The cerebral cortex is a rich and diverse structure that is the basis of intelligent behavior. One of the deepest mysteries of the function of cortex is that neural processing times are only about one hundred times as fast as the fastest response times for complex behavior. At the very least, this would seem to indicate that the cortex does massive amounts of parallel computation.This paper explores the hypothesis that an important part of the cortex can be modeled as a (...) connectionist computer that is especially suited for parallel problem solving. The connectionist computer uses a special representation, termed value unit encoding, that represents small subsets of parameters in a way that allows parallel access to many different parameter values. This computer can be thought of as computing hierarchies of sensorimotor invariants. The neural substrate can be interpreted as a commitment to data structures and algorithms that compute invariants fast enough to explain the behavioral response times. A detailed consideration of this model has several implications for the underlying anatomy and physiology. (shrink)

This paper is a commentary on the target article by Dana H. Ballard, “Cortical connections and parallel processing: Structure and function”, in the same issue of the journal, pp. 67–120. -/- I raise some issues about the connectionist or neural-network implementation of information and information processing. Issues include the sharing of information by different parts of a connectionist/neural network, the copying of complex information from one place to another in a network, the possibility of connection weights not being synaptic weights, (...) and the possibility of fast communication within single neurons as complex systems in their own right. (shrink)

Several hundred thousand intellectually talented 12-to 13-year-olds have been tested nationwide over the past 16 years with the mathematics and verbal sections of the Scholastic Aptitude Test (SAT). Although no sex differences in verbal ability have been found, there have been consistent sex differences favoring males in mathematical reasoning ability, as measured by the mathematics section of the SAT (SAT-M). These differences are most pronounced at the highest levels of mathematical reasoning, they are stable over time, and they are observed (...) in other countries as well. The sex difference in mathematical reasoning ability can predict subsequent sex differences in achievement in mathematics and science and is therefore of practical importance. To date a primarily environmental explanation for the difference in ability has not received support from the numerous studies conducted over many years by the staff of Study of Mathematically Precocious Youth (SMPY) and others. We have studied some of the classical environmental hypotheses: attitudes toward mathematics, perceived usefulness of mathematics, confidence, expectations/ encouragement from parents and others, sex-typing, and differential course-taking. In addition, several physiological correlates of extremely high mathematical reasoning ability have been identified (left-handedness, allergies, myopia, and perhaps bilateral representation of cognitive functions and prenatal hormonal exposure). It is therefore proposed that the sex difference in SAT-M scores among intellectually talented students, which may be related to greater male variability, results from both environmental and biological factors. (shrink)

The central problem in Geary's theory is how differences are conceptualized. Recent research has shown that between-sex differences on certain tasks are a consequence of averaging within sex differences. A mixture distribution models between-sex differences on several tasks well and does not appear congenial to a sexual-selection perspective.

Geary's model is a worthy effort, but ambiguous on important issues. It ignores differential resource allocation, although this follows directly from sexual selection via differential parental investment. Dimorphism in primary traits is arbitrarily attributed to sexual selection via intramale competition, rather than direct evolutionary pressures. Dubious predictions are made about the consequences of raising mathematics achievement.

Geary's emphasis on hunting ignores the possible importance of other human activities, such as scavenging and gathering, in the evolution of spatial abilities. In addition, there is little evidence that links spatial abilities and math skills. Furthermore, such links have little practical importance given the small size of most differences and girls' superior performance in mathematics classrooms.

This paper discusses spatial cognition in the domain of minimally invasive surgery. It draws on studies from this domain to shed light on a range of spatial cognitive processes and to consider individual differences in performance. In relation to modeling, the aim is to identify potential opportunities for characterizing the complex interplay between perception, action, and cognition, and to consider how theoretical models of the relevant processes might prove valuable for addressing applied questions about surgical performance and training.

To the extent that Geary's theory concerning biologically primary and secondary behaviors depends on factor analytic methods and findings, it is woefully weak. Factors have been mistakenly called primary mental abilities, but the adjective “primary” represents reification of a mathematical dimension defined by correlations. Fleshing out a factor beyond its mathematical properties requires much additional quantitative experimental and correlational research that goes far beyond mere factoring.

Criticism of sex differences in mathematical ability and sex roles in sociobiology and the pernicious influence of these ideas on education.

Although Geary's partitioning of mathematical abilities into those that are biologically primary and secondary is an advance over most sociobiological theories of cognitive sex differences, it remains untestable and ignores the spatial nature of women's traditional work. An alternative model based on underlying cognitive processes offers other advantages.

Geary proposes a sociobiological hypothesis of how sex differences in math and spatial skills might have jointly arisen. His distinction between primary and secondary math skills is noteworthy, and in some ways analogous to the closed versus open systems postulated to exist for language. In this commentary issues concerning how genes might affect complex cognitive skills, the interpretation of heritability estimates, and prior research abilites are discussed.

In Darwinian terminology, “sexual selection” refers to purely reproductive competition and is conceptually distinct from natural selection as it affects reproduction generally. As natural selection may favor the evolution of sexual dimorphism by virtue of the division of labor between males and females, this possibility needs to be taken very seriously.

The principles of sexual selection were used as an organizing framework for interpreting cross-national patterns of sex differences in mathematical abilities. Cross-national studies suggest that there are no sex differences in biologically primary mathematical abilities, that is, for those mathematical abilities that are found in all cultures as well as in nonhuman primates, and show moderate heritability estimates. Sex differences in several biologically secondary mathematical domains are found throughout the industrialized world. In particular, males consistently outperform females in the solving (...) of mathematical word problems and geometry. Sexual selection and any associated proximate mechanisms influence these sex differences in mathematical performance indirectly. First, sexual selection resulted in greater elaboration in males than in females of the neurocognitive systems that support navigation in three-dimensional space. Knowledge implicit in these systems reflects an understanding of basic Euclidean geometry, and may thus be one source of the male advantage in geometry. Males also use more readily than females these spatial systems in problem-solving situations, which provides them with an advantage in solving word problems and geometry. In addition, sex differences in social styles and interests, which also appear to be related in part to sexual selection, result in sex differences in engagement iii mathematics-related activities, thus further increasing the male advantage in certain mathematical domains. A model that integrates these biological influences with sociocultural influences on the sex differences in mathematical performance is presented in this article. (shrink)

The male advantage in certain mathematical domains contributes to the difference in the numbers of males and females that enter math-intensive occupations, which in turn contributes to the sex difference in earnings. Understanding the nature and development of the sex difference in mathematical abilities is accordingly of social as well as scientific concern. A more complete understanding of the biological contributions to these differences can guide research on educational techniques that might someday produce more equal educational outcomes in mathematics and (...) other academic domains. (shrink)

We challenge the notion that differences in spatial ability are the best or only explanation for observed sex differences in mathematical word problems. We suggest two ideas from the study of autism: sex differences in theory of mind and in central coherence.

Geary's project faces the severe methodological difficulty of tracing the biological effects of gender on mathematical ability in a system that is massively open. Two methodological stratagems he uses are considered. The first is that pancultural sex differences are biological in nature, which is dubious in the domain of mathematics, since it is completely culture-bound. The second is that sociosexual differences are partly caused by biosexual differences, which renders his thesis unfalsifiable and empirically empty.