A specific calculating ability

We report two experiments that investigate the calculating strategy used by a low IQ savant to identify prime numbers. Hermelin and O'Connor (1990) had suggested previously that this subject may use a procedure first described by Eratosthenes to detect a prime number, namely, dividing a target number by all primes up to the square root of the target number and testing for a remainder. In the first experiment, we compare the reaction times of the savant to decide whether a number is prime with those of a control subject proficient in mathematical calculation. In addition, we measured the savant's speed of information processing using an inspection time task. We found that the reaction times of the savant, although generally faster, followed the same pattern of the control subject who reported using the Eratosthenes procedure. The savant's inspection time indicated that his speed of processing was far superior to that expected from someone of his IQ. In the second experiment, we measured the time it takes mathematics students to divide by different prime numbers and we also tested them on the prime identification task. We used their division times to simulate their performance on the prime number identification task under the assumption that they used the Eratosthenes procedure. We also simulated the reaction times that would result from a simple memory-based procedure for identifying primes. We found that the Eratosthenes simulation, in contrast to the memory simulation, provided a good fit to both the students' and the savant's reaction times. We conclude that the savant is using a complex computational algorithm to identify primes and suggest two explanations of how the apparent contradiction between his low general intelligence and his superior numerical ability might be resolved.     

Analyzing human random generation behavior: A review of methods used and a computer program for describing performance

In this paper, we consider the different methods that have been developed to quantify random generation behavior and incorporate these measurement scales into a Windows95 computer program called RgCalc. RgCalc analyzes the quality of human attempts at random generation and can provide computer-generated, pseudorandom sequences for comparison. The program is designed to be appropriate for the analysis of various types of random generation situations employed in the psychological literature. The different algorithms for the evaluation of a dataset are detailed and an outline of the program is described. Performance measures are available for assessing various aspects of the response distribution, the sequencing of pairs, the ordinal relationships between sets of items, and the tendency to repeat alternatives over different lengths. A factor analysis is used to illustrate the multiple dimensions underlying human randomization processes.     

The mean-integral representation of rectangles

To assess perceptual interaction between the height and width of rectangles, we used an accuracy variant of the Garner paradigm. We measured the discriminability of height and width (baseline tasks) and size and shape (correlated tasks). From thed′ values in these conditions, we estimated perceptual distances and inferred amean-integral representation in which height and width corresponded to nonindependent dimensions in a perceptual space. This model accounted well for performance in these two-stimulus conditions, and it also explained 70% –80% of the decline in performance in selective and divided attention. In a second experiment, conducted for purposes of comparison with the rectangle discrimination Experiment, we studied the discrimination of horizontal and vertical line segments connected in an L-shape. In size discrimination, observers were equally good with line pairs and rectangles, suggesting holistic perception; but in shape discrimination, they appeared to combine information from the two line-pair components of the rectangle independently. The mean-integral model was again successful in relating performance in the Garner tasks quantitatively.     

Classical conditioning of the nictitating membrane response of the lemon shark (Negaprion brevirostris)

An experimental group of lemon sharks received 100 daily presentations of light flash as the conditioned stimulus (CS) and electric shock as the unconditioned stimulus (US) in a classical conditioning situation. The conditioned responses (CRs) and unconditioned responses (URs) under observation consisted of extensions of the nictitating membrane. Separate control groups received either (a) no CS or US, (b) CS-alone, or (c) completely random presentations of CS and US. Few CRs occurred in the experimental group at the outset of conditioning, but the percentage of CRs during the second half of the first acquisition session exceeded 95%. Conditioning stabilized above 95% CRs during Acquisition Sessions 3 through 7. These responses could not be attributed to pseudoconditioning, sensitization, or other nonassociative factors. When the experimental group was subsequently given six CS-alone sessions, the course of extinction was gradual. Most results seemed similar to those previously obtained during classical conditioning of the nictitating membrane in rabbits.     

Detection and recognition of intensity changes in tone and noise: The detection-recognition disparity

Recognition of increments vs decrements in auditory intensity improves with signal duration, relative to detection of increments and decrements. This effect obtains whether the background stimulus is a tone, noise, or a tone with noise masker, and is largely uninfluenced by the rise time of the signals. These data are inconsistent with detection models in which the O makes only one sensory observation during each observation interval, but can be described in terms of a neural timing model in which transients play a critical role.