I have to thank two short women and a tall man for revealing to me that “axes of near-symmetry” are intimately related to the phenomenon of “orientation constancy”. The tall man was looking over a low wall and he was depicting its top as sloping down from left to right. The short women drew it as horizontal. The fact that the man could see a particular field beyond it that the women were unable to see, meant that he was the only one of the three that was being influenced by what I later came to call the “bakery facade illusion”. The women were right that the top of the wall was horizontal. To find why the man was also right, click on the link below to Chapter 18 of my book “Drawing with Knowledge”. Its title is “Axes of symmetry, recession and the constancies”.
Establishing an eye-line is the first step if you are going to use the the rules of linear perspective for constructing an image. The same is true, if you are using the same rules as an aid to drawing from observation. However, whereas its use in construction is straightforward, its use in drawing from observation is far from it. The purpose of this Post is to explain why. Below you will find a link to “Chapter 16 – Finding the eye-line“. I have also included a slightly edited version of the Introductory to that chapter.
After the session in the studio, we move out into the street. From the demonstrations using the opening window, we have learnt that any straight edge that lines up with the eye-line remains horizontal no matter at which angle it is relative to our line of vision. If we are to make use of this knowledge, we need to find the eye-line. As a general rule, students who come to my school assume that this is easy to do, but the evidence of the drawing they make suggests that they are likely to be deceiving themselves.
Chapters so far published from
Book 1 and Book 2 of “Drawing on Both Sides of the Brain” (Volume 1 of the series of four volumes)
The eye is full of surprises. The biggest ones come from the structure of retina that is situated at the back of it. The purpose of this Post is to provide a link to images and explanatory captions that tell us more about this starting gate of visual processing. At first sight, much of what we find strikes us as bizarre. But, when we delve more deeply, we discover the considerable advantages of the way things actually are. It turns out that nothing would work nearly as well as it does, if things were arranged any differently. The images and their captions will go a long way towards explaining why.
In the process, they will help readers to get a better understanding of how the eye/brain combination makes practical use of the information contained in the ever-changing patterns of light coming into the eye.
The link to the diagrams
Click on the link below to access the images and captions referred to. They are extracted from ‘The Glossary‘ to the four volumes I am in the process of publishing on this website.
Upon leaving the retina, the neural signals travel in two directions. Some go up the optic nerve to the region of the neocortex known as ‘Visual Area 1′. Others take a completely different route that makes contact with the regions of the “Old Brain”. These play a central role in visual perception as we experience it. For example, they play their part in eye movements, spatial awareness, affective responses, multimodal processing, whole-field relations and much besides. Images and captions relating to both these routes will be posted later on this website, in a separate entry, entitled, “Visual Regions in the Brain”.
Images of blood vessels, neurons and and neural processes in the eye.
The human retina contains a very large number of neurons (cells) and a very much lager number of neural of processes providing links between them. It also features a dense network of blood vessels that supply blood to the neural processes. Together these three components make a significant barrier to the passage of any light that strikes the receptors. Until I learnt better, this light-blocking function did not seem to be of much of interest.
What changed my mind was the discovery that the light-sensitive cone and rod receptors that transform light-energy into neural signals, do not face towards the incoming light, but away from it. Consequently, the light coming into the eyes has to penetrate this light-impeding layer of neurons, neural processes and blood vessels, before it reaches the receptors. To add to my surprise, it turned out that the light-receiving end of the receptors is buried in a layer of dark matter. It was some time before I realised how these seemingly bizarre arrangements make possible visual perception as we know it.
The barrier confronting the light that enters the eye
It turns out that the barrier of neurons, neural processes and blood vessels compensates for the fact that the rod receptors are very much more sensitive to light than the cone receptors. The benefit of this state of affairs is that it enables a necessary degree of functional equality between the responses to the incoming light of the two different receptor-types. Needless to say, this equalling up would not take place, if the light striking the less sensitive cone receptors were to be subjected to the same impediments. This explains why the forces of evolution have created a gap in the neuron and blood vessel barrier in front of the region known as the fovea, exactly where the incoming light strikes the cone receptors.
If the equalling up process did not take place, the rod receptors would be bleached out whenever the incoming light was strong enough to activate the cone receptors. The result would be a massive degree of glare-blindness in daylight conditions.
If they were effectively blind, the rod receptors would not be able to participate in daylight visual processing. As a consequence, the neural computations of whole-field relations could take place. One of the many aspects of visual processing that would rendered impossible would be the separation of reflect-light from body-colour. As a result there would be neither colour constancy, nor the use of the information residing in the reflected-light that has been separated out.
If this were so, pretty well all that I have written in my book “Painting with Light” would be nonsense.
Burying the receptors in dark matter
The burying of the light-sensitive receptor heads in the dark matter is easier to explain. It prevents the light from scattering from one receptor to the next and, consequently, reduces blurring.
Some numbers and sizes
One estimate for the number of the light-sensitive receptor cells is in the region of 150 million. Although the precise number of neurons and neural processes in the retina is unknown, it is certainly in the hundreds of millions. All this packs into an astonishingly thin layer (less than 0.5 mm) whose extent can be compared to that of a 10p piece.
If you want a comprehensive account of the component parts and structure of the retina, you could consult the relevant pages of the website of the The National Library of Medicine. You will find them dizzyingly more complex than the grossly oversimplified information given either above or in the ‘Glossary‘ extract.
The purpose of this “Post” is to provide the link (below) to my introduction to “Chapter 15 : The core ideas“, the third chapter of “Drawing with Knowledge” (the second BOOK in the two book volume). The main subject dealt with is how to use the core ideas of Linear Perspective as a guides to looking, when drawing from observation. As far as I know, this is the the only place you will find it discussed at length. A preliminary idea of what this means can be found in first paragraph of the “Introductory” to this chapter (you will find a slightly edited version next, under the title of “Some core ideas introduced“). Further below, you will find links both to all published chapters from “Drawing with Feeling” (the first BOOK in the two book volume) and to earlier chapters of BOOK 2.
As already explained, the rules of linear perspective were developed by Renaissance artists as aids to image-construction. This chapter starts the process of showing ways in which they can be used as a guide to looking. For this purpose a sound understanding of the core ideas that underpin them is necessary. Although many books attempt to provide this by referring to different examples of perspective constructions, using a variety of diagrams, they never really show how these relate (or fail to relate) how we see in the real world. My approach is very different. Eschewing diagrams, it makes use of participatory demonstrations, using real world props. In addition to revealing the core ideas behind the standard rules, these provide a fascinating introduction to some of the seeming anomalies of visual experience.
Few people would disagree with anyone who tells them that objects appear to get smaller as they recede into the distance. This phenomenon is one of two core ideas behind of the laws of linear perspective, as taught in art schools. The other is the influence of the eye-line. If these were all that mattered, there would be a great deal less to write about in this chapter. However they are far from being so. The reason is not only that the crucial role of the picture plane, as the third variable, is too often neglected, in the interests of simplicity. Even more important, from the point of view of the ideas presented in this chapter, is the fact that appearances can be dramatically influenced by the constancies of size, orientation and shape, as well as by the context in which they occur. This is because the constancy phenomena, which are context dependent, push appearances in different, often opposite directions to those predicted by the laws of linear perspective as conventionally taught. The resulting confusion can cause all sorts of problems for those who seek to use them as an aid when attempting to make accurate drawings from observation. This chapter shows how interactive demonstrations can be used to help people understand the reasons why. Subsequent chapters both continue this process and suggest many practical ways of using the knowledge that will be made available.
Two views of the Chateau Corduries, followed by a question,
A question: “How do you change the size of the château as seen from the studio, without leaving the studio or without using a magnifying glass?”
Chapters from BOOK 1 and BOOK 2 of “Drawing on Both Sides of the Brain” (Volume 1 of the series of four volumes)
The purpose of this “Post” is to provide the link (below) to my introduction to “Chapter 14 : Linear Perspective“, the second chapter of “Drawing with Knowledge” (the second BOOK in the two book volume). The main subject dealt with is uses and abuses of Linear Perspective. The chapter explains the purpose for which the rules the rule of linear perspective were developed and how over the years artists and teachers came to use them for other purposes for which they are not suited. It also explains how the rules of linear perspective can be used in new ways. A preliminary idea of what this means can be found in first paragraph of the “Introductory” to this chapter, which I have included below. Also see below for links to all published chapters from “Drawing with Feeling“, the first BOOK in the two book volume.
“Introductory” – from Chapter 14 : Linear perspective
Academic tradition divides the subject of “perspective” into two aspects, known as “aerial” and “linear”. Aerial perspective concerns colour changes due to the influence on appearances of atmospheric particles situated between the eye and an object being viewed at a distance, and is dealt with in a separate volume. In this book attention will be confined to linear perspective. Moreover, to avoid misunderstandings, it is important to stress that no attempt will be made to compete with the many existing texts on this subject which demonstrate that, when properly applied, the well-known laws can enable the construction of moderately realistic images without the need to actually look at anything. As far as I know there is nothing of interest to add to these, although, a great deal needs modifying in many of the texts on the subject which regrettably give us oversimplified and therefore misleading versions of this complex and elegant subject. Rather, in this volume, the laws of linear perspective are treated in a completely novel way: not as a set of instructions for the placement of lines on but as a tool for guiding looking strategies. This transformation is achieved by placing them in the context of ideas coming both from 19th century research into visual phenomena and from much more recent discoveries relating to the functioning of eyes and brains. In PART 2, the subject of anatomy will be treated in an analogous way for analogous reasons.
Some images relating to the theme of linear perspective
A list of chapters from “Drawing with Feeling“, book 1 of “Drawing on Both Sides of the Brain“
The purpose of this ‘Post’ is to provide the link (see below) to my introduction to “Drawing with Knowledge”, the second BOOK in the two book volume (See below for links with the published chapters of “Drawing with Feeling“, the first BOOK in the two book volume). The two main subjects dealt with are Linear Perspective and Anatomy.
This post is to provide a link to Chapter 30, “Practical applications”, the penultimate chapter of my book “Painting with Light and Colour”. As explained in its “Introuctory”, This suggests sixteen exercises: The first eight of these are designed to make clear the practical value of ideas presented in the chapters dedicated to “painting with colour”. The second eight bring in ideas found elsewhere, not only in the part of this volume dedicated to “painting with light”, but also in the separate volumes, “Drawing on Both Sides of the Brain” and “New Perspectives on Creativity”.
Physics books tell us that colour can be defined by the three variable of “hue”, “saturation” and “lightness”. However, as explained earlier, if we are to consider whole field colour relations and their effect tn picture perception, the fourth variable of “texture” must be added. As a result, the definition of “colour” must be stretched to include achromatic elements. The exercises in Chapter 30 keep this fourth variable and its implication for achromatic images in mind.
The purpose of this Post is to provide a link with Chapter 29 of my book “Painting with Light and Colour“. Its focus is on the nature of I have been calling “experienced reality”. Here I will introduce it with a slightly edited extract from the “summing up” at the end of the chapter.
How far does a combination of this chapter and earlier ones help us to pin down the nature of what I have been calling “experienced reality”? I am afraid the answer has to be,“very little”, for what we mean when we use the word “see”, will always remain inherently elusive. There is no escaping the fact that this intimate aspect of our daily lives is in constant flux. First, we are confronted with one of the most fundamental truths of visual processing, namely that, in order to look at anything, we have to take it out of context. Second, we find that, when we do so, the object of our attention is subject to the ‘constancies’, a state of affairs which catastrophically disrupts whole-scene-relations. Third, the only way of approaching the task of finding out what these relativities actually are is by means comparative looking. True, this provides us with a succession of instances of what, in some senses, can be called reliable information about differences. But it only does so at the expense of finding a new starting point for each comparison, and this is a manoeuvre that entails resetting the whole system to what is almost certain to be a different lightness range.
One thing this inherent instability of visual perception means is that, when we try to analyse a scene (including if it is a painting), we will be facing a problem in some ways analogous to representing running water with a still image. No doubt this is what made Cézanne describe painting as “So damned difficult”.
But, perhaps finding a definitive solution is not what we really want. As Robert Browning wrote, “Man’s reach should exceed his grasp or what’s a heaven for?” The advantage to artists of the ideas presented in these books is that they can at least help us struggle fruitfully towards this goal. It may be unattainable but, as many of us can testify, groping our way towards it can be a richly rewarding experience. Maybe, this is why Cézanne followed his statement about the difficulty of painting with the heart felt assertion, “I want to die painting.”
The purpose of this Post is to provide a link to “Synthesis of colour ideas”, Chapter 28 of my book, “Painting with Light and Colour”. In combination with the next chapter, its role is to prepare for the practical applications of the ideas presented in Chapter 30. It brings together a number of the more important proposals found in both this book and the book on drawing, “Drawing on the Both Sides of the Brain”. In particular, ones relating to:
The history of artistic thought and practice in Europe, since the Italian Renaissance.
The evolution of the science of visual perception, from its origins in the middle of the Eighteenth Century to the present day.
Venetian Colourists not colourists
Before the arrival of this new science, artists, following the lead of the “Venetian Colourists”, had learnt a lot about introducing effects of light into the illusory pictorial space that they sought to create in their paintings. They had arrived at the conclusion that mastery of this ephemeral aspect of depiction depends on control of “lightness relations”. To do this they adopted the rule that there should be no repetitions of lightnesses across the entire picture surface. Paradoxically, it follows from this that the innovation which led to their being known as “colourists” had nothing to do with two of the three variables that are usually thought to be necessary to define colour, namely “hue” or “saturation”. Perhaps a better name for them would “Venetian lightists”.
The purpose of this POST is both to introduce and provide a link to “Cast Shadows”, Chapter 26 of my book “Painting with Light and Colour”.
A fundamental difference
The book as a whole is full of what both the Impressionists and their academic predecessors called “rules of nature”. However, though referring to the same body of phenomena, these two schools of painting viewed them differently: Whereas the Academies seem to have wanted artists to follow them slavishly, the Impressionists were apt to question their value. For example, a quotation from Claude Monet makes his position clear : “I only know that my aim is to convey what I experience before nature and that most often, in order to succeed… I have to totally forget the most elementary rules of painting, if they exist that is.” Which of the two was right? My answer is “both of them”.
One of the reasons for Monet’s irreverent attitude to the rules was almost certainly a result of being faced with consequences of the “constancies”, those brain-created distortions that mean rules concerning “measured reality” far from always correspond to actual experience. However, the particular focus in Chapter 26 is on the rules of “aerial perspective”, which derive from the fact that the depth of atmosphere between the viewer and the object of interest can influence the way we perceive it. More precisely, they state that the deeper the atmospheric screen between the object and our eyes, the more desaturated the colour of objects seen through it .
However, this rule oversimplifies actual appearances, for in every scene there are a multiplicity of other factors in play, all of which can interfere with it to such an extent that it becomes worse than useless. The only way of finding out the truth in any one situation is to follow Monet’s lead and do your best to find out the actual hue, saturation and lightness relationships in the particular scene you are in the process depicting.
The focus of this chapter
In Chapter 26, the main focus is on one of the multiplicity of “other factors” and the very different rules that apply to it. It relates to our perception of “cast shadows” . What we find is that they regularly influence appearances in ways that run counter to the rules of aerial perspective. As in the previous chapter, an understanding of Mack Bands can help us to discover how and why.