Origami Plus and Origami Minus

This is something I've long wanted to write about. Let me first say that plus and minus here are not value markers in themselves. Plus is not good and minus bad. Or vice versa. It's about ethics and practice not values. Both plus and minus indicate a departure from a norm, but in different directions.

Oh ... What I mean by ethics in this sense are self-imposed rules that tend to apply across the board to a paperfolder's or designer's work. No cuts, no glue, only convex shapes ... that sort of thing. By practice I mean practical stuff that affects just one particular individual design.

My starting point is simple. Origami means folding paper (or paperfolding, I guess). It's a process - folding - applied to a material - paper. As simple and straightforward as that. Just paper and just folding in fact.

So ... Origami Minus is something that is more restrictive than just paper, just folding and Origami Plus is paper plus folding plus something else.

The main ethical restriction of the Origami Minus kind that springs to mind is about the starting shape that paperfolders are happy to use. Just paper comes in any kind of shape ... long strips, squares, rectangles, other polygons, stars etc ... but many ... perhaps probably most ... paperfolders have some kind of underlying ethic, or belief, that not all shapes are created equal. At it's most extreme this kind of ethic holds that folding from a square is 'more pure' than folding from any other shape (an idea that I call 'squarism'). In a less extreme form many paperfolders prefer to fold from a convex shape rather than from a star.

Other Origami Minus ethics are about the process rather than the material. John Smith famously invented a type of origami known as Pureland which seeks to discover what can be achieved if only a sequence of individually made mountain or valley folds are allowed (ie no swivel folds or complex collapses). Other paperfolders believe in aiming for elegance ... a somewhat ambiguous concept said to be an inherent quality of some folding sequences and not of others. This is also Origami Minus. I subscribe to this particular ethic myself. I am not entirely sure what it is ... but, like many other paperfolders, I think I know it when I fold it!

On a practice level there is a kind of Origami Minus that comes into play when a design only works from one particular kind of paper ... say because it perhaps needs to be wetfolded ... or because some areas of the design have so many layers that the paper needs to be extremely thin if the design is to succeed. So just ordinary paper, and just ordinary folding are not sufficient to express this design attractively (if at all).

Minimalist origami is also a kind of Origami Minus. Here the restriction is the ideal that the subject should be created in the smallest possible number of folds.

Origami Plus is different. It is not just paper and just folding (and therefore not on my definition strictly origami at all) but it is sufficiently close or similar, or contains a sufficient origami element that it seems reasonable to cover it with the same umbrella.

So, for instance, we commonly use the term origami to include the folding of materials that are not just paper - like paper-backed foil. This is clearly Origami Plus. (I am not sure whether the folding of plastic wrapping or metal mesh - which are not paper at all - should technically be included as Origami Plus as well - but it seems reasonable to do so - if only to avoid having to invent new words.)

The idea of Origami Plus also covers additional processes ... like cutting, glueing, dampening and decorating ... which may be used in making, or enhancing, an origami design.

Why am I interested in this? Well because I feel that in trying to analyse, understand and appreciate origami designs and the work of origami designers the ideas of Origami Plus and Origami Minus are more useful than the traditional way of describing origami as pure or (presumably, though it is not often used) impure.

An example? Well ... take multi-piece origami, for instance. Some folders used to believe, and still may for all I know, that folding from multiple sheets was not as good, pure etc as folding from a single sheet. So if I use 3 sheets to create a dragon it's somehow not as good a design as if I created a virtually identical one from just a single sheet.

However, if the pieces for my multi-sheet dragon are created just by folding ordinary paper, and the design can be assembled without using glue or sellotape etc, then it is clear that this is just origami, not either Origami Plus or Origami Minus. If my one-piece dragon is also just created by folding a sheet of ordinary paper then ethically the two designs are equivalent, and there is no basis for preferring one of them over the other. (Though there may be on other grounds, of course.)

This is important to me personally because when I first started designing origami polyhedra I always used single sheets, and almost always squares. It was only later that I realised the same results could be achieved in just as ethical a way using multiple sheets (and sometimes multiple sheets folded from unusual rectangles). This realisation allowed me to concentrate on designing and folding in a simpler and more elegant way.

 'Where are these single sheet designs?' I hear you say. Long disposed of, I assure you, though sometimes I wake at night shaking at the thought that one or two may still linger in the damp and mould-ridden archives of the BOS library, where nothing is ever willingly thrown away. (Though we may hope that occasionally the odd thing is lost!)

Making judgements about designs

Once upon a time in an Origamiland far away designs used to be judged on their merits. It it was a good design we knew why and could say so. Similarly if it wasn't we could say why and then try to improve it. But then something changed. The people of Origamiland somehow agreed (though the mechanism by which such agreements occur isn't at all clear to me) that all designs are created equal. All designs are equally good, if not fabulous. But are they?

How do we know if a design is a good design or not? What criteria can we use to make this judgement? What qualities should we look for? Where does excellence in origami design reside?

Here are some of the things I think need to be taken into account. You may wish to add others (or delete some).

Ethics - Issues about techniques other than paperfolding that are used to create the design, materials, starting shape etc

Elegance - Issues relating to the folding sequence (and if modular to the assembly sequence as well)

Difficulty - How easy / hard / forgiving etc is the folding (and if modular, the assembly)

Strength - Is the design robust / able to carry it's own weight?

Finished appearance - Issues of aesthetics (Is it attractive?) and verisimilitude (If it's a cow does it look like a cow?)

Originality - What is it that is new about the way the design is folded (or assembled)?

Added value - Does the design do something except exist? If so how good is it at what it does?

Functionality - If the design has a practical purpose how good is it at meeting that purpose?

Extendability - Does the design lead on to other designs?

Answering these is, of course, not always straightforward, but it seems to me that breaking things down like this helps us understand a design's strengths and weaknesses. It also makes it clear that you cannot judge a design unless and until you have folded it. Final appearance is not everything!

Let's see how one of my all time favourite designs, Paul Jackson's Cube, fares on this analysis. I will score it out of 10 under each heading. My scores are, of course, subjective, though I will give my reasons for the scores as well.

Ethics - 10. Paul Jackson's Cube can be folded from six squares of ordinary paper of virtually any type.

Elegance - 8. An average of 6 for the folding sequence (location creases are required) and 10 for the assembly sequence.

Difficulty - 10. Easy, straightforward and very forgiving. (I rate easy higher than difficult. You may choose to do the opposite!)

Strength - 8. Surprisngly strong given the assembly method (though not, for instance, as strong as the Sonobe Cube).

Finished appearance - 10. Very clean. No creases or edges across the face.

Originality - 10. Completely original when first designed / discovered.

Added value - 0. Hey ... it's just a cube!

Functionality - 2. You can stand things on it.

Extendability - 10. Paul Jackson's Cube leads on to many other designs. See Homage to Paul Jackson's Cube in my recently published book Building with Butterflies. See http://freespace.virgin.net/dave.mitchell/origamiheavenpublications.htm

So ... all in all a very, very good design.

I welcome your thoughts on this.