Posts Tagged ‘History’

A New Agenda for Measurement Theory and Practice in Education and Health Care

April 15, 2011

Two key issues on my agenda offer different answers to the question “Why do you do things the way you do in measurement theory and practice?”

First, we can take up the “Because of…” answer to this question. We need to articulate an historical account of measurement that does three things:

  1. that builds on Rasch’s use of Maxwell’s method of analogy by employing it and expanding on it in new applications;
  2. that unifies the vocabulary and concepts of measurement across the sciences into a single framework so far as possible by situating probabilistic models of invariant individual-level within-variable phenomena in the context of measurement’s GIGO principle and data-to-model fit, as distinct from the interactions of group-level between-variable phenomena in the context of statistics’ model-to-data fit; and
  3. that stresses the social, collective cognition facilitated by networks of individuals whose point-of-use measurement-informed decisions and behaviors are coordinated and harmonized virtually, at a distance, with no need for communication or negotiation.

We need multiple publications in leading journals on these issues, as well as one or more books that people can cite as a way of making this real and true history of measurement, properly speaking, credible and accepted in the mainstream. This web site http://ssrn.com/abstract=1698919 is a draft article of my own in this vein that I offer for critique; other material is available on request. Anyone who works on this paper with me and makes a substantial contribution to its publication will be added as co-author.

Second, we can take up the “In order that…” answer to the question “Why do you do things the way you do?” From this point of view, we need to broaden the scope of the measurement research agenda beyond data analysis, estimation, models, and fit assessment in three ways:

  1. by emphasizing predictive construct theories that exhibit the fullest possible understanding of what is measured and so enable the routine reproduction of desired proportionate effects efficiently, with no need to analyze data to obtain an estimate;
  2. by defining the standard units to which all calibrated instruments measuring given constructs are traceable; and
  3. by disseminating to front line users on mass scales instruments measuring in publicly available standard units and giving immediate feedback at the point of use.

These two sets of issues define a series of talking points that together constitute a new narrative for measurement in education, psychology, health care, and many other fields. We and others may see our way to organizing new professional societies, new journals, new university-based programs of study, etc. around these principles.

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LivingCapitalMetrics Blog by William P. Fisher, Jr., Ph.D. is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 United States License.
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Simple ideas, complex possibilities, elegant and beautiful results

February 11, 2011

Possibilities of great subtlety, elegance, and power can follow from the simplest ideas. Leonardo da Vinci is often credited with offering a variation on this theme, but the basic idea is much older. Philosophy, for instance, began with Plato’s distinction between name and concept. This realization that words are not the things they stand for has informed and structured each of several scientific revolutions.

How so? It all begins from the reasons why Plato required his students to have studied geometry. He knew that those familiar with the Pythagorean theorem would understand the difference between any given triangle and the mathematical relationships it represents. No right triangle ever definitively embodies a perfect realization of the assertion that the square of the hypotenuse equals the sum of the squares of the other two sides. The mathematical definition or concept of a triangle is not the same thing as any actual triangle.

The subtlety and power of this distinction became apparent in its repeated application throughout the history of science. In a sense, astronomy is a geometry of the heavens, Newton’s laws are a geometry of gravity, Ohm’s law is a geometry of electromagnetism, and relativity is a geometry of the invariance of mass and energy in relation to the speed of light. Rasch models present a means to geometries of literacy, numeracy, health, trust, and environmental quality.

We are still witnessing the truth, however partial, of Whitehead’s assertion that the entire history of Western culture is a footnote to Plato. As Husserl put it, we’re still struggling with the possibility of creating a geometry of experience, a phenomenology that is not a mere description of data but that achieves a science of living meaning. The work presented in other posts here attests to a basis for optimism that this quest will be fruitful.

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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LivingCapitalMetrics Blog by William P. Fisher, Jr., Ph.D. is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 United States License.
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Permissions beyond the scope of this license may be available at http://www.livingcapitalmetrics.com.

False Modesty and the Progress of Science (or Lack Thereof)

April 5, 2010

In a talk given in 1999, Freeman Dyson, Professor Emeritus at the Institute for Advanced Study in Princeton, New Jersey, proclaimed the stature of James Clerk Maxwell in the history of science, positioning him at the rank of Newton and Einstein. Maxwell’s 1865 theory explaining and unifying the phenomena of electricity and magnetism turned out to be, according to Dyson (1999),

“the prototype for all the great triumphs of twentieth-century physics…the prototype for Einstein’s theories of relativity, for quantum mechanics, for the Yang-Mills theory of generalised gauge invariance, and for the unified theory of fields and particles that is known as the Standard Model of particle physics.”

Maxwell was a leading figure in British science in the period from 1856 until his death at 48 in 1879. He was an academic department head at 25, elected to the Royal Society at 30, was president of the section on mathematical and physical sciences of the British Association for the Advancement of Science at 35, and at 40 became the first Cavendish Professor of Physics at Cambridge, personally overseeing the building of the Cavendish Laboratory.

In addition to his intelligence and imagination, Maxwell had a wry sense of humor, and a rich spiritual life. But in 1870, giving an overview of recent advances in his presidential address to the British Association, he downplayed the importance of what we now know as his landmark 1865 paper on electromagnetism. He instead spoke enthusiastically about William Thomson’s work in electrical theory. Perhaps he did not want to take on the double challenge of trying to explain the new and complex mathematics of his own theory to the physicists, and the physical application of the equations, to the mathematicians. Maybe he thought it would be unfair to take advantage of his position to showcase his own work. But Dyson thinks Maxwell’s colleagues could have been motivated to overcome the difficulties experienced in interpreting the published work if only Maxwell had encouraged them to.

Dyson contends that, in being so “absurdly and infuriatingly modest,” Maxwell set back progress in physics by 20 years, just as Mendel’s monkish isolation held back biology by 50. Referring to his own work toward the end of his address, Maxwell began by saying, “Another theory of electricity which I prefer…”.  He then briefly described his work without taking credit for it.

But what if, as Dyson asks, Maxwell had instead had the confidence of Newton, who, at the start of the third volume of his Principia Mathematica, announced, “I now demonstrate the frame of the system of the world.” What if Maxwell had directly stated the truth with some panache, saying something to the effect of, “I now demonstrate the structure of the models integrating mathematics and physical phenomena that will dominate physics for the foreseeable future, and that will lead to revolutionary advances”? Even if he had not been so grandiose, if someone of his stature in the scientific community, known for his humility and personable nature, had spoken straightforwardly about what he believed to be true, people would have listened, and Freeman Dyson would not have been talking about 20-year delays in the advancement of science brought about by one of its most illustrious contributors.

It would seem that Maxwell’s legacy of self-deprecating modesty might have been inherited by one of his intellectual heirs, Georg Rasch, and the vast majority of those who have adopted Rasch’s measurement models in their research. Rasch explicitly based the mathematics of his approach to psychological measurement on Maxwell’s mathematics (see my previous postings here for more). Rasch accomplished for psychology the same integration of mathematics with substance that Maxwell accomplished for physics. Rasch’s students, Wright, Andrich, Andersen, and Fischer among them, poured passion and insight into developments in models, theory, estimation, software, fit statistics, applications, students, publications, and professional associations for decades. But you would never know that from reading most of the research using his models over the last 30 years, or from taking courses with most of the university professors who purport to apply Rasch’s ideas.

So, all that just to say that there are reasons and purposes motivating these blog postings that may not be readily apparent, but which have their historical precedents and future potentials. There is no more worthy challenge for me, personally, than following Rasch’s lead in figuring out how to demonstrate the frame of the system of the world of social relationships and intangible assets. After all, if no one does this, how many additional decades might be lost before researchers gain the thorough understandings of Rasch’s models that will lead the way to whole new classes of human, scientific, and economic triumphs?

Dyson, F. (1999, July). Why is Maxwell’s theory so hard to understand? In Fourth International Congress Industrial and Applied Mathematics (http://www.clerkmaxwellfoundation.org/DysonFreemanArticle.pdf). Edinburgh, Scotland.

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LivingCapitalMetrics Blog by William P. Fisher, Jr., Ph.D. is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 United States License.
Based on a work at livingcapitalmetrics.wordpress.com.
Permissions beyond the scope of this license may be available at http://www.livingcapitalmetrics.com.

Review of “The Science of Liberty” by Timothy Ferris

February 15, 2010

The topic of Timothy Ferris’ (2010) “The Science of Liberty” is fascinating; the author recounts many entertaining and illuminating historical episodes in science, with their often profound implications for political and economic experimentation. But as Gary Rosen says in his New York Times review, Ferris ultimately gives up “on any real effort to argue for the decisive influence of science as such. He is content to speak of science metaphorically, as the model for openness and experimentalism in all the major realms of liberal-democratic endeavor.” This is unfortunate, as there is much to say and more to be done in documenting and extending the material practices of science into political and economic applications (Ashworth, 2004; Jasanoff, 2004, 2005).

And more than that, Ferris misses two important opportunities that could have made this book into something more compelling. First, the voluminous literature on the co-production of social orders across political, economic, and scientific contexts is almost completely ignored. Worse, when Ferris does touch on it, as he does in the work of Bruno Latour, he turns it into an example of an antiscientific attitude that he is content to “jeer and dismiss,” as Rosen puts it in the Times.

Latour’s work, however, is part of an area of academic research that has emerged in the last 30 years with a focus on the way scientific values embody, insinuate, and disseminate implicit moral, political, and economic values, values that are ineluctably spread and adopted along with the technologies that carry them. The basic idea is expressed in Alder’s (2002) history of the meter:

“Just as the French Revolution had proclaimed universal rights for all people, the savants argued, so too should it proclaim universal measures. And to ensure that their creation would not be seen as the handiwork of any single group or nation, they decided to derive its fundamental unit from the measure of the world itself.” (p. 3)

“Ought not a single nation have a uniform set of measures, just as a soldier fought for a single patrie? Had not the Revolution promised equality and fraternity, not just for France, but for all the people of the world? By the same token, should not all of the world’s people use a single set of weights and measures to encourage peaceable commerce, mutual understanding, and the exchange of knowledge? That was the purpose of measuring the world.” (p. 32)

But instead of capitalizing on this primary theme in Alder’s book, the only mention of it by Ferris (p. 124) is as a source for a contemporary’s comment on the execution of Lavoisier by the Revolutionaries. Hunt (1994), however, points out that this focus on standardization provides the medium through which the material practices and implicit values of science are exported from the laboratory into the broader social world, where they have unintended political and economic effects. Recounting the development of electrical standards, Hunt observes that

“Such standardization—first of resistance coils, then of production materials—is a good example of the process Bruno Latour discusses in the section ‘Metrologies’ in Science in Action. Standardization of instruments and materials enables scientists and engineers to extend their networks of calculation and control by simply making and sending out what are, in effect, little pieces of their laboratories and testing rooms. They can then travel around the world without, in a sense, ever having to leave their laboratories—as long as they are able to put certified copies or extensions of their instruments wherever they have to go.” (p. 56)

Hunt continues, providing more detail on how the social order implied by standard values comes to be constructed:

“As useful as the precision and control afforded by standardization was within a single company’s system, it became even more important when an exchange of materials was involved—when standardization became part of contract specifications. By providing fixed and agreed reference points in which both parties could have confidence, standard resistances were crucial in settling or heading off possible disputes. By enabling engineers to secure the comparability and even uniformity of their copper and gutta-percha, to identify and police deviations, and to reproduce the properties of successful cables in a predictable way, reliable standards were crucial to the growth of the cable manufacturing industry and to the efficient operation and extension of the world cable system.” (p. 57)

Electrical engineers, then, rigorously established the natural properties of resistance as it shows itself in repeated experiments, designed their systems to conform with those properties, earned economic and legal successes by efficiently deploying standard resistances, and worked together to create a global system. In other words, as Ferris himself emphasizes, scientific practices imply and lead toward democratic practices by being antiauthoritarian, self-correcting, meritocratic and collaborative. And every year on World Metrology Day (May 20), the National Institute for Standards and Technology (NIST) repeats the same mantra emphasizing the vital importance of technical standards and common product definitions for free trade and liberal democracy.

The same basic point made by Latour is also made by Schaffer (1992; also see Wise, 1995 and many others), working in the same area of the history of electrical standards as Hunt:

“The physical values which the laboratory fixes are sustained by the social values which the laboratory inculcates. Metrology has not often been granted much historical significance. But in milieux such as those of Victorian Britain the propagation of standards and values was the means through which physicists reckoned they could link their work with technical and economic projects elsewhere in their society. Instrumental ensembles let these workers embody the values which mattered to their culture in their laboratory routines. Intellectualist condescension distracts our attention from these everyday practices, from their technical staff, and from the work which makes results count outside laboratory walls.” (pp. 22-23)

Had Ferris taken the trouble to look at Latour’s 1999 book, Pandora’s Hope: Essays on the Reality of Science Studies, or Latour’s 1990 and 1993 contrasts of the postmodern and amodern, he would have found lengthy replies to exactly those disputes he unknowingly re-provokes. Far from denying that anything exists objectively in nature, as Ferris implies, Latour and the field of science studies examines how we enter into dialogue with nature, and how things come into words as objects of discourse by asserting their independent real existence in very specific and reproducible ways. Ferris commits a gross reductionism in casting as postmodern nonsense this field’s efforts in tracing out the microscopic details of what is said and done, how instruments are read and the readings recorded, and how the recorded values take their places in forms, memos, bills, invoices, laws, accounting spreadsheets, manufacturing specifications, operating instructions, etc. Ferris would have had quite a different book to write if he had followed the implications of networked thinking coordinated via standards and brought them to bear on recent developments in the social sciences and economics (Fisher, 2000, 2005, 2009, 2010a).

Ferris does his “jeer and dismiss” thing again in a second way, instead of engaging substantively with the likes of Heidegger or Derrida. In joining with Gross and Levitt (1994), and Alan Bloom (1987), in their dismissals of Derrida and deconstruction, for instance, Ferris (pp. 258-259) has simply found it easier to project irrational conclusions on writers whose work he cannot be troubled to read carefully enough to understand (as on page 238, where “logocentric” is said to be “a fascist epithet aimed at those who employ logic”). Derrida’s comment that “a critique of what I do is indeed impossible” (quoted on page 242) hardly renders his work “immune to criticism,” as Ferris says. The point is that it is impossible to critique effectively what Derrida does without doing it yourself, which puts you in the unresolvable situation of having to employ the same assumptions as the ones you’re criticizing.

Closer attention to Derrida’s extensive considerations of this issue would show the sensitivity and care that are required in trying, for instance, to be as faithful as Levi-Strauss was to the double intention of being able “to preserve as an instrument something whose truth value he [Levi-Strauss] criticizes” (Derrida, 1978, p. 284). Postmodernism is essentially this kind of a twist on the old maxim about being able to continue thinking critically while holding two mutually exclusive ideas at the same time. This double intention permeates Derrida’s writings from the beginning of his career. In a 1968 discussion of his work, for instance, he said, “I try to place myself at a certain point at which—and this would be the very ‘content’ of what I would like to ‘signify’—the thing signified is no longer easily separable from the signifier” (Wahl, et al., 1988, pp. 88-89). In saying this, the speaker is obviously making an effort at a clear separation of what is signified from the signifiers representing it.

What complicates things is that what are signified in that sentence are precisely the difficulties entailed in effecting the separation referred to. Though this point is lost on those unable or unwilling to do the work of thinking these self-referential recursive patterns through, the discourses of deconstruction often show awareness of the need to assume the convergence and separation of signifier and signified even while specific instances of their inseparability are analyzed (Gasché, 1987; Spivak, 1990, 1993). This follows from the fact that deconstruction is but the third of three moments in the ontological method (Heidegger, 1982, pp. 19-23, 320-330), where the prior two moments are reduction and application (Fisher, 2010b).

Any time things are put into words in spoken or written expressions of limited lengths, reduction takes place. Reductionism occurs when things are misrepresented, when the utility or fairness of the way something is conceptualized is biased, prejudiced, or ineffective. Of course, language is historical and cultural, human attention is inevitably selective, and so words and concepts are always colored by the interests and prejudices of their times. These places in which the meaning of things remains stuck on and inseparable from local particularities may become increasingly apparent over time, as words are applied constructively in creating meaning, socially. Eventually, new distinctions and new aggregations of previously lumped or segregated classifications will be demanded just to be able to continue meaningful communication. And so the cycle progresses through applications to a period of critical evaluation and on to new reductions with new applications.

But this process need not be construed only negatively, since it also stands for nothing more than the fact that there is always room for improvement. Industrial quality improvement methods adopted over the last 60+ years are well-known, for instance, for asserting that there is no best way of doing something, that the standard way of doing something is always flawed in some way. The ontological method comprehensively outlines the life cycle of concepts (Fisher, 2010b), and so offers positive potentials for informing experimental evaluations of new possibilities in science, capitalism, and democracy.

And so, though one could never gather this from reading Ferris, late in his life Derrida diligently urged his critics to read him as closely as he was reading them, saying in one interview (Derrida, 2003) that:

“…people who read me and think I’m playing with or transgressing norms—which I do, of course—usually don’t know what I know: that all of this has not only been made possible by but is constantly in contact with very classical, rigorous, demanding discipline in writing, in ‘demonstrating,’ in rhetoric. …the fact that I’ve been trained in and that I am at some level true to this classical teaching is essential. … When I take liberties, it’s always by measuring the distance from the standards I know or that I’ve been rigorously trained in.” (pp. 62-63)

This is from someone who holds “truly meaningful utterance is impossible” (Gross & Levitt, 1994, p. 76), and who stands as the representative of a movement (deconstruction) that “is the last, predictable, stage in the suppression of reason and the denial of the possibility of truth in the name of philosophy” (Bloom, 1987, p. 387)? Far from defeating or debunking “lackluster scholars,” which is how Ferris (pp. 257-258) credits Gross and Levitt, and Bloom, they actually do nothing but demonstrate their failure to grasp the issues. The situation is again similar to one brought up by Thomas Kuhn regarding the nature of interpretation.

As I’ve noted previously in this blog, Kuhn (1977) recounts an experience from the summer of 1947 that led to his appreciation for an explicit theory of interpretation. He had been completely perplexed by Aristotle’s account of motion, in which Aristotle writes a great many things that appear blatantly absurd. Kuhn was very puzzled and disturbed by this, as Aristotle made many astute observations in other areas, such as biology and political behavior. He eventually came to see what Aristotle was in fact talking about, and he then came to routinely offer the following maxim to his students:

“When reading the works of an important thinker [or anyone else who is held by some to have a modicum of coherence], look first for the apparent absurdities in the text and ask yourself how a sensible person could have written them. When you find an answer, I continue, when those passages make sense, then you may find that more central passages, ones you previously thought you understood, have changed their meaning.” (p. xii)

As Kuhn goes on to say, if his book was addressed primarily to historians, this point wouldn’t be worth making, as historians are in the business of precisely this kind of interpretive back-and-forth, as are many philosophers, literary critics, writers, social scientists, educators, and artists. But as a physicist, Kuhn says that the discovery of hermeneutics not only made history seem consequential, it changed his view of science. As is well known, his skill in practicing hermeneutics changed a great many people’s views of science.

Derrida’s efforts to explain the meaning of his difficult language and prose are not, then, late after-thoughts presented only in response to critics—and to followers who often seem to misunderstand deconstruction as much as those presenting themselves as defenders of truth and reason. His purpose is akin to Kuhn’s in that he is urging people who find absurdities in his writing to reconsider and ask themselves how a sensible person could have written them.

Derrida’s reference to measuring the distance from standards clearly intersects with Latour’s interests in metrology. Standards in rhetoric, grammar, orthography, etc. in fact form an implicit model for metrological standards and their coordinations of thoughts and behaviors on mass scales. This sense of measuring is no empty metaphor, as is plain in Derrida’s (1989) book-length study of Edmund Husserl’s (1970) Origins of Geometry, one of the founding documents of Continental philosophy and postmodernism.

“The mathematical object seems to be the privileged example and most permanent thread guiding Husserl’s reflection… [on phenomenology] because the mathematical object is ideal. Its being is thoroughly transparent and exhausted by its phenomenality” (Derrida, 1989, p. 27).

Accordingly, its “universality and objectivity make the ideal object into the ‘absolute model for any object whatsoever'” (Bernet, 1989, p. 141, quoting Derrida, 1989, p. 66). Heidegger (1967) similarly reflected at length on the mathematical object. He was, after all, Husserl’s student, dealt extensively with mathematical thinking (Heidegger, 1967; Kisiel, 1973), took more courses in mathematics and physics at one point in his studies than he did in philosophy (Kisiel, 2002, p. x), and remained well enough versed in mathematics to serve on dissertation committees for his university (Krell, 1977, p. 12).

Far from being the antiscientific nonsense portrayed by Ferris, there are strong parallels between mathematical logic and the themes being played out in postmodern studies (Tasic, 2001; Fisher, 2003a, 2003b, 2004, 2010b). In direct opposition to Ferris’ characterization of logocentricism as a charge levied against those who use logic, Derrida (1981) wrote that those most guilty of logocentrism are those who resist logic, saying that

“…resistance to logical-mathematical notation has always been the signature of logocentricism and phonologism in the event to which they have dominated metaphysics and the classical semiological and linguistic projects.” (p. 34)

“A grammatology that would break with this system of presuppositions, then, must in effect liberate the mathematization of language, and must also declare that ‘the practice of science in fact has never ceased to protest the imperialism of the Logos, for example by calling upon, from all time, and more and more, nonphonetic writing.’ [see Of Grammatology, pp. 12, 10, 3, 284-6] Everything that has always linked logos to phone’ has been limited by mathematics, whose progress is in absolute solidarity with the practice of nonphonetic inscription. About these ‘grammatological’ principles and tasks there is no possible doubt, I believe. But the extension of mathematical notation, and in general the formalization of writing, must be very slow and very prudent, at least if one wishes it to take over effectively the domains from which it has been excluded so far.” (p. 34)

“The effective progress of mathematical notation goes along with the deconstruction of metaphysics, with the profound renewal of mathematics itself, and the concept of science for which mathematics has always been the model.” (p. 35)

Derrida is here speaking to a form of nonphonetic writing, a kind of mathematical symbolization that effects a transparency inaccessible to forms of notation that stand for words representing some kind of particular thing. Though the problems are complex, the project Derrida describes follows in specific ways from Heidegger (1967; Kisiel, 1973, 2002; Fisher, 2003a, 2003b, 2004) and from other influences on him.

So, contrary to Ferris’ claims (p. 259), Latour, Heidegger, and Derrida have not ignored science as a source of knowledge, reduced it to arbitrary social constructs, or turned their back on learning. In fact, Heidegger (1967) traces the roots of mathematical thinking to learning, to how we learn through what we already know, and to how things that can be taught and learned were the original mathematical objects. There are indeed great potentials for further advancing the impact of science on democracy, but we are needlessly blinded to real possibilities when our ideas are driven more by unexamined prejudices than by the critical application of clear thinking. In this review, I’ve hardly been able to crack open the door to the issues in need of careful study, but I offer it in the hope that others will take the time to stop, study, and think in future work in this area.

References

Alder, K. (2002). The measure of all things: The seven-year odyssey and hidden error that transformed the world. New York: The Free Press.

Ashworth, W. J. (2004, 19 November). Metrology and the state: Science, revenue, and commerce. Science, 306(5700), 1314-7.

Bernet, R. (1989). On Derrida’s ‘Introduction’ to Husserl’s Origin of Geometry. In H. J. Silverman (Ed.), Derrida and deconstruction (pp. 139-153). New York: Routledge.

Bloom, A. (1987). The closing of the American mind: How higher education has failed democracy and impoverished the souls of today’s students. New York: Simon & Schuster.

Derrida, J. (1976). Of grammatology (G. C. Spivak, Trans.). Baltimore, MD: Johns Hopkins University Press.

Derrida, J. (1978). Structure, sign and play in the discourse of the human sciences. In Writing and difference (pp. 278-93). Chicago: University of Chicago Press.

Derrida, J. (1981). Positions (A. Bass, Trans.). Chicago: University of Chicago Press (Original work published 1972 (Paris: Minuit)).

Derrida, J. (1989). Edmund Husserl’s Origin of Geometry: An introduction. Lincoln: University of Nebraska Press.

Derrida, J. (2003). Interview on writing. In G. A. Olson & L. Worsham (Eds.), Critical intellectuals on writing (pp. 61-9). Albany, New York: State University of New York Press.

Fisher, W. P., Jr. (2000). Objectivity in psychosocial measurement: What, why, how. Journal of Outcome Measurement, 4(2), 527-563 [http://www.livingcapitalmetrics.com/images/WP_Fisher_Jr_2000.pdf].

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. (2005). Daredevil barnstorming to the tipping point: New aspirations for the human sciences. Journal of Applied Measurement, 6(3), 173-9 [http://www.livingcapitalmetrics.com/images/FisherJAM05.pdf].

Fisher, W. P., Jr. (2009, November). Invariance and traceability for measures of human, social, and natural capital: Theory and application. Measurement (Elsevier), 42(9), 1278-1287.

Fisher, W. P., Jr. (2010a). Bringing human, social, and natural capital to life: Practical consequences and opportunities. Journal of Applied Measurement, 11, in press.

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

Gasché, R. (1987). Infrastructures and systemacity. In J. Sallis (Ed.), Deconstruction and philosophy: The texts of Jacques Derrida (pp. 3-20). Chicago, Illinois: University of Chicago Press.

Gross, P. R., & Levitt, N. (1994). Higher superstition: The academic left and its quarrels with science. Baltimore, MD: Johns Hopkins University Press.

Heidegger, M. (1967). What is a thing? (W. B. Barton, Jr. & V. Deutsch, Trans.). South Bend, Indiana: Regnery/Gateway.

Heidegger, M. (1982). The basic problems of phenomenology (J. M. Edie, Ed.) (A. Hofstadter, Trans.). Studies in Phenomenology and Existential Philosophy. Bloomington, Indiana: Indiana University Press (Original work published 1975).

Hunt, B. J. (1994). The ohm is where the art is: British telegraph engineers and the development of electrical standards. In A. van Helden, & T. L. Hankins (Eds.), Instruments [Special issue]. Osiris: A Research Journal Devoted to the History of Science and Its Cultural Influences, 9, 48-63. Chicago, Illinois: University of Chicago Press.

Husserl, E. (1970). The crisis of European sciences and transcendental phenomenology: An introduction to phenomenological philosophy (D. Carr, Trans.). Evanston, Illinois: Northwestern University Press (Original work published 1954).

Jasanoff, S. (2004). States of knowledge: The co-production of science and social order. (International Library of Sociology). New York: Routledge.

Jasanoff, S. (2005). Designs on nature: Science and democracy in Europe and the United States. Princeton, NJ: Princeton University Press.

Kisiel, T. (1973). The mathematical and the hermeneutical: On Heidegger’s notion of the apriori. In E. G. Ballard & C. E. Scott (Eds.), Martin Heidegger: In Europe and America (pp. 109-20). The Hague: Martinus Nijhoff.

Kisiel, T. J. (2002). Heidegger’s way of thought: Critical and interpretative signposts (A. Denker & M. Heinz, Eds.). New York: Continuum.

Krell, D. F. (1977). General introduction: “The Question of Being.” In D. F. Krell (Ed.), Basic writings by Martin Heidegger (pp. 3-35). New York: Harper & Row.

Kuhn, T. S. (1977). The essential tension: Selected studies in scientific tradition and change. 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. (1990). Postmodern? no, simply amodern: Steps towards an anthropology of science. Studies in History and Philosophy of Science, 21(1), 145-71.

Latour, B. (1993). We have never been modern. Cambridge, Massachusetts: Harvard University Press.

Latour, B. (1999). Pandora’s hope: Essays on the reality of science studies. Cambridge, Massachusetts: Harvard University Press.

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.

Spivak, G. C. (1990). The post-colonial critic: Interviews, strategies, dialogue. New York: Routledge.

Spivak, G. C. (1993). Outside in the teaching machine. New York: Routledge.

Tasic´, V. (2001). Mathematics and the roots of postmodern thought. New York: Oxford University Press.

Wahl, J., Parain, B., Derrida, J., Comtesse, G., Hersch, J., Goldmann, L., et al. (1988). The original discussion of “Différance” (D. Wood, S. Richmond, & M. Bernard, Trans.). In D. Wood & R. Bernasconi (Eds.), Derrida and Différance (pp. 83-95). Evanston, Illinois: Northwestern University Press. (Reprinted from Wahl, J., Parain, B., Derrida, J., Comtesse, G., Hersch, J., Goldmann, L., et al. (1968, July-September). Bulletin de la Société Française de Philosophie, 62.)

Wise, M. N. (1995). Precision: Agent of unity and product of agreement. Part III–“Today Precision Must Be Commonplace.” In M. N. Wise (Ed.), The values of precision (pp. 352-61). Princeton, New Jersey: Princeton University Press.

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LivingCapitalMetrics Blog by William P. Fisher, Jr., Ph.D. is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 United States License.
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Contesting the Claim, Part III: References

July 24, 2009

References

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

Andersen, E. B. (1995). What George Rasch would have thought about this book. In G. H. Fischer & I. W. Molenaar (Eds.), Rasch models: Foundations, recent developments, and applications (pp. 383-390). New York: Springer-Verlag.

Andrich, D. (1988). Rasch models for measurement. (Vols. series no. 07-068). Sage University Paper Series on Quantitative Applications in the Social Sciences). Beverly Hills, California: Sage Publications.

Andrich, D. (1998). Thresholds, steps and rating scale conceptualization. Rasch Measurement Transactions, 12(3), 648-9 [http://209.238.26.90/rmt/rmt1239.htm].

Arnold, S. F. (1985, September). Sufficiency and invariance. Statistics & Probability Letters, 3, 275-279.

Bond, T., & Fox, C. (2001). Applying the Rasch model: Fundamental measurement in the human sciences. Mahwah, New Jersey: Lawrence Erlbaum Associates.

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].

Burdick, H., & Stenner, A. J. (1996). Theoretical prediction of test items. Rasch Measurement Transactions, 10(1), 475 [http://www.rasch.org/rmt/rmt101b.htm].

Choi, E. (1998, Spring). Rasch invents “Ounces.” Popular Measurement, 1(1), 29 [http://www.rasch.org/pm/pm1-29.pdf].

Cohen, J. (1994). The earth is round (p < 0.05). American Psychologist, 49, 997-1003.

DeBoeck, P., & Wilson, M. (Eds.). (2004). Explanatory item response models: A generalized linear and nonlinear approach. (Statistics for Social and Behavioral Sciences). New York: Springer-Verlag.

Dynkin, E. B. (1951). Necessary and sufficient statistics for a family of probability distributions. Selected Translations in Mathematical Statistics and Probability, 1, 23-41.

Embretson, S. E. (1996, September). Item Response Theory models and spurious interaction effects in factorial ANOVA designs. Applied Psychological Measurement, pp. 201-212.

Falmagne, J.-C., & Narens, L. (1983). Scales and meaningfulness of quantitative laws. Synthese, 55, 287-325.

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

Fischer, G. H. (1995). Derivations of the Rasch model. In G. Fischer & I. Molenaar (Eds.), Rasch models: Foundations, recent developments, and applications (pp. 15-38). New York: Springer-Verlag.

Fisher, W. P., Jr. (1988). Truth, method, and measurement: The hermeneutic of instrumentation and the Rasch model [diss]. Dissertation Abstracts International, 49, 0778A, Dept. of Education, Division of the Social Sciences: University of Chicago (376 pages, 23 figures, 31 tables).

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. (1997, June). What scale-free measurement means to health outcomes research. Physical Medicine & Rehabilitation State of the Art Reviews, 11(2), 357-373.

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. (2000). Objectivity in psychosocial measurement: What, why, how. Journal of Outcome Measurement, 4(2), 527-563.

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. (2008, Summer). The cash value of reliability. Rasch Measurement Transactions, 22(1), 1160-3 [http://www.rasch.org/rmt/rmt221.pdf].

Fisher, W. P., Jr. (2009, July). Invariance and traceability for measures of human, social, and natural capital: Theory and application. Measurement (Elsevier), in press.

Goodman, S. N. (1999, 15 June). Toward evidence-based medical statistics. 1: The p-value fallacy. Annals of Internal Medicine, 130(12), 995-1004.

Guttman, L. (1985). The illogic of statistical inference for cumulative science. Applied Stochastic Models and Data Analysis, 1, 3-10.

Hall, W. J., Wijsman, R. A., & Ghosh, J. K. (1965). The relationship between sufficiency and invariance with applications in sequential analysis. Annals of Mathematical Statistics, 36, 575-614.

Linacre, J. M. (1993). Rasch-based generalizability theory. Rasch Measurement Transactions, 7(1), 283-284 [http://www.rasch.org/rmt/rmt71h.htm].

Luce, R. D., & Tukey, J. W. (1964). Simultaneous conjoint measurement: A new kind of fundamental measurement. Journal of Mathematical Psychology, 1(1), 1-27.

Meehl, P. E. (1967). Theory-testing in psychology and physics: A methodological paradox. Philosophy of Science, 34(2), 103-115.

Meehl, P. E. (1978). Theoretical risks and tabular asterisks: Sir Karl, Sir Ronald, and the slow progress of soft psychology. Journal of Consulting and Clinical Psychology, 46, 806-34.

Michell, J. (1999). Measurement in psychology: A critical history of a methodological concept. Cambridge: Cambridge University Press.

Moulton, M. (1993). Probabilistic mapping. Rasch Measurement Transactions, 7(1), 268 [http://www.rasch.org/rmt/rmt71b.htm].

Mundy, B. (1986, June). On the general theory of meaningful representation. Synthese, 67(3), 391-437.

Narens, L. (2002). Theories of meaningfulness (S. W. Link & J. T. Townsend, Eds.). Scientific Psychology Series. Mahwah, New Jersey: Lawrence Erlbaum Associates.

Newby, V. A., Conner, G. R., Grant, C. P., & Bunderson, C. V. (2009). The Rasch model and additive conjoint measurement. Journal of Applied Measurement, 10(4), 348-354.

Pelton, T., & Bunderson, V. (2003). The recovery of the density scale using a stochastic quasi-realization of additive conjoint measurement. Journal of Applied Measurement, 4(3), 269-81.

Ramsay, J. O., Bloxom, B., & Cramer, E. M. (1975, June). Review of Foundations of Measurement, Vol. 1, by D. H. Krantz et al. Psychometrika, 40(2), 257-262.

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.

Roberts, F. S., & Rosenbaum, Z. (1986). Scale type, meaningfulness, and the possible psychophysical laws. Mathematical Social Sciences, 12, 77-95.

Romanoski, J. T., & Douglas, G. (2002). Rasch-transformed raw scores and two-way ANOVA: A simulation analysis. Journal of Applied Measurement, 3(4), 421-430.

Rozeboom, W. W. (1960). The fallacy of the null-hypothesis significance test. Psychological Bulletin, 57(5), 416-428.

Smith, R. M., & Taylor, P. (2004). Equating rehabilitation outcome scales: Developing common metrics. Journal of Applied Measurement, 5(3), 229-42.

Thurstone, L. L. (1928). Attitudes can be measured. American Journal of Sociology, XXXIII, 529-544. Reprinted in L. L. Thurstone, The Measurement of Values. Midway Reprint Series. Chicago, Illinois: University of Chicago Press, 1959, pp. 215-233.

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

Velleman, P. F., & Wilkinson, L. (1993). Nominal, ordinal, interval, and ratio typologies are misleading. The American Statistician, 47(1), 65-72.

Wright, B. D. (1977). Solving measurement problems with the Rasch model. Journal of Educational Measurement, 14(2), 97-116 [http://www.rasch.org/memo42.htm].

Wright, B. D. (1997, Winter). A history of social science measurement. Educational Measurement: Issues and Practice, pp. 33-45, 52 [http://www.rasch.org/memo62.htm].

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LivingCapitalMetrics Blog by William P. Fisher, Jr., Ph.D. is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 United States License.
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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].

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

July 14, 2009

In the late 18th and early 19th centuries, scientists took Newton’s successful study of gravitation and the laws of motion as a model for the conduct of any other field of investigation that would purport to be a science. Heilbron (1993) documents how the “Standard Model” evolved and eventually informed the quantitative study of areas of physical nature that had previously been studied only qualitatively, such as cohesion, affinity, heat, light, electricity, and magnetism. Referred to as the “six imponderables,” scientists were widely influenced in experimental practice by the idea that satisfactory understandings of these fundamental forces would be obtained only when they could be treated mathematically in a manner analogous, for instance, with the relations of force, mass, and acceleration in Newton’s Second Law of Motion.

The basic concept is that each parameter in the model has to be measurable independently of the other two, and that any combination of two parameters has to predict the third.  These relationships are demonstrably causal, not just unexplained associations. So force has to be the product of mass and acceleration; mass has to be force divided by acceleration; and acceleration has to be force divided by mass.

The ideal of a mathematical model incorporating these kinds of relations not only guided much of 19th century science, the effects of acceleration and force on mass were a vital consideration for Einstein in his formulation of the relation of mass and energy relative to the speed of light, with the result that energy is now separated from mass in the context of relativity theory (Jammer, 1999, pp. 41-42). He realized that, in the same way humans experience nothing unpleasant or destructive as body mass (or, as is now held, its energy) increases when accelerated to the relatively high speeds of trains, so, too, might we experience similar changes in the relation of mass and energy relative to the speed of light. The basic intellectual accomplishment, however, was one in a still-growing history of analogies from the Standard Model, which itself deeply indebted to the insights of Plato and Euclid in geometry and arithmetic (Fisher, 1992).

Working an independent line of research, historians of economics and econometrics have documented another extension of the Standard Model. The analogies to the new field of energetics made in the period of 1850-1880, and the use of the balance scale as a model by early economists, such as Stanley Jevons and Irving Fisher, are too widespread to ignore.  Mirowski (1988, p. 2) says that, in Walras’ first effort at formulating a mathematical expression of economic relations, he “attempted to implement a Newtonian model of market relations, postulating that ‘the price of things is in inverse ratio to the quantity offered and in direct ratio to the quantity demanded.'”

Jevons similarly studied energetics, in his case, with Michael Faraday, in the 1850s. Pareto also trained as an engineer; he made “a direct extrapolation of the path-independence of equilibrium energy states in rational mechanics and thermodynamics” to “the path-independence of the realization of utility” (Mirowski, 1988, p. 21).

The concept of equilibrium models stems from this work, and was also extensively elaborated in the analogies Jan Tinbergen was well known for drawing between economic phenomena and James Clerk Maxwell’s encapsulation of Newton’s second law. In making these analogies, Tinbergen was deliberately employing Maxwell’s own method of analogy for guiding his thinking (Boumans, 2005, p. 24).

In his 1934-35 studies with Frisch in Oslo and with Ronald Fisher in London, the Danish mathematician Georg Rasch (Andrich, 1997; Wright, 1980) made the acquaintance of a number of Tinbergen’s students, such as Tjalling Koopmans (Bjerkholt 2001, p. 9), from whom he may have heard of Tinbergen’s use of Maxwell’s method of analogy (Fisher, 2008). Rasch employs such an analogy in the presentation of his measurement model (1960, p. 115), pointing out

“…the acceleration of a body cannot be determined; the observation of it is admittedly liable to … ‘errors of measurement’, but … this admittance is paramount to defining the acceleration per se as a parameter in a probability distribution — e.g., the mean value of a Gaussian distribution — and it is such parameters, not the observed estimates, which are assumed to follow the multiplicative law [acceleration = force / mass].
Thus, in any case an actual observation can be taken as nothing more than an accidental response, as it were, of an object — a person, a solid body, etc. — to a stimulus — a test, an item, a push, etc. — taking place in accordance with a potential distribution of responses — the qualification ‘potential’ referring to experimental situations which cannot possibly be [exactly] reproduced.
In the cases considered [earlier in the book] this distribution depended on one relevant parameter only, which could be chosen such as to follow the multiplicative law.
Where this law can be applied it provides a principle of measurement on a ratio scale of both stimulus parameters and object parameters, the conceptual status of which is comparable to that of measuring mass and force. Thus, … the reading accuracy of a child … can be measured with the same kind of objectivity as we may tell its weight ….”

What Rasch provides in the models that incorporate this structure is a portable way of applying Maxwell’s method of analogy from the Standard Model. Data fitting a Rasch model show a pattern of associations suggesting that richer causal explanatory processes may be at work, but model fit alone cannot, of course, provide a construct theory in and of itself (Burdick, Stone, & Stenner, 2006; Wright, 1994). This echoes Tinbergen’s repeated emphasis on the difference between the mathematical model and the substantive meaning of the relationships it represents.

It also shows appreciation for the reason why Ludwig Boltzmann was so enamored of Maxwell’s method of analogy. As Boumans (1993, p. 136; also see Boumans, 2005, p. 28), “it allowed him to continue to develop mechanical explanations without having to assert, for example, that a gas ‘really’ consists of molecules that ‘really’ interact with one another according to a particular force law. If a scientific theory is only an image or a picture of nature, one need not worry about developing ‘the only true theory,’ and one can be content to portray the phenomena as simply and clearly as possible.” Rasch (1980, pp. 37-38) similarly held that a model is meant to be useful, not true.

Part II continues soon with more on Rasch’s extrapolation of the Standard Model, and references cited.

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