Co∼eventum mechanics (twice revised version)

THE XVII CONFERENCE ON FAMEMS AND THE III WORKSHOP ON THE HILBERT’S SIXTH PROBLEM, KRASNOYARSK, SIBERIA, RUSSIA, 2018 Co∼eventum mechanics Oleg Yu. Vorobyev Institute of mathematics and computer science Siberian Federal University Krasnoyarsk mailto:[email protected] http://www.sfu-kras.academia.edu/OlegVorobyev http://olegvorobyev.academia.edu Abstract: For a long time, one of my dreams was to describe the nature of uncertainty axiomatically, and it looks like I’ve finally done it in my co∼eventum mechanics! Now it remains for me to explain to everyone the co∼ventum mechanics in the most approachable way. The main objective of co∼eventum mechanics and eventology [1] is the penetration of a new event-based language into all scientific and technological spheres and the development of the ability of the eventological potential of science and technology to transform the objects of study by event-based way, the formation of an interdisciplinary eventological paradigm that unifies, in the first place, socio-humanitarian, ecological, psycho-economic and other spheres, where scientific and technological research is difficult to imagine without including the observer in the subject of research, as well as the natural sciences in which the understanding of the impossibility of completely separating the subject of research from the observer has long been maturing. This is what I’m trying to do in this work. You yourself, or what is the same, your experience is such “coin” that, while you aren’t questioned, it rotates all the time in “free light”. And only when you answer the question the “coin” falls on one of the sides: “Yes” or “No” with the believability that your experience tells you. Eventology, probability theory, event, probability, entropy, negentropy, matter, life, mind, Kolmogorov’s axiomatics, co∼event, believability, certainty, believability theory, certainty theory, co∼events theory, Keywords: theory of experience and chance, co∼eventum mechanics, co∼eventum mechanistic approach, co∼event dualism, co∼event axiomatics, experienced-random experiment. MSC: 60A05, 60A10, 60A86, 62A01, 62A86, 62H10, 62H11, 62H12, 68T01, 68T27, 81P05, 81P10, 91B08, 91B10, 91B12, 91B14, 91B30, 91B42, 91B80, 93B07, 94D05 1 Milestones that discovered the path to co∼eventum mechanics I think that both mind and matter are merely convenient ways of grouping events. Bertrand Russel [2, 1946]. Die Welt ist alles, was der Fall ist.1 . Ludwig Wittgenstein [3, 1921]. An event is always co∼being, co∼event. Mikhail Bakhtin [4, 1920]. The co∼eventum mechanics is the science of co∼events. [2018]. The co∼eventum mechanics is a science of co∼events that grew out of the eventology [1] which in turn arose on the event-based “verge” of probability theory as a synthesis of unusually easy observations by several attentive observers: ∙ “an event is always co∼being, co∼event” [4, Bakhtin, 1920]2 ∙ “an event is a set of alternative outcomes; happens when one of them happens”. “... certain real numbers (probabilities) are aligned with events that may or may not happen ...” [6, Kolmogorov, 1933]3 ; c 2018 O.Yu.Vorobyev ○ This is an open-access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited. Oleg Vorobyev (ed.), Proc. of the XVII FAMEMS’2018, Krasnoyarsk: SFU, ISBN 978-5-9903358-7-5 1 “The world is all that is the case.” Mikhail Mikhailovich, 1895–1975, was a Russian philosopher, literary critic, semiotician and scholar who worked on literary theory, ethics, and the philosophy of language; he holds such literary concepts as polyphony, laughter culture, chronotop, carnivalization; believed (1920) that “an event is always co∼being, co∼event” [4] (see also [5]). His writings, on a variety of subjects, inspired scholars working in a number of different traditions (semiotics, structuralism, religious criticism) and in disciplines as diverse as literary criticism, history, philosophy, sociology, anthropology, and psychology. 3 Kolmogorov, Andrei Nikolaevich, 1903–1987, was a Russian mathematician; the founder of modern probability theory, within the framework of which he gave a mathematical definition of event and probability; basic works in the field of probability theory and mathematical statistics, topology, logic, theory of turbulence, theory of algorithm complexity. 2 Bakhtin, 60 THE XVII FAMEMS’2018 AND THE III H’S6P WORKSHOP ∙ “... we can identify that quantity which is usually called entropy, with the probability of the state in question ...” [7, Boltzmann, 1866]4 ; ∙ “every process, event, happening ..., everything that is going on in Nature means an increase of the entropy ... ; what an organism feeds upon while alive is negative entropy ...” “... consciousness is associated with the training of living substance ... its know-how is unconscious ... consciousness is a teacher of the unconscious ...” [8, Schrödinger, 1943], [9, 1958], [10, 1964]5 ; ∙ “... both mind and matter are merely convenient ways of grouping events” [2, Russel, 1946]6 ; ∙ “Die Welt ist alles, was der Fall ist7 ” [3, Wittgenstein, 1921]8 ; ∙ “a mind is born there and then, where and when the ability of living matter originates to make a probabilistic choice” is a paraphrase of the Lefebvre’ hypothesis [11, Lefebvre, 2001]9 ; ∙ “an event and a probability are two mutually related concepts, like two poles of a magnet that lose meaning in isolation from each other” [1, 2001]; ∙ “the world is all that occurs, when that is experienced, what happens” [12, 2016]. The main objective of co∼eventum mechanics and eventology [1] is the penetration of a new event-based language into all scientific and technological spheres and the development of the ability of the eventological potential of science and technology to transform the objects of study by event-based way, the formation of an interdisciplinary eventological paradigm that unifies, in the first place, socio-humanitarian, ecological, psycho-economic and other spheres, where scientific and technological research is difficult to imagine without including the observer in the subject of research, as well as the natural sciences in which the understanding of the impossibility of completely separating the subject of research from the observer has long been maturing. This work in a lot is more of a reference only: I just wanted to collect the arguments of different sciences and subject them to eventological transduction in order to later to link of their aggregate in a single picture of evolution: Matter — Life — Mind where Nature knows itself with the help of the co∼eventum mechanics it has created. I refer the scientists–pioneers to my supporters and opponents, who at various times made an indispensable contribution to the creation of this event-based picture, and throughout the whole work with pleasure and gratitude I refer to their statements. 1.1 Bakhtin about the event and co∼event Virtually the entire 20th century, the work of the philosopher and linguist Bakhtin was inaccessible to the scientific community. Today its scientific heritage is studied all over the world, especially in England, where the Bakhtin Center was created at Shefield University10 . So now, with the works of this remarkable scientist, it’s faster to get acquainted in English. For many years the American literary scholar Holquist dedicated the study of Bakhtin’s heritage11 : “The Russian word used, “sobytie”, is the normal word Russian would use in most contexts to mean what we call in English an “event”. In Russian, “event” is a word having both a root and a stem; it is formed from the word for being — 4 Boltzmann, Ludwig Eduard, 1844–1906, is generally acknowledged as one of the most important physicists of the nineteenth century. Particularly famous is his statistical explanation of the second law of thermodynamics. The celebrated formula S = kB · ln W , expressing a relation between entropy S and probability W has been engraved on his tombstone (even though he never actually wrote this formula down which was written down in this form by Plank, 1906). Boltzmann’s views on statistical physics continue to play an important role in contemporary debates on the foundations of that theory. 5 Schrödinger, Erwin Rudolf Josef Alexander, 1887–1961, was an Austrian theoretical physicist, one of the creators of quantum mechanics and the wave theory of matter; Nobel Prize in physics (1933); author of many works on statistical mechanics and thermodynamics, dielectric physics, color theory, electrodynamics, general theory of relativity and cosmology, unified field theory; philosopher and scholar; introduced the concept of negative entropy (negentropy) to describe living systems; radically changed the foundations of our modern world view, modern biology, philosophy of science, philosophy of reason and epistemology; his theory of life and self-organization of matter anticipated the current fusion of natural, social and human sciences, influenced the philosophy of nature and the modern view of the world, creating an evolutionary picture of the continuing synthesis of nature and culture: one of the most interesting events of modern thought. 6 Russell, Bertrand Arthur William, 1872–1970, was an English mathematician and philosopher; Nobel Prize in literature (1950). 7 “The world is all that is the case.” 8 Wittgenstein, Ludwig Josef Johann, 1889–1951, was an Austrian-British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. During his lifetime he published just one slim book, the 75-page Tractatus Logico-Philosophicus [3, 1921]. His manuscript were edited and published posthumously in 1953, and has since come to be recognised as one of the most important works of philosophy in the twentieth century. His teacher, Bertrand Russell, described Wittgenstein as “the most perfect example I have ever known of genius as traditionally conceived; passionate, profound, intense, and dominating”. 9 Lefebvre, Vladimir Alexandrivich (b. 1936) is a Russian and American psychologist and mathematician; the founder of the theory of reflection, located at the junction of many sciences: psychology, philosophy, mathematics, sociology, ethics, etc.; determines the mind as the ability to make a probabilistic choice. 10 The Bakhtin Center, The University of Sheffield: http://www.sheffield.ac.uk/bakhtin. 11 Holquist, J. Michael, 1935–2016, was an American literary critic; scholar of scientific heritage of Bakhtin. OLEG YU VOROBYEV. CO∼EVENTUM MECHANICS 61 “bytie” — with the addition of the prefix implying sharedness, “so-”, (or, as we should say in English, “co-” as co-operate or co-habit), giving “sobytie”, event as co-being. “Being” for Bakhtin then is, not just an event, but an event that is shared. Being is a simultaneity; it is always co∼being”. [13, Holquist, p. 25]. The co∼eventum mechanistic point of view. Bakhtin’s verbal formula “an event is always co∼being” is his brilliant anticipation and vision of the duality of being. The given idea underlies all his philosophy of language and his other writings on a variety of subjects. In the co∼eventum mechanics, his verbal formula acquires a strict mathematical meaning: “an event is always co∼event” that is a binary relation defined on the Cartesian product of the space of experience and the space of chance. 1.2 Kolmogorov about the event and probability “They assume a certain set of conditions, allowing an unlimited number of repetitions. They are studying a certain range of events that can happen as a result of the implementation of this set of conditions. In some alternative outcomes, these events may or may not happen in different combinations. In the set Ω they include all possible alternative outcomes of occurrence or non-occurrence of the events under study. If, after the next realization of this set of conditions, the alternative outcome that has happened in practice turns out to be part of the subset x ⊆ Ω, then it is said that the event x happened. Thus, each event they consider as a set of alternative outcomes” [6, Kolmogorov, 1933]. “... it can be assumed that certain events that may happen, or not happen after the implementation of this set of conditions, are associated with certain real numbers possessing axiomatic properties ... and called probabilities of events” [6, Kolmogorov, 1933]. The co∼eventum mechanistic point of view. Since Kolmogorov’s probability theory is one of the dual halves of the co∼eventum mechanics, and Kolmogorov’s axiomatics is a part of co∼eventum mechanistic axiomatics, Kolmogorov’s ideas about the event and its probabilities remain unchanged. Except for forced changes in terminology: Kolmogorov’s events, which are measured by probability, are called ket-events in the co∼eventum mechanics, which can only happen or not happen. Therefore, quotations from Kolmogorov can be translated into the co∼eventum mechanistic language as follows: “They assume a certain set of conditions, allowing an unlimited number of repetitions. They are studying a certain range of ket-events that can happen as a result of the implementation of this set of conditions. In some alternative outcomes, these ket-events may or may not happen in different combinations. In the set |Ω⟩, they include all possible alternative outcomes of happening or non-happening of the ket-events under study. If, after the next realization of this set of conditions, the alternative outcome that has happened in practice turns out to be part of the subset |x⟩ ⊆ |Ω⟩, then it is said that the ket-event |x⟩ happened. Thus, each ket-event they consider as a set of alternative outcomes” [12, 2016]. “... it can be assumed that certain ket-events that may happen, or not happen after the implementation of this set of conditions, are associated with certain real numbers possessing axiomatic properties ... and called probabilities of ket-events” [12, 2016]. This is a co∼eventum logic of the future chance. Since all those ket-events, that will happen, can serve as the possible future consequences of the present outcome of the chance observation. As for the other half of the co∼eventum mechanics, called the believability theory, the dual idea underlying it can be formulated in the same Kolmogorov style as follows: “They assume a certain set of conditions, allowing an unlimited number of repetitions. They are studying a certain range of bra-events that can be accumulated as a result of observations of ket-events that can happen as a result of the implementation of this set of conditions. In some joint incomes, these bra-events may be accumulated or not accumulated in different combinations. In the set ⟨Ω|, they include all accumulable joint incomes of accumulating or non-accumulating of the braevents under study. If, after the next realization of this set of conditions, the set of joint incomes all of which are accumulated in practice turns out to contain the subset ⟨x| ⊆ ⟨Ω|, then it is said that the bra-event ⟨x| was accumulated. Thus, each bra-event they consider as a set of joint accumulated incomes” [12, 2016]. “... it can be assumed that certain bra-events that may be accumulated, or not accumulated after the implementation of this set of conditions, are associated with certain real numbers possessing axiomatic properties ... and called believabilities of bra-events” [12, 2016]. This is a co∼eventum logic of the past experience. Since all those bra-events, that are accumulating in the observer’s experience at present, can serve as the past causes of the set of joint present incomes. 1.3 Feynman about the event and probability There’s a big difference between knowing the name of event and knowing event. Richard Feynman. “Other problems which may be further analyzed are those dealing with the theory of knowledge. For example, there seems to be a lack of symmetry in time in our knowledge. Our knowledge of the past is qualitatively different than that of the future. In what way is only the probability of a future event accessible to us while the certainty of a past 62 THE XVII FAMEMS’2018 AND THE III H’S6P WORKSHOP event can often apparently be asserted? These matters again have been analyzed to a great extent. I believe however a little more can be said to clarify the situation. Obviously, we are again involved in the consequences of the large size of ourselves and of our measuring equipment. The usual separation of observer and observed which is now needed in analyzing measurements in quantum mechanics should not really be necessary, or at least should be even more thoroughly analyzed. What seems to be needed is the statistical mechanics of amplifying apparatus.” [14, Feynman, 1951] The co∼eventum mechanistic point of view. The logic of the theory of experience and chance is the union of the co∼eventum logic of the future chance and the co∼eventum logic of the past experience. Since all those ket-events, that will happen, can serve as the possible future consequences of the present outcome of the chance observation. And because all those bra-events, that are accumulating in the observer’s experience at present, can serve as the past causes of the set of joint present incomes. In co∼eventum mechanics, a co∼event is defined as a binary relation between the observer’s experience and the chance of observation. Bra-events serve as models of the observer’s experience, and ket-events — as a model of the chance of observation. Any co∼event generates an element-set labelling of the Cartesian product of the space of observers and the space of observations. In this labelling, the accumulated bra-events play the role of the names of the happening ket-events. That is why Feynman’s quotation to this section has the following form in the language of co∼eventum mechanics: “There’s a big difference between knowing the bra-events and knowing the ket-events.” “The statistical mechanics of amplifying apparatus”, which Feynman lacked, is nothing more than the co∼event mechanics of bra-events. Because the result of the work of any amplifying apparatus is always a “some name” of what is observed with its help, in other words, it is a bra-event of observed ket-event. “If all the difficulties of quantum mechanics are gathered into one point, then it will be called “negative probabilities”.” [15, Feynman, 1982], [16, Feynman, 1987]. The co∼eventum mechanistic point of view. The paradox of negative probabilities in quantum mechanics is naturally formulated in the theory of co∼events as a paradox of phantom distributions of sets of co∼events (see [17]). However, the solution of this paradox is still to be discovered in the framework of the co∼eventum mechanics. 1.4 Boltzmann about the probability and entropy The foundation of all statistical physics is the statistical interpretation by Boltzmann of the second law of thermodynamics. The famous Boltzmann H-theorem justifies the second principle in application in an ideal gas. Boltzmann showed [7, 1866] that he discovered the connection of entropy and probability12 defines a measure for the entropy of systems of atoms and molecules in the gas phase, thereby providing a measure for entropy in classical thermodynamics. The logical completion of Boltzmann’s ideas was the statistical mechanics of Gibbs13 , which formed the basis of statistical thermodynamics. And the logical continuation of his ideas is quantum mechanics, born out of the quantum Planck hypothesis14 on the discreteness of the energy to which Planck came based on the assumption of the same Boltzmann on the discrete energy of molecules. The co∼eventum mechanistic point of view. In the most usual present sense, the Boltzmann entropy is interpreted as a measure of the observer’s uncertainty in the microstate of the system. The macrostate of the equilibrium of the system maximizes its entropy because then the observer loses a maximum of information about the microstates of the system except for its fixed macro variables. The maximization of entropy maximizes ignorance of the observer about the microscopic details of the system. It is commonly “believed” that this uncertainty is not everyday subjective uncertainty but rather the uncertainty that is inherent in its experimental method and interpretation model. In the co∼eventum mechanics this observer’ everyday subjective uncertainty is the uncertainty that is generated by observer’ experience and measured by the believability measure. However, in co∼eventum mechanics, the observer’s experience is understood in the broadest sense in such a way that it, of course, includes the experimental methods and interpretation models that the observer can use for her/his observations. It can be said that in co∼eventum mechanics both models and methods of observation are just a continuation or strengthening of the means of observation that the observer possesses. 12 See. the footnote 7 on page 60. Josiah Willard, 1839-1903 was an American mathematician, physicist, chemist and mechanic; one of the founders, statistical physics, mathematical theory of thermodynamics, vector analysis; established the fundamental law of statistical mechanics, the Gibbs distribution, generalized the entropy principle, applying the second law of thermodynamics to a wide range of physical processes; in many respects predetermined the development of modern exact sciences and natural science in general. 14 Plank, Max Karl Ernst Ludwig, 1858-1947, was a German theoretical physicist, founder of quantum physics; Nobel laureate in physics (1918); Basic works on thermodynamics, theory of thermal radiation, quantum theory, special theory of relativity, optics; formulated the second law of thermodynamics in the form of the principle of increasing entropy and used it to solve various problems of physical chemistry. 13 Gibbs, OLEG YU VOROBYEV. CO∼EVENTUM MECHANICS 63 So, the co∼eventum mechanics has more sophisticated means of describing and measuring entropy as a measure of disorder. First, it is the usual Boltzmann entropy, which I call the entropy of the observation’s chance, i.e. entropy of the set of ketevents. Secondly, this is the entropy of the observer’s experience, i.e. the entropy of the set of bra-events. And, finally, it is the entropy of experience and chance, or the entropy of the co∼event, which is simply equal to the sum of these two entropies. 1.5 Schrödinger about the matter, life, and mind evolution In his book “What is life?”15 Schrödinger introduced [8, 1943] the concept of negative entropy (most likely ascending to Boltzmann) which living organisms must receive from the surrounding world in order to compensate for the growth of entropy that leads them to thermodynamic equilibrium and, consequently, to of death. According to Schrödinger an import of negentropy, or export of entropy by living organisms is one of the main differences of life from inanimate nature: “Every process, event, happening — call it what you will; in a word, everything that is going on in Nature means an increase of the entropy of the part of the world where it is going on. Thus a living organism continually increases its entropy — or, as you may say, produces positive entropy — and thus tends to approach the dangerous state of maximum entropy, which is of death. It can only keep aloof from it, i.e. alive, by continually drawing from its environment negative entropy — which is something very positive as we shall immediately see. What an organism feeds upon is negative entropy. Or, to put it less paradoxically, the essential thing in metabolism is that the organism succeeds in freeing itself from all the entropy it cannot help producing while alive”. [8] The origin and evolution of life and mind Schrödinger also examines in detail in two other of his equally famous books “Mind and matter”[9, 1958]16 and “My view of the world”[10, 1963]17 . The co∼eventum mechanistic point of view. I would like to think that what Schrödinger called negative entropy is nothing else than the entropy of the observer’s experience in the co∼eventum mechanics. In my fairly long-ago paper [18], the first wording and the proof of the eventological H-theorem (the eventological generalization of Boltzmann H-theorem) is presented, which relates the entropy of experience and the entropy of chance. This is a very promising direction in the co∼eventum mechanics, which promises many discoveries and will require rigorous proofs. 1.6 Russell about the mind and matter as the events in “History of Western Philosophy” “Einstein substituted events for particles; each event had to each other a relation called interval, which could be analyzed in various ways into a time-element and a space-element. ... From all this it seems to follow that events, not particles, must be the stuff of physics. What has been thought of as a particle will have to be thought of as a series of events. The series of events that replaces a particle has certain important physical properties, and therefore demands our attention; but it has no more substantiality than any other series of events that we might arbitrarily single out. ... Thus matter is not part of the ultimate material of the world, but merely a convenient way of collecting events into bundles. ... While physics has been making matter less material, psychology has been making mind less mental. ... Thus from both ends physics and psychology have been approaching each other, and making more possible a neutral doctrine. ... I think that both mind and matter are merely convenient ways of grouping events. ... Some single events, I should admit, belong only to material groups, but others belong to both kinds of groups, and are therefore at once mental and material. ... This doctrine effects a great simplification in our picture of the structure of the world.” 15 “What Is Life? The Physical Aspect of the Living Cell” is a 1944 science book written for the lay reader by physicist Erwin Schrödinger in which he expounds his views of the physicist on the problems of biological life and for the first time introduces into science the concept of negentropy (negative entropy); written on the basis of three popular lectures, read by him in Dublin in February 1943 on the basis of the “Green Notebook”. 16 “Mind and Matter” is Schrödinger’s book (1958), in which he analyzes the physical principles of consciousness and the unconscious: “Consciousness is the teacher of the unconscious”, and examines issues that are traditionally considered the prerogative of philosophers, theologians , psychoanalysts and politicians: are the mind and matter, the subject and the object, the inner self and the external world completely different things or are they the same thing; what place does consciousness take in the evolution of life, which is the basis of morality; can one still expect the biological development of modern man and how will his intellectual development take place. 17 “My view of the world” is the Schrödinger’s book (1963), where he analyzes the philosophical problem of spatio-temporal multiplicity and the unity of observing and thinking subjects in whom no thought can arise, not a continuation of the thought of their ancestors, and also — the problem of the birth and evolution of the mind in the living, where consciousness plays the role of an instrument for the evolutionary learning of organic life, and the organic abilities of the living are unconscious: consciousness is something becoming ( this is the point of application of evolution), the unconscious is something that exists. 64 THE XVII FAMEMS’2018 AND THE III H’S6P WORKSHOP The co∼eventum mechanistic point of view. Following Bertrand Russell, the co∼eventum mechanic says with a “little clarification” that both mind and matter are merely convenient ways of grouping co∼events. Therefore, the theory of sets of co∼events, i.e. the co∼eventum mechanics can serve as the axiomatic basis of what can be called a unified theory of mind and matter. 1.7 Wittgenstein about events, mind and world By defining the world as all that occurs [3, 1921] and by showing the application of modern logic to metaphysics, via language, Wittgenstein provided new insights into the event-based relations between world, mind and language and thereby into the nature of philosophy. If in the initial items 1, 1.1, 1.11, 1.12, 1.13, 1.2, 1.21, and 2 of the English version [19, 1966] of the main Wittgenstein’s book, the term “a fact” we will naturally translate as “an event” then we will learn the description of the event-based picture of Wittgenstein’s world: “The world is all that occurs. The world is the totality of events, not of things. The world is determined by the events, and by their being all the events. For the totality of events determines what occurs, and also whatever doesn’t occur. The events in logical space are the world. The world divides into events. Each event can occur or can don’t occur while everything else remains the same. That what does occur, an event is the existence of states of the world”. The co∼eventum mechanistic point of view. Following Ludwig Wittgenstein, the co∼eventum mechanics says with a “little clarification” that the world is everything that occurs, i.e. what accumulates when something happens. In co∼eventum mechanics language this means that the world is everything that is co∼events. This means that the co∼eventum mechanistic generalizations of the ideas of Russell and Wittgenstein completely coincide, which again indicates a successful choice of the co∼eventum axiomatics for the theory of experience and chance. 1.8 Lefebvre about the origin of the mind You will not find in Lefebvre’s works literally the same utterance as on page 60, but having become better acquainted with his works [11], you will come with him, namely, to this conclusion: “a mind is born there and then, where and when the ability of living matter originates to make a probabilistic choice”. This event-probabilistic 18 hypothesis about the origin of the mind, which Lefebvre put forward, based on the results of experimental psychology [20], immediately follows from the fundamental Bakhtin definition of the event as co∼being, co∼event, [4] and the basic eventological idea [1]: “an event and a probability are two mutually related concepts, like two poles of a magnet that lose meaning in isolation from each other”. The co∼eventum mechanistic point of view. Following Lefebvre, the co∼eventum mechanics says with a “little clarification” that “a mind is born there and then, where and when the ability of living matter originates to make a believabilistic choice on the basis of its experience”. This assertion is based on the dual co∼eventum mechanistic idea: “a bra-event and a believability are two mutually related concepts, like two poles of a magnet that lose meaning in isolation from each other”. 2 What is the co∼eventum mechanics? “The world is all that occurs, when that is experienced, what happens” [12, 2016] “The co∼eventum mechanics is a science of co∼events that occurs, when that is experienced, what happens” [2018] “A man is the ability of living matter to co∼be, to group co∼events and to make a believabilistic choice of them” [2018] For a long time, one of my dreams was to describe the nature of uncertainty axiomatically, and it looks like I’ve finally done it in my co∼eventum mechanics19 ! Now it remains for me to explain to everyone the co∼eventum mechanics in 18 One can not but admit that Lefebvre in his works, operates only with probabilities, without using the concept of an event explicitly, although he always silently assumes it. 19 See [12, 21, 22], for example. OLEG YU VOROBYEV. CO∼EVENTUM MECHANICS 65 the most approachable way. This is what I’m trying to do in this work. In the modern theories of uncertainty a “belief” is usually defined as a measure in the space of probability distributions [23, 24]. In other words, this is a “probability of probability”, i.e., a probability of the second order. The co∼eventum mechanics approach is fundamentally different. It is grown from eventology [1], the science of the sets of Kolmogorov events. It can be said that random sets of “names” of Kolmogorov events are studied in eventology. The co∼eventum mechanics [12, 21, 22, 25, 26, 27, 28, 29] appears as a natural mathematical consequence of the eventological theory and the theory of random sets [30] only after the dual character of probability description of a set of events has been discovered [12, 21]. The concept of co∼event appeared that is defined as a measurable binary relation on the Cartesian product of a space of “names” (of bra-events) and a space of Kolmogorov events (of ketevents). A measure defined on this Cartesian product is defined as a product of a “probability measure of ket-events” and a “believability measure of bra-events”. This new measure is called the “certainty of co∼events”. The co∼eventum mechanics is another name for the co∼event theory, i.e., for the theory of experience and chance which I axiomatized in 2016 [12, 21]. In my opinion, this name best reflects the co∼event-based idea of the new dual theory of uncertainty, which combines the probability theory as a theory of chance, with its dual half, the believability theory as a theory of experience. In addition, I like this new name indicates a direct connection between the co∼event theory and quantum mechanics, which is intended for the physical explanation and description of the conflict between quantum observers and quantum observations [31]. Since my theory of uncertainty satisfies the Kolmogorov axioms of probability theory, to explain this co∼eventum mechanics I will use a way analogous to the already tested one, which explains the theory of probability as a theory of chance describing the results of a random experiment. The simplest example of a random experiment in probability theory is the “tossing a coin”. Therefore, I decided to use this the simplest random experiment itself, as well as the two its analogies: the “scrolling a coin” and the “spinning a coin” to explain the co∼eventum mechanics, which describes the results of a combined experiencedrandom experiment. I would like to resort to the usual for the probability theory “coin-based” analogy to explain (and first of all for myself) the logic of the co∼eventum mechanics as a logic of experience and chance. Of course, this analogy one may seem strange if not crazy. But I did not come up with a better way of tying the explanations of the logic of the co∼eventum mechanics to the coin-based explanations that are commonly used in probability theory to explain at least for myself the logic of the chance through a simple visual “coin-based” model that clarifies what occurs as a result of a combined experienced-random experiment in which the experience of observer faces the chance of observation. I hope this analogy can be useful not only for me in understanding the co∼eventum mechanics [12]. In the probability theory, the terms “throwing a coin”, “tossing a coin”, “scrolling a coin”, “rotating a coin”, “spinning a coin” and so on are used as classical synonymous for the name of a typical example of a random experiment. So at first I thought the co∼event theory [12] requires three different terms that distinguish similar experiments with a “coin”, but which are implemented within the framework of probability theory, believability theory [12], and co∼event theory correspondingly. Therefore, at first sight it seemed to me in the co∼eventum mechanics these usual synonymous are forced to get strictly different mathematical meanings. And I would have to choose the three terms to define for them the different meanings: ∙ “tossing a random coin”20 for the random experiment in the probability theory, ∙ “flipping all the experienced coins,” or in detail: “flipping all the experienced coins accumulated by an observer relevant to the observed outcome of some random coin” for the experienced experiment in the believability theory, and ∙ “spinning the experienced-random coins”, or in detail: “tossing a random coin and then flipping all the experienced-random coins accumulated by an observer relevant to 20 You can find an interesting attempt to construct a quantum model of “a random coin” in [32, 33]. I only note that in this paper I use a different co∼event approach and I am only interested in co∼event models, the construction of which does not go beyond the co∼eventum mechanics. 66 THE XVII FAMEMS’2018 AND THE III H’S6P WORKSHOP the observed outcome of this random coin” for the experienced-random experiment in the co∼event theory. However, everything turned out to be much more complicated than I expected. As a result, I was able to finally recognize that neither a random experiment nor an experienced experiment can be determined separately, but only together with each other, like the dual halves of a one experienced-random experiment. In this work, I’m going to discuss the way of definition and the need to introduce this terms into the new theory to axiomatically describe the co∼eventum mechanics in a conflict between an observer and an observation of co∼event. The author hopes this co∼eventum axiomatics will be useful in the study of quantum entanglement, which characterizes the collision of quantum observers and quantum observations. 2.1 The battle to find a satisfactory co∼eventum mechanistic ontology 2.1.1 “Coins in free rotation” I’m sure you will not have much trouble imagining “a real coin in free rotation”. I would like to consider this image as the “superposition state” of the real coin, as a natural state of the coin at a time when it is not observed by an observer. In a random experiment of tossing a coin, the coin turns out to be in such a “superposition state” in order to fall on one of its states/sides: “head” or “tail” at the moment of observation of the result of this experiment by an observer. For example, it can be said that “the real coin in free rotation” is an ordinary real coin that has already been tossed during a random experiment but has not yet fallen on one of its sides. It is not difficult to imagine “a real coin in free rotation”. This visualization of reality, which often appeared before your eyes, can be easily caused by your imagination. It is much more difficult to imagine what you have never seen. I mean your accumulated experience, which is also always in a “superposition state” as “a real coin in free rotation”, until the moment of an observation of the outcome of a random experiment that expands this your given experience. Such a “superposition state” of your experience I will imagine as “an imaginary experienced coin in free rotation”. What occurs at the moment of “a tossing a real coin” observation by an observer whose coin-based experience is in a “superposition state”, i.e. whose “experienced coin is in free rotation”? The emergent co∼event mechanics gives the completely clear answer: “The result of this experienced-random experiment is a co∼event, i.e., a bra-ket-event that is defined as the Cartesian product of a bra-event and a ket-event. The bra-event describes an accumulating the observer’ experience at the moment of observation, and the ket-event describes the chance of observation at the same moment. In other words, the bra-event is accumulated and the ket-event happens at the moment of collision between the observer’ experience and the chance of observation. This means that the bra-ket-event, i.e. the co∼event occurs at the same moment.” However, I continue to reasonably fear that the meaning of these theoretical explanations is understandable so far only to me alone. Therefore, I will try to illustrate them with the help of my “coin-based model” or maybe “dice-based model”. But foreseeing the reader’s inadequacies, I want to emphasize in advance three principal statements that relate to the observability properties of all three types of experiments, the strict definitions of which unusual for the reader will be given below. ∙ The result of the random experiment is unobservable because there is no one to observe. ∙ The result of the experienced experiment is unobservable because there is nothing to observe. ∙ And only the result of the experienced-random experiment is observable because there is something to observe, and there is one who observes. OLEG YU VOROBYEV. CO∼EVENTUM MECHANICS 67 2.1.2 An experienced-random experiment Neither a random experiment (see Definition 2) nor an experienced experiment (see Definition 3) exists separately. They are like two poles of a magnet, or as on two sides of a coin, either as a mind and matter, or as a mental and real, or as an experience and a chance, or as an observer and an observation. If you notice, each of them is defined in connection with another. Both of these experiments are inseparable halves of what I call an experienced-random experiment. Definition 1 (an experienced-random experiment, a bra-ket-experiment, a bra-ket-trial). An experiencedrandom experiment (a bra-ket-experiment, a bra-ket-trial) is a pair of two inseparable experiments that are carried out simultaneously. One of them is a random experiment, and the other is an experienced experiment21 . The result of each experiment from this pair is unobservable separately. Only the overall result of the pair is observable and indicates that some kind of co∼event has occurred, and what kind of co∼event it has been. At the time of observation, the unobservable chance in a random experiment generates in the experienced experiment an unobservable accumulation of the observer’s experience. This unobservable accumulated experience of the observer in a pair with the unobservable chance, is the overall observable result of the given experienced-random experiment, the observable co∼event. Figures 1, 2, 3, and 4 illustrating some experienced experiments depict Venn diagrams of co∼events in the bra-ket spaces ⟨Ω|Ω⟩ that occur as the results of appropriate experienced-random experiments, the dual halves of which are the random experiments and experienced experiments, which I have discussed above (see details in figure captions). 2.1.3 A random experiment Definition 2 (a random experiment, a ket-experiment, a ket-trial). A random experiment (a ket-experiment, a ket-trial) is a dual half of experienced-random experiment the result of which is unobservable in the absence of an observer, and in the presence of an observer its future result can not be predicted until its observation. In other words, a random experiment (a ket-experiment) is an experiment whose future result becomes available to the observer at the time of observation and can not be predicted until this moment of observation by the observer, regardless of her/his past experience. In the probability theory, the “tossing a random coin” is the typical example of a “random experiment”. However, in this theory, a “random experiment” is defined differently than in the co∼event mechanics, since the role of an observer in such a “random experiment” is completely ignored, and one can only guess at a tacitly existing abstract observer with an indefinite experience. Below I will also consider and define two more examples of a random experiment (”tossing a gray random dice” and “tossing a colored random dice”22 ), which, in my opinion, can most transparently explain the meaning of definition of a random experiment in the co∼eventum mechanics and its difference from a “random experiment” in probability theory. Example 1 (tossing a random coin). Imagine an urn contains balls, well-mixed together, that are colored by black or white in equal proportion23 . A ball is drawn at random from the urn, its color is observed by an observer, who is characterized by her/his own experience. From the point of view of probability theory an observer observes a value of the Boolean random variable, for example, the zero is “black” and the unit is “white”. The observer asks her/himself a question: “Is this ball black or white?”, in other words, “Which side of the coin fell: black or white?”24 Example 2 (tossing a gray random dice, all shades of gray from black to white). Imagine an urn contains balls, well-mixed together, that are colored by shades of gray from black to white. A ball is drawn at random from 21 See Definitions 3 and 2 below. a “random dice” I will understand as an ordinary random dice with six equiprobable faces, and a generalized random dice that has infinitely many equiprobable faces. 23 An urn model in probability theory is an idealized mental exercise in which some events that occur with objects of real interest (such as atoms, people, cars, etc.) are represented as a pulling/drawing/taking/dropping out colored balls from an urn. 24 The observer gives her/himself an answer based on her/his own experience The observer’s answer is the result of an experienced-random experiment in which the given random experiment serves as one of two inseparable halves of it. The other half of it is an experienced experiment, which consists in how the observer perceives and interprets this random experiment, accumulating her/his own experience. 22 By 68 THE XVII FAMEMS’2018 AND THE III H’S6P WORKSHOP the urn, its color is observed by an observer, who is characterized by her/his own experience. From the point of view of probability theory an observer observes a value of random variable uniformly distributed in the unit interval. The observer asks her/himself a question: “Is this ball rather black than white, or rather white than black?”, in other words, “On which side did the coin fall, on white or black?”24 Example 3 (tossing a colored random dice, all shades of any colors). Imagine an urn contains balls, wellmixed together, that are colored by all shades of any colors. A ball is drawn at random from the urn, its color is observed by an observer, who is characterized by her/his own experience. From the point of view of probability theory an observer observes a value of random vector uniformly distributed in the unit three dimension cube. The observer asks her/himself a question: ”Is this ball rather red, or orange, or yellow, or green, or blue, or violet than another color of the six-color rainbow?”, in other words, “On which side did the dice fall: on red, or on orange, or on yellow, or on green, or on blue, or on violet?”24 2.1.4 An experienced experiment To define and understand what an experienced experiment is, I will need to define who and what is involved in this experiment. Of course, and this has been said many times by me above, an indispensable participant in the experienced experiment is the observer with her/his experience. What I still need here is to define the models of the observer’s experience within the framework of my dice-based approach. These dice-based models I call a “gray experienced dice” and a “colored experienced dice”25 . Definition 3 (an experienced experiment, a bra-experiment, a bra-trial). An experienced experiment (a braexperiment, a bra-trial) is a dual half of experienced-random experiment the result of which is unobservable in the absence of an observation, and in the presence of an observation its future result can not be predicted until its observation. In other words, an experienced experiment (a bra-experiment) is an experiment whose future result becomes available to the observer at the time of observation and can not be predicted until this moment of observation by the observer, regardless of her/his past experience. Definition 4 (a gray experienced dice). A gray experienced dice is a hypothetical dice, which is colored by the observer’s experience in one shade of gray quite definite for the observer. This is a dice, which in each trial of the observer’s experience can fall on either side: “black” or “white” with the observer’s believability, which are defined by the observer’s experience of the degree of “grayness” of this hypothetical coin. Definition 5 (the singular gray experienced dices). The “black experience dice” and the “white experienced dice” are the two extreme singular cases of a gray experienced dice, which are defined by the observer’s experience with full believability. These dices are called the singular gray experienced coins. Definition 6 (a colored experienced dice). A colored experienced dice is a hypothetical dice, which is colored by the observer’s experience in one color quite definite for the observer. This is a dice, which in each trial of the observer’s experience can fall on either side: “violet”, “blue”, “green”, “yellow”, “orange”, or “red” with the observer’s believability, which are defined by the observer’s experience of the degree of “rainbow color” of this hypothetical dice. Definition 7 (the singular colored experienced dices). The “violet, blue, green, yellow, orange, or red experience dices” are the six extreme singular cases of a colored experienced dice, which are defined by the observer’s experience with full believability. These dices are called the singular colored experienced dices. “A flipping all the experienced dices”26 is the typical example of an experienced experiment in the believability theory. Below I will consider and define such examples of an experienced experiment (“a flipping all the singular gray experienced dices”, “a flipping all the gray experienced dices” and “a flipping all the colored experienced dices”) which, in my opinion, can most transparently explain the meaning of definition of an experienced experiment in the co∼eventum mechanics. 25 By an “experienced dice” I will understand as an ordinary experienced dice with six faces, and a generalized experienced dice that has infinitely many faces. 26 see terms in detail on page 65. OLEG YU VOROBYEV. CO∼EVENTUM MECHANICS 69 Example 4 (a flipping all the singular gray experienced dices). Imagine you are an observer and observe outcomes of the random experiment a “tossing a black-white random coin” in which the outcome “a coin fell on black side” happened. You observe this random outcome and, of course, come to the following conclusion. When you are asked: “On which side did the coin fall?” you need to say with full believability that the coin fell on the black side. Of course, this your conclusion is trivial here because this experienced experiment is singular. |Ω⟩ ⏟ ⏞ ∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘ |{x}⟩ |∅⟩ ⎧ ⏞  ⎪  ⎪  ⎪  ⎪   ⎪  ⎪  ⎪  ⎪   ⎪  ⎪  ⎪  ⎪   ⎪  ⎪  ⎪  ⎪   ⎪  ⎪  ⎪  ⎪   ⎪  ⎪  ⎪  ⎪   ⎪  ⎪  ⎪  ⎪   ⎪  ⎪  ⎪  ⎪   ⎪  ⎪  ⎪  ⎪   ⎪  ⎪  ⎪  ⎪   ⎪  ⎪  ⎪  ⎪   ⎪  ⎪  ⎪  ⎪   ⎪  ⎪  ⎪  ⎪   ⎪  ⎪  ⎪  ⎪   ⎪  ⎪  ⎪  ⎪   ⎪  ⎪ ⎪  ⎨    ⟨Ω| ⟨x|  ⎪  ⎪  ⎪   ⎪  ⎪  ⎪  ⎪   ⎪  ⎪  ⎪  ⎪   ⎪  ⎪  ⎪  ⎪   ⎪  ⎪  ⎪  ⎪   ⎪  ⎪  ⎪  ⎪   ⎪  ⎪  ⎪  ⎪  ⎪  ⎪   ⎪  ⎪  ⎪  ⎪   ⎪  ⎪  ⎪  ⎪   ⎪  ⎪  ⎪   ⎪  ⎪  ⎪  ⎪   ⎪  ⎪  ⎪  ⎪   ⎪  ⎪  ⎪  ⎪   ⎪  ⎪  ⎪  ⎪   ⎪  ⎪  ⎪  ⎪   ⎪  ⎪  ⎪  ⎩   ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ⏟ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ⏞ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ⏟ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ Table 1: A tossing the random coin and a flipping all the singular gray experienced coins. Venn diagram illustrates an income-outcome of the 24×24 experienced-random experiment (the “black-white observer” is making 24 “black-white random coin observations”) as a result of which co∼event R ⊆ ⟨Ω|Ω⟩ ( ○ ) occurs with the element-set labellings ⟨X|SX ⟩ = ⟨{x}|{∅, {x}}⟩. However, ask yourself: “Why do I give this answer with full believability?” You can explain this in a variety of ways, but all of them will, of course, be based on your own rich experience of observing the outcomes of this random experiment. The co∼event theory gives the following exact answer, based on its axioms [12]. So, you are absolutely right, the full believability is prompted by your experience of observing the outcomes of this random experiment. But how is this your experienced mechanism that allows you to come to conclusions with some degree of believability? The co∼event theory gives an axiomatic description of this experienced mechanism, which in a coin-dice-based 70 THE XVII FAMEMS’2018 AND THE III H’S6P WORKSHOP language is interpreted as follows. For such an experienced experiment, your experience has accumulated two sets of singular experienced dices. In one set, it has the black experienced dices, in the other it has the white experienced dices. At the very moment when you observe that the random coin has fallen on the black side, your experience begins its “experiment”: “a flipping all the black experienced dices accumulated by an observer relevant to the blackoutcome of the random coin”, which ends with all, without exception, black experienced dices falling on the black face. Precisely, the fact that all the dices that have been without exception dropped on the black face, allows you to give the answer with full believability. Otherwise, at the very moment when you observe that the random coin has fallen on the white side, your experience begins its another “experiment”: “a flipping all the white experienced dices accumulated by an observer relevant to the white-outcome of the random coin”, which ends with all, without exception, white experienced dices falling on the white face. Precisely, the fact that all the dices that have been without exception dropped on the white face, allows you to give the answer with full believability. (See Fig. 1) |Ω⟩ ⏟ ⏞ ∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘ |X1 ⟩ |X2 ⟩ |X3 ⟩ |X4 ⟩ |X5 ⟩ |X6 ⟩ |X7 ⟩ |X8 ⟩ |X9 ⟩ |X10⟩ |X11⟩ |X12⟩ |X13⟩ |X14⟩ |X15⟩ |X16⟩ |X17⟩ |X18⟩ |X19⟩ |X20⟩ |X21⟩ |X22⟩ |X23⟩ |X24⟩ ⎧ ⎪ ⟨x1 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x2 | ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x3 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x4 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x5 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⟨x6 | ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x7 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⟨x8 | ⎪ ⎪ ⎪ ⎪ ⟨x9 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x10 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x11 | ⎪ ⎪ ⎪ ⎪ ⎨⟨x12 | ⟨Ω| ⎪ ⟨x13 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x14 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x15 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x16 | ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x17 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x18 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x19 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⟨x20 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⟨x21 | ⎪ ⎪ ⎪ ⎪ ⟨x22 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x23 | ⎪ ⎪ ⎪ ⎪ ⎩⟨x | 24 ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ Table 2: A tossing the gray random dice and flipping all the singular gray experienced coins. Venn diagram illustrates an income-outcome of the 24×24 experienced-random experiment (24 “black-white observers” are making 24 “all shades of gray random dice observations”) as a result of which co∼event R ⊆ ⟨Ω|Ω⟩ ( ○ ) occurs with the element-set labellings ⟨X|SX ⟩ = ⟨{x1 , . . . , x24 }|{X1 , . . . , X24 }⟩. OLEG YU VOROBYEV. CO∼EVENTUM MECHANICS 71 Example 5 (a flipping all the gray experienced dices). Imagine you are an observer and observe outcomes of the random experiment a “tossing a gray random dice” in which the outcome “a dice fell on gray face” happened. You observe this random outcome and come to the following conclusion. When you are asked: “What gray color is the face on which the dice fell?” you need to say with some degree of believability that the dice fell on the black face or on the white face. This your conclusion is not trivial here because this experienced experiment is not singular. However, ask yourself: “Why do I give this answer with some degree of believability?” You can explain this in a variety of ways, but all of them will, of course, be based on your own rich experience of observing the outcomes of such random experiment. The co∼event theory gives the following exact answer, based on its axioms [12]. So, you are absolutely right, the some degree of believability is prompted by your experience of observing the outcomes of such random experiment. But how is this your experienced mechanism that allows you to come to conclusions with some degree of believability? The co∼event theory gives an axiomatic description of this experienced mechanism, which in a co∼eventum mechanistic language is interpreted as follows. For such an experienced experiment, your experience has accumulated the set of gray experienced dices. At the very moment when you observe that the gray random dice has fallen on the face of some degree of gray, your experience begins its own “experienced experiment”: “a flipping all the gray experienced coins accumulated by her/his observer’s experience relevant to this gray-outcome of the gray random dice”, which ends with some gray experienced dices falling on the black face and some gray experienced dices falling on the white face. This allows you to give the answer: “the black face” with a degree of believability equal to the share of gray experienced dices falling on the black face; and — the answer: “the white face” with complementary degree of believability. (See Fig. 2) Example 6 (a flipping all the singular colored experienced dices). Imagine you are an observer and observe outcomes of the random experiment a “tossing a rainbow color random dice” in which the outcome “a dice fell on red face” happened. You observe this random outcome and, of course, come to the following conclusion. When you are asked: “On which face did the dice fall?” you need to say with full believability that the dice fell on the red face. Of course, this your conclusion is trivial here because this experienced experiment is singular. However, ask yourself: “Why do I give this answer with full believability?” You can explain this in a variety of ways, but all of them will, of course, be based on your own rich experience of observing the outcomes of such random experiment. The co∼event theory gives the following exact answer, based on its axioms [12]. So, you are absolutely right, the full believability is prompted by your experience of observing the outcomes of such random experiment. But how is this your experienced mechanism that allows you to come to conclusions with some degree of believability? The co∼event theory gives an axiomatic description of this experienced mechanism, which in a co∼eventum mechanics language is interpreted as follows. For such an experienced experiment, your experience has accumulated six sets of singular colored experienced dices: the set of violet experienced dices, the set of blue experienced dices, the set of green experienced dices, the set of yellow experienced dices, the set of orange experienced dices, and the set of red experienced dices. At the very moment when you observe that the rainbow color random dice has fallen on the red face, your experience begins its own “experienced experiment”: “a flipping all the red experienced coins accumulated by an observer relevant to the red-outcome of the rainbow color random dice”, which ends with all, without exception, red experienced coins falling on the red face. Precisely, the fact that all the dices that have been without exception dropped on the red face, allows you to give the answer with full believability. And so on for each random outcomes: “the rainbow color random dice has fallen on the violet, blue, green, yellow, orange, red face”. (See Fig. 3) Example 7 (a flipping all the colored experienced dices). Imagine you are an observer and observe outcomes of the random experiment a “tossing a colored random dice” in which the outcome “a dice fell on colored face” happened. You observe this random outcome and come to the following conclusion. When you are asked: “What rainbow color is the face on which the dice fell?” you need to say with some degree of believability that the dice fell on one of the six rainbow color faces: the violet, blue, green, yellow, orange, or red face. This your conclusion is not trivial here because this experienced experiment is not singular. However, ask yourself: “Why do I give this answer with some degree of believability?” You can explain this in a variety of ways, but all of them will, of course, be based on your own rich experience of observing the outcomes of such random experiment. The co∼event theory gives the following exact answer, based on its axioms [12]. So, you are absolutely right, the some degree of believability is prompted by your experience of observing the outcomes of such random experiment. But how is this 72 THE XVII FAMEMS’2018 AND THE III H’S6P WORKSHOP your experienced mechanism that allows you to come to conclusions with some degree of believability? The co∼event theory gives an axiomatic description of this experienced mechanism, which in a co∼eventum mechanistic language is interpreted as follows. |Ω⟩ ⏟ ⏞ ∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘ |X1 ⟩ |X2 ⟩ |X3 ⟩ |X4 ⟩ |X5 ⟩ |X6 ⟩ |X7 ⟩ |X8 ⟩ |X9 ⟩ |X10⟩ |X11⟩ |X12⟩ |X13⟩ |X14⟩ |X15⟩ |X16⟩ |X17⟩ |X18⟩ |X19⟩ |X20⟩ |X21⟩ |X22⟩ |X23⟩ |X24⟩ ⎧ ⎪ ⎪⟨x1 | ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x2 | ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x3 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x4 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x5 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x6 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x7 | ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x8 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x9 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x10 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x11 | ⎪ ⎪ ⎪ ⎪ ⎨⟨x12 | ⟨Ω| ⎪ ⟨x13 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⟨x14 | ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x15 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x16 | ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x17 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x18 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⟨x19 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x20 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⟨x21 | ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x22 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⟨x23 | ⎪ ⎪ ⎪ ⎩⟨x | 24 ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ Table 3: A tossing the six-rainbow colored random dice and flipping all the singular colored experienced dices. Venn diagram illustrates an incomeoutcome of the 24×24 experienced-random experiment (24 “six-rainbow observers” are making 24 “six-rainbow color random dice observations”) as a result of which co∼events R1 ( ○ ) +R2 ( ○ ) +R3 ( ○ ) +R4 ( ○ ) +R5 ( ○ ) R6 ( ○ ) = ⟨Ω|Ω⟩ occur with the overall element-set labellings ⟨X|SX ⟩ = ⟨{x1 , . . . , x24 }|{X1 , . . . , X24 }⟩. For such an experienced experiment, your experience has accumulated the set of rainbow colored experienced coins each of which corresponds to one or another observable color on the face of the colored random dice. And in each such set, the believabilities of falling out of one or another rainbow colored face, accumulated by your experience, corresponds to the observed color of the fallen face of a colored random dice. At the very moment when you observe that the colored random dice has fallen on the colored face, your experience begins its own “experienced experiment”: “a flipping all the rainbow colored experienced coins accumulated by her/his observer’s experience relevant to this color-outcome of the color random dice”, which ends with the six set of colored experienced coins falling on the violet, blue, green, yellow, orange, and red face correspondingly. This allows you to give the OLEG YU VOROBYEV. CO∼EVENTUM MECHANICS 73 answer: “the violet, blue, green, yellow, orange, and red face” with the corresponding degree of believability equal to the share of this rainbow color coins falling on the corresponding rainbow color face. (See Fig. 4) |Ω⟩ ⏟ ⏞ ∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘∘ |X1 ⟩ |X2 ⟩ |X3 ⟩ |X4 ⟩ |X5 ⟩ |X6 ⟩ |X7 ⟩ |X8 ⟩ |X9 ⟩ |X10⟩ |X11⟩ |X12⟩ |X13⟩ |X14⟩ |X15⟩ |X16⟩ |X17⟩ |X18⟩ |X19⟩ |X20⟩ |X21⟩ |X22⟩ |X23⟩ |X24⟩ ⎧ ⎪ ⟨x1 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x2 | ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x3 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x4 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x5 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x6 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x7 | ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x8 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x9 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⟨x10 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x11 | ⎪ ⎪ ⎪ ⎪ ⎨⟨x12 | ⟨Ω| ⎪ ⟨x13 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x14 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x15 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x16 | ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x17 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x18 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x19 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x20 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x21 | ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x22 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x23 | ⎪ ⎪ ⎪ ⎪ ⎩⟨x | 24 ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ Table 4: A tossing the all colored random dice and flipping all the singular colored experienced dices. Venn diagram illustrates an income-outcome of the 24×24 experienced-random experiment (24 “six-rainbow observers” are making 24 “all color random dice observations”) as a result of which co∼events R1 ( ○ ) +R2 ( ○ ) +R3 ( ○ ) +R4 ( ○ ) +R5 ( ○ ) R6 ( ○ ) = ⟨Ω|Ω⟩ occur with the overall element-set labellings ⟨X|SX ⟩ = ⟨{x1 , . . . , x24 }|{X1 , . . . , X24 }⟩. 3 A tossing, a flipping, and a spinning the “coins”, and ... organ pipes Now I will allow myself to reformulate in the bra-ket-notations three principal statements that relate to the observability properties of all three types of experiments, the strict definitions of which were given above. ∙ The ket-result of the random experiment is unobservable because there is no one to observe. ∙ The bra-result of the experienced experiment is unobservable because there is nothing to observe. ∙ And only the bra-ket-result of the experienced-random experiment is observable because there is something to 74 THE XVII FAMEMS’2018 AND THE III H’S6P WORKSHOP ⟨bra-success| ⏟ ⟨b bra ra -k -fa et ilu -fa re ilu |k re et = -r es ul t⟩ ⟨∅| ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ |∅⟩ ⏞ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ = ⟨b bra ra -k -s et uc -s ce uc ss ce |k ss et = -r es ul t⟩ R |ket-result⟩ ⏟ = ⎧ ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎨ ⟨Ω| ⟨x| ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ ⎪ ⎩ |{x}⟩ ⏞ |Ω⟩ ⏟ ⏞ Rc |ket-result⟩ |Ω⟩ ⏟ ⏞ ⟨bra-failure| Table 5: A Bernoulli bra-ket-trial. Venn diagrams for two accumulable-possible results of a Bernoulli bra-ket-trial of a co∼event R: R occurred (“bra-ket-success”= ⟨“bra-success”|“ket-result”⟩, left), or R didn’t occur, i.e. the co∼event Rc = ⟨Ω|Ω⟩ − R occurred, or the co∼event R didn’t occur (“bra-ket-failure”= ⟨“bra-failure”|“ket-result”⟩, right). observe, and there is one who observes. I will also note that in the bra-ket-terms a random experiment is a ket-experiment or a ket-trial, an experienced experiment is a bra-experiment, or a bra-trial, and an experienced-random experiment is a bra-ket experiment, or a bra-ket-trial. Thus, in the co∼eventum mechanics, only the results of the bra-ket-trial can be observed, and the ket-trial result and the bra-trial result serve only as inseparable unobservable halves of the bra-ket-trial result. ⏞ ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⟨Ω| ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ ⟨x| ︁ ⟨∅| ︁ ︁ ⟨∅| ︁ ⟨x| ︁ ⟨x| ︁ ⟨∅| ︁ ⟨x| ︁ ⟨x| ︁ ⟨x| ︁ ⟨∅| ⏞ |Ω⟩ ⏟ |{x}⟩ ⏟ bra-ket-success= ⟨bra-success|ket-result⟩ bra-ket-failure= ⟨bra-failure|ket-result⟩ bra-ket-failure= ⟨bra-failure|ket-result⟩ bra-ket-success= ⟨bra-success|ket-result⟩ bra-ket-success= ⟨bra-success|ket-result⟩ bra-ket-failure= ⟨bra-failure|ket-result⟩ bra-ket-success= ⟨bra-success|ket-result⟩ bra-ket-success= ⟨bra-success|ket-result⟩ bra-ket-success= ⟨bra-success|ket-result⟩ bra-ket-failure= ⟨bra-failure|ket-result⟩ ⏞ |Ω⟩ ⏟ |{x}⟩ ⏞ ⏟ ⎧ ⎪ ⎪ bra-ket-success= ⟨bra-success|ket-result⟩ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ bra-ket-success= ⟨bra-success|ket-result⟩ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ bra-ket-success= ⟨bra-success|ket-result⟩ ⟨x| ⎪ ⎪ ⎪ bra-ket-success= ⟨bra-success|ket-result⟩ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ bra-ket-success= ⟨bra-success|ket-result⟩ ⎪ ⎪ ⎪ ⎪ ⎩ bra-ket-success= ⟨bra-success|ket-result⟩ ⎧ ⎪ ⎪ bra-ket-failure= ⟨bra-failure|ket-result⟩ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ bra-ket-failure= ⟨bra-failure|ket-result⟩ ⟨∅| ⎪ ⎪ ⎪ bra-ket-failure= ⟨bra-failure|ket-result⟩ ⎪ ⎪ ⎪ ⎪ ⎩ bra-ket-failure= ⟨bra-failure|ket-result⟩ Table 6: 10 Bernoulli “bra-trials”. Two equivalent Venn diagrams for accumulable results of the ten Bernoulli bra-trials of a co∼event R: R accumulable (“bra-success”), or R didn’t accumulate, i.e. the co∼event Rc = ⟨Ω|Ω⟩ − R accumulable (“bra-failure”). In conclusion, I would like to underline once again a difference what is usually meant by “tossing a random coin” in probability theory, and what is meant by “flipping a set of experienced coins” and “spinning a set of experienced OLEG YU VOROBYEV. CO∼EVENTUM MECHANICS bra-ket-failure = ⟨bra-failure|ket-result⟩ ⏟ bra-ket-failure = ⟨bra-failure|ket-result⟩ bra-ket-failure = ⟨bra-failure|ket-result⟩ |∅⟩ ⏞ bra-ket-failure = ⟨bra-failure|ket-result⟩ ⏟ bra-ket-success = ⟨bra-success|ket-result⟩ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ |{x}⟩ |Ω⟩ ⏟ bra-ket-success = ⟨bra-success|ket-result⟩ bra-ket-success = ⟨bra-success|ket-result⟩ bra-ket-success = ⟨bra-success|ket-result⟩ bra-ket-success = ⟨bra-success|ket-result⟩ bra-ket-failure = ⟨bra-failure|ket-result⟩ bra-ket-success = ⟨bra-success|ket-result⟩ bra-ket-success = ⟨bra-success|ket-result⟩ bra-ket-failure = ⟨bra-failure|ket-result⟩ bra-ket-failure = ⟨bra-failure|ket-result⟩ bra-ket-failure = ⟨bra-failure|ket-result⟩ bra-ket-success = ⟨bra-success|ket-result⟩ ⟨x| ⎧⏞ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ bra-ket-success = ⟨bra-success|ket-result⟩ |∅⟩ |{x}⟩ |{x}⟩ |∅⟩ |{x}⟩ |{x}⟩ |{x}⟩ ⎧ ⎧⏞ ⏟ ⏞ ⏟ ⏞ ⏟ ⏞ ⏟ ⏞ ⏟ ⏞ ⏟ ⏞ ⏟ ⏞ ⏟ ⏞ ⏟ ⏞ ⏟ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎨ ⟨Ω| ⟨x| ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ ⎩ bra-ket-success = ⟨bra-success|ket-result⟩ |∅⟩ ⏞ bra-ket-success = ⟨bra-success|ket-result⟩ |{x}⟩ |∅⟩ |Ω⟩ ⏟ bra-ket-success = ⟨bra-success|ket-result⟩ ⏞ 75 Table 7: 10 Bernoulli “ket-trials”. Two equivalent Venn diagrams for random results of the ten Bernoulli ket-trials of a co∼event R ⊆ ⟨Ω|Ω⟩ ︁ ︁ : R happened (“bra-ket-success”), or R didn’t happen, i.e. the co∼event Rc = ⟨Ω|Ω⟩ − R happened (“bra-ket-failure”). coins with a random coin” in the co∼eventology of experience and chance [12]. A coin toss has all the attributes of a “random experiment” in probability theory. There is more than one possible ket-result. We can specify each possible outcome in advance — head (ket-success) or tail (ket-failure). And there is an element of chance. We cannot know the ket-result until we actually toss the coin. At last, what is very important, for this random experiment it is completely indifferent whether this experiment is observed by an observer or not. An experienced coin flip has all the attributes of a “experienced experiment” in the co∼eventum mechanics. There is more than one accumulable bra-result. We can specify each accumulable bra-result in advance — head (bra-success) or tail (bra-failure). And there is an element of experience. We cannot know the bra-result until we actually flip the experienced coin. At last, what is very important, for this experienced experiment it is very important who observed it and what experience she/he has. A set of experienced coins with a random coin spin has all the attributes of a “experienced-random experiment” in the co∼eventum mechanics and the co∼eventology of experience and chance. There is more than one accumulablepossible bra-ket-result. We can specify each accumulable-possible bra-ket-result in advance — head (bra-ket-success, the co∼event occur) or tail (bra-ket-failure, the co∼event doesn’t occur). And there is an element of experience. We cannot know the bra-ket-result until we actually spin all coins. And, of course, what is very important, for this experienced-random experiment it is very important who observed it and what experience she/he has. At last, I will note the Venn diagram of any co∼event reminds me very much the organ with its pipes. Moreover, in this organ analogy, the co∼event occurs whenever “only one of the organ pipes sounds”, i.e., the ket-event corresponding to this pipe happens and the set of bra-events corresponding to this pipe are accumulated by the observer’s experience (see Tab. 8 and ?? for comparing). 4 Milestones that the co∼eventum mechanics opens to us We are all experienced observers in the world of chance observations. Nothing occurs with us except co∼events which describe the conflict of our past experience with the future chance. Our being is always co∼being, which occurs with us as a succession of sets of co∼events. Co∼eventum mechanics suggest that our world can be viewed as the universal experienced-random experiment, and we are all participants of it without exception. At any coincidence, each of us makes decisions based on her/his own past experience. Only our experience tells us what 76 THE XVII FAMEMS’2018 AND THE III H’S6P WORKSHOP |Ω⟩ ⏟ ⏞ |X1 ⟩ |X2 ⟩ |X3 ⟩ |X4 ⟩ |X5 ⟩ |X6 ⟩ |X7 ⟩ |X8 ⟩ |X9 ⟩ |X10⟩ |X11⟩ |X12⟩ |X13⟩ |X14⟩ |X15⟩ |X16⟩ |X17⟩ |X18⟩ |X19⟩ |X20⟩ |X21⟩ |X22⟩ |X23⟩ |X24⟩ × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × bra-ket-success × × × × × × × × × × × × × × × × × × × × × × × × bra-ket-success × × × × × × × × × × × × × × × × × × × × × × × × bra-ket-success × × × × × × × × × × × × × × × × × × × × × × × × bra-ket-success × × × × × × × × × × × × × × × × × × × × × × × × bra-ket-success × × × × × × × × × × × × × × × × × × × × × × × × bra-ket-success × × × × × × × × × × × × × × × × × × × × × × × × bra-ket-success × × × × × × × × × × × × × × × × × × × × × × × × bra-ket-success × × × × × × × × × × × × × × × × × × × × × × × × bra-ket-success × × × × × × × × × × × × × × × × × × × × × × × × bra-ket-success × × × × × × × × × × × × × × × × × × × × × × × × bra-ket-success × × × × × × × × × × × × × × × × × × × × × × × × bra-ket-success × × × × × × × × × × × × × × × × × × × × × × × × bra-ket-success × × × × × × × × × × × × × × × × × × × × × × × × bra-ket-success × × × × × × × × × × × × × × × × × × × × × × × × bra-ket-success × × × × × × × × × × × × × × × × × × × × × × × × bra-ket-success × × × × × × × × × × × × × × × × × × × × × × × × bra-ket-success × × × × × × × × × × × × × × × × × × × × × × × × bra-ket-success × × × × × × × × × × × × × × × × × × × × × × × × bra-ket-success × × × × × × × × × × × × × × × × × × × × × × × × bra-ket-success × × × × × × × × × × × × × × × × × × × × × × × × bra-ket-success × × × × × × × × × × × × × × × × × × × × × × × × bra-ket-success bra-ket-success × × × × × × × × × × × × × × × × × × × × × × × ⟨x24 | × bra-ket-success ⎧ ⎪ ⎪ ⎪⟨x1 | ⎪ ⎪ ⎪ ⎪ ⟨x2 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x3 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x4 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x5 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x6 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x7 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x8 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x9 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x10 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x11 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎨⟨x12 | ⟨Ω| ⎪ ⟨x13 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x14 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⟨x15 | ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x16 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⟨x17 | ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x18 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⟨x19 | ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x20 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⟨x21 | ⎪ ⎪ ⎪ ⎪ ⎪ ⟨x22 | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⟨x23 | ⎪ ⎪ ⎪ ⎪ ⎩ Table 8: The bra-ket-trial and “organ analogy”. Venn diagram of the co∼event R ⊆ ⟨Ω|Ω⟩ ( bra-ket-success ) and the co∼event Rc = ⟨Ω|Ω⟩ − R ( bra-ket-failure ) with the element-set labellings ⟨X|SX ⟩ = ⟨{x1 , . . . , x24 }|S{x1 ,...,x24 } ⟩ and Φ(R) = 1/2 (see Tab. ??, left, for comparing with the “organ analogy”). decision should be chosen at the moment of chance observation with some degree of believability in the correctness of this decision. From the point of view of the co∼eventum mechanistic approach, each of us represents a set of her/his past experiences, and each of these experiences is a set of elementary experienced which are identified with experienced coins in a free rotation ready for this or that random elementary observation. In turn, any random observation is a set of elementary random observations which are identified with random coins in a free rotation ready to be observed by some or other experienced observers. So, the co∼eventum mechanics sees our world filled with only coins in a free rotation, experienced coins and random coins. The collision of these sets of coins creates sets of co∼events, which is our co∼being. The reader is free to interpret this co∼eventum mechanistic view of the world of co∼events in terms of her/his paradigm of the scientific world picture. In my humble opinion, in the co∼eventum mechanistic approach, every coin in free rotation, both an experienced and random, is a superposition state, which in quantum mechanics is described OLEG YU VOROBYEV. CO∼EVENTUM MECHANICS |ket-result⟩ ⟨b bra ra -k -s et uc -s ce uc ss ce |k ss et = -r es ul t⟩ = R ⟨bra-success| ⟨∅| ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ |∅⟩ ⏞ ⏟ ⟨b bra ra -k -fa et ilu -fa re ilu |k re et = -r es ul t⟩ ⏟ = |{x}⟩ ⏞ |Ω⟩ ⏟ ⏞ Rc |ket-result⟩ |Ω⟩ ⏟ ⏞ ⎧ ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎨ ⟨Ω| ⟨x| ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ ⎪ ⎩ 77 ⟨bra-failure| Table 9: A Bernoulli bra-ket-trial. Venn diagrams for two accumulable-possible results of a Bernoulli bra-ket-trial of a co∼event R: R occurred (“bra-ket-success”= ⟨“bra-success”|“ket-result”⟩, left), or R didn’t occur, i.e. the co∼event Rc = ⟨Ω|Ω⟩ − R occurred, or the co∼event R didn’t occur (“bra-ket-failure”= ⟨“bra-failure”|“ket-result”⟩, right). by the Schrödinger wave equation. 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