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design& THE


The absence in art of a well-formulated

Depending on the nature of the problem,

and systematized body of literature

some or all of the psychological and

makes the problem of teaching a

intellectual factors implicit in game-

perplexing one. The subject is further

playing are equally implicit in successful

complicated by the elusive and personal


nature of art. Granted that a student’s ultimate success will depend largely on his natural talents, the problem still


remains: how best to arouse his curiosity,


hold his attention, and engage his


creative faculties.


Without specific formal limitations, without the challenging possibilities of introducing the element of play, both teacher and student cannot help but be bored. Without the basic rules or disciplines,

bored. The product may take the form of

however, there is no motivation, test of

a superficial (but sometimes “professional


skill, or ultimate reward—in short, no

looking”) literal translation of the


game. The rules are the means to the

problem, or of a meaningless abstract

large extent, on two factors: the kind of


end, the conditions the player must

pattern or shape, which, incidentally, may

problem chosen for study, and the way in


which it is posed. I believe that if, in the


statement of a problem, undue emphasis


in much the same way. “Limited means,”

Similarly, there are badly stated problems


says Braque, “beget new forms, invite

in basic design, stressing pure aesthetics,


creation, make the style. Progress in art

free expression, without any restraints or

Conversely, a problem with defined


does not lie in extending its limits, but in

practical goals. Such a problem may be

limits, implied or stated disciplines which


knowing them better.”2)

posed in this fashion: arrange a group

are, in turn, conducive to the instinct of


play, will most likely yield an interested

Unfortunately, in some of our schools

see fit, using any number of colors, to


little attempt is made to guide the

make a pleasing pattern. The results of


student’s thinking in a logical progression such vagaries are sometimes pretty, but


from basic design to applied design. We

mostly meaningless or monotonous. The

are all familiar with the so-called practical

student has the illusion of creating great

problems which attempt to duplicate the

art in an atmosphere of freedom, when

conditions of industry-the atmosphere of

in fact he is handicapped by the absence

Through trial and error, I have found that the solution to this enigma rests, to a

is placed on freedom and selfexpression, the result is apt to be an indifferent student and a meaningless solution.

student and, very often, a meaningful and novel solution.

understand thoroughly, and work with, in be justified with enthusiasm but often order to participate. For the student, the

with specious reasoning.

limits of a well-stated problem operate

of geometric shapes in any manner you

Of the two powerful instincts which exist


in all human beings and which can be


used in teaching, says Gilbert Highet, one


is the love of play. ”The best Renaissance


problems are frequently stated in the

ideas, make playing with those ideas


broadest terms with emphasis, if any, on

possible, work absorbing, and results

to the play-principle. They made games


style and technique in advertising, rather


out of the chore of learning difficult


subjects—Montaigne’s father, for


instance, started him in Greek by writing


Without specific formal limitations,

the possibilities of relationships:


without the challenging possibilities of

harmony, order, proportion, number,


introducing the element of play, both

measure, rhythm, symmetry, contrast,


teacher and student cannot help but be

color, texture, space.

teachers, instead of beating their pupils, spurred them on by a number of appeals

the letters and the easiest words on playing cards and inventing a game to play with them.”1)

the advertising agency, for example. Such of certain disciplines which would evoke

than on interpreting advertising in terms of visual design principles.

The basic design problem, properly stated, is an effective vehicle for teaching

It is an equally effective means for

If possible, teaching should alternate

exploring the use of unorthodox

between theoretical and practical

materials and for learning to work within

problems-and between those with

specific limitations.

tightly stated “rules” imposed by the

To insure that theoretical study does not

teacher and those with rules implied by

end in a vacuum, practical applications

the problem itself. But this can happen

of the basic principles gleaned from

only after the student has been taught

this exercise should be undertaken

basic disciplines and their application.

at the proper time (they may involve

He then is able to invent his own system

typography, photography, page layout,

for “playing the game”. “A mind so

displays, symbols, etc.). The student

disciplined should be both more abstract

learns to conceptualize, to associate,

and more concrete. It has been trained in

to make analogies; to see a sphere, for

the comprehension of abstract thought

example, transformed into an orange,

and in the analysis of facts.”4)

or a button into a letter, or a group of letters into a broad picture. “The pupils,”

There are many ways in which the play-

says Alfred North Whitehead, “have got

principle serves as a base for serious

to be made to feel they are studying

problem-solving, some of which are

something, and are not merely executing

discussed here. These examples indicate,

intellectual minuets.”3)

I believe, the nature of certain disciplines

Without the basic rules or disciplines, however, there is no motivation, test of skill, or ultimate reward—in short, no game.

and may suggest the kind of problems which will be useful to the student as well as to the teacher of design.

The crossword puzzle is a variation

one square, and one rhombus. The rules

on the acrostic, a word game that has

are quite simple: rearrange to make any

been around since Roman times. There

kind of figure or pattern.

have been many reasons given for the popularity of the game. One is that

Here above is one possibility. Many

it fulfills the human urge to solve the

design problems can be posed with

unknown, another that it is orderly, a third

this game in mind, the main principle

that it represents, according to the puzzle

to be learned being that of economy

editor of the New York Times, “a mental

of means-making the most of the least.

stimulation… and exercise in spelling and

Further, the game helps to sharpen

vocabulary-building”.5) But the play in

the powers of observation through the

such a game is limited to finding the exact

discovery of resemblances between

geometric and natural forms. It helps the

word to fit a specific number of squares in

student to abstract: to see a triangle, for

a vertical and horizontal pattern. It allows

example, as a face, a tree, an eye, a nose,

for little imagination and no invention or

depending on the context in which the

aesthetic judgment, qualities to be found in abundance, for example, in the simple children’s game, the Tangram. The Tangram is an ingenious little Chinese toy in which a square is divided

AlI this work on proportioning and measures is the outcome of a passion, disinterested and detached, an exercise, a game.

pieces are arranged. Such observation is essential in the study of visual symbols. This drawing is reproduced from the first volume of Hokusai’s Rapid Lessons in Abbreviated Drawing (Riakougwa Hayashinan, 1812). In the book Hokusai

into this configuration. It consists of

shows how he uses geometric shapes

seven pieces, called “tans”: five triangles,

as a guide in drawing certain birds.

This exercise may be compared to the

potentialities is evident from

Tangram in that both use geometric

the numerous references

means. The Tangram, however, uses

to the game and play

geometry as an end in itself to indicate

in his book, such as:

the grid calls for the ability to classify and organize miscellaneous material, with sufficient foresight to allow for flexibility in handling content which may, for

or symbolize natural forms-whereas

“AlI this work on

one reason or another, be altered. The

Hokusai uses it as a clue or guide to


grid must define the areas of operation

illustrate them. In the artist’s own words,

and measures

and provide for different techniques,

his system “concerns the manner of

is the outcome

pictures, text, space between text and

making designs with the aid of a ruler

of a passion,

pictures, columns of text, page numbers,

or compass, and those who work in this

disinterested and

picture captions, headings and other

manner will understand the proportion

detached, an exercise,

miscellaneous items.

of things”. This character for the word “tan” (sunrise) is designed within an imaginary grid. Geometry functions here in a manner

most useful,

similar to the previous illustration, namely

because it prevents rigid symmetry and

as a guide to filling the space correctly, but

helps to achieve balanced asymmetry.6)

not to produce a geometric pattern.

At the same time it makes the writer aware of negative and positive spaces. Each part

The Chinese character is always written in

of the character touches one of the nine

an imaginary square. The ninefold square,

squares, thus achieving harmony between

invented by an anonymous writer of the

the two elements and the whole.

T’ang dynasty, has been employed as the

The playfulness and humor in the production of some of these compositions in no way detracts from the end result—a serious work of art. a game.”9) Further, he goes on to say,

Here is a simple grid system for a

“for if you want to play modular…”10)

booklet. Devising such a grid involves

Within this rather simple discipline the

two creative acts: developing the pattern

calligrapher is able to play with space,

In comparison to most so-calIed systems

that is suitable for the given material

filling it as he feels would be most

of proportion, the Modulor is perhaps

and arranging this material within the

appropriate. The composition of Chinese

the least confining. The variations,

pattern. In a sense, the creative ability

characters, says Chiang Yee, “is not

as wilI be seen from this ilIustration,

required for the former is no less than

governed by inviolable laws… however,

are practicalIy inexhaustible (and this

that for the latter, because the making

there are general principles which cannot

example utilizes only a very limited

of the grid necessitates analyzing

be ignored with impunity”.7)

number of possibilities). If, however, the

simultaneously all the elements involved.

system presents any difficulties which

But once it is evolved, the designer is

The Modulor is a system based on a

happen to go counter to one’s intuitive

free to play to his heart’s content: with

mathematical key. Taking account of the

judgment, Le Corbusier himself provides

pictures, type, paper, ink, color, and with

human scale, it is a method of achieving

the answer: “I still reserve the right at any

texture, scale, size and contrast.

harmony and order in a given work.

time to doubt the solutions furnished by the Modulor, keeping intact my freedom

The grid, then, is the discipline which

In his book, The Modulor, Le Corbusier

which must depend solely on my

frees him from the time-consuming

describes his invention as “a measuring

feelings rather than on my reason.”11)

burden of making certain decisions

tool (the proportions) based on the

(dimensions, proportions) without which

human body (6-foot man) and on

Like the architect’s plan, the grid system

fruitful and creative work is extremely

mathematics (the golden section).

employed by the graphic designer

difficult. He can move directly to

provides for an orderly and harmonious

those aspects of the problem in which

A man-with-arm-upraised provides,

distribution of miscellaneous graphic

individual expression, novel ideas, and

at the determining points of his

material. It is a system of proportions

freedom of choice are essential.

occupation of space-foot, solar plexus,

based on a module, the standard of

head, tips of fingers of the upraised

which is derived from the material itself.

The grid system has as many detractors

arm-three intervals which give rise to

It is a discipline imposed by the designer.

as it has adherents. It has been

a series of golden sections, called the

condemned as stifling, rigid and cold.

Fibonacci series.”8) (1, 1, 2,3,5,8, 13, etc.)

Unlike the Modulor, it is not a fixed

But this is to confuse the product

The Modulor is a discipline which offers

system based on a specific concept of

with the process. The grid does not

endless variations and opportunities for

proportion, but one which must be

automatically insure an exciting product.

play. Le Corbusier’s awareness of these

custom-made for each problem. Creating

The designer must still exercise all the experience at his command, discretion, timing, and a sense of drama and

Devising such a grid involves two creative acts: developing the pattern that is suitable for the given material and arranging this material within the pattern.

sequence. In brief, the intelligent designer

or standard from which the plan of the

will recognize that the grid can help him

house grows. Edward S. Morse, in his

achieve harmony and order, but also

book, Japanese Homes, describes the mat

that it may, when and if necessary, be

system as follows: “The architect invariably


plans his rooms to accommodate a certain number of mats; and since these mats

In addition to those already discussed,

have a definite size, any indication on

variations of the geometric plan are to be

the plan of the number of mats a room

found, among other places, in Japanese

is to contain gives at once its dimensions

architecture, modern painting, and in

also. The mats are laid in the following

Byzantine masons’ marks, such as the seal

numbers: two, three, four-andone-half,

at left. This seal “employs a mathematical

six, eight, ten, twelve, fourteen, sixteen,

key as its design basis. The thick lines

and so on.”13) This illustration shows the

represent the mark, the thin lines

“plan” of a four and-one-half mat room.

represent the ground lattice which allows

Once the outer dimensions of the house

an infinite number of combinations.”12)

are determined, the mats, together with

The geometric scheme is the discipline

the Japanese system

in which the designer works. Designs

of sliding doors, give

stemming from such a scheme are limited

complete flexibility

only by his imagination.

in the arrangement and number of

Much of the painting of Josef Albers is

rooms. A perfect

based on this geometric pattern. The

example of form

pattern is not used, however, in the same

and function, of

manner as the masons’ lattice. Here it is

discipline and play.

the painting itself. It represents a strict, immutable arrangement (theme) in

There are disciplines

which the artist, by juxtaposing colors

other than

(variations) plays the fascinating game

those based on

of deceiving the eye. The squares as we

geometry, among

see them here appear to recede into

them availability

the picture plane. However, by skillful

of materials,

manipulation of colors, the painting


flattens out and is thus seen as a two-


dimensional picture.

mechanical limitations,

The many variations based on this and

economic considerations, legal

similar designs attest to the fascination

requirements, time factors, physical

the artist finds from the interplay of a

handicaps. Some of these are self-

great variety of color schemes and an

imposed, others are involuntary, but in the

extremely limited geometric format.

hands of the artist each may contribute to,

The kind of grid employed by Japanese

rather than detract from, the end product.

architects in their traditional houses combines the virtues of determining the

It is inconceivable to consider Matisse’s

size of various rooms in the house, floors,

compositions with cut paper without,

walls, furniture, etc., and creating the

in some way, linking them to the play

style and appearance of the house. The

element—the joy of working with simple

Tatami, a straw mat approximately 3 by

colors and the fun of “cutting paper dolls”.

6 feet and 2 inches thick, is the module

But the greatest satisfaction, perhaps, is

derived from creating a work of art with

and humor in the production of some of

ordinary scissors and some colored

these compositions in no way detracts

paper—with so simple means, such

from the end result—a serious work of

satisfying ends.


Similarly, the early Cubist collages, in

One cannot underestimate the

which cut paper played an important

importance of restraint and playfulness

part, are products of strict rules, limited

in almost any phase of Picasso’s work.

materials: newspaper mounted on

Here, for example, one sees a restrained

a surface, with the addition of a few

use of the brush and one flat color.

charcoal or pencil lines, usually in black and white and sometimes with tan

The drawing of the child’s face, the

or brown or similarly muted colors.

ornament and the lettering are all one.

These elements were juggled until they

Lettering is not used as a complement

satisfied the artist’s eye. The playfulness

to the drawing, but as an integral part of the drawing. It serves as both a garland and a verbal image—a visual pun. What emerges is a kind of game itself, revealing the ingenuity and playfulness of the artist, his ability to deal with problems in the simplest, most direct, and meaningful manner. Similarly, this ability to do much with little—to find a bull’s head in a bicycle seat

and handle bars—is another aspect of

for this advertisement for the Dutch

Picasso’s wizardry, his humor, his childlike

firm Nederlansche Kabelfabriek, was

spontaneity, his skill as a punster and

associated with this group.

I demand of art the role of the challenger… of play and interplay, play being the very manifestation of the spirit.

ability to improvise and invent with limited, often surprising means.

The disciplines which de Stijl encouraged—functional use of material

This monochrome, Persimmons, by Mu

and meaningful form, and the restrained

Ch’i, a thirteenth century Zen priest

use of color (black and/or primary

and painter, is a splendid example of a

colors)—are evident in this design. With

painting in which the artist plays with

a few simple typographic elements

contrasts (the male and female principle

and an ingenious play on the letter

in Chinese and Japanese painting): rough

“O”, a humorous, yet significant design

and smooth, empty and full, one and

was evolved. A picture is created by

many, line and mass, black and white, tint

typographic means: a few type characters

and shade, up and down. It is a study in

and type rules are so manipulated as to

the metamorphosis of a fruit, as well as of

make a useful product, an advertisement.

a painting. (The artist, incidentally, never

Many examples of this artist’s work reveal

used any color but black.)

this same playful approach and are

The reader may find a parallel, at least

worthy of serious study.

in spirit, between this painting and the

The earth colors of Africa, the ice of the

preceding one by Picasso. Both employ

polar regions, the bamboo of Japan, are

a single color, and exploit this limitation

among the many challenging materials

to achieve as much variety as possible,

with which artists and artisans create their

and both undoubtedly were painted very

idols, their utensils, and their houses—all

rapidly, a condition often conducive to

natural limitations which provide their

utmost simplification and improvisation.

own built-in disciplines which, in turn,

In modern times artists like Man Ray

contribute to the creative solution.

- Le Corbusier

and MoholyNagy, working with the most limited photographic means, the

Some years ago in Kyoto I was fortunate

photogram, created highly significant

enough to witness a young Japanese

pictures. This technique offers the artist

craftsman make the “chasen” you see here.

ample opportunity to play with light

It is a whisk used in the tea ceremony and

and a great variety of materials, opaque,

is cut from a single piece of bamboo with

translucent, and transparent, to produce,

a simple tool resembling a penknife. Both

very rapidly, rich and unexpected effects.

the material and manufacturing process (about one-half hour) are the quintessence

The photogram, at the left, made by the

of discipline, simplicity and restraint. The

1. Gilbert Highet, The Art of Teaching, Alfred A. Knopf, New York (1950), p. 194

writer some years ago, shows how simply

invention of such an article could not

2. Cahier de Georges Braque, Maeght Editeur, Paris (1947)

one is able to capture movement and

possibly have been achieved by anyone

achieve interesting tonal effects. Because

lacking the ability to improvise and the

the technique itself dictates a certain

patience to play with a specific material: to

degree of speed the time factor becomes

see the myriad possibilities and discover the

7. Ibid., p. 166.

an additional discipline, which acts as a

ideal form.

8. Le Corbusier, The Modulor, Harvard University Press (1954), p. 55

3. Alfred North Whitehead, The Aims of Education, Mentor, New York (1949), p. 21  4. Ibid., p. 24  5. The New York Times Magazine, December 15, 1963  6. Chiang Yee, Chinese Calligraphy, Methuen & Co., Ltd., London (1938), p. 167

9. Ibid., p. 80

creative stimulus. It has not been the purpose of this The de Stijl movement, founded in

discussion to provide a glossary of

1917, had a profound influence on

disciplines or recipes, but merely to indicate

painting, architecture, and typography.

the virtue of the challenge implicit in

Piet Zwart, the designer responsible

discipline. 14)

10. Ibid., p. 101 11. Ibid., p. 63 12. Matila Ghyka, The Geometry of Art and Life, Sheed & Ward, New York (1946), p. 120 13. Edward S. Morse, Japanese Homes, Ticknor & Co., Boston (1885), p. 122 14. Le Corbusier, op. cit., p. 220

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