A calculus for learning your body

The basics of "learning to understand"

There used to be a store in Toronto called the World's biggest bookstore. It opened before I moved to England to join the army. And it was still there when I moved back to Canada to attend university.

I used to go there by myself and spend ages in the sci-fi and fantasy sections. Sometimes I would go there with my dad and when I'd finished my browse I would go up to find him, usually in the art section.

On one such occasion I came across a book called Dynamic Anatomy by Burne Hogarthe. It was filled with drawings of the body, both whole and in in pieces, drawn from any conceivable angle.

I was transfixed.

I loved the style of the drawings and simply enjoyed looking at them while at the same time wishing I could draw in the same way.

I ended up buying the book, and a few others by the same author, all with the word dynamic in some part of the title.

The aim of the author was to teach the reader how to draw the human body freely, and realistically without having to resort to a model.

And so to that end the first part of the instruction was in learning basic proportions of the human body. How the length of one part related to another.

From there the focus was on the basic shapes of each element, and then from there noticing how the view of the parts of the body changed depending on viewing angle. This was all stuff that had to be practiced, learned, memorized.

I learned the basics of this method. Then later on I applied the same rules to doing "actual" anatomy drawings (bones and muscles). This was nowhere to the level of detail and expertise I wanted to, but still being able to draw well enough to do my own illustrations for my website and in the process understand basic muscle and skeletal anatomy.

What has this to do with basic principles?

Perhaps it is something that is even more basic than basic principles.

What Burne was working to teach in his book was "understanding". Understanding the body well enough to draw it convincingly in any pose from any angle without needing recourse to an external model.

  • And to do that you had to understand the parts.
  • You also had to understand how the parts related.

The nice thing was that this same understanding could also be applied to drawing from life. It's just that there was also the built in option of not needing a model.

A framework for balanced self-expression in yoga

I had a similiar experience working with my most important yoga teacher, Andrey Lappa. When I was trying to figure out a method of applying the method of understanding burne was using to actually using the body, Andrey was the one who led the way.

Actually, prior to meeting Andrey and attending one of his classes, I didn't think there was a way.

Andrey did more or less the same thing that Burne did, but in the sphere of yoga and expressing one's own body. I should be more specific. At the time, doing yoga, I only knew the ashtanga yoga system. I didn't understand how to sequence poses or how poses should be sequenced or combined relative to each other.

Andrey provided a way of understanding the body so that I (and any of his students) could sequence poses intelligently, while maintaining muscular balance. But he also provided a framework for creating new poses.

How? By looking at the body in terms of the things that made it up from the perspective of movement, and how those things related.

He looked at the joints, each major joint and the movement possibilities for each joint. He also looked at combinations of joints, say knees and hips, shoulders and elbows.

But he also looked at the body, how it was positioned relative to the earth.

This all provided a framework for exploring the body and expressing it while at the same time providing a framework for a "balanced" yoga practice.

Learning to understand weapons

Personally, my journey didn't stop with Andrey. He was the guy who provided me with the tools so that I could continue the journey by myself.

And in a way this mirrored the mindset that was in place when I was in the British army undergoing trade training.

As an armourer, my job was to learn how to fix guns, mainly rifles. But we learned to fix other things as well. Part of the process was understanding the weapons we were expected to work on. This meant understanding the pieces and how they related. But it also meant understanding common problems. But more importantly, the idea was that we understood how the parts or the weapons were supposed to relate so that we could find problems and fix them, even if they weren't problems we'd previously encountered.

Additionally, we had some limited course work on bench fitting and tool making so that we could make our own tools if we needed to, the idea being, that in a war, stuff gets blown up. we might not have the spares we need. And so we would have to make them. and in addition we might need to make the tools we need to make them.

The main ingredient in being able to do all of this was in seeing "things" and how they related.

This was what we "understood".

Understanding is built on memory

I had further exposure to these same ideas learning to write Chinese characters.

This was something I fell in love with at around the same time as I started doing yoga. At the time the internet wasn't a thing, and so finding resources to do the things you wanted to was a bit more challenging. I bought all the books I could find on Japanese calligraphy, even going as far at to take a trip to California to visit and study with a calligraphy teacher who lived there.

Later, I made the switch to Chinese calligraphy (which is what Japanese calligraphy is based on.)

When I moved to Taiwan, one of my earlier calligraphy teachers would have me copying the works of masters. He'd paint first, and then I'd copy his painting. I'd look at a few brush strokes, paint them, then look at the next few brush strokes.

Basically what I was learning was how to copy.

And while I did improve my brush skills, it wasn't what I was after. I imagined being able to write Chinese characters freely without having to copy.

And so what I ended up doing was memorizing characters, and strings or characters and painting them from memory.

One of my first experiences of this was learning a verse rom the Dao de Ching. I painted it frequently, and often found myself getting into the flow as I painted it. This couldn't have happened unless I'd memorized the characters first.

Additionally, because I had memorized them, I could paint more freely. So rather than painting the same thing in exactly the same way over and over again, I was expressing myself with the painting.

Note that while I understood how to paint characters, I didn't always know their pronounciation. I had a basic understanding of their meaning. But In terms of painting, I had enough understanding to paint them.

Understanding brush strokes and how they relate

At various stages in my "learning to write Chinese characters" career, I played around with learning to paint characters by breaking them down into smaller sets of brush strokes. I later realized that this was the key to improving because when I focused on only a few brush strokes at a time I could both see how those strokes related and work at controlling the relationship as I painted it.

In addition, because I was practicing only a few brush strokes at a time, repeatedly, it became easy to get into the flow, even while practicing.

An additional benefit was that as I learned more and more characters, I began to re-use elements that I'd already learned. As a result my learning time for new characters became shorter.

My previous understanding became the foundation for further understanding.

But at the basis of this overall understanding was a simple understanding of how brush strokes related to each other

The calculus of understanding

So what has this all to do with calculus?

Calculus is made up of two basic operations. One is differentiation. The other is integration.

Differentiation basically involved creating lots of little squares to mimic the area beneath a curve. The smaller the squares, the better they approached the area under the curve. With a differentiated curve, you could easily figure out the slope of the curve at any point.

And actually, what you ended up with was a general equation that represented the shape of that curve irrespective of its position relative to some reference position. As a result, when you integrated, and went the opposite way, what you ended up with was not the original curve, but the family of curves that it belonged to. Basically, any curve with the same shape but positioned anywhere on the coordinate system.

When you differentiate something or divide it into smaller parts, you can then use those smaller parts as building blocks.

A smallest unit of understanding doesn't have to be infinitesimally small

An important point is the scaling you use or how you divide into smaller elements.

In calculus, you imagined squares that were infinitely small. That way the squares made the best match to the area of the curve they were in. So a question to ask when applying this sort of calculus to other things isn't how small can we make our blocks of differentiation but rather, how small should we make them?

So for example, learning the body, a useful element is the muscle (and related connective tissue). Why?

  • First of all it is something that you can actually learn to feel and control.
  • Second of all it can easily scale to movement and posture.

Learn to feel and control muscles, and you can use that in anything that you use your body to do.

Note that some intelligence is required here, some flexibility. With larger muscles it is possible to feel and control individual muscles. With smaller muscles, like the spinal erectors, you can look at groups of related muscles.

Other important elements include bones and joints. Bones are the things that muscles control the relationship of. In addition, bony reference points provide references for feeling muscles and controlling them. But via muscles, joints can also be felt, and controlled.

An important point is that muscle control is key. Without muscle control you can't feel bones. Neither can you feel (and control) joints.

Why muscles are a key element to understanding your body (and experiencing it)

So why are muscles so important in understanding the body, in particular, your own body?

They allow you to feel it, to sense it, to experience it.

To draw the body freely I could use pencil and paper. I repeatedly draw parts over and over again. I thus in the process gain experience which builds undersstanding. Likewise with painting Chinese characters. And in the army, we learned to understand through repeated experiences. Taking guns apart to the last clip or pin and then putting them back together again.

How do you gain a similiar experience of the body?

By learning to feel individual parts and how they relate. Those parts include bones, muscles and joints. But the key ingredient to feeling the parts and how they relate isn't your eyes and a mirror. It's your muscles.

(That being said, mirrors can be helpful.)

Learning to notice repeated changes in sensation

When you focus on activating and relaxing a muscle in relative isolation (while at the same time putting your awareness on that muscle) you can notice changes in sensation, whether the sensation is generated within the belly of the muscle or the tension it helps to create in related connective tissue structures. You can thus experience the muscle, the joint (or joints) and bones it works on.

Do this same thing in different postures or actions and you build on that understanding. Learn to experience different muscles in the same way and you work on developing an overall understanding of your body based on actually experiencing it.

And like with calculus, you can start by learning individual parts, differentiating. And then when you "integrate", you can use the awareness of that individual part in a multitude of positions. i.e. you can feel it and control it in a multitude of positions.

Basic principles for art, engineering and learning your body

Learning to feel and control the individual (groups of) muscle is a lot like taking motorcycle riding lessons. You learn how to use the brakes in relative isolation. Likewise you learn how to balance, steer, change gears, indicate and accelerate in relative isolation. You learn all of these to the point where you can execute them without having to think about how to do them so that you can use all of those skills while dealing with traffic.

In terms of basic principles, perhaps what makes understanding (or "learning to understand") "basic" is that it can be used in art, engineering, math, programming, and in skills like learning to ride a motorbike.

It can also be used to help you learn your body.

When learning to understand:

  • Learn the parts
  • Learn how the parts relate

And in things where it's easy to define "parts" in different ways, such as the body, then learn them in terms of all of those different ways. Because that too is part of learning to understand.

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