzzy equilibrium state (-0.5, +0.5) for import-export balance is more precise than the equilibrium condition of the second law of thermodynamics where higher precision are not settheoretically supported. While fuzzy set does not satisfy the law of excluded middle, bipolar fuzzy set does not compromise the law when fuzzy equilibrium is taken as bipolar unitary truth illuminated with the geometry of light and logic of photon. This tells why causality is undefinable with BL and FL [85] but logically definable with BDL/BDFL[3], [4]—a major reason for Lotfi Zadeh [13] to recognize YinYang bipolar fuzzy sets [26]. It can also be posited the reason that Einstein refused to recognize quantum mechanics as a complete theory.

It could be argued that an unbalanced bipolar variable such as (-0.5, +0.7) violates the equilibrium condition of the second law. Actually, it is a major scientific extension toward bipolar interactive and collective adaptivity because, without imbalance there would be no cause, no quasi-equilibrium, no thermodynamics and no equilibrium. So bipolar fuzzy set theory provides a set-theoretic basis for an equilibrium-based unification of the physical and mental worlds to reach logically definable causality and mind-light-matter unity for AI&QI. After all, the static equilibrium of the second law is essentially an unbalanced condition with only input but no output in bipolar terms.

Notably, fuzzy sets, especially bipolar fuzzy sets, have been misunderstood as an imprecise theory. The misunderstanding is partially due to the systematic abuse of fuzziness by some researchers in the field and partially due to the longstanding impasses of logically definable causality and mind-lightmatter unity in science (cf. [3], [4]). Hopefully, the findings that bipolar fuzzy sets have reached set-theoretic fuzzy equilibrium with logically definable causality can help in our understanding on the nature of equilibrium, collective adaptivity, and ICC—a highly technical scientific area that deserves further research efforts. Is error correction still necessary in dealing with quantum noises? Of course. But this work is focused on analytical quantum computing and AI&QI.Experimental quantum noise and error correction are beyond the scope of this research.

F. On the Geometrical and Logical Basis of the Grand Unification of General Relativity and Quantum Theory

Notably, without logically definable causality, Einstein’s grand unification has been unreachable, Bohr’s quantum mechanics has been plagued with logical paradoxes. The analytical paradigm of AI&QI with mind-light-matter unity would undoubtedly be one of the most important scientific discoveries in human history should the theory be systematically and experimentally confirmed at the logical and physical levels—a research topic for decades to come beyond the reach of this work. Different from the first cause principle, however, Ground-0 Axioms have provided a dynamic, set-theoretic, equilibrium-based approach to scientific unification backed by the geometry of light and logic of photon. Now, we have the questions:

1) Can the geometry of light and the logic of photon serve as a geometrical and logical (not quantitative) basis for the grand unification of general relativity and quantum theory?

2) Can the geometry of light and the logic of photon serve as a geometrical and logical (not quantitative) conclusion for the Einstein-Bohr debate of the 20th century?

Arguably, BDL in BQG as a minimal but most general axiomatization of physics [3], [4], [66], [86] has to serve as the logical basis for the grand unification and, if the logic and geometry can resolve the EPR and Schr?dinger’s Cat paradoxes, the answer to the second question is derivable.Furthermore, since spacetime geometries and truth-based logics have been disproven as the geometries of light and the logics of photon, respectively, the Einstein-Bohr debate has to come to a logical conclusion with the geometry of light and logic of photon.

VII. CONCLUSIONS

Ground-0 Axioms have been introduced and justified as a self-evident, equilibrium-based, dynamic and bipolar settheoretic generalization and/or unification of the first principles of science and the second law of thermodynamics where truths are revealed from equilibria. A critical review has identified a major misinterpretation or misconception in quantum mechanics that has disproved spacetime geometries and truth-based logics as the geometry of light and the logic of photon regardless of their significance in science. On the other hand, wave-particle complementarity has been disproven as the most fundamental quantum property. Conversely, BQG and BDL have been identified as the geometry of light and the logic of photon, respectively, backed with logically definable causality, mind-light-matter unity, Dirac 3-polarizer experiment and a class of unique AI&QI applications in computational psychiatry, cognitive neuroscience, international relations,business intelligence, information conservational computing/cryptography, quantum-neuro-fuzzy AI-machinery, and whitebox brain modeling. Ground-0 Axioms have made the following set-theoretic extensions:

1) Classical (crisp) set theory is truth-based and paradoxprone to the “set of all sets” dilemma or the barber paradox;bipolar (crisp) sets are equilibrium-based and have led to the geometry of light and logic of photon for mind-light-matter unity.

2) Fuzzy set theory [12] as a truth-based static extension to classical set theory does not satisfy the law of excluded middle for definable causality [85]; bipolar fuzzy set theory is equilibrium-based, does not compromise the law of excluded middle, and has led to logically definable causality,information conservation, and part-whole unification.

3) The first principle of thought by Plato is truth-based and fundamentally unipolar and static; Ground-0 Axioms are equilibrium-based and fundamentally bipolar dynamic.

4) The first cause principle by Aristotle is logically undefinable in truth-based terms; Ground-0 Axioms assert logically definable causality in bipolar equilibrium-based terms.

5) Classical modus ponens or MP by Theophrastus as a generic inference rule for thousands of years does not provide logically definable causality; bipolar universal modus ponens or BUMP provides logically definable causality for equilibrium-based logical deduction and bipolar quantum entanglement. MP is derivable from BUMP but not vice versa—a formal proof of bipolar dynamic generalization and equilibrium-based revealing of truths.

6) The second law of thermodynamics provides a specific static equilibrium condition in truth-based terms; Ground-0 Axioms assert dynamic set-theoretic bipolar fuzzy equilibria as ubiquitous existence in the quantum and classical worlds as well as in the physical and mental worlds. Thus, Rorty’s philosophical inquiry [14] has found a scientific answer: Truth cannot be out there, but equilibrium is ubiquitous.

7) Space-time and the X, Y dimensions of spacetime geometries are not equilibrium-based, not bipolar interactive,and cannot form bipolar superposition/entanglement; the YinYang bipolar dimensions of the geometry of light and logic of photon are bipolar interactive and can form bipolar quantum superposition or entanglement with logically definable causality for spacetime emergence/submergence — a deeper geometrical and logical theory.

8) Missing direct bipolarity, particle-wave complementarity in quantum mechanics cannot reach logically definable causality for bipolar quantum superposition/entanglement;Ground-0 Axioms have led to an analytical quantum computing paradigm named QI with a resolution of major quantum paradoxes. Thus, the bipolar interpretation is more fundamental than the Copenhagen interpretation.

As a result, the geometry of light and logic of photon has made Ground-0 Axioms self-evident. It has been shown that with the geometry of light and logic of photon, mind-lightmatter unity has become logically reachable. It has brought computational psychiatry, sociology, physics, cosmology,cognitive neuroscience, and quantum information science together into an analytical unifying computing paradigm of AI&QI.

Philosophically, the origin of Ground-0 Axioms can be traced to YinYang bipolarity. Notably, 17th century German mathematician and philosopher Leibniz invented the modern binary numeral system with a bivalent interpretation to YinYang hexagrams [87] that eventually led to modern digital computing technologies; 20th century Danish physicist Niels Bohr invented quantum mechanics with a wave-particle complementarity interpretation [6] to YinYang that eventually led to quantum computing. While the two earlier interpretations remain truth-based and stopped short of reaching the geometry of light and logic of photon for logically definable causality and mind-light-matter unity, the bipolar equilibriumbased interpretation of Ground-0 Axioms has reached the goal. Should the theory be confirmed experimentally and systematically, analytical quantum computing and humanlevel AI&QI would become reality—one of the ultimate frontiers of modern science.

Notably, while all interpretations in quantum mechanics have so far been commonly claimed “l(fā)eading to the same answers regarding observation and prediction,” the bipolar equilibrium-based interpretation has led to fundamentally different answers. Arguably, the Einstein-Bohr debate of the 20th century has come to a logical settlement. While Bohr was right on the existence of quantum superposition and entanglement as well as their measurement in Hilbert space at his time,the geometry of light and logic of photon has revealed the logical nature of a deeper universe where quantum superposition/entanglement is neither Schr?dinger’s Cat nor spooky action at a distance. Indeed, Spinoza-Einstein’s God does not play dice but plays a game of equilibrium and harmony with logically definable causality as Einstein stated [88]: “I believe in Spinoza’s God, who reveals himself in the orderly harmony of what exists, ...”

In summary, while the logic of AI matches the classical world in spacetime, the logic of QI matches both the quantum and classical worlds for developing analytical quantum-neurofuzzy AI-machinery with mind-light-matter unity beyond spacetime. It is contended that Ground-0 Axioms have opened a new era—the era of mind-light-matter unity. In the new era,human-level AI&QI is analytically prompted to join Einstein’s grand unification for fostering major scientific advances in the quantum and classical worlds as well as in the mental and physical worlds.

Of course, many questions remain unanswered. A major counterargument to the new era has been whether the preliminary experimental observations are sufficient for a contention in its magnitude. This is left open for further exploration, especially by experimentalists. To conclude this work, we recall Einstein’s inspiration [9]:

“Physics constitutes a logical system of thought which is in a state of evolution, whose basis (principles) cannot be distilled, as it were, from experience by an inductive method,but can only be arrived at by free invention. The justification(truth content) of the system rests in the verification of the derived propositions (a priori/logical truths) by sense experiences (a posteriori/empirical truths). Evolution is proceeding in the direction of increasing simplicity of the logical basis (principles). We must always be ready to change these notions—that is to say, the axiomatic basis of physics —in order to do justice to perceived facts in the most perfect way logically.”