CÁLCULO TARIFARIO

In a biotensegrity structure there is a continuous tension network in which discontinuous compression elements are suspended. The compression struts do not touch each other. This is the first challenge to notions derived from general anatomy books. Our bones do not touch each other and, according to Levin, the cartilage lining our joints in the living body is not tough and strong, such as we might imagine from the knuckle on a chicken bone (by the time we see it to get that impression, that knuckle is dead or cooked, which makes it hard). The cartilage in the living form is more like the texture of a boiled egg-white. In a healthy body it is hydrated and intimately organised in the joint it is part of. It is not fundamentally designed to withstand direct compression forces as the cement between the bricks in the walls of a house does.

Unlike the drawings in many books, where the bones appear to overlap, in healthy organisation our bones act something like spacers in the network of our tensional body suit. Their action is not simply explained by levers as if they were overlapped or hinged like a mechanical joint as they can appear in many representations. If you think about it, it is rare that we actually move our limbs or joints in one plane as if they were levers. Indeed, on the yoga mat, we do things that would permanently twist or break a form designed by the linear logic that some of the mechanical theories we are more familiar with might suggest.

Our dynamic arrangement is a tensional organisation in which the joints are perhaps more aptly described as “floating fulcrums”.3 The intricate geometry of the whole form is organised so that the tensional and compressional forces press and pull each other simultaneously all the time. This intimate relationship means the compression part contributes to and elaborates the tensional aspect, which reciprocally compresses the compression part. They work in complementary (if apparently opposing) forces. Their combination is the key to understanding biotensegrity.

In its entirety and continuity, such an architectural design is resilient, and it can rapidly transmit and distribute forces to all parts of the structure. It is a relatively economical and lightweight design of a structured volume-in-space that can independently move and withstand dynamic stress while balancing multiple forces. It is an elegant model that makes a great deal of sense, despite the complexities of its finer detail.

Living Architecture

Once the overall principles are understood, biotensegrity can be readily seen as a means by which many living things successfully manage their architectural ability to defy gravity, that is, moment by moment,

from the inside out and the outside in, through multiple angles in space and in real time.

All living things, from flowers to vertebrates, share this fundamental ability to oppose the gravitational forces pulling them towards the centre of the earth. This is achieved throughout our volume in space. It is not just as opposite ends of a “push-me-pull-me” or “a pressing down and pushing up” line. It is the whole of our structure, the “all of us” that we explore in yoga on the mat. How, in the techniques of the postures, can we hold positions at all sorts of angles and still restore our shape? How do we do that so rapidly throughout a practice?

The general logic behind biotensegrity is appealing, if we let go of the concept of individual muscle units moving local joints in isolation (Ch. 9).

Despite its appeal and elegance, by comparison with many traditional, long-held concepts of levers and fulcrums, biotensegrity is an emerging theory. It is an inspiring perspective on how we do yoga. It is also being adopted in the relatively new field of soft robots6 and research is gradually developing in prosthetics as interest and understanding grow. Until there has been further research, however, in strict scientific terms, biotensegrity is something of an extended metaphor in this context.

We will go on to see that biotensegrity offers some compelling explanations in answer to that and many other questions. It applies to the wholeness of our cells and organs. It scales up to include how we contain the organisms that are our bodies, as we move them around in their entirety. It challenges the premises upon which many classical biomechanical theories are based.

“Levers and fulcrums describe idealised Platonic conditions that exist in fixed structures.”5 We are not fixed structures; rather we are nonlinear biologic structures that move around and manage dynamic forces constantly and with relative ease. We are self-motivated, without necessarily thinking about it.

Theories of simple levers are clearly not sufficient to account for all that we can learn to do and make possible in a yoga practice. Nor are they easily expanded into symbolic aspects beyond the classroom, where tension–compression recapitulates the positive–negative, attract–repel forces we come across on every level of our awareness.

What Tom Flemons terms “a comprehensive theory” has yet to show in precise detail exactly how biotensegrity translates the forces through the joints. It is compelling nonetheless, with clear evidence on a micro scale, as we will see. Flemons offers elegant explanations for such a theory7 and adds:

“it is clearly a more comprehensive account of how living structure operates on all micro-scales but to describe macro structural anatomy in biotensegrity terms requires a leap in analysis that hasn’t been achieved yet. … The most we can say about the joints in our body is that they are floating fulcrums which forces percolate through. If muscles and tendons are acting like levers, they are not simple levers [see Ch. 7] because the fascial net which wraps everything transmits forces across

the joints as well.”8

Such polarities are symbolised everywhere in yoga by the more metaphysical aspects of the practice (see Part 3). Philosophically, levers represent linear and intellectual thinking. Yoga includes and moves beyond the restrictions that kind of thinking can impose. (We can move as if we had levered joints, but we rarely do; it is hardly natural.) What is so welcome is an evolving perspective such as biotensegrity, that accounts for body, mind and being in a united, congruent whole, beyond the sum of the parts. If the fascial matrix provides the weave of our fabric, the biotensegrity might describe the form as volume that allows it to move around, all joined together and appropriately organised. According to Kenneth Snelson, weaving is the “mother of tensegrity”. Tensegrity provides the opportunity for a (woven) fabric (area) to contain and occupy space (as a volume), given the spacers – the floating compression members. This, in

the vertebrate body, is represented by the bones of the skeleton and the particular ways in which they hold the soft tissues apart, while being held together by them. The essence of the research into the fascial matrix is that it is changing the nature of enquiry into how we move. This is permitting a new light of curiosity to shine on many historically accepted theories. Let us look into biotensegrity to see how it presents such a powerful metaphor in yoga.

How Biotensegrity Came About

People often refer to Newton as if he invented gravity. If this were so then Kenneth Snelson (see Margin note, below) would be responsible for creating an art form called “floating compression”, the genesis of this concept of tensional integrity, or tensegrity. In truth, as Caroline Myss points out,9 the force of gravity existed long before any theories emerged. Newton’s genius was to animate and apply the idea, recognising it as a natural law. Just as apples have been falling out of trees for many centuries, tensional integrity, as a principle of living architecture, has been the basis of all things growing and moving in the earth’s gravitational field since long before the dinosaurs. We simply did not recognise it.

Yoga seeks to bring intellectual knowledge into being, realising it as a physical wisdom translated into the body’s own experience. A beautiful sequence of Vinyasa Flow Yoga, for example, does not benefit from reductionist theory. Biotensegrity, however, offers a kinaesthetic appreciation of form that makes absolute sense of every twist, turn and breath of a flowing sequence or a slow series of held poses and the balancing act they incorporate. It makes sense of what actually happens in class. Biotensegrity seems to be so much more than a model. It offers a context that illuminates a much fuller realisation of form and functional movement on every scale and throughout nature. Levin discusses the principle of biotensegrity in terms of spinal mechanics and shoulder movement in specific detail (see notes). What Newton did was to animate the distinction of gravity as a governing physical law. This allowed him to apply its logic universally. He was able to ignite the discovery of this existing principle of forces, to make it mean something in many fields of endeavour and generate its power as a law of nature on every scale. In his day, Newton had to prove the merit of his discovery mathematically and by careful philosophical logic. The pull of gravity is a law we now take for granted. Of course it goes beyond the apple; it also includes how the rest of the tree grows upward and, crucially, maintains its volume in spite of gravitational forces acting along all its branches and its extremities in space. Tensegrity is the principle the tree uses to solve that problem. We are in exciting times as we learn to reveal its apparently universal application.

An Art Form

Kenneth Snelson (born in 1927) is an artist, sculptor and geometer. His profound understanding of how nature shapes form in space can be seen applied to many aspects of science and art. He writes: “My art is concerned with nature in its primary aspect, the patterns of physical forces in three dimensional space.”12 Snelson was a student of Buckminster Fuller and it was from Snelson’s floating compression sculptures that Fuller coined the term tensegrity, from “tensional” and “integrity”. Snelson’s work and articles can be viewed through his website.13 His article “Weaving, Mother of Tensegrity” brings us closer to the idea of the fascial matrix bridging the micro and the macro scales of our form in its local weave and its global structural integrity.

gravitational downward force and constantly responds to it in intimate relationship. Through his understanding and development of compression members “floating” in a sea of continuous tension, he identified a companion law of nature. Tensegrity takes the application of gravity working on living creatures into three-dimensional life (Figs 4.1 and 4.2). For Snelson it was an art form, and in the 1980s tensegrity was not generally considered in terms of human biomechanics. Figure 4.1 This beautiful image from Albinus, drawn by Jan Vandelaar, shows the human skeleton. This is the classical model. However, it cannot stand up like this without the connective tissues that are missing from the drawing. Figure 4.2 This model of the human form as a biotensegrity architecture, by Tom Flemons (reproduced with his kind permission) does stand up on its own.

Figure 4.3

Dr Stephen Levin standing under Snelson’s Needle Tower in Washington DC.

Fig. 4.3 shows Snelson’s famous Needle Tower. The bars (compression members) are held in place by continuous wires (tensional members) that are not made of elastic material. However, the net result of this architectural form is that it contains space using the minimum of materials, with high elastic storage capacity (see Ch. 8). It is relatively light and completely free to respond to forces acting upon it with a remarkable resilience and ability to restore its shape (integrity of form). If the wind blows the Needle Tower in one direction it responds architecturally as a whole and then returns to its centred position. It is naturally responsive to any change in force. Importantly, however, it resists deformation and is easily moved as a whole, despite its scale. (This huge form can be lifted and moved with relatively little effort given its overall size. This is part of the economy of material and scale that makes it so appealing in nature.) Forces can also move through it.

The mathematical implications of this geometry are to be found everywhere in the natural world and the human form seems to be no exception. It certainly invites us to consider it, particularly given what we can do in the yoga class. The Needle Tower is an example of how the third neutral force (see Ch. 1) plays an essential role, as the uniting of two opposites, or paired structures. These two forces (tension and compression) combine in one whole architecture and form a third force, or unity, to create form. They cause each other to be. This is the form we live in or are contained in, as a volume in space. This is not just up and down force, but omnidirectional: side to side, corner to corner, inner to outer, outer to inner.

Think of a tree, solving the business of growing (upward and outward), taking up space and moving with the wind, without breaking. It uses tensegrity as the basis of its architecture. The structure and fabric itself (of the tensional and compressional elements) become the force transmission network. It is profoundly economical.

Snelson’s artistic creation of a tensional network simultaneously holds the compression “struts” together and keeps them apart, while it is held open by them. It is constructed on the principle of triangulation, which in this design forms a cross-section of the star tetrahedron when viewed from one particular direction. The geometry of this, in plan view, is clearly visible from underneath the structure (Fig. 4.4).

“Chirality” is the term given to the spiralling nature of the structure in volume. The chirality is the direction of its spiral, achieved on all scales. (Chirality in trees refers to the direction of the twist of each growth ring. Each layer has counter-chiralling properties so the tree can grow upright. Research suggests they respond to their environment; see Ch. 7.) The model in Figures 4.5 and 4.6 is about a meter long and exhibits the same structural properties as Snelson’s tower.10

Figure 4.4 The view from underneath the Needle Tower; note the geometric pattern of a star tetrahedron in cross-section. Figure 4.5 A biotensegrity mast. It begins as continuous strings, which are not elastic, joined together, without tension, at specific points, into which the metal tubes are inserted. As the whole mast tightens, the spacers take up their roles. It assumes this shape which, when dropped on its end, bounces several inches off the ground and maintains its tensional integrity and innate elasticity. Reproduced in kind acknowledgement of Bruce Hamilton, designer of this mast. Figure 4.6 As in Snelson’s Needle Tower, the end elevation of the mast appears in cross-section, at any point, as a plan view of the star tetrahedron (Ch.

2 and 21).

The architect Buckminster Fuller recognised the innate structural principle in Snelson’s work and applied it to architecture. About five years later, Fuller coined the term “tensegrity” from “tension integrity” and designed the geodesic dome based upon its architectural economy and resilient form. This is fundamentally based upon the principles of architecture and the Sacred Geometry of the Renaissance that we examined in Leonardo da Vinci’s work (see Ch. 2 and Fig. 4.7). It is now being recognised as a possible explanation of our internal organisation on every scale. The layers of tubing in a blood vessel, for example, are considered to have counter-chiral weave, which gives them elasticity and resilience as well as structural integrity.11 We will consider the context of whole body movements here, but the appeal is that biotensegrity applies on every scale of our form.

In the early 1980s, Tom Flemons, another artist and inventor, was working in a different way in Canada. He revealed the same fundamental principles. Flemons also refers to himself as a geometer and his own applications of tensegrity were focused on their relevance to human form and representing functional anatomy. Stephen Levin, an orthopaedic surgeon, followed a line of enquiry along the same theme. Levin’s questions arose from his own surgical practice. He sought answers in his local Natural History Museum, located not far from Snelson’s Needle Tower.

Figure 4.7

Leonardo da Vinci saw architecture when he studied human form. The weave of the myofascial matrix, taken globally, expands the possibilities of how we define form.

Having written expansively about this subject since the early 1980s, Levin began to work with Tom Flemons in the late 1990s, and their respective approaches are gradually revealing the depths and

application of tensegrity principles in the broadest sense, applied to human structure and motion. Their work is transforming our understanding of biomechanics and balance and certainly inviting new questions about more traditional ideas. Examples of Flemons’s work are shown in Figs 4.8 and 4.9.

Micro to Macro Scale

Figure 4.8 This is a new model, rendered by Tom Flemons, of the pelvis and spine; reproduced with his kind permission. One aspect to highlight is that tensegrity is found to be the basis of living architecture on many different scales. The cell used to be considered as a bag of water, held up by hydraulic pressure. It is now understood that it contains tension and compression elements and actually conforms to biotensegral architecture in its fullness of form and motility. (New research suggests it is a special kind of water structure too.)14 Professor Donald E. Ingber,15 a cell biologist and bioengineer, has studied and researched tensegrity principles on the molecular level while Dr Levin has sought to show how biotensegrity applies to the whole body – macro-movement.

“Despite centuries of study, researchers still know relatively little about the forces that guide atoms to self assemble into molecules. They know even less about how groups of molecules join together to create living cells and tissues. Over the past two decades, however, I have discovered and explored an intriguing and seemingly fundamental aspect of self-assembly. An astoundingly wide variety of natural systems, including carbon atoms, water molecules, proteins, viruses, cells, tissues and even humans and other living creatures, are constructed using a common form of architecture known as tensegrity. The term refers to a system that stabilises itself mechanically because of the way in which tensional and compressive forces are distributed and balanced within the structure.”16

Thus the principle called “tensegrity”, now more developed and referred to by Levin as “biotensegrity”, became animated through different areas of study as diverse as art, engineering, surgery and molecular biology. Uniting them all is the nature of living architecture. Biotensegrity can be applied to a multiplicity of living structures and the research of the last few decades has evolved alongside

In document ALCANCE NO 39 A LA GACETA NO 36 (página 107-112)