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Autonomy of Geometry

100%

Baldwin J. T. , Mueller A.

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

2019

tom 11

5-24

In this paper we present three aspects of the autonomy of geometry. (1) An argument for the geometric as opposed to the ‘geometric algebraic’ interpretation of Euclid’s Books I and II; (2) Hilbert’s successful project to axiomatize Euclid’s geometry in a first order geometric language, notably eliminating the dependence on the Archimedean axiom; (3) the independent conception of multiplication from a geometric as opposed to an arithmetic viewpoint.

NEUROPSYCHOLOGY AND THE NEUROPHYSIOLOGY OF PERCEPTUAL MICROGENESIS

80%

Pąchalska M. , Góral-Pólrola J. , Mueller A. , Kropotov J. D.

Acta Neuropsychologica

2017

tom 15(4)

365-389

Perception is one of the psychological operations that can be analyzed from the point of view of microgenetic theory. Our study tests the basic premise of microgenesis theory – the existence of recurrent stages of visual information processing. The event related potentials in two variants of a cued GO/NOGO task (contrasting images of Animals and Plants in the first variant, and contrasting images of Angry and Happy faces in the second variant) were studied during the first 300 ms following stimulus presentation. The independent component analysis was applied to a large collection of ERPs. The functional independent components associated with visual category discrimination, comparison to working memory, action initiation and conflict detection were separated. Information processing in the ventral visual stream (the temporal independent components) occurs at two sequential stages with positive/negative fluctuations of the cortical potential as indexes of the stages. The first stage represents the comparison of the pure physical features of the visual input with the memory trace. The second stage represents the comparison of more sophisticated semantic/emotional features with the working memory. The two stages are the results of interplay between bottom-up and top-down projections in the visual ventral stream.