Newton, Metaphysics, and Measurement

Though Newton claimed to deduce quantitative propositions from phenomena, the record shows that he brought a whole cartload of presuppositions to bear on his observations (White, 1997), such as his belief that Pythagoras was the discoverer of the inverse square law, his knowledge of Galileo’s freefall experiments, and his theological and astrological beliefs in occult actions at a distance. Without his immersion in this intellectual environment, he likely would not have been able to then contrive the appearance of deducing quantity from phenomena.

The second edition of the Principia, in which appears the phrase “hypotheses non fingo,” was brought out in part to respond to the charge that Newton had not offered any explanation of what gravity is. De Morgan, in particular, felt that Newton seemed to know more than he could prove (Keynes, 1946). But in his response to the critics, and in asserting that he feigns no hypotheses, Newton was making an important distinction between explaining the causes or composition of gravity and describing how it works. Newton was saying he did not rely on or make or test any hypotheses as to what gravity is; his only concern was with how it behaves. In due course, gravity came to be accepted as a fundamental feature of the universe in no need of explanation.

Heidegger (1977, p. 121) contends that Newton was, as is implied in the translation “I do not feign hypotheses,” saying in effect that the ground plan he was offering as a basis for experiment and practical application was not something he just made up. Despite Newton’s rejection of metaphysical explanations, the charge of not explaining gravity for what it is was being answered with a metaphysics of how, first, to derive the foundation for a science of precise predictive control from nature, and then resituate that foundation back within nature as an experimental method incorporating a mathematical plan or model. This was, of course, quite astute of Newton, as far as he went, but he stopped far short of articulating the background assumptions informing his methods.

Newton’s desire for a logic of experimental science led him to reject anything “metaphysical or physical, or based on occult qualities, or mechanical” as a foundation for proceeding. Following in Descartes’ wake, Newton then was satisfied to solidify the subject-object duality and to move forward on the basis of objective results that seemed to make metaphysics a thing of the past. Unfortunately, as Burtt (1954/1932, pp. 225-230) observes in this context, the only thing that can possibly happen when you presume discourse to be devoid of metaphysical assumptions is that your metaphysics is more subtly insinuated and communicated to others because it is not overtly presented and defended. Thus we have the history of logical positivism as the dominant philosophy of science.

It is relevant to recall here that Newton was known for strong and accurate intuitions, and strong and unorthodox religious views (he held the Lucasian Chair at Cambridge only by royal dispensation, as he was not Anglican). It must be kept in mind that Newton’s combination of personal characteristics was situated in the social context of the emerging scientific culture’s increasing tendency to prioritize results that could be objectively detached from the particular people, equipment, samples, etc. involved in their production (Shapin, 1989). Newton then had insights that, while remarkably accurate, could not be entirely derived from the evidence he offered and that, moreover, could not acceptably be explained informally, psychologically, or theologically.

What is absolutely fascinating about this constellation of factors is that it became a model for the conduct of science. Of course, Newton’s laws of motion were adopted as the hallmark of successful scientific modeling in the form of the Standard Model applied throughout physics in the nineteenth century (Heilbron, 1993). But so was the metaphysical positivist logic of a pure objectivism detached from everything personal, intuitive, metaphorical, social, economic, or religious (Burtt, 1954/1932).

Kuhn (1970) made a major contribution to dismantling this logic when he contrasted textbook presentations of the methodical production of scientific effects with the actual processes of cobbled-together fits and starts that are lived out in the work of practicing scientists. But much earlier, James Clerk Maxwell (1879, pp. 162-163) had made exactly the same observation in a contrast of the work of Ampere with that of Faraday:

“The experimental investigation by which Ampere established the laws of the mechanical action between electric currents is one of the most brilliant achievements in science. The whole, theory and experiment, seems as if it had leaped, full grown and full armed, from the brain of the ‘Newton of electricity.’ It is perfect in form, and unassailable in accuracy, and it is summed up in a formula from which all the phenomena may be deduced, and which must always remain the cardinal formula of electro-dynamics.

“The method of Ampere, however, though cast into an inductive form, does not allow us to trace the formation of the ideas which guided it. We can scarcely believe that Ampere really discovered the law of action by means of the experiments which he describes. We are led to suspect, what, indeed, he tells us himself* [Ampere’s Theorie…, p. 9], that he discovered the law by some process which he has not shewn us, and that when he had afterwards built up a perfect demonstration he removed all traces of the scaffolding by which he had raised it.

“Faraday, on the other hand, shews us his unsuccessful as well as his successful experiments, and his crude ideas as well as his developed ones, and the reader, however inferior to him in inductive power, feels sympathy even more than admiration, and is tempted to believe that, if he had the opportunity, he too would be a discoverer. Every student therefore should read Ampere’s research as a splendid example of scientific style in the statement of a discovery, but he should also study Faraday for the cultivation of a scientific spirit, by means of the action and reaction which will take place between newly discovered facts and nascent ideas in his own mind.”

Where does this leave us? In sum, Rasch emulated Ampere in two ways. He did so first in wanting to become the “Newton of reading,” or even the “Newton of psychosocial constructs,” when he sought to show that data from reading test items and readers are structured with an invariance analogous to that of data from instruments applying a force to an object with mass (Rasch, 1960, pp. 110-115). Rasch emulated Ampere again when, like Ampere, after building up a perfect demonstration of a reading law structured in the form of Newton’s second law, he did not report the means by which he had constructed test items capable of producing the data fitting the model, effectively removing all traces of the scaffolding.

The scaffolding has been reconstructed for reading (Stenner, et al., 2006) and has also been left in plain view by others doing analogous work involving other constructs (cognitive and moral development, mathematics ability, short-term memory, etc.). Dawson (2002), for instance, compares developmental scoring systems of varying sophistication and predictive control. And it may turn out that the plethora of uncritically applied Rasch analyses may turn out to be a capital resource for researchers interested in focusing on possible universal laws, predictive theories, and uniform metrics.

That is, published reports of calibration, error, and fit estimates open up opportunities for “pseudo-equating” (Beltyukova, Stone, & Fox, 2004; Fisher 1997, 1999) in their documentation of the invariance, or lack thereof, of constructs over samples and instruments. The evidence will point to a need for theoretical and metric unification directly analogous to what happened in the study and use of electricity in the nineteenth century:

“…’the existence of quantitative correlations between the various forms of energy, imposes upon men of science the duty of bringing all kinds of physical quantity to one common scale of comparison.’” [Schaffer, 1992, p. 26; quoting Everett 1881; see Smith & Wise 1989, pp. 684-4]

Qualitative and quantitative correlations in scaling results converged on a common construct in the domain of reading measurement through the 1960s and 1970s, culminating in the Anchor Test Study and the calibration of the National Reference Scale for Reading (Jaeger, 1973; Rentz & Bashaw, 1977). The lack of a predictive theory and the entirely empirical nature of the scale estimates prevented the scale from wide application, as the items in the tests that were equated were soon replaced with new items.

But the broad scale of the invariance observed across tests and readers suggests that some mechanism must be at work (Stenner, Stone, & Burdick, 2009), or that some form of life must be at play (Fisher, 2003a, 2003b, 2004, 2010a), structuring the data. Eventually, some explanation accounting for the structure ought to become apparent, as it did for reading (Stenner, Smith, & Burdick, 1983; Stenner, et al., 2006). This emergence of self-organizing structures repeatedly asserting themselves as independently existing real things is the medium of the message we need to hear. That message is that instruments play a very large and widely unrecognized role in science. By facilitating the routine production of mutually consistent, regularly observable, and comparable results they set the stage for theorizing, the emergence of consensus on what’s what, and uniform metrics (Daston & Galison, 2007; Hankins & Silverman, 1999; Latour, 1987, 2005; Wise, 1988, 1995). The form of Rasch’s models as extensions of Maxwell’s method of analogy (Fisher, 2010b) makes them particularly productive as a means of providing self-organizing invariances with a medium for their self-inscription. But that’s a story for another day.

References

Beltyukova, S. A., Stone, G. E., & Fox, C. M. (2004). Equating student satisfaction measures. Journal of Applied Measurement, 5(1), 62-9.

Burtt, E. A. (1954/1932). The metaphysical foundations of modern physical science (Rev. ed.) [First edition published in 1924]. Garden City, New York: Doubleday Anchor.

Daston, L., & Galison, P. (2007). Objectivity. Cambridge, MA: MIT Press.

Dawson, T. L. (2002, Summer). A comparison of three developmental stage scoring systems. Journal of Applied Measurement, 3(2), 146-89.

Fisher, W. P., Jr. (1997). Physical disability construct convergence across instruments: Towards a universal metric. Journal of Outcome Measurement, 1(2), 87-113.

Fisher, W. P., Jr. (1999). Foundations for health status metrology: The stability of MOS SF-36 PF-10 calibrations across samples. Journal of the Louisiana State Medical Society, 151(11), 566-578.

Fisher, W. P., Jr. (2003a, December). Mathematics, measurement, metaphor, metaphysics: Part I. Implications for method in postmodern science. Theory & Psychology, 13(6), 753-90.

Fisher, W. P., Jr. (2003b, December). Mathematics, measurement, metaphor, metaphysics: Part II. Accounting for Galileo’s “fateful omission.” Theory & Psychology, 13(6), 791-828.

Fisher, W. P., Jr. (2004, October). Meaning and method in the social sciences. Human Studies: A Journal for Philosophy and the Social Sciences, 27(4), 429-54.

Fisher, W. P., Jr. (2010a). Reducible or irreducible? Mathematical reasoning and the ontological method. Journal of Applied Measurement, 11(1), 38-59.

Fisher, W. P., Jr. (2010b). The standard model in the history of the natural sciences, econometrics, and the social sciences. Journal of Physics: Conference Series, 238(1), http://iopscience.iop.org/1742-6596/238/1/012016/pdf/1742-6596_238_1_012016.pdf.

Hankins, T. L., & Silverman, R. J. (1999). Instruments and the imagination. Princeton, New Jersey: Princeton University Press.

Jaeger, R. M. (1973). The national test equating study in reading (The Anchor Test Study). Measurement in Education, 4, 1-8.

Keynes, J. M. (1946, July). Newton, the man. (Speech given at the Celebration of the Tercentenary of Newton’s birth in 1642.) MacMillan St. Martin’s Press (London, England), The Collected Writings of John Maynard Keynes Volume X, 363-364.

Kuhn, T. S. (1970). The structure of scientific revolutions. Chicago, Illinois: University of Chicago Press.

Latour, B. (1987). Science in action: How to follow scientists and engineers through society. New York: Cambridge University Press.

Latour, B. (2005). Reassembling the social: An introduction to Actor-Network-Theory. (Clarendon Lectures in Management Studies). Oxford, England: Oxford University Press.

Maxwell, J. C. (1879). Treatise on electricity and magnetism, Volumes I and II. London, England: Macmillan.

Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests (Reprint, with Foreword and Afterword by B. D. Wright, Chicago: University of Chicago Press, 1980). Copenhagen, Denmark: Danmarks Paedogogiske Institut.

Rentz, R. R., & Bashaw, W. L. (1977, Summer). The National Reference Scale for Reading: An application of the Rasch model. Journal of Educational Measurement, 14(2), 161-179.

Schaffer, S. (1992). Late Victorian metrology and its instrumentation: A manufactory of Ohms. In R. Bud & S. E. Cozzens (Eds.), Invisible connections: Instruments, institutions, and science (pp. 23-56). Bellingham, WA: SPIE Optical Engineering Press.

Shapin, S. (1989, November-December). The invisible technician. American Scientist, 77, 554-563.

Stenner, A. J., Burdick, H., Sanford, E. E., & Burdick, D. S. (2006). How accurate are Lexile text measures? Journal of Applied Measurement, 7(3), 307-22.

Stenner, A. J., Smith, M., III, & Burdick, D. S. (1983, Winter). Toward a theory of construct definition. Journal of Educational Measurement, 20(4), 305-316.

Stenner, A. J., Stone, M., & Burdick, D. (2009, Autumn). The concept of a measurement mechanism. Rasch Measurement Transactions, 23(2), 1204-1206.

White, M. (1997). Isaac Newton: The last sorcerer. New York: Basic Books.

Wise, M. N. (1988). Mediating machines. Science in Context, 2(1), 77-113.

Wise, M. N. (Ed.). (1995). The values of precision. Princeton, New Jersey: Princeton University Press.

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