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The Forms of Origami

As the years have passed, I have been fascinated by the intricate landscape of Paperfolding, with all its highways and byways, wide vistas and secret corners. At one time I cherished a dream of compiling a book called: "The Styles of Paperfolding". Such a book would devote one chapter to each style and after and introduction and discussion of where the style fitted into the general scope of paperfolding, it would contain a diagram of two with instructions for folding a model in that style and also have an illustrated picture to show the models. The book would, where appropriate, place the style in its historical context.

I'm guilty of starting the recent debate on the Forms of Origami myself, in my article on Carbon 60 in which I casually muttered: "The connection between modular folding and ordinary origami has always seemed to me somewhat tenuous because the only aspect of real paperfolding involved is the folding of countless identical modules of minimal paperfolding interest." Notice that I distinguished modular folding from "ordinary origami" but I did go on to say that I, too, was captivated by modular folding".

Valerie Vann (7th December) immediately came to the defence of modular origami in a long and very interesting posting and suggested that modular folding was at least as much "origami" as folding from some other materials, such as foil, foil-backed tissue , plastic or other paper substitutes. A telling point she made was that modulars had to made to "lock" and that locking procedures were very origamic. (The rest of her posting concerned the relationships between modular origami and geodesics.)

Also on 7th, December Jerry Harris took up the question of what is and is not "Origami" by postulating three different kinds; 1. Single sheet origami. 2.Modular origami, where multiples of identical modules are pieced together and 3.Composite origami, where a model is made from two or more different pieces each folded in different ways. I can readily respond to this, because it is one of the basic classifications that has also occurred to me.

In another communication dated 7th December , Jean Villemaire rightly broadened the enquiry into principles of categorisation by asking how many kinds of paperfolding could be distinguished. He suggested a multi-dimensional classification involving 1. Number of sheets, 2.shape of paper, 3.historical distinctions, 4. Figurative v. abstract, 5. Function 6. Etc. etc.

On 9th December, James Sakoda added further catagories: 1, the technique of linking squares of paper as in the Sembazuru orikata, 2. Origami collages as in Kyo Araki's "Kyo Origami", .3. pop-ups as by Chatani, 4. Gift-wrapping and 5. Origami flower arrangement.

James added: "The Japanese have never been shy about taking these steps when they seemed necessary to achieve an attractive result. Setting up a limited number of categories may obscure the differences among them and it may be better to recognise them as separate kinds of effort which can still be included under origami." This view met the approbation of Steve Woodmansee, also on 9th, December. Steve especially liked the idea of referring to all of the branches of Origami as "separate kinds of effort , which can still be included under origami". Nevertheless, he went on to admit his own preference for square paper.

On 12th, December, Steven Casey came up with "The unified Fold Theory" in which he discussed the acceptable limits in various fields (Cuts, Modular, Pre-Cutting and the Shape of the initial paper), beyond which the style crossed the boundary and ceased to qualify as "Origami"

Steve's distinctions are acceptable suggestions. It is unlikely that all folders would necessarily draw the lines where he does, but this does not invalidate his suggestions Steve also mentions a category of his own in "kirikomi" origami where the paper is cut into (but with removing any paper) before folding. This was advocated by the elder Michio Uchiyama. (He claimed it saved wasting paper!).

Steve adds; "I also believe that any definition of origami should come from an internal frame of reference, that is among the practitioners of the art/science and not be hijacked by others simply because [their techniques] contain a minor element of folding" He mentions packaging, paper sculpture, pop-ups and multi-piece pop-ups, "which are all great in their own right and can stand alone".

Taking all these contributions together, we have a wide field of origami styles and techniques. I could add a few of my own. There is the form of cutting practised by Dr. Solorzano in which he "slashed" the paper with a knife along an existing crease. There are various subdivisions of mathematical paperfolding, from demonstration of simple theorems of Euclid to the trisection of angles and formation of conic sections by folding. The folding of polyhedra from one sheet of paper (Lewis Simon, Bennett Arnstein and Rona Gukewitz) is a separate catagory and I would even place box-pleating and technical folding in categories of their own The Second international meeting of Scientific Origami at Utsu, Japan in 1994 showered us with what seemed a myriad of new approaches.

So the dicussion about the Philosophy of origami has continued. One feeling that seems to have widespread acceptance is that Origami is what you make of it. An artist is at full liberty to choose his own medium., even to the extent of mixing media, as in a combination of oil paint and clay modelling.

Even Paper Quilling has been brought under the umbrella of Origami, on the basis that curved paper is acceptable and quilling (that is making tight rolls of narrow ribbons of paper and then arranging the little spirals into pictures) is only an extreme kind of curved paper. I begin to start asking questions here. Why does every paper craft have to be brought under the origami umbrella? When we keep a hold on ourselves, we all know what we mean by Origami in the proper sense of the word. There is a perfectly good word, "Papercraft" which can be used to encompass all the remoter styles of manipulating paper.

It is still possible to identify folding from an uncut square of paper as being distinctive in its own right. This is the core of paperfolding and if one keeps one's feet on the ground, one can see that the assembling of modules from multiple pieces of paper is just not the same thing. One of my favourite sayings is that one must keep one's feet on the ground, but one's head in the clouds. So I revel in the sheer abundant variety of folding techniques, whatever one chooses to call them.

I hope to say more on how we can arrange all this variety in our minds to give it some semblance of order, without imposing a rigid classification system on it and without abusing our useful names and definitions. Long though this posting is, I have still more to say, but I will keep it for another time.

Faced with the multiplicity of styles and categories of paperfolding, should we attempt to classify them, or should we lump them all together under the portmanteau heading of Origami? If so, what are the boundaries of our art? How do we define it?

It must be remembered that all systems of definition and classification are man-made. Nature itself does not place an eagle in the order "Hawks" or a frog in the class "Amphibians" : both the names, and the classifications are invented by humans for their own purposes. Sometimes Nature simply mocks these man-made systems. The same applies to the classification of artefacts and systems created not by nature, but by humans themselves.. It also extends to the classification of papercrafts. In fact, the difficulties with human ideas and creations are even greater than with Nature. Present-day natural species are fairly fixed, and while they change over the centuries and millennia, the larger species do not mutate or fluctuate wildly. Human endeavours, on the contrary can evolve and change rapidly as new ideas are spread like wildfire. Human preferences and activities, including papercrafts can be looked at from many angles. For example, cutting or not cutting; square paper or other shapes; one piece of paper or many. Only a multi-dimensional classification system could fully cope with a full analysis. Would it be worth it? Would not a broader empirical system be just as adequate for our purpose?

We do have a perception that the heart of paperfolding is the uncut square of paper. (I do not intend to explore the rationale of the square in Origami here. There has been some useful consideration of theis in Origami-L in the past few days and a full discussion of this topic must wait for another occasion.) Cutting, for instance is just one deviation from uncut folding. More than one piece of paper is another; other deviations are using different shapes of paper, or use of foil instead of paper. John Smith has devised a simple way of distinguishing between the different forms of paperfolding and yet bringing them together in a way that is easy to understand. I have to say that this part of my contribution derives entirely from John. I have his permission to use it here and I hope that I do not misrepresent John's ideas.

John's article appears under the title: "Origami Profiles" in British Origami No. 58 for June 1976. It also appears on later dates in the Italian and one or two other origami magazines.

John's device is a sort of compass rose design, which generates a characteristic shape or "profile", which can be used for a variety of purposes. It may indicate the paperfolding preferences of an individual folder. Or it can give a profile of the make-up of a particular kind of paper craft.

The diagram looks very much like a compass, with eight lines radiating from a centre point. The point at the centre represents the strictest form of paperfolding, namely, folding from a single uncut square of plain paper. Each of the eight radiating lines represents the relaxing of one particular constraint. The further one goes out from the centre, the greater the relaxation of the constraint The names John gives to his eight radiating lines are Modelling, Shaping, Slitting (or cutting), Supporting (wire and glue), Multi-layers, Multi-sheets, Lengthening and Decorating. Perhaps he could have chosen more lines incorporating other aspects; perhaps the names could be different. The system is not rigid, but John's choices do create a workable system.

One line measures the extent to which cutting is permitted. Another line represents the extent to which shapes other than the square are acceptable. Other lines relate to different shapes of paper, beginning with an equilateral triangle and going on through regular stars and polygons to irregular and ad hoc shapes. Other lines relate to the use of supports, such as glue or wire or even mechanisation and the addition of colour, of texture or pattern or painting. Yet other lines indicate the use of more than one sheet of paper (as Yoshizawa often does and Momotani does in his in some of his larger pictorial models), the use of multiple layers of paper and the lengthening of paper, first to rectangles and then to ribbons and eventually to string figures and macrame. Wet folding and modelling leading up to papier mache follow another line. Along each line the degree that that particular restraint is relaxed is marked off.

When the points on each of the eight lines have ben marked off, a curved line is drawn connecting the points into the shape like a cloud. The resulting shape is the Profile of the particular folder's preference, or alternatively, of the style of papercraft being considered. John uses eigtht lines from the centre. Others could, no doubt be added to include other kinds of deviation. There is no reason why the whole of paperrcrafts should not find a place somewhere in the diagram

In the arts, in crafts and in pastimes, there is no law as to what is right and what is not right. Every person can choose to do as he pleases. But the combined choices of many people will tend to form generalised "nodes" in the continuous spectrum, because some possibilities are more popular than others. So, folding from a plain square of uncut paper has its place as one identifiable "node" , the possible reason being that may people are attracted to the severest combination of constraint or the "purest" style of folding.. Other nodes represent modular folding, cut-and fold origami and "knot origami" which uses long ribbons of paper. No style in art or recreation is any more valid than any other.

John's diagram has the merit of making a definition of Origami either irrelevant or of only secondary importance. It does not exclude any papercrafts, but it does show their relationship with the core of origami. John has chosen an uncut square as his centre point. He could have chosen a circle or a triangle.. He has also placed paperfolding at the centre. Could some other technique, such as papercutting have been made the standard Would this result in a differently faceted view of the profiles?

David Lister Grimsby, England.

17th December, 1996

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