Mathematics as a Device to Adjust the Distance to God: Its Relationship with the Humanities-Sciences Divide, Ancient Greece, Medieval Christianity, Modern Science, and Japanese Culture

Mathematics as a Device to Adjust the Distance to God: Its Relationship with the Humanities-Sciences Divide, Ancient Greece, Medieval Christianity, Modern Science, and Japanese Culture Abstract The argument of this paper is simple: mathematics has served as a device for adjusting the "distance" between humanity, God, religion, and science. In antiquity and the Middle Ages, arithmetic, geometry, music, and astronomy—as the Quadrivium—mediated order and harmony for theology. In the modern era, empirical proof and mathematical science became autonomous from religion. In Japan, Edo-period philology and Meiji-era systemic reforms uniquely reconfigured this sense of distance. Summary Mathematics was a device for modulating the distance between religion and knowledge. In the Middle Ages, it was a theological art; in modernity, it became the autonomous language of empirical science. Japan formed a unique sense of this distance through its Edo-period philology and the adoption of Meiji systems. Today, the challenge is to re-position logic and mathematics as a cross-disciplinary literacy for the AI era. Mathematics as a Mediator of the Distance to God When looking at the history of religion and science in antiquity, the Middle Ages, and the modern era, mathematics has been a tool for approaching God, or rather, for adjusting one's distance to Him. In ancient Greece, Plato inscribed at the entrance to his private academy, "Let no one ignorant of geometry enter here." Furthermore, while medieval universities were fundamentally places to study Christianity, four of the seven liberal arts required before specialization—geometry, arithmetic, astronomy, and music—were regarded as mathematics and given special status as the Quadrivium. The other three subjects (the Trivium) were likely Latin (perhaps with Greek studies), logic, and rhetoric. Among these, logic might be included in mathematics today, but for now, let's consider it a common subject for both arts and sciences. However, it seems that modern logic, such as symbolic logic, is not properly studied in contemporary humanities (Bunkei) education. Major universities, like the former imperial universities, may offer logic as a general education course, but it is often an elective for both arts and science students. In that sense, it might be better for modern universities to make logic mandatory. This is because the world seems to be filled with "pseudo-logic," or rhetoric that merely mimics logic, causing confusion. (Although, perhaps a certain amount of confusion makes the world more stimulating.) As for the Trivium, these subjects, including the study of language for academia, were made compulsory for reading the Bible and served as a lingua franca for scholarship, similar to the instrumental role English plays today. If one wanted to read the Bible in its original languages, studying Hebrew and Aramaic, in addition to Greek, would be necessary. The reason these were not required as common compulsory subjects was likely because being able to read the Latin Vulgate translation of the Bible was deemed sufficient. This reflects the university's strong aspect as an educational institution for training clergy, rather than as a pure research institution. Why Was Mathematics Required Before Specialization? Although the situation has changed somewhat recently, Japan has long had a custom of separating the humanities (Bunkei) and the sciences (Rikei). This tendency may have also existed, to varying degrees, in modern Western academia. Today, perhaps because financial literacy and economics have become more widespread and mature, and because we are in the midst of an industrial revolution where information science, technology, and industry are transforming people and society, there seems to be a greater emphasis on science and mathematics. Humans have a short historical perspective, or rather, a fundamental cognitive bias that can lead to certain illusions. We sometimes fall into the cognitive trap of thinking, "What has always been true, has been true since ancient times." From a modern perspective, "medieval theology" might seem to be the epitome of the humanities, completely unrelated to mathematics or science. In reality, the opposite was true. The first reason is that the mathematical world, as a pure concept embodying God's ideal world, was seen in a Platonic, Idealist sense as a good method for approaching God. The second reason is the belief that the world God created must be maintained in harmony and order. As a method for pursuing a world of harmony and order, a world of reason and law, mathematics was considered an essentially necessary art for theology. Therefore, upon entering a university, even if one intended to specialize in medicine or law rather than theology, the seven elementary liberal arts included four mathematical subjects. Geometry was the mathematics of quantity, arithmetic the mathematics of number, music the mathematics of time, and astronomy the mathematics of space-time. The Meaning of the Word "Mathematics" The word "mathematics" comes from the Greek mathēmatikos, which meant "that which is to be learned" or "disposed to learn." There are various opinions on why "that which is to be learned" was translated as "mathematics" (Jp: 数学, lit. "study of numbers"), and in some respects, it could be considered a mistranslation. The reason why these four subjects, known as sūgaku in Japanese, were considered "that which is to be learned" in medieval universities lies in the reasons described above. There may be others, but there are two main ones: first, the world of mathematics most purely embodies the world God created and is a method for approaching Him; and second, it was believed that the world God created could not be disorderly or random, so studying and researching mathematics was necessary to understand and investigate the order, harmony, laws, and reason of that world. The Great Modern Shift: "Logic is No Longer Required!" The Middle Ages are often perceived as a "Dark Age," an era of ignorance, superstition, and hopelessness. However, the intellectuals who attended medieval universities, regardless of their eventual specialization (if such a "humanities/sciences" distinction even existed in medieval Europe), were all required to study mathematics (plus logic). What the situation was in the preceding Greek era is not well understood. The anecdote about Plato's Academy is famous, but E.T. Bell, the early 20th-century American mathematician and president of the MAA, famous for his book Men of Mathematics, wrote sarcastically that it is doubtful Plato himself understood geometry. Well, whether Plato understood geometry or not, it seems that ancient Greece possessed, to some extent, a mindset that valued mathematical science, technology, machinery, and symbolic logic. Elaborate astronomical measuring devices (like the Antikythera mechanism) have survived, and from the Middle Ages through the modern era, ideas leading to the modern computer, and people like Pascal who actually built calculators, existed—and not just one or two. Modern Western Science and Technology Developed First from Mathematics (and Philosophy) The four specialized courses in the higher faculties of medieval universities were Theology, Law, Medicine, and Philosophy. (However, there is also the view that philosophy was not a specialization but part of the "Arts," or general education.) Among these, philosophy was a sort of "miscellaneous" field, like "other." That "philosophy" evolved into what it is today in the modern and contemporary eras. And above all, the development of mathematics and related fields was splendid. All four subjects of the medieval Quadrivium—geometry, arithmetic, music, and astronomy—developed dramatically. The medieval system of learning must have contributed significantly to this. What blossomed in the modern era were philosophy, Protestant classical music, Descartes's algebraic geometry (which combined Renaissance-era algebra imported from Arabia), and the astronomy of Galileo and Copernicus. In this way, the four mathematical subjects of the medieval seven liberal arts spectacularly came into flower. Concurrently, among the four specialized subjects, philosophy, which had been a handmaiden to theology, brilliantly leaped to the role of protagonist. Conversely, classical languages like Latin went into decline. With the rise of nationalism, particularly in places like France, this trend became pronounced, and various subjects began to be written in the vernacular rather than classical languages. Furthermore, the medieval specialized subjects, compared to the advancements in natural science and mathematics, seem to have fared poorly in the modern era. Of Theology, Law, and Medicine, Law is a quiet field, but Medicine, along with other natural sciences, seems to have improved gradually. Mathematics, astronomy, physics, and philosophy seem to have taken the "starting dash," followed by visible progress in other natural sciences and applied chemistry, while the social sciences appear to have lagged. I don't know about the humanities. While there may be dissenting opinions, the image of modernity's "starting dash" being led by mathematics (astronomy, algebraic geometry, music) and philosophy is likely not far from the truth. Medieval Mathematics as a Method of Spiritual Discipline Zooming in a bit more on medieval mathematics, it was a form of spiritual discipline. Contemplating the Ideenwelt (world of Ideas) may have led to the feeling of creating God's perfect world, allowing one to feel closer to God. Simultaneously, sensing the order and stability of God's created world, and understanding the mechanisms, laws, and reason of the world as a creation, was perhaps also religiously important. Were Medieval Universities "Science-Focused"? Perhaps due to these circumstances, the world of medieval university intellectuals was heavily focused on mathematics. To understand God and Christianity, mathematics was, as its etymology suggests, "that which must be learned." The Renaissance and Neo-Platonism During the Renaissance, which bridges the late Middle Ages and the early modern period, Neo-Platonism became popular. This, too, can be seen as a form of spiritual discipline or spiritualism. For example, the Medici family established a Platonic Academy, and Michelangelo was educated there. When one looks at Michelangelo's Pietà in the Vatican or the ceiling of the Sistine Chapel, one can feel a deep spirituality. Through this spiritual immersion, there may have been a sense of drawing slightly closer to God, or at least attempting to. Catholicism, among the Abrahamic religions, is weak on the prohibition of idolatry, and the Renaissance itself, with its revival of ancient humanism, fostered a climate that moved away from a strictly Jewish view of the Bible and God, permitting a sense of divinity to be felt in created things. This perhaps left room for the creation of supreme works of art like Michelangelo's. This stands in interesting contrast to the Protestants, who destroyed sacred images but developed classical music. Does the Autonomy of Mathematics Mean Estrangement from God and Religion? In Japan, there has long been concern about "disengagement from science" (Rikei-banare), and for many years, there has been discussion about needing to increase the number of students going into STEM fields and for the government to support them. Globally, the emphasis on STEM talent seems to be accelerating. Outside of some humanities fields, we live in an age where scientific and mathematical knowledge is necessary in all academic fields, including the social sciences. The image of the medieval "universal man" (polymath) was one who was well-versed in all fields, a master of both arts and sciences, and this ideal may have persisted into the early modern period. People who were masters of both science/mathematics and philosophy, and active in other fields, are conspicuous in the early modern era. However, as the modern era progresses, such people become fewer. Does the development of knowledge lead to specialization? Looking at the modern era, mathematics seems to be moving in a direction where it is no longer studied by all intellectuals or scholars. As a result, the "culture" of humanities and sciences may have split. Pascal, Descartes, and Leibniz were somewhat philosopher-mathematicians, but Kant, Fichte, Schelling, and Hegel are not famous for their work in mathematics or physics. Likewise, in the scientific fields, while Newton is an exception, Laplace, Lagrange, and Gauss do not seem to have done famous work in philosophy. The historic medieval universities of Europe were conservative, so they may have continued to teach the seven liberal arts and the Quadrivium in their general education. However, they could not teach the four mathematical subjects in the same way as in the Middle Ages. Geometry might be fine, but arithmetic would need to incorporate advanced algebra, astronomy would require starting from Newtonian mechanics, and music, with changes in notation and the evolution of instruments, would be anachronistic if taught in the medieval style. Yet, teaching the cutting-edge mathematics, physics, and music of the time would also present its own difficulties. Dualism, the Materialistic Nature of Science, Empiricism and Theory In the past, "fuzzy" concepts like the geocentric theory, Euclidean geometry, Gothic music, or simple arithmetic perhaps aligned well with theology or Idealism, serving as "just right" tools for contemplating God's perfect world. However, setting aside Galileo and Copernicus, when Newtonian classical mechanics and books like the Principia Mathematica Philosophiae Naturalis became bestsellers, second only to the Bible or Euclid's Elements, the story changed completely. Solving astronomical problems using classical mechanics is an objective, "process-oriented game" (Jp: sagyō-gē). If God is the one who created it, then perhaps it doesn't contradict religion or theology. But interest in God or religion relatively wanes, or in the worst case, the existence of God or religion becomes irrelevant. This could lead to a direction not of atheism, but of "indifferent-theism" or "ignore-theism." One can simply reduce the time spent contemplating God and religion, and pour effort into mathematics, physics, and experiments. This can be justified under the pretext of piously studying the laws of the world God created. However, modern scientists and mathematicians may have viewed religion and the Church with suspicion. The Middle Ages were called "dark" and the Reformation occurred precisely because of the arrogance and exploitation of the Church, so a backlash was inevitable. Newton, though not publicly, held Arian beliefs (the view that Jesus was human), which was heretical to both Protestants and Catholics. Yet, to non-Christians—including Jews and Muslims—this is an entirely reasonable view. From a broader perspective, trying to equate a single human being with the one and only God, despite various rationalizations like the Trinity, is a rather peculiar ideology (this is not a criticism of Christianity, which I love, for the record). Furthermore, the methodology of modern science is completely different from the "fuzzy" scientific nature of the Middle Ages. Modern science is an extremely pragmatic and laborious (Jp: kinrō-teki) process of rigorously advancing empirical verification and theorization. Mathematics involves only theorization, but it still rigorously advances fields like analytical mechanics. This rigorous advancement is fine, but this focus on practical work (Jp: jitsumu) shortens the time spent thinking about God and religion. Moreover, there is no need to involve talk of God or religion in the practical work itself, so God and religion "float away" from, or become distant from, science and mathematics (theorization and verification). The practical work itself is objective or "materialistic" (Jp: yuibutsu-teki). God and religion become things that, in practical terms, are fine if they exist, but fine if they don't—they become optional. This is the separation of God from science and medieval mathematics. Theologians and clergy, in turn, may find the rationale of "studying analytical mechanics to get closer to God" to be unconvincing or entirely disagreeable. In Antiquity and the Middle Ages, Mathematics and Science Connected God and Man It's a strange story, but it can be seen that in antiquity and the Middle Ages, mathematics and natural science at the standards of the time connected God and man, religion and people—it brought them closer. The university system of compulsory subjects was a device for this. It was a happy era where learning these subjects was synonymous with acquiring cosmology, a comprehensive explanatory system for the world, and various religious and theological knowledge. And there were social attitudes, institutions, and systems to support this. However, the "science," mathematics, and natural sciences of antiquity and the Middle Ages were, from our modern perspective, "fuzzy" (Jp: fuwa-tto shita). The Separation of Science (Rikei) from Religion and Humanities (Bunkei) from Modernity to the Present Even in the modern era, prestigious universities with long histories may have taught the medieval seven liberal arts in their original form in the early years of general education. However, this gradually changed into the form seen in universities today. In the general education departments of today's Japanese universities, science (Rikei) students are likely required to take calculus and linear algebra, at least. Other subjects depend on their specific scientific discipline. With the abolition or shortening of general education, some curricula may push students directly into specialized education, with introductory mathematics like calculus and linear algebra included as compulsory subjects within that. On the other hand, what about humanities (Bunkei) departments? Today, even economics likely includes some elementary mathematics as a required subject. However, in the humanities and social sciences, such as law or political science, there may be universities where it is possible to graduate without taking any mathematical-scientific courses at all. I am not sure about the present, but around the end of the 20th century, there were many such universities. This is a clear separation of Rikei and Bunkei at the university level. Unlike medieval universities, in modern universities, in the academic fields labeled "Bunkei," there is no need to study mathematics or natural science. Or, at least, there was a time when this was the case. This change probably did not happen abruptly somewhere between the Middle Ages and the modern era, but rather gradually shifted in that direction. The Specialization of Academia and the Problem of God and Religion The mathematics (the mathematical sciences and the medieval, religious, theological natural sciences) that was required for everyone in the Middle Ages gradually separated into faculties and departments that study it and those that do not, throughout the modern era. From one perspective, this can be viewed as the specialization of academic disciplines. (I apologize if I am wrong and these subjects are required, but) in literature departments (e.g., French Literature), philosophy departments (excluding analytical philosophy), and law faculties, it is often the case that mathematics is not part of the required curriculum throughout one's undergraduate studies. The reason why mathematics and the sciences, which were compulsory in the Middle Ages, are no longer compulsory in modern and contemporary universities is presumably because they are not "necessary." However, viewing this through the filter of necessity or specialization is only one layer. It is also necessary to view it from a religious and theological perspective. European universities, though exceptions may exist, are fundamentally advanced versions of seminaries. Theological education was central, and many were founded on the basis of training clergy. In that era, the four mathematical subjects of the seven elementary compulsory arts were considered essential for theology and religion. In modern and contemporary universities, mathematics, and broadly the sciences and natural sciences, are no longer required as a foundational, necessary component of learning for all students. This signifies not only a specialization of disciplines but also a major theological and religious paradigm shift, whether it was radical or gradual. Mathematics (Science) Became a Tool for Distancing from God, Not Approaching Him The decisive change is this: in the Middle Ages, mathematics (geometry, arithmetic, astronomy, music) was a tool for approaching God, but in the modern and contemporary eras, this has reversed (or been perverted), and mathematics has become a tool for distancing from God. Some might argue, "Studying modern natural science and cosmology is a pious act of faith, as it means knowing the world God created." That has its own logic. However, the claim that "Modern natural science and cosmology are independent of and separate from theology and religion, and should be considered separately" is more logical in its consideration of autonomy, and is a more natural way of thinking. (Perhaps it only seems "natural" because I am from a non-Biblical culture.) However, as time passed from the Middle Ages to the modern era, this way of thinking probably grew stronger and more prevalent. The reversal occurred: "The more one studies mathematics, the closer one gets to God" became "The more one studies mathematics, the more distant one becomes from God." This sometimes leads to the "conflict between religion and science" narrative in the modern Western world. While there is the position of co-existence as separate entities, or even of friendly, complementary roles, there are inevitably a certain number of people and forces that see them in conflict, and this tends to be conspicuous. Conflict might be better than the truly frightening alternative: indifference. In the medieval framework, knowing the laws of the world was directly linked to approaching God. But this sensation was interrupted or completely severed, and Japan's importation of Western civilization was mainly an importation completely severed from this context. The Wane of the Platonic Worldview in Modernity There was another reason why mathematics was compulsory in medieval universities, as mentioned before. Studying mathematics (science, natural philosophy) seems to have carried a sense of approaching God by contemplating the perfect world God created, rather than the imperfect real world. The Ideenwelt has strong connotations of "perfection," "harmony," and "order," so Platonism and Christianity were perhaps easily fused. However, idealists are sometimes weak against pragmatists. Idealists may gain power, absolutize their ideology, and persecute realists, but pragmatists can also deflate idealists by presenting them with reality. Modern natural science is a "grimy" (Jp: dorokusai) task, requiring sweaty, hard work: designing, repeating, and refining experiments, observations, and measurements for empirical proof, and then theorizing. Modern mathematics is the same. It abstracts past mathematical and natural scientific phenomena. The finished product is beautiful, like the Ideal world, but the process to get there is a realistic and steady consumption of thought and immense time, dependent on how one continues to persevere, obsess, struggle, and gain flashes of insight or inspiration. Whether in Christianity, Judaism, or Islam, there may be daily, fixed times for prayer to God. Perhaps in the Middle Ages, people thought about mathematics, nature, or the Ideal world during such times. But in the modern era, if one were to think about mathematics or natural science while praying, one might feel, or be accused of, not praying to God. In this way, the distance between religion, God, and mathematics, the sciences, and natural philosophy steadily wides. There are many brilliant researchers who are Jewish, and scientists who are fundamentalist Christians like Southern Baptists, but they are probably not thinking about their specialized fields during prayer. Broadly Speaking: Science, Humanities, and God All Went Their Separate Ways In Japan, God and science were not linked when Western civilization was imported in the first place, and just as the University of Tokyo has long been divided into Bunkei and Rikei, the humanities and sciences were likely separate from the very beginning. In Europe, from the Middle Ages, society and universities centered on religion and God, and universities were developments of seminaries. There, regardless of any Bunkei/Rikei distinction, mathematics—along with Latin as a common language, rhetoric, and logic—was studied as a common, elementary subject necessary for theology, God, and religion. Only after that did they create schools to study specialized subjects like theology, or subjects that served it—law, medicine, and philosophy (as "miscellany"). After all, in the Biblical cultural sphere, the ideal was a theocracy, where the church and religion (be it Christianity, Judaism, or Islam) managed both religious and political affairs as one. A clear example is Islam: Shiite Iran is one, and Saudi Arabia (though I don't know which sect) may have similar aspects. In Judaism, during parts of the ancient Kingdom of Judah, religion and secular governance were unified. The Bible during the prophetic era is like a critique of how religious the king was; the king's evaluation seems based solely on that. For example, a certain period of King David, or the Maccabean dynasty after the Babylonian exile (when prophets no longer appeared), would be a Jewish theocracy. In Christianity, the world split into East and West. In the West, religion was (led by) the Pope, and the secular (led by) the Emperor, and European medieval history is the story of their power struggle. In the East, the Emperor served as both (but this fell). In England, the King served as both the head of the Church of England and the head of state, but in a typically English, pragmatic, and "loose" system (though the reality at the time was harsh by modern standards). Well, universities were formed through various entangled intentions, and each university has its own history. For example, the official names of prestigious German universities often include the name of a Holy Roman Emperor. Historically, there were many variations, but in the end, the major trend in developed countries today is separation: God (religion), the humanities (Bunkei), and the sciences (Rikei) are all on separate tracks. This "separation" doesn't necessarily mean conflict, but rather a "cold" relationship of being separate entities. Japan and the World of Biblical Cultures In the Biblical cultural sphere, Christianity (aside from the Bible Belt or the Vatican) has seen a separation of science, humanities, and God. Islam is still in flux, and perhaps even in a developing phase as a religious force. Jews in the medieval and modern eras co-existed within both worlds, often without a nation, like gypsies. The other major forces would be the Hindu and Buddhist spheres, and perhaps some primitive religious groups completely independent of the three major world religions, remaining in undeveloped regions (though even these, in Africa, the Amazon, or among Native Americans, have likely been heavily influenced by Christianity or Islam). The main representatives of non-Biblical religions might be Hinduism (derived from Brahmanism) and Buddhism. While the overall situation is complex, Japan is one such Buddhist country. However, just as European Christianity syncretized with pre-existing religions, "Buddhist Japan" is also a product of syncretism with other religions, and thus contains great diversity and difference. Japan's Characteristic: Whether or Not to "Put Your Heart In" Among the non-Biblical, Brahman-derived religions (Hinduism and Buddhism), Japan has a quality that likely prevents it from becoming a "Biblical culture," no matter how much its systems or education are changed. It has a certain affinity with Catholicism, which (within the Biblical sphere) came to "OK" idolatry, but it is incompatible with Islamic fundamentalism or ultra-Orthodox Judaism, which strictly enforce the biblical prohibition of idolatry. It's not about conflict; the fundamental nature of the spirit is entirely different. The idea that "all people are the same" is true on one level, but completely untrue on another. Sometimes, there is no desire to find common ground. Jews, with their "chosen people" concept and the high hurdles for converting to Judaism, have virtually no proselytizing mindset like Christianity, and might even be called exclusive (not in a bad way). Christianity once aimed to convert the entire world, though this impulse seems to have weakened recently. Japanese people, too, while enjoying YouTube videos praising Japan, might prefer non-Japanese not to become Japanese unless they are willing to assimilate. This is getting long, so to summarize the point: Japanese people have a characteristic of trying to "put their heart into" (Jp: kokoro wo komeru) things in which they sense divinity, and of trying to find a "heart" (Jp: kokoro) even in things where they do not sense divinity. For Japanese people, sensing divinity or a heart in objects is affirmed; rather, we actively try to find it. This can be called the "OS," the "DNA," or the "identity" of the people. This is not about having Japanese ancestry, Japanese citizenship, or speaking Japanese. "Being Japanese" probably means "having acquired Japanese culture," and while acquiring a culture has many levels, the most fundamental requirement for "being Japanese" can be defined, with high probability, as: "To feel a heart or divinity in things, and to try to find a heart or divinity in things." The Core of the Bible If the necessary condition for being Japanese is "to feel a heart or divinity in things, and to try to find a heart or divinity in things," then the more fundamentalist thinking of the Biblical cultural sphere is the opposite. That is, "To not feel a heart or divinity in things, and to try not to find a heart or divinity in things" is the core of Biblical culture. If we consider this in terms of human intellect, emotion, and will—human sensibility, feeling, volition, and thought—then the two cultural spheres (or, if we consider Japanese culture a religion, "Japan-ism") are opposed at a fundamental doctrinal level. This is an "antimony" (Jp: niritsu-haihan), a conflict so fundamental that if both sides clearly recognized it, religious conflict could easily erupt. But it remains a critical, deep-rooted problem that almost no one clearly understands (or only vaguely understands). This may also be because, to the Biblical cultural sphere, Japan is—in a calmly objective, non-self-deprecating way—a tiny, supporting, irrelevant "mob" or "small fry" (Jp: zako), so few have tried to understand it deeply. In Japan, Everything is Separate, But the "Heart" is Put In During the Meiji Restoration's "Civilization and Enlightenment" (Jp: Bunmei Kaika), Japan imported a massive amount of Western "things" (Jp: bunbutsu). In doing so, while there may have been efforts to import or understand the Western "spirit," there were also aspects that were completely misunderstood, unnoticed, or understood but intentionally not imported or adopted. One of the biggest of these may be the mindset of "not feeling a heart or divinity in things, and trying not to." Of course, in business, finance, politics, national interest, and various other cases, this mindset of "not feeling a heart or divinity in things" is necessary. Such thinking existed in Japan long before the Meiji Restoration—in the Edo, Warring States, and earlier periods. In fact, there is likely no culture that completely lacks this way of thinking. If anything, Japan was perhaps the fastest in the world at "slicing things up" (separating) ahead of the West. Taira no Kiyomori and Oda Nobunaga tried to separate medieval religion from secular politics and actively adopted a money-based, free-market economy. This requires the separation of secular and religious authority (though it's a complex relationship that also requires using religion). In the Edo period, Ogyū Sorai completely separated "Heaven" (nature, the supernatural world) from humans and society. From the Kogaku (Ancient Learning), Kogigaku (Study of Ancient Meanings), and Komojigaku (Study of Ancient Characters)—the so-called Confucian textual criticism—to Kokugaku (National Learning), the Kaitokudō academy, Rangaku (Dutch Learning), medical history, Honzōgaku (herbalism), and Mitogaku (Mito School), all of them were empirical, philological studies. This predates Chinese textual criticism, and Western biblical criticism (empirical philology) only began in the 20th century. In this sense, Japanese people separate everything and have a strong tendency to sharply distinguish (Jp: shunbetsu) independent phenomena. However, the base layer is a sense of "connection" (Jp: tsunagari-kan) to all things, feeling a heart or divinity in bambutsu (all things). Meanwhile, Western culture, as it aged, also proceeded to separate God, the humanities, and the sciences. On the other hand, they are unable to make a clean break, and aspects of this (separation) are still confusingly debated or in conflict. Or perhaps as a backlash or "perversion" (Jp: tōsaku), they excessively emphasize things like DEI (Diversity, Equity, Inclusion), SDGs, or ESG. This over-abundance of ideology bursts forth, acting destructively, in a left-wing radical way, against its intended purpose. If you don't make something an issue, it isn't one. Emphasizing something often means there's a reason it must be emphasized. This is a binary opposition (Jp: nikō-tairitsu). For example, an authority that already exists, like the Emperor, doesn't need to emphasize its authority or decorate itself with extravagance to prove it. But an authority with a shallow history will be intense in its display and appeal of power. In Japan, "safety, water, and air were free" (Jp: tada). In countries where they are not free, one must be conscious of their importance. God and "heart" are the same. If they are omnipresent, they are like a "stone" (Jp: ishikoro)—unnoticed. (Like Doraemon's "Pebble Hat" [Jp: ishikoro bōshi]). Conversely, in a cultural sphere that must be nervous about feeling God's existence or presence, they must constantly be conscious: "Do not feel divinity in things," "Do not make idols," "Do not acknowledge other gods." Conclusion: The Vicissitudes of Humanities and Sciences, Mathematics and Natural Science (Knowledge) This discussion has expanded, but in short, the treatment of mathematics (including mathematical and natural sciences) has fluctuated through antiquity, the Middle Ages, modernity, and the present. Or rather, society has fluctuated, mediated by the treatment of mathematics. In antiquity and the Middle Ages, it was the foundation of God, religion, and society, something all elites (and ideally, commoners, but at least the upper classes) had to learn. In modernity and the present, it has become just a specialized field. While basic arithmetic is learned by everyone in elementary education, in higher education and science, it is something to be learned if required by one's specialty, but unnecessary if unrelated to one's field. In the future, as the frontiers of advanced science, technology, and industry—like computers and robotics—expand, it may become compulsory again. Or, conversely, AI may develop to such a point that in ten or several decades, humans may no longer need to study mathematics or science at all. However, even as the times change, the Japanese characteristic of "feeling a heart or divinity in things, and trying to find it" and the Biblical cultural characteristic of "not feeling a heart or divinity in things, and trying not to" will likely remain surprisingly deep-rooted for a long time. This is my conclusion.