The Mathematics of Sewing!

I have been thinking about the mathematics of sewing for some time. It seems to me that one could develop a really interesting little memoir on the subject. Here's a mini table of contents for such a text :

1. Introduction
   
2. Metric spaces - from 1D to 2D
   
3. Metric spaces - from 2D to 3D
   
4. Fabric, manifolds and topology
   
5. Tilings and prints
   
6. Draping, gravity and constrained dynamic systems
   
7. Conclusion
   

I'm sure I haven't exhausted the possible topics, either. Here's a few notes about each of these topics.

Metric spaces - from 1D to 2D : The practice of drafting a sloper or block (or pattern) is one familiar to engineers and users of Computer-Aided Design (CAD) software - it consists of using interconnected lines of pre-determined length to lay out a set of two-dimensional shapes. In addition, the process of weaving threads to form two-dimensional sheets is another example of extruding one dimensional objects (threads under simplification) to form two dimension objects (sheets). The process of manipulating patterns (or fabric, for that matter) by cutting and then reattaching cut pieces at different locations exploits particular sets of the metric properties of 2D spaces. The relationship between the metric and its properties on the one hand, and the manipulation of sewing patterns on the other, could be rendered explicit.

Metric spaces - from 2D to 3D : The process of stitching fabric together in complex ways to form 3D objects constitutes a second class of transformations that could be explored.

Fabric, manifolds and topology : During the process of taking pieces of fabric that have been cut and sewing them to form 3D objects, topological properties of the sheets are also exploited. Indeed, whether sheets, tubes (thread) or 3D objects (garments), we are dealing with entities that are mathematically described as 'manifolds'. The topology of the objects concerned affects the fabrication process - for example, turning a jacket inside out is a manifestation of certain topoological properties of the garment.

Tilings and Prints : The procedure by which one generates a print pattern through repetitions of a motif is a form of tiling, for which there is a very interesting mathematics derived of both very old and very new ideas. Hence exploring tilings presents an interesting area of study, inlcuding repetitive tilings but also non repetitive tilings such as Penrose tilings.

Draping, gravity and constrained dynamic systems : Once garments are design, printed and constructed, they are worn. How they are worn depends upon the behavior of dynamic systems under gravity, especially in the presence of particular classes of constraints (e.g. adjacency or connectivity constraints).

A full exposition of these different aspects would make fascinating reading!

Footprints in the sand...

As part of my ongoing work on the fabric wiki, I have been researching so-called "eco-friendly" fabrics and the issues that surround them. This makes fascinating reading (see my wiki article on this for more details). It turns out there is no "perfect" eco-fabric - all of them have issues (even recycled fabrics), despite what some people on the net seem to believe. That said, it is possible to make intelligent choices that can put pressure on the system to change for the better.

What I found particularly interesting, though, is the whole notion of a "footprint". First of all, there seem to be several footprint concepts being used now, including the "ecological footprint", the "carbon footprint", even the "water footprint" or the "energy footprint", with a certain amount of confusion as to what each represents. Although we probably hear more about the carbon footprint, the most general concept is actually the ecological footprint. The ecological footprint is the amount of land that would be needed to produce and/or absorb the materials needed and/or generated by our activities. The reason for the "slashes" in this statement is that land is required to make things, but the pollution or garbage generated by our activities (and the nature of the world means that waste products are ALWAYS generated by activities) also requires land support. This notion of footprint is hence, truly a footprint - it is expressed in surface area that activity generates. The footprint per capita is then multiplied by the total population of the Earth to determine the total surface area needed to support all our current activities. Well, it turns out that we would need, roughly 1,5 planet Earth's to support current activity levels. In other terms, we are using up the planet's resources faster than they can be renewed. This is NOT a GOOD state of affairs for future generations.

Interesting, and perhaps surprisingly to many, our use of fabric is a primary component of our overly large ecological footprint. The textile industry is a heavy polluter as well as an energy gourmand, and the result is a direct contribution of something near 15 to 20% of our ecological footprint, due mainly, of course, to the use of fabrics in the developed world (Europe and North America). It should be noted that the ecological footprint of the developed world rings in at five (5!) planet Earths - we are using resources five times faster than the planet can renew itself. Therefore, the 15% to 20% contributed by the world of fabrics actually represents one whole Earth ON ITS OWN. This is a serious problem, and one that those of us interested in sewing and fashion need to be aware of and doing something about!

This means not just what and how we buy, but also how we talk about and promote fashion, how we engage with the community, and so forth.

MycoAnna and Recycled Fabrics

While in Montrreal for a visit with my brother (who was staying with mutual friends), one of my friends suggested that I go and visit the MycoAnna boutique on St-Laurent. Although she didn't quite remember the name, when I finally found the shop, the name rang a bell, although I couldn't remember from where or when. Well, it turns out this is a company that started in Quebec City, right down the road from where I live (no wonder the name resonated!). I was stunned by the garments showcased on the store in Montreal. This is the first time I've really gotten excited over the aesthetics of using recycled fabrics (no doubt from personal ignorance - I haven't gone out of my way to find out more). Interestingly, MykoAnna has been in business for 15 years, long before the current interest in recycled fabrics developed. It seems that the store hit mainstream only about 8 years ago and has been expanding ever since.

I've always considered working with recycled fabrics to be an interesting but challenging task for a beginner sewer, and one that I would eventually explore but would leave until I mastered better some of the basic techniques. MycoAnna uses a majority of stretch fabrics in their designs, which is another area I have "left for later", although working with stretch fabrics is one of my spring projects this year. I don't understand much about stretch fabrics, but I was as much impressed with the shape as well as the eclectic colors and textures of the MycoAnna designs. Since different fabrics have different stretch properties, sewing these fabrics together higgly-piggly would no doubt leave a garment with odd shaping properties - their garments obviously do not do this. I also noticed that their fabrics are sewn without apparent attention to the grain, even when non-stretch fabrics are used. I'm sure this apparent inattention is an illusion, but it seems to me that doing this kind of sewing well would require a lot of knowledge and know-how about how fabrics work together and drape. One can shape a stretch fabric by changing its flat pattern seam shapes. It would be great to better understand this process.

The saleswoman in the Montreal boutique mentionned that these garments work well for both older women and for bigger women - the color contrasts draw the eye in interesting ways that result in a strong appearance for women across a range of sizes and body shapes. I get it, looking at the garments, even though the models on display on the runways are the classic thin models.

Anyway, MykoAnna turned me on to the possibilities of working with recycled fabrics. And I shall certainly check out the Quebec store. This is a story to watch as it unfolds. See MycoAnna Creations for more on their collections.

Pencil Skirt....and Indian clothes

Took a break over the fall from my sewing, as I had a very busy teaching session since mid summer. In preparation for Christmas, I made a pencil skirt for my niece - it worked out well, although I have already modified the design for the next time - for some reason, I had the button panels open to the front instead of the back, which would have been more discrete and just as effective as a fashion embellishment. The photo shows my niece, Melina, wearing the finished skirt! I am now working on a jacket to go with the pencil skirt, made out of the same fabric. While in Vancouver over Christmas I bought some tartan fabric which will make a great lining.

Also, while in Vancouver, I found a two block section of Scott Road in North Delta with 10 fabric stores for Indian fabrics, saris and other Indian clothes. I bought some fabulous fabric there to begin making my first salwar kameez, another of my projects for the spring. More soon.

Designing for Plus Sizes

I've also been reflecting on the process of designing for what have come to be called "Plus Sizes" - essentially, big people. Now, I'm big, although that wasn't always the case - in high school I was the "skinny" kid. And I've started to design clothes that change my image and work with my size and shape. But I'm also interested in designing for big women (as well as smaller ones :) ).

I've noticed that a lot of big women who are slightly (or perhaps more strongly) ill at ease with their size and shape, choose clothes that serve to hide or distract from their body shape - lots of embellishments, for example, loose clothes (although that may also be a question of comfort), often combined color choices that are bland or dark.

One of my ideas to rethink designs for big people is to imagine a world in which the average person IS big. In this world, "small people" are the exception. What would our fashions look like in such a world? How would these fashions be different from today's "plus size fashions"? I think the answer is, they might be dramatically different than they are.

On the Burqa and the Skirt

In my attempts to rethink certain aspects of clothes we take for granted, I have arrived at a somewhat surprising understanding of the role of the skirt among our clothes. Fundamentally, how does a skirt differ from a pair of pants? Here's an answer, no doubt not the only one, but an interesting one. The skirt hides the lower structure of the body, whereas the pants work with this structure.

If one stops to think about this statement, one realizes that history, indeed, confirms it. The history of the skirt moves from a form that is more covering towards one with at least the possibility of minimally covering the structure of the lower body.

One can argue that the skirt is primarly a practical garment - simple to construct and useable in a wide range of situations. However, the skirt actually is of considerably lower utility than are pants - a skirt does not protect the body from harsh physical conditions, where the pants do provide protection. Hence I believe that the role of the skirt to hide the lower body is actually its primary purpose.

Today, of course, the skirt often hides little. A miniskirt reveals all, but, of course, that is partly why they are appreciated over other skirts. The existence of the miniskirt, and its effects, hence reinforces the argument that the skirt's function is to hide.

In Elizabethan times, the 18th century and the Victorian era, the skirt hid the lower structure even more, by providing additional structures that were very different from the actual body. Today's skirts follow the body's natural shape much more than did these garments.

Once one accepts the argument that the basic function of the skirt is to hide the body and its structure, it then becomes possible to think about suggesting other structures or body expressions - the different ways of embellishing skirts allow one to present a very different statement of who one is.

Interestingly, this argument casts an interesting light on the resistance of men to adopt skirt-like garments in our culture. It is not merely a question of avoiding being "feminized", but also a need to stay close to one's actual body shape rather than to allow this to be disguised in the variety of ways that women are used to. Again, since make-up is also a form of disguise, there is a consistency in men's resistance to disgusing the body in such ways.

Furthermore, it becomes clear that the essence of the way our culture treats the feminine is as a play between hiding and revealing. We are obsessed with both of these and their interplay, especially as expressed through women's garments. The whole argument is almost absent from our way of viewing men. Only tha phallus falls fully into a similar role.

I believe this tension between showing and hiding is also partly why our culture feels so violently about the muslim traditions of hiding the woman's body completely. Such a goal is not inconsistent with the basic principles behind our own "feminine clothing", which was designed also to hide from view the women's body. There's something a bit hypocritical about opposing msulim practices that seek to hide the body completely or almost completely, when the principles behind today's women's fashions, which accept the skirt as a distinctly "feminine" garment follow the some logic. I'm not in favor of a culture that imposes such full covering on all its female adherents, but I think part of the irritation is because it reveals something shadowy about our own fashions.

Lessons from the Crotch

Yes, I've been learning to make pants, and I think the main issues are to be found in the crotch (although the front opening makes a close second!). I was working from the Aldritch book. Her blocks show the hip line well above the crotch line, but the measurements of the women I've been making pants for are characterized by a crotch depth that is only slightly deeper than the waist to hip length. Now, it is possible that part of the problem is that the latter measurement is over-estimated - locating the hip line is not actually all that easy, since it is one of the gentler curves on the body of many people. Nonetheless, faced with this apparently unusual small difference between the hipline and the crotch line (although perhaps not so unusual, if two out of two women I'm making pants for have this!), I was for some reason tempted to lower the crotch line rather than raise the hip line! Quelle gaffe!

This makes for a Very Baggy crotch area, not at all very feminine in style, nor very flattering to the female figure. Women react very strongly to this - it would have been safer to have erred towards a tighter crotch than towards a looser one! Admittedly this depends to some extent on the type of pants one is making - my first pair were the harem pants described in the previous blog, and a lower crotch area in these looks like a design choice! For the exercise pants, however, the result was disastrous! Now I have to correct by lowering the waist to compensate, but of course this screws up the shaping I did for the waist. Arghhh!

I think the problem may have been that we men often go for a looser than a tighter crotch area, and that led me astray. Even for men, however, a low crotch line, although sometimes a design choice, looks sloppy.

The front fly also causes me problems. I got to thinking, we men generally prefer an opening with fastenings there, but women don't need this in the same way men do. On the other hand, there is usually more shaping between the hips and the waist for women than for men. Having an opening at the front therefore serves to allow more elegant shaping of the pants. Openings at the side often add bulk to the pants in a location which is not appreciated by women. So a front opening is still the ideal location, even though the purpose of this is slightly different.

Finally, I have learned to avoid installing four pockets - I spend more than half the sewing time on the pockets. One at the front (either side) is plenty.