Bella Z. Veksler, Rachel Boyd, Christopher W. Myers, Glenn Gunzelmann, Hansjörg Neth, Wayne D. Gray
Abstract: Visual working memory (VWM) is a construct hypothesized to store a small amount of accurate perceptual information that can be brought to bear on a task. Much research concerns the construct’s capacity and the precision of the information stored. Two prominent theories of VWM representation have emerged: slot-based and continuous-resource mechanisms. Prior modeling work suggests that a continuous resource that varies over trials with variable capacity and a potential to make localization errors best accounts for the empirical data. Questions remain regarding the variability in VWM capacity and precision. Using a novel eye-tracking paradigm, we demonstrate that VWM facilitates search and exhibits effects of fixation frequency and recency, particularly for prior targets. Whereas slot-based memory models cannot account for the human data, a novel continuous-resource model does capture the behavioral and eye tracking data, and identifies the relevant resource as item activation.
Abstract: Melioration — defined as choosing a lesser, local gain over a greater longer term gain — is a behavioral tendency that people and pigeons share. As such, the empirical occurrence of meliorating behavior has frequently been interpreted as evidence that the mechanisms of human choice violate the norms of economic rationality. In some environments, the relationship between actions and outcomes is known. In this case, the rationality of choice behavior can be evaluated in terms of how successfully it maximizes utility given knowledge of the environmental contingencies. In most complex environments, however, the relationship between actions and future outcomes is uncertain and must be learned from experience. When the difficulty of this learning challenge is taken into account, it is not evident that melioration represents suboptimal choice behavior.
|… how information is represented can greatly affect how easy it is
to do different things with it. (…) it is easy to add, to subtract,
and even to multiply if the Arabic or binary representations are used,
but it is not at all easy to do these things — especially multiplication —
with Roman numerals. This is a key reason why the Roman culture failed
to develop mathematics in the way the earlier Arabic cultures had.
|D Marr (1982): Vision, p. 21
[Copyright neth.de, 2008]:
Dirk Schlimm and Hans Neth (2008).
Modeling ancient and modern arithmetic practices: Addition and multiplication with Arabic and Roman numerals. Paper presented at CogSci 2008.
Dirk Schlimm, Hansjörg Neth
Abstract: To analyze the task of mental arithmetic with external representations in different number systems we model algorithms for addition and multiplication with Arabic and Roman numerals. This demonstrates that Roman numerals are not only informationally equivalent to Arabic ones but also computationally similar — a claim that is widely disputed. An analysis of our models’ elementary processing steps reveals intricate trade-offs between problem representation, algorithm, and interactive resources. Our simulations allow for a more nuanced view of the received wisdom on Roman numerals. While symbolic computation with Roman numerals requires fewer internal resources than with Arabic ones, the large number of needed symbols inflates the number of external processing steps.