Evaluating gambles using dynamics.

Gambles are random variables that model possible changes in wealth. Classic decision theory transforms money into utility through a utility function and defines the value of a gamble as the expectation value of utility changes. Utility functions aim to capture individual psychological characteristics, but their generality limits predictive power. Expectation value maximizers are defined as rational in economics, but expectation values are only meaningful in the presence of ensembles or in systems with ergodic properties, whereas decision-makers have no access to ensembles, and the variables representing wealth in the usual growth models do not have the relevant ergodic properties. Simultaneously addressing the shortcomings of utility and those of expectations, we propose to evaluate gambles by averaging wealth growth over time. No utility function is needed, but a dynamic must be specified to compute time averages. Linear and logarithmic "utility functions" appear as transformations that generate ergodic observables for purely additive and purely multiplicative dynamics, respectively. We highlight inconsistencies throughout the development of decision theory, whose correction clarifies that our perspective is legitimate. These invalidate a commonly cited argument for bounded utility functions.

Consciousness, reduction, and emergence. Some remarks.

Consciousness is often seen as requiring a special kind of explanation. But the various aspects of self-awareness can presumably emerge when certain levels of complexity are reached in an organism: it is not necessary to assume additional mechanisms or hidden causes. Looking at the most fundamental level, that of elementary particle physics, three principles appear--the conformability of nature to herself, the applicability of the criterion of simplicity, and the utility of certain parts of mathematics in describing physical reality--which are in themselves emergent properties of the fundamental laws of physics. At successive levels, it is the availability of similar mathematical descriptions from related problems that makes the next step appear with simplicity and elegance. Thus, once the concept of emergence is properly established, a huge burden is lifted from the inquiring mind. The whole explanatory loop may be closed by looking at the ability of the human mind to figure out the laws of nature. All the other sciences emerge in principle from fundamental physics plus historical accidents, even though "reduction" is obviously inadequate as a strategy. While bridges or staircases are under construction connecting the various sciences, each science needs to be studied at its own level as well. Although the idea of "vital forces" in biology alien to physics and chemistry has largely disappeared, consciousness remains the last refuge of obscurantists. Finally, it is argued that appeals to the alleged weirdness of quantum mechanics are based on a misunderstanding and are unlikely to have any place in a discussion of consciousness.