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SCInetwork » Talking to Michelangelo’s David or how a mathematician killed Goliat - Olga Mucharraz
   

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Talking to Michelangelo’s David or how a mathematician killed Goliat
Engineering and humanities
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Olga Mucharraz


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The Michelangelo’s David [ Note 1 ] has been classified like an "apolinear" or "herculear" representation [ Note 2 ] by several scholars. This double speech can be tragic if we don’t talk about it from the beginning. This double speech leads us to the current problem about male and female archetypes and to those of disciplines and professions.

I have already talked about this Greek pithagorique reality, rebuilt through centuries, that has given many archetypes in occidental civilization [ Note 3 ]. We can now emphasize what has characterized this work as : "apolinear", that is, its visual characteristics as image of generosity, strength and love; and "herculear", that is physic strength, sacrifice and responsibility. We should consider as well the "dionisiac" component to integrate this image in the personal sphere of will. It is in this way that Michelangelo’s David can be interpreted as a male archetype almost reached.

The limit between an image and its symbol is very subtle. This limit can lead us to see the David in a new way, a way in which we are able to establish a new visual representation, giving to its essence exactly what it represents, after having seen it as a male archetype. Neither Hercule, nor Apollo, just David.

Once again with the experience developed in the class, we present the four pictures that were the starting point of this reflection and that make us asking several questions:

What do we see, what we do not see, what we do feel with Michelangelo’s David?

At first sight we notice the anatomical characteristics of a physic activity. The artist uses his skills and emphasizes the expression that should allow us a correct interpretation. The sling over the back, muscles working in a particular way, hands ready to execute, hair in a free way and many other details talk to us if we stop to listen to them.

It is obvious the interest of the Renaissance in human body, we can see it looking the study of muscles in this work. We can even find similarities with our time where human body is sometimes, almost a merchandise. Nevertheless, if we go further, we can find another dimension. Through its gestures the sculpture is developed in harmony around its symmetry axis. Muscular tension and relaxation talk about the "terribilita" that characterizes Michelangelo’s art. In this, we see the original human duality: day and night, war and peace, yes and no, yin and yang, tension and relaxation, and that, can be solved in the subtle difference that exists in the choice between add or multiplication sign.

1 + 1 = 2

1 x 1 = 1

An original and simple way to characterize the unity of the work.

Once the reflection made before was finished the next question was very complex but solved in a very simple way. If the work is presented as a thematic unity, in which physical point the contradiction is solved?, how do our eyes see this image and perceive the resolution?

I have to confess that as originally I am formed in the social sciences it was very difficult to me to reach the abstraction levels necessary to this reflection. If it was possible it was because I was able to use this capacity of memory called eidetics that is the ability to join different objects through mental images [ Note 4 ] and that I could be introduced to mathematics and geometry, discovering the fascination they produce in some people. We should thank cognitive science for being able to integrate new fields of knowledge and for promoting inter and trans disciplinary specializations, such as artificial intelligence or, less known, computational ergonomy.

We had four different views of Michelangelo’s David. Which one we need for the resolution of this corporal duality? Which were the essential possibilities?

We needed the up and bottom views, we hadn’t them.



This is a strange way to reach the "centrum" and look for David’s essence. This is a complex way to reach the schema of the image. [ Note 5 ]

We have then one point with two possibilities, two possibilities that are solved with one point, three lines that are solved in one point.

In this point of our reflection we find a primary node of an interpretation system that joins visible elements and invisible ones. These are integrated without any question in esthetic contemplation because emotional sphere is integrated with rational thought. We start talking about perception.

We remember now some Gestalt exercises : having two different images synthesized in one, each person see a different thing depending on his experience before, if he has been in contact with one or the other of the images. As we desire an objective knowledge it is sometimes difficult for us to accept this idea, we start thinking or seeing since our experience before.

To clear a little bit more this exercise we can have a walk through the number’s world.

What is it?



Possible answers are :

A vertical and a circle, a one and a zero, a ten…

b = 2d

We have to accept that we have a history. We can listen to Ortega y Gasset : I am myself and my own circumstances explaining an individual question. We can also listen to the popular refrain : nothing is true neither it is false, it depends on how we look at it. We should ask ourselves about objectivity that only could be reached if we don’t accept the fact that we can only see and listen what we have learnt to see and listen. [ Note 6 ]

In this point we can link our reflections about the archetypes in Michelangelo’s David, the physic centrum of the work, its essence, and how different personal interests play in the reconnaissance of a thought, an action or a work.

We recognized one point and fixing on it we started to feel it.



The treasure of contemplating this point, allows us to become closer to Einstein in the formulation of his theory and to become closer to the microcosm of our genes as well. Maybe we should feel mathematics in the same way we feel art



About size.

Looking at David, again and again, our question was: what is he doing? The answer was simple, " he is facing Goliat the giant" (sic). And, who was this giant? Why were they facing each other?, questions that became to a second plan, our attention was mainly directed to this question : which was Goliat’s size? Asking in different environments, answers were amazingly interesting, personal imagination was largely deployed. Each person talked about his personal idea and somebody, without a great enthusiasm said: he is calculating a parabola. For somebody who is still looking for the Newton’s binomial this answer was amazing. If we talk here about estimation of Goliat’s size is because we have learnt with it, if somebody is interested in it : [ Note 7 ]



What a parabola is?

Again we were in face of the problem of clear and simple language. We were in front of communication problems between different branches of knowledge. We arrived to homonym, synonym and antonym without realizing it.

We found that a parabola was at the same time a teaching presented in an allegorical way in religious books and a conical plane. Going inside mathematical definitions allowed us to increase amazement before something such us simple and big as the social work that we enjoy nowadays, and that was cumulated by human race. In twenty years of scholar studies we want to recover all human knowledge.

Fig. Elipse, Parábola e Hipérbola



To find this definition amazed us. Man is able to build in an abstract plan or in his imagination, first a cone, then a generating line, then cut in parallel to it and establish a curved line in which all points are at the same distance to a fixed point called focus and to the line called directing line. [ Note 8 ].



We schematized the representation of this fact in a mathematical way.

In our reflection we wanted to find the gesture that could validate the theory that Michelangelo represented David calculating a parabola. For this we needed not only David but the giant that was certainly as tall as David. We used this exercise to find a sixth view.

So we reached the look. A look that is often far away from our perception, but that we can find if we look at the sculpture as a whole with intuition’s sight. A look that makes us to think about this popular refrain that says eyes are the soul’s mirror.



Many objectives are achieved but have not recognition. A great truth is hidden in this phrase saying that we can not see the forest if we are inside it. To see the Michelangelo’s David, it is necessary to look at it in its moment and at its proper dimension. Michelangelo represented David in the same moment of calculating the shot over Goliat, who was not as big as we think, but that was recognized as a fighter, meanwhile David was a peaceful man.

We see the young shepherd that faced Goliat. We did it because he was confident in the technique that he knew, he believed in a transcendental project and he thought in all the variations to a parabolic shot. With all this it was possible to consider a point, with a visual angle, the capacity to relate a stone’s weight, a distance, a height, a gravity strength not yet calculated, and develop a trigonometric function even before its definition.

The final questions we asked were not: Which was Goliat’s size?, but basically Where did David find the energy to win Goliat? And mainly, how did he dare to do that? in recognition to David’s answer his people made him a king, and Michelangelo represented this and we dedicate our reflections to this. Energy to win Goliat was inside David.





[1] Here we introduce ideas from the following books, shortened in the text. Umberto Eco, Los límites de la interpretacion , Josef Perner, Comprender la mente representacional, e Historia y Psicoanális de Michel de Certeau. [ Back ]



[2]
Kenneth Clark, Le Nu [ Back ]



[3]
Vid. Joan Pijoan en Historia del Arte, Editorial Salvat. T. VI, p .228. [ Back ]



[3]
Vid Olga Mucharraz, Construyendo el mañana con los ladrillos de ayer, en Moderna Madurez, No.3 [ Back ]



[4]
Arheim, El pensamiento visual, ed Paidos. Estética No. 7 p. 114 y sig. [ Back ]



[5]
We have to notice here the importance of studies made by Ernest Gombrich and Arnold Arheim and others, to understand artistic work as an object of knowledge. [ Back ]



[6]
I still remember how Khun or Baschelard influenced me about the idea of the necessity to find new schemas of thought, that could allow us as an intellectual community to advance. [ Back ]



[7]
We thank Mtro. Rafael Ochoa, master in Optics and Acoustics in the Engineering School, for his appreciated help to find Goliat’s size. [ Back ]



[8]
From Diccionarios Rioduero, Matemática, Ediciones Rioduero, 1971 p. 51 [ Back ]

   



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