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Drawing: an intuitive kind of mathematics perception

Luís Filipe Salgado Pereira Rodrigues

Collaborating member of CIAUD (Research Centre of Urbanism and Design)

from Faculty of Architecture, Lisbon/Portugal)

luisfiliperodrigues@yahoo.es; http://www.thinking-through-art.com/

co-authoring of Ana Leonor Madeira Rodrigues, artist, Associate Professor at Faculty for Architecture - University of Lisbon

Figure 1. 100x73cm, white pencil on black card. 2012

Abstract. My statement consists in an approach of what is the definition of drawing and what kind of drawings are my artworks. I intend to establish links among drawing, mathematics and intuition, because I believe that drawing is a way of intuitive application of mathematics. But in the field of drawing we may approach the real drawing or we may take distance from it, either through intuitive mathematics in the application of proportionality in the support of the drawing itself, or using - at the same time - our perception to grasp the reality that we observe outside the drawing support.

Keywords: Drawing, mathematics, intuition, proportionality, visual thoughts.

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Figure 2. 100x73cm, white pencil on black card. 2012

Between drawing and mathematics

I start my arguments by asking a question: are my artworks drawings or a

mathematical play with representation of the shapes? And, is drawing always a

mathematical application on the registration of proportionality through

perception? Let’s try to know more about it.

My artworks are, really, conceptual representations from which I get an

aesthetically sensible set of shapes, as it happens with any type of drawings, as

images that they are. And it is my belief that the drawing process is not dissociable

either from mathematics or aesthetics or even from perception. When we draw, we

record amounts of shapes or of lightness or, in a broad sense, amounts of visual

information. When we work literally with our perception, we do that more

cognitively; when we make imaginative drawings, we do that more intuitively;

when we make geometric drawings, we do that in a way in which there are no

borders between the literal imagination and cognition, using, however, the visual

perception only as an intuitive mathematics perception, i.e., not using perception

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as a way to understand the reality that one observes and that one would transpose

into a support.

The process of learning to draw involves the exercise of intuitive calculation

where some shapes are compared to others and where the dimension of the parts

of a shape are compared to the remaining parts; in one word, we compare

measures as a mathematical way of thinking. What is the meaning of proportion

implicit in any kind of drawing or observed object? It is a measure of dimensions

that correlate with one another comparatively. The perception of the implicit

proportion is an inherent visual thought but it’s also a relationship that nature

created. For example, “a part of this is the third part of that”, “this part is half of

that part”, et cetera. This is a mathematical thought. What are numbers but

measures of quantity? We quantify all kinds of information, and, in this case, even

percepted visual information.

Fig. 3 100x73cm, white pencil on black card. 2012

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An intuitive play with proportions

I can state that these drawings are shapes that have a rotational movement,

in which they move some inside the others, in a rotary way towards a centre

direction, therefore concentrically (even having an infinite developing towards the

exterior); moreover they are similar and may describe spirals (present in nature

and explained mathematically). This may happen because there are well definite

dimension proportionalities but without a relation with an outer and observable

reference.

Mathematics is not beautiful only because its basis is a pure content; it is

beautiful because it is the core. This is both a philosophical and ontological

concept. However, in spite of studying these dimensions during my research in my

practice, what attracts me the most are the visible shapes of mathematics that

allow me to think visually and which guide my drawings in a specific way, even if

that happens in an intuitive way.

We use mathematics to solve problems, either functional or operational – so

it has a rational strength –, but I use those issues to create, achieving a fluid

thinking (thinking without effort and without being aware of its process). In this

way, my feelings and emotions will drive my constructive action in order to get a

beautiful result and, in spite of being aesthetically pleasing, they have both a

rational and mathematical basis. I dare to say that I think that it is by using

mathematics intuitively that we will be able to draw.

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Fig. 4 100x73cm, white pencil on black card. 2012

Dialectical movement between reason and aesthetic sensibility

Reason, applied in geometric constructions with a paradigmatic explanation,

drives us to conclusions which allow us to put on other reasonable situations. But

when we don’t wish to get conclusive ideas, when we wish to open our mind, the

reason opens itself to creation and also in drawing, the pure reason may transform

the shapes in mathematics geometry when the cognition takes advantage of visual

perception.

But when we make a drawing, sensibility changes it into an aesthetic object

due to senses and to the balance between our body and our mind. Mathematics

doesn’t need senses to be appreciated; mathematics is purely mental and drawing

is mental and bodily, rational and sensible. Drawing is a way of putting emotions in

order by using mathematical dimensions quantification in shapes.

Nature is beautiful. But everything within it (or almost everything) has a

possible explanation based on mathematics theories. For instance, equilibrium

may be a closed mathematics formulation and definitely solved. But the nature

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beauty doesn’t remain in an equilibrium stage but in the re-equilibrium process –

precisely that one which gives life to the desire of creation in the human being; that

strength of searching this equilibrium is what creates beauty; it’s the strike against

annoyances, like in the creation of any drawing that improves the beauty of the

expression. The process of becoming balanced is a dynamic state.

Drawing is originally dynamic within its rebalancing and inherent process. To

draw is to search the dynamic balance; a search that is driven through the

reformulation of proportionality. You can get it from what you see or from what

you wish to see. My drawings are a demand of the proportionality I wish to see,

although this requires an education on the competence of representing the

proportionality of what I really see outside of the drawing.

What is art but the search of the inner balance of ourselves through the

search of the external beauty or even in the game of rebalancing shapes? How

would my drawings be if they were made by someone who hasn’t had the chance

to learn how to draw? They would be pure plays with shapes without the influence

of the real drawing (without any education towards sensibility of visual

aesthetics). But my artworks are plays with drawn shapes, because my

autobiographical history includes the practical learning of drawing, in which I was

able to develop my gaze education. Thus, my sensibility to the shapes is different

comparing to someone who hadn’t learnt how to draw. I mean, through several

self-oriented exercises, I’ve educated my intuition, my perception, my sensibility

and my gestures to draw, being able to be more aware of the visual reality.

And, this created in me a change that drives me to a different behaviour as far

as shapes creation is concerned. Perhaps, my artworks are too much rational, but

this rationality is driven towards the aesthetics creation. I do this with the

influence of mathematics: transforming a rational way into sensibility.

Neither absolute order nor the opposite one

My creation process involves the internalization of certain patterns, rational

thoughts, coherence, equilibrium, intrinsic proportionalities, and the ability of

letting ourselves go in an emotional and aesthetics way. The rational (in

mathematics or other areas of knowledge) moves the thinking with energy, but its

fuel is the emotion the feeling. The well-run of this engine in a drawing process, is

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the aesthetics where there is a balance between reason and emotion – that are the

conditions needed to go on creating.

I suggest: neither only rationality nor only emotionality. Creativity works if

there is no excess from one or another. Reason without emotions is a mathematical

organization as if it was an Apollo thought. Emotion without reason is the

uncontrolled drunkenness typical from Dionysus. Reason with emotion improves

our ability to (re)create mathematics; it allows us to be innovators and creators on

it. Drawing is a “come-and-go” between both trends and methods of creating in this

oscillatory and dynamic journey between what is rational and emotional.

Fig. 5 100x73cm, white pencil on black card. 2012

The perception without an exterior reference

In my drawings there isn’t any direct relationship between perception and

what I observe in reality. But I have developed a relationship between perception

in my own drawings during their emergence and their construction. Here one

doesn’t apply the cognitive process to understand the intrinsic proportions of the

shapes that we observe; instead, it is applied to create artificial proportions in the

shapes that I draw. In this last case, the cognitive process was more instinctive

after all. As I was seeing the creations of my own proportions, there was a close

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link with the proportions that my mind determines, which belongs to the

cosmological nature and its mathematics organization. The creation of my

drawings was purely mental because of the inexistence of an exterior reference

observation. This helped me to have my own visual thinking, not to understand

what I see but to see what I wish to see. What I did was to make my way of thinking

more aesthetic. Therefore, the things I observe may improve the aesthetics of my

imagination, if I draw when I observe them; I’ve educated my gaze through

perception.

As long as the drawing has an exterior reference, it starts having a connection

with the exterior and the way of making the drawing itself – in my creation of that

drawing – and there’s a closer link between: the instinct and feelings, wishes and

the practice, my values and their products. In a word there is a direct link between

mental working and practice working.

I use drawing to make aesthetic images, but the real drawing needs a

connection with an exterior and observed figure/an observed shape in that precise

moment or remembered figure by using our memory. Thus, there’s an approach

between thoughts and aesthetics to the extent that drawing depends on a sensitive

reception phenomenon of the things we are observing, which after mindset is

translated following taste criteria according to the cognitive and mathematic

application on constructive creation of shapes.

Luís Filipe Salgado Pereira Rodrigues

Luisfiliperodrigues@yahoo.es

I was born in 1971, in Portugal, I took a course in Fine Arts from the University of Porto (Portugal) (finished in 1996), I did an MA in Art Education in Fine Arts from the University of Lisbon (Portugal) (finished in 2007), I am a student of Architecture Doctorate (PhD) in the Faculty of Architecture of the University of Lisbon (Portugal) since 2008. I live in Santo Tirso (22 Km from Oporto) and currently I am working in a school in Santo Tirso. I am married and I have two children. I play tennis and my preferred philosopher is Immanuel Kant.Since 1992, I have participated in nearly 70 exhibitions of paintings (three of them in Amsterdam, two in Spain, one in Seoul (Korea), and the others in Portugal). Since 2002, I have made eight solo exhibitions of painting, one with photographs, and another with drawings. I’ve made 13 lectures about art and drawing. I’ve published 22 articles on art and drawings. I’ve also published a book called "Drawing, Creating and Consciousness" with a text made by myself (280 pages) and, in the same book, 11 interviews (250 pages) to 2 (architects Álvaro Siza Vieira and Alcino Soutinho) and 9 artists. (This book was in the best bookstores in the country: FNAC, Bertrand, Almedina, Wook, Bulhosa, etc.). As

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far as awards are concerned, I’ve won two: one on education and the other with my own paintings.Recent solo exhibitions:

1. 2015: Centro Cultural de Macedo de Cavaleiros.https://www.facebook.com/video.php?v=427961637369526&pnref=story

2. 2013/2014: Ars GEometrica Galéria, Eger (14 drawings) – Hungary.http://www.elmenymuhely.hu/?page_id=127

3. 2013: Galeria Monumental (22 drawings) – Lisbon (Portugal)http://www.galeriamonumental.com/pt

4. 2011: Estúdio UM (8 drawings) – Guimarães (Portugal) http://www.estudioum.org/cartoes/luisrodrigues.htm

5. 2010: Centro de Arte e Espetáculos da Figueira da Foz (25 photos) (Portugal)http://www.cae.pt/

6. 2006: Casa do Médico (Ordem dos médicos no Porto) (13 paintings) – OPorto (Portugal)http://aeicbasup.pt/congressomedicina/index.php/local/localizacao

7. 2005: Galeria Vilar (ÁRVORE) (28 paintings) – OPorto (Portugal)http://www.arvorecoop.pt/

8. 2004: Galeria Quasiloja (14 paintings) – Oporto (Portugal)http://quasiloja.blogspot.pt/

9. 2002: Galeria OM (8 paintings) – Penafiel (Portugal)http://www.igogo.pt/galeria-de-arte-om/