Abstract not found

A series of arguments is presented showing that words are not stored in memory in a way that resembles the abstract, phonological code used by alphabetical orthographies or by linguistic analysis. Words are stored in a very concrete, detailed auditory code that includes nonlinguistic information including speaker’s voice properties and other details. Thus, memory for language resembles an exemplar memory and abstract descriptions (using letter-like units and speaker-invariant features) are probably computed on the fly whenever needed. One consequence of this hypothesis is that the study of phonology should be the study of generalizations across the speech of a community and that such a description will employ units (segments, syllable types, prosodic patterns, etc.) that are not necessarily employed as units in speakers’ memory for language. That is, the psychological units of language are not useful for description of linguistic generalizations and linguistic generalizations across a community are not useful for storing the language for speaker use.

Pythagorean numbers Let Pythagorean number be triple, with first two elements as projections and third as arrow of where is called projection of distinction and projection of hologram. Pythagorean numbers should be used both as cognitive and mathematical term, but, of course, in different outline. For Pythagorean number in mathematical outline we may always attribute as its meaning cognitive Pythagorean number, either in trivial sense or as physical interpretation or maybe in some other sense. Taking Pythagorean number in cognitive sense we of course maybe loose possibility to find directly corresponding mathematical pair, but we may assume always its existence as we will soon see. Main element that makes Pythagorean number be Pythagorean number is its arrow: If there exists transform then this transform defines pair as Pythagorean number. Pythagorean number, Arrow of thinking or arrow of cogito. For a Pythagorean number being triple, arrow, if we use Pythagorean number in cognitive sense, we call arrow of thinking or arrow of cogito. We suggest for thinking simple

We argue that computation via quantum mechanical processes is irrelevant to explaining how brains produce thought, contrary to the ongoing speculations of many theorists. First, quantum effects do not have the temporal properties required for neural information processing. Second, there are substantial physical obstacles to any organic instantiation of quantum computation. Third, there is no psychological evidence that such mental phenomena as consciousness and mathematical thinking require explanation via quantum theory. We conclude that understanding brain function is unlikely to require quantum computation or similar mechanisms.

Four levels of complexity in mathematics and physics are considered, how they are interrelated, how this all has impact on other subjects of epistemology.

Recent advances in robotics leads us to consider, on the one hand, the notion of a kernel, a set of stable algorithms that drive developmental dynamics and, on the other hand, variable body envelopes that change over time. This division reverses the classic notion of a fixed body on which different software can be applied to consider a fixed software that can be applied to different kinds of embodiment. Thus, it becomes possible to study how a particular embodiment shapes developmental trajectories in specific ways. It also leads us to a novel view of the development of skills, from sensorimotor dexterity to abstract thought, based on the notion of a fluid body in continuous redefinition. 1

We forward hypothesis that all what we refer to as mathematics are cognitive aspects of life, moreover, we have right to refer to mathematics as reference system of life. Mathematics and cognition are not distinguishable between themselves because what we call mathematics refer to the functionality by means of what (or via what) we are created by nature, or by God, be it question of our religious persuasion. Thus, according to this hypothesis, mathematics turns out to be considrable more as primary in many points as before, when we attributed to mathematics role of sort of descriptor of nature. When we are going to say that mathematics is reference system of life, we mean that today's mathematics is only some starting state of what might be referred to as mathematics as subject / object of reality.

In his excellent book (Smolin, 2006) Lee Smolin speaks about crisis in physics, blaming mainly string theory. We argue that modern physics should change its attitude towards what is called observer, but should be called cognitive machine or rather two distinctively different, inner and outer, cognitive machines.

Two parallel strands in mathematics-education research—one that delineates students ’ embodied schemas supporting their mathematical cognition and the other that focuses on the mediation of cultural knowledge through mathematical tools—could converge through examining reciprocities between schemas and tools. Using a gesture-based methodology that attends to students ’ hand movements as they communicate their understanding, data examples from design research in two domains illustrate students ’ spontaneous spatial articulation of embodied cognition. Such embodied spatial articulation could be essential for deep understanding of content, because in performing these articulations, students may be negotiating between their dynamic image-based intuitive understanding of a concept and the static formal mathematical formats of representing the concept. Implications for mathematics education are drawn. The growing body of literature on ‘situated cognition ’ and ‘cognition in context ’ (e.g., Lave & Wenger, 1991; Hutchins & Palen, 1998) is informing research in mathematics education. In particular, we are challenged to think of mathematical cognition not as “abstract ” in-the-head processes devoid of concrete grounding, but as phenomenologically, intrinsically, and necessarily dwelling in student interactions with objects in their environment (Heidegger, 1962;

In this article I argue that modern Neoplatonism can contribute to a revitalization of science and an improved human relationship to nature. I begin by considering the role of Neoplatonism in the history of science, considering both ideas that have contributed to the constitution