Mathesis Or Simple Joys, 1934

excerpt I On cultures of a geometric kind Nowadays in science it is a well known fact that, from the point of view of the form, the whole universe, as well as its parts, can be contained in an expression of the form f (x, y, z). A contemporary scientist even thought that it was possible to write the equation of a statue, for example that of Venus of Milos. Surely, it will be long and probably of a gruesome form. So many numbers in the simple and direct beauty of that statue! But why should we care? It will be an equation, nonetheless. It will be a new beauty, the other beauty of Venus of Milos. Will we ever learn to see this beauty as well? And still, the whole culture we have behind us does nothing but to lead us to this understanding of reality, to this new beauty of hers. Finding out that every part of the world, and the whole world as well, are known, they belong to us, they can be written in numbers – this European culture, or Greek, or whatever it is called, seems to have proved everything it wanted to prove and put an end to its own questions. Thus, our culture answered the questions it had asked itself, discovering at the same time the new beauty, the formal, linear one, of the mathematical truth, which it had been looking for in things. From now on there are only certain calculations to be made… Of course, I have to add something, for the sincerity of the discussion: things can be put in a formula only when they have stopped moving. Waters can't be written down unless they have frozen. The living can't be reached – at least not by following the road taken from the beginning by our culture, by the problems for which it has been looking for a solution. But except for this objective, of reaching the living, which culture hasn't set, it is about to reach all the others it has striven for overtly. There are signs that one happy day, our culture will find out answers to all thoughtful questions. If one wants answers to other questions, he should look for them somewhere else. In other words, all in all, or at least in one of the leading orientations, our culture seems to be of a certain type, which asks for further clarifications than before. The purpose of this book is mainly to do this on the dimension of the inner life. But our type of culture also calls for a scientific discussion, which we should have one day. Undoubtedly, no type of culture stands alone and no type of culture is self-made. Hence, the type of culture which we want to describe here has cohabited with another type, or elements of theirs have always lived with one another and inconvenienced one another. The questions of one passed on to the other and many minds, fed up with the fighting, fell into skepticism, simply because they didn't know what doors to knock on. The statement we put forth is: a great part of our culture is of the mathematical type, and this type is opposed to the culture of the historical type. Therefore, we think we are able to pin down this dualism: geometry-history, whose polemics, transposed on the dimension of culture, is the opposition of the two types of culture. Properly speaking, it is not necessarily about the content of geometry, but only some of its features. Its atmosphere. It seems that but for this atmosphere, our culture can't fulfill itself thoroughly. For geometry is not only syllogistic development based on principles. It is also: idea of order, a certain style, immanence and a whole series of problems, which we will have to account for right to the end. It seems that our culture believes in some of these. So, it is in no way about the content of geometry as such, about its theorems, its problems and its developments in a logical sequence of time. That is why we often say geometry instead of mathematics: because geometry is an elementary science, first of all, and here we speak only about elements, certain elements underlying the dialectics of the spirit; and because, secondly, the term of geometry has always meant other things than mathematical calculations (esprit de géometrie, opposing esprit de finesse, or for example Plato's statement that "God geometrizes"). There has always been a little poetry, some lyricism, something else than the simple science named geometry. Therefore, our culture is of a geometric type – beyond its material, made up of spiritual creations of different levels – in its justifications and its meanings. It is obvious that this cultural content can be mathematical and it is preferable that, up to a point, it should get a mathematical aspect. Didn't a philosophical school such as French positivism want to mathematize all sciences? However it is not the aspect which is decisive. There is something deeper and more necessary, which makes all the values of our culture belong to one family. Perhaps cultures have their own destiny and the destiny of our culture could be that of geometrizing. We would like to state that, in a way, our creations in the order of spirit lead only to geometry, although geometry is not always simple geometry. For it is about the spirit of the things we do. And maybe that is why we should say: the guiding spirit is geometrical. And it is very true that we have the right to discuss in culture more than: which is the sum of the angles in a triangle… but whatever we do, no matter how many rights we may have, we will always stand under the pure sign of geometry. Our destiny is to draw regular figures. The most important observable feature of a culture of a geometric type is its ideal: the universal science, Mathesis universalis. And what does our whole culture tend to, if not to a simple final expression, to a system that should account for everything that happens in the universe, possibly to a catch-all formula?The ideal of our culture is unification. A Plato, a Descartes, a Leibniz, a Husserl want it explicitly. But which particular discipline, which sustained, self-aware scientific effort doesn't stand under the domination of the same unifying urge? It seems that our whole culture suffers from a nostalgia of the self. Some of the monotheist spirit is still alive in culture. It is worth mentioning that monotheism, in its final form, was not touched as long as man looked outside himself, to the world; only when the eyes turned to the inner space, did he have the revelation the outer world wouldn't give him. Hence, one can say that the great feat of Christianity was to replace God-nature with God-spirit, and transcendence with immanence. It seems that our culture did the same. And it was only natural to do so, for religious order is generally joined with the cultural one. Possessed by its ideal of strict order, culture looked for it in the world for a long time, to find it eventually in man himself. Nature is not order, astronomical worlds are not the great mathematical harmonies: it is the spirit that is order, and it gives rhythm to the realities it takes into consideration. If a Mathesis universalis can be reached, its elements should lie in ourselves, in the first place, and they should be universally human, in the second place. Grouped and constituted, these series of elements are under two extensive disciplines: logic and mathematics. They are our ideal of order; they are the ones we would like to insert in the world, to make the latter clearer and more human. It is for them that we run, for these goods, which are in fact very handy, it is for them that we run in spaces over hundreds of light years. In the history of human thinking, a process took place, a process that can't be followed very well, first because it associates with all sorts of other human orientations and ideals, then because it is not on the surface, but in the depths of history. But this process stands out as the only responsible, self-aware process, in the history of culture: that is to say, thinkers became aware of the fact that science belongs to man, culture is his, the laws of the universe and its geometries are all his. While the religious experience unveiled all the reserves of spirituality in him, its scientific experience brought out into the light all the reserves of culture. Culture is human; it is our truth, it is the order that resembles us. It doesn't necessarily follow that truth is relative to the human conscience and therefore constitutes a degradation of any absolute truth. But truth per se has no meaning but outside our conscience. Science and culture are not beyond us. Whatever we do, a certain anthropologism dominates all our creations. Therefore, to speak of a relativization of a culture is to consider it something else than it actually is. Culture is but man himself. That is why Kant was able to state, one day, a thing that accounts for our whole culture. "Sciences, he wrote, were constituted only when they became aware that reason could find out in things only what it itself had put in them". "Reason found out in things only what it itself had put in them"…hence, the spirit looks for itself in things. The spirit has an activity of its own, which the world reveals to us. For the world does not exist – it does not exist for us, it does not exist for science and for culture – if it does not exist in the spirit as well. The world has no meaning for us without conscience. But, somebody asked once, if it is true that the world is constituted only by conscience, then what was there when there was no conscience at all? What was there when man didn't exist ? What was there? There was no science, that is all. Was it true that the world existed? But existence has no meaning outside science. Existence is a presupposition of our calculations, a given hypothesis in the problems which we discuss. Well, existence has another meaning: that of presence. But who could say that the world was present when there were no people, since, precisely, there were no people? Who could tell us about a presence when there was nobody present? Then the spirit looks for itself in things. It could seem surprising that it looks for itself elsewhere than in itself. But we needn't believe that things are so far from the spirit. The spirit looks for itself in things, just like it looks for itself in a geometrical figure, which it creates on its own, in order to explain its own syllogism, the demonstration it wants to give to its theorem. The spirit looks for itself in things only to this purpose: in order to explain itself. Nature is a pretext. "Nature, wrote a contemporary scientist, puts the spirit to a test. The latter answers, by constituting mathematics." How can man give values to this endless universe? All astronomical worlds, the distances compared to which we are so small – how can we believe that they exist only by virtue of the significations given by our spirit? To this the answer was that the legal universe, this articulated universe, although endless, is still a construct of our mind. Then it is only natural that man give it values. I, the parent of things… I wonder how people haven't seen how much of a geometric spirit there is in this constructivist science of our culture! Until recently culture was of a geometric type, because it strove for order: Mathesis. Now it turns out to be of a geometric type also because it is constructive, not only interpretative or descriptive. Our culture introduces a primacy of the "made" over the "given". For example, scientists asked themselves what we know about the existence of things. We take into consideration only their movement – showed the philosopher Hermann Cohen – and the movement does not belong to things, but it is a category of our mind. Instead of taking into consideration the things, we take into consideration the movements, which, in fact, were put into things by our spirit. For we don't feel the movement – the scientific one –, but we think about it: we think about it placing in it infinitely smaller movements, we think about it due to the infinitesimal method. The nature in science is not, therefore. This nature is made, it is constructed by the intellect, by the calculation. Nevertheless, it is generally said that the world is given. But what does given mean, in science? Given, answered the same Hermann Cohen, represents what I come up with in order to construct a theme. The given is a method of work. I give myself certain things, certain hypotheses and I can make the world with them, for the world, the world in science, is a made world. If my hypotheses turn out to be wrong, I destroy the world and I build another one. Isn't this the way in which the whole contemporary world operates? And isn't then the " made" one of the dominant features of our culture ? Finally, besides the idea of order and the constructive effort, our culture comprises one last geometric meaning: immanence. The fact that it doesn't transcend is characteristic to the geometric object. If you give yourself an angle and examine a problem related to it, you never stop to think about an external existence and about a possible transcendence of the limits you have imposed to yourself. The geometric fact doesn't make the intellect get out of itself. It does not force it to accept something that is strange to it. In a sense, the whole geometry is in us and it never gets out, no matter how many drawings we make. Similarly, the cultural fact tends to remain forever closed in a circle: in the conscience. There is a certain orientation towards the subject, which can be tracked down on the whole culture plan, over its whole expanse. This is a tendency which is very clear in philosophy. Thus, it has been known for a while that, instead of examining the outer thing, philosophy has started examining the intellect, and instead of nature, the science of nature. And it was rightly said that the object of philosophy is less the world than sciences. Philosophy seems, more than everything, an orientation towards the subject, towards what happens there, inside. But it is also inside that the other cultural phenomena are realized. Especially since Kant, subjectivity can even become the theater of operations of all spiritual activities. It is not only science that is inside the conscience, morality and art are inside the conscience as well; and the whole conscience holds on only due to the unity given by the "cultural conscience". The conscience cannot surpass itself. How would it, and where to? No kind of ontology seems to answer this vast subjectivity, just like no kind of ontology can answer the questions of geometry. The positivism of the 19th century thought it had abolished metaphysics simply by ignoring it. But nowadays we witness the other death of metaphysics, the true death of metaphysics. Like geometry, culture is starting to give up on what has been called reality. Why the need to assert reality? Things stay in me, together with all their imaginable evolutions. The world is just my pretext to highlight them. But no surpassing is possible in this way. The spirit doesn't reach anything, doesn't have any target. The systems of knowledge are just like monads, simple points of view. Closed, with no windows. With a system of knowledge you don't reach anything – except the point in which you already are. The spirit doesn't move from the spot. That is why, in fact, it is impossible to our conscience for something absolutely new to exist in the world. For example, what does this new thing, other than myself, mean: reality? It might mean something, but my work methods don't lead me to it. The world as a presence, as a living, given, fact, is a presupposition of historical cultures, those cultures in which the flowing, destiny and actuality take precedence. But the world of the cultures of geometric types is an ideal of order, created by the human conscience and preserved in the human conscience. Therefore, these are the constitutive features of a culture of a geometric type: order, constructivism, immanence. Is it an exaggeration to assert that our whole culture turns out to be of this type? Maybe it is. Throughout our culture, there are, indeed, so many philosophical systems which are not idealist and so many nostalgias for a "beyond"… But our intention was to distinguish radically between this type of culture and the other one, with which it generally co-habits. The two having mixed, the problems melted one into the other, and everything is hazy and unclear. Our types of culture must be separated and we must have them stand in the right way: face to face. The motto of the culture of the geometric type could be that of some fanatical spirits of the Middle Ages: multa habentes, nihil possidentes. Geometry knows many things, but does not posses anything. The cultures of a geometric type have laws, have a Mathesis, or tend towards one, have magnificent buildings and never stop constructing new ones. In exchange, they lack a reality, something concrete, something other than the pale concrete thing constructed by the spirit, for the grand glory of the spirit. To the geometries that the conscience gives itself nothing opposes, except for the history which gives itself. The culture of a geometric kind belongs to the order of spirit, whereas that of a historical type belongs to the order of nature. But then, what is the meaning of a culture of a historical type ? We say it is a culture in which destiny take precedence. It is therefore a blind culture. Full of presences, it is true. But to live directly among presences, to be one with them, to exist along with them – this is tantamount to giving up humanness, or surpassing it. To live as a person of a culture of a historical type may mean to live like the trees, like the birds, or – who knows? – like the angels. On the plane of the culture, it is a different life than human life. It is less or much too much. Does historianism want to take us back to the perspectives of biology ? But – we are answered – it is not simple biology. What is suggested to us is a transfigured biology.Transfigured biology? We believe that what hides behind this transfiguration is still respect for biology. And culture was born out of ignoring biology, out of an excess against it. At least half of our culture, everything that is geometry and geometrical in it, lies beyond biology. Culture seems to have been born out of two heart beats; during a break. Which doesn't necessarily mean that culture is no longer life. Culture is still life – more precisely, what life has more generous in it, that is, excess. It is inappropriate to say: culture and life. Culture grows out of the excess of life over itself, therefore it prolongs life. There are some examples in the history of culture which should be displayed everywhere, to let everybody know the true origin of meaning. Such is the parable of Pascal which should be forever in our mind. Pascal had a terrible toothache and the biographer said his sufferance was awful. What could he do? He could have cried out, like the rest of us, he could have made himself heard. But he preferred to do something else instead: geometry. Whenever the pain was exasperating, he drew regular figures and, in the mess of his sufferance, he thought of regular things. There was so much human dignity in his gesture… sometimes it is necessary to forget life. There are circumstances when you have to surpass yourself through culture. To estrange yourself through culture. To put some distances inside you. Isn't this what culture does? For example, how many people didn't "get lost" in knowledge ? They put aside what they had been wearing till that moment, all their joys and sorrows. Our personal quotient, or the obscure system of small things that give us our local madness, this moral specific tone, our coloring – all have nicely disappeared under the big, homogenous stain of knowledge. Thus, we managed to move from the local to the universal, the spiritual leap from the unique place to the common place. "The great common places of the spirit". The whole culture, with its theorems of geometry, with its natural laws, with its esthetic fever and religious ennoblement, what are these if not common places for all the individual structures, the meetings with itself of the spirit dissipated in the world? It seems that we all meet in a big market place. Everyone had something to forget and, the better they managed to forget what they had left behind, the closer they managed to get to the others. In this sense, we should always think that there is something crazy about the tendency of historicize ourselves, to divide ourselves. To divide ourselves into what? It is crazy to refuse to see that the things and ourselves is more or less the same. Maybe to divide ourselves into our small, everyday singularities. But hasn't anyone felt how much triviality there is in this? Why, are we ourselves because we have some particular resonances, this emotiveness, this disease that make us small and mean, only because of that ? And when is Pascal himself: when he has a toothache or when he takes up geometry ? We may be spirit. We are a universally emotive capacity: dissipated in the world as we are, we are still rhythms. If we are supposed to expect something from culture, that should be to help us get rid of the shame of being outside the rhythms. But why should one think that to live rhythmically is not to live to the full? Why can't life be lived effectively and with its all parts, among the great common places of the spirit? What a surprising idea –namely, if life isn't trivial anymore, life simply isn't anymore. The whole of life is on all the planes we wager it. It can't be partial, but can give up certain contents of hic et nunc. Nonetheless, there are all sorts of official misconceptions according to which, if it is not lived in all its immediate contents, life must be partial. Thus, we are told that people perform certain cultural activities not wholeheartedly, but only when in certain moods. It is said that people take up science only for the sake of the truth, that is all. The rest of their lives, when they just take up science, is dead. But this is utterly wrong! People believe less in abstractions than it is said. They take up science in order to forget a beloved one, because they have a headache, because they are pleased with some work method. If the truth is a work method, then to take up science for the sake of the truth is understandable, for we deal with science with our whole heart: we can love a method and we can believe in it. If the truth is order, systematic posing of problems and success, then it still makes sense to think about the truth. But, as a simple abstraction? It is necessary to promote abstractions, of course. But he who believes that an abstraction is devoid of feelings, that science is anemia, and that in its laboratories, culture is made dispassionately, hasn't learned anything from the lesson of culture. Because, imprudently, men of science and culture have become proud of this apparent calm and dryness – that is why they managed to disgust so many people when it comes to culture, and make them believe that to promote culture is to lose something of life. Or, in other words: because those who practiced the culture of a geometric type abused their formalism, the culture of a historical type was always needed. But the promotion of forms does not mean killing life. One must not believe the scientists who claim that they are calm and untroubled. One must not believe Pascal when the exercise of pure things calms down his pain. Its apparent quietness is just a different anxiety, that is all. It is a displacement, it is the translation from biology and its dramas, to formalism and formal dramas. The cry turns into a song, and the imbalance into a dance. Who said that life was lost through this? This statement is illogical. How can one lose life? It can be forgotten, but that is a different thing. I forget it and get lost in forms, in the forms, however, that don't devitalize me, but vitalize me on a different plane. I am not happy about the content of life. I simply don't like what happens, and that is why I look for a different content, even if it is a content of forms. For, what else can I find in myself if not forms? Who, of those who gave up this world, was able to come up with another world instead, a palpable world, a world of presences, not one of phantoms? In fact, the whole polemic between the culture of a geometric type and the one of a historical type is about one and the same thing. Fed up with presences, with actuality, with the immediacy of his life, man tried his luck in the inactuality and started the elaboration of forms. Instead of emotions he put creations. But this does not mean that he killed himself by doing this. It is true that generally the geometrician is paler than the man in the forest. But what was it about? About this life? About the elementary life of tissues? Nobody has thought of denying life out of "metaphysical prudishness". What has always seemed obvious is the fact that the exclusive attachment to life hasn't put forth any new meaning. The immediate content of life is uninteresting simply because it is not problematic. The tree in front of me, the pain inside me, the star-lit sky, all these are uncontestable. What I would like instead is to be able to dispute something, to get richer by a new meaning. Is death a presence? All right. Then let us keep quiet and await for it. But, if it is also a problem, then we can only term it as such: in terms of natural sciences, for example, or to research it in the philosophy of culture and folklore. The rest is indisputable. That is why, instead of these indisputable things, some people tried to resort to oscillatory things, phantoms you could choose from and indifferences you could opt for. Only the culture of a geometric type was able to create an indifferent topic of discussion. That is why its dialectics is never-ending. It heads for nowhere with necessity, since it replaced the inner necessities of the historical duration with the liberties without duration of the geometric eternity. That is why, instead of the immediate content of life, which the culture of a geometric type rejects as unproblematic from the very beginning, it created its own topic of discussion, which is problematic, uncertain, but disinterested. How did it create it? Ex nihilo? No. From the depth of unknown life; from the unbroken will of man to surpass himself. Therefore, we should protest against a category of people who, dedicating themselves to immediate biology, believe they are the only owners of life. Definitely not. They are not the only owners of life. In fact, the life they have is shallow and trivial. This is the kind of life we want to bring to an end. But then the other one, the life of man, remains. And this one goes on here, among the schemas. Here is one example: the moral man of Kant. Isn't this man alive? Doesn't he suffer, doesn't he laugh, doesn't he die? Nevertheless, he seems absurd to many people. What do you mean – we are told – by a man who doesn't live by instincts, who contains his impulses… a man who lives by imperatives. How ludicrous! How ludicrous to incorporate sayings and rules, instead of incorporating nerves and passions. How ludicrous to behave formally. To give up all the immediate mobiles of life and to believe in the "sovereign good". To be a law, to be a schema… Yes, to be a schema, why not? This is how our culture, our humanness wants us: schematized, formalized, geometrized. It is insane, people will say. But it follows that our whole culture is insane, then. Is there somebody who thinks about barbarism or return to nature? All right. But then be, don't speak; die, don't declaim. Why are they stealing our way of posing problems, our presentation methods, our ars probandi – to prove things that needn't be proved? But no matter what they say about Kant's moral man, even if no man in history was as programmatic as he wanted, this is still the representative man of our culture, and his life is our true destiny. Plus something else. Man needn't be formalized on a moral plane alone. Kant's revolution must be generalized. Kant, the legitimate representative of the culture of a geometric type, Immanuel Kant, the idealist and the formalist, must be taken further on the plane of life, up to excess. This may be, up to a point, the justification of the pages on inner life that follow. They are seeking the new excess, the new absurdity, our human absurdity. They describe a true inner life, a life that rhymes with the premises of our culture. But they are only the suggestion of geometric feelings, the outer rhetoric of the new geometries. Then, how else could one describe completely the whole universe of pure acts that our culture is dreaming of, how could one describe, only in a few pages, the miracle of the man meeting his fate? All these pages do is to suggest. They have one purpose: to make the others smile every now and then. If they don't make anyone smile, it means they have been written in vain. For we have this conviction that the true meaning of our culture – which is supposed to be the topic of the present essay – and the true fate of man must be ridiculous. Kant's moral man is ridiculous. Formalized man must be ridiculous as well. The deepest understanding of the historical life is maybe to feel its whole ridicule, the whole ridicule of culture, to feel that you are ridiculous yourself, you, who try to create yourself, who must try your own creation by yourself – when everything else is. Around us in this world, there are many things, both living and non-living. They do not see and they do not understand. But if one day they understood, they would laugh at us a little bit. And beyond this world there is a cheerful god, who truly understands things and laughs wholeheartedly.

by Constantin Noica (1909-1987)