Chapter 4 - The Theory of the Elements, cont.
The Elements in Isolation
Air
We meet the element Air primarily as the substance of the same name, composed of a mixture of various gasses such as nitrogen, oxygen, argon, and carbon dioxide. Air is what fills up the space between the lower elements (earth and water) and the outer void of space. Gases are also found underneath the Earth, as well as dissolved in the oceans. The air element is also within all living creatures in varying amounts: in both the earthy and watery parts such as bone and blood, not to mention its central role in respiration in animals as well as plants. In short, it is difficult to find places without some kind of airy element, although by far the atmosphere is its most direct and voluminous manifestation.
Air shares a number of properties with water, and in fact scientists consider both liquids and gases to be “fluids”, precisely because of their similarities; yet the two types of substances are unique in their manifestation. Air is somewhat paradoxical in its nature: it is the most directly all-encompassing element, yet is simultaneously the hardest to notice. We move in the air and the air moves in us, but it is invisible, almost intangible. It is that element whose nature it is to let the nature of the other elements become manifest. We see the objects around us precisely because the nature of the air does not disturb the connection between our eyes and the objects we gaze upon. It is as if the air is continually in a process of getting out of the way of the other elements – and in this sense can be considered selfless.
The forces of levity are more apparent in the air element, which actively fills any container equally, no matter the size. It disperses itself with great speed into any volume, and can penetrate into areas that water cannot reach. Where water conforms to the sides and bottoms of its containers, air conforms to the whole volume – it seeks the periphery of its container with little regard for the direction of gravity’s pull. In this sense, the form of the air is always an exact inverse of its container – its complement.
Air has no equivalent of water’s surface tension, and in fact is marked not by self-association but self-dissociation. The kinetic molecular theory of gases even postulates that the molecules in a gas act as essentially volumeless points, that collisions between molecules are perfectly elastic (no energy is gained or lost), and that attractive or repulsive forces between molecules are negligible. These tiny points zoom around at tremendous speeds: molecules of oxygen gas move on average approximately 750 miles per hour, while hydrogen – the lightest gas – averages more around 3,500 miles per hour (these numbers vary greatly with temperature). So we have a picture of a truly staggering number of collisions between an uncountable number of tiny molecules, while at the same time each collision is the most transient possible, characterized primarily by changes in momentum. In other words, diffusion is a key aspect of gases; smells propagate with great quickness throughout a given volume of air, allowing, for example, the smell of morning coffee to permeate a whole house with ease. At this small scale, the movement of each molecule is essentially random, and is best described by a probability distribution. Air is itself the most diffuse element, and our atmosphere simply fades out into the not-quite-empty-void beyond – it is borderless in its nature and finds no boundary that is not imposed upon it by some other element.
The micro scale picture of air exhibits some interesting polarities with its macro scale behavior, in which large, coherent effects, both in time and space, play a central role. In particular, the movement of air as a whole in the process of convection is paramount. Whereas the density of water varies within only a very small range, gas densities can fluctuate wildly. The effect of these differences is what drives our entire climate, as well as local weather, in a phenomenon known as convection. Less dense masses of air rise while denser masses fall towards the Earth’s surface, driving convection cells across a range of scales. Although such patterning is the dominant feature of both climate and weather, these are two phenomena which are very difficult to predict – the underlying physics is so difficult that most weather predictions begin simply as averages of past data, rather than as analytical determinations based on physical models. Trying to physically predict climate and weather requires the fastest supercomputers on the planet just to get reasonable estimates.
An important quality of air is brought to light when we consider its strange capacity to be highly random at small scales while yielding ordered, predictable patterns at larger scales. When examined analytically, even though the patterns formed are predictable in their general forms (convection cells, spiral vortices, etc.), their occurrences in any particular instance is almost impossible to predict. The larger ordered patterns are not simply organized, but retain a level of unpredictability in their sequencing. The technical word that describes this kind of behavior is chaotic 9, which is a strange simultaneous mix of order and randomness, predictability and unpredictability. Indeed, air is the most sensitive of the elements, responding simultaneously to the slightest changes in heat, volume, and pressure. Air has very little momentum because of its small mass, and of all elements it therefore responds most quickly to environmental shifts, particularly changes in heat. Additionally, any change in the air can and does propagate down to the smallest possible scales, whereas in water such effects are mitigated by the stronger internal forces between individual water molecules. Such sensitivity can easily be seen by opening a door at one end of a house and observing how the slight change in pressure is transmitted almost instantaneously throughout the connected volume of air in the rest of the house. Such sensitivity is a breeding ground for chaotic effects; in fact the technical term for one of the major qualities displayed by chaotic systems is “sensitive dependence upon initial conditions” (also known more colloquially as the ‘butterfly effect’). Indeed, it was the accidental discovery of just this quality which led Edward Lorenz, a meteorologist concerned with modeling movements of the air, to become one of the pioneers of the field now known as chaos theory. (Gleick, 1987)
Chaos (which manifests also as turbulence in connection with fluids), understood in this way and not simply as disorder or randomness, is the natural domain of air, whose intrinsic movements take the shape of the vortex, the infinitely layered spiral of dynamically shifting energy. On the one hand air, considered in comparative relation to its environment (composed usually of water and earth), is boundaryless and seeks the periphery. On the other hand, when considered in relation only to itself, air consists of nothing but an infinite series of internal boundaries. As a consequence of air’s quality of self-dissociation, internal boundaries between one layer of activity and another are continually formed and dissolved in a chaotic, invisible dance. These internal boundaries are the signature of air’s supreme sensitivity, and are constantly in flux according to the whole variety of influences that the environment transmits to the air. For example, any object embedded in flowing air is associated with a dynamic shape that is formed out of the streaming air as it passes around the object. Every object, even to the smallest scales, creates some disturbance in the air, which dynamically responds by forming a series of layered internal boundaries marked by changes in speed and direction. The resultant form is not simply a static inverse to the object, but is itself a continually moving and forming shape that responds with the utmost sensitivity to the details of the original shape and its relative speed through the air. Of course this is precisely the quality that leads experimentalists to use wind tunnels to analyze the shapes of objects that have to move efficiently through the air – something that is simply too complicated to be understood through theoretical understanding only.
As Schwenk indicates, it is in the nature of air to flow much faster than water, and indeed the characteristics particular to air are more greatly expressed as its speed increases. (Schwenk, 1965 p. 114) As the most sensitive element, the vortices formed in air naturally span a wider range of scales than those in water, while at the same time having more complexity. Every obstacle to the flow of air creates a moving train of vortices that is in constant interaction with the whole volume of air. Indeed, the flying formation of birds utilizes just this phenomenon in order to dynamically share the energy costs of migration; the vortices formed by the birds act as a unitary whole into which and out of which energy is given and taken by each individual bird as needed (Schwenk, 1965 p. 115).
Of all the elements, air has the greatest tendency to exhibit chaotic effects. It is true that many aspects of air considered here apply also to water – convection and chaotic effects being two of the most important (these, among other, qualitative similarities are what prompt scientists to call both liquids and gases fluids) – but air exhibits the effects more prominently and readily. Indeed, when forced by other means to flow faster, water begins to behave more like air in this respect. When a blockage in an air stream occurs, the resulting air formation that results is generally not static as in the case of water, but is itself involved in a constant shifting and oscillation. Where in the water element the wave form, an expression of oscillation, is essentially static with continually changing substance flowing through it, in the air element both the substance and the form itself continually change. The vortexial train itself oscillates chaotically – a phenomenon which performance aircraft manufacturers must take into account. Objects create their own particular vortexial forms, and when the relative speed of the air increases, such forms become more chaotic. In aerodynamics, the meeting between streaming air and objects creates what is known as a “boundary layer”, which at higher speeds can actually become detached from the object itself, lifting off it and creating its own shape which is quite different than that of the physical object – a boundary formed entirely of air that itself changes sensitively with the shape of the object, the speed of the flow, and so forth. (Benson, 2006)
Air is thus uniquely interesting in that its qualities do not manifest only through one fairly restricted set of possibilities, but rather seem to span much wider ranges of potential activity. Its variable relationships between temperature, density, and volume, as well as its chaotic movements over time and scale, demonstrate this well. In other words, the air element seems to manifest through sets of polarities: rising/falling, less dense/more dense, warm/cool, ordered/random, borderless/all-border, contracting/expanding, selfish/selfless, as well as the polarity between its abundance and lack of obvious presence. In fact, when considering air, it is not simply a question of static polarities, but of a process of active reversal. This is most clearly seen in the reversing oscillation of the vortex trains in the motion of air, which curl alternately one way and then the other, yet is a hallmark of all of its polarities. For example, a warmer mass of air will become less dense and thus rise. But the very activity of rising has the effect of expanding, and thus cooling the air mass, which then as a result becomes denser, falling around the rising warm air. It is a characteristic of air that any change it undergoes has a tendency to engender another shift that is polar (opposite, complement, or reciprocal) to the original change, whether it be in temperature, pressure, density, or motion.
Seen from the perspective of polarity, we can take a deeper look at the micro/macro levels of air. We can imagine that on the micro scale the individual molecules do not share their own properties with the other molecules – their chemical properties are less active with respect to each other. It is as if each molecule were selfish. Each molecule shares as little as possible of itself, transferring only momentum to any other molecule it encounters. Also, at this level, each molecule encounters hundreds of thousands of neighbors every second, with a little momentum transfer at each encounter – they are very busy bumping around while trying to keep to themselves. Yet at the same time, it is precisely this ‘selfishness’, along with the molecular flurrying of activity on the micro scale that gives rise to air’s selfless and clear nature on the macro scale. In particular, the ability for air to be invisible and to allow light to be transmitted coherently and undisturbed between objects and our eyes is due in large part directly to the fact that air molecules are, as we have indicated, ‘selfish’. If they interacted more strongly with one another the potential for disturbances would increase and could cause a variety of distortions. Additionally, we have the polarity of the high speed and number of molecular interactions on the micro scale, while on the macro scale we have coherent, ordered effects such as pressure gradients, convection cells, and the ability to clearly transmit vibrations (sound) without distortion.
A special note must be made here about the special connection between the air element and sound. Although all physical mediums are capable of transmitting sound, it is only in the air that sound finds its true home, as it were. The sensitivity of air is, we could say, tuned to the nature of sound, a fact clearly demonstrated by an examination of the difference in aquatic animals and animals that live in the air. Although underwater animals can, and often are, sensitive to sound vibrations, nothing can rival the variety of audible expressions, and ears to hear such expressions, that occur in animals that live in the air. Air, which is most easily able to transmit both sound and light, is the element of communication par excellence. One physical reason for this again lies in air’s lack of internal connection and low inertia – the most subtle vibrations are able to be transmitted because the internal forces between individual air molecules are negligible, attenuating the vibrations least of all the elements.
A last polarity can be considered when we examine the properties of the two most abundant gases in the air: nitrogen and oxygen. It is interesting to note that nitrogen as an element is very benign, and for this reason is used (for example) in preservation of paintings such as the Mona Lisa, which are held in sealed, pressurized containers of nitrogen. What is being kept out of the containers? Oxygen! It is precisely the oxygen present in the air which would act to degrade the paintings over time. This occurs because oxygen is a highly reactive substance – it has a tendency to ‘burn’ (oxidize) many common elements in a destructive chemical process. Thus our air (78% nitrogen and 21% oxygen) is composed of gases which have qualitatively polar aspects.
Footnotes:
9: Back Hence the title of Schwenk’s book about the patterns of fluids: Sensitive Chaos
