The power to influence world views and stimulate ideas and feelings possessed by a language which communicates by visual means of expression is undeniable. Although all our senses participate in building our thoughts and understanding of the world we live in, the commonly used metaphor of ‘being in the dark’ uses the inability to see to refer to the state of being in ignorance.

I do enjoy revisiting art history studies, as for me it is an effective method to understand the development of practices over time, however distant in form and means of expression current activities and artforms seem in comparison with those of the past.

The practice of painting and drawing, which are both attempts to depict a three-dimensional image on two-dimensional plane, have been the dominant fields of artistic expression for a long period of time and have moved from one achievement in creating an illusion to another. This happened as different philosophical backgrounds and aspirations provided a new base to work from, reflecting our cultural windows to the world.

The technique of visual representation, or system, most widely used in the ‘western world’ and still persisting, is linear perspective. The introduction of this system has been attributed to the Italian Renaissance architect, designer and sculptor Filippo Brunelleschi.[1] There is some evidence that similar depictive methods were also known in ancient Egypt and Greece, though narrowly used. The hypothesis is that there was a conscious decision not to adopt this method as a mainstream way of depiction as it might unsettle the well-established language of symbolic representation, which dominated in the cultures of antiquity. So it would be inaccurate to claim that it was a new invention, but in the Renaissance period this method of visual representation became consciously applied and directed towards achieving definite results.

The Renaissance was a time when mathematics was closely integrated into art practices and there was a strong desire to create as perfect illusion of visible reality as possible. Many ‘tricks’ beside the use of linear perspective were employed to achieve this effect. The deliberately applied distortions to achieve optical correctness, include: use of sfumato[2], shadows and size variations of the object, depending on the perceived distance from the viewer. Also the choice of vertical, horizontal, square or even round format of a painted area was made in order to direct the viewer’s eye towards a particular element. All these means of artistic expression were used with consummate skill and attention to detail. 

With all due respect to the exactness of mathematical calculations, for the images to be true to what we see with our eyes something more than a strictly numeric interpretation of the visible world is required.

The work of Paolo Uccello[3]  is a good example of remarkable passion for a mathematical approach in visual representation. According the legend based on Giorgio Vassari’s book Lives of the Most Excellent Painters, Sculptors, and Architects’[4] we encounter a mathematician with an enthusiasm close to obsession, who would spend late night hours trying to calculate the vanishing point for an object he wished to depict in his drawing or painting. His work is somewhat underrated in comparison with other well-known artists of the Italian Renaissance period, nevertheless the legends about his life have been an inspiration to such writers of the 19th and 20th centuries as Marcel Schwob, Antonin Artaud and Bruno Tolentino.

Linear perspective became a powerful tool for leading a viewer’s gaze in a particular direction, so as to unlock the intended interpretation and understanding of the artwork. It depicts the world as a whole and requires a set and static viewing point to enable one to ‘read’ the presented artwork correctly.

A method of visual depiction which required a solid rule system, logic, and a mathematically calculated outcome as well as an unchangeable viewpoint from the observer was an attractive and suitable ideological background of the Renaissance period. It created a believable 2-D representation and a 3-D illusion of what one’s eye can see in the real world.

However, there are occasions when the consistent use of a rational method of depiction is not present or purposefully avoided. Sometimes the method deliberately chosen has an empirical rather than a realistic basis. This means it can be rather difficult for the present-day viewer to harmonise their perception, based on their beliefs and rule-set, with the method of depiction used by the artist. For example, when we see images of important persons shown larger than others, or when some parts of the composition may seem not as ‘real’ or true to life as others. This approach was taken for granted, as contemporary viewers were very comfortable with this mixture of symbolic and an optical illusion based visual narrative of the artwork.

Erwin Panofsky[5] in his essay Perspective as Symbolic Form (1924), in spite of the title, seeks to establish central perspective as a convention which is less related to ‘natural’ seeing in comparison with another representational system – curved or spheroidal perspective. His thesis was that straight lines are perceived by the human eye as curves and it is only because we have learned linear perspective that we accept them as straight in a drawing or painting in front of us.

The existence of interesting alternatives to linear perspective was evident well before its adoption as the preferred way of representing the visible world on a two-dimensional plane (the picture plane), and they continued to be used now and then, albeit sometimes as a curiosity. The use of these alternative methods is not always obvious. Even where the use is obvious the interpretation of the image is not, and so requires careful examination on the part of viewer. The departures from the dominant system seem purposefully disguised, obscured from the immediately perceivable part of an artwork. These seeming exceptions from the ‘mainstream’ representational systems show the depth of knowledge and wide range of capability of the artists. Evidence of this can be found in one very well-known example, where an anamorphic image of a scull is painted in the foreground of the painting The Ambassadors (1533) by Hans Holbein the Younger[6].

There was also an alternative and very well-developed representational system described as ‘reverse perspective’, which is used in Greek and Russian Orthodox Christian art. The images here were deliberately distorted and exaggerated to express the ‘Divine status’ of the artwork. Viewers much preferred to look at an icon where depicted images were far removed from what the eye of human can see.

In his 1919 essay Reversed Perspective Pavel Florensky[7] notes:

“When two or three icons of approximately the same period and more or less the same skill of painting are placed next to each other, the viewer sees with complete certainty a huge artistic superiority in that of the icons in which the violation of the rules of perspective is the greatest, while the icons with the drawing more ‘correct’, seem cold, lifeless and deprived of the closeness of connection to the reality depicted on them.”[8]

The ‘beauty’ of the image had nothing to do with the conventional understanding of the word, that being ‘aesthetically satisfying for senses or mind’. It represented something far beyond what is apparent to the eyes when we just look at the appearance of something. Both of the above-mentioned representational systems – linear perspective and reverse perspective, were connected with particular worldviews. Closely following the precisely defined methods of depiction made each more meaningful in their own context. 

There are other representational systems which require the viewer to agree with its ruleset. The axonometric method of drawing, for example, depicts an object rotated around one or more of its axes to reveal multiple sides. The parallel lines of a depicted cube, for example, are not directed to a vanishing point as in linear perspective, but they continue to be parallel thus requiring the viewer to accept the visual rules set by this method. 

Many examples of the axonometric method of depicting images can be found in Chinese painting about the same time that linear perspective gained mainstream acceptance in the Renaissance period in Europe. This representational system is widely used nowadays in technical drawing and illustration and is accepted as one of the main methods of visual depiction. 

Critical attitudes towards mainstream aesthetics, the established and unquestionable values of society, become clearly noticeable at the end of the 19th century emerging in the numerous artist practices, manifestos and prominent movements of the 20th century. At this point it becomes more difficult to differentiate between personal choices of an individual artist to self-express in order to communicate the concept of the work and choices made, freely or under coercion, to promote a counter-ideology challenging the wider establishment.

New or newly rediscovered systems of visual representation appear with each new artistic expression – a multitude of simultaneous perception points, for example, is already present in works by Paul Cézanne and then fully demonstrated in Cubism. Representation like that, even if it is done just by intuitive means, clearly reflects the existence of a philosophical stance of the creator of the artwork and shows that it is impossible to create a visual representation of any kind without the adoption of a method of depiction or the invention of a new one. 

The advancement of technologies has given many new possibilities to perceive the world from a different ‘angle’, using a variety of observational methods. There is nothing surprising in being presented with an aerial view or an image captured by satellite. We are competent to read maps and able to understand stylised images of data diagrams. There are numerous ways of how the visual image can be depicted, none of them have overwhelming advantages or disadvantages in all situations. There are numerous ways to adapt one’s perception to be able to read the visual language of representation.

If a system is defined by a set of rules which must be more or less applied then one must wonder what are the rules of art which is abstract – art which does not contain any narrative or image to describe any objects or create an association? These rules do exist and can even be extended in the process of creation of a particular work. However, as abstract art, by definition, deals with the intangible, those rules are less apparent than when the system in use is applied to represent a particular scene or tangible object with which the viewer is already familiar. 

There is a comparison that can be made with music and how we experience that, as most music is abstract. The structure of a work is created with elements from the field selected to create the composition and the rules used define the genre. So too in abstract art, similar to music where sound, silence and rhythm are the basic elements, colour, line, light and other means of artistic expression can become the main protagonists and form the rule set, without any need to illustrate something concrete. 

The parallel continues, with both art and music the perception of an abstract work depends on the circumstances and context, where and how the work is presented to us. It can both create a mood or experience or be selected to reflect one. Yet there is a huge difference in ability to access abstract art and music. Most people easily access a piece of music and experience particular feelings, whether or not the feelings are pleasurable. 

How many times, though, with abstract art have we have encountered the response: “My five-year-old child can do better!”? Yet, how many parents would claim their child could achieve something ‘better’ than an established musician? Maybe only those who find a particular piece unpleasant.

Whilst it might be a possibility for a five-year old to produce a great piece, there are prodigies in both fields, it’s much more likely such a statement indicates that the speaker does not understand that the creation of an abstract artwork requires as much training and experience as any other serious artform, nor do they know what to see or experience in an encounter with such a creation.

The key to unlocking any abstract work, music or painting is to adopt the right mindset, rather than contemplating what it might depict or mean concentrate on how it makes you feel.

[1]Filippo Brunelleschi (1377 -15 April 1446), considered to be a founding father of Renaissance architecture, was an Italian architect, designer, and sculptor, and is now recognized to be the first modern engineer, planner, and sole construction supervisor. In 1421, Brunelleschi became the first person to receive a patent in the Western world.

[2]Sfumato is one of the canonical painting modes of the Renaissance, and is a painting technique for softening the transition between colours, mimicking an area beyond what the human eye is focusing on, or the out-of-focus plane.

[3]Paolo Uccello (1397 – 10 December 1475), born Paolo di Dono, was a Florentine painter and mathematician who was notable for his pioneering work on linear perspective in art.

[4]The Lives of the Most Excellent Painters, Sculptors, and Architects (Italian: Le vite de’ più eccellenti pittori, scultori, e architettori), often simply known as The Lives (Italian: Le Vite), is a series of artist biographies written by 16th-century Italian painter and architect Giorgi Vasari, which is considered the most famous, and even today the most-read work of the older literature of art, some of the Italian Renaissance’s most influential writing on art, and the first important book on art history.

[5]Erwin Panofsky (1892 – 1968) was a German-Jewish art historian. His essay Perspective as Symbolic Form (1924) is among the most widely commented works in twentieth-century aesthetics. It discusses with regard to art theory, Renaissance painting, Western codes of depiction, history of optical devices and psychology of perception.

[6]Hans Holbein the Younger (1497–1543) was a German painter and printmaker. His painting known as The Ambassadors (1533) is now located in the National Gallery in London.

[7]Pavel Alexandrovich Florensky (Russian: Па́вел Алекса́ндрович Флоре́нский 1882 – 1937) was a Russian Orthodox theologian, priest, philosopher, mathematician, physicist, electrical engineer, inventor, polymath and neomartyr.

[8]Когда иконы две или три, приблизительно одного периода и более или менее одинакового мастерства письма удается поставить рядом друг с другом, то зритель с полною определенностью усматривает огромное художественное превосходство в той из икон, в которой нарушение правил перспективы наибольшее, тогда как иконы более “правильного” рисунка кажутся холодными безжизненными и лишенными ближайшей связи с реальностью, на них изображенною.”

From Reversed Perspective 1919 by Pavel Florensky

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