Mathematics as the language of faith

Chaos is a term which has been linked to cosmogonies and cosmologies since the very first conscious steps of humans on earth. The eternal struggle between order and disorder, harmony and Chaos, represents, instead, a deeply rooted human conception of the Universe which was depicted in myths and theories. Chaos was the first element of the cosmogony of the philosophers of ancient Greece34. «Chaos» is presented for the first time in the Theogony of Hesiod (8th century BC) as the primary matter of the Universe: “To Xaog npwwywqKe ki q rq ptTa q nlarvar^Qa ... Ki an' to Xaog nahv yevv^dqKe to Epefiog Kai q Tptopavpq q NvyTa”. In our chaotic world, randomness, complexity, contradictions result in perfect synthesis and coordinated states. Anaximenes (585 BC) explains the various forms of primary matter, Chaos, by thickening and thinning. Anaxagoras (500 BC) admits that «all the elements, in the beginning, were mixed and confused. Everything was in everything. Everything that is separate today was a separate and calming mass. This mixture would not come out of its calmness if the mind did not give it the movement and did not separate it». Thus, he deals with the unstable, random, mixed and confused elements of the infinite primordial matter. In the «Genesis» of the Old Testament we read with a different orientation that: “the Earth was invisible and unconstructed and darkness was brought over the abyss” Ian Stewart, Does God play dice? The New Mathematics of Chaos, Pub. Penguin Books Ltd., 1997, p. 15. Holy Bible, New King James Version, Genesis 1:1-2..

Some innate impulse impels humanity try to understand the normality in nature, to investigate the laws behind the strange complexity of the Universe, to bring some order out of the Chaos. In modern times, scientists, physicists, biologists, mathematicians, engineers, chemists and others, by researching various elements to explain some of the Chaos that prevails in the chaotic organic and inorganic world, are led to find a way in which they could change in any case the multiform elements in uniform etc.

Today Chaos describes the subject that studies some too complicated systems whose evolution over time is strongly dependent on the initial conditions under which it is analysed. In particular, Chaos Theory studies the behaviour of specific non-linear dynamical systems, which are characterised mainly by a sensitive dependence on initial conditions but also by a non-periodicity. This sensitivity results in the apparent randomness of the systems' observed behaviour, even though these systems are causal or deterministic, in the sense that their laws of evolution are well defined and do not contain random parameters. Commonly a non-linear dynamic system presents immobility, expansion or explosion, (semi) periodic motion and chaotic motion. The most difficult to observe and predict is the chaotic motion, a complex, non-periodic motion, which has given its name to the theory. Sensitivity to the initial conditions means that two points in such a system can follow radically different trajectories in the phase space, even if the initial conditions' difference is tiny. Systems behave in the same way only when the initial configuration is precisely the same.

Consequently, Chaos affects Physics, Biology, Mathematics, Economy, Meteorology, Geology, Astronomy and other scientific fields. The Science of Chaos is the third great revolution of the 20th century, after that of quantum mechanics and relativity. It aims to restore order and balance in modern life, after subduing with knowledge the uncontrollable forces of the Universe.

From a mathematical point of view, Chaos Theory studies the behaviour of specific non-linear dynamical systems, which under certain conditions show chaotic behaviour. It is characterised mainly by a sensitive dependence on the initial conditions (butterfly effect) and then by non-periodicity. This sensitivity results in the apparent randomness of the systems' observed behaviour, even though these systems are deterministic, in the sense that their laws of evolution are well defined and do not contain random parameters. We know today that it is possible to have extremely complex, e.g. chaotic, motion and therefore unpredictable, even in simple dynamic systems with two degrees of freedom, while until then it was believed that we have erratic, unexpected motion only in complex systems with many degrees of freedom, such as, e.g. in the movement of air molecules in a room.

With the advent of quantum mechanics, the clockwork of the world became a global roulette wheel. Fundamental phenomena, such as the decay of a radioactive nucleus, are determined by blind chance and not by strict law. We are beginning to discover that systems that obey fixed and specific regulations do not always work in a standard, predictable way. Chaos is a whole new world, a new kind of mathematics, a fundamental innovation in understanding disorder in nature.

We live in an age where the mechanistic, clock-like view of the world has changed to the perception of the world as an ecology. From determinism, we moved to probabilism (statistic)M. Begzos, Contemporary Physics and Philosophy of Religion, Athens 2009, p. 211.. The phrase of Pierre Simon Laplace which supports the uniqueness is now considered hyperbolic and is not applicable:

“An intellect which at any given moment knew all the forces that animate nature and the mutual positions of the beings that comprise it, if this intellect were vast enough to submit its data to analysis, could condense into a single formula the movement of the greatest bodies of the universe and that of the lightest atom: for such an intellect nothing could be uncertain; and the future just like the past would be present before its eyes.”.

A great example of chaotic movement is the incident that occurred during Voyager's one trip on the 5th of September in 1977 where the predictions had no mistake, Newton's law was not disproved but may cause false predictions and does not imply any absence of physical laws. Nevertheless, Voyager came across Hyperion, which was somersaulting in a complicated way and not facing down as usual.

The Father of Chaos is considered to be Poincare with his discovery of the problem of three celestial objects (earth, moon and sun). At first, everyone neglected him. Then the soviet scientist Kolmogorov understood and others followed. If it were not for Edward Lorenz, we would not have known that iteration creates Chaos. Lorenz's theory of the butterfly that flies to Hong Kong and could create a storm in New York is due to him as well. Suddenly scientists realised that in causal dynamical systems, the possibility of the birth of Chaos (unpredictability) lurks in every detail. And as Lorenz used to say: Any physical system that behaves non-periodically is unpredictable.

One way to visualise chaotic motion, or any other motion, is to construct a phase diagram of activity. In such a diagram time is implicitly entered and, in each axis, a variable of the state is represented. An easy way to portray a chaotic tractor is to start with a point in the `basin' of the tractor's attraction, and then plot its next trajectory. And this can probably produce a picture of the whole ultimate attraction. These phenomena are better described with fractals and fractal mathematics. Basically, Fractal is a pattern that never ends, driven by recursion to form an image of a dynamic system or a picture of Chaos. For instance, we observe those images in nature, e.g. trees and rivers.

To conclude with the definition of Chaos in Science, I will refer to Quantum Chaology. It is said that Chaos was revealed by mathematical imagination, and was born of physics. The term Chaology had long referred to the study of the era of Chaos - the period when «the Earth was empty and without shape». Chaology is no longer an active field of Theology, so the term is free for a more modern meaning: the study of deterministic Chaos. Quantum mechanics is modern physics for the Universe on atomic scales. In quantum mechanics, quantities such as energy are not continuous: on the contrary, quanta appear in discrete pieces. Einstein could not cope with this view and said that God does not play dice, and that hoped that someone would find a more “realistic” explanation according to his word.

Nevertheless, quantum mechanics events still seem to take place in the way that quantum mechanics determines. And while radioactive decay statistics, for example, follow specific laws, no one can predict when a given individual will reach the critical point of decomposition. Einstein then proposed a second Idea to Max Born that we do not understand the more in-depth game. In my opinion, we do not do, and we will never do because we do not have the mental capacity to understand the created world.

But where does Theology jump in the equation? Most of the western scientists would say in the matter of free will and creation. All the books we read are about God playing dice, determinism and the autonomy of the Cosmos. Surprisingly, I will not go down that road. I will take my time though to answer to “laymen's opinions” of scientists like Sabine Hossenfelder in whose video “You do not have free will, but do not worry' she makes statements like: “let me tell you what science says” & “I proved that free will is nonsenseThose opinions are overgeneralised and unproved. Starting from the unprecedented logical leap that a possible deterministic behaviour of particles imparts, it saves for good, determinism of thought. As if to say that the same hardware will produce the same results in the software.

Continuing with the logic of rejecting the deterministic «Laplace Demon» that chaos theory combined with Heisenberg's indeterminacy sealed his tombstone forever. Yes, chaos theory is based on determinism. Still, it loses it along the way, except that no one will ever be able to know position and speed with absolute precision at the same time, so as not to put forces and interactions, not even a single particle, let alone of the whole Universe. The complete disconnection that she tries to indicate between the confirmed random quantum events and the thought/consciousness exposes her irreparably. The most accepted scientific interpretation (of Copenhagen) considers that the collapse of wave- functions occurs with observation, which is caused by the will to control, and probably leads to consciousness or otherwise free will. Quantic Probabilism shattered determinism at its root. All the great Nobelists suggest we search into the unknown waters of quantum physics with cognitive sciences' help to find the answer. We do not have answers on that subject yet, and it is not necessary to support one in order to fulfil your scientific vainglory. Accordingly, Orthodox Theology cannot be placed into a narrow box of a philosophical movement like determinism or libertarianism. Those movements cannot describe the state of freedom Human has like the Fathers of the Church do. Theology cannot identify as the other sciences but can have an interactive relationship with them.

The intersection point that will be tried to be found is that of Chaos and God's Intervention, also known as miracles. At first, we have to define miracles in Orthodox Theology, so they are not conceived as they do in the West. The miracle is part of the relationship between the created and the uncreated and often contradicts the sciences. This contradiction though is shallow, like the one Science and Theology have. Science and Theology cannot be compared but can intersect if sciences retire this positivistic model. They should not come in controversy because they are different. In the case of the miracle, the natural law (Science) seems to conflict with the metaphysical law of Theology and vice versa. But the miracle confirms nature and is not metaphysical or supernatural. Must we always distinguish between the natural and the unnatural. We define natural as the one that exists while unnatural is the state of man's Fall, rather than nature's state and life. It is not natural for a human to decay and wear out, but it is somewhat unnatural and a consequence of the Fall. A miracle for Westerners is God's intervention in the world by exception, and it is not a natural event. For the Orthodox Tradition, however, there is no deviation from the natural law. It is a historical event and not an extraordinary intervention of God. The grace of God and his glory is our daily life. The miracle is done to glorify God and not to solve a problem or to make a man believe. Thus, it is neither metaphysical nor the extraordinary intervention of God but something natural and the point of presence of God in the world. The miracle does not correct nature but restores it, and we interpret it from the perspective of the created-uncreated and not on a moral basis. Christ refuses to perform miracles in front of the unbelievers because they are unbelievers, and they will interpret it as they want. Faith and communion with God precede the miracle as it happens for those who do not see it as a miracle, because, precisely, they believe. For the believer, the miracle is the natural consequence of his faith and communion with God. As long as one communicates with God, he lives in the society of miracles, when someone lives despite nature, then he sees it as a miracle. Both the miracle and the presence of God are achieved through a man's realisation for his oneness with God.

The final observations indicate the existence of a mathematical order behind what seems to us as random events occurring in the Universe. Chaos Theory eventually supports the idea of a Creator who gave motion governed by mathematical principles. The illustration of Sierpinski's Triangle will help us understand. After random choices of points, we begin to notice a pattern which is clearly shown in the picture. This could be related to the passage from Romans 8:28: “And we know that in all things God works for the good of those who love him, Holy Bible, New King James Version, Romans 8:28.. Daily in our life, faithful people experience the uncreated energies of God and his miracles. Positivistic scientists and atheists try to rationalise it and call it luck.

In chaos theory, we observe that the things we call luck or exceptions are instead natural. So, we go back to our definition of miracles. It is a natural event that occurs as a result of the relationship between the Uncreated (God) and the created world. Those miracles are natural events and those who characterise them as lucky and exceptional eventually help me prove the point that is not luck but planned events that seem spontaneous and chaotic to us as a result of our insufficient mental capacity. Lucky coincidences are basically God's completely natural miracles. We cannot scientifically find those energies and trace them as they are uncreated and they do not have a specific pattern precisely because they are chaotic, but they are natural, and they are planned and not random. But we notice their aftermaths both in our daily life and experience but also on a cosmological scale. The glorification that God offers is a miracle that happens in history and God always test and help us in order to set sail according to His purpose and will. Western Theology cannot cope with that perception as it considers that man's features of His image are completely tarnished and does not believe in the uncreated energies of God, thus enlarging the distance between man and God.

Consequently, it assumes that God's intervention is exceptional and mostly for our help and not His glorification. For example, the Immaculate conception of Holy Mary is a miracle. Still, if you try to rationalise it, it would seem like a lie or a lucky case of parthenogenesis, but this is not merely the case as we inspect that there is no thing as luck just God's plan and human's freedom in the context of the natural laws.

ASYMMETRICAL CHRISTOLOGY AND PERFECTION

In this chapter, we are going to relate Assymetrical Christology according to the doctrine Chalcedon and the golden ratio 9. Before diving into the theological part, it is necessary to give a clear picture of the 9 number and Fibonacci sequence.

The golden number 9 was first detected by the ancient Greeks, who observed that everything on earth, from plants to the human body itself, developed in an analogy. Pythagoras was the first to formulate the mathematical definition of proportion using two straight lines. His thought was that if a line segment and an intersection point is intersecting it asymmetrically so that the length of the largest segment to the entire length of the segment is equal to the length of the largest segment to the length of the smallest, then their ratio reveals some kind of analogy. The result that is always given is 1.618, which is the golden number. It is the only number for which the relation 9 = 9 + 1 and 9 = 1 + ^5 / 2 applies. The main finding is that a result is an implicit number. This shows that a smaller line segment can't fit in a larger one exactly. Therefore, there are some numbers whose function is beyond human comprehension, and their field of the definition is the ideal. Thus, the concept of the idea was discovered, which Plato researched and formulated the theory of Ideas. For instance, the pentagram, which was the symbol of the Pythagorean school is subject to this analogy, showing they knew everything about this number.

Pythagoras was the first to observe that plants and animals do not grow randomly, but according to precise mathematical rules. That is, the beautiful designs of the flowers are not accidental. The ancient Greeks found that flower designs are based on geometric proportions. The sequence also makes its appearance in the arrangement of the sexes around the stem. With the actions of the Italian mathematician Fibonacci, who was well known in his day and is still recognised today, he found that the key to beauty is the ratio 1 to 1.618, the number 9. Later, the architect Le Corbusier (1887-1965) built a scale of proportions called Le Modulor, which is based on the human body. According to her, the navel divides the human body into a golden ratio. Also, the width of the mouth is 9 times the width of the nose.

The ancient Greeks considered the Golden Number as the divine analogy where its application in artistic creations and constructions led to «excellent» and ««beautiful» results. After many years, Fibonacci discovered a sequence of numbers that had the property of displaying the golden ratio. We daily encounter many forms of art that have used (consciously or subconsciously) the 9 number. The Parthenon's faзade, Michelangelo's David, music, Quran, Pyramids etc. have all used the golden number. The Geometry of fractals, the ones we mentioned in the previous chapter also has golden tome. The human body itself, our DNA and even cyclones use the number above. We even saw it with Alan Turing's Tommy flowers. Many other examples and forms of 9 number could be mentioned but will be avoided because the topic is not about the golden number itself but its relation with Christology.

Therefore, 9 is an «implicit» or «asymmetric» number, that is, a number that cannot be written in the form of an integer fraction. Why is it simultaneously both asymmetrical and symmetrical? In contrast to the static symmetry (symmetry of equilibrium, also known as balance), the dynamic symmetry (golden tome division) is the perfect asymmetry form. The theory of perception states that there are two different optimal possibilities of a harmonic division of a whole: first is the mirror reflection (also known as symmetric division) and the golden section division (an asymmetric division, where basically the ratio of the smaller part to the bigger is the same as the ratio of the bigger to the whole). Dynamic symmetry is a characteristic of living matter, while static symmetry exists in the world of crystals.

Analogically we can spot the divine analogy, the golden number in Christology. First, it is necessary to distinguish between the asymmetrical Christology of the West and many other misconceptions. We have seen Thomas Aquinas' asymmetry Thomas Aquinas, Summa Theologiae I, q. 28, a. 1, co., which generates the whole tension, followed by Calvin, Bonhoeffer, Austin Farrer and last but not least, Balthasar. The asymmetry they introduce considers the Divine nature of the word (uncreated) and the nature of Christ (created). The same asymmetry is used in Rowan Williams's book “Christ the Heart of Creation” but in the extent of perceiving Christ as two different agencies and not one as a result of the two natures' interpenetration. He is leaning towards the separation of God and the world that Scotus and Ockham introduced, even though he rejects this opinion in his book.

Georges Florovsky, in his book “Collected Works, vol. 9: The Byzantine Fathers of the Sixth to the Eighth Century” introduced the Asymmetrical Christology considering the doctrine of Chalcedon. The principle does not state an asymmetry in nature as mister Jordan Daniel Wood falsely states in his article “Against Asymmetrical Christology: A Critical Review of Rowan Williams `Christ the Heart of Creation'”. What Florovsky tried to say is that Christ has one hypostasis and two natures and not one hypostasis and one nature as we do. Also, Christ has two natural wills and not a gnomic will (jvw^iko/ fallen human will), in contrast to us that have one natural will and one gnomic will. This view could be understood as a symmetry according to the Tome of Leo J. Zizioulas, F. Georges Florovsky: The ecumenical teacher, magazine “Synaxis”, 64/1997.. Thomas Aquinas, for instance, introduced `De unitate Christi quantum ad voluntatem' (The unity of Christ's will) and `De unitate operationis Christi' (The unity of Christ's energy) respectively, which leads to the perception of one end-product rather than the two end-product Orthodoxy supports (both John of Damascus40 and Maximus41 the Confessor and not only Maximus as Doucet states). In fact, Maximus embodies the asymmetry of the personal hypostasis (which in Christ's case is divine) with the symmetry of the two, both human and divine, natures, whose unity constitutes the “material” hypostasis42. There is a danger for Christology to lose its balanced asymmetrical symmetry (or symmetrical asymmetry) if there is no analogy between the asymmetrical personal hypostasis and the proportional material hypostasis leading to over(a)symmetrical and eventually damaging directions. An entirely symmetrical Christology would restrict humanity in the context of self-existence of the created, and in this case, theosis as the true communion with God would be unachievable.

Consequently, we notice a connection between the asymmetrical Christology and the golden number. As the dynamic symmetry is the perfect form of asymmetry, similarly Christ's dynamic existence, which is also living matter, is the ideal form of asymmetry by being symmetrical or it is the perfect form of symmetry by being asymmetrical. Christ's asymmetrical symmetry follows the pattern of the golden section. As Christ has two natures, one hypostasis and two natural wills and not a gnomic one, therefore having an asymmetrical symmetry by having the symmetry of hypostasis, will, nature but at the same time exceeding it by also having the divine nature and not a second hypostasis. The same way an asymmetrical symmetry could be found in nature where two eyes exist, but they are not identical, but still, they result in balance and analogy. Eventually, we see the name “divine analogy” might not be a coincidence because after all, Christ is the perfect human and the perfect God at the same time. Indeed language and nature cannot and does not exhaust or deplete the reality, but it is supposed to picture it authentically and reliably.

Epilogue. In this paper, we tried to bridge the sciences of Mathematics and Theology. Their methodologies may vary but eventually both concern the same reality we all live into. Through the philosophy of religion, I tried to bring down the wall between those two sciences and show how God's intervention or economy is displayed in the reality we measure with mathematics. Surely others, like John Lennox, who are both mathematicians and theologians, could find this paper shallow, lacking both profound theology or mathematics, or even including mistakes. The point was not to dive deeper into either Mathematics and

John of Damascus, Expositio Fidei, 59. 41-3, 104-18 (Kotter (ed.), pp. 146, 148 respectively), and De duabus in Christo voluntatibus, 43. 7-13 (Kotter (ed.), p. 229).

1 Maximus the Confessor, Disputatio, PG 340D-341A.

D. Bathrellos, The Byzantine Christ (Person, Nature, and Will in the Christology of Saint Maximus the Confessor), Oxford Early Christian Studies, 2005, p. 68.

Theology but to show their connections and show that our faith is logical and not hyper-logical or illogical. Newton, for instance, who introduced the physics, which is considered deterministic, considered atheism senseless and odious. It is an important debate about whether post-modernity is an atheistic or a faithful era. What is important though is not to exclude Theology and religion from universities as a result of a political agenda. After all, in this paper, we had a great insight that they share many similarities according to axioms and faith. I will finish my dissertation with a quotation of Robert Jastrow from his book “God. and the Astronomers” which says:

“At this moment it seems as though Science will never be able to raise the curtain on the mystery of creation. For the scientist who has lived by his faith in the power of reason, the story ends like a bad dream. He has scaled the mountains of ignorance; he is about to conquer the highest peak; as he pulls himself over the final rock, he is greeted by a band of theologians who have been sitting therefor centuries.”

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