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Experimental identification of the organization of mental calculations of the person on the basis of algebras of different associativity

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The work continues research on the ability of a person to improve the productivity of information processing, using parallel work or improving the performance of analyzers. A person receives a series of tasks, the solution of which requires the processing of a certain amount of information. The time and the validity of the decision are recorded. The dependence of the average solution time on the amount of information in the problem is determined by correctly solved problems. In accordance with the proposed method, the problems contain calculations of expressions in two algebras, one of which is associative and the other is nonassociative. To facilitate the work of the subjects in the experiment were used figurative graphic images of elements of algebra. Non-associative calculations were implemented in the form of the game “rock-paper-scissors”. It was necessary to determine the winning symbol in the long line of these figures, considering that they appear sequentially from left to right and play with the previous winner symbol. Associative calculations were based on the recognition of drawings from a finite set of simple images. It was necessary to determine which figure from this set in the line is not enough, or to state that all the pictures are present. In each problem there was no more than one picture. Computation in associative algebra allows the parallel counting, and in the absence of associativity only sequential computations are possible. Therefore, the analysis of the time for solving a series of problems reveals a consistent uniform, sequential accelerated and parallel computing strategy. In the experiments it was found that all subjects used a uniform sequential strategy to solve non-associative problems. For the associative task, all subjects used parallel computing, and some have used parallel computing acceleration of the growth of complexity of the task. A small part of the subjects with a high complexity, judging by the evolution of the solution time, supplemented the parallel account with a sequential stage of calculations (possibly to control the solution). We develop a special method for assessing the rate of processing of input information by a person. It allowed us to estimate the level of parallelism of the calculation in the associative task. Parallelism of level from two to three was registered. The characteristic speed of information processing in the sequential case (about one and a half characters per second) is twice less than the typical speed of human image recognition. Apparently the difference in processing time actually spent on the calculation process. For an associative problem in the case of a minimum amount of information, the solution time is near to the non-associativity case or less than twice. This is probably due to the fact that for a small number of characters recognition almost exhausts the calculations for the used non-associative problem.

Keywords: parallel counting, engineering psychology, testing, algebra, associativity, recognition of visual images
Citation in English: Koganov A.V., Rakcheeva T.A., Prikhodko D.I. Experimental identification of the organization of mental calculations of the person on the basis of algebras of different associativity // Computer Research and Modeling, 2019, vol. 11, no. 2, pp. 311-327
Citation in English: Koganov A.V., Rakcheeva T.A., Prikhodko D.I. Experimental identification of the organization of mental calculations of the person on the basis of algebras of different associativity // Computer Research and Modeling, 2019, vol. 11, no. 2, pp. 311-327
DOI: 10.20537/2076-7633-2019-11-2-311-327
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International Interdisciplinary Conference "Mathematics. Computing. Education"