Developing pictures, developing minds: Lots of heuristics but no algorithm

by Constance Milbrath

Cambridge, U. K., Cambridge University Press, 1998 421pp. ISBN 0-541-44313-X $59.95

Who is not delighted by children's drawings? Or amazed by the abilities shown by some kindergartners who can draw perfectly recognizable Matisse-like figures when their peers are producing tadpoles? Little wonder we now have a mountainous literature about children's pictures.

For many years Constance Milbrath studied the drawings of talented and average children, from infancy to high school, as a Resident Scientist in a MacArthur program. In this book she offers us an eye-opening look at their works. This is the most scholarly, comprehensive review of children's artwork to date.

Milbrath speculates on what makes the difference between drawing talent and average ability. Her views reflect much of the best of today's theorizing. But I think her conclusions are often wrong in a helpful way and what Milbrath's ambitious and very detailed undertaking may be showing us, ultimately, is that our theories in this area must be piecemeal.

From outline to constancy

Milbrath's story, like all good tales, has a startling beginning. Almost unbelievably (but I do believe), she presents us with drawings by 2-year-olds that remind us of Thurber. Toddler Peregrine drew a mother, a baby and himself. The figures are drawn by continuous lines that outline the referent. Most two-year-olds just scribble and the occasional one can draw a circle, add some lines as legs and perhaps dots for eyes and a line for a mouth. By four or five years old, children Milbrath identifies as talented are remarkable. At 4, Peregrine drew a harpist, and a lady with an Elizabethan pointed hat. Kate drew an easily-identified elephant, a mouse, a juggler in costume, and a lady in a long dress with her nose in the air. A four-year-old girl drew the 'frisco Bay bridge. At 5, Hondo drew trucks and used oblique parallels to show the sides in depth. Claire drew a baby in a crib, with flowing hair overlapped by an outstretched arm, surrounded by a baby-bottle, a doll, a Xmas tree, and more. Milbrath points out that the preschoolers' pictures are often well composed. Kate uses juggled objects on the right to "balance" the juggler's body on the left. Claire's baby in the crib is large and centered and has a border of smaller objects on the left and right.

Outline, Milbrath, concludes, is something the talented children use especially effectively: "talented children quickly caught on to the idea that a line should stand for an edge and a plane for a surface" (p. 357). This much is innocuous, and follows from the observations of two-year-olds and kindergartners. But Milbrath extends this induction, claiming most children do not catch on easily to outline (p.181-2), and indeed by adolescence only "some of the less talented children" have done so (p. 357).

Schemas for objects are drawn by all preschoolers in an "object-centred" way at first, but the talented ones move on rapidly, in two ways. First, they develop a large vocabulary of schemas, many schemas for people, for example. They are often based on more accurate recall than is common in children. Occasionally this is evident in the proportions of figures. In a sample of drawings of the human figure by talented children aged 3-6 the mean leg-to-body ratio was found to be .46 (p. 113). The correct ratio is indeed .46! Second, the schemas of the talented children show they caught on to outline, and edges of objects, and frontal surfaces, all of which are "viewer-centred".

Perception of an object entails a bias towards discovering the object's properties while ignoring "the ephemeral specific view" (p.365). In a viewer-centred representation some parts of the object are shown as nearer, and others as farther. The talented children copy a "half a dozen or more" (p.370) salient viewer-centred features of the object in their schemas where less-talented children target only one or two. To show an object in a viewer-centred way we can show overlap of parts, put shadows on the object, attempt side, back or three-quarter views, and include foreshortening and convergence. We can also restrict our viewpoint to just a single one and add a ground plane.

As a result of tackling many viewer-centred features in one drawing the child is forced to consider issues of shape, constancy and projection. The result is talented kids are somewhat in advance of the typical child in the use of geometrical matters such as informal perspective, foreshortening and convergence, but the rule of thumb is by only about two years.

Advances in the talented child's informal use of perspective are made piecemeal, just as they are in typical children, and in the same order. Talented Kate for example gradually improved her ability to show figures rotated by various amounts over a period of two years. Her first recorded attempt to show a figure three-quarter rotated was at age 6. Also, she used first one indicator of perspective at a time, and only later combinations of two or three.

Children's drawings are usually from memory, rather than inspection of a model. This internal representation is static until 7 or 8 and with Piagetian concrete operations the child "gains the ability to imagine objects in motion" (p. 141), that is to operate on shapes mentally. The child knows the object's shape is conserved during these operations because they are reversible: reverse the motion and the object returns to its original state.

Prior to this conservation the child is restricted to stereotypes that show the object's shape without misleading ephemera of rotation, such as people from the front and dogs from the side.

Outline shows corners and edges

Milbrath's theory is that outline allows viewer-centred schema, and they in turn foster projective geometries. To develop an alternative account, perhaps we should be like Christopher Robin, and begin at the beginning and go on from there.

Outlines show boundaries of flat and curved surfaces e.g. convex and concave corners, occluding boundaries of balls and occluding edges of rooflines. Children see what is depicted in outline drawings before they can speak or draw. Indeed, less-talented children use outline for edges of surfaces in their simple drawings, Milbrath's own figures show. Her displays reveal use of outline by less-talented children of every age up to adolescence (e.g. p. 94, Figure 3.10a, aged 4: the chin of a person; p.119, Figure 4.2b, age 5; person's profile; p.123, Figure 4.5b, age 6, arm drawn as two parallel lines: p. 159, Figure 5.1b, age 7, brows of hills).

Outline works well because all black-white boundaries, static or kinetic, are inherently ambiguous. They simply indicate "there is a change here". Consider a horizontal straight edge made by a white region on the top and a black region on the bottom. Is it flat, like wallpaper? Or a nearby black wall against a distant white sky? Let there be white texture spots flowing down from the straight edge (accreting), and crossing the black region. Does this white-texture accretion boundary remove ambiguity about what is near or far? I'm afraid not. This could be a dark speckled surface (a fish) moving out from behind a white foreground object (a rock). Or it could be foreground snow falling from a white, winter Attica sky, and only becoming visible against a black background prison wall.

Outline reaches the same visual command centre as boundaries projected by surface corners, occlusions, and texture accretion. This command centre is so basic that human perception of the environment is unthinkable without it. All children have this centre. If so, this is not a discovery many less talented children fail to make.

If this argument is correct, and all of Milbrath's children use outline readily, then they all have some use of projective geometry and viewer-centred features in their first schemas: they use lines to depict occlusions, and occlusion indicates where the viewer is. An object-centred outline picture is a contradiction.

Schema, reversibility and viewer-centred shapes

While I object to Milbrath's ideas about outline, I think her views on schema are often well grounded. But they deserve to be expanded. Let me explain.

There is no single plan for patterns one can make from lines. Therefore, there is no algorithm of development to bring to bear here. There are only heuristics, rules of thumb.

Consider the "many routes to Rome" rule of thumb.

You can learn to draw a horse indefinitely many ways. Did you learn to draw a dog first? Or a cat? Or a pig? Maybe you never drew a horse till you were 30. Maybe then you copied a model. Also, schemas can be taught to children with comparative ease. Very detailed schemas can be taught to patient young children by teachers, and children in a given class room pick up schemas from each other, the media in general, etc.. There are many theories about schemas, but all of them are makeshift heuristics since there is no fixed, limited set of shapes and no fixed order in which a set has to be acquired in perception or cognition. Our pattern perception and cognition mechanisms are general, and revisable, not fixed and immutable, otherwise we could not learn to read.

Milbrath is surely correct in asserting that talented children come early to the use of many devices for viewer-centred matters, including devices such as overlap, shading and projective geometry. She is also surely correct in asserting children operate on their knowledge of object shapes and orientations. But I think her ideas about how this works need revision.

Her proposal is that concrete operations, and reversible operations, are important for drawing because they help with mental stability and object constancy.

I am afraid the claim that reversibility is information that an object's properties remained constant through an operation is false. Imagine a bar is heated, and then cooled. After heating and cooling it returns to the same length. Was it the same length all along? No. When heated it was longer.

I change into my swim gear, swim, dry off, get back into street clothes. I am now wearing the same clothes as at the start. Does this mean I wore my street clothes all along? No. I did not swim in my shirt.

An object is constant if properties that define the object's features (shape and size, etc.) do not change while ephemera change. If so, constancy is achieved by distinguishing relevant from irrelevant properties, and by knowing how to assess the relevant properties to get information about shape, size, etc.

What we do with objects as we change our imagined vantage point is ask ourselves what is to the left, the right, up and down, what is more curved in its projection, or less curved, what surface has become aligned with our eye and so is now just a line, and what surface has gone behind another. This series of questions is not especially easy to answer, if it is applied to objects with a lot of features. So progress in the skill of changing our vantage point is acquired relatively slowly, by practice. If there are only a few relevant features to the set of objects (such as front and back), and only one dimension is being changed (such as moving horizontally around to be in-back of an object), the task is easy for preschoolers. If it involves several objects and several vantage points to be distinguished, it is harder, and may challenge adults.

Do preschoolers only have static images? No, surely a child can see and imagine a door opening and closing, or food being eaten, or running down a hill.

Images are not 'whole objects' in our heads like little statues to which operations such as rotations can be applied holus bolus. Rather, drawings are likely controlled by knowledge of features of objects. Mental rotation likely entails realizing what one key feature would project to a certain vantage point, and then what implications follow for a neighbouring key feature, then another neighbour and so on. Turn one feature of a statue and the rest has to go along. Turn one feature of an image and you still have to twist the others.

Foreshortening and convergence

The idea that rotation and projective geometry comes late to less talented children, if it comes at all, needs to be revised, though likely Milbrath's idea that talented children tend to be two or so years ahead is spot on. From the age of 8 or 9 perfectly average children draw the receding sides of cubes as about 60% of the size of frontal edges of cubes. This is foreshortening. The reason is that this makes the front and receding edge look as if they are the same size. That is, perceptual effects often drive the drawings children make. It is a mistake to attribute what children are doing in dealing with projection to knowledge of laws of projection. The laws of projection do not stipulate 60% as the correct and best ratio. They allow an infinite number of percentages in foreshortening, all the way to 0% as a limit (and of course a much larger per cent than 60% at the other extreme).

Milbrath's point about the advanced drawings by talented children falls into place here, neatly. Hondo, a talented child, foreshortened a rectangular object (a panel truck) at age 5 by about 60% (p. 184, Figure 5.7b).

What is relatively late in children's drawings is effective use of convergence, i.e. depicting two receding edges of parallels as coming together at a point. We can safely say that proper, formal use of convergence is not on our everyday developmental trajectory since it was discovered only once in history, in Italy, in the Renaissance, and every culture using perspective fully and correctly got it from that event.

However, a kind of convergence is widespread culturally and used by children. Objects in the distance make small angles at our vantage point. Many drawings from cultures not using formal perspective convergence and from children in Western cultures use large figures to show nearby objects and tiny figures to show far-off objects (p. 236, Figure 6.9, a landscape by Joel age 9). And of course in vision it is perfectly easy to see that a truck in front of us on the highway, taking up most of our view, subtends a large angle at our vantage point, but a tall building in the distance -- perhaps it is our hotel, we might be judging -- makes a tiny angle, and is hard to make out.

So it is false to assert that perception ignores ephemera of our vantage point. Sometimes the relations to our vantage point are quite plainly obvious.

Also, vision allows us to see the differences in angular projection fairly easily, even if the differences are small, if we take the trouble to align objects. This is why artists hold their brushes vertically, at arm's length, and line them up with objects they want to paint on the canvas. The fact that the distant flagpole subtends say 30% of the brush is immediately apparent.

I do not wish to sweep past Milbrath's point about metric size (size in cm) interfering with judgments of size of angular projection. The difference in the angle subtended by our hands can be 100% and be invisible despite full attention. Try this: pose the left hand vertical, palm towards you, at arm's length, off to your left side. Now bend your right arm and pose your right hand vertical, palm towards you, but off to your right side. The right hand is say half an arm's length distance from your eye. Your arms should be at least 90 degrees apart. Now try to judge the relative angles made by the two hands. They'll look almost equal. In fact one is double the other. (To check this, slowly bring your arms together until the hands almost line up, but always keep one hand at arm's length and the other at the bent-arm distance. The fact that one hand is twice the angular size of the other will become increasingly plain, especially if you close one eye and make the judgment monocularly.)

The hand demonstration shows some conditions (arms apart) make us judge angular sizes (one hand subtending twice the other) as if they were metric sizes (the hands are the same size in cm). So perception does make judging relative angular subtense hard, sometimes.

Let us now consider what happens when children do become aware of projection and try to use it to draw. Is there some natural or necessary order of events in development? Foreshortening of a side of a cube is obvious as it rotates. Convergence of railroad tracks as they go to the horizon of a flat plane is obvious too. So both foreshortening and convergence have conditions that would readily result in their use. Neither has absolute priority empirically. But foreshortening is a part of every object rotating. As surfaces rotate they go from face-on to zero and out of sight. Children mostly draw objects, not landscapes. So for empirical reasons foreshortening may have priority in development. Further, we could foreshorten a line of Hondo's trucks or a railroad track without using convergence, but we cannot apply convergence to a point to a line of trucks or to railroad tracks without running into the need for foreshortening. So logically as well as empirically foreshortening is simpler and likely developmentally prior to convergence.

Drawing devices are independent

I wonder whether any other drawing devices have any kind of principled algorithm for development. Overlap, shadowing, lining up objects along a ground line, or vertically, may be quite independent methods of showing depth, a jumble of devices. Perhaps a moment's consideration of their bases will tell us whether to expect an algorithm of development or not.

Overlap is indicated by T junctions. The crossbar shows the overlapping surface. The stem is the border of the overlapped object. Alas, a T can arise for reasons that have nothing to do with overlap. (Three surfaces abutting form a T. Also, the two top surfaces of two cubes put together offer two T junctions. Also, a string hanging from a bar forms a T.) So the device used in overlap does not have status irrespective of its context. Rather, what makes a T be an overlap is the pattern or schema in which the T is found. Therefore, overlap is likely to be part and parcel of schema development, not a distinctive device on its own merits.

Shadow involves matters of degree. A few simple dark patches on a sphere can help suggest its form nicely. High-contrast photographs showing nothing but the complex attached shadows on faces sometimes are very highly recognizable. A few artists aspire to capture this level of shadow structure. Children will attempt simple shadow structure. But since shadows range from simple to complex there is no well-defined age at which we have grasped shadowing.

Lining-up objects is something children do to draw things such as 'my family.' Lining up from baby to parents is helpful. Lining-up is also a depth device, using order in the horizontal to suggest order in depth. It follows from the rule "use any convenient dimension spatially to stand for any another dimension (age, depth, etc.)". Hence, it is diagrammatic. It is not strictly speaking a drawing stage, driven by viewer effects, but follows from the ability to put two sets in correspondence.

Conclusion

I have suggested overlap is not a distinct module, but to do with ambiguous T set in a schema. There is no age where children master shadows. Lining up is more to do with diagrams than drawings. Schemas have no particular order, bar including more and more features. Outline is available to all children, via perception, before they can draw. Viewer-centred features are what all children draw when they use outline at any age.

If I am correct, there is no core to drawing from which components develop in a well-ordered sequence, sometimes quickly (as Milbrath convincingly shows in the talented) and sometimes slowly (in the lesser). Drawing is a hodgepodge of development, a set of heuristics not an algorithm.

Drawing is related closely to perceptual effects. But each effect is sui generis. They are wonderful effects, and taken as a composite group they can achieve superb combinations. And when we see young children adroitly put several together the results can be highly expressive and communicative. But there is no possibility of a genuine overarching theory here, just bits and pieces of a theory: three such bits I suggest are that foreshortening precedes convergence for empirical and logical reasons, the geometry which is the basis for both foreshortening and convergence, namely full proper, polar perspective, is not on our everyday developmental trajectory, and on a variety of independent drawing devices the talented are generally ahead across the board.

Information about author

Title of the book reviewed:

"Patterns of artistic development in children: Comparative studies of talent", Cambridge University Press, Cambridge, UK, 1998

$59.95

xvi + 421pp

ISBN 0-541-44313-X

Author's name and affiliation:

Constance Milbrath

Department of Psychiatry

University of California at San Francisco

San Francisco

Home phone: 415--547--6408

Office phone: 415--476--7024

Fax:

Email: milbrath@macpsy.ucsf.edu

INFORMATION OBTAINED FROM APA MEMBERSHIP REGISTER

Information about reviewer

John M. Kennedy

University of Toronto,

1265 Military Trail,

Toronto Ontario M1C1A4, Canada

Home phone: 416--444--1856

Office phone: 416--287--7435

Fax: 416--287-- 7642

Email: kennedy@scar.utoronto.ca