John White : Masaccio

(this is chapter 9
of John White's "Birth and Rebirth of Pictorial Space".
Quoted text is in YELLOW.
Text quoted from other authors is in GREEN)

Masaccio, "The Tribute Money" 1427

Ten years before Alberti’s book was written, the ideas which Brunelleschi first translated into paint were given monumental form in fresco by Masaccio. Yet, as the spectator stands in the Brancacci Chapel and looks out on the pictorial world beyond the window of the wall, there may come the sudden feeling that although this world has grown a mightier race of men, who walk in their majestic certainty upon a freer, wider, and a firmer earth, his own relation to it has not changed as much as might have been expected. This realization calls to mind the slow, century long preparatory process by which the whole meaning of the picture surface was seen to be transformed. Once again the past gives scale and meaning to the present.

I also get that feeling from this painting - but linear perspective is only part of the story.



Here, the architecture is gone -- but the same feeling that "the world has grown a mightier race of men, who walk in their majestic certainty upon a freer, wider, and a firmer earth" is still there, isn't it?















White also notes that
"slow, century-long preparatory process by which the whole meaning of the picture surface was seen to be transformed" so that "once again, the past gives scale and meaning to the present"

Just as it does in the history of any other technology, like what occurred between Kitty Hawk and the Houston Space Center.

But can religious imagery be studied as a history of technology?

The Wright Bros. would have used 21st C. technology if they had it - but I'm not sure that Giotto, Maso, Duccio etc wanted to make their paintings feel like windows onto an ordinary, non-sacred world.








There is nothing in between this architectural frame and the pictorial world which it encloses. Equally, nothing intervenes between the architecture and the onlooker, now firmly placed in the middle of the chapel, his position determined with new emphasis by the central focus of the unified vanishing points in all the compositions on the side walls. This stationing is further reinforced in the Shadow Healing and Almsgiving scenes on the end wall by the recession of the orthogonals towards the centre of the altar which divides them. These two external vanishing points, without actually coinciding, give sufficient emphasis to the spectator’s central placing as he stands, enclosed by the framework of the architecture, and looks out into the depths beyond. The wall has melted, and reality and picture are one world to the imaginative eye.


Of Masaccio’s own beginnings little enough is known. It seems probable that Brunelleschi’s famous panels had a considerable, direct influence upon his earliest productions. The reconstruction of the view of the Piazza della Signoria adds to the significance of a passage in which Vasari, having emphasized the artist’s close relationships with Donatello and Brunelleschi, says, in addition, that:
‘He diligently studied methods of work and perspective, in which he displayed wonderful ingenuity, as is shown in a scene of small figures now in the house of Ridolfo Ghirlandaio, in which besides Christ releasing the man possessed there are some very fine buildings so drawn in perspective that the interior and the exterior are shown at the same time, as he took for the point of view, not the front, but the corner for its greater difficulty.’









The probable accuracy of Vasari’s description is supported by the existence of the panel in the Johnson Collection which, if it is not actually the picture that is mentioned, must be very closely associated with it. The added difficulty of the viewpoint is naturally present only in Vasari’s eye, conditioned as he was by the then century-old dominance of the foreshortened frontal patterns fostered by Alberti’s pictorial method. The obliquely set representation of the Florentine Duomo in the Johnson panel is not an accurate bifocal structure. Only the main architectural lines receding to the left run to a single point, and there is a similar uncertainty in the perspective of the arches. The picture does, however, prove that in the circle of Masaccio, as well as amongst artists such as Lorenzo Monaco, the interest in the patterns of the previous century survived, although, as was suggested earlier, the immediate impetus in the former case was probably provided by Brunelleschi.

Smith and I discussed this painting here . I speculated that as a processional banner, it was designed to be seen from either side but not from the front. Which would account for the oblique setting which White finds so important.







This is confirmed by the predella of the Pisa altarpiece which is Masaccio’s one remaining documented work. Here the strongly oblique setting of the righthand panel with the story of St. Nicholas, of which the execution by Masaccio has been doubted, is balanced by the softer, but quite definite recession in the opposite sense that is apparent in ‘The Crucifixion of St. Peter’. In this scene the forward surface of the left-hand pyramid is in recession, and its base lies in a slightly deeper plane than that of its counterpart upon the right. There is therefore a soft slipping backwards into space upon both wings of the predella, in conformity with the Florentine empirical tradition that had also influenced Brunelleschi’s compositions.








The development of Masaccio’s figure style, which is evident in the various panels of the altarpiece, is reflected in perspective by the accurate vanishing point construction of the monumental throne. The same interest in spatial problems is also revealed by the foreshortened halo of the Christ Child, and in the bold attempt to foreshorten both the cross and the figure of Christ Crucified in the panel which surmounted the whole altarpiece.

White tells us that this attempt was "bold", rather than successful, because it does seem that Christ's arms would reach down to his knees.

But it's a powerfully compelling scene, none the less.







In the frescoes in the Brancacci Chapel the fundamental idea of the new perspective is expressed by the architectural framing. In the scenes themselves the compositional patterns indicate something of the potentialities of the system, and are, in their turn, influenced by it in a way that is characteristic of its effect on pictorial decoration throughout the fifteenth century.


In all the scenes containing architecture, the horizon line, marked by the vanishing point, is at the same height as the general level of the heads of the participants. In this way the onlooker is placed on the same level as the figures, precisely as Alberti later recommended. In each scene the frontal surfaces of the houses all lie undistorted in the plane, expressing the underlying ideas of artificial perspective which were crystallized in the rectangularity of Alberti’s foreshortened pavement. The single vanishing point reveals itself not only as a symptom of the new spatial unity, knitting together all the contents of the scene—landscape, houses, figures, every detail—but also as a powerful compositional weapon.








In ‘The Shadow Healing’ and ‘The Almsgiving’ it is used, as has been noted, to express the relation of all the frescoes to the observer at the centre of the chapel. The simplicity and unity of the composition needs no further emphasis in either case, and the external vanishing point is used to great advantage in ‘The Shadow Healing’ to increase the sense of movement. In the companion scene the figure design is stressed in Giottesque fashion by the ‘verticals of the architectural setting. A very different problem is posed, however, by the three large frescoes on the side walls. Each is made up either of a complex of several episodes within a single story, or else of a single episode in time involving several centres of attention.








One of these three scenes, namely ‘The Healing of the Lame Man, and the Resurrection of Tabitha", is distinguished by the structural peculiarity that the vanishing point expresses nothing but the unity of the space in which the separate incidents take place. It enhances neither narrative. Even the attempt to strengthen the connection across the central void by associating it with a pair of youths, who walk diagonally from the background past one episode in the direction of the other, is largely foiled. They themselves are so engrossed in conversation that they seem to be oblivious of the miracles of resurrection on the one side and of healing on the other. Only the mechanical qualities of the spatial unity are recogmzed. This essentially non-dramatic use of artificial perspective does nothing to detract from the exploitation of its depth creating qualities. The eye is swept straight into the pictorial space, and the abrupt change of architectural and figure scale gives instantaneous expression to the distance travelled. The very drama of the change of scale itself reveals, however, that the journey has no close connection with the action concentrated in the foreground. Here is the joy of space creation largely for itself— exuberant exploitation of a new-found power.




This scene is now attributed to Masaccio's senior colleague, Masolino da Panicale, who doesn't quite share his gritty sense of reality.





‘The Tribute Money’ on the opposite wall betrays a striking difference in emphasis. Nothing is for itself alone, and everything for the story told in terms of monumental human figures. The threefold action weaves the composition. The receding lines of the perspective hold the eye within the circling stillness of the central galaxy. Christ, the source of action and the centre of the composition, is the focus of the spatial unity. Trees recede into the distance, and the mountains loom and fade into a landscape at once closer and more spacious than any in the art of the preceding centuries. The forms of nature give expression to the monumental calm of the majestic figures. Space surrounds them like the heavy-folded cloak of the apostle on the right. It has its own reality, its own existence. Yet its meaning lies within the figures it contains. So cloak and body, individual and group; so man and architecture, house and landscape, space itself; each, gaining independence and reality, gains new power which may be harnessed in the service of the story.

Smith discusses that story here

As with the text quoted at the beginning of this post, this seems like a good description - but how relevant is it to White's topic, i.e. the treatment of rectangular shapes ?

The space we enjoy seeing is more the result of Masaccio's feeling for it rather than some kind of geometric program.






The architecture in ‘The Tribute Money’, owing its new independence of the figures to its increased structural certainty, takes on fresh importance, both in terms of spatial definition and of compositional control, through its single focus in the head of Christ. At the same time, both in this scene and in that of ‘The Raising of the King’s Son’, it shows its clear subordination to the action by its scale. Masaccio exercises similar control of its extension into depth.

















The simple, shallow, firmly limited space in the scene of ‘The Raising of the King’s Son’ is the monumental counterpart of the carefully controlled complexity of the architecture in the small tondo of the Birth Plate in Berlin.

These are also good examples, as Smith has suggested, of architecture providing a rational regulation of human activity, quite distinct from the mystical settings that came earlier or the turbulent settings that would follow.

The "Raising of the Son of Theophilus" (as it is also called) is a bit cluttered, but that's only because other artists worked on it after Masaccio's death.






The role of the architecture on the walls of the Brancacci Chapel is not confined to its effect upon the composition of a single fresco. It also plays a new part in relation to the spatial content and essential function of the chapel as a whole. The house on the right of ‘The Tribute Money’, framing a separate incident in the action, is beside the altar. In ‘The Healing of the King’s Son’, immediately below, a similar architectural division again enframes a separate action. The enthroned figure of St. Peter praying, with the kneeling circle at his feet, in fact underlines Masaccio’s compositional creation of a sort of choir, or alcove for the altar. Only in ‘The Healing of the Lame Man, and the Resurrection of Tabitha’ does the pattern falter. But in this case the design, and to a great extent the execution, are attributed by many to Masolino rather than to Masaccio.


It is solely through the power of the new perspective, carefully controlled at every stage, that Masaccio is able, at one stroke, to use the architectural features of his compositions as individual frames for the separate elements of a complex action, and as a means for the articulation of the space in which the observer stands, so that its ritual significance and functional divisions gain new emphasis, whilst actually reinforcing the pictorial unity of each composition as a whole.

I'll have to remember to look for this if I ever visit Florence again.

In what is probably the latest of Masaccio’s works in Florence, the fresco of ‘The Trinity’ in Sta. Maria Novella, architecture and perspective play not merely an important, but almost a dominant role in the design. The casual quality of the Brancacci architecture, despite its intricate compositional function, the seemingly effortless relation of the figures to the space surrounding them, give way to something more ambitious. The grandeur of the massive barrel vault, and of the Ionic and Corinthian columns and pilasters, is a new departure. The architectural majesty of the design is only equaled by the calm ability of the figures to retain their rightful mastery. The interaction of the two creates dramatic tension.

The foreshortening of the architecture, in accordance with the principles of artificial perspective, is accurate both in the diminution of the coffering and in the single vanishing point which lies slightly below the plane on which the donors kneel. The space in which the figures stand is rectangular, and the precise depth at which they are placed cannot be determined. The sarcophagus-like platform upon which the figure of God the Father stands is not to be placed against the back wall, or supported upon consoles that project from it. Its upper surface is about four-fifths of the height of the furthest columns from the ground. This, in terms of the foreground columns, is on a level with the chest of the figure of Christ upon the cross. Such a position would, apart from anything else, leave insufficient head-room to contain the figure of God the Father. The considerable masking of the inner columns must therefore be attributed to the low viewpoint in conjunction with the placing of the sarcophagus well forwards in the vaulted space, the ends of its supports being hidden by the standing figures. How far forwards it is impossible to tell exactly. It is equally impossible to say precisely how far back the figures of the Virgin and St. John, and indeed the cross itself, are placed. From the way in which the front line of the floor cuts off the feet of the two standing figures, and the fact that St. John turns sideways, and not backwards, to look at Christ upon the cross, the whole group seems to be at least within the first half of the chapel space, and probably in the first third. There is no reason, on grounds of perspective, for thinking that the relation of the figure of God the Father to the cross he holds is, in any way, either impossible or improbable. The fact that these two figures of the Trinity are approximately the same height would seem to show that they are indeed as closely related as they appear to be, and there is nothing in the fresco to contradict this supposition.

In his footnotes, White alludes to various attempts at reconstructing the space behind the altar as if it were real. How far back are the figures standing? How far is God standing in front of the back wall? White proposes that such questions cannot be answered, though I would suggest that there's no good reason to ask them.

Though he does not mention that the columns on either side remain parallel even as recede into the distance above, and regarding the heads of the figures, there even seems to be a reverse perspective in the vertical axis, as they increase in size in proportion to their distance from the floor, pulling the viewer up into their midst.

Indeed, the figure of God seems to be ominously looming over all - which is, I suppose, what he is supposed to be doing.

As quoted below, White agrees that "foreshortening that would do nothing to enhance the intrinsic value of the central figures is avoided."

But why is he raising this issue at all, if his purpose is only to discuss how artists have depicted geometric shapes ?

Isn't "spiritual quality" outside his area of concern ?




The general accuracy of construction does not mean that Masaccio was prepared to follow rules beyond the limits of their usefulness. This is shown by the varied handling of the foreshortening of the figures. Those of the Virgin and St. John are seen from the low viewpoint of the architecture, greatly adding to the realism of the composition. The undersides of both arms of the cross are likewise visible. But the experiment of ‘The Crucifixion’ in the Pisa Altarpiece is not repeated as a whole. Here there is no foreshortening of the figure of Christ or of that of God the Father. The previous example of the altarpiece proves that this is no error, but a definite intention. The reasons for it are not far to seek. The general foreshortening, consistent with the placing of the fresco, gives a strong impression of reality to the spectator looking upwards at the scene. The unforeshortened setting of the principal figures, on the other hand, has the effect of raising him to their own level, bringing them closer, and, in this particular case, increasing their emotional and apparitional impact. At the same time a foreshortening that would do nothing to enhance the intrinsic value of the central figures is avoided. Here, where a low viewpoint is combined with a relatively high positioning of the figures in question, the distortion involved would have resulted in a bold theatricality which might detract from, rather than intensify the spiritual quality of the scene. The shifting of the viewpoint is a device often used, in various forms, throughout the fifieertth ceitury. The added power to control the onlooker’s attention gained through the use of several points of view within a single composition was of more importance to the artist than the mathematical implications of his action.


In Masaccio’s fresco this controlled manipulation of the new perspective plays an essential role in making it possible for the Eternal, at the apex of the great sloping triangle of figures, to dominate the monumental, architectural space created with the aid of that same science. As soon as this is realized, the analytic mind is able suddenly to comprehend the full artistic value of a thing which the inarticulate eye accepted from the first. It is precisely because the entire central group is not irrevocably anchored to a single, sharply indicated point in space that it can take its place either within the spatial pyramid of figures running into that great cavity which Vasari so admired, or as part of a triangle piling up the surface of the wall. The sloping arms of this plane- stressing triangle continue through the capitals of column and pilaster, forming a St. Andrew’s cross, which ties the massive verticals together and builds up a surface pattern of a strength and severity that is equal to the task of balancing the thrust of mathematically determined, space.


This structural pattern seems to echo the work of Brunelleschi both as an architect, and as the creator of perspective. How much it may also reflect the vision of the sculptor Donatello, whose influence is so evident in the figures, will, perhaps, appear in the discussion of that artist’s revolution of the art of the pictorial relief.





White has discussed this painting as if it were a geo-form abstraction from the 1950's.

What about the figures?

What about the compelling face of Mary as shown above?

Doesn't that fit somehow into the "structural pattern" of the space?

This area of detail would command attention even if, heaven forbid, it were cut off the wall with a chain saw and shipped to an American museum (just like the heads of Boddhisatvas that were cut from shrines in Asia)

But without it, this painting is hardly worth seeing.

***************





BTW - since the vanishing point for all those lines in the vault was placed upon the altar, Here's a book that proposes that: "the invention of one-point perspective is inextricably tied up with the promotion of the Eucharist and belief in transubstantiation during the Renaissance. "

Index

*************************************
"Where I Stand"
Norris Kelly Smith
*************************************

Introduction

The Lost Tavolette

On the Relation of Perspective to Character

Two Allegiances

Perspectives on the Last Supper

An Eccentric Stance (Uccello)

Family and Church

End of the Matter

Epilogue

My Conclusions



****************************************************
John White:
The Birth and Rebirth of Pictorial Space
****************************************************


Introduction

Upper Church of San Francesco, Assisi

Giotto: The Arena Chapel

Giotto: Bardi and Peruzzi Chapels

Early Sienese Masters

Maso Di Banco

Lorenzetti

Late 14th C. Painting and the Meaning of the Picture

The Development of the Theory of Artificial Perspective

Masaccio

Masolino

Donatello and Ghiberti

Filippo Lippi

Illusionism and Perspective

Manuscript Illumination in France

Spatial Design in Antiquity

Present Problems

My Conclusions



****************************************************
Martin Kemp:
The Science of Art: Optical Themes in Western Art

 from Brunelleschi to Seurat
****************************************************


The Science of Art: Introduction

Linear Perspective from Brunelleschi to Leonardo

Linear Perspective from Durer to Galileo

Linear Perspective from Rubens to Turner

Machines and Marvels

Seeing, Knowing, and Creating

Color

Coda



****************************************************
Meyer Schapiro:

Words, Script, and Pictures: Semiotics of Visual Language ****************************************************


The Artist's Reading of a Text

Theme of State, Theme of Action

Frontal and Profile as Symbolic Form

Script in Pictures

Conclusion 


****************************************************
Georg Simmel:

Rembrandt: An Essay in the Philosophy of Art ****************************************************

Rembrandt: The Expression of Inner Life

Individualization and the General

Religious Art

Conclusion

****************************************************
Eric Kandel:
The Age of Insight
****************************************************


Preface

Vienna, 1900, An Inward Turn

The Depiction of Modern Women's Sexuality (Klimt)

The Depiction of the Psyche in Art  (Kokoshka)

The Fusion of Eroticism, Aggression, and Anxiety  (Schiele)

The Top Down Processing of Information

The Artistic Depiction of Emotion

The Beholder's Share

Conclusion




****************************************************
Ernst Gombrich:
The Preference for the Primitive
****************************************************

Introduction

Plato's Preferencs

The Ascendency of the Sublime

The Pre-Raphaelite Ideal

The Quest for Spirituality

The Emancipation of Formal Values

The Twentieth Century

Primitive in What Sense

Conclusion 



****************************************************
The Blue Rider Almanac
****************************************************
 

Franz Marc

David Burliuk

August Macke

Roger Allard

Erwin Von Busse

Obituary for Eugen Kahler

Kandinsky: On the Question of Form

Vasily Rozanov

Preface


****************************************************
Kandinsky : Concerning the Spiritual in Art ****************************************************


Concerning the Spiritual in Art



****************************************************
Sventlana Alpers' "The Art of Describing: 

Dutch Art in the Seventeenth Century"

****************************************************
Introduction

Constantijn Huygens and the New World

Kepler's Model of the Eye

The Craft of Representation

The Mapping Impulse 

 
The Representation of Text

Epilogue

****************************************************
Martin Kemp
****************************************************

Living with Leonardo

****************************************************
Thierry De Duve
****************************************************

When Form has Become Attitude

Presentations

****************************************************
Clive Bell
****************************************************

Clive Bell: Art


****************************************************
Franz Schulze
****************************************************

Made in Chicago : A Revisionary View


****************************************************
Norman Bryson:  Word and Image :

 French Painting of the Ancien Regime
****************************************************

Preface

Chapter One : Discourse, Figure

Chapter Two : The Legible Body: LeBrun

Chapter Three : Watteau and Reverie

Chapter Four : Transformations in Rococo Space

Chapter Five: Greuze and the Pursuit of Happiness

Chapter Eight: David

 

****************************************************

Kermit Champa: The Rise of Landscape Painting in France
Corot to Monet

****************************************************

Two Introductions

Essay by Fronia Wissman

Photography and the Japanese Print

Catalog: Bazille to Corot

Catalog: Courbet to Jongkind

Catalog: Michel to Troyon

Conclusion 

***********************************************

Paul Crowther : The Phenomenology of Modern Art

Deleuze, Bacon,and modern art

Origins of Modernism and the avant garde

Merleau-Ponty's Cezanne

Interpreting Cubist Space

***********************************************

 

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)

CHAPTER VIII

The Development of the Theory of Artificial Perspective

FILIPPO BRUNELLESCHI




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 façade 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.

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LEON BATTISTA ALBERTI




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?

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LORENZO GHIBERTI


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.