It is improbable that more nonsense has been written about aesthetics than about anything else: the literature of the subject is not large enough for that (Clive Bell)


The Index is found here

Monday, September 19, 2011

John White : Theory of Artificial Perspective

(this is chapter 8
of John White's "Birth and Rebirth of Pictorial Space".
Quoted text is in YELLOW.
Text quoted from other authors is in GREEN)


The Development of the Theory of Artificial Perspective


It is a vivid reminder of the continuity of historical processes that the invention of a mathematically based perspective system during the early years of the fifteenth century was heralded, not by the publication of a treatise, but by the painting of a pair of panels. It is also characteristic of the ever- increasing unity of the arts and sciences in the Renaissance that it was Filippo Brunelleschi, firstly an architect and secondly a sculptor, who chose to publicize his new discovery in this way. The importance of the contents of these pictorial manifestos can hardly be overestimated. Although they themselves are lost, it is fortunately possible to reconstruct all their essential compositional features with unusual accuracy.

And how can that accuracy be tested?

Happily, Norris Kelly Smith has given this subject a thorough discussion in his chapter entitled The Lost Tavolette

Unfortunately, this discussion involves graphs or reconstructions rather than actual period paintings, which makes it much less appealing to me.

But still.... we shall proceed.

Antonio Manetti, in his "Life of Brunelleschi", which was probably written only a few decades after the latter’s death, states quite firmly that the new perspective was the master’s own creation.’

Thus in those days, he himself proposed and practised what painters today call perspective; for it is part of that science, which is in effect to put down well and with reason the diminutions and enlargements which appear to the eyes of men from things far away or close at hand: buildings, plains and mountains and countrysides of every kind and in every part, the figures and the other objects, in that measurement which corresponds to that distance away which they show themselves to be: and from him is born the rule, which is the basis of all that has been done of that kind from that day to this.’

Smith's reconstruction of Brunelleschi's
painting of the Baptisty

Manetti describes the painting of S. Giovanni and the Piazza del Duomo’, which was the first of Brunelleschi’s demonstration pieces. He records it in these words:

‘And this matter of perspective, in the first thing in which he showed it, was in a small panel about half a braccio square, on which he made an exact picture (from outside) of the church of Santo Giovanni di Firenze, and of that church he portrayed, as much as can be seen, at a glance from the outside: and it seems that in order to portray it he placed himself inside the middle door of Santa Maria del Fiore, some three braccia, done with such care and delicacy, and with such accuracy in the colours of the white and black marbles, that there is not a miniaturist who could have done it better; picturing before one’s face that part of the piazza which the eye takes in, and so towards the side over against the Misericordia as far as the arch and corner of the Pecori, and so of the side of the column of the miracle of Santo Zenobio as far as the Canto alla Paglia; and as much of that place as is seen in the distance, and for as much of the sky as he had to show, that is where the walls in the picture vanish into the air, he put burnished silver, so that the air and the natural skies might be reflected in it; and thus also the clouds, which are seen in that silver are moved by the wind, when it blows.’

White then tries to establish exactly what Brunelleschi would have been able to see if he were standing "three braccia" within the doorway of the cathedral and looking out upon the piazza. White has calculated that 3 braccia = 1.75 meters (although elsewhere on the internet it would figure at 2.1 ), and has taken into account subsequent alternations to the doorway.

Smith's reconstruction of Brunelleschi's
painting of the Piazza della Signoria

White's ground plan

He then quotes Manetti as follows:

‘In which painting, because the painter needs to presuppose a single place, whence his picture is to be seen, fixed in height and depth and in relation to the sides, as well as in distance, so that it is impossible to get distortions in looking at it, such as appear in the eye at any place which differs from that particular one, he had made a hole in the panel on which there was this painting, which came to be situated in the part of the church of Santo Giovanni, where the eye struck, directly opposite anyone who looked out from that place inside the central door of Santa Maria del Fiore, where he would have been positioned, if he had portrayed it; which hole was as small as a lentil on the side of the painting, and on the back it opened out pyrami dally, like a woman’s straw hat, to the size of a ducat or a little more. And he wished the eye to be placed at the back, where it was large, by whoever had it to see, with the one hand bringing it close to the eye, and with the other holding a mirror opposite, so that there the painting came to be reflected back; and the distance of the mirror in the other hand, came to about the length of a small braccio; up to that of a true braccio, from the place where he showed that he had been to paint it, as far as the church of Santo Giovanni, which on being seen, with the other circumstances already mentioned of the burnished silver and of the piazza etc. and of the perforation, it seemed as if the real thing was seen: and I have had it in my hand, and I can give testimony.’

.... and draws the following conclusion:

This passage confirms that, besides showing all of the Piazza del Duomo that was visible from a carefully chosen position, the construction of the picture was dependent upon its being seen from a single viewpoint set at a particular distance from the picture surface. In this case the viewing distance was about twice the width of the painting. There must, therefore, have been a true vanishing point system, with the mathematically controlled rate of diminution which was implied in Manetti's opening remarks on the new discovery"

As Smith pointed out, however, such a painting could have been made based strictly on observation. No mathematical control was necessary.

Mathematics was Manetti's primary concern, but it need not have been used by Brunelleschi.

‘He made in perspective the piazza of the palace of the Signori of Florence, with everything on it and round about it, as much as can be seen, standing outside the piazza or really on a level with it, along the fa├žade of the church of Santo Romolo, past the corner of the Calimala Francesca, which rises on the aforesaid piazza, a few braccia towards Orto Santo Michele, whence is seen the palace of the Signori, in such away, that two faces are seen completely, that which is turned towards the West and that which is turned towards the North: so that it is a wonderful thing to see what appears, together with all the things that the view includes in that place. Afterwords Paolo Uccello and other painters did it, who wished to counterfeit and imitate it; of which I have seen more than one, and it was not as well done as that. Here it might be said: why did he not make this picture, being of perspective, with that hole for the eye, like the little panel from the Duomo towards Santo Giovanni This arose, because the panel of so great a piazza, needed to be so big to put in it so many different things, that it could not, like the Santo Giovanni, be held up to the face with one hand, nor the mirror with the other; for the arm of a man is not of sufficient length that with the mirror in his hand he could hold it at its distance opposite the point, nor so strong, that he could support it. He left it to the discretion of the onlooker as happens in all the other paintings of all the other painters, although the onlooker may not always be discerning. And in the place where he put the burnished silver in that of Santo Giovanni, here he left a void, which he made from the buildings up: and betook himself with it to look at it in a place, where the natural air showed itself from the buildings upwards.’

And again White concludes:

Once again the nature of the focused perspective system is underlined. The painting, whilst approaching the normal practice in dispensing with the eyehole and the mirror, still reveals, in its silhouetted upper border, the unusual interest in pure illusionism to be expected in a perspective manifesto demonstrating a new system in the most forceful terms possible.

But illusionism does not require the use of mathematics - and no mention is made of any construction lines that B. might have used.

White then digresses into a discussion of how Vasari's description of the second panel differs from Manetti's, is improbable, and he suggests that Vasari probably never saw it ---- which also reminds us that we have never seen it either.

And he reiterates his conclusion that :

It is clear that he developed a complete, focused, system of perspective with mathematically regular diminution towards a fixed vanishing point.

However, he adds in a footnote:

No detailed reconstruction of the technical procedure used in drawing these pictures has attempted, since there is no way of deciding between the various possibilities. It should,however, be noted that the oblique setting could have been accurately achieved without recourse to the distance point construction. Nevertheless, in view of the evidence discussed by Klein .. the possibility that the latter system was used cannot be disregarded. An illuminating discussion of Brunelleschi’s possible technical procedures in A. Parronchi, Studii su la dolce prospettiva, Milano, 1964, pp. 226-95, but it remains unlikely that none of the ground in front of the Baptistry was shown, whilst the unbalanced design of the second panel is both improbable in the early fifteenth century and only generated an unwarranted and radical diagrammatic reorientation of the west side of the Piazza.

White does not share with us the "evidence discussed by Klein", and without the Parronchi text, I have no idea what White is disputing in the final sentence.

But still, he seems to be aware that the discussion of Brunelleschi and mathematical construction is built on sand.

At the same time, in the very compositions with which Brunelleschi chose to demonstrate the new invention, he is careful to respect as far as possible the particular, simple, visual truths which underlie the achievements of Giottesque art. In the view of the Piazza del Duomo the whole problem of dealing with the forward surfaces of foreshortened, cubic buildings is, as far as possible, avoided. On either side orthogonal coulisses run inwards from the very edge of the painting.4 In the panel of the Piazza della Signoria, the viewpoint is chosen so as to draw the eye diagonally across the open space. Every building is obliquely set, and the jutting sharpness of the forms must have given dramatic emphasis to the new realism. Nevertheless, in its fundamental structure, the composition is exactly that of Taddeo Gaddi’s fresco of ‘The Presentation of the Virgin’ in the Baroncelli Chapel

Brunelleschi must have been well aware of the one point of unavoidable conflict between his new mathematical system and the simple observation of reality which underlies the oblique disposition of Giotto’s compositions. This conflict he succeeded in reducing to a minimum by the careful selection and manipulation of his viewpoint.

Unfortunately, White has not told us what the "one point of unavoidable conflict" might be. But then, he also has no idea just what "new mathematical system" Brunelleschi might have been using.



It is in Alberti’s Della Pittura, which he wrote in 1435, that a theory of perspective first attains formal being outside the individual work of art.Theoretical dissertation replaces practical demonstration. The way is open, in art also, for that separation of theory and practice; that particular kind of self-consciousness which, in the wider view, showed itself most significantly in the growing realization of the historical remoteness of antiquity, and which underlies modern scientific achievement.

And so Alberti serves as hero/pioneer/role-model for the contemporary university art academic working within an institution that priveleges scientific achievement over any other kind.

But we might note that though apparently he made paintings, and he writes of "we painters", none of them have survived, probably because, as Vasari judged, they weren't much to look at.

The complete text of "De Pittura" is posted here .

Where we can find the credo:

I say the function of the painter is this: to describe with lines and to tint with colour on whatever panel or wall is given him similar observed planes of any body so that at a certain distance and in a certain position from the centre they appear in relief, seem to have mass and to be lifelike. The aim of painting: to give pleasure, good will and fame to the painter more than riches. If painters will follow this, their painting will hold the eyes and the soul of the observer.

Truly a modern man, working only to serve his own reputation. Some deference is shown to "the soul of the observer", but the only criterion that he mentions here is that the objects represented "have mass and appear to be lifelike".

Whatever kind of space the painter will construct is there only to enhance the lifelike qualities of the figures within them, and so he offers us the Albertian grid within an Albertian box, based upon the single P.O.V. of an observer.

Self centered optics for a self centered art theory.

Alberti starts his treatise by explaining the simple geometric terms which he will have to use. He then begins immediately to describe the pyramid of visual rays which joins the objects that are seen to the beholder’s eye. There follows an explanation of the relationship between apparent quantities and the visual angle formed within the eye. In a single sentence Alberti sets forth the fundamental principle of Euclidean optics, and establishes the optical foundation of the pictorial diminution to a point, on which the new perspective system is constructed. The definition of the picture plane as an intersection of the visual pyramid is followed by a demonstration of the fact that all the pictured quantities are proportional to those found in the actual objects which are being reproduced. This also establishes the further fundamental point that there is no distortion of the shape of objects lying parallel to the picture plane. Artificial perspective is therefore, in its treatment of the individual object, essentially a development of the foreshortened frontal system which had reached its highest level of perfection in the Sienese school of the early, and the Paduan and Veronese circles of the late fourteenth century. It is fundamentally opposed in structure to that vision of reality espoused by Giotto and by Ambrogio Lorenzetti.

White does not spell out the reasoning that takes us from Alberti's discussion of "extrinsic rays" and the triangles they create between the eye and the either edge of an object being seen -- but I think his conclusions are correct.

Alberti is only concerned with the silhouettes of objects as they appear in a plane that is 90 degrees from the line that connects the center of that object to the eye.
So if an artist wishes to display the facade of a building, he would set it into that plane, i.e. use the foreshortened frontal system.

Even the bare summary of a few aspects of Alberti’s new construction reveals the autonomy achieved by the idea of space. During the thirteenth and fourteenth centuries it was possible to see space gradually extending outwards from the nucleus of the individual solid object, and moving, stage by stage, towards emancipation from its tyranny. Now the pictorial process is complete. Space is created first, and then the solid objects of the pictured world are arranged within it in accordance with the rules which it dictates. Space now contains the objects by which formerly it was created. The change in pictorial method is a close reflection of the crystallization of ideas which were slowly taking shape in the preceding century, and which were earlier discussed.

But this autonomous idea of space is mathematical, not visual. It does not need to be seen to be understood. While the space that is felt in a painting, depending as it does on color, texture, and edges defies mathematics. Though, of course, that feeling might be ignored, as it is when reading the text on a page, or when White looks at a 14th C. painting and sees "space gradually extending outwards from the nucleus of the individual object".

Visual sensitivity to spatial design cannot be taken for granted. If it's not cultivated, it won't develop, as it does not appear to have done in either White or Alberti.

The artificial perspective which Albert codified and himself conceived in part, and which dominated Italian art throughout the fifteenth century, has four principal characteristics.....(a) There is no distortion of straight lines. (b) There is no distortion, or foreshortening, of objects or distances parallel to the picture plane, which is therefore given a particular emphasis. (c) Orthogonals converge to a single vanishing point dependent on the fixed position of the observer’s eye. (d) The size of objects diminishes in an exact proportion to their distance from this observer, so that all quantities are measurable. The result is an approximation to an infinite, mathematically homogeneous space, and the creation of a new, and powerful means of giving unity to the pictorial design.

These characteristics are precisely those which stood revealed in the construction which Brunelleschi demonstrated in his paintings of the Florentine piazze.

How does he know that?

Manetti says nothing about whether the horizontals are perfectly straight from one edge of the painting to the other, and Smith's reconstruction of the Signoria panel would suggest otherwise (since the line of windows on the left is not running parallel to the line on the right)

The power generated by Alberti’s systematic clarity can be demonstrated by the abrupt change which overtakes the choice of viewpoint in representations of the Piazza della Signoria. In the fourteenth-century fresco of ‘The Expulsion of the Duke of Athens’, and in an early fifteenthcentury relief, the Palazzo Vecchio is obliquely set. But this diagonal view of the piazza virtually disappears between the time of Brunelleschi’s own design and Stella’s etching in the early seventeenth century.

An interesting observation. Norris Kelly Smith never discussed the avoidance of the oblique setting during that time period.

The innate pictorial qualities of artificial perspective were not the only sources of its popularity and prestige. Already in the Della Pittura, it is used as a lever with which to ease the humble craft of painting into the lordly circle of the liberal arts. With this ascent the formerly humble, but now scientific, painter was to move into the sphere of the princely patrons and attendant men of letters. Social and economic pressures were combined with the aesthetic and the practical. It was Alberti’s contribution to the history of spatial realism in painting that, at one blow, made an essential technical improver ment and disseminated the new idea in palatable form, whilst harnessing it to the driving force of the whole current of contemporary ideas and aspirations.

Another interesting observation.

Did an association with natural science and mathematics confer higher social status on 15th C. artists in northern Italy the same way it does with artists, and art historians, associated with 21st C. universities?



Ghiberti was something of a scholar, as well as a great sculptor, and White draws our attention to his Commentarii which compiled the then known theories of optics,
primarily those of the 11th C. Arab, Alhazen:

In a long series of extracts from Alhazen and Peckham, five main propositions are put forward. These are that: (a) Visible things are not comprehended by means of the visual sense alone. (b) It is only possible to judge the distance of an object by means of an intervening, continuous, series of regular bodies. (c) The visual angle alone is not sufficient for the judgement of size. (1) Knowledge of the size of an object depends upon a comparison of the base of the visual pyramid with the angle at its apex, and with the intervening distance. (e) Distance is most commonly measured by the surface of the ground and the size of the human body.

All of this is common sense.

Why this is important?, other than to demonstrate the enthusiasm that the quattrocento Florentine artworld had for optical theories, and the fact they had neither invented nor rediscovered them. All they did was make it fashionable.

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