Between Mathematics and Transcendence. The Search for the Spiritual Dimension of Scientific Discovery

In the fourteenth century, Nicole of Oresme tried to describe human emotions mathematically. But human psychic processes finally turned out to be too complicated for mathematical formulae, and this ambitious attempt ended in failure. Seven centuries later, the astonishing variety of physical processes can be described in the language of mathematics, no matter whether these processes take place in New York, Beijing, or Kinshasa. One cannot avoid the question as to why the language of mathematics has been so effective in the physical description of Nature and why physical processes are described by universal physical laws even when they could have been nothing but an uncoordinated mess. These questions could be regarded as the counterpart of the classical philosophical problem: Why does being exist when there could have been mere nothingness? This question, criticized as trivial and meaningless by empirical positivists in the 1930s, now can be expressed in a new form that now also is meaningful for empiricists: Why do mathematically described laws of physics exist at all when Nature could have been manifested as uncoordinated chaos?

The Mysterious Effectiveness of the Language of Mathematics

The effectiveness of mathematical language in describing natural phenomena has amazed many authors. At the beginning of modern physics, an important controversy arose between Isaac Newton, author of the Philosophiae naturalis principia mathematica, the work containing the first theoretical exposition of new physics, and John Flamsteed, the first Astronomer Royal and founder of the Greenwich Observatory. Newton determined the positions of celestial objects on the theoretical basis underlying his principle of gravity. Flamsteed determined them on the empirical basis using the best observational equipment accessible at that time. Finally, after an emotional debate, Flamsteed had to correct his observational results. Mathematical formulae, worked out theoretically, better revealed the structure of the physical world in our cosmic neighborhood than did the observational evidence. Three centuries later, Eugene Wigner called this mysterious and astonishing property “the unreasonable effectiveness of mathematics in the natural sciences” (Wigner 1960).

The same “unreasonable effectiveness of mathematics” was revealed by Albert Einstein when, on the basis of field equations in his general theory of relativity, he discovered the expansion of the universe, which was confirmed by observation several years later. In 1965, the same effect was illustrated by the discovery of the microwave radiation that originated fourteen billion years ago with the Big Bang. The main problem was that the existence of such radiation was already predicted on the basis of mathematical calculations in the late 1940s. How does one explain that the language of mathematics is not only adequate to describe physical processes, but that it also helps us to discover new phenomena previously unknown? To better understand this astonishing property of our world, let us refer to an analogy closer to our everyday experience. Imagine that someone had created a new language as a purely artificial product. Had he later discovered that an African tribe spoke this very language, such a coincidence would have amazed him. It would be as improbable as the existence of a tribe reciting fragments of James Joyce’s Ulysses or using, as a means of communication, a new language created specifically for computers. Such occurrences could not be considered obvious or natural.

Perhaps the people who either do not know computers or who are critical of Joyce would not find anything amazing about such a situation; for them, any sequence of English or English-like words would be only an unintelligible jabber. A similar situation occurs among the people who do not understand mathematics and do not appreciate its role in the physical description of Nature. Those who do understand the role of mathematics in science think like Paul Davies, who, when awarded the Templeton Prize in 1995, expressed the essence of his philosophy by saying: “It is impossible to be a scientist, even an atheist scientist, and not be struck by the awesome beauty, harmony and ingenuity of nature. What most impresses me is the existence of the underlying mathematical order.” This order described by abstract mathematical formulae has often been regarded as either a bare fact or an unintelligible mystery.

In my opinion, to explain the nature of such an order one has to go beyond mathematics as well as beyond the natural sciences. This transcending of the level of scientific discovery brings us to the divine Logos underlying the mathematical structure of the world. Some authors call such a structure “the rationality field” or “the formal field.” Jan Lukasiewicz, the well-known representative of the Polish School of Logic, argued that the reality of ideal mathematical structures independent of human experience could be regarded as an expression of God’s presence in Nature (Lukasiewicz 1937). Such an approach seems justified because this mysterious reality provides us with an experience of the sacred, which transcends the domain of empirical observations and seems to precede all observation. Consequently, I call this astonishing reality permeating our physical world the theosphere.

Mathematical Presuppositions for Cosmic Mysticism

For methodological reasons, references to the theosphere were eliminated from modern science in the time of Galileo. Although he never denied the value of theological explanation, the author of the Dialogo was right when he claimed that all references to metaphysical or theological factors must be excluded from the domain of astronomical research. If, in the spirit of medieval astronomy, one were to refer to the role of angels to explain the motion of planets, one could always introduce the hypothesis of angels to explain any set of empirical data. As a result, in such an approach astronomy would merely remain a branch of applied “angelology” (Galileo Galilei, 1890).

Galileo’s methodological distinctions were important in separating science from philosophy. They do not eliminate, however, philosophical questions inspired by new scientific discoveries. Neither do they eliminate the aesthetic contemplation of Nature or our reaction to its beauty. In premodern science, this very beauty, as well as the contemplation of it, were regarded as a purely subjective factor. Thanks to the growth of modern science, one discovers that the physical order and its mathematical description constitute the objective basis for our aesthetic fascination. In its strongest form, this fascination has been called “mystical” because it provides a non- conceptual experience of the deepest level of physical reality. Albert Einstein called this kind of experience, inspired by “a deep conviction of the rationality of the universe” and its mathematical description, “cosmic religious feeling.”

The question therefore arises: What would be the ultimate rational justification for this expression of the rationality of Nature, which combines mathematical description and mystical insight? The contemporaries of Galileo never asked such a question because they used mathematics without ever discussing why its use was so effective. As a matter of fact, again for methodological reasons, the question of the mysterious effectiveness of mathematics transcends the cognitive level of both mathematics and physics. It could be answered on the level of philosophy and theology when we refer to the transcendent reality of God, which ultimately justifies the cosmic order as well as its sophisticated mathematical description.

Cosmic Harmony and Human Ecology

Because of their dislike for pantheism, in their reflections about God many philosophers spoke mainly about transcendent reality as it exists outside the world of Nature. However, in the Judeo-Christian tradition, the immanence of God within Nature was no less important. We see this especially in Psalms, which presents God clothed in majesty and splendor, wearing light as a robe (Ps. 103:1–4). In this perspective, harmony exists between the world of Nature and that of spirituality. Harmony is created by the great cedars of Lebanon and also by tiny herbs, by mountains full of marmots and also by wild goats—as well as by the Spirit of God, which renews the face of the Earth (Ps. 103). Specific aspects of this harmony are seen in the Gospels, in which unseen divine reality reveals itself in some of the basic elements of Nature—the lilies of the field and the vine plant, the fig tree and the storm on the lake, the Bethlehem plain and the Garden of Olives. In the biblical perspective, as in the philosophical reflections of Plato and Leibniz, God reveals his presence not in the gaps of our knowledge about Nature, but in the harmony of Nature. To this tradition also belongs Teilhard de Chardin, who, writing in The Divine Milieu, speaks of divinity revealing itself in the heart of the universe. A particular form of this tradition would be developed in A. N. Whitehead’s process philosophy, in which the role of God, immanent in his creation, has been compared with that of the “Poet of the world.”

The Poet not only creates his poems, but also expresses his nature in their beauty. Aesthetic categories are important for mathematical equations as well as for our spiritual harmony because they reflect the initial harmony of the world created by the divine Poet. God’s presence can be discovered in the various forms of harmony: physical, aesthetic, mathematical, ethical, spiritual. The different expressions of this harmony make up a human ecology, which facilitates our personal growth thanks to continuous cooperation with the divine Poet of the world. In this dynamic framework, all of us are invited to multiply the beauty of existence while spiritual harmony becomes an important component of our human ecology.

The spiritual consequences of human interaction with the immanent God can be described in St. Luke’s well-known words “hearts burning” (Luke 24:32). Our fascination with aesthetic beauty and our openness to altruistic actions such as human gentleness and kindness disclose the presence of the immanent God at the level of intentional processes. Of course, this presence cannot be reduced to intentional or psychological factors. The physical study of supersymmetry discloses the most basic forms of cosmic harmony that were ignored earlier in physics in the same way that the aesthetic aspects of physical theories were ignored at a time when empiricism dominated in science.

To come to know our human ecology means to discover in our existence the role of physicobiological determinants and their relationship to the patterns of existence proposed by the divine Poet. Describing the nature of our interaction with God, we can follow Whitehead when in his Process and Reality he uses the expression “the lure for feeling.” The causal influence of this lure can be described in categories of subtle persuasion, which can influence our decisions not only at the conscious but also at the subconscious level. This form of divine persuasion leads to human behavior in which special attention is paid to real values and gives rise to a fascination, thoughtfulness, and amazement in situations that may previously have seemed trivial. God, as a subtle Artist, never forces his patterns of beauty on us. He respects our freedom as well as the possibility of our rejecting his subtle persuasion.

In some physical processes, such as those described in classical Newtonian dynamics, mutual dependencies of interacting objects are strictly determined. In deterministic chaos, such strict determinism disappears, and many marginal factors can influence the final result. In our interaction with God, the subtle divine Poet never violates human freedom. Our personal decisions are ultimately free in the sense that God never determines them independently from us, but only influences us through subtle persuasion. For this reason, Whitehead compares God’s role with that of a Poet who introduces his vision of truth, beauty, and goodness into our world. This form of introduction merely brings a proposal of harmonious existence, but never a strong, necessary determination. The better our cooperation with the immanent God in our personal growth, the more mature become our actions and the more evident our spiritual search for the basic harmony of human existence.

St. Paul, speaking to the inhabitants of Athens on the Areopagus, powerfully expresses the presence of God in the created world when he says: “In Him we live, move and have our being” (Acts 17:28). This divine presence constitutes a world of meaning, and thanks to this the reality in which we live is neither governed by the logic of dreams nor is a manifestation of the absurd. Mathematical equations, the effectiveness of which allows us to affirm that the world is a manifestation of the Logos and not a mere result of absurd and meaningless coincidence, are a special example of this world of meaning.

Immersed in this world of meaning, all of us are inhabitants of the invisible theosphere, which consists not only of the rationality discovered in scientific experiments, but also of the beauty experienced both in direct contact with Nature and in contemplation of Einstein’s field equations. We have become used to this reality and tend not to notice it, just as in our daily lives we take gravity and genetic conditioning for granted. The invisible world of the divine Logos that penetrates our daily lives shows that, just as the fox says in Saint Exupery’s Little Prince, “what is essential is invisible to the eye.”

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