Sunday, April 29, 2007

Her Majesty the Paper (Part I)

Frequently people ask me about what kind of paper I prefer to fold one or another model, if I have a preferred generic one, or if there is a "traditional" or "classic" paper from Japanese origami and what gives it its "special" condition. Then I gave answers like "to complex figures and very detailed is better to use tissue foil ", or "if I want the models to keep their shape in time you can use metalized paper", or "kraft paper is good if you want to wetfold or fold with brush". And everybody get happy thinking how much I know about this handcraft; everybody except me of course who realize that in fact I don't have a clue about what paper is, nor how it works, or why it has this or that quality.

How much knows an origamist about the paper he uses, how it was made, what's the secret that keep it tight and how to select the best for their purposes? And what about the making processes of paper and the ecological problems they mean to nature?

So I decided to do some research.

Maybe a good starting-point should be what paper is not. Word came from latin papirus which signed the plant which were used by the egipcians to make their famous writing rolls .. However, yet the principle is the same, paper we know and use today doesn't have its origins there. Papirus is a plant with long leafs, soft stalk and a triangular wide base and the rolls were made directly from its medulla, a paste which is spread over molds and hydrated with water, pressed and the left dry, to finally be rubbed with ivory or shell to soften its surface. Its origins goes back until 3000 BC and its use s to Greece and the entire Rome Empire until the Vth century. After that, writing was done over parchments, made from fine layers of cow, sheep or ram leather(1).

The true origin for paper lies on China. Around AD 105, emperor Ho Ti ordered his eunuchs chief Tsai Lun the study of new materials for writing, since the wood tablets and silk patches were unpractical for the growing usage of writing. His work concluded with the making of a vegetable pulp made with fibers from bamboo cane, mulberry and other plants, along with the development of a procedure for the making of the paper, which was kept absolutely secret for more than 500 years.

Only after AD 500 the technique of paper making passed to Korea and in AD610, priest Ramjing traveled to Japan for bringing assessment in the production of paper; both countries will upgrade it according to their own resources and technology (in AD700 rice flour was added to the pulp). In 750 it passed to Central Asia, Tibet and India, to finally reach the Arabian world and his vast empire, which ran through all Northern Africa until Spain in Europe.

Here there is an important change in the technique. Arabs, not having many fresh plants, started to use clothe fibers and to recycle materials like old carpets, tapestry or damaged cane products. Pulp then obtained produced a finer paper but with a shorter life; also they incorporated starch, which improved its resistance to the stroke of writing. The first workshop installed in Europe was in the Hispanic Arabian city of Cordoba in AD1036.

Perhaps it is a good moment to start explaining what is paper and how does it work. It is a irregular structure formed by entangled fibers in a paste which is hydrated and left decant in a layer relatively homogeneous. The size of the fibers plays a main part to achieve some properties in the paper; long fibers will give it strength and rigidity, but with a rough finish, and short fibers will produce fine paper, formed, flexible, textured and opaque, but not resistant, better for writing. In mixture of both fibers lies the secret to obtain specific results.

a)raw white paper (1000x), b) secondary cellulose fiber (400x)

secondary cellulose substrate (200x)

With Crusades the manufacturing process arrived to Italy, country where it was incorporated to it a glossy finish with animal grease that gave paper a great surface resistance, which allowed the sharp scribe's pens (made from feather) to write without wrapping it, this made the parchment to disappear very quickly from Europe. The writing technique with feather, dominant in Europe, against the calligraphic brush painted one in the East, determined the final differences between European and Chinese-Japanese paper (2).

With the creation of the printing press on XVth Century, needs of paper grew explosively and clothing resources started to lack, and also hands to do it. In 1798, french Nicholas Louis Robert created the first effective paper machine, which was improved later on 1803 by english brothers Henri and Sealy Fourdrinier. They incorporated on 1840 the crushing of wood to the making process of the pulp. Finally, on 1850, the chemical process to produce pulp was created, which made the production much cheaper. On 1852 Meillier discovered cellulose and Tilghman patented the process to obtain it from wood. Just on 1853, the circle was closed, when paper machines arrived to China and Japan, country that produces the 15% of world's paper needs.

Bibliography (in Spanish):

Friday, April 06, 2007

My workshop in Purranque: The Kawasaki Rose

A classic figure in origami is the rose created by Toshikazu Kawasaki from his famous twist folding. Its delicate curve petals had made it one of the most popular and spread models inside origami (and outside).

History of this rose is easier to build than the one of its author. There is very few about this japanese mathematician, who teachs in the Sasebo Technologycal School and became the first "Doctor in Origami" of History. He is also known for his theoretical studies about the relationship between origami and mathematics, developing, among others, the Theory of Iso-Areas (Mirror Areas). In 1998 he pulished Roses, Origami & Math (which should be now on its way to my home :) )

On this book there is a complete chapter dedicated to this rose and its variations, being this the first version "from the author" of its diagram. Before, in 1994, during the New York Convention, Kawasaki teached the rose to the american creator Joseph Wu and he folded and gifted one to his friend Winson Chan. He unfolded the gift and developed a folding sequence and diagram, which was published and spread trough the net, becoming very popular and known as the "New Kawasaky Rose". Later, japanese Kunihiko Kasahara published in his book "Origami for the Connoisseur" a diagram a little less elaborated than Chan's and called it the "Original Kawasakai Rose". Many other variations has been created over this three diagrams, to get a larger number of petals or diferents finishing details, but the heart of this figure, the twisting fold, remains unvariable as a testimony of the geniality of its author.

Chan's diagram remains being my favourite, mostly because its final result and also I guess because sentimental reasons (it was one of the first figures I've memorized and gifted) However, I have to admit that its 22.5º grid pre-folded takes out all ellegance to the next steps in the folding. Here there is a video about how the rose is collapsed from its pre-folded CP.

It is precisely the analysis of the New Rose what gave the folder a deep learning about the relationship between geometry and origami. To build this rose is almost being creating, step by step, the CP of the figure, to collapse it then in a couple of master moves. The point I want to remark is that anyone who has folded this a couple of times can realize that the pre-folding of the grid is unnecessary to get tits main folds (step 12 of Chan's diagram). The perfect geometry of Kawasaki give us a large number of references to achieve every one of them from two simple diagonal lines at 22.5º. This is especially useful when you use thick papers o textured to fold the rose, because Chan's method to draw the grid lose accuracy over the edges.

With this in mind, and studying a little, I could develop a diagram to get the full figure from a couple of reference lines, including the secondary petals from steps 9 to 11 on Chan's diagram.

For example, to generate folds from Chan's step 12, it is only necessary the axial line and a reference point, aligning the line over itself and marking the fold passing through the reference point, as I show in the next image:
Is when I remember my old Maths teacher at school, saying by memory: "there is one and just one perpendicular line to a given line which passes through a given point". That can be read as an Origami Theorem: "To fold a perpendicular line of a given one is necessary only that line and a given point"

There are also other references to follow in this particular fold, as I show them in the image above.

Same thing occurs with the other folds from that step:

My hope was to get the rose whit the less possible number of foldings, to get the petals as much clean as possible, but at the end, just a few of them can be avoided. Also the sequence itself is as complicated as Chan's (or even more). All I could keep was the great experience of having learned a lot and grown-up in my relationship with folding and geometry, both things which justify the experience and that's why I share it to anyone who desires to try it. This is the link to the document Google Base page and thi is the direct link to the document (it is zip pdf file and its size is about 1 Mb):

Many regards and luck if you try it :), I'll be happy to answer any question about it.