The science of water

Ovidiu Babeș

Alan Chalmers, One Hundred Years of Pressure – Hydrostatics from Stevin to Newton Springer, 2017.

Alan Chalmers’ book really makes us wonder what we know about the physics of liquids and about how science got to this knowledge. The book provides a great historical reconstruction of the major episodes in the development of modern hydrostatics. It shows how the apparent familiarity of a physical concept mislead and continues to be misleading. The concept of pressure is usually presented as a ‘given’, but it’s far from being self-evident, and its hundred years of intellectual development attest this.

Think about the ordinary things in everyday life. Some of them seem to be as trivial and boring as things can get. They aren’t surprising in any way, and only rarely arouse any thoughts or reflections. We simply take them for granted. The behavior of liquids belongs here: everyone knows that liquids flow. It’s self-evident that water takes the shape of its container, that some objects float, or that the smallest crack in a filled vessel might cause a leak. Even my cat has a habit that suggests he’s perfectly aware he can spill all the water from his bowl.If we think about it, these common intuitions are really strong. Not only do we have some idea about what a liquid is, but we rather feel we know exactly what liquids are, at least when we daily interact with them: stuff that flows, completely fills space, presses on its container without being compressible. So what’s the big deal, don’t we have the same feeling about any aspect of day-to-day life? We probably do. But liquids, even when they are not moving, can be pretty counterintuitive. Have a look at this: just one liter of water, if raised to a sufficient height by a very narrow straw, can break the base of a strong vessel. Or look at this picture:[i]

water Water presses with the same force on all three bases of the containers—that is, the pressure on the bases of the containers is the same—even if the first one clearly has more water than the last. Well, for all these kinds of counterintuitive phenomena, physics is there to help, right?

The interesting thing is that physics describes liquids in terms of pressure. That is, the very definition of a liquid is not so commonsensical as it seems to be. This is because the (scalar) concept of pressure is not trivial. Historically, it took a lot of time to be acquired—or constructed—in modern physics. Forging this technical concept wasn’t a job for a single scientist/philosopher, it was a long and complex process. It had many layers: a constant rethinking of the role of experiment and observation, inventing practical and heuristic devices, even redesigning the aims of some scientific disciplines. But what’s probably most important is that the articulation of pressure involved, for scientists of the 17th century, overcoming their casual intuitions about how liquids exert pressure. The people who invented this concept had to reeducate their common sense, as Kuhn used to say[ii]. Sure, the intuitions of 17th century scientists might have been shaped by other factors than ours, but they were, no doubt, very important in their understanding of liquids.

Alan Chalmers’ book, One Hundred Years of Pressure – Hydrostatics from Stevin to Newton, wonderfully illustrates the emergence of pressure. The science of the equilibrium of liquids arose in antiquity with Archimedes’ On Floating Bodies. Pressure and modern hydrostatics, however, were pioneered by Simon Stevin in 1586 and completed by Isaac Newton one hundred years later, with only a few details left for Leonhard Euler to polish. Chalmers tells an insightful tale of the conceptual route took by the early science of waters, of the blind spots caused by the trivial understanding of liquids, and of how hydrostatics—via the modern concept of pressure—improved our understanding of liquids. In a nutshell, Chalmers’ argument is this: In order for hydrostatics to become a modern successful science, a technical, precise concept of pressure needed to be devised. Chalmers goes to great lengths to show how the trivial understanding that liquids press on their containers was simply insufficient to shape modern hydrostatics.

It’s interesting, however, to read Chalmers’ book not only as an episode of how 17th century scientists struggled to best describe the behavior of liquids. It’s also a story about how science defines its concepts, and how these concepts get to be related. I’ll elaborate on this a bit. In 1586, Simon Stevin develops a geometrical science with the aim of explaining the (static) behavior of water. The definition of water itself was not (seen as) problematic. Stevin’s geometrical explanations implied a (proto)version of the modern concept of pressure. One hundred years later, by the time of Newton, the concept of pressure was much more articulated. With it, Newton turned, in a way, Stevin’s science upside down: Newton defines fluids in terms of applied force or pressure. In the early manuscript of De gravitatione, he writes that a fluid body is “one whose parts yield to an impressed pressure” and in the Principia he defines fluids as “any body whose parts yield to any force applied to it and yielding, are moved easily with respect to one another”, while pressure is defined as the amount of force applied on a surface (P=F/A). Historically, of course, many things happened between Stevin and Newton. More on this below. At this point, it’s just good to keep in mind that these general definitions don’t just describe physical properties, but they also help the community of scientists discern the very objects of their inquiry. In Thomas Kuhn’s words, “These generalizations look like laws of nature, but their function for group members is not often that alone. [T]hey function in part as laws but also in part as definitions of some of the symbols they deploy. Furthermore, the balance between their inseparable legislative and definitional force shifts over time.”[iii] Pressure is one of these generalizations, which doesn’t only describe nature, but also provides a sharp razor to distinguish, e.g. liquids from non-liquids. Gaston Bachelard put it even more bluntly: “In fact, as has often been said, these general laws define words rather than things. The general law of the fall of heavy bodies defines the word heavy. The general law of the straightness of light rays defines both the word straight and the word ray, the ambiguity of the a priori and the a posteriori here being such that we personally suffer from a kind of logical vertigo.[iv]” Long story short, 17th century scientists weren’t only learning how liquids behave, they were also rigorously defining the concept of liquid itself.

In his book, Chalmers mainly explores the conceptual depth of the transition to modern pressure. He explains why pressure was needed, what prompted its development, what stood in its way. His story describes how major players of the scientific revolution articulated their mechanistic accounts of the equilibrium of liquids, showing how they sometimes contributed and sometimes strayed away from what was to become their legacy in modern hydrostatics. Chalmers keeps a fine balance between philosophical aims, historical contextualization and methodological description. The structure of his book is recursive in character, with each chapter presenting a rather self-contained episode. The first two chapters display Chalmers’ methodology and the basic historical/conceptual premises of his study of pressure. The middle chapters present episodes of the methodology and conceptual machinery involved in each important version of 16th-17th century hydrostatics, belonging to Stevin, Galileo, Descartes, Pascal, Boyle, and Newton. Even if the story is linear, the accounts are methodologically (and epistemologically) complex. As Peter Dear said, “The actors in the story are really styles of argument rather than individuals”[v]. Yet it’s clear that no two actors had exactly the same ambitions, nor did they employ the same conceptual resources. Still, Chalmers identifies some overarching features of the development of modern hydrostatics. These features function as premises on which the historical reconstructions are centered. Let’s rehearse some of these premises.

Blind spots and hinges

Chalmers frames his story in Bachelardian terms. The road to a technical concept of pressure was, first and foremost, shaped by the epistemic obstacles which the actors eventually overcame. Very crudely, for Bachelard, an epistemic obstacle is a habit of thinking of which we are unreflective[vi]. When we regard a way of thinking as self-evident, we no longer question it, and it gains unwarranted inertia and value. In the long run, these habits can hinder scientific research, as they make people unaware of the possibility that things might not be so self-evident. Epistemic obstacles have many sources: personal experience, education, discursive practices, or some scientific ideals. By definition, these obstacles can only be identified retrospectively, but they are real, nevertheless, in shaping historical research practices.

Remember how we take knowledge of liquids for granted? Our daily intuitions about pressure were, according to Chalmers, one major epistemic obstacle. These intuitions have impeded 17th century savants from understand the need for an explicit formulation of the mechanics of pressure in liquids. For example, our common intuition is that pressure is a vector, a directional pushing. Yet the modern understanding is that pressure is a scalar (it only has magnitude), and acts isotropically within liquids.

Statics as an ideal. Another obstacle was inherited from the idealizations of statics. Statics, the science of simple machines, was highly developed in the 17th century. It provided a paradigm for the new science of waters. Levers and balances informed the way in which equilibrium of liquids was to be mathematized. In a balance “Unequal weights can only be in equilibrium at unequal distances, the greater weight being at the lesser distance” (as Archimedes said). However, there are many idealizations and implicit assumptions in the science of weights. For instance, the arms of a balance are presumed to be perfectly rigid (not elastic), in order for the downward movement of the heavier weight to be instantly converted into the upward movement of the lighter weight. If we are to apply the principle of unequal weights to liquids, the conversion between upward and downward thrust is not trivial, and the concept of pressure was tailored to account for this conversion.

Weight. A related obstacle came with the object of statics, weight. Chalmers argues that treating weight as the only cause of hydrostatic phenomena hindered the development of the technical concept of pressure. This epistemic obstacle is evident when the behavior of liquids is (apparently) paradoxical. People knew from ancient times that water presses sideways against lock gates. But why does water push just as hard when the lock gates are separated by one meter, as it does when the gates are one kilometer apart (provided the height of the water is the same)? This even seems paradoxical nowadays. Or, suppose you fill with water a ‘U’ tube with one side much wider than the other. The water will rise at the same horizontal level in both sides. How is it that the smaller volume of water can balance the larger volume of the wider part? These types of phenomena constituted the rather stable experimental repertoire on which the 17th century versions of hydrostatics arose. Their role as experiments greatly differed from one version to another, as Chalmers argues.

The spring of air. On the positive side, the concept of pressure was aided by advances in pneumatics. Boyle’s concept of the “spring of air” provided an example of mechanistic concept as an intermediate cause. It did not aim to explain the ultimate structure of matter, but it could explain its effects. The spring of air as a mechanistic concept is to be contrasted with mechanical concepts which provide foundational explanations of nature.[vii] 

The story 

Chalmers joins these elements together in a history of the towering figures of early modern hydrostatics. It all starts with Archimedes, who compared floating bodies with a balance in equilibrium. One of his most famous postulates is “Any solid lighter than a fluid will, if placed in a fluid, be so far immersed that the weight of the solid will be equal to the weight of the fluid displaced”. However, his account of floating (or of the more counterintuitive phenomena) doesn’t focus on how downward movement is converted into upward push—and this was only acknowledged in modern times. Archimedes also sets the pace in another way, which Stevin wholeheartedly embraced: the epistemological ideal of hydrostatics.

Stevin tried to develop a Euclidean science of waters. Hydrostatics was presented as a corpus of phenomena mathematically deduced from principles. It resembled an abstract science. The definitions and postulates do all the epistemological work—by this account, phenomena simply cannot prove or disprove principles. It would be—as Chalmers notes—like saying that “Pythagoras’s theorem is to be proved by measuring the sides of material triangles” (p. 9). Still, the Euclidean character of Stevin’s hydrostatics is more like a mode of presentation. Chalmers convincingly argues that Stevin’s explanations and deductions are imbued with practical insights, probably acquired from his experience as an engineer. Anyway, Stevin’s hydrostatics implicitly admits the isotropy of pressure in liquids, even if it did not provide a mechanistic account of pressure continuously acting in all the body of the liquid.

From Stevin onwards, hydrostatics was conceived as a science akin to the simple machines, and floating was explained in terms of a balance in equilibrium. Galileo refined this picture, and somewhat extended the experimental repertoire. He observed that bodies can flow in very little water—less than their submerged part. Galileo amended the analogy with simple machines, describing floating as similar to equilibrium in an uneven balance. However, Galileo did not move beyond Stevin in considering weight as the only cause of hydrostatic phenomena.

Descartes did not take this route. Instead, he tried to provide a very mechanical/foundationalist account. He understood isotropy, and explained the hydrostatic paradoxes by the minute corpuscular structure of water. Pressure was the instantaneous lines of ‘force’ produced by corpuscles pressing on and through each other. Chalmers portraits Descartes as ultimately facing a dilemma: either try to develop a mechanistic account of the isotropy of pressure and admitting that light does not only travel in straight lines, either drop his ambitions in hydrostatics. The former was, of course, not an option. Descartes is somehow at the antipode in Chalmers’ narrative. Even if his mechanical hydrostatics did not directly contributed to the development of the precise concept of pressure, his foundational ambitions did, in the end, push hydrostatics beyond its usual scope.

Pascal, on the other hand, directly contributed to the mechanistic account. Not only did he introduce novel mental devices (like pressure acting on planes), but he also shifted the methodological focus of hydrostatics. If Stevin was a Euclidean, Pascal ‘relaxed’ his conceptual framework so as to arrive at experimental innovation. He used his famous press more like a heuristic device than a practical tool. This device could help explain why the pressing of the liquid is the same for any surface of a container, regardless of its orientation. Pascal also attributed hydrostatic effects to the “continuity and fluidity” of liquids, in addition to weight. With the effects of hydrostatics not ‘deduced’ from principles, Pascal could use experiments as pivots for reassessing and improving the concepts at play. His method can be seen as the beginning of the experimental turn in hydrostatics: and experiments were not necessarily new, but had new functions—supporting the theory.

It was Boyle who championed this not-so-Euclidean method in hydrostatics. In his effort, he owed much to pneumatics. Chalmers takes a small detour in experimental advances involving the air-pump. He does so more to illustrate the status of Boyle’s ‘spring of air’. The ‘spring of air’ was not fashioned as a mechanical causal concept, but as an ‘intermediate cause’—something causally active in mathematical-mechanistic accounts, but nevertheless assumed as a given, not in need of further explanation—just like weight is assumed in the science of simple machines. By this exemplar, Boyle explicated the mechanistic assumptions in play. Hydrostatics was, after Boyle, a science about how liquids can push with the same force around corners, not a science about the minute structure of matter, and not one deduced from abstract principles.

Newton was, however, to go back to the Euclidean ideal in presenting hydrostatics. Only this time not from ‘postulates evident to anyone’ (like Stevin), but relying, in his definitions, on the new technical concept of pressure. The concept itself was, now, experimentally warranted and mechanistically intelligible. It provided the perfect tool to distinguish liquids (fluids, generally) from solids, and to deductively explain the hydrostatic phenomena. Chalmers examines Newton’s methods in some depth, explaining how Newton got to think of liquids as continua in a strict sense.

As I said, one premise that links Chalmers’ historical episodes is the gradual shift away from weight as the cause responsible for hydrostatic phenomena. This culminated in Newton’s description of liquids as genuinely distinct from solids because of their real (not abstract) continuity. Once this continuity is established, pressure becomes a necessary property of all liquids. The road towards this understanding was experimental, only not by devising new experiments/observations, but by reinterpreting/reassessing old ones. After Newton’s development, the ‘reeducation of common sense’ about liquids and their properties was complete. The definition of liquids had changed, and pressure became one of its constitutive elements.

Some other thoughts

 There was a debate about Chalmers’ methodology in history and philosophy of science. Peter Dear presented Chalmers’ account as teleological—that is, informed by the present state of science and retrospectively reconstructed with an eye towards the 18th century concept of pressure[viii]. Chalmers wrote a reply, insisting that his account is not teleological, insofar as he presents the conditions and concepts of past scientists and how they reached the present ones. Schuster agrees, comparing Chalmers’ method to intellectual archeology[ix].

Dear’s point is interesting, however. The so-called obstacles were indeed not the actors’ obstacles, i.e. the actors did not regard them as obstacles. This is true, since they are recognized only retrospectively. In this case, Chalmers’ account can only be teleological in a way, since it is the present which indexes past scientific practices and concepts as obstacles or advances. This is not necessarily a bad thing, since without any (admittedly teleological) pivot, one would be rather incapable of making sense of past science, and would probably simply drown in the immense ocean of the history of physical sciences. But there might be a distinction to be made between the ways in which history (and philosophy) of science can be teleological. It’s one thing to view scientific progress as more or less inevitable, while triumphantly explaining how Newton got it right, and quite another to take a modern concept as an explanandum, and historically dissect its constituents. Chalmers’ account is of this latter sort—it’s a kind of historical epistemology (as he says it himself). In the end, it’s not really about who arrives at the *correct* concepts, but about how we got to have the concept in the first place. While doing this, Chalmers does not write as if the modern pressure acted “like a kind of magnetic force which draws the past towards it”, but by considering, describing and evaluating the past practices as relative to their original environment. For instance, Chalmers describes Stevin as not being consistent with his own norms. Anyway, Chalmers’ book is very welcome, especially because it invites these kinds of questions.


[i] You can read the nowadays physical explanation of these phenomena at The picture is taken from the same source.

[ii] Thomas Kuhn used this expression to refer to the extra-astronomical (read: extra-geometrical) implications of Copernicus’ planetary system. See Kuhn’s 1957 The Copernican Revolution.

[iii] Kuhn [1962] 1996, postscript to SSR, p. 183. Kuhn’s point here was to explain how abstract (formal) concepts are a part of what scientists share as a community—symbolic generalizations, as he called them. However, his distinction between the legislative/definitional function of generalizations are very instructive for Chalmers’ episodes of the history of hydrostatics.

[iv] Bachelard [1938] 2002, The Formation of the Scientific Mind, p. 65.

[v] Peter Dear, “Under pressure: Alan Chalmers: One hundred years of pressure: Hydrostatics from Stevin to Newton”, Metascience (2019) 28, p. 187.

[vi] See more on this in Bachelard [1938] 2002, The Formation of the Scientific Mind.

[vii] Chalmers really draws a sharp distinction between mechanical and mechanistic explanations. The former aims to explain the ultimate causes of physical effects in terms of, e.g., the nature of matter or the movement of the smallest corpuscles, while the latter takes effects like weight, spring, pressure for granted and explains how they account for phenomena. Chalmers’ view is that mechanical ambitions were a major obstacle in the emergence of pressure.

[viii] See Dear, “Under pressure: Alan Chalmers: One hundred years of pressure: Hydrostatics from Stevin to Newton”, Metascience (2019) 28.

[ix] See John Schuster “One Hundred Years of Pressure: Hydrostatics from Stevin to Newton”, Annals of Science (2018).


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