The formalized hodological methodology

The formalized hodological methodology The instructions of Feynman’s pathways interpretation of quantum mechanics for philosophy

Vasil Penchev Bulgarian Academy of Sciences: Institute for the Study of Societies and Knowledge: Dept. of Logical Systems and Models vasildinev@gmail.com

“Between the Visible and the Invisible�

Institute for Advanced Studies of Asia at University of Tokyo with Temple University Japan Campus & Universite libre de Bruxelles 3-4 July 2017, The University of Tokyo

Introduction: Something like a parable

The idea of that parable • We can imagine the following: o One tries to explain something exceptionally complicated to somebody who has not either corresponding experience or knowledge, or even the relevant ability of cognition • For example, one attempts to explain quantum mechanics to a child o How it should be done?

The problem of how to be explained • It would be meaningless:  Quantum mechanics to be explained as to a student of physics for a few semesters in a good university  Noting to be explained • Something should be explained, but how not be meaningless?

Pathways of explanation • One should use child’s experience o Meaning that experience, independently of how much and as far as it is extremely restricted and insufficient, one might construct a model of quantum mechanics exceptionally on that quite limited circle of representations • The feedback would be exceptionally important: o One must follow child’s questions and commentaries for the explanation to be directed and fitted in the course of exhibition • Child’s attention is too unstable and the “lesson” shall be ceased too soon…

Many “children” …

• The result of that explanation would be rather random o Further, we can figure a collection of children, to whom quantum mechanics is explained separately, e.g. in each child’s own home • A corresponding collection of explanations would appear o The difference between the explanations would be huge for each child’s experience is quite different as well as too, too insufficient and thus arbitrary to quantum mechanics

A conference of the “children” • At last (as a provocative joke): those children might make a conference (e.g., such as ours) on quantum mechanics and thus compare their knowledge and representations of quantum mechanics o Of course, they would find those huge differences between them, reflecting the difficultness for the explanation to be relatively understable by each child • They can start a dispute about whose version is true o Of course, no one and all are true equally and simultaneously

o One can postulate some entity called “God” much more reasonable than human beings trying to explain to them God’s knowledge or principles of cognition • The metaphor of the parable would fit very well to that situation o Even still one “child”, meaning quantum mechanics properly, might be added complementarily • That “child” will obtain the explanation in terms of quantum mechanics for it would be the most appropriate circle of representations necessary for the explanation to that “child” o That “child” might try to explain to others the entire collection of quite different explanations right in terms of quantum mechanics therefore transforming it into a meta-explanation • That “child” might be me

My motivation

About me ‌ • Anyway, I am a scientist rather than a theologian and my viewpoint will be from the science o However, I hope a dialog with theologians • I do not belong to that large group of scientists tended to reject religion initially and fundamentally as wrong, false, misleading, and primitive o Nevertheless, I self-determine myself as an atheist

Science and religion • I think both science and religion are two great achievements of humankind, though o They might join and unify their efforts and approaches in a whole much bigger than the sum separately • To take place that, they should overcome the age-old hostility and mutual misunderstanding o I intend my presentation as a quite, quite modest and humble gesture in that direction

My explanation (right in terms of quantum mechanics)

About Feynman’s interpretation • Quantum mechanics was forced to resolve the problem of how to describe uniformly both discrete and continuous motion o Its mathematical formalism is the separable complex Hilbert space • Feynman suggested an equivalent interpretation generalizing the discrete motion as if in all possible trajectories, each of which with different probability

Generalizing Feynman’s interpretation …

• The talk interprets and generalizes Feynman’s interpretation “hodologically” as a formalized methodology for hodology o After that, the equivalence of the jump-like insight inherent for religious cognition and the continuous and causal method of science can be seen in turn as similar to Feynman’s approach generalized hodologically now

Religious and scientific cognition • Then, the cognition by religious experience can be both justified by, and decomposed into a fan distribution of alternative scientific theories or disciplines inconsistent, irrelevant or contradictory to each other o Each of them would represent the religious cognition only probably, in a single “hodosâ€?, pathway, but achievable by a reliable and causal method repeatable by many others

Religious cognition • On the contrary, religious cognition is fundamentally random o It cannot be linked to any definite method and even to any certain religion • The origin of different religions or religious practices should be searched for in different traditions and societies representing in turn different religious pathways rather than in the essence of religious cognition by itself

A philosophical idea about theology as a rigorous science • One may generalize Husserl’s idea about “philosophy as a rigorous science” on his “phenomenon” identifying form and content, to religious cognition defined consistently and linked to science o In fact, philosophy would coincide with theology after form and content are identified to each other • “Philosophy as a rigorous science” is theology in essence o Spiritual reality researched by theology is therefore that realm which may be defined philosophically by the identification of form and content, or as Husserl’s “phenomenology”

A comment to that scientific kind of explanation as a meta-explanation

About the discourse of quantum mechanics: 1 • That explanation is as any other one: one among all the rest o It cannot claim to be truer than any other “child”’s explanation (in the sense of the introductory parable) • However it is rather different from the others for the following features: o It is able to serve as a meta-explanation therefore explaining the complete collection of all explanations as a whole • It offered a mathematical model o The same model is interpreted by an experimental science such as quantum mechanics

About the discourse of quantum mechanics: 2 • Here are more extraordinary features of that approach based on quantum mechanics: o It includes a possible scientific definition of what that entity called God is or should be • It allows of the experimental study of that entity as any other subject of any experimental science o Nevertheless, it does not contain any proof for its discourse, though an experimental and theoretical one, is better than other discourse properly religious and meaning the same entity in a different way

An example of that scientific discourse to entity called “God�: God in terms of Experimental Science

Two “dogmas” in the Christian discourse of God: the first one • The perception of God generates a specific domain of human experience: religion o God being omnipresent is within all spheres of human activity and cognition, and He is their unity • Nevertheless, the finiteness and limitedness of all human beings imposes that area of religion

Two “dogmasâ€? in the Christian discourse of God: the second one • Science and especially experimental science is inappropriate for the cognition or study of God as to human beings for science addresses the repetition, reiteration, recurrence, and resettability of result as well as the materiality of phenomena o Thus, God is fundamentally inaccessible in science for He is creative and nonmaterial

A few comments of those “dogmasâ€?: 1 • Quantum mechanics calls much criticism ostensibly violating the fundamental principles of science requiring just the repetition, reiteration, recurrence, and resettability of all experimental data: o Indeed, any given result in quantum mechanics is initially random and thus it cannot be forecast in principle

A few comments of those “dogmasâ€?: 2 • What is forecastable is only the probability distribution of a big enough statistical ensemble of experimental data, which changes itself gradually and causally in time o Nevertheless, some rather incredible state of any quantum system can occur with some nonzero probability and thus as a given result of measuring

A few comments of those “dogmas”: 3 • Quantum mechanics describes the state of any quantum system as a wave function o That wave function can be represented as a point in Hilbert space and interpreted both as a trajectory in space-time (a “fermion”) and as a coherent mix (i.e. a “superposition”, using the proper term of quantum mechanics) of possible states (a “boson”)

A few comments of those “dogmas”: 4 • Whether “belonging” to a fermion or a boson, wave function can be interpreted as a form of generalized information: quantum information which is furthermore a nonmaterial generalization of matter o That is: matter is a particular case of quantum information, which is nonmaterial in general

A few comments of those “dogmas”: 5 • Quantum information is not less another generalization of the usual concept of information, according to which information is the quantity of elementary choices such as bits (an abbreviation of “binary digits”) o A bit is defined as the choice between two equiprobable alternatives • Thus any finite series of choices of an element among any finite sets can be exactly calculated as a real number of bits, i.e. as that information containing in the series in question

A few comments of those “dogmas”: 6 o Consequently, the nontrivial generalization of information should refer both to infinite series of choices and to the choice of an element among any infinite set therefore requiring the axiom of choice to be involved o Quantum information is that generalization of “information” though it is introduced by quantum mechanics as still one interpretation of wave function in terms of information

A few comments of those “dogmas”: 7 • So a qubit (an abbreviation of “quantum bit”) is both the above equivalence of transfinite series and a choice among an infinite set and the normed superposition of any two orthogonal subspaces of Hilbert space in spirit of quantum mechanics o Furthermore, quantum information is the quantity of those “infinite choices”, i.e. qubits • Any wave function is a given value of quantum information, and Hilbert space can be interpreted as that variable of quantum information

Conclusions

Conclusions • Feynman’s interpretation of quantum mechanics admits a hodological generalization: o The jump-like insight featuring religious cognition can be described as fundamentally random and thus unrepeatable as well as decomposable in many pathways simultaneously • It can serve as a formal and mathematical methodology of hodology o Quantum mechanics though being an experimental and mathematical science can offer a discourse to God • A shared pathway of reconciliation for science and religion can be outlined …

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