Friday, April 27, 2018

Psychology and the Big Adventure of the Elastic Yardstick

A psychologist looks to color science to resolve old measurement quandaries.

 A news flash:  psychology is hard if you don’t have the right tools.  Psychology has a significant problem with measurement.  Call its problem what you will: a crossing of ideas, a confluence of concepts, a tired old mistake, or even a methodological thought disorder (the last phrase is from Michell 1997, p. 374). Psychology has had a perennial problem with measurement since the mid-1800s (if not before) when Gustav Fechner announced his law to relate psychological qualities to physical magnitudes.  The heart of the problem is that measurement in psychology is taken to be the same activity as quantitative measurement in physics.  Measurement in physics involves knowing how to measure distances and knowing how to measure time, among other notions; it is clear that we cannot extend the same activities of measurement to psychology without some conceptual upheaval in our understanding of measurement.  "It is as if I were to say, 'You surely know what "It’s 5 o’clock here" means; so you also know what "It’s 5 o’clock on the sun" means.' " (Wittgenstein, 1953/2009, § 350, p.118e)  We do not, at least not without a lot more work and a few conventions about astrophysics.  The one activity (in psychology) is just not the same as the other (in physics).  More than that: it is meaningless to begin to describe how the two activities are the same or different, before we think harder about measurement and psychology.

One can begin in psychology by honoring Fechner and repealing his law, repeating a phrase from Stevens (1957).  We are not rid of the problem of measurement in psychology merely by repealing Fechner’s law, though.  Stevens himself caused as much trouble by introducing another procedure he called ‘magnitude estimation’: a procedure of attaching number words to stimulus magnitudes.  The very act of attaching numbers to perceptible magnitudes was supposed to constitute measurement, somehow.  One can’t just attach numbers to situations and expect the procedure to stand as measurement: such an attitude trivializes psychology in a parody of physics. “The proposition that one conversation is ten times as boring as another is neither true nor false, but is simply a string of words to which no sense may be attached.” (von Kries in Niall, 1995).  Stevens only created trouble by introducing one more procedure unworthy of being called measurement.  So let us honor Stevens and repeal his law of magnitude estimation in turn.
Is there hope left for measurement in psychology ?  Measurement continues to be a problem all over psychology today, but hope remains.  We do know what constitutes effective measurement.  The formal or mathematical conditions for quantitative measurement are well-known (as in Krantz, Luce, Suppes, and Tversky, 1971).  Problems of measurement do matter, if a coherent description of color space matters in colorimetry – as one example.   What can be done to resolve issues of the application of measurement in psychology?  We can begin by recognizing that measurement is something that may be possible in psychology, or else it may fail to obtain.  There may be no measurement in most domains of psychology: we just do not know when measurement makes sense. 

Quantitative structure is a contingent matter for colorimetry as it is for psychology generally – not a law at all, not by Fechner and not by Stevens and not by anyone.  I venture to say the quantitative nature of color space has not been demonstrated in full: we still do not know if measurement works within colorimetry in the same way it does for other, physical magnitudes.  In a profoundly ironic twist though, measurement in color space has a far better chance of working than the application of quantitative measurement in a geometry of ‘visual space’.  Color theory has a better legacy: the pioneers of modern color theory were acutely aware of problems of measurement as they advanced the notion of color space, and a ‘line element’ for color space.  In contrast my bet is that ordinary measurement is meaningless for visual shape, that is, under what has been called ‘the geometry of visual space’.  But that conclusion follows from a long and abstract argument which I leave for another day (though see Suppes, 1991, p.48).


Krantz, D.H., Luce, R.D., Suppes, P. & Tversky, A. (1971).  Foundations of measurement. vol.1.  Academic Press.

Michell, J. (1997).  Quantitative science and the definition of measurement in psychology.  British Journal of Psychology, 88(3), 355 – 383.

Niall, K.K. (1995).  Conventions of measurement in psychophysics: von Kries on the so-called psychophysical law.  Spatial Vision, 9(3), 275 – 305.

Stevens, S.S. (1957).  On the psychophysical law.  Psychological Review, 64(3), 153 – 181.

Suppes, P. (1991).  The principle of invariance with special reference to perception.  In: J.-P. Doignon & J.-C. Falmagne, Eds.  Mathematical psychology: current developments.  New York: Springer, pp. 35 – 53.

Wittgenstein, L. (1953).  Philosophical investigations / Philosophische Untersuchungen.  Revised 4th edition, 2009.  Wiley-Blackwell.

Keith K. Niall
Keith lives in Toronto, Canada.  He is translator and editor of Erwin Schrödinger’s Color Theory, and he is looking forward to writing a book about vision in his own voice. His email address is