"Pregeometry is a combination of hope and necessity, of philosophy and physics and mathematics and logic."(John A. Wheeler)
"To understand this reality more fully, we must take into account other dimensions of
a broader reality" (John A. Wheeler)
Pregeometry
The physicist John Wheeler −Bohr's pupil and Feynman's teacher− was a visionary and a creative, thanks to his great intuition. He contributed many original ideas to theoretical physics. He coined the term "black hole" (a gravitationally collapsed object that let nothing escape, not even photons). He coined the term "wormhole" (a hypothetical topological feature of space-time, described by the equations of general relativity, which is essentially a "shortcut" through space and time). He was one of the main disseminators of the anthropic principle (the universe is adapted to man and man to the universe, any valid theory about the universe has to be consistent with the existence of man). He was one of the pioneers in the theory of nuclear fission. He was also a pioneer in the subject of quantum gravitation (the attempt to unite quantum physics and gravitation).
One of his most original ideas was the "single electron" theory to explain the indistinguishability of electrons. In a communication to his disciple Feynman he said: "Feynman, I know why all electrons have the same charge and the same mass. Because they are the same electron!". This theory agrees with what we advocate in this work: the principle of downward causality. In this case, all electrons would be manifestations of a single archetypal or deep electron.
In his conception of physics, Wheeler always sought a unified theory, a "theory of everything" that would be as simple as possible. In this regard, he went through three stages:
In the first, he believed that "everything is a particle." He thought that all subatomic entities (neutrons, protons, mesons, etc.) were derived from two fundamental particles: the electron and the photon.
In the second, he believed that "everything is field". Particles were manifestations of fields. The concept of field −introduced by Faraday in 1831− is one of the great landmarks in the history of physics: all forces of nature can be expressed as forces associated with points in space. Objects that show some form of interaction or interconnection, beyond material interaction, are said to be connected by an underlying field. Fields are invisible, only their manifestations in objects can be observed.
Today modern physics is written in the language of force fields. There are electric, magnetic, gravitational, etc. fields. Electromagnetic waves (radio, television, light, infrared light, ultraviolet light, X-rays, microwaves, and gamma rays) are vibrations of Faraday's force fields. Einstein developed his general theory of relativity in terms of force fields. In quantum physics, it gave rise to quantum field theory, which describes three fundamental forces (weak nuclear, strong nuclear and electromagnetic) very well, but does not include the gravitational force. And it is also used by modern string theory.
During the last 30 years of his life (between 1925 and 1955), Einstein searched, without success, for a "unified field theory," an essentially simple theory that would explain at once electromagnetic theory, general relativity theory, and quantum theory. Einstein's efforts were premature, for the strong and weak nuclear forces were not yet known in his time.
In the third and final stage, he hypothesized that the physical world was the manifestation of a deep structure that he called "pregeometry." Wheeler intuited that physics should have neither a physical nor a geometrical foundation, since he considered that physics was essentially geometry, and therefore it had to be transcended through a primary "pregeometrical" realm that founded the physical world.
According to Wheeler, a theory of pregeometry must not include any geometrical concepts. The only form he admitted as distance was that of "adjacent points," which are considered to be at the distance of a unit.
Wheeler's search for pregeometry went, in turn, through several stages:
A first attempt was his "sewing machine", based on binary-choice logic. It consisted of a set of rings or loops of space of abstract type and without size. These rings were connected or not according to a binary information (yes/no) encoded for each pair of rings.
He then attempts to formalize pregeometry as a "bucket set" as a Borel set. Assigned probability amplitudes to the points in the Borel set to stochastically establish spatiotemporal adjacency.
A Borel set is a set of points that have not yet been assembled to form varieties of different dimensions.
A manifold is a geometric object that generalizes the intuitive notion of curve (1-variety), surface (2-variety), volume (3-variety) or any other dimension (n-variety). Varieties have properties such as: dimensionality, metric, continuity, topology, symmetry and locality. Varieties are formed by numberable unions and intersections of closed or open sets.
The "dust cube" consisted of a set of Borel points with no mutual relations and which could be assembled into varieties of different dimensionality, even made into combinations of varieties of different dimensionality.
Finally, Wheeler abandons this conception of pregeometry because it presupposed geometric concepts, and a credible pregeometric theory must be totally free of them. In particular, the way of assigning probability amplitudes was a disguised metric.
A subsequent idea, also based on binary decision logic, was to formalize pregeometry as propositional calculus. It establishes an isomorphism between the truth values of propositions to establish the idea that physics emerges from the statistics of many very long propositions. A thermodynamic type analogy.
Subsequently, inspired by self-referential propositions −such as the liar's paradox ("this sentence is false")− conceives pregeometry as a self-referential universe based on events and stochastic processes between events that generate the geometric forms.
Finally, he concludes that "everything is information". The foundation of theoretical physics lies in logic and information. In his classic text "Gravitation" [1973], he suggested that propositional logic could potentially serve as pregeometry, in the sense that physical geometrical structures could be derivable from patterns based on logical properties. He extended this idea in later writings [Wheeler, 1997] to consider that "everything is information", coining the phrase "it from bit".
The "it from bit" theory holds that information (the bit) is a profound factor that manifests itself in the reality of physical phenomena (the "it"). Wheeler proposed to do physics without geometry by means of information, which is the simplest way to develop theories. In turn, he chose digital information because it is the simplest possible information.
All physical things are information in origin, deep down. Information is the foundation of the universe. Information is responsible for all physical phenomena. Every item in the physical world has an immaterial source of explanation: information.
Every "it", every particle, every force field, even the space-time continuum itself derives its function, its meaning and its very existence from information.
To every object in the physical world underlies an immaterial source and explanation. "It is not unreasonable to think that information sits at the core of physics, as it sits at the core of a computer."
Information has a dual or digital nature. The basic ingredients of the universe are bits, pieces (chunks) of information that when processed manifest at the surface level as matter.
All the laws of physics can be expressed in terms of information. Someday the whole of physics may be understood in the language of information. Instead of talking about particles, waves, matter or energy, one can talk in terms of digital information.
From information, meaning is constructed.
There is a "feedback loop" which is the meaning circuit. The loop is: physics gives rise to information in the observer-participant, which in turn defines the physics.
Nature is discrete. The use of irrational numbers in the formulations of physical laws is only an artifice to simplify them, but these numbers have no existential character. When we measure a distance or a time interval we can never say that the result is an irrational number. There is no limit to the detail of a measurement. Since we cannot make infinite measurements, we can never obtain an irrational number.
Space and time are not physical entities, but conceptions created by man to make reality intelligible. Space and time must be derived from the informational universe.
If there are no questions, there are no answers. The choice of a question and the time of asking it plays a determining role in the physical fact. This is the essence of the Copenhagen interpretation of quantum physics.
Following this approach, in the light of this paradigm connecting physics with information, Wheeler raised a number of philosophical questions: What does it mean that a physical object exists? What is physical existence? What does a physical process mean? Where do physical laws come from? How does the objective world arise from information?
Other Proposals for Pregeometry
Goertzel's proposals.
A pregeometry proposal was made by Ben Goertzel [2007]: the multiboundary algebra, a generalization of George Spencer-Brown's Laws of Shape [see Applications - Mathematics - The Laws of Shape].
Subsequently, Goertzel himself proposed in the work "Mind in Time. The Dynamics of Thought, Reality, and Consciousness" [2003] the hypothesis that "mind is pregeometry". This author attempted to go beyond the physical world and beyond Bohm's theory of implicate order by attempting to unify the mental world and the physical world. The human mind is the implicate order from which the explained order of physical reality is generated. The formalization of pregreometry is realized by a mathematical model of the mind as a dynamical system using abstract algebras.
The Quantum Graphity, a model introduced by Fotini Markopoulou.
In a pre-geometric phase, at extremely small scales and extremely high energies (the Big Bang conditions), there is no space-time. All that exists is an abstract network: a graph of nodes, all interconnected with each other. As cooling occurs, the nodes become progressively disconnected, giving rise to space, time and the notion of distance. This process is called "geometrogenesis".
Internal Relativity, a model proposed by Olaf Dreyer of MIT.
The pre-geometric state is based on a quantum system of spins (where each spin can be in the up or down state) and random distribution. At an elevated critical temperature, the system undergoes a phase transition in which the spins align to produce an ordered pattern. In that pattern the underlying spins are no longer perceived; only space-time and matter are perceived. Space-time emerges from the pre-geometric state and the laws of special relativity (time dilation and length contraction) also emerge.
Philosophical Background
Pregeometry actually posits the existence of a realm situated beyond the physical world, i.e., a metaphysical realm that is the foundation of the physical world. We therefore enter philosophical terrain. According to metaphysical idealism, there is a reality beyond the physical world of sensible experience and the human mind. This transcendental reality is the fundamental one and is the cause of the changing world of sensible experience. Plato's world of ideas falls into this category.
Some background concerning a grounding of physics beyond physics itself is:
William Kingdon Clifford, in "The Unseen Universe" [2011], wondered about the existence of something that is not part of the phenomenal or material world but is its non-phenomenal counterpart. This can be interpreted as the existence of theoretical or abstract entities at a deeper existential level than the physical and providing the foundation for physical phenomena.
According to Spinoza and his "neutral monism" doctrine, there is only one substance which is neither mental nor physical.
Leibniz saw the universe as constituted by fundamental entities, which he called "monads". Monads are the ultimate constituents of reality, the "metaphysical atoms". Everything is constituted by monads. Monads are simple, indivisible, active and independent entities (they do not interact with each other). They are bundles of energy or abstract mental entities. Monads reflect the universe. There are reflexive relations between monads, they only reflect each other.
Leibniz, Berkeley and Ernst Mach argued that space and time should be considered as formed by the relations between objects. We infer space and time indirectly. Classical physics, on the other hand, proceeds the other way around: they start with space and time and then place objects in them.
Ernst Mach believed that space and time do not exist in the absence of matter. Mach's principle states that the inertia of objects should be considered as the result of their relation to other objects, not to space and time: "The inertia of any system is the result of its interaction of that system with the rest of the universe. In other words, every particle in the universe exerts an effect on every other particle."
Eddington said that we should transcend geometrical notions. He alluded to some transcendental geometrical magnitudes. For example, he said that the primitive units of measurement are the simplest concepts, are non-quantitative in nature, and are not analyzable. He emphasized the role of the human mind in the construction of physical theories.
Whitehead described dynamical monads of a close-to-mental and creative type. He claimed that physical entities are actually constructed of mental entities.
Russell defended in his last vital and philosophical stage the "neutral monism", according to which there is a common underlying entity that is neither physical nor mental.
Jung and Pauli sought a "neutral language" capable of explaining physical and psychic phenomena.
MENTAL as Pregeometry
Wheeler's philosophy of seeking the foundation of physics in a deeper reality is a universal principle, i.e., it is applicable to the foundation of every discipline.
The pre-geometric approach is of the bottom-up type, i.e., from the deep to the shallow. Particle-based physics (Wheeler's first approach) is of the top-down type, i.e., from shallow to deep. It is clear that the first approach is the correct one.
Pregeometry, as it stands, is not a rigorous, formal theory, but a set of hypotheses concerning a hypothetical realm from which the physical world emerges. But pregeometry is actually the search for the fundamental language of physics, a deep, non-physical, non-geometric language, a "theory of everything", a universal theory. In this sense, MENTAL is postulated as such a language for the following reasons:
Its formalism is the most simple, abstract and profound. From it naturally emerge all possible structures (static and dynamic), of any dimension, including all structures of physics (quantum, classical and relativistic). One of these structures is the Clifford algebra, which according to many authors is at the core of modern theoretical physics. [see Applications - Mathematics - Algebraic Geometry].
It is an abstract geometry, but it allows expressing all kinds of concrete geometries, including Euclidean, hyperbolic and elliptic, i.e., those of zero, negative and positive curvature, respectively.
It also allows to generate abstract graphs in the environment, which can be converted into concrete graphs with the help of a graphical representation device [see Applications - Computer Science - MENTAL, a Graphical Language].
It is a language based on primary archetypes. Everything is the manifestation of primary archetypes. Therefore, it is the foundation of all that exists. Physical and mental reality arise from the same primary archetypes. The physical world is a particular case of the abstract world: it emerges from the abstract world.
It is based on the expressions of the primary archetypes, not on information, although expressions and information can be considered equivalent. Moreover, digital information takes us away from meaning because every sequence of bits requires an external interpretation. The dual is really a meta-archetype; it is at a deeper level than the archetypes. With digital information we cannot construct a language
The objective world does not arise from information −as Wheeler said − but because the inner and outer world share the same archetypes.
At a deep level, space and time are abstract and both are linked.
Real numbers (including irrational numbers) exist in the mental world but irrational numbers do not manifest at the physical level because they involve infinity. That is why, in Zeno's famous paradox of Achilles and the tortoise, Achilles never catches up with the tortoise at the abstract (or logical) level, but he does catch up with it at the physical level because the space-time lines of Achilles and the tortoise cross.
Consciousness is the engine that connects the inner with the outer. It is the third factor, the third world. From consciousness, ontology is the same as epistemology. Wheeler ignored consciousness in his information theory. He only considered meaning as emerging from information. But meaning actually emerges from the archetypes of consciousness and its manifestations.
It is really a "theory of everything," including the physical world, the mental world, and the possible worlds. Metaphysical idealism is abstraction based on archetypes.
There is no geometrical space, but the abstract space in which expressions inhabit and in which they are related. Space is formed by the relationships between the elements. And with space, time is formed, since both go together.
The distance between elements occurs only in sequences. This distance is abstract, not physical. There is also the concept of length (the length of a sequence), which is also abstract.
There is no feedback loop −as Wheeler said. Wheeler was looking in "the reflective universe" for consciousness. But consciousness resides at the junction of the internal and the external, where ontology equals epistemology.
The quantum world is an intermediate world between the mental and the physical (macroscopic) but it is more similar to the mental. Hence MENTAL is the most appropriate language to formalize the quantum world. The mental world is a world of possibilities, and so is the quantum world, since a quantum entity can manifest itself in different ways.
In conclusion, MENTAL is the foundation of pregeometry, it is the language of pregeometry and pregeometry itself.
Bibliography
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Brassard, Gilles. Is information the key? Nature Physics 1:2-4, 2005. Disponible en Internet.
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Combs, Allan; Germine, Mark; Goertzel, Ben (eds.). Mind in Time. The Dynamics of Thought, Reality, and Consciousness. Hampton Pr., 2003. [Incluye el capítulo “Mind as Pregeometry”, por Ben Goertzel.]
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