语言与数量认知关系的新认识

数量认知研究近年有长足发展。文章从新近提出的独立于语言的两个数量表征核心系统,语言与精确数量运算,语言与算术事实的储存,语言对儿童早期数概念发展的影响,语言与数量认知关系的最新脑科学证据,以及语言在数量认知模型中的角色等方面,介绍和评述了人类存在依赖和不依赖语言的两级数量能力的新认识。对于是否还存在其它不依赖语言的理解数量的系统,以及这些非语言数量表征系统的认知机制,文章认为有待进一步研究     

Integration of melody and text in memory for songs

Two experiments examined whether the memory representation for songs consists of independent or integrated components (melody and text). Subjects heard a serial presentation of excerpts from largely unfamiliar folksongs, followed by a recognition test. The test required subjects to recognize songs, melodies, or texts and consisted of five types of items: (a) exact songs heard in the presentation; (b) new songs; (c) old tunes with new words; (d) new tunes with old words; and (e) old tunes with old words of a different song from the same presentation (‘mismatch songs’). Experiment 1 supported the integration hypothesis: Subjects' recognition of components was higher in exact songs (a) than in songs with familiar but mismatched components (e). Melody recognition, in particular, was near chance unless the original words were present. Experiment 2 showed that this integration of melody and text occurred also across different performance renditions of a song and that it could not be eliminated by voluntary attention to the melody.     

计算的脑科学研究及其对数学教育的启示

脑科学研究发现,简单心算主要涉及算术事实的提取,依赖于左半球的语言中枢,而复杂心算激活了左侧顶—额叶网络和双侧颞下回,与视觉空间表征和视觉表象加工有关;精算主要激活左额叶下部区域,而估算激活了两半球更大的区域。在计算过程中所激活的脑区受年龄发展与个体差异以及训练的影响。研究对有效地促进儿童计算能力的发展提供了重要启示。     

A Deep Inference System for the Modal Logic S5

We present a cut-admissible system for the modal logic S5 in a formalism that makes explicit and intensive use of deep inference. Deep inference is induced by the methods applied so far in conceptually pure systems for this logic. The system enjoys systematicity and modularity, two important properties that should be satisfied by modal systems. Furthermore, it enjoys a simple and direct design: the rules are few and the modal rules are in exact correspondence to the modal axioms. Presented by Heinrich Wansing     

The exact vs. approximate distinction in numerical cognition may not be exact, but only approximate: How different processes work together in multi-digit addition

Two types of calculation processes have been distinguished in the literature: approximate processes are supposed to rely heavily on the non-verbal quantity system, whereas exact processes are assumed to crucially involve the verbal system. These two calculation processes were commonly distinguished by manipulation of two factors in addition problems: the identity of the target and the distance of the distractor. However, in all previous studies, these two factors were not manipulated independently. In this fMRI study, we could disentangle the two factors by using a different (two-digit) number stimulus set. Both behavioral and neurofunctional data suggest that the cognitive processes involved could be best explained by the (independent) factors target and distractor distance. Based on these data we suggest that the exact/approximate distinction does not seem to be as generally valid as previously assumed. We conclude that this study may be a starting point for a closer examination of the experimental, procedural and strategic conditions of when the exact/approximate distinction is valid and when it is not.     

Algebraic Biology: Creating Invariant Binding Relations for Biochemical and Biological Categories

The desire to understand the mathematics of living systems is increasing. The widely held presupposition that the mathematics developed for modeling of physical systems as continuous functions can be extended to the discrete chemical reactions of genetic systems is viewed with skepticism. The skepticism is grounded in the issue of scientific invariance and the role of the International System of Units in representing the realities of the apodictic sciences. Various formal logics contribute to the theories of biochemistry and molecular biology and genetics. Various paths of extension are invoked in these formal logics in order to express the information of biological apodicticism. Symbolizing the appropriate notations for invariant relations and for biological extensions of relations is fundamental to the exact generating functions of discrete algebraic biology. Aspects of philosophical perspectives of the relation scientific number systems are contrasted. The deep distinction between physical motion and biological motion is expressed in terms the roles of Aristotelian causes. The interior motion within perplex numbers is contrasted with the exterior motion of physical systems. The need for a new mathematics for biology is suggested.     

A note on the information-theoretic basis of Fitts' law

Fitts' law is an information-theoretic view of human motor behavior developed from Shannon's Theorem, 17, a fundamental theorem of communications systems. Using data from Fitts' original experiments, we demonstrate that Fitts' choice of an equation that deviates slightly from the underlying principal is perhaps unfounded, and that the relationship is improved by using an exact adaptation of Shannon's equation.     

Relations between 18-month-olds’ gaze pattern and target action performance: A deferred imitation study with eye tracking

Deferred imitation studies are used to assess infants’ declarative memory performance. These studies have found that deferred imitation performance improves with age, which is usually attributed to advancing memory capabilities. Imitation studies, however, are also used to assess infants’ action understanding. In this second research program it has been observed that infants around the age of one year imitate selectively, i.e., they imitate certain kinds of target actions and omit others. In contrast to this, two-year-olds usually imitate the model's exact actions. 18-month-olds imitate more exactly than one-year-olds, but more selectively than two-year-olds, a fact which makes this age group especially interesting, since the processes underlying selective vs. exact imitation are largely debated. The question, for example, if selective attention to certain kinds of target actions accounts for preferential imitation of these actions in young infants is still open. Additionally, relations between memory capabilities and selective imitation processes, as well as their role in shaping 18-month-olds’ neither completely selective, nor completely exact imitation have not been thoroughly investigated yet. The present study, therefore, assessed 18-month-olds’ gaze toward two types of actions (functional vs. arbitrary target actions) and the model's face during target action demonstration, as well as infants’ deferred imitation performance. Although infants’ fixation times to functional target actions were not longer than to arbitrary target actions, they imitated the functional target actions more frequently than the arbitrary ones. This suggests that selective imitation does not rely on selective gaze toward functional target actions during the demonstration phase. In addition, a post hoc analysis of interindividual differences suggested that infants’ attention to the model's social-communicative cues might play an important role in exact imitation, meaning the imitation of both functional and arbitrary target actions.     

Feeling Our Way Forward: Continuity and Discontinuity Within the Cosmic Process

Though their philosophical systems differed in many respects, both Charles Sanders Peirce and Alfred North Whitehead were united in their opposition to what they saw as the materialistic presuppositions of modern science and both urged instead a new psycho-physical approach to reality with emphasis on subjectivity/contingency as well as objectivity/necessity within all natural processes. This article reviews both systems and indicates how, taken in conjunction rather than seen as rival cosmologies, they offer a strong argument for rethinking the way Nature works both within us and around us.     

On the representational systems underlying prospection: Evidence from the event-cueing paradigm

The ability to think about the future-prospection-is central to many aspects of human cognition and behavior, from planning and decision making, to self-control and the construction of a sense of identity. Yet, the exact nature of the representational systems underlying prospection is not fully understood. Recent findings point to the critical role of episodic memory in imagining specific future events, but it is unlikely that prospection depends solely on this system. Using an event-cueing paradigm in two studies, we here show that specific events that people imagine might happen in their personal future are commonly embedded in broader event sequences-termed event clusters-that link a set of envisioned events according to causal and thematic relations. These findings provide novel evidence that prospection relies on multiple representational systems, with general autobiographical knowledge structures providing a frame that organizes imagined events in overarching event sequences. The results further suggest that knowledge about personal goals plays an important role in structuring these event sequences, especially for the distant future.     

Time-of-day clocks and SKED: Techniques and applications

Modifications of SKED have been developed which incorporate a time-of-day clock into the basic SKED run-time systems. These clocks provide the experimenter with a means of recording the exact time of day at which events occur, as well as starting and stopping experiments and dumping data at specific times of the day. One type of clock is a hardware device that can be read to provide the number of minutes elapsed since midnight. A simple algorithm can be used to convert this value to hours and minutes. A second type of system maintains the current time by accumulating system clock ticks.     

Eleven-year career stability and change as reflected in Project Talent data through the Flanagan,Holland, and Roe occupational classification systems

The vocational psychologist seeks classifications of occupations which maximize career stability as occupations change from time to time in the life. This study investigates the extent of career stability and the patterns of career change which have occurred in the lives of Project TALENT twelfth grade students in the 11 yr elapsing since they were tested. “Career” plans in the last year of high school and at 1, 5, and 11 yr after testing were classified by the Flanagan, Holland, and Roe occupational classification systems in order to study the career stability and patterning within each system and to contrast both among systems. Career stability proved to be about the same in all three classification systems but decreased in all cases as the interval over which it was measured increased. Career stability increased as subjects grew older, proving to be the greatest from 5 to 11 yr after high school. Patterns of change mildly conformed to the circular patterns claimed by Holland and Roe for their systems and the linear pattern hypothesized for the Flanagan system. Generally, the direction of “career” flow was away from intellectual careers to careers in business and sales but each system had unique results as well.     

Majority influence,minority influence and conversion behavior: A replication

A recent experiment by Moscovici and Personnaz (Journal of Experimental Social Psychology 1980, 16, 270–282) showed that whereas a majority produces merely compliance, or a change in the individual's verbal responses, a minority induces conversion, or a true change in one's subjective judgments. Because of the theoretical significance of these findings and because of their inconsistency with data from other experiments, an exact replication and extension of this experiment was performed. There was no evidence of compliance in any social influence condition. Instead, and in contrast to Moscovici and Personnaz, both a majority and a minority produced “conversion” behavior. Subjects' behavior is interpreted as the expression of an improved perception, resulting from a heightened level of attention to the object of judgment under social influence conditions.     

Correcting errors in eye-position data arising from the distortion of magnetic fields by display devices

Eye-position recordings have been used to produce detailed information about sampling and search behavior. The melding of magnetic head-tracking technology with eye-tracking systems has allowed for freer head movement, but not without problems. Although the requisite calibrations made before and after a reading might indicate good eye-tracking accuracy, point-of-gaze errors can occur if the reader leans toward a display, such as a film alternator. The error results from the characteristic that large metal masses can distort magnetic fields, leading to false magnetic sensor data. Corrections for this type of error have involved mapping the exact location and orientation of the magnetic sensor in the magnetic field by using a precision positioning device. We have devised a much cheaper method that relies on a fixture that holds the magnetic sensor in identical positions, with and without the distorting effect.     

An Exactification of the Monoid of Primitive Recursive Functions

We study the monoid of primitive recursive functions and investigate a onestep construction of a kind of exact completion, which resembles that of the familiar category of modest sets, except that the partial equivalence relations which serve as objects are recursively enumerable. As usual, these constructions involve the splitting of symmetric idempotents.     

Numerical vs Cardinal Measurements in Multiattribute Decision Making: How Exact Is Enough?

Multiattribute decision making can involve consideration of both quantitative and qualitative measures of criteria attaintment. Some decision support systems (decision aids) to help multiattribute decision making quantify value functions. One of the most popular of these systems, multiattribute utility theory (MAUT), requires two types of input. Decision makers need to express the relative value of different attainment levels on each criterion, as well as express the relative importance of these criteria. Some systems (such as DECAID) require simple direct graphical input of value and criterion importance. Other systems (such as LOGICAL DECISION) use more complex means of expressing relative value. Either way, MAUT converts expressions of criterion importance into quantitative form. This study compares the relative stability of numerical results obtained through two decision support systems, DECAID and LOGICAL DECISION (LD), used in the task of evaluation of multiattribute alternatives. Additionally the relative stability of results was measured by comparison with results obtained using an ordinal method, ZAPROS. ZAPROS is a decision support system for construction of a partial order over the set of alternatives. It does not require conversion of qualitative measures into quantitative form. The relations among alternatives are close to those based on ordinal dominance. The results of experiments show that ordinal relationships between task parameters are much more stable than those obtained from quantitative measures. Results from DECAID and LD are much less coincident with each other than with results obtained through ZAPROS. Many inconsistencies were found in subject responses. It is concluded that more attention should be given to the means of testing judgment consistency, and that in some cases, attempts to solve decision tasks through more "exact" judgments of value function parameters may lead to erroneous results.     

The approximate number system and its relation to early math achievement: Evidence from the preschool years

Humans rely on two main systems of quantification; one is nonsymbolic and involves approximate number representations (known as the approximate number system or ANS), and the other is symbolic and allows for exact calculations of number. Despite the pervasiveness of the ANS across development, recent studies with adolescents and school-aged children point to individual differences in the precision of these representations that, importantly, have been shown to relate to symbolic math competence even after controlling for general aspects of intelligence. Such findings suggest that the ANS, which humans share with nonhuman animals, interfaces specifically with a uniquely human system of formal mathematics. Other findings, however, point to a less straightforward picture, leaving open questions about the nature and ontogenetic origins of the relation between these two systems. Testing children across the preschool period, we found that ANS precision correlated with early math achievement but, critically, that this relation was nonlinear. More specifically, the correlation between ANS precision and math competence was stronger for children with lower math scores than for children with higher math scores. Taken together, our findings suggest that early-developing connections between the ANS and mathematics may be fundamentally discontinuous. Possible mechanisms underlying such nonlinearity are discussed.     

Toward a theory of apractic syndromes

Theoretical development on human motor behavior has occurred largely independently of data on pathological movement disorders. This paper represents an initial attempt to interface findings from studies of apraxia and those of normal motor behavior with a view to formulating a common theoretical framework. Such an integration may ultimately aid in understanding the nature of skill acquisition and provide insights into the organization of motor systems. Three putative theoretical models of movement control are discussed with reference to apractic syndromes. The most commonly accepted view—the hierarchy—possesses properties such as linear transitivity and unidirectionality of information flow that render it inadequate in explaining functional plasticity in the central nervous system. The heterarchy, which incorporates reciprocity of function and circular transitivity, is a more likely candidate but suffers from an inability to regulate the degrees of freedom of the system. Our favored candidate is the coalition model which embodies heterarchical principles, but in addition, offers a solution to the problems of degrees of freedom and context for motor systems. Evidence is reviewed from apraxia of speech and limbs in terms of a coalitional style of control and an experimental approach, consonant with coalitional organization, is developed. We promote the claim that an understanding of apractic behavior—and perhaps motor systems in general—will benefit when clinicians and experimenters embrace a theory of context and constraints rather than a theory of commands as is currently in vogue.     

Multiple correlation: exact power and sample size calculations

This article discusses power and sample size calculations for observational studies in which the values of the independent variables cannot be fixed in advance but are themselves outcomes of the study. It reviews the mathematical framework applicable when a multivariate normal distribution can be assumed and describes a method for calculating exact power and sample sizes using a series expansion for the distribution of the multiple correlation coefficient. A table of exact sample sizes for level .05 tests is provided. Approximations to the exact power are discussed, most notably those of Cohen (1977). A rigorous justification of Cohen's approximations is given. Comparisons with exact answers show that the approximations are quite accurate in many situations of practical interest. More extensive tables and a computer program for exact calculations can be obtained from the authors.