Inventing Temperature Page 8
By a "free surface" he meant, somewhat tautologically, "a surface at which the water is free to change its condition." In an earlier article, Aitken (1878, 252) had argued that a free surface was formed between any liquid and any gas/vapor (or vacuum), which would seem to indicate that he thought the point of contact between any two different states of matter (solid, liquid, or gaseous) constituted a free surface enabling changes between the two states involved.44 I am not aware whether Aitken ever developed of his concept of "free surface" in a precise way. As it turned out, the
43. Aitken's first observations about the condensation of steam were made in the autumn of 1875. But he had already presented his theoretical paper on the subject, titled "On Boiling, Condensing, Freezing, and Melting," in July 1875 to the Royal Scottish Society of Arts (Aitken 1878).
44. He also said: "[W]henever a liquid comes in contact with a solid or another liquid, a free surface is never formed." This can only mean that a solid-liquid interface cannot serve as a free surface for the transformation of the liquid into vapor (which would make sense, since the passage occurs in his discussion of boiling in particular). Compare Aitken's notion of free surface with Dufour's idea about the necessity of "alien molecules" for ordinary boiling.
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exact mechanism by which dust particles facilitated the condensation of vapor was not a trivial issue, and its elucidation required much theoretical investigation, especially on the effect of surface curvature on vapor pressure.45 It is unclear whether different kinds of "free surfaces" would have shared anything essential in the way they facilitated changes of state.
When applied to the case of boiling, Aitken's free-surface theory fitted very well with the De Luc-Donny-Dufour line of thought about the role of dissolved air in boiling, which he was quite familiar with. But his ideas did not necessarily go with the pressure-balance theory of boiling, and in fact Aitken actively rejected it: "The pressure itself has nothing to do with whether the water will pass into vapour or not" (1878, 242). Instead, he thought that what mattered for boiling was "the closeness with which the vapour molecules are packed into the space above the water." He redefined the "boiling point" as "the temperature at which evaporation takes place into an atmosphere of its own vapour at the standard atmospheric pressure of 29.905 inches of mercury." This definition is unusual, but may well be quite compatible with Cavendish's operational procedure adopted by the Royal Society committee for fixing the steam point. Aitken recognized that his definition of the boiling point did not require any "boiling" in the sense of vapor rising from within the body of the liquid: Where, then, it may be asked, is the difference between boiling and evaporation? None, according to this view. Boiling is evaporation in presence of only its own vapour; and what is usually called evaporation is boiling in presence of a gas. The mechanical bubbling up of the vapour through the liquid is an accident of the boiling. … [W]e may have no free surface in the body of the liquid, and no bubbles rising through it, and yet the liquid may be boiling. (Aitken 1878, 242)
Aitken was clearly working at the frontiers of knowledge. But the fruit of his labors, as far as the theory of boiling was concerned, was only an even more serious disorientation than produced by De Luc's pioneering work on the subject a century earlier.
At the end of his major article on dust and fogs, Aitken expressed his sense that he had only opened this whole subject: Much, very much, still remains to be done. Like a traveller who has landed in an unknown country, I am conscious my faltering steps have extended but little beyond the starting point. All around extends the unknown, and the distance is closed in by many an Alpine peak, whose slopes will require more vigorous steps than mine to surmount. It is with reluctance I am compelled for the present to abandon the investigation. (Aitken 1880-81, 368)
Well over a century after Aitken's humble pronouncement, we tend to be completely unaware that boiling, evaporation, and other such mundane phenomena ever constituted "many an Alpine peak" for science. Aitken lamented that he had only been able to take a few faltering steps, but the vast majority of us who have
45. For further details, see Galison 1997, 98-99, and Preston 1904, 406-412.
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received today's scientific education are entirely ignorant of even the existence of Aitken's unexplored country.46
Already in Aitken's own days, science had gone far enough down the road of specialization that even elementary knowledge became neglected if it did not bear explicitly on the subjects of specialist investigation. In an earlier article Aitken blasted some respectable authors for making inaccurate statements about the boiling and melting temperatures. After citing patently incorrect statements from such canonical texts as James Clerk Maxwell's Theory of Heat and John Tyndall's Heat A Mode of Motion, Aitken gave a diagnosis that speaks very much to the spirit of my own work: Now, I do not wish to place too much stress on statements like these given by such authorities, but would look on them simply as the current coin of scientific literature which have been put in circulation with the stamp of authority, and have been received and reissued by these writers without questioning their value. (Aitken 1878, 252)
Analysis: The Meaning and Achievement of Fixity
Ring the bells that still can ring.
Forget your perfect offering.
There is a crack in everything.
That's how the light gets in.
Leonard Cohen, "Anthem," 1992
In the preceding narrative, I gave a detailed historical account of the surprising practical and theoretical challenges involved in establishing one particular fixed point for thermometry. But fixing the fixed points was an even less straightforward business than it would have seemed from that narrative. For a fuller understanding of fixed points, some further discussions are necessary. In this part of the chapter, I will start in the first two sections with a philosophical consideration of what it really means for a phenomenon to constitute a fixed point, and how we can judge fixity at all in the absence of a pre-established standard of fixity. Philosophical concerns about standards of fixity did not come into the narrative significantly because the scientists themselves tended not to discuss them explicitly; however, the establishment of fixed points would not have been possible without some implicit standards being employed, which are worth elucidating. Once the standards are clearly identified, we can reconsider the business of assessing whether and to what extent
46. There are, of course, some specialists who know that the boiling and freezing of water are very complicated phenomena and investigate them through sophisticated modern methods. For an accessible introduction to the specialist work, see Ball 1999, part 2.
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certain phenomena are actually fixed in temperature. As indicated in the narrative, even the most popular fixed point (the boiling point or steam point) exhibited considerable variations. In "The Defense of Fixity" section, I will discuss the epistemic strategies that can be used in order to defend the fixity of a proposed fixed point, drawing from the salient points emerging in the boiling-point story. Finally, in "The Case of the Freezing Point," I will take a brief look at the freezing point, with the benefit of the broader and deeper perspective given by the foregoing discussions.
The Validation of Standards: Justificatory Descent
Consider, in the abstract, the task of someone who has to come up with a fixed point where none have yet been established. That is not so different from the plight of a being who is hurled into interstellar space and asked to identify what is at rest. Even aside from Einstein saying that there is no such thing as absolute rest, how would our space oddity even begin to make a judgment of what is moving and what is fixed? In order to tell whether something is fixed, one needs something else that is known to be fixed and can serve as a criterion of judgment. But how can one find that first fixed point? We would like to put some nails in the wall to hang things from, but there is actually no wall there yet. We would like to lay the foundations of a building, but there i
s no firm ground to put it in.
In the narrative, I paid little attention to the question of how it is that the fixity of a proposed fixed point can be assessed because the scientists themselves did not discuss that question extensively. However, a moment's philosophical reflection shows that there must be some independent standard of judgment, if one is going to say whether or not a given phenomenon happens at a fixed temperature. Otherwise all we can have is a chaotic situation in which each proposed fixed point declares itself fixed and all others variable if they do not agree with it. To overcome such chaos, we need a standard that is not directly based on the proposed fixed points themselves. But standards are not God-given. They must be justified and validated, too—but how? Are we stuck with an infinite regress in which one standard is validated by another, that one is validated by yet another, and so forth?
It is helpful to think this issue through by means of a concrete case. Recall Newton's supposed failing in using "blood heat" (human body temperature) as a fixed point of thermometry. It seems that the master instrument-maker Daniel Gabriel Fahrenheit (1686-1736) also used blood heat as one of his three fixed points. Now, we all know that the human body temperature is not constant, even in a given healthy body, which means that using it as a fixed point of thermometry is a mistake.47 But
47. The modern estimate is that there is variation of around 1°C in the external body temperature of healthy humans, the mean of which is about 37°C (or about 98.5°F); see Lafferty and Rowe 1994, 588. In 1871 the German physician Carl Wunderlich (1815-1877) asserted that in healthy persons the temperature ranged from 98.6 to 99.5°F; see Reiser 1993, 834. But according to Fahrenheit, it was only 96°F. The divergence in early estimates owes probably as much to the differences in the thermometers as to actual variations; that would explain the report in the Encyclopaedia Britannica, 3d ed. (1797), 18:500, that the human body temperature ranged from 92 to 99°F. Of course, the temperature also depends on where the thermometer is placed in the body.
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how do we "know" that? What most of us in the twenty-first century do is go down to the shop and buy a good thermometer, but that would not have been a possible way of criticizing Newton or Fahrenheit. No such thermometers were available anywhere at that time. Our convenient standard thermometers could not come into being until after scientists settled on good fixed points by ruling out bad ones like blood heat. The issue here is how we exclude blood heat initially as a fixed point, not the vacuous one about how we can obtain measurements showing blood heat not to be fixed, using thermometers based on other fixed points.
The key to resolving this impasse is to recognize that it is sufficient to use a very primitive thermometer to know that blood heat is not fixed. For example, any sealed glass tube filled partway with just about any liquid will do, since most liquids expand with heat. That was the arrangement used by Halley in the experiments reported in his 1693 article discussed in "Blood, Butter, and Deep Cellars" (or one can use an inverted test tube or a flask containing air or some other gas, with the open end plunged into a liquid). To help our observations, some lines can be etched onto the tube, and some arbitrary numbers may be attached to the lines. Many of the early instruments were in fact of this primitive type. These instruments should be carefully distinguished from thermometers as we know them, since they are not graduated by any principles that would give systematic meaning to their readings even when they are ostensibly quantitative. I will follow Middleton in dubbing such qualitative instruments thermoscopes, reserving the term thermometer for instruments with quantitative scales that are determined on some identifiable method.48
In the terminology of standard philosophical theories of measurement, what the thermoscope furnishes is an ordinal scale of temperature. An ordinal scale may have numbers attached to them, but those "numbers," or rather numerals, only indicate a definite ordering, and arithmetic operations such as addition do not apply meaningfully to them. In contrast, a proper thermometer is meant to give numbers for which some arithmetical operations yield meaningful results. However, not all arithmetical operations on temperature values yield meaningful results. For instance, a simple sum of the temperatures of two different objects is meaningless; on the other hand, if the temperatures are multiplied by heat capacity, then adding the products gives us total heat content. But this last example also reveals a further subtlety, as that arithmetical operation would be meaningful only for someone who accepts the concept of heat capacity (in the manner of Irvine, to be explained in "Theoretical Temperature before Thermodynamics" in chapter 4). In fact, there are complicated philosophical disputes about just what kind of quantity temperature is, which I will avoid for the time being by vaguely saying that what proper thermometers give us is a numerical temperature scale.49
48. See Middleton 1966, 4. He thinks that Sanctorius was the first person to attach a meaningful numerical scale to the thermoscope, thereby turning it into a veritable thermometer.
49. See, for example, Ellis 1968, 58-67, for some further discussion of the classification of scales with some consideration given to the case of temperature.
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A thermoscope is exactly what is needed for the establishment of fixed points. It does not measure any numerical quantity, but it will indicate when something is warmer than another thing. If we put a thermoscope in our armpit or some other convenient place at regular intervals, we can observe the indications of the thermoscope fluctuating up and down. If we rule out (without much discussion for the moment) the unlikely possibility that the temperature is actually perfectly still while the thermoscope goes up and down in various ways, we can infer that blood heat is not constant and should not be used as a fixed point. The main epistemic point here is that a thermoscope does not even need to have any fixed points, so that the evaluation of fixed points can be made without a circular reliance on fixed points. Employing the thermoscope as a standard allows an initial evaluation of fixed points.
But we have only pushed the problem of justification one step away, and now we must ask why we can trust the thermoscopes. How do we know that most liquids expand with heat? The thermoscope itself is useless for the proof of that point. We need to bring ourselves back to the original situation in which there were no thermoscopes to rely on. The initial grounding of the thermoscope is in unaided and unquantified human sensation. Although sensation cannot prove the general rule that liquids expand when temperature rises, it does provide a justification of sorts. We get the idea that liquids expand with heat because that is what we observe in the cases that are most obvious to the senses. For example, we put a warm hand on a thermoscope that feels quite cool to the touch and see it gradually rise. We stick the thermoscope into water that scalds our hand and note its rapid rise. We put it into snow and see it plunge. We wet the thermoscope bulb and observe it go down when we blow on it, while remembering that we feel colder if we stand in the wind after getting soaked in the rain. What we see here is that human sensation serves as a prior standard for thermoscopes. The thermoscope's basic agreement with the indications of our senses generates initial confidence in its reliability. If there were clear and persistent disagreements between the indications of a thermoscope and what our own senses tell us, the thermoscope would become subject to doubt. For example, many of us would feel colder when it is 0°C out than when it is 4°C, and question the reliability of the volume changes in water as a standard of temperature when we see it occupy a larger volume at 0°C than at 4°C.
But have we not once again simply pushed the problem around? How do we know that we can trust sensation? From ancient times, philosophers have been well aware that there is no absolute reason for which we should trust our senses. That brings us to the familiar end of foundationalist justification, unsatisfying but inevitable in the context of empirical science. As Ludwig Wittgenstein (1969, 33, §253) puts it: "At the foundation of well-founded belief lies belief that is not founded." The groundlessness cannot be contained: if we follow through
the empirical justifications we give for our beliefs, as we have done in the case of thermometric fixed points, we arrive at bodily sensation; if that final basis of justification is seen as untrustworthy, then none of our empirical justifications can be trusted. If we accept that sensations themselves have no firm justification, then we have to reconceptualize the very notion of empirical justification. The traditional notion of justification
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aspires to the ideal of logical proof, in which the proposition we want to justify is deduced from a set of previously accepted propositions. The trouble arises from the fact that proof only generates a demand for further proof of the previously accepted propositions. That results either in an infinite regress or an unsatisfying stopping point where belief is demanded without proof. But, as the next section will make clearer, justification does not have to consist in proof, and it is not likely that the justification of a standard will consist in proof.
I would like to propose that the justification of a standard is based on a principle of respect, which will be shown in action elsewhere in this book, too, and which I will have occasion to define more precisely later. To see how the principle of respect works, consider generally the relationship between human sensation and measuring instruments. Although basic measuring instruments are initially justified through their conformity to sensation, we also allow instruments to augment and even correct sensation. In other words, our use of instruments is made with a respect for sensation as a prior standard, but that does not mean that the verdict of sensation has unconditional authority. There are commonly cited cases to show that sometimes the only reasonable thing to do is to overrule sensations. Put one hand in a bucket of hot water and the other one in cold water; after a while take them out and put them both in a bucket of lukewarm water; one hand feels that the water is cool, and the other one feels it is warm. Our thermoscopes, however, confirm that the temperature of the last bucket of water is quite uniform, not drastically different from one spot to another.50 Still, these cases do not lead us to reject the evidence of the senses categorically. Why is it that the general authority of sensation is maintained in spite of the acknowledged cases in which it fails?