Week 9: Rope

In my undergrad studies, I did a deep dive into archaeology and gained an immense appreciation for just how amazing homo sapiens sapiens is. I attempted to make obsidian points and experimented with clay-firing, and bark/root-weaving. I didn't give stone-knapping the years it takes to become passably adept at controlling the process. Working with clay is much more low-floor, although with an impressive high ceiling. Same with root and bark weaving: I could do it, but only well-enough to really appreciate the masters. 

This week's reading (The art and science of rope by Aström & Aström) took me back to those undergrad years. Rope-making is ancient...possibly as ancient a craft as working with stone. Unlike stone, rope is made of perishable, organic material: stuff like jute, flax, nettles, sinew, or rawhide. There is indirect evidence of its use and therefore of its existence, however: ancient clay pots decoratively marked with that unmistakable diagonal rope pattern, stone tools with perfectly round holes possibly created by using a rope (bow) drill, or wear marks on tools that were likely caused by the rub of rope over time. There are even human accomplishments that must have involved rope in some capacity, such as the domestication of horses or the settlement of New Guinea and Australia some 45,000 years ago. The limited direct evidence is significant: ~32,000 year old twisted fibres found in Dzudzuana Cave in Georgia being the oldest. Even with limited direct evidence there is no doubt: homo sapiens sapiens has been a rope maker for tens of thousands of years.

So what does this have to do with math? There is quite a lot of math in the study of rope, actually. Even though human beings can make rope with only basic mathematics, we can improve it and understand its strength and beauty by using a more complex mathematical lens. Creating a rope that is maximally strong and light is a feat of engineering. It helps to understand a rope's linear density, elongation, and breaking force. These are all properties that are measured and explored through mathematics. Laid rope (which is not braided, but a column of ropes twisted into a cable) is a structure that is defined by the curve and torsion of each helical spiral. When the strands of the ropes are twisted harder, the angle of the helix changes. In the Industrial Revolution, it was discovered that the strength of rope is directly proportional to the angle of the strand twist and not the number of yarns.

An important property of rope--that it will not unwind itself if two strands are twisted in opposite directions--can be mapped and represented by using combinations of the letter S (which represents twisting in the counter-clockwise direction) and the letter Z (twisting in the clockwise direction). Most ropes are laid in either an SZSZ pattern or a ZSZS pattern. The first letter represent the twist of the fibres, the second represents a twist of the yarns, the third is the strand twist, and the fourth is the rope twist.

In all, the Aström & Aström article got me thinking a lot about the need for complex mathematics in our world. My hypothesis is that math seems to make a significant appearance as soon as we humans want to scale up our engineering efforts, create patents, consistently manufacture goods of a specified quality, increase production, and track transactions of buying, selling, and borrowing. We can make incredibly strong, useful, and beautiful rope knowing only basic mathematics: mostly pattern recognition, measuring, and estimation. As stated in the film "Closed by Hand": the knowledge is in the body and the hands. The rest is impressive, but most definitely a hallmark of complex, hierarchical societies with big economies and impressive monuments. Not to mention armies and armadas.

Making my own rope...

I was lucky to have done a poor job of trimming back my garden in the fall. As a result I had a lot of potential rope-making material. I chose handfuls of damp pampas grass and went to work!

Here is the start of the second twist: a Z-twist following my initial S-twist of the fibres. 

And here is my completed strand. 

Yes, it holds together tight. I was also impressed at how I could arrange the pampas grass into a basic, uneven line of fibres and easily twist it into a pretty strong strand. I'm pretty sure I could have made it much longer by laying out a rough grouping of fibres along the length of my table. So interesting! And I'm very curious about how much weight it possibly supports. 

Amazingly, the grass bridge at Q'eswachaka starts with strands as simple as mine. The type of grass used is a little different, but the structure is the same. Strands become ropes, become cables. Cables are braided, anchored and woven together. Way cooler than the Capilano Suspension Bridge. It makes me wonder how many societies built grass bridges like the one at Q'eswachaka. And I again think about the mathematics: no complex formulas dictated the design of this amazing grass bridge, but can you imagine the non-standard measuring and estimating? Or the pattern sequence? Actually, I wonder if the pattern sequence for building the bridge is recorded or kept in the memory of the bridge master and than passed along to the community?

I'm going to end this week's reflection with a poem to my oldest son and our old dog Ollie, who passed away today. It's been a rough month for the poor old guy. We decided that his quality of life has declined to the point that it was time to let him go. Ollie has been my 18 year old son's companion since he was a year old. 

My

Love

Crescent

Moon-lit eyes

Beautiful old boy

Soft gentle Ollie-Bollie Boo