Accounting for a most dynamic world—Part 1

And how awkward is the human mind in divining the nature of things, when forsaken by the analogy of what we see and touch directly?

—Ludwig Boltzmann, in a letter to Nature, 28 February, 1895 [1]

Last week, in describing the observed invariances associated with each of the three energy laws, I phrased these as tendencies associated with systems. Presenting the laws in this way involved a deliberate effort to avoid the default approach of privileging real entities. What I mean by this is that it was very tempting to simply write “Energy law 1 recognises that some thing is conserved” instead of writing this as I actually did: “Energy law 1 recognises a conserving tendency”. I did this in order to make clear that I was not assuming prior existence of a thing or entity that is conserved.

To continue in this way would make everyday discourse pretty awkward. Proposing an entity-like thing to stand for the observed tendency provides a very practical way of proceeding as we communicate about our experiences with one another. More importantly though, proposing such a conceptual entity—in the case of law 1, this is in fact the system’s total or internal energy—allows for the formalisation of the observed tendency, and in particular, its quantification. It would be difficult to overemphasise the significance of this enablement of quantification. With quantification comes the ability to reduce our descriptions of situations in which we’re interested to a relatively small number of parameters. This in turn allows us to divert our attention from most of what we experience—it gives us a structured basis on which to organise our thinking about any situation, allowing us to deal with much more ‘experiential territory’ at one time than would otherwise be the case. As a consequence of this, we’re afforded increased instrumental power to manage and control the situations in which we’re interested. The formalisation aspect of this is very important: when a concept is formalised, we establish an agreed common basis on which to compare our understanding with one another, and hence to know what each other means when we talk about something. This enables highly effective coordination of actions amongst and across social groups—provided that those whose actions are so coordinated give sufficient attention to maintaining the structures supporting the formal status of their coordinated understandings. In contemporary societies, the default responsibility for this tends to be assigned to specific groups of knowledge experts, and the typical means for managing this is via formal educational institutions, such as the social infrastructure of schools, universities and the government bureaucracies that regulate them.

We might ask though how reasonable it is to cede responsibility for such care and upkeep to relatively restricted groups of specialists. The proliferation of increasingly specialised technical knowledge in modern societies, coupled with ubiquitous access to representations of that knowledge via the whole spectrum of communications media, means that each of us has unprecedented access to conceptual domains for which access in the not-so-distant past was much more likely to have entailed training within a lineage of competent knowledge practitioners. Within the sciences, such lineage training means that, in principle, it is not necessary to merely accept conceptual knowledge generated by others on their authority. Training involves carrying out the same experimental investigations conducted by the originators of that knowledge, providing experiences in relation to which students can make their own assessments of the validity of the established conceptual account of what is going on. Where these conceptual accounts are adopted in fields of specialisation that don’t require students to undertake that training, or where they spill over into popular discourse, it is far more likely that the connection between direct personal experience and accepted conceptual accounts might be broken. This leads to situations where, in effect, the conceptual knowledge must be accepted either in terms of our own secondary assessment of its congruence with our established conceptual systems, or—with potential for more concerning implications—on the basis of others’ authority alone. On this basis, while it may be popular to characterise ours as “an age of scientific reason”, this is so only in a limited sense. For the vast majority of us, most of the knowledge underpinning the techno-scientific infrastructure on which our ways of life depend must simply be taken at face value. As always, faith, and more importantly, trust, in one another provides the foundations for ‘what we know that we know together’.

An important entailment of all this is that we can’t guarantee that what one person means when they make use of a concept—such as energy—to communicate with others will be understood by those others in the same way. The best recourse we have to address this situation is perhaps to recognise it—and in doing so, to recognise also the need for us to take collective responsibility for ensuring that our shared understandings are effectively coordinated. Let’s return then to my phrasing last week of the regularities or invariances associated with each of the three energy laws, and my efforts to avoid suggesting the prior existence of some inherently existent thing with which the invariance is related. I took this approach so that we can then intentionally introduce the appropriate conceptual object into our thinking, and in doing so, take ownership of and responsibility for its meaning to us, rather than just taking this as given—or worse, as assumed without question.

There is another dimension to this also though. It’s a curious feature of the construction of conceptions, that, when a particular concept captivates minds collectively, its explanatory power reduces the need for most of us to individually come to terms with the original phenomena that its proposition is intended to explain. This is particularly significant in relation to our most subtle concepts, dealing with phenomena that for most of us would remain beyond our grasp without the public availability of that concept itself. A concept, once disseminated widely and carrying a certain authority of its own simply by virtue of its social acceptance and perceived utility, both makes visible to us something that its originators saw but that would otherwise remain invisible to most of us, while at the same time—by encouraging us to think in terms of its particular way of constructing meaning—making it harder for us to see beneath its generality. Once we become accustomed to making sense of our experience in terms of a particular conceptual explanation—especially where this is as universal as that afforded by the energy concept—attending to the raw perceptual experiences of phenomena free of the concept’s influence can present significant challenges. We start both to think and in important respects even to perceive in terms of the concept itself. It captures our minds and our imaginations, and influences even our sensing. This is the reification cycle introduced in an earlier post: the originator holds a concept, and if it becomes influential, the concept can eventually come to hold us. These foundational posts are aimed at loosening the grip of such a hold, in the expectation that this will then allow us to reach pathways for responding to energy challenges for which this hold previously restricted access.

A brief—and highly selective—history of the modern energy concept’s emergence

Motivated by this introductory discussion, I’ll focus for the remainder of this post and for the next two on a different approach to such a task, by looking at a selection of pivotal highlights in the historical unfolding of the insights summarised in energy laws 1, 2 and 3. This should provide us with some sense of the experiences in relation to which the conceptual insights arose for their originators. On the surface, it might seem that these investigators would be hampered in their efforts by not having available to them the modern energy view that is so influential today. As we’ve discussed though, there’s a flip-side to such explanatory power, relating to the way in which it can hold us back from better appreciating the phenomena underlying our default conceptual explanations. By considering some key investigators whose work was unencumbered by the ideas that they helped to bring to light, we might ourselves get a better sense of what the energy concept and related ideas we’ve been looking at are all about.

The main source that I’ll draw on for this discussion is Jennifer Coopersmith’s 2010 book Energy: the Subtle Concept [2], the aim of which is “to explain energy and to use the history of its emergence for this purpose” (p. ix). By way of highlighting Beyond this Brief Anomaly’s point of departure from existing approaches to this area of inquiry, it’s worth kicking off the discussion by first considering some of the conclusions Coopersmith arrives at via her approach. The book’s final chapter begins and ends with two different positive statements about what energy is:

To return to the physicist at the start of this book, she can now explain energy as the ‘go’ of the universe, what makes things happen. (p. 350)

In one sentence, energy is: the ceaseless jiggling motion, the endless straining at the leash, even in apparently empty space, the rest mass and the radiation, the curvature of space-time, the foreground activity, the background hum, the sine qua non. (p. 360)

A couple of points are worth noting here. Firstly, this illustrates the substantial nature of the challenge presented to us in attempting to come to terms with what energy is all about. Even for someone so intimately familiar with the intricacies of the concept’s multitude of facets, in reaching beyond the conventions of discourse that these establish, there’s little that can be said beyond characterising energy as an essential condition or ingredient.  The ways we use the conceptual object, especially in technically rigorous contexts, create the impression that we know what underlies physical phenomena with great certainty. Scratch the surface of that object though, and despite its utility, in trying to establish for it some sort of more essential nature, we find ourselves grasping after shadows. Secondly, by demonstrating the limits we face in trying to grab hold of energy as a thing independent of us, Coopersmith’s concluding views show why Beyond this Brief Anomaly’s complementary approach is important. Rather than trying to explain energy, what we’re doing here is inquiring into the use of energy, understood as a conceptual construct, for creating satisfactory—’good enough for practical purposes’—explanations of the experiences that arise for us in relation to physical situations. This starts by recognising energy primarily as a product of human cognition, rather than starting by assuming it as a feature of our physical environment. This opens the way to viewing it as a set of conventions—a series of social agreements—for interpreting our experiences of living within a physical world, and hence for guiding our action within such a world.

Given the importance widely accorded to an energy-centred view in contemporary understandings of the nature and instrumental success of industrial society, there’s some irony in recognising that the modern view of energy has been with us only since the mid-nineteenth century. The significance of this timing is that the upheavals in economic organisation that we group under the banner of the Industrial Revolution are by most informed accounts regarded as originating somewhere in the second half of the eighteenth century, and continuing to the middle of the nineteenth century (for instance, Ashton’s history of this period is titled The Industrial Revolution, 1760-1830).[3] The irony stems from the fact that the view of energy as we know it today—characterised especially by recognition of the equivalence of and transformability between work and heat—emerged only at the end of this period, despite the changes to production by which the period is perhaps best known being centred on the coal-fired steam engine. For most of us, arrival of this transformational technology for converting heat input to work output is viewed as the defining innovation of industrialism. And yet the steam engine began the march towards its dominant role in the manufacturing sectors of the first industrial nations several decades prior to arrival of the insight that the operation of these machines could best be explained in terms of energy transformations. The energy concept was not necessary in its own right for enabling the dramatic societal changes that today we find so conveniently explained in terms of energy-related considerations.

That’s not to say, though, that the general tendencies—the perceived physical invariances—that today we account for in formal terms by the energy concept had not been noticed. The long process of constructing the modern energy concept can for all practical purposes be regarded as having its earliest origins in the work of Galileo Galilei (1564-1642) in the seventeenth century. Even so, prior to this the insight that came to be codified in what we’ve called energy law 1, the conservation of energy, can be found in documented proofs of the impossibility of machines acting with perpetual motion. Despite the recurrence of the perpetual motion idea throughout history— given the implications of success in such a fantastic endeavour, this is perhaps quite understandable given our very human propensity to associate happiness with freedom from work—many people have intuited from their direct experience that the overall effect for a given process cannot exceed its causes. As we proceed, we’ll find this intuition of cause equals effect emerging as a recurrent theme. Let’s start though with Galileo. In light of earlier discussion about the role of quantification, Galileo’s contributions are doubly significant. His work is foundational not only for development of the modern energy concept, but for the scientific inquiry method in general. In extending beyond observation of physical processes to measurement of those processes, Galileo introduced a means for enabling independent verification of the general conclusions drawn by investigators in relation to contextually distinct situations. Measurement and quantification allowed experiments to be repeated, and results to be compared. It also enabled very clear communication about the nature of the precise features that an investigator regarded as significant in any experimental situation. This allowed experimental inquiry to become, in effect, a collaborative effort—investigators had a ready means of better appreciating what it was that their colleagues might have experienced directly, even when geographically, culturally and temporally distant from one another.

In tracing the modern energy concept’s historical lineage to Galileo, the specific insight that is so significant is his recognition (published in 1638) of the proportional relationship, for an object falling under gravity, between the height through which it passes and the square of its attained speed of motion.  This is expressed mathematically in the form

 speed^{2}  \propto height

In order to arrive at this though, Galileo first had the more fundamental insight that the feature of primary interest in studying physical phenomena was motion—position changing with time. His work focused on the study of what we might now characterise as changing system configurations. In fact, Galileo explicitly recognised the motion under investigation as relative in nature, and hence appreciated that it must be studied in relation to an appropriately defined system. We can discern in this once again the essential connection between the energy view and the systems view of physical phenomena. It’s particularly noteworthy that Galileo’s work tends to focus on measuring and describing mathematically the motion of bodies, rather than explaining the cause of such motion. From his work we can get some sense of what it’s like to deal with the direct experience of the physical phenomena that interested him without recourse to more abstract concepts. Today, Galileo’s proportionality between the square of speed and change in height for a body is immediately recognisable as the equivalence between change in gravitational potential energy and increase in kinetic energy. In 1638 though, the idea of associating the observed behaviour with a specific conceptual object was still half a century away.

In the work of René Descartes (1596-1650) and the German polymath Gottfried Leibniz (1646-1716) we find the earliest clear precursors to the modern energy view. Descartes’ major contribution in this respect was to propose the product of weight and change in height of a body as a measure of what he called the ‘action’ (a different quantity to the action introduced in energy law 3) carried out on that body, and that is recognisable today as equivalent to what we would call work against gravity. Descartes recognised that for a given ‘action’ applied to a body, the product of weight and change in height will be constant.[4]  This insight would play an instrumental role in Leibniz’s work.  Leibniz regarded matter as being fundamentally active in nature, and in doing so moved beyond describing the motion of bodies to providing an explanatory account of that motion in terms of an active principle. In fact, as Coopersmith points out, “Leibniz was a rationalist, like Descartes, and built up a total picture of the world from considerations of how it ought to be rather than from just looking and seeing how it is.”[5] It’s significant that the origins of the abstract conceptual entity that we know today as energy are found in the work of someone who experienced their world as fundamentally principled in nature. There’s more than a hint of suggestion here that in holding an expectation that abstract concepts have an inherent existence, one’s own experience might be interpreted in ways that seem to confirm this. At the very least, if Coopersmith’s characterisation of his starting position is indeed a reliable account, it’s not surprising that Liebniz seems to explain his experience as if this is the case. The principle central to Liebniz’s view is that of cause equals effect—that mechanical effects cannot be greater than their causes, or that the activity associated with a cause must be conserved in its effects. This is the basic view accounted for by what we’ve called energy law 1. Demonstrating that this principle was in fact valid required though that cause and effect be quantified—they required an appropriate measure. For Leibniz, it was the quantity of a body’s motion that was important. He regarded the appropriate measure of this to be mv2, the product of the body’s mass and the square of its speed, a quantity derived from Descartes’ recognition of the product of weight and height as constant, and Galileo’s recognition of the proportional relationship between the height through which a body falls under gravity and the square of its speed.[6] To this quantity Leibniz gave the name vis viva, or ‘live force’—the equivalent of what we know today as kinetic energy.

While today we can recognise Leibniz’s view of vis viva as being consistent with the modern energy view, this wasn’t so apparent at the time. In fact, Leibniz’s ideas on this were part of a publication in1686 refuting Descartes’ earlier view that mv, the product of a body’s mass and speed, would be conserved under all circumstances, and hence was the appropriate measure for the ‘quantity of motion’. Both views were, in a sense, right and wrong. Leibniz demonstrated correctly that Descartes’ mv was not in fact conserved in the situations for which it was intended to apply. Taking into account the direction of motion as well as its speed, however, ‘mv’ becomes the momentum for a body, and  this quantity is conserved, for a system of  bodies in isolation from any externally applied forces. On the other hand, Leibniz’s mv2 is conserved in certain specific contexts that he focused on. These findings, though, couldn’t be generalised to all physical situations, and as such did not provide a suitable basis to account for all ‘activity’. In recognising what we now know as kinetic energy, vis viva provided an essential part of such an account of mechanical behaviour. A complete account, however, of the ‘conservation of cause and effect’ would also require what we now know as potential energy. The emergence of this concept was still some way off. Nonetheless, as Coopersmith highlights, Leibniz was far ahead of his time: in his thinking about the ‘quantity of motion’, he also recognised that when the motion of large bodies apparently disappears or is used up on colliding with one another, it has in fact been transferred to smaller scale motions of the larger bodies’ parts. It was more than a century before these small-scale motions came to be understood as the physical basis for the phenomenon known as heat. So we find in Leibniz’s work not only the basic ideas behind our energy law 1, but germinal insights also into the phenomena with which energy law 2, in particular, is related. It seems that it might be reasonable to infer from this that the modern energy concept is not in its own right necessary in order for us to understand our experience of a physical world in ways that are nevertheless quite consistent with it.

So far, we’ve been looking at the story of the energy concept’s emergence from the point of view of  a lineage of investigators that today we recognise as including the early physicists and mathematicians. I’ll pause here and take up the the story in Part 2 next week, where a second lineage will enter the picture—the engineers.


[1] Cited in Brush, Stephen G. (1964). Translator’s introduction. In L. Boltzmann, Lectures on Gas Theory, (S. G. Brush, Trans.). (pp. 3-17). Berkeley: University of California Press, p. 17.

[2] Coopersmith, Jennifer (2010). Energy: the subtle concept, Oxford University Press, Oxford.

[3] Ashton, Thomas S. (1948).  The Industrial Revolution, 1760-1830, Oxford University Press, Oxford.

[4] Coopersmith, Energy: the subtle concept, p. 25.

[5] Ibid, p. 41.

[6] Ibid, p. 42.

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