Lecture held at the Museum of Modern Art   -  Udine – Italy,  by the artist

 Attilio Taverna, on May 19,  1994

 Geometry as language of man’s inner and outer space.

 Isabelle Reale ( director )  :  The presence of Attilio Tavernais particularly meaningful in the series of meetings we are holding on the relationship between art and science : there is in fact a close relationship between the theoretical research in the field of physics, mathematics and, above all, of the philosophy of art, of aesthetics and his work as a painter and artist.


We have already met G. Alviani; we havw talked with him more extensively on the relationship between artistic production and its scientific nature in the field of vision.

Today, with Attilio Taverna, whom I thank for coming from his town, Bassano del Grappa, where he works and has his studio, we will discuss more complex questions from a theoretical point of view; we would like him to explain what made him start such a complex research even thought I must admit there is a little time for such a discussion.

We would also like him to talk of his latest works –the ones on show here – which witness the last phase, in the 90’s, of his artistic research. I am the moderator here  - a most difficult role, if I know the personality of the artist, so rich in ideas, like some spatial figures which fascinate him.

 He has given you, as you see, an outline of what is, from his point of view, the sequential aspect of the relationship between art and science. He has discussed his idea in the volume we have here  - at disposal of those who might be interested in it – “ Ricognizione per un’ipotesi di forma “, which is the response as an artist to the most advanced research in the field of vision. We will talk about the past but we are more interested to know -–thanks to his testimony -  what the effects are of the latest discoveries in theoretical physics on this hypotesis of form, of a new form of art that he is studying.

 As a first, warming-up question, I want to ask : “ as your artistic search is based on a deep knowledge of aesthetic doctrine  - what is there at the basis of your need to probe these problems “ ?

 Attilio Taverna :  first of all I would like to thank you for welcoming me, for the flattering presentation and for this occasion.  As to your question : aesthetic experience is said to be an integral experience by definition. What does that mean ?

It means it involves man, mankind I mean, in their wholeness as producers of theoresis, of praxis and of phatos, that is to say of thoughts, of techne, of structured emotions.

But it is not just that.  Aesthetic experience is a total one also because it cuts at the roots all relationships based on power ;  it is grounded on creativity, on dedication and as such it is ethical. The fact that aesthetic experience is itself ethical might make one say – and indeed one can  - that, at a certain level of philosphy of art, Aesthetics is the mother of Ethics.

This, however, upsets man’s traditional conceptions of art. Since Aesthetics is the mother of Ethics that means that aesthetic experience is more integral than other integral experiences like mistycs or politics.

 Mystics ( from mystos = dumb ) is an inner experience which  - as is clear from the term – cannot be communicated, is solipsistic by nature, accomplished inside the subject. Politics is essentially the science of power, science of potency which acts on what is feasible but cannot bring forth something which did not exist before. Only aesthetic experience can do that. Schiller  - who was a great german philosopher of aesthetics, in his  - “ Letters on Man’s Aesthetic Education “ – even proposed to build a State on aesthetic experience.

Aesthetic experience is extraordinarily important for man because it is through it that man can live his life under perpective of creativity. There is only an other experience that reaches up to this level of creativity…child bearing…

 Isabelle Reale :  let me bring you back to our discussion…

We have heard some very general considerations on the all-pervading nature of aesthetics experience : I know there is one thinker of ancient times that you have been particularly interested in, Plotinus, in fact. Shall we start form this landmark to look at the present times ?

 Attilio Taverna :  Yes, we’ve got to have a very informal conversation : any of you can stop me whenever they wish.

 The topic of our conversation is “ Geometry as the language of man’s inner and outer space “.  First of all let me say which Geometry we are talking – or, rather  - not talking about.

We are not talking of Geometry as the theory of physical space as this is the domain of architecture, of town planning, of the disposition of volumes.

We are not talking of analytic geometry as this was invented by Descartes : it is geometry as the domain of mathematics –pratically speaking, it amounts today to reflections on the relationships of numbers, sequential reflections of points along a line. So, we are not talking of analytic geometry, either.

We are not talking of topology, either, which is the science of surfaces mathematically treated, which has to do with invariants to which geometrical figures are submitted through twistings and tractions and whose aim is to detect the fundamental structures undergoing no modifications. This very important science  - topology  - is very close to the geometry we are referring to.

 Which geometry are we talking about then ?

We mean geometry as the theory of visual space. We try to talk about the meaning of geometry, that is of its most difficult, hidden aspect. It is extremely difficult and complex to try and get the meaning of geometry, it is an almost unattainable goal.

But what is geometry ?  Let us put it this way. In the accepted conception of the term – when geometry is mentioned – forgive me the reference but let me say it, it means at best, Euclides, Pythagoras or, etymologically, the science which measures the Earth.

 But here the first problem arises :  geometry means the measuring of the Earth. But to ancient people ( Greek)  Earth was not what it means to us. Earth was to them the exemplary whole, inside wich all beings existed and were to find their appropriate collocation.

So, geometry is the language of totality, a language which was needed to assign all beings their appropriate place. That is why Plato wrote on the door of his Academy : “ Entrance forbidden to those who do not know Geometry “.

 What did that mean ? If we speak of beings we refer to ontology; it meant that only those who could speak the language of the investigation of beings were allowed to enter. That is the meaning of Geometry.

 It is almost impossible now to retrace the origin of this fascinating history in spite of several research studies on the subject : let us mention Husserl’s “ Origin of Geometry” at the beginning of the century, and Derrida’s “ Origins of geometry ”of the 60’s.

We know very little of the origin of geometry. Of course we know that it started 4,000 years ago….may be Indian arrived in Babylonia during the first period of Jewish captivity, with a system “ to read “ the constellations quite unlike the babylonians’s : the latter was arithmetical-chronological, the indian’s “ visual”.

This knowledge spread into Egypt and returned to the mediterranean world with Pythgoras  - as you know – he went to Crotone, southern Italy, to the temple of Hera and at night, by torchlights, held conversations “ on the science of figures “.

He founded a secret sect : those who revealed the secrets of this science would be put to death. Why ?

The “ language of geometry” might be said to have these characteritics : it is universal – it goes beyond all other languages; it is cumulative – it increases by successive additions without corresponding losses; it is innate  - this is a deepth we cannot fathom as there would be miles to cover, but this quality of geometry is proven by Plato in the dialogue “Meno” where he affirms that it is reminiscence – like any form of knowledge, as a matter of fact.

The illiterate slave of that “ dialogue” is asked a series of questions by Socrates and reveals a knowledge that  - being illiterate  -  he could not have. Socrates concludes : “ if you cannot count, then show…”, that is :  show the truth through the vision”.

 You might say : ok. This is all about Plato’s dialogues, it has nothing to do with….

All right. But in the 70’s there was a sensational confirmation of the fact that the language geometry is innate.

Chomsky, the well know Harvard linguist, whose texts are famous all over the world, with his generative grammar has found an answer to a question nobody had been able to answer :  how is it possible that children at about one and a half year of age speak the language of the place where they are born, be it Lapland, China, South America or Europe or Usa ? How is it possible ?

Chomsky, through his generative grammar shows how inside children’s brains there is, may-be, a sort of geometrical network which is filled by the grammatical and syntactical structure of the local language. And once filled it cannot be filled again in the same way. So, that is innate…

 Then geometry has another extraordinary characteristic : it is reversible.

What does that mean ? if it is innate and reversible that means we are all on the same level, as to geometry, of course. It means that the contributions given to this knowledge are - in principle -  accessible to everybody. We have the same dignity as far as these contributions are concerned.

The structure of power in ancient times was oligarchic : the knowledge of what the God had said went through the Pythia or the oracle who, in their turn, were interpreted through hermeneuticus to be later spread. Well, the verticality of the structure of power in ancient times was like that. This type of knowledge of the science of shapes, geometry, cut at the root such a structure of power. So we can understand why Pythagoras formed a secret community or sect.

 When this language that is Geometry – through the doctrine of Plato’s Ideas  - finds a connection between the real and the idea fully expressed in the dialogue “Timeus”, well from this doctrine of Ideas derives more geometrico the greatest idea of Beauty which has pervaded all western thought for 2,000 years down to Kant, to his “ Kritik der Urteiskraft “, that is to say antother doctrine of beauty, this time founded by the subject, starting from the subject.

Where was this doctrine of Beauty by Plato  - this great Theory, as Tatarkiewics calls it – founded ?

 It was founded on symmetry, harmony, proportionality, on the golden section. This doctrine of Beauty derived from Plato is codified  - as far as the human figure is concerned – by Policleto, and, as regard architecture, by Vitruvious and will permeate all history of art in the West.

There is a problem here : you certanly know that Plato had a relationship with painting which was – to say the latest – conflicting. He thought of painting as mimesis, that is a copy. What was his thought ? We might put it like this : the tangible world is this one and the intangible world is up there; the world of perfection is placed in the hyperuranium and the phenomenological world is a corrupted one, degenerate in comparison with the former ;  if intelligible world exists in the still perfection of the hyperuranium  - represented by platonic geometric shapes as ideal essences  - it is evident that as painting is a copy of the tangible and phenomenological world which was in turn a copy of the intelligible world and, as such, a corruption, painting was then a corruption of the corruption.

 This was Plato’anathema on painting and art, till the great “ Aesthetics” by Hegel in 1826 : according to Hegel, art is the manifestation of the Spirit, together with religion and philosophy  :  and the Spirit is the Absolute.

 It was then that art began to be self-conscious and to have consciousness of its own nature as spirit – that is the manifestation of the absolute. When this process rooted itself in the very consciousness of art the latter lost an external refrence and was no longer mimesis. The first hints of an acquired sef-consciousness can be found in Monet, in his waterlilies, and in Cezanne.

In the case of Monet, the appearance melts and only traces of a luminous formation remain. In Cezanne’s painting the visual relationship between the phenomenological world and the language geometry is reduced to the basic shapes of Geometry. Since then we have had the vertigo of the history of modern art.

 Yet, inside this great Theory of Beauty, inside this great platonic theory of symmetry, proportionality and golden section, there is an extremely refined thinker of the 3rd century, whose thinking is like a cutting blow : Plotinus.

He says : there is no theory of Beauty without light being involved !

 And light is not an aggregate, while the theory of beauty derived from Plato was made exclusively of aggregates : symmetry, proportionality, the relation of parts.

Plotinus does not say that this theory is wrong, he only affirms it is incomplete because it does not take into consideration the most important part which is light, without which no theory of Beauty can exists.

The direction taken by Plotinus was to be followed by Pseudo-Dionysius, elaborated by Thomas Aquinas in his “Summa”, implemented by other thinkers; there is a metaphysics of light, Grossatesta, Telesio, and others. This metaphysics of light will go through all the great medieval cosmogonies : Dante’s  Commedia, with its point of light, the Mistic Rose, and the cosmogony of Islam. We do not know where that line of thought finishes : at a certain point it belongs exclusively to theological speculation as it could no longer be used in the history of art or in art as technique. It could not be used in art because sculpture was not involved. This problem of light concerned just painting but on painting weighed the platonic anathema which considered it as mimesis.

And it took painting twenty centuries to get rid of it. Where then has this line of thought about the nature of light gone ?

 It was taken up again by the neoplatonic thinkers of the Renaissance, Marsilio Ficino, Pico della Mirandola, and created  - or was a contribution to the creation of – the Perspective Cone, the great Renaissance attainment.

We have no time to follow this story, but certainly this metaphysical speculation on light produced a “ celestial world” which existed through the Renaissance : pulchrum, which means splendour. And there is also a previous radical position in the Aquinas who  said in fact  proportionality and splendour “.

Where then has this line of thought gone ?

In the mysticism of pre-Lutheran Angela da Foligno, Meister Echkart, Hildegarde from Bingen, San Juan de la Cruz ecc.

Here this speculation about light finished : in the mystic height of the luminosity of the Absolute.

 As we have already seen it has nothing to do with the history of art, nor can it have, for the reason we said before. But what happened ?

 It happened that Physics, that is to say science of reality, the exact science par excellence, the ancient physics founded on faith in the real elements, did not describe the real world  - through matter  - any more : since 1905, on the basis of a document by Albert Einstein on the review of the Zurich Polytechnic, it has seen a vertiginous series of revolutions and has got rid of the matter and found hat as basis of the real there is a problem of Form.

But Form is an ontological notion belonging to the realm of Aesthetics as philosophy of art. Here we have the paradigmatic superimpositions of descriptions of reality which are characteristic of the whole century.

The  realms which can legitimately “ tell “ the truth about the real are : philosophy, art, science.

Theology instead has a revealed immutable truth and goes its way. But the other three are in deep dialectics among them. In this last half a century physics, notwithstanding its specificity and autonomy, has abandoned its own foundation  - matter :  finding that the answer to its final question on the nature of the real was no matter but Form, it went to interfere with the foundation of another realm, that of aesthetics as the philosophy of art, in which Form lives.

And here there is this suoerimposition, in the description of the real, which involves this reflection upon science and art and their superimposition, which is the origin of my modest reflection : “ Recognition for a hypothesis of Form “.

 Isabelle Reale :   Let me interrupt you as you have got to a crucial point; you have made an excursus but now we are at the very point you mentioned, of Physics that leaves matter to “ move on” to the field of Form which is investigated by Aesthetics.

 Attilio Taverna :  But this reitroduces very well the problem of light.

 Isabelle Reale :  Exactly ! And it is fundamental !

 Attilio Taverna :  It reintroduces the problem of light and here the line of speculation which comes from Plotinus within the Great Theory of proportionality ties up with the discoveries made in the very field of Physics and so in the field of Form. Why ? In the 60’s a theoretical physicist, Richard Feynman, won the Nobel prize for his discovery of a law in quantum electrodynamics, in which he described a “ way of travelling “ of light.

This “ quantum vectoriality” of light shows the interaction light – matter :  it is this vectoriality of light that creates the phenomenological world. We must ask ourselves, therefore, in which “ place” this mechanism of light, of Beauty that creates everything, comes  to existence. Here lies the fascination of this point of view : if this theory produced by physics on the vectoriality of light shows that light travels in a certain way and we know that light is the foundation of phenomenology then the only horizon that opens up for investigation on that part of artistic creativity, in my opinion, is this.

Not for nothing does the Bible say ( Genesis )  :  in primis fiat lux “.

 Isabelle Reale :   And now you have come to the present day. But, in the outline we had planned, we wanted to tie up these two moments, 1905 – as you can see in the handout you have – is a turning point not only for the scientific discoveries but also because it sees the beginning of the historical “ art – avanguards”.

 Attilio Taverna :   Sure, there is almost a parallel.

 Isabelle Reale :  I just wanted underline this vertiginous sequence which from Cubism and Futurism to Neoplasticism completely modifies the common idea of the Beauty and the various aesthetic theories. Let us mention them up to contemporary art.

 Attilio Taverna :  Yes, even though I must say this research is of such a high level that you cannot find example in any museum, be it small or grand ; we cannot find it anywhere. Let me give an example : the texte I quoted “ Philosophy of Geometry “, published two or three years ago, mentions a research made at Princeton University on the relationship between the meaning of the notion of space in Einstein’ Relativity and in Cubism. So, it is Princeton University that published this research a few years ago : you realize there are no many people in the world who make this parallels between the revolution in Physics and the historical “art avanguards”. The theme is extremely sophisticated and arose when, in the last twenty years, Physics abandoned its description of the real founded on matter to find, at its core problems of Form.

 We know that at about 1829 non-euclidean geometries developed. That was an epochal revolution – it would take months to talk about that as they are geometries on the curved space and the nature of space has changed since then, as have so many scientific descriptions. It was a real revolution : Gauss, Riemann, Bolyai, Lobatchewsky.

After non-euclidean geometries, a great mathematician, Minkoswky, of the Gottinga school  - one of the most famous, perhaps the most important, department of Mathematics in Europe before the Second World War – started his course during the year 1900 saying :  “ …there is no longer any theoretical reason to maintain the notion thet the conception of space and that of time should be considered as divided..”

 Five years later Einstein’ intuition on Relativity made one thing of space and time. That has completely changed our notion on the nature of space.

 Next time when I have the possibility to meet Emmer, I want to ask him just this, what science has proven so far of Riemann’ hypotheses on nature of space, for instance, because on the nature of space we know almost nothing, apart from what arisen from these great transformations, these great revolutions such a Relativity, and the Quantum Theory and the present-day Geometry of Chaos.

But the most extraordinary thing is that the very moment in which the value of “ simultaneusness” into the space was reversed by Einstein, cubist artists “ broke the object “ and showed its circularity : the object is no longer seen frontally, but simultaneously from all sides. It is an extraordinary thing that these artists were doing, conceptually speaking, the very same thing as Einstein was doing concerning Relativity, at the same time Einstein was making his discoveries.

 I do not wish to maintain that they knew of each other, that was no possible, but I do maintain there is a “ spirit of time “, there are intuitions that go beyond the limits of any discipline an dgo beyond the limits of any ideological, conceptual, or even linguistic systems. This situation did not happen just once : the relationship between Relativity and Cubism is just one istance of a constant factor in the history of modern art.

Just when Mondrian engaged in such a struggle as to break off with Van Doesburg  - who was also his theoretical referent  -  because he did not want to extend the squaring to the diagonal – and at the same time – the theoretical physicists of “ Copenaghen school’ interpretation “, discovered “ quantum mechanics” where the formal problem of the “ Tetracktis, the Squareness “, is central and whose real meaning we do not fully understand.

Well, if this “ quantum physics “ has been in existence for 60-70 years and we do not yet know the deep meaning of what it tell us, then it means there are enormous underlying  problems regarding the nature of space.

I find it extraordinary that a man, an artist, Mondrian, sticks obstinately to his idea of “ squareness”, of “ tetracktis”, to point of breaking up with his best friend. Besides, it is clear that the form of “ squareness, tetracktis “ is the very formal basis of the mistery in this scientific revolution called “ quantum mechanics”.

This holds for the Neoplaticism, but what about Malevitch ?

Malevitch wrote a theoretical book “ The world without Objects “. In 1928 Lunacharsky, Commissioner of the Arts, grated him a three months journey to Berlin, where he delivered 30 paintings, 200 drawings and the said book. When he went back, he disappeared during Stalin’s purges.

His book are very upsetting document for the Western conscience even in their metaphysical implications.  When he writes : “ .. I have taken paintings into the realm of Nothingness..” that means he has reached the furthest point in the annihilation of the world of senses, you can’t go beyond that, “ a black square on a white background, then a white square on a white “. That means that our final question – even though we know the final question are not accessible to man  - just because of their progressive distancing. i.e. as they are made nearer, recede…

To be sure everybody asks himself the final questions, even without finding answers. Also Malevitch had asked himself the final question and his answer was “ a square form : the tetracktis ! “ Just the same form identified by quantum mechanics theory in the middle of its spatial and formal mysteries !

 If I think that one of the central problems of form in the quantum theory of physics is the “ tetracktis”, and that if there is a scientific theory that is almost irrefutable, this is the quantum theory, or that quantum theory haa a degree of reliability, of scientific verifiability of three parts in ten billions, so, that means that if a scientific theory is true, it is this  - others may be true, but this is certanly true. And if I wonder that within this problem, many dimensions open up in the form of “ tetracktis” and enormous problems of the nature of space, of the form of space which after 70 years have not yet been solved, and then,  I see an artist like Malevitch who spent all his life asking himself this question and got  to identify the real with a “ white square on a white background “,  then I say that here there are subterranean relations between form seen by art and form identified by science that are conclusive to explain the reality.

 Does that mean that the formal language which is Geometry touches on the real and on what is perceived by the senses at once ? Us and the world at the same time ? I must  say it does !

 Let me make an example :  about the “ Ulm group “ you heard Alviani to talk of Max Bill : at the time the science of Mathematics, believed final answers had been found about reality; what was art doing at the same moment ?

At that moment it was taking mathematical structures and making them perceivable to the senses and in making them real it conceived them as the real made true in a way apprehensible to the senses. And in fact what Max Bill is most proud of, is the fact that he has discovered the Mobius’ ribbon, which is a recursive ribbon, but had already been discovered by the Egyptians.

He himself knows that now, he has also said so. And in fact, since the formulation of Godel’s theorems we cannot presume any one-to-one correspondence between mathematics and reality and, as consequence, between reality and any formal representation of the latter :  Thruth is always greater than any of its demonstrations !

 I have been to Locarno at  Casa Rusca to the opening Max Bill’ latest great exibhition. The opening speech was by Caramel, a contemporary art-critic of the form of rationality in painting. I went up to him and said : “.. well, what about Godel’s theorems..”

Carmel replied : “..I cannot say these things, otherwise Max Bill will slap me in the face…”

 What did that mean ?  It meant that Max Bill was going through a period in which the rationality of mathematics was so sure of itself it believed it was the final answer to reality and that  Constructivism- Art “ was dreaming the same dream.

Max Bill is one of the great fathers of the rational way in the modern painting. I have come to grips with him, with Dorazio, Vasarely, I consider these great masters as relatives, as uncles. I have held for many years an ideal theoretical debate with them, so I am not speaking disrespectfully of them, I am speaking of the relationships between the description of reality by mathematics and what art showed at same time.

 Well, it was not just art to be beaten as far as mathematical constructivism is concerned ( which was the path of Loshe, of Lowesberger, of Max Bill ), but also the very idea of mathematics as axiomatic, indisputably true knowledge.

When there come Godel’s equations on  arithmetic undecidable propositions “, it was clear that this aesthetical “ path” had  coicided with thet idea mathematics had of itself. But with his theorems Godel proved there is a real of which we cannot say whether it is true or false : that cannot be decided.

So, truth, the real, is greater than its own demonstration.

Conclusion : the Constructivism-Art must be abandoned after Godel’ math…evidence

 Since then certitudes of arithmetic constructivism have failed, also the road of constructivism in art, like Bill, Loshe, Lowesberger path, has revealed itself as inadequate as description of reality. And so, it will be necessary to continue to do art in another visual way on the road of rationality. But the relationships between art and science I was referring to before have always existed. I could make another example, a recent one : soon after the Second War World, when kinetics started, and Shannon’s information theory and all the technological dimensions we call era od computers, of chips, in a word, the era of telematics started, in Italy there was the called “ N group”, from Padua, the group of “ programmed art “ with Biasi, Massironi and others. They did this kind of painting and they were on the same wavelenght as Alviani, Vasarely, and Soto for kinetics; it was an international syntony with reality. Now, the “ N group” from Padua got international recognition only 20 years later, due to the provincial situation they lived in the lack of political support : it happened in 1986 at Biennale-Spazio in Venice, at which, apart from this legitimate group there were also heaps of  imitators in the train of the winners….but 20 years later the way science to describe reality had completely changed. And also painting and aesthetic analysis started to investigate  - in the field of Geometry – other eidetic dimensions of space and were finding other things….

 Isabelle Reale :  We have now reached the 90’s and I would like you to speak of the close relationship between science and your paintings in front the paintings themselves.

 Attilio Taverna :  Well, as I said before it has taken me time to get where I am now. I have gone through the great lessons of rationalism ways…I was abroad a long time. I was 24 or 25 years old, I was in France, Paris, to study modern painting, I saw the great museums; I have travelled to all the European capital cisties to see contemporary painting; since 1979 I have made frequent visits to America, overall New York to see contemporary art and museums. In short I possess a visual heritage of a kinf I am happy about and also satisfied with because I have seen a lot; yet on this path…to be sure, how could I ignore the great experiences of “ italian rationalism” of the 30’s, with Rho, Radice, Reggiani, Soldati, Veronesi, the so-colled

Como group “, and then Magnelli, who lived abroad, or the experience of “ Forma Uno”, in the 50’s with Dorazio, Perilli, Accardi, Consagra, and the one with the “ Group of eight “, that is Afro, Vedova, Turcato, Santomaso, Birolli and then Pizzinato…and then the experience of kinetic painters of the “ Padua group” ?

 Yet for the last 5 or 6 years I have been doing a kind of painting which has never appeared in the history of abstract rationalism, either italian or foreign, that is this aesthetic experience whose results I defend unequivacally. When I go and speak with the directors of some museum of modern art, those who can influence cultural tastes and resources, I am usually pretty severe : where does this severity come from ?

It is founded on this : either one knows who referents are and understands that what is here in this aesthetic-experience has never appeared before and so also my collocation becomes right, or one doesn’t know  - I am not blaming anyone, but I can prove then that somebody has got some gaps  -  and so they cannot evaluate this experience of mine.

I am not complaining, I personally have not compliant, I am only defending this aesthetic experience and I am trying to defend it for what it is, not for what it isn’t.

I accept all demonstrations in this respect, provided they are legitimately argued and not arbitrary.

It is not question of money, you understand, aesthetic experience is pursue not for money, but for something else : it is life lived from a different point of view, in a perspective of dedication of creativity, of giving life to things which did not exists before. That, in my opinion, is very important. But I mean to say I have worked hard all my life, I have made sacrifices, I have made all I could and sometimes even what I couldn’t…

 Isabelle Reale :  But I hope you will talk about your painting now..

 Attilio Taverna :  Have we run out of time ?

 Isabelle Reale :  No, no…

 Attilio Taverna :  They are oil paintings.

 Isabelle Reale :  Here we can see a type of formal research and in these two there is the idea of interaction…

 Attilio Taverna :  Yes, exactly.

 Isabelle Reale :  …of analysis

 Attilio Taverna :  I have forgotten to say something very important, or at least I think it is : I have been doing this kind of painting for 25 years. I have never met prof. Metelli who use to teach Psychology of perception at Padua University; he was the one who discovered the mathematical model-system of  so-called “ perceptive transparences “. He is dead now, one of this disciples is now writing a little essay about my painting.

In 1970 Metelli was pursuing his theoretical and experimental analyses on “ perceptive transparences” and at same time I was doing this kind of painting with “ perceptive transparences “ but I never met him and also i didn’t know what it was. Simply, I was doing it in painting.

In 1974 “ Scientific American “ published a cover image on Metelli’s research of “ perceptive transparences” and there is a catalogue from my exibhition of the same year on “ perceptive transparences”. I have always worked in painting around this concept without knowing its important in science, in Psychology overall. And as we all know very well, it is not a physical transparence, there is nothing physical in it, there is just the surface of the painting, it is a perception of transparence that happens inside our mind and is only given by painting.

Now this concept of “ perceptive transparence “ is extremely important for visual research on the nature of space.   Why ?

Because first of all it sweeps away all dogmatically established spatial languages, i.e. in the case of geometry, you understand it is not a measuring system because when you have “ perceptive transparence “ it is no longer a question of the various planes, you no longer know which is the first, which the second, the third, or the fourth planes. That amounts to saying we no longer know how many spatial dimensions there are, as I said before talking about “ quantum theory “.

I do not mean to say I have done “ perceptive transparences “ in painting in an absolute conscious way :  I was working in the dimension of painting and, as I was doing these things, I realized their theoretical implications.

In fact, if I had consciously had the idea of doing that kind of painting I would have gone to  Metelli, who was a specialist in the field, but I never did so, as I was at that time not interested in this theoretical aspect, which even created problems for me as my painting developed.

I affirm that because in my opinion painting has  a corporeity of its own, it is not in the first place a theory; it may become so afterwards, when it has been created.

 Painting is not theory writing, even though I have written that book about that : such theoretical research has changed me, has made me very happy, that’s true, but painting is first and foremost corporeity, sensitivity, it arises from the capability of connecting oneself to sensible, an aesthetical approach to the Wonder… it certainly poses some problems which are theoretical and so things tie up together. That is why aesthetic experience is so rich : it makes one grow simultaneously under the three aspects we have already mentioned : theoretics, praxis and pathos…. that is to say, it enwraps one completely.

 With “ perceptive transparence” I was  already doing, 25 years ago, things which were extremely competitive with Vasarely’s work. Since then, I have gone my own way and I have paid the cultural debts I had towards these great masters. Then, as in every fields, a new visual horizon opened up where no one had stepped. Within visual horizon I believed I could find a great possibility:  a new eidos on the nature of space !  Here I am.

This is the present state of my painting. I cannot to night – and I dont’ want to – probe deeper into these aspects because there are things which are extremely difficult even to mention, as they revolutionize deeply set conceptions, I can anly say that the visual horizon this painting has  opened up is a visual horizon full of wonderings and meanings which fill you with awe. The same happens in the theories and in the descriptions of present-day Physics.   It is an aesthetical plateau which has certainly never been reached before. It concerns a new eidos of spatiality which was continually becoming other than it was…

 Isabelle Reale :  In a continuous movement….

  Attilio Taverna :  which is continually becoming other than it was…

 Isabelle Reale :  .. where light…

 Attilio Taverna :  where light plays a role of close complicity.

 Isabelle Reale : constructs and it denies…

 Attilio Taverna :  exactly. It constructs, deconstructs, reconstructs, fins further syntheses … and then I make a lot of plans, of drawings…then I garther up a formal unit which seems to me the most interesting and I draw thi thing on canvas. It is there that all corporeity intervens, which is apprehensible through senses; even as a body I never had any problem with colours. Everybody used to tell me I was “ a seigneur of colour “.

So, I have no problem in deciding on consonances, on the emotional power : colours, to me, call upon one another ina continuous complicity. So, starting from this “ situation” I felt the necessity of a counterbalancing, very mysterious, very strong space. There is no meaning whatsoever, only this aesthetic necessity. Then from this, the space started requiring other relations and so on, until this image was built : an image of an extremely mysterious spatiality which denies itself; look at this column of light inside there, in this volume here. should also have an idea of what curved space means…because…but this light here…there is a continuous breaking up of symmetry. The algorithm of the declension of light is continually breaking up and building up again, affirming and denying itself at same time : there is here a notion of space which was unimaginable before it was realised. Here space is acted upon by light in an absolutely surprised way…it is a surprising space…which keep surprising us, that is, light in its declension, creates notions of space which keep surprising us… and there..there is the mystery…notice the behaviour of this space and of this structure and this….

 Isabelle Reale : space denied is to you…

 Attilio Taverna : is space surprised in its becoming…

 Isabelle Reale : your aim is a continually stimulated research which tries to find formal resisting places in this chromatic moment…

 Attilio Taverna : .. not exactly… the aim is to create eidos, new eidos on nature of space which did not exist before; of a space we did not know before, through this vectorial movement of light which is perfectly in syntony with the research of contemporary physics. Today, in fact, it is believed that the geometry of chaos are one of final limit. It is this vectoriality of light which allows entrance into a space which did not exist before : this  is the surprise, the fascination, the horizon of discovery. Where there was formerly a white wall there is now an unforeseen notion of space and we can grasp it aesthetically. Here there are all these vibrations, this breaking up of algorithm.

I have brought an earlier painting – just a bit earlier: I want to show you that even though we can read it polysemically, as it can be read vertically, horizontally, it has underlying structures, broken up rhytms, a certain slant of light, yet it is still inside e sequentiality of light which is still unaware of what breaking up symmetry means.

If we compare the two paintings we can see that in the former light manifests itself in a way it semms “ to know” it does this, whereas in the letter does not : there such a modality of light creates avery misterious space, whereas here light creates very beatiful things but not this visual horizon of mistery due this particular vectoriality of light.

 Isabelle Reale : ..let us go back to our theme, the relationship between internal and outer space : we might say, in conclusion, that any so-called geometrical – or, rather, chromatic-geometrical – situation of cheap painting affect also your inner life.

 Attilio Taverna : ..thank you for mentioning it, as you give me the opportunity to say something I would otherwise have forgotten. When we read in the Plato’ dialogue “ Protagoras “ the well known dictum “ man is the measure of all things” we must understand exactly what that means : in a classical interpretation it meant : if thought arises in man and, by thinking itself, discovers its infinity ( and it was within this thought that Geometry as formal language that measures totality was born ), it is clear that man himself was the measure of totality.

 But let us see the conclusion we have reached at the end of this century, which is also the end of a millennium : if we consider what has happened in the human sciences and in the hard sciences we find for example that psychoanalysis has opened up an unimaginable, incommensurable spaces within man.

On the other hand, physics has opened up unimaginable spaces outside man. Than the latest great reflections on nature of Geometry  - the two “ Origin of Geometry” by Husserl and Derrida respectively  - tell us Geometry is the language of “ un-chained idealities “.   What  does that mean ?

It means there is an unlimited ground of freedom : a visual ground where arises the undeterminated original dimension reminiscent of Anaximandre ‘ apeiron.

 So that well dictum in Plato’ Protagoras, “ man is the measure of all things” assumes another meaning nowadays : man becomes the point of crystallization, the meeting point of two infinites, crushed as he is in between one within and another without; as such, could he measure these two infinites that, by definition, are immeasurable ?

 And what can his formal language Geometry measure, now that man has discovered all that ?  He can no longer be the measure of all things : his being the measure of all things might mean only he is the measure of his life-bearing will, of his potence of life. And as a consequence, the signs of his formal language Geometry cannot but be the signs of his life-bearing will and for this very reason will be the signs of Art.






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