BAMΞ’s Measurement Theory Sprint is concerned with measurement in Consciousness Science.

Over the past three decades, several measures and tests of consciousness have been developed, in part based on earlier work in psychophysics and related disciplines. They allow experimenters to make inferences about both the content and presence of conscious experiences in empirical investigations and are also applied in clinical practice.

What isn’t available so far, however, is a measurement theory that provides a foundation and unification of the various forms of measurement available in the field.

BAMΞ’s Measurement Theory Sprint aims to bring together experts across empirical and theoretical domains in Consciousness Science to explore whether and how a useful measurement theory might be constructed.

Measurement Theories in other Fields

Measurement theories are an important part of those sciences where measurement is not straightforward. Consider, as an example, the case of psychology. In the first part of the 20th century, the question of whether there is measurement at all in psychology has been heavily debated, so much so that in 1932 a committee of the British Association for the Advancement of Science was appointed “to decide whether or not there was such a thing as measurement in psychology” (Borsboom, 2005; Ferguson et al., 1940). The committee's report was highly divided, with a majority of members around the physicist Norman Campbell strongly rejecting claims about the possibility of measurement in psychology.

In response to this rejection by part of the committee, psychologists started to develop theories of measurement that are targeted specifically at psychological experiments, first in the form of scales by Stevens (1946) and then in the form of axiomatic theories of measurement (Cliff, 1992), the most well-known of which is Representational Measurement Theory (Krantz, Luce, Suppes, & Tversky, 1971). These developments were pivotal to the progress of psychology in the 20th century (Michell, 1999; Borsboom, 2005) and still form the basis of much of the empirical work that is being carried out.

Another example of where a theory of measurement was crucial for understanding the intricacies of measurement is quantum theory in physics. Quantum theory comprises a comprehensive account of measurement, where complex measurement apparati, that might fill a whole room, are represented by comparably simple mathematical objects: self-adjoint operators on Hilbert spaces, or POVMs more generally.

Based on these mathematical representations of measurement devices, quantum theory provides an account of how measurement interfaces with the time evolution of a system, which includes means to calculate possible results of the measurement procedure, as well as an account of how a measurement changes or modifies the state of the system. While this account of measurement is also the source of the notorious measurement problem of quantum theory (cf. e.g. (Myrvold, 2022)), it is hard to imagine which progress could have been possible without the introduction of this part of the theory by von Neumann (1932).

Towards a Measurement Theory for Consciousness Science

Given consciousness' unique epistemic context, it is likely that a measurement theory can be as important for Consciousness Science as it has been for other fields. And because measurement theories usually are mathematical in nature (Tal, 2020), it might be reasonable to assume that a mathematical perspective can support the development of a measurement theory for Consciousness Science.

BAMΞ’s Measurement Theory Sprint aims to explore whether and how mathematical representations of measurements in consciousness science can be constructed. Is there a common mathematical representation of measurement that can be seen to underlie measurement in consciousness science, as in psychology and physics?  What constitutes a measurement, and what not? How does measurement integrate with theories of consciousness? Which aspects of consciousness are measurable, and which not?

We are currently in the process of organizing workshops, invited talks, and discussion sessions for this sprint. Please reach out if you would like to contribute to this sprint.

Updates about activities related to this sprint will be distributed via our mailing list.

References

• Borsboom, D. (2005). Measuring the mind: Conceptual issues in contemporary psychometrics. Cambridge University Press.
• Cliff, N. (1992). Abstract measurement theory and the revolution that never happened. Psychological Science, 3(3), 186-190.
• Ferguson, A., Meyers, C., Bartlett, R., Banister, H., Bartlett, F., Brown, W., … others (1940). Quantitative estimates of sensory events. Report of the British Association for the Advancement of Science. The Advancement of Science, 2, 331–349.
• Krantz, D., Luce, D., Suppes, P., & Tversky, A. (1971). Foundations of Measurement, Vol. I-III. Academic Press.
• Michell, J. (1999). Measurement in psychology: A critical history of a methodological concept (Vol. 53). Cambridge University Press.
• Myrvold, W. (2022). Philosophical Issues in Quantum Theory. In E. N. Zalta & U. Nodelman (Eds.), The Stanford Encyclopedia of Philosophy (Fall 2022 ed.). Metaphysics Research Lab, Stanford University.
• Stevens, S. S. (1946). On the theory of scales of measurement. Science, 103(2684), 677–680.
• Tal, E. (2020). Measurement in Science. In E. N. Zalta & U. Nodelman (Eds.), The Stanford Encyclopedia of Philosophy (Fall 2020 ed.). Metaphysics Research Lab, Stanford University.
• von Neumann, J. (1932). Mathematische Grundlagen der Quantenmechanik (Mathematical Foundations of Quantum Mechanics). Julius Springer.