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Philosophies

Time and Life in the Relational Universe: Prolegomena to an Integral Paradigm of Natural Philosophy

Abir U. Igamberdiev

Published Oct 16, 2018• 15 citations
Publisher

Abstract

Relational ideas for our description of the natural world can be traced to the concept of Anaxagoras on the multiplicity of basic particles, later called “homoiomeroi” by Aristotle, that constitute the Universe and have the same nature as the whole world. Leibniz viewed the Universe as an infinite set of embodied logical essences called monads, which possess inner view, compute their own programs and perform mathematical transformations of their qualities, independently of all other monads. In this paradigm, space appears as a relational order of co-existences and time as a relational order of sequences. The relational paradigm was recognized in physics as a dependence of the spatiotemporal structure and its actualization on the observer. In the foundations of mathematics, the basic logical principles are united with the basic geometrical principles that are generic to the unfolding of internal logic. These principles appear as universal topological structures (“geometric atoms”) shaping the world. The decision-making system performs internal quantum reduction which is described by external observers via the probability function. In biology, individual systems operate as separate relational domains. The wave function superposition is restricted within a single domain and does not expand outside it, which corresponds to the statement of Leibniz that “monads have no windows”.

DOI
10.3390/philosophies3040030

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Internal Quantum Measurements and the Growth of Information

Abir U. Igamberdiev

Introduction In the processes of adaptation, development and evolution, living systems interpret themselves in the environment resulting in changes of both. This leads to the growth of information via rescaling of internal time (heterochrony) followed by spatial reconstructions of morphology (heterotopy). The growth of information is based on perpetual changes in its interpretation in the changing world. Biological evolution involves the anticipatory epigenetic changes in interpretation of the genetic information which cannot be generally forecasted but can provide canalization of structural changes defined by the existing organization leading to predictable patterns of form generation. Social evolution is accompanied by unprecedented growth of the informational field that leads to progressive development of human society. In modern theoretical biology, the internal measurement concept was suggested as a background for explanation of the phenomenon of life (Matsuno, 1995). The quantum measurement represents the action of a measuring device on the measured system. The quantum measurement is an irreversible phenomenon exhibiting itself as a reduction of the potential field. It has also a relation to the irreversibility of time (Igamberdiev, 1993). The collapse of wave function is not equivalent to time until it does not generate a measurable duration, but when its pattern is repeated consistently, the clock can be set, and the system becomes organized in time. When the measuring device is a part of measured system, the measurement proceeds internally in relation to the whole system and the latter becomes more complex as a result of measurement itself. The aim of this study is to discuss the role of internal measurement in the growth of information in evolving systems. This can refer to biological evolution, social evolution, and as well to the cosmic evolution, which is represented in the phenomenon of expansion of the Universe. Internal Measurement and the Generation of New Information The internal measurement leads to an iterative recursive process which appears as the development and evolution of the combined system containing the measuring device and the measured object. The quantum measuring device can be organized in such way that it “encodes” the system in the course of interaction with the measured object, and makes it possible for the measurement to proceed in a regular way. In this case, such system can memorize the evolutionary complication of organization in a digital information-bearing subsystem and evolve further; in other words it contains an internal description memorizing the result of measurement. The logical precondition of the growth of information in this evolving process is the incompleteness of biosystem’s internal description, while the physical precondition is the uncertainty of quantum measurement. The evolutionary increase of complexity becomes possible when genotype appears as a system distinct from phenotype and is embedded into it, which separates energy-degenerate rate-independent genetic symbols from the rate-dependent dynamics of construction that they control (Pattee, 2001). Evolutionary growth of information becomes its own cause, a universal property of our world. The growth of information accompanies the appearance of measurable time that occurs in the systems performing quantum measurements in a regular way, with low dissipation of energy (Igamberdiev, 1993, 2004). These systems are modelled as hypercycles and can be defined as structures in which the subset of a substrate set of the catalytic system happens to be the matrix for generating and reproducing the set of catalysts itself (Igamberdiev, 1999). This definition keeps the main features of the original notion of hypercycle given by Eigen and Schuster (1979). The hypercyclic system is closed in the way that all of the catalysts needed for an organism to stay alive (representing an efficient causation according to Aristotle and forming organism’s spatiotemporal structure) must be produced by the organism itself, only relying on matter and energy from the outside (Letelier et al., 2011). When hypercycles appear in evolution, time becomes an independent measurable variable due to the internal reproducible changes. Hypercycle organizes irreversibility of quantum measurement into a measurable duration. Eigen’s hypercycle is a formalized representation of the autopoietic system of Maturana and Varela or Rosen’s (M,R) system (Leteiler et al., 2011). The system becomes an internal autonomous clock that distinguishes the past (memory), the present (life), and the future (anticipation based on the reproducible model), so the modeling, logic and digital information growth become possible within the system (Rosen, 1985). The hypercycle having own embedded description, becomes a structure that realizes computation in accordance with its internal logic defined by the embedded description. The latter has the property of incompleteness which is reflected in the fact that quantum correlations of the states of the system are associated with undecidable logic theories, i.e., they can potentially generate the statements not defined within the system. The undecidability can be interpreted in the sense similar to the Gödel’s incompleteness theorem, meaning that there exist propositions, expressible in the formal logic, which cannot be proven or disproven (Briegel et al., 2009). These propositions become the grounds of expansion of the system and its informational growth. From the quantum mechanical point of view, the emergence of a new statement results in acquiring a new error-correction meaning to support the internal quantum state (IQS) (Igamberdiev, 2004, 2007). The IQS keeps the system organizationally invariant. It is supported by the set of error-correcting commands that aim to keep IQS free from external demolitions. The error-correction information becomes an important part of the whole informational field. A new statement makes the system more complex (it leads to an increase of its informational content), with its all spatiotemporal organizational invariance be rescaled. In the course of evolution, an available element of a formal system (similarly to a word when used as a metaphor) can acquire another (in addition to already existing) value that contributes to formation of a new level of organization in the system. The logical basis of this action is the incompleteness of the existing formal system that allows assigning arbitrary values to the statements non-provable within that system, while the physical basis is the quantum uncertainty arising in quantum measurement. A new statement can arise from existing elements by acquiring the double function, however, for fixation of this new statement via expansion of existing formal system, some informational redundancy of the system is needed, which can be achieved by multiplication of some of its elements. Genome is a system which possesses an internal complementarity between the linear texts and their superposition. Relevantly to this, complementarity means that text and hypertext cannot be viewed at the same moment: they should be separated by a time interval. It is an example of uncertainty between the system and its embedding. Overlapping genes, alternatively splicing sequences, RNA and DNA editing, introns, and recombination according to molecular addresses are the features of this hypertext generating a potentially infinite number of language games. Genome as a complete language exists as a complementary set of its alternative combinations resulting in logical paradoxes which determine its temporal dynamics (Isalan, 2009). This superposition is a basis for ontogenesis, adaptation and evolution. Thus, the total “true” genome is a superposition of contradictory arrangements, which generate one single arrangement at a concrete moment of time. The pool of mobile genetic elements expands the combinatorial capacity of the genome by many times. An ambiguity in meaning is analogous to the quantum uncertainty principle in which it is impossible to define strictly the position and impulse of a particle simultaneously, or to fix certain energy in a very short period of time necessary for its registration. The question of a minimal size of the autocatalytic self-reproducing system and its composition has been discussed in several works (Sharov, 2009; Steel et al., 2013). Self-reproduction itself is a creative process of placing text in text with following self-growing of this joint structure. Any evolutionary change also begins from the placing of “text into text”. This is possible because genome is structurally adapted for realization of such a non-trivial function. Moreover, even a point mutation or deletion may be considered as generative if it is placed in the repeated (e.g., diploid) structure. The doubling is a premise of metasystem transition, which includes duplication of the original system and the establishment of control over multiple copies (Turchin, 1977). The evolutionary significance of gene duplication was considered by Ohno (1970) as a premise of neofunctionalization. The advantage of sexual reproduction is in the casual combinatorial generating of new statements from two separate texts that can acquire meanings, thus it resists evolutionary degradation. It becomes a prerequisite for growing of information and complexity (Igamberdiev, 2014). The combinatorial interaction of heterochronic texts generates a new system in which the internal time is rescaled in a new way that generally cannot be forecasted. The heterochronic duplication (via hybridization of temporally different organisms) generates more possibilities for the metasystem transition. Thus, the incompleteness of embedded set of symbols is the formal cause of evolution. The physical representation of this incompleteness is a quantum uncertainty in the course of measurement (Matsuno, 1992). It spans from the level of elementary particles to biological evolution and to the phenomenon of free will and consciousness. Growth of Information in the Expanding Universe The growth of information that we discuss here mainly in relation to biological evolution is relevant also to the physical space-time scales. The self-growing principle of quantum measurement has a property of intrinsic expansion of the informational field. The relationship between observable nature and a hidden “potential” nature is modeled, according to Kineman (2010), as an imaginary space-time domain geometrically represented as radial “Minkowski-space”. Despite of the fact that local space and time are normally represented as real numbers, the general relationship in this geometry is hyperbolic in accordance with the special theory of relativity. When mapped as a radial geometry, the space-time is seen to be intrinsically dynamic (expanding) and self-similar across all scales. The geometry has the properties of early and present acceleration. This representation eliminates the “light cone” and thus all regions in this model are the domains of existence and are observable over time. Nevertheless a domain of general, non-local reality is represented in the imaginary axes that exist simultaneously with measurable, local domains. The Universe in the concept of Kineman (2010) consists of the units called “holons”, which vaguely correspond to Leibniz’s monads. They possess simultaneous properties of location and non-location, as a point of non-differentiated whole appearing in a subject-object relation. The Everett’s interpretation of quantum mechanics works in these isolated domains but not between the domains, the same idea has been suggested by Matsuno (2012) for the individual biological systems taken as separate domains. The reality of superposition of the wave function is limited by the single monad and does not expand outside it, and in this sense monads do not have windows as originally proposed by Leibniz. Conclusion The growth of information is the basic property of evolving systems and it follows from the interaction between non-local and local domains in the course of internal quantum measurements. The internal measurement leads to an iterative recursive process which appears as evolution of the combined system containing the measuring device and the measured object. The system through measurement acquires the property of expansion, which is seen in biological evolution, social development, and at cosmic scales as expansion of the Universe. References Briegel, H.J.; Browne, D.E.; Dur, W.; Raussendorf, R.; Van den Nest, M. Measurement-based quantum computation. Nature Physics 2009, 5, 19-26. Eigen, M.; Schuster, P. The Hypercycle: A Principle of Natural Self-Organization. Springer, Berlin, 1979. Igamberdiev, A.U. Quantum mechanical properties of biosystems: A framework for complexity, structural stability and transformations. Biosystems 1993, 31, 65‐ Igamberdiev, A.U. Foundations of metabolic organization: coherence as a basis of computational properties in metabolic networks. Biosystems 1999, 50, 1-16. Igamberdiev, A.U. Quantum computation, non-demolition measurements, and reflective control in living systems. Biosystems 2004, 77, 47–56. Igamberdiev, A.U. Physical limits of computation and emergence of life. Biosystems 2007, 90, 340–349. Igamberdiev, A.U. Time rescaling and pattern formation in biological evolution. Biosystems 2014, 123, 19-26. Isalan, M. Gene networks and liar paradoxes. Bioessays 2009, 31, 1110-1115. Letelier, J.C.; Cárdenas, M.L.; Cornish-Bowden, A. From L'Homme Machine to metabolic closure: steps towards understanding life. Journal of Theoretical Biology 2011, 286, 100-113. Matsuno, K. The uncertainty principle as an evolutionary engine. Biosystems 1991, 27, 63-76. Matsuno, K. Quantum and biological computation. Biosystems 1995, 35, 209-212. Matsuno, K. Chemical evolution as a concrete scheme for naturalizing the relative-state of quantum mechanics. Biosystems 2012, 109, 159-168. Kineman, J.J. Relational self-similar space-time cosmology revisited. Proceedings of the 54th Meeting of the International Society for System Sciences. Waterloo, Canada, 2010. Ohno, S. Evolution by Gene Duplication. Springer, New York, 1970. Pattee, H.H. The physics of symbols: bridging the epistemic cut. Biosystems 2001, 60, 5-21. Sharov, A.A., 2009. Coenzyme autocatalytic network on the surface of oil microspheres as a model for the origin of life. International Journal of Molecular Sciences 2009, 10, 1838-1852. Steel, M.; Hordijk, W.; Smith, J. Minimal autocatalytic networks. Journal of Theoretical Biology 2013, 332, 96-107. Turchin, V. Phenomenon of Science. Columbia University Press, New York, 1977.

ISIS Summit: The Information Society at the Crossroads•Jun 23, 2015•0 citations
Relational ideas for our description of the natural world can be traced to the concept of Anaxagoras on the multiplicity of basic particles, later called “homoiomeroi” by Aristotle, that constitute the Universe and have the same nature as the whole world. Leibniz viewed the Universe as an infinite set of embodied logical essences called monads, which possess inner view, compute their own programs and perform mathematical transformations of their qualities, independently of all other monads. In this paradigm, space appears as a relational order of co-existences and time as a relational order of sequences. The relational paradigm was recognized in physics as a dependence of the spatiotemporal structure and its actualization on the observer. In the foundations of mathematics, the basic logical principles are united with the basic geometrical principles that are generic to the unfolding of internal logic. These principles appear as universal topological structures (“geometric atoms”) shaping the world. The decision-making system performs internal quantum reduction which is described by external observers via the probability function. In biology, individual systems operate as separate relational domains. The wave function superposition is restricted within a single domain and does not expand outside it, which corresponds to the statement of Leibniz that “monads have no windows”.
Two narratives – natural science and religious, intersect in the area of ​​unobserv­able ontology – an immaterial, transcendental, but real area that paradoxically exists outside and inside ordinary physical space-time. It is assumed that mathe­matical constructs, physical laws, physical constants, quantum objects, and even biological laws can be associated with this area. It is argued that physical laws are not invented by man, but are discovered, since they contain physical con­stants measured in special experimental works. Universal constants were not invented for reasons of convenience – physics accepts them as an inevitable con­sequence of the coincidence of the results of all special measurements. Observa­tional data are presented that indicate an extremely small change in fundamental constants or even their constancy over the entire time of the existence of the Uni­verse, although this interesting problem cannot be considered finally solved. The ontology of quantum objects is considered within the framework of Seval­nikov's polyiontic paradigm, according to which two modes are distinguished – potential and actual. The potential existence of quantum objects is described by the Schrödinger wave function, and the actual one appears during the transition from the spectrum of possible states to the only observable one. It is emphasized that potential being does not belong to the classical space, but is in an unobserv­able ontology. The observed state, on the contrary, is already in ordinary space – time and can be recorded by the device. This determines the existence of a spe­cial transcendental layer of reality, along with the material, which may indicate a certain duality in the structure of the Universe. Then it should be assumed that our Universe is not a universal, but a multiverse – a set of different worlds onto­logically having a different nature. In addition, the polyiontic paradigm leads to the idea that, at the quantum level, matter can be derived from information hid­den in an unobservable ontology.
The relationship between mind and reality is usually perceived as an event that takes place in reality and producing simultaneously an internal image in the mind. So it takes place twice, so to speak, and there is a one-to-one correspondence between the two events. Within this conception, matter is embedded in space and time, and can be designated as "container-principle". This monograph emphasizes that the well-known philosopher Immanuel Kant denied this principle and he stated that reality is principally not recognizable to a human being, and modern biological evolution seems to lead exactly to Kant's point of view. Within the theory of evolution, man's image about reality in mind does not have to be complete and true in the sense of a precise reproduction, and it is relatively easy to recognize that even space and time should not be elements of reality outside. Within this conception, only a certain part of reality, which the human being needs for mastering life, is projected onto space and time, and we come to the so-called "projection principle". Then, spacetime defines the window to reality, leading to a number of exciting and essential questions, some of which are discussed in this monograph. As is known, current physics is mainly based on the container-principle. But this monograph proposes that the projection principle is obviously more suitable and could help to solve open-ended questions as, for example, in connection with the nature of time, the particle-wave duality, the cosmological constant, etc. Regarding the statistical behavior of matter, Einstein's statement "God does not play dice" has to be seen in a new light, but also Feynman's general viewpoint on quantum theory that it cannot be understood by man. However, conventional quantum theory is obviously not a consistent framework as per the projection principle. The term "world equation" is critically probed in this monograph. Readership: Students, researchers and academics interested in quantum physics and evolutionary biology.
The origin of space and time is the deepest question in fundamental physics. This paper addresses it from quantum-theoretic perspective, deriving both concepts from elementary principles. Time appears as a measure for the stream of decision acts, collapsing quantum potentialities of the future to actual reality. Guiding of this construction is identified as fundamental function of life, thus obtaining definition in cybernetic style. This entails specific geometric structure of subjective meaning identical to that of the simplest quantum state, the qubit. Alignment of individual meaning spaces then produces 3-dimensional Euclidean space as biologically fixed format of common sense. The problem of space-time is thereby triangulated with the nature of life, identifying these three concepts as integral sides of the same fundamental phenomenon. The theory opens new prospects for scientific and ethical progress.
In resisting attempts to explain the unity of a whole in terms of a multiplicity of interacting parts, quantum mechanics calls for an explanatory concept that proceeds in the opposite direction: from unity to multiplicity. Being part of the Scientific Image of the world, the theory concerns the process by which (the physical aspect of) what Sellars called the Manifest Image of the world comes into being. This process consists in the progressive differentiation of an intrinsically undifferentiated entity. By entering into reflexive spatial relations, this entity gives rise to (i) what looks like a multiplicity of relata if the reflexive quality of the relations is not taken into account, and (ii) what looks like a substantial expanse if the spatial quality of the relations is reified. If there is a distinctly quantum domain, it is a non-spatial and non-temporal dimension across which the transition from the unity of this entity to the multiplicity of the world takes place. Instead of being constituents of the physical world, subatomic particles, atoms, and molecules are instrumental in its manifestation. These conclusions are based on the following interpretive principle and its more direct consequences: whenever the calculation of probabilities calls for the addition of amplitudes, the distinctions we make between the alternatives lack objective reality. Applied to alternatives involving distinctions between regions of space, this principle implies that, owing to the indefiniteness of positions, the spatiotemporal differentiation of the physical world is incomplete: the existence of a real-valued spatiotemporal background is an unrealistic idealization. This guarantees the existence of observables whose values are real per se, as against “real by virtue of being indicated by the values of observables that are real per se.” Applied to alternatives involving distinctions between things, it implies that, intrinsically, all fundamental particles are numerically identical and thus identifiable with the aforementioned undifferentiated entity.
Introduction In the processes of adaptation, development and evolution, living systems interpret themselves in the environment resulting in changes of both. This leads to the growth of information via rescaling of internal time (heterochrony) followed by spatial reconstructions of morphology (heterotopy). The growth of information is based on perpetual changes in its interpretation in the changing world. Biological evolution involves the anticipatory epigenetic changes in interpretation of the genetic information which cannot be generally forecasted but can provide canalization of structural changes defined by the existing organization leading to predictable patterns of form generation. Social evolution is accompanied by unprecedented growth of the informational field that leads to progressive development of human society. In modern theoretical biology, the internal measurement concept was suggested as a background for explanation of the phenomenon of life (Matsuno, 1995). The quantum measurement represents the action of a measuring device on the measured system. The quantum measurement is an irreversible phenomenon exhibiting itself as a reduction of the potential field. It has also a relation to the irreversibility of time (Igamberdiev, 1993). The collapse of wave function is not equivalent to time until it does not generate a measurable duration, but when its pattern is repeated consistently, the clock can be set, and the system becomes organized in time. When the measuring device is a part of measured system, the measurement proceeds internally in relation to the whole system and the latter becomes more complex as a result of measurement itself. The aim of this study is to discuss the role of internal measurement in the growth of information in evolving systems. This can refer to biological evolution, social evolution, and as well to the cosmic evolution, which is represented in the phenomenon of expansion of the Universe. Internal Measurement and the Generation of New Information The internal measurement leads to an iterative recursive process which appears as the development and evolution of the combined system containing the measuring device and the measured object. The quantum measuring device can be organized in such way that it “encodes” the system in the course of interaction with the measured object, and makes it possible for the measurement to proceed in a regular way. In this case, such system can memorize the evolutionary complication of organization in a digital information-bearing subsystem and evolve further; in other words it contains an internal description memorizing the result of measurement. The logical precondition of the growth of information in this evolving process is the incompleteness of biosystem’s internal description, while the physical precondition is the uncertainty of quantum measurement. The evolutionary increase of complexity becomes possible when genotype appears as a system distinct from phenotype and is embedded into it, which separates energy-degenerate rate-independent genetic symbols from the rate-dependent dynamics of construction that they control (Pattee, 2001). Evolutionary growth of information becomes its own cause, a universal property of our world. The growth of information accompanies the appearance of measurable time that occurs in the systems performing quantum measurements in a regular way, with low dissipation of energy (Igamberdiev, 1993, 2004). These systems are modelled as hypercycles and can be defined as structures in which the subset of a substrate set of the catalytic system happens to be the matrix for generating and reproducing the set of catalysts itself (Igamberdiev, 1999). This definition keeps the main features of the original notion of hypercycle given by Eigen and Schuster (1979). The hypercyclic system is closed in the way that all of the catalysts needed for an organism to stay alive (representing an efficient causation according to Aristotle and forming organism’s spatiotemporal structure) must be produced by the organism itself, only relying on matter and energy from the outside (Letelier et al., 2011). When hypercycles appear in evolution, time becomes an independent measurable variable due to the internal reproducible changes. Hypercycle organizes irreversibility of quantum measurement into a measurable duration. Eigen’s hypercycle is a formalized representation of the autopoietic system of Maturana and Varela or Rosen’s (M,R) system (Leteiler et al., 2011). The system becomes an internal autonomous clock that distinguishes the past (memory), the present (life), and the future (anticipation based on the reproducible model), so the modeling, logic and digital information growth become possible within the system (Rosen, 1985). The hypercycle having own embedded description, becomes a structure that realizes computation in accordance with its internal logic defined by the embedded description. The latter has the property of incompleteness which is reflected in the fact that quantum correlations of the states of the system are associated with undecidable logic theories, i.e., they can potentially generate the statements not defined within the system. The undecidability can be interpreted in the sense similar to the Gödel’s incompleteness theorem, meaning that there exist propositions, expressible in the formal logic, which cannot be proven or disproven (Briegel et al., 2009). These propositions become the grounds of expansion of the system and its informational growth. From the quantum mechanical point of view, the emergence of a new statement results in acquiring a new error-correction meaning to support the internal quantum state (IQS) (Igamberdiev, 2004, 2007). The IQS keeps the system organizationally invariant. It is supported by the set of error-correcting commands that aim to keep IQS free from external demolitions. The error-correction information becomes an important part of the whole informational field. A new statement makes the system more complex (it leads to an increase of its informational content), with its all spatiotemporal organizational invariance be rescaled. In the course of evolution, an available element of a formal system (similarly to a word when used as a metaphor) can acquire another (in addition to already existing) value that contributes to formation of a new level of organization in the system. The logical basis of this action is the incompleteness of the existing formal system that allows assigning arbitrary values to the statements non-provable within that system, while the physical basis is the quantum uncertainty arising in quantum measurement. A new statement can arise from existing elements by acquiring the double function, however, for fixation of this new statement via expansion of existing formal system, some informational redundancy of the system is needed, which can be achieved by multiplication of some of its elements. Genome is a system which possesses an internal complementarity between the linear texts and their superposition. Relevantly to this, complementarity means that text and hypertext cannot be viewed at the same moment: they should be separated by a time interval. It is an example of uncertainty between the system and its embedding. Overlapping genes, alternatively splicing sequences, RNA and DNA editing, introns, and recombination according to molecular addresses are the features of this hypertext generating a potentially infinite number of language games. Genome as a complete language exists as a complementary set of its alternative combinations resulting in logical paradoxes which determine its temporal dynamics (Isalan, 2009). This superposition is a basis for ontogenesis, adaptation and evolution. Thus, the total “true” genome is a superposition of contradictory arrangements, which generate one single arrangement at a concrete moment of time. The pool of mobile genetic elements expands the combinatorial capacity of the genome by many times. An ambiguity in meaning is analogous to the quantum uncertainty principle in which it is impossible to define strictly the position and impulse of a particle simultaneously, or to fix certain energy in a very short period of time necessary for its registration. The question of a minimal size of the autocatalytic self-reproducing system and its composition has been discussed in several works (Sharov, 2009; Steel et al., 2013). Self-reproduction itself is a creative process of placing text in text with following self-growing of this joint structure. Any evolutionary change also begins from the placing of “text into text”. This is possible because genome is structurally adapted for realization of such a non-trivial function. Moreover, even a point mutation or deletion may be considered as generative if it is placed in the repeated (e.g., diploid) structure. The doubling is a premise of metasystem transition, which includes duplication of the original system and the establishment of control over multiple copies (Turchin, 1977). The evolutionary significance of gene duplication was considered by Ohno (1970) as a premise of neofunctionalization. The advantage of sexual reproduction is in the casual combinatorial generating of new statements from two separate texts that can acquire meanings, thus it resists evolutionary degradation. It becomes a prerequisite for growing of information and complexity (Igamberdiev, 2014). The combinatorial interaction of heterochronic texts generates a new system in which the internal time is rescaled in a new way that generally cannot be forecasted. The heterochronic duplication (via hybridization of temporally different organisms) generates more possibilities for the metasystem transition. Thus, the incompleteness of embedded set of symbols is the formal cause of evolution. The physical representation of this incompleteness is a quantum uncertainty in the course of measurement (Matsuno, 1992). It spans from the level of elementary particles to biological evolution and to the phenomenon of free will and consciousness. Growth of Information in the Expanding Universe The growth of information that we discuss here mainly in relation to biological evolution is relevant also to the physical space-time scales. The self-growing principle of quantum measurement has a property of intrinsic expansion of the informational field. The relationship between observable nature and a hidden “potential” nature is modeled, according to Kineman (2010), as an imaginary space-time domain geometrically represented as radial “Minkowski-space”. Despite of the fact that local space and time are normally represented as real numbers, the general relationship in this geometry is hyperbolic in accordance with the special theory of relativity. When mapped as a radial geometry, the space-time is seen to be intrinsically dynamic (expanding) and self-similar across all scales. The geometry has the properties of early and present acceleration. This representation eliminates the “light cone” and thus all regions in this model are the domains of existence and are observable over time. Nevertheless a domain of general, non-local reality is represented in the imaginary axes that exist simultaneously with measurable, local domains. The Universe in the concept of Kineman (2010) consists of the units called “holons”, which vaguely correspond to Leibniz’s monads. They possess simultaneous properties of location and non-location, as a point of non-differentiated whole appearing in a subject-object relation. The Everett’s interpretation of quantum mechanics works in these isolated domains but not between the domains, the same idea has been suggested by Matsuno (2012) for the individual biological systems taken as separate domains. The reality of superposition of the wave function is limited by the single monad and does not expand outside it, and in this sense monads do not have windows as originally proposed by Leibniz. 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