Posts Tagged ‘Maxwell’

Newton, Metaphysics, and Measurement

January 20, 2011

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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The “Standard Model,” Part II: Natural Law, Economics, Measurement, and Capital

July 15, 2009

At Tjalling Koopmans’ invitation, Rasch became involved with the Cowles Commission, working at the University of Chicago in the 1947 academic year, and giving presentations in the same seminar series as Milton Friedman, Kenneth Arrow, and Jimmie Savage (Linacre, 1998; Cowles Foundation, 1947, 1952; Rasch, 1953). Savage would later be instrumental in bringing Rasch back to Chicago in 1960.

Rasch was prompted to approach Savage about giving a course at Chicago after receiving a particularly strong response to some of his ideas from his old mentor, Frisch, when Frisch had come to Copenhagen to receive an honorary doctorate in 1959. Frisch shared the first Nobel Prize in economics with Tinbergen, was a co-founder, with Irving Fisher, of the Econometric Society,  invented words such as “econometrics” and “macro-economics,” and was the editor of Econometrica for many years. As recounted by Rasch (1977, pp. 63-66; also see Andrich, 1997; Wright, 1980, 1998), Frisch was struck by the disappearance of the person parameter from the comparisons of item calibrations in the series of equations he presented. In response to Frisch’s reaction, Rasch formalized his mathematical ideas in a Separability Theorem.

Why were the separable parameters  significant to Frisch? Because they addressed the problem that was at the center of Frisch’s network of concepts: autonomy, better known today as structural invariance (Aldrich, 1989, p. 15; Boumans, 2005, pp. 51 ff.; Haavelmo, 1948). Autonomy concerns the capacity of data to represent a pattern of relationships that holds up across the local particulars. It is, in effect, Frisch’s own particular way of extending the Standard Model. Irving Fisher (1930) had similarly stated what he termed a Separation Theorem, which, in the manner of previous work by Walras, Jevons, and others, was also presented in terms of a multiplicative relation between three variables. Frisch (1930) complemented Irving Fisher’s focus on an instrumental approach with a mathematical, axiomatic approach (Boumans, 2005) offering necessary and sufficient conditions for tests of Irving Fisher’s theorem.

When Rasch left Frisch, he went directly to London to work with Ronald Fisher, where he remained for a year. In the following decades, Rasch became known as the foremost advocate of Ronald Fisher’s ideas in Denmark. In particular, he stressed the value of statistical sufficiency, calling it the “high mark” of Fisher’s work (Fisher, 1922). Rasch’s student, Erling Andersen, later showed that when raw scores are both necessary and sufficient statistics for autonomous, separable parameters, the model employed is Rasch’s (Andersen, 1977; Fischer, 1981; van der Linden, 1992).

Whether or not Rasch’s conditions exactly reproduce Frisch’s, and whether or not his Separability Theorem is identical with Irving Fisher’s Separation Theorem, it would seem that time with Frisch exerted a significant degree of influence on Rasch, likely focusing his attention on statistical sufficiency, the autonomy implied by separable parameters, and the multiplicative relations of variable triples.

These developments, and those documented in previous of my blogs, suggest the existence of powerful and untapped potentials hidden within psychometrics and econometrics. The story told thus far remains incomplete. However compelling the logic and personal histories may be, central questions remain unanswered. To provide a more well-rounded assessment of the situation, we must take up several unresolved philosophical issues (Fisher, 2003a, 2003b, 2004).

It is my contention that, for better measurement to become more mainstream, a certain kind of cultural shift is going to have to happen. This shift has already been underway for decades, and has precedents that go back centuries. Its features are becoming more apparent as long term economic sustainability is understood to involve significant investments in humanly, socially and environmentally responsible practices.  For such practices to be more than just superficial expressions of intentions that might be less interested in the greater good than selfish gain, they have to emerge organically from cultural roots that are already alive and thriving.

It is not difficult to see how such an organic emergence might happen, though describing it appropriately requires an ability to keep the relationship of the local individual to the global universal always in mind. And even if and when that description might be provided, having it in hand in no way shows how it could be brought about. All we can do is to persist in preparing ourselves for the opportunities that arise, reading, thinking, discussing, and practicing. Then, and only then, might we start to plant the seeds, nurture them, and see them grow.

References

Aldrich, J. (1989). Autonomy. Oxford Economic Papers, 41, 15-34.

Andersen, E. B. (1977). Sufficient statistics and latent trait models. Psychometrika, 42(1), 69-81.

Andrich, D. (1997). Georg Rasch in his own words [excerpt from a 1979 interview]. Rasch Measurement Transactions, 11(1), 542-3. [http://www.rasch.org/rmt/rmt111.htm#Georg].

Boumans, M. (2001). Fisher’s instrumental approach to index numbers. In M. S. Morgan & J. Klein (Eds.), The age of economic measurement (pp. 313-44). Durham, North Carolina: Duke University Press.

Bjerkholt, O. (2001). Tracing Haavelmo’s steps from Confluence Analysis to the Probability Approach (Tech. Rep. No. 25). Oslo, Norway: Department of Economics, University of Oslo, in cooperation with The Frisch Centre for Economic Research.

Boumans, M. (1993). Paul Ehrenfest and Jan Tinbergen: A case of limited physics transfer. In N. De Marchi (Ed.), Non-natural social science: Reflecting on the enterprise of “More Heat than Light” (pp. 131-156). Durham, NC: Duke University Press.

Boumans, M. (2005). How economists model the world into numbers. New York: Routledge.

Burdick, D. S., Stone, M. H., & Stenner, A. J. (2006). The Combined Gas Law and a Rasch Reading Law. Rasch Measurement Transactions, 20(2), 1059-60 [http://www.rasch.org/rmt/rmt202.pdf].

Cowles Foundation for Research in Economics. (1947). Report for period 1947, Cowles Commission for Research in Economics. Retrieved 7 July 2009, from Yale University Dept. of Economics: http://cowles.econ.yale.edu/P/reports/1947.htm.

Cowles Foundation for Research in Economics. (1952). Biographies of Staff, Fellows, and Guests, 1932-1952. Retrieved 7 July 2009 from Yale University Dept. of Economics: http://cowles.econ.yale.edu/P/reports/1932-52d.htm#Biographies.

Fischer, G. H. (1981, March). On the existence and uniqueness of maximum-likelihood estimates in the Rasch model. Psychometrika, 46(1), 59-77.

Fisher, I. (1930). The theory of interest. New York: Macmillan.

Fisher, R. A. (1922). On the mathematical foundations of theoretical statistics. Philosophical Transactions of the Royal Society of London, A, 222, 309-368.

Fisher, W. P., Jr. (1992). Objectivity in measurement: A philosophical history of Rasch’s separability theorem. In M. Wilson (Ed.), Objective measurement: Theory into practice. Vol. I (pp. 29-58). Norwood, New Jersey: Ablex Publishing Corporation.

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. (2007, Summer). Living capital metrics. Rasch Measurement Transactions, 21(1), 1092-3 [http://www.rasch.org/rmt/rmt211.pdf].

Fisher, W. P., Jr. (2008, March 28). Rasch, Frisch, two Fishers and the prehistory of the Separability Theorem. In Session 67.056. Reading Rasch Closely: The History and Future of Measurement. American Educational Research Association, Rasch Measurement SIG, New York University, New York City.

Frisch, R. (1930). Necessary and sufficient conditions regarding the form of an index number which shall meet certain of Fisher’s tests. Journal of the American Statistical Association, 25, 397-406.

Haavelmo, T. (1948). The autonomy of an economic relation. In R. Frisch &  et al. (Eds.), Autonomy of economic relations. Oslo, Norway: Memo DE-UO, 25-38.

Heilbron, J. L. (1993). Weighing imponderables and other quantitative science around 1800 Historical studies in the physical and biological sciences, 24 (Supplement), Part I, 1-337.

Jammer, M. (1999). Concepts of mass in contemporary physics and philosophy. Princeton, NJ: Princeton University Press.

Linacre, J. M. (1998). Rasch at the Cowles Commission. Rasch Measurement Transactions, 11(4), 603.

Maas, H. (2001). An instrument can make a science: Jevons’s balancing acts in economics. In M. S. Morgan & J. Klein (Eds.), The age of economic measurement (pp. 277-302). Durham, North Carolina: Duke University Press.

Mirowski, P. (1988). Against mechanism. Lanham, MD: Rowman & Littlefield.

Rasch, G. (1953, March 17-19). On simultaneous factor analysis in several populations. From the Uppsala Symposium on Psychological Factor Analysis. Nordisk Psykologi’s Monograph Series, 3, 65-71, 76-79, 82-88, 90.

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.

Rasch, G. (1977). On specific objectivity: An attempt at formalizing the request for generality and validity of scientific statements. Danish Yearbook of Philosophy,  14, 58-94.

van der Linden, W. J. (1992). Sufficient and necessary statistics. Rasch Measurement Transactions, 6(3), 231 [http://www.rasch.org/rmt/rmt63d.htm].

Wright, B. D. (1980). Foreword, Afterword. In Probabilistic models for some intelligence and attainment tests, by Georg Rasch (pp. ix-xix, 185-199. http://www.rasch.org/memo63.htm) [Reprint; original work published in 1960 by the Danish Institute for Educational Research]. Chicago, Illinois: University of Chicago Press.

Wright, B. D. (1994, Summer). Theory construction from empirical observations. Rasch Measurement Transactions, 8(2), 362 [http://www.rasch.org/rmt/rmt82h.htm].

Wright, B. D. (1998, Spring). Georg Rasch: The man behind the model. Popular Measurement, 1, 15-22 [http://www.rasch.org/pm/pm1-15.pdf].