Two parallel developments in the 1940s set the stage both for the cognitive revolution of the 1950s and for the discussion presented in the target article. The development of information theory explored ways to characterize the information content of a message and ways to consider how to best pass messages (Shannon Reference Shannon1949). At the same time, the architecture for digital computing led to advances in discrete mathematics that facilitated the analysis of the efficiency of algorithms (Turing Reference Turing1950).
One consequence of the cognitive revolution was that that it became common to characterize the mind as a computational device. Thus, researchers began to formulate theories of mental processes in computational terms. As Marr (Reference Marr1982) points out, a process can be defined at either a computational level or an algorithmic level of description. At the computational level, the process is defined by a mapping between information available at the start and end of the process. For example, Anderson (Reference Anderson1990) advocates a Bayesian, “rational-level” analysis of the information relationship between inputs and outputs of a system. At the algorithmic level, a process is specified in terms of a set of steps that implements this computational-level description. Any given algorithm can be analyzed for its efficiency in time. The efficiency of a cognitive process can be established at either the computational level of description or at the algorithmic level. The Bayesian approaches described in the target article are focused on defining the optimality of a cognitive process at the computational level (Anderson Reference Anderson1990; Tenenbaum & Griffiths Reference Tenenbaum and Griffiths2001). Anderson (Reference Anderson1990) does point out that computational costs can also play a role in determining a rational model, but, in practice, these considerations did not have a significant influence on the structure of his rational models.
The danger in casting optimality purely at the computational level is that human cognition is implemented by a physical system. Indeed, it has been proposed that any characterization of the optimality of actions or beliefs should take into account the resource-limited nature of the human cognitive apparatus (Cherniak Reference Cherniak1986; Stanovich & West Reference Stanovich and West1998). As the target article points out, the brain consumes a significant amount of energy. Thus, energy minimization is likely to be an important constraint on cognitive processing.
The idea that energy-minimization is an important constraint on cognitive processing is implicit in the focus on efficient computational procedures. We do not suppose that the metabolic cost of cognition is completely invariant of the type of thinking that people are engaged in, but marginal changes in metabolic rates attributed to different types of cognition pale in comparison to the metabolic cost of simply keeping the brain running. Thus, the time taken by a process is a good proxy for energy conservation. On this view, for example, habits minimize energy, because they allow a complex behavior to be carried out quickly (e.g., Logan Reference Logan1988; Schneider & Shiffrin Reference Schneider and Shiffrin1977).
Of course, effort-minimization is not the only constraint on cognitive processing. It is crucial that a process be carried out to a degree sufficient to solve the problem faced by the individual. This view was central to Simon's (Reference Simon1957b) concept of satisficing. This view suggested that cognitive processes aim to expend the minimal amount of effort required to solve a problem. On this view, the costs of additional effort outweigh the gains in decision accuracy. This idea was elaborated in the effort accuracy framework developed by Payne et al. (Reference Payne, Bettman and Johnson1993). Their work examined the variety of strategies that people utilize in order to balance decision accuracy with effort – the cognitive costs of gathering and integrating information about choice attributes – in decision-making. Payne et al. point out that these strategies differ both in the effort required to carry them out as well as in their likelihood of returning an accurate response. People negotiate the trade-off between effort and accuracy by selecting decision strategies that minimize the effort required to yield an acceptable outcome from a choice.
A key shortcoming, then, of the Bayesian Fundamentalist approach is that it optimizes the wrong thing. The ideal observer or actor defined purely in terms of information is quite useful, but primarily as a point of comparison against human cognitive or sensory abilities rather than as a statement of what is optimal as a cognitive process (e.g., Geisler Reference Geisler1989). A definition of optimal behavior needs to take energy minimization into account. Thus, the key limitation of Bayesian Fundamentalism is that it focuses selectively on optimality of information processing rather than on the combination of information and time.
Two parallel developments in the 1940s set the stage both for the cognitive revolution of the 1950s and for the discussion presented in the target article. The development of information theory explored ways to characterize the information content of a message and ways to consider how to best pass messages (Shannon Reference Shannon1949). At the same time, the architecture for digital computing led to advances in discrete mathematics that facilitated the analysis of the efficiency of algorithms (Turing Reference Turing1950).
One consequence of the cognitive revolution was that that it became common to characterize the mind as a computational device. Thus, researchers began to formulate theories of mental processes in computational terms. As Marr (Reference Marr1982) points out, a process can be defined at either a computational level or an algorithmic level of description. At the computational level, the process is defined by a mapping between information available at the start and end of the process. For example, Anderson (Reference Anderson1990) advocates a Bayesian, “rational-level” analysis of the information relationship between inputs and outputs of a system. At the algorithmic level, a process is specified in terms of a set of steps that implements this computational-level description. Any given algorithm can be analyzed for its efficiency in time. The efficiency of a cognitive process can be established at either the computational level of description or at the algorithmic level. The Bayesian approaches described in the target article are focused on defining the optimality of a cognitive process at the computational level (Anderson Reference Anderson1990; Tenenbaum & Griffiths Reference Tenenbaum and Griffiths2001). Anderson (Reference Anderson1990) does point out that computational costs can also play a role in determining a rational model, but, in practice, these considerations did not have a significant influence on the structure of his rational models.
The danger in casting optimality purely at the computational level is that human cognition is implemented by a physical system. Indeed, it has been proposed that any characterization of the optimality of actions or beliefs should take into account the resource-limited nature of the human cognitive apparatus (Cherniak Reference Cherniak1986; Stanovich & West Reference Stanovich and West1998). As the target article points out, the brain consumes a significant amount of energy. Thus, energy minimization is likely to be an important constraint on cognitive processing.
The idea that energy-minimization is an important constraint on cognitive processing is implicit in the focus on efficient computational procedures. We do not suppose that the metabolic cost of cognition is completely invariant of the type of thinking that people are engaged in, but marginal changes in metabolic rates attributed to different types of cognition pale in comparison to the metabolic cost of simply keeping the brain running. Thus, the time taken by a process is a good proxy for energy conservation. On this view, for example, habits minimize energy, because they allow a complex behavior to be carried out quickly (e.g., Logan Reference Logan1988; Schneider & Shiffrin Reference Schneider and Shiffrin1977).
Of course, effort-minimization is not the only constraint on cognitive processing. It is crucial that a process be carried out to a degree sufficient to solve the problem faced by the individual. This view was central to Simon's (Reference Simon1957b) concept of satisficing. This view suggested that cognitive processes aim to expend the minimal amount of effort required to solve a problem. On this view, the costs of additional effort outweigh the gains in decision accuracy. This idea was elaborated in the effort accuracy framework developed by Payne et al. (Reference Payne, Bettman and Johnson1993). Their work examined the variety of strategies that people utilize in order to balance decision accuracy with effort – the cognitive costs of gathering and integrating information about choice attributes – in decision-making. Payne et al. point out that these strategies differ both in the effort required to carry them out as well as in their likelihood of returning an accurate response. People negotiate the trade-off between effort and accuracy by selecting decision strategies that minimize the effort required to yield an acceptable outcome from a choice.
A key shortcoming, then, of the Bayesian Fundamentalist approach is that it optimizes the wrong thing. The ideal observer or actor defined purely in terms of information is quite useful, but primarily as a point of comparison against human cognitive or sensory abilities rather than as a statement of what is optimal as a cognitive process (e.g., Geisler Reference Geisler1989). A definition of optimal behavior needs to take energy minimization into account. Thus, the key limitation of Bayesian Fundamentalism is that it focuses selectively on optimality of information processing rather than on the combination of information and time.