3. The Fractal Structure of the Sacred Number 3 in Nakazawa Shin'ichi's Mythology

If Campbell is based on Jungian psychoanalysis, the mythologist grounded in Freudian–Lacanian psychoanalysis is Nakazawa Shin'ichi. The first case of applying psychoanalysis to the study of religion is the research of Freud himself, the founder of psychoanalysis. Freud, from a direction different from that of his disciple Jung, expanded psychoanalysis—which had been a matter of the individual—into cultural analysis and the like, and finally published a religious-analytical work, Moses and Monotheism. Freud argues that religion, like the Oedipus complex of an individual life, arose from the guilt of the sons who had murdered the collective father—that this is religion and God. Freud's research opened a new chapter in psychoanalytic religious studies, but in his religious analysis, under the tradition of Christian culture, he mentioned only the father—the Supreme Lord—within his own achievement, the psychoanalytic system of triadic differentiation of father–mother–son, so that his analytic framework for the mother-side divinity, which may be said to be Eastern religion, was somewhat lacking, and he could not give a universal explanation of Eastern religion.

Nakazawa Shin'ichi holds that, just as 3 today is the root of modern complexity science, the sacred number 3 that appears commonly in the world's myths originated from a rational mode of thought like that of modern science. Recently, psychoanalysis has been studied interdisciplinarily as a more universal complexity science of triadic differentiation, in connection with Kant's theory of trisection. As psychoanalysis that expanded Kant's philosophy of trisection more broadly into a complexity theory of the triadic differentiation system in relation to the Oedipus-complex structure, one may cite Lacan's structuralist psychoanalysis and Deleuze–Guattari's schizoanalysis. Whereas Lacan mainly connected the static fractal-symmetry theory among complexity theories to the Oedipus complex and emphasized the balance of the Imaginary–Symbolic–Real, Deleuze–Guattari applied the dynamic chaos-transversality theory among complexity theories and emphasized the schism of desire. If Lacan, by introducing linguistics and structuralism into psychoanalysis, contributed to psychoanalytic research a contribution like that of Descartes to geometry through analytic geometry in which he inserted numbers, then Deleuze may be said to have played the role of Newton, who applied Descartes's geometry to all things.

Deleuze–Guattari, whom Lacan clarified, hold from a materialist standpoint that all things are composed of the triadic differentiation system of the Oedipus-complex structure of father–mother–son. Through the concept of transversality, Guattari holds that all things are the workings of desire and that desire works in diverse Oedipal ways. The triadic differentiation system that begins with Kant is connected to the chaos-fractal science in which all things resemble one another as they attune to one another. Deleuze–Guattari, after interpreting Kantian philosophy as an Oedipal structure, expand it into complexity science and apply it to all things.

According to Deleuze–Guattari, Kant, who completed modern philosophy up to now, has been understood not through a trichotomy but through a dichotomy, and thus modern philosophy has suffered much misunderstanding. Kant's Critique of Pure Reason can be seen as the mother–son relationship, the Critique of Practical Reason as the mother–son relationship, and the Critique of Judgment as the harmonious relationship of the father–mother–son relationship. Deleuze–Guattari interpret Kant's tripartite system in the direction of expanding centrifugal force as disjunction, conjunction, and connection, while Lacan interprets it in the direction of strengthening centripetal force as the Real–Symbolic–Imaginary. Deleuze–Guattari's understanding of Kant as psychoanalysts is carried on to Lacan–Žižek, Karatani Kōjin, and others.

Deleuze–Guattari's Oedipal logic can be interpreted differently in the Eastern Daoist system of divinities as the logic of the Supreme Lord (Heaven)–divine spirit (Earth)–human being (Human). Deleuze–Guattari, connecting complexity theory with the Oedipus complex, defined the modern age as an Oedipal-complex-like complex system in which desire is suppressed, and held that desire can be liberated through the logic of the Anti-Oedipus. This article agrees that Deleuze–Guattari saw all things as a complex system of the triadic differentiation system, but it sides with Žižek's logic that, if the mother is interpreted as the world of divine spirits from the standpoint of Daoist divinity, then a Lacanian solution rather than an Anti-Oedipal solution is more valid.

Kant's categorical–hypothetical–disjunctive mode of reasoning, after being combined by Deleuze–Guattari with Spinoza's pantheism, is expanded from the logical structure of the human being and appears as the materialist Oedipus-complex structure of all things. Since Kant's categorical mode of reasoning requests the judgment of reason, it is the father–son relationship; the hypothetical mode, which conditionally and selectively accepts the father's judgment, is the mother–son relationship. Since the disjunctive must judge both the hypothetical and the categorical, it may be said to be the father–mother–son relationship. Deleuze and Guattari, who interpreted Kant materialistically, in Anti-Oedipus explain the material world's Oedipal structure through Kant's logical machine, describing the disjunctive imperative connected by "and, and" as the son of the connective synthesis of production, the hypothetical imperative "if ~ then ~" as the disjunctive synthesis—the mother—that may be called Symbolic registration, and the categorical imperative "therefore ~ is" as the Real—the father—of the conjunctive synthesis of consumption.

Kant's three logical machines of categorical–hypothetical–disjunctive are integrated into the single system of Matte Blanco's symmetry. Matte Blanco grasps Kant's categorical imperative, the father, as supersymmetry; the hypothetical imperative, the mother, as asymmetry; and the disjunctive imperative, the son, as symmetry. Since Matte Blanco's concept of symmetry is a concept based on natural-scientific symmetry, it provides a starting point that unifies the psychoanalysis of Lacan and Deleuze–Guattari and mathematically integrates the complexity-based triadic differentiation system of natural science with psychoanalysis. Matte Blanco interprets the unconscious of psychoanalysis through the mathematical and universal property of symmetry. Through symmetry, the two cultures—the human science of the unconscious and the natural science of complexity—became able to find a common point of contact easily.

Matte Blanco's concept of symmetry was expanded and developed into the concept of the "gift" by Nakazawa Shin'ichi, who fused it with sociology and religious studies, so that it became possible to verify it in reality. Nakazawa Shin'ichi discovered the psychoanalytic triadic differentiation system in the capitalism, Christianity, and science of modern society, and came to argue that the problem of the modern age lies in its failure to recover the triadic differentiation system. As an alternative, Nakazawa Shin'ichi argued for activating the "gift," which may be called the expression of symmetry.

Matte Blanco's concept of symmetry was also developed by Guattari into "transversality," the eco-psychoanalytic concept centered on Deleuze. Guattari, on the basis of a materialist worldview, calls the unconscious the machinic unconscious, as if evoking the relationship of nature and divine spirit. Guattari holds that psychoanalysis can overcome the Oedipus complex only when it is composed of a triadic relationship that includes the ecological standpoint of seeing the Earth as mother.

The research of Nakazawa Shin'ichi and Guattari forms a still clearer triadic differentiation system of desire in René Girard. René Girard discovers the triangular structure of desire in literary works and myths. Desire, like father–mother–son, has an object of desire and two persons who imitate that desire. Whereas in the modern age it was an external mediation in which one person imitated another, modern capitalism has become an internal mediation in which the two persons imitate each other's desire together, so that the symmetry of the triangle has collapsed. In Girard's system, the Oedipus complex becomes the inevitable yoke of the human being.

Girard's triangular structure of desire had already been verified in Erich Fromm's argument, in Escape from Freedom and To Have or to Be and elsewhere, that the only way for modern humans to escape the Oedipus complex is to change from the mode of having to the mode of being. Erich Fromm held that, since the human attitude toward nature—namely, having-possession of mother–nature—is the fundamental Oedipus-complex structure, the human being cannot escape the Oedipus complex without a change from the mode of having to the mode of being. In fact, much of modern psychological and physical healing research presents union with nature as the ultimate cure.