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Art, Origami and Education

Introduction
It is a source of wonder to me that the simple idea of making folds in paper can have so many fascinating aspects. Thus Origami can appeal to those with an interest in geometry or in the problems of constructing particular shapes. It can have many social aspects such as therapy, making gifts or envelopes, or studying its fascinating history in many different countries and cultures. In this paper I want to look at art and Origami and the relevance to education.

Art and Origami 
Folders often pose the question, 'Is Origami art?' If Origami is an art form why is it missing from art exhibitions and galleries? In England for example there is no Origami on display at the National Gallery or the Tate. I did not see any Paper-folding in the Louvre or in the Prado. It is necessary to decide whether Origami is, or can be art and if so why it does not appear in exhibitions and galleries. I therefore set out to answer the questions what is Origami and what is art. 

Origami
By Origami I mean the achieving of a desirable shape or pattern solely by folding a regular polygon of paper. 

Defining art in words 
The Encyclopaedia Britannica first edition of 1769 defines art as, 'a system of rules serving to facilitate the performance of certain actions'. Painting is defined as, 'the art of representing natural bodies and giving them the appearance of life'. So if I was giving this paper 200 years or so ago there would be no doubt that Origami was an art. By 1968 the Encyclopaedia reflects the changing views of society and we now find that the attributes of art include:-

the pursuit of truth; the subjective world of imagery and feeling; the exploration of individual reaction to reveal unique qualities of experience; a final statement standing for all time; giving permanence to an instant, and so on. Apart from the increase in the number of words now needed to define art the emphasis is on the subjective world of the artist rather than on art as a craft or means of representation.

In the latest edition of the Encyclopaedia (1994) a short definition is given as:-

'The use of skills or imagination in the creation of aesthetic objects, environments or experiences that can be shared with others. Fine arts are more concerned with purely aesthetic ends, or in short with the beautiful.'

The great Oxford Dictionary 2nd edition defines art as:-

'Having to do with skill, particularly to subjects of taste, as poetry, music, dancing, drama and the like. Skill displaying itself in the perfection of workmanship, the perfection of execution as an objective in itself. The skilful production of the beautiful in visible forms'. (This later meaning was not used before 1880 according to the dictionary.)

We have so far seen that art may be concerned with skill or craft, with representation or the creation of aesthetic objects, and possibly with the beautiful.

Philosophers from the Greeks onwards have struggled with the meaning of art. The only thing that seems certain is that they disagree with each other. Professor Collingwood [2] is an authoritative voice in the philosophy of art. We learn from him that art proper is not a craft, it cannot be concerned with representation, magic, or amusement. It is not concerned with beauty as a special attribute. A work of art is said to be a total activity which the person enjoying it apprehends by the use of his imagination. After a long discussion on the meaning of imagination we learn that 'every utterance and every gesture that each of us makes is a work of art'.

Looking at these attempts to define art in words I see nothing that would rule out Origami as an art. Certainly it is a skill or craft, it may well express something of the subjective world of imagery and feeling. It may convey concepts of order, it can represent natural bodies and it can involve the creation of aesthetic objects or even the beautiful. But I am doubtful whether a work of art can be defined in words that are clumsy things at the best. I do not find myself any clearer about how to recognise a work of art when I see it than I was before I studied these definitions. Perhaps the key is to look at the works of art that appear in art galleries. 

Defining art by art exhibits
 A study of masterpieces [1] up to the 18th century in various countries does show that they were largely concerned with representing the human form for illustrating religious ideas, military conquests, and portraiture, for example in the works of Michleangelo, Leonardo da Vinci, Rubens, Raphael, etc. In the 19th century subjects became wider in scope but still the human figure was of great importance. The Impressionists began a revolution their works usually involved the human figure or landscapes and city scenes. I do not see anyway in which Origami could have been a serious contender for the type of representation used by these great artists. Does this mean therefore that we have to discard the idea that Origami can be art?. Before taking such a step let us look at modern art and its ideas [10].

In 1913 Malevich placed a black square on a white ground claiming 'art no longer cares to serve the state and religion; it no longer wishes to illustrate the history of manners, it wants nothing to do with the object as such' In 1917 Marcel Duchamp exhibited a bottle rack as an example of ready made art. He assigned aesthetic value to purely functional objects by a simple mental choice rather than through the exercise of manual skill. Thus art was removed from the task of representation. From these rejections of previous ideas sprang such movements as Minimalism & Conceptual art. Thus we have the abstract severity of Frank Stella's 'Aluminium paint on wood', 'Canvas and Wood' by Barry Flanagan which is precisely a canvas sheet supported by three sticks of wood. 'Away from the flock' by Damien Hurst that consists of a dead sheep suspended in preservative in a glass tank and 'Sae Collé sur toile' by Antoni Tàpies, a paper bag stuck on to painted canvas. Perhaps the best statement of the modern view of art comes from Judd who re-iterating Duchamp said 'if someone says it's art, it's art'!.  

What has this little excursion into modern ideas shown us? The old ideas of skill, perception and representation are simply one way of looking at art, they need not be the only way of defining the role of an artist and of art. The modern ideas of Constructivism, Abstract Expressionism, Minimalism and Conceptual art [26] have liberated our thinking about the meaning of art. I am not saying modern art is good or bad I am simply concerned with the ideas involved.

What does this mean for Origami? If we go by the definitions of art in words or the images of modern art there is nothing to stop an artist using Origami as a medium for expression, or Origami artefacts as an aesthetic declaration. Where Paper-folding meets the needs of an Artist there is no reason why it should not be used.

But it is still true that Origami does not seem to be adopted by artists as a medium of expression. I want now to look more closely at Origami and see if there are inherent constraints that would inhibit its use as a medium for artistic expression. 

Origami and its constraints
The definition I have given of Origami as 'just folding' necessarily imposes limitations in the freedom of choice available to the artist. When an artist chooses a medium such as oil, water colour, pencil, charcoal, etc. to express his or her ideas then in general the first marks do not impose a serious limitation on the next particularly in a medium such as oil or acrylic. This is not true for Origami, if I fold a square in half diagonally then my next available moves are limited by the previous step. In fact the technique of Origami is based on the creation of surplus material that can be manipulated independently of the rest [16].

Further limitations result from the paper. I have only the two surfaces and textures that I start with. The characteristics of the paper, its thinness and flexibility, are all fixed. The process of folding means that I am limited to straight line construction and to connected polygons.

In the purest form of Origami I have only the one entity that gets smaller as my folding progresses. Origami is also an indirect medium with a possibly mechanical and mathematical feel about the process. Compare these constraints with say those of oil on canvas. There is no limit to textures or colours. The medium is direct with as many separate entities as you wish and one step is largely independent of the next.

Folding means straight lines and linked polygons, this type of structure is fundamental to Origami and is therefore well worth further analysis. 

The Linked polygon structure of Origami
In this diagram a square is folded along the line 'F' to give a triangle. Thus the original square is divided into two polygons by the fold line 'F'. If a fold line cuts a corner then the total angle count is increased by 1. If the fold line cuts a boundary elsewhere but at an angle the total fold count is increased by two. Thus the original square has 4 angles but with the fold line cutting two angles the total angle count is increased by 2 giving 6. This is made up of two triangles. The act of making a flat fold is to superimpose one polygon on another. In this case they exactly match so the observed polygon count after folding is 3.

Look at the second drawing now we have a fold line at 'F' that cuts one angle and one side. Thus the total angle count will be increased by 3, and indeed we have two triangles giving 6 angles. If we make a mountain fold a long the 'F' line we superimpose the larger triangle on the smaller and vice versa if we use a valley fold. A reverse fold (outside) gives us the equivalent of both a mountain and a valley fold. The total angle count stays at 6.This diagram illustrates that pure Origami proceeds by dependent linked polygons and hence imposes a very serious constraint on the artist compared with traditional media.

However the above analysis does suggest a way of analysing models with the possibility of a powerful way of building a data base.

These are the 6 diagrams for folding my simple swan. Look at the third diagram, under the drawing it shows that the folded or raw edges outline two polygons. In the angle analysis this is shown as 3 connected to 3 (by the arrow). The total angles in the drawing is 6 and 2 folds have been completed. After the 5th fold we have 17 angles in total from 5 polygons. The beak has in fact two triangles. I have only drawn the front of the model here but in fact since all the folds are valley or mountain the polygons will be different for the back. In this series of diagrams it will be seen that we have a way of classifying both the sequence of folds as well as of the final model.

Counting the number of angles in each polygon and in the total model suggests a further way of analysing the structures of folding. The following table shows the basic moves of Origami and the number of folds that have to be manipulated to make them. The resulting flat polygon then gives the number of angles in the final shape. Using these basic moves it is then possible to show the number of folds involved and the angles in the final shape for a number of classic bases.

Type of fold No. of folds No. of Angles manipulated to make in final shape

BASIC MOVES
Valley/Mountain 1
Reverse 4
Squash 5 (1 reverse+1 valley)
Petal 9 (2 reverse + 1 valley)
Sink, simple 10

BASES
Kite Base 3 9
Fish base 9 10
Prelim. Base 9 4
Bird base* 27 6
Frog Base 61 10

* as an example a Bird Base consists of 6 reverse folds plus 3 valley folds ( Flaps in upright position) = 27.

Applying these ideas to a more complex model I give below the polygram analysis of a dog by Alice Gray. Below the drawing I show the connections between the polygons thus the nose is a triangle = 3 angles connected to the muzzle with 4 angles.

Such a diagram gives a very good picture of the complexities of the final flat shape but would be difficult to handle in a computer. By giving up the connecting links it is possible to simplify the analysis. The simplest statement is 17 areas and 66 angles. This can be improved considerable by using a frequency distribution of the polygons:-

No. of angles. 3 4 5 6
No. of polygons 7 6 3 1

Thus there are 7 triangles in the dog fold. The dog fold could easily be recorded as 7 6 3 1 the number of angles being assumed as 3 upwards. Another more complex possibility is to use the highest angle count path through the model.

This short review of the possibilities of polygon analysis makes clear that an index of models using say a frequency distribution is feasible. However with a shape such as an envelope it may be necessary to develop a simple index of the actual folds.. A linkage to these ideas and my Origami Instruction language [17] is an interesting possibility. Much work needs to be done.

Extending the repertoire of Origami
I have so far restricted my discussion to flat Origami to simplify the approach. However many attempts have been made to overcoming the lack of resources in flat Origami. In 1976 I published an Origami profile [18] that showed some of the choices available to folders in extended the range of Origami.

By putting the diagram in the form of a Radar map it is possible to draw on a profile of preferred practice. The centre of the diagram represents the purest form of Origami. For example no cutting or no decoration. The end of the line outwards gives the more extreme use of the action. Thus if the length of the paper is increased a great deal we arrive at ribbon. I do not accept cutting and decoration as Origami, to my mind they are alien to the beauty and spirit of our art.

The most important way of extending the scope of Origami while remaining true to its spirit is by 3D. In its simplest and purest form the 3D shapes follow the fold lines this is typical of geometric folding. I am less persuaded about the use of wet folding in my view we are moving towards papier-mâché. I believe the inducement of curves as a consequence of folds is a method truly in the spirit of Origami and should be encouraged.

Ribbon folding has enjoyed something of vogue in the West recently but to me we are moving towards knitting or macramé. Multi- piece folding that does not depend on gluing for assembly is, I suppose, a legitimate technique, but in excess where hundreds of pieces are used to create a model or picture, it seems to be a long way from the heart of our art.

We need to ask whether the increase in richness available by the more legitimate methods overcomes the inherent constraints on an artist's freedom of expression.

I think it is important to note that the enrichment methods still preserve the straight line structure of connected polygons. We are still dependent on paper with its 2 colours and textures. The achievement of a work of art is still an indirect process. It seems to me therefore unlikely that an artist would select Origami as a medium for expression ahead of the more powerful, direct and flexible traditional methods. Of course on occasions it may be that a folded artefact will be exactly what the artist wants, either in its own right or as a selected and designated object. 

Artists and Paper-folders
Having looked at artists and paper folders it is interesting to map their interest levels. In this diagram I have allowed four categories according to the strength of interest in art and Paper-folding. I would suggest the majority of people have a weak interest both in art and Origami that is box C in the diagram.

Artists in the main will be in box A with a strong interest in Art but very little in Origami (if they have ever heard of it). Box D are the dedicated Paper folders with little interest in Art. These folk are very strong in the West. The technical folders are mainly in this group for example, Rohm, Elias, Hume, Montroll. They may well have an interest in display but the challenge of Origami as a cognitive business is likely to be dominate. I must stress here that I have selected a few people merely to illustrate my ideas. The fact that I have not mentioned someone does not mean they do not possess the attributes in the highest possible measure.

The special group B has very few members in the West, I suspect that in Japan we would find a great many. These are people who are artists as well as paper folders. Eric Kenneway [8] was both an artist and a paper folder. He attempted to draw in Origami using the 2 colour contrasts and the raw or folded edges. As far as I know his work is unique. Perhaps most striking of all is the work of Jean-Claude Correia [3] here is an artist who understands art and Paper-folding and brings them together in a dramatic way. I must also mention Paulo Barreto who is an artist through and through but also a great folder, his abstract patterns will compare easily with any of the more established artists. Others I should mention are Vincent Floderer and David Brill. David is particularly interesting in the he has exhibited paintings at the Royal Academy in England and is also a brilliant creative folder. His artistic sensibility is clearly demonstrated in his final models but he has never used Origami in Art proper. Paul Jackson is an artist and designer who has combined his great skills in Paper-folding with art, he has opened up the world of abstract shapes for many people with his teaching of curve induced folding.

In Japan I must pay homage to the great master Akira Yoshizawa who combines immense skill as a folder with extraordinary aesthetic sensibility. 

What kind of people are folders? 
The crude classification I have used above does raise the question, are there dimensions or factors that underlie the interest in Origami?. Some time ago I carried out a pilot study to see if I could throw light on the possible dimensions behind an interest in Origami. I asked a lot of questions of people most of whom had been practising Origami for 10 years or more. I covered mathematics, art, religion, sport and so on. I used factor analysis to see if the dimensions existed and to try to identify them. It turned out that there were two main factors that explained most of the variation in the correlation matrix. The cognitive and the artistic. This diagram illustrates the results.

The cognitive dimension was concerned with puzzles, mathematics, etc. the artistic dimension with design, art, music and so on. Men showed a bias towards the cognitive rather than the artistic with women on average scoring highly on the artistic and less on the cognitive. Of course many folders score highly on both dimensions. It will be seen that this result lines up quite well with my previous diagram of folders and artists. Japan seems to have a remarkable number of folders who have a high cognitive drive as well as deep artistic sensibility.

Origami as a performance art
As Eric Kenneway [9] pointed out Origami is not just about the final model but the folding as well. Because of the stringent initial constraint, just folding, we can have folding diagrams like a musical score. This is incredible it makes both the performance and the creation of a work of art available to anyone. I do not know of any art form employing only the hands and the base material for which this is true.

So we need to look at the performance as well as the final result if we are to truly examine Origami art. The sequence of hand movements when folding can be choreographed to form a miniature ballet. Obviously an eloquent series of moves is required to give full scope to the potential artistry. The little theatre performances of Marieke de Hoop and the superb artistry of master Akira Yoshizawa come closest to what I have in mind. 

Origami as a Total art
I have no doubts at all that Origami artefacts can be art, although it is unlikely that pure artists will make use of Origami with its inbuilt limitations as a medium. However because of its unique nature Paper-folding should be regarded as an art in its own right not confused with other art forms. If we want to realise the full scope of Origami we must move away from the judgement of folding simply on the basis of the final artefact, it is the totality with which we need to be concerned. 

The Great Art of Origami
I wish to appeal then for the recognition of Origami as a total art- that it is the great art based on the performance as well as the final outcome. To my mind there is very little Great Art in the West where the dominant interest is in the technology and puzzle elements of folding. The true spiritual home of the Great Art of Origami is surely in Japan. We need to recognise and study with the great masters who are at one with the paper, the folds and the final result. In such masters' hands the paper almost folds itself in an aesthetic dance of the hands to achieve a result of beauty. I am reminded of the tea ceremony [6] in writing about the Great Art. The reverence for paper would show in feeling and listening to it. The ballet of movements would express the unity of the folder, the paper, and the form. The resulting model would show in all of its folds the mastery and humility of everything that went before. I am not sure these ideas will be understood or accepted in the West. I hope Japan will continue to show us the way. 

Art and Education
Once again the problem of definition raises its head. There are so many views on what education is or should be that I felt unequal to the task of making sense of them. I have therefore chosen to adopt the Oxford Dictionary definition:-

'The systematic instruction, schooling or training given to the young in preparation for the work of life, (and by extension to adults)

What then, if any, is the connection between art and education? Some remarkable work recently published suggests that the much maligned ideas of beauty may have a place. Dr. Rauscher and Professor Shaw [13] of the University of California found that student brainwaves when they played chess strongly resembled musical patterns. The students were then asked to undertake tasks involving abstract reasoning after listening to some early Mozart music. Students who listened to the music consistently turned in a higher performance on the tasks than students who did not. The test seemed to show that some music can assist with the exercise of higher order brain functions including chess, mathematics and learning a language. The sense of beauty in the music of Mozart may well have be due in part to the fact that the patterns are related to the brain's activity when dealing with the higher order functions. If this is true for music then surely it must also be true for that most developed and important of our senses that of sight. The work of Gustav Flechner [25] tended to support the idea that certain visual relationships are attractive to us in particular the so called golden section or ratio. The Greeks and later many artists and architects used such ratios in their work to invoke mental responses. The architect Corbusier is a recent and famous example.

I think it is likely that the strong visual attraction in the connected polygons of Origami may be due to underlying relationships that are found attractive in that they echo brain patterns. The use of Origami by advertisers is an interesting commentary on these ideas. It is also likely that hand movements themselves can evoke a similar reaction. Thus it is possible that the connection between beauty (Mozart's music) and cognitive ability may well be found in Paper-folding. Much work needs to be done in this area, particularly in studying the attractiveness or otherwise of joined polygon structures. 

Origami and Education
The constraints that I have identified in Paper-folding may well limit Origami's appeal as a medium for artists but have major advantages when we come to education. I have tried to show in this organic map the main categories in which Origami can have a strong input into education [28,29]. A few key points are worth noting. In its simplest form Origami can be practised by almost anyone pupil or teacher, handicapped or not. Yet it can be immensely challenging to the most advanced pupils and teachers in its intellectual, artistic and motor skills..

The use of the hands in this way is important in development of the brains' perceptions [27]. We learn about the world by touch and its co-ordination with seeing and the other senses. There is immense scope for creativity in Origami. It is little wonder that Froebel and his disciples included Paper-folding in their gifts [30,32]. These ideas were taken up in both Europe and Japan in the Kindergartens. It is a tragedy that it has largely fallen into disuse in Europe at least.

To get the final model children must follow directions more or less exactly, an excellent introduction to discipline. Origami is appealing and highly motivating in its own right, yet on the back of folding can be carried a wide range of associated learning, language [31], diagrams, geometry, mathematical ideas, animals and birds, countries and so on. Folding is a simple direct but immensely rich activity. Paper is cheap and easy to obtain, no other tools or expensive kits are needed. Origami offers a non threatening way of developing social skills. There are no ethnic or language barriers.

A great deal of work needs to be done to encourage teachers to again make use of Paper-folding. I hope future COET's will address this problem.

References

1 Art Treasures of the World Hamlyn 1968
2 Collingwood, R.G., The principles of Art, Oxford University Press 1958
. Correia, Jean-Claude, L'art en Pli, Angers 1985
4 Encyclopaedia Britannica, 1769, 1969,1994
5 de Falter, No. 14 Origami Deutchland Juni 94
6 Herrigel, G.L. Zen and the Art of Flower Arrangement, Routledge & Kegan Paul 1974
7 Hokusai, Twelve Views of Mount Fuji, Brit, Museum Publications.
8 Kenneway, E. Folding Faces, Paddington Press 1978
9 Complete Origami Ebury Press 1987
10 Lynton, N. The Story of Modern Art, Phaidon 1989.
11 National Museum of Tokyo, Hamlyn 1969
12 Oxford Dictionary 2nd Edition. Oxford University Press 1993
13. Raucher, R.H.; Shaw,G.L.; Kye, K.N. Music and Spacial Performance, Nature Oct. 1993
14 Ross, N.W. The World of Zen, Vintage Books 1960
15 Smith, J.S. A Contribution to the Theory of Bases. BOS Library J003 1967
16 A Contribution to the Theory Of Origami Technique BOS Library J023 1968
17 An Origami Instruction Language BOS Booklet No.4 1976
18 Origami Profiles BOS Magazine No. 58 1976
19 I t's All Relative BOS Magazine No. 61 1976
20 Attributes of Excellence BOS Magazine No. 64 1977
21 Origami as an Art of Constraints Proceedings of 1st Origami Science 1989
22 Patterns in Paper BOS Booklet No. 32 1990
23 COET Proceedings (Editor) 1992
24 Bibliography of Origami in Education & Therapy BOS Booklet 1993
25 Fechner, G. T. Vorschule der Aesthetik, Leipzig 1876
26 Stangos, N. (Editor) Concepts of Modern Art, Thames & Hudson 1993
27 Pomeron, C. Paper Folding an Art in your Hands, Proceedings COET91 BOS 1992
28 Syrett, B. Origami as an Educational Tool, Proceedings COET91 BOS 1992
29 Temko, F. Paper Folding in Schools, Proceedings COET91 BOS 1992
30 Liebschner, J. Paper Folding in Froebel's Educational Theory Proceedings COET91 BOS 1992
31 Ball, C.R. , Origami as a Second Language Tool Proceedings COET91 BOS 1992
32 Heerwart, E., Course in Paper Folding (Froebel) Proceedings COET91 BOS 1992

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