cific values. It doesn’t matter how different two states are if they lead to similar structures, since (or so I will hypothesize) what the mind perceives is structure.
Theoretically, to measure the L.-, S.-, R.S.- or S.S.-sensitivity of a system, one merely
averages the respective sensitivities at all points x in X. But of course, the word "measure" must be taken with a grain of salt.
The metric d# is, in general, an uncomputable quantity. For practical purposes, we must work
instead with dC, the distance which considers only patterns in the computable set C. For example, C could be the set of all n’th order Boolean patterns, as discussed at the end of Chapter 3. If one replaces d# with dC in the above definitions, one obtains L.-, S.-, R.S.- and S.S.-sensitivities relative to C.
Estimation of the sensitivity of a system in these various senses could potentially be quite
valuable. For instance, if a system were highly sensitive to initial conditions, but not highly
structurally sensitive, then although one could not reasonably predict the exact future condition of the system, one would be able to predict the general structure of the future of the system. If a system were highly structurally sensitive but not highly S.S.-sensitive, then, although knowledge of the present state would tell little about the future structure, knowledge of the past structure would tell a lot. If a system were highly R.S.-sensitive but not highly S.S.-sensitive, then by studying the structure of a system one could reasonably predict the future structure but not the exact future state. The precise relation between the various forms of unpredictability has yet to be explored, but it seems likely that all these combinations are possible.
It seems to me that the new sensitivity measures defined here possess a very direct relation to
unpredictability as it occurs in real social, psychological and biological situations — they speak of what studying a system, recognizing patterns in it, can tell about its future. L.-sensitivity, on the other hand, has no such connection. L.-sensitivity — in particular, the Liapunov exponent — is profoundly incisive in the analysis of intricate feedback systems such as turbulent flow.
However, speaking philosophically, it seems that when studying a system containing feedback
on the level of structure as well as the level of physical parameters, one should consider
unpredictability on the level of structure as well as the level of numerical parameters.
In conclusion, I would like to make the following conjecture: that when the logic relating self-
organization with unpredictability is untangled, it will turn out that real highly self-organizing systems (society, the brain, the ecosystem, etc.) are highly Liapunov sensitive, structurally sensitive and R.S.-sensitive, but are not nearly so highly S.S.-sensitive. That is: roughly speaking, it should turn out that by studying the structure of the past, one can tell something about the structure of the future, but by tracking or attempting to predict specific events one will get nowhere.