“Another approach that is suggestive in this direction is one proposed recently by John Tukey (1966) for models of attitude change, based on the theory of absolute reaction rates in chemistry. Each state of a chemical entity is characterized by a ‘free energy level’, and each boundary between states by a free energy level that is higher than the levels of the states it separates.

The transition rate from each state to the other is an exponential function of the difference between the free energy level of the state and that of the boundary. Tukey's proposal is that an attitudinal state may be characterized by a tension level, and the boundary between states by a higher tension level, with the transition rates an exponential function of the difference between tension levels.

This conception has the virtue that in any system with three or more intercommunicating states, it can be tested, because the number of transition rates is greater than the number of tension levels. In such a system, of course, the individual in effect ‘seeks out’ that state that has the lowest tension level, although the expected time to arrival depends upon the tension level of the boundaries that separate it from other states.

In a system with three states: 1, 2 and 3, there are six transition rates qij, two between each pair of states. Tukey's proposal would define three tension levels, s1, s2, and s3, for the three states, and three for the boundaries between states, s12, S13, and s23. The transition rate qij is a function of the difference in tension levels between state i and boundary ij.

That is, qij is a function of sij – si, in particular, qij = exp (sij – si). This formulation, analogous to that of absolute reaction rates in chemistry, allows estimation of the values of sij and si, from the values of qij for all i and j. Further, since the zero point of the tension levels does not affect these differences, one tension level can arbitrarily be set equal to zero with no loss of generality. Thus, in a three-state system, there are only five tension levels to estimate, and six empirically-obtained qij's. This allows testing of the underlying model that Tukey proposed. When the number of states is greater than three, the test can be made stronger, since the number of transition rates is n(n— 1), while the number of tension levels is ½n(n—1)+n-1.”

“Tukey was a prodigy. His parents had not realized that he had learned to read until on a driving trip there was concern over whether a particular bridge over the Susquehanna was closed. Aged 3 years, he spoke up to say that the bridge was closed. He had read a legal notice in the newspaper announcing the closure.”

“Far better an approximate answer to the right question, which is often vague, than an exact answer to the wrong question, which can always be made precise.”

— John Tukey (c.1960) (Ѻ)