Seeing Matters: The Remarkable Relevance of the Object-Representation Relationship to Science … and to Society!

The basic relationship between consciously-experienced representations, and material objects they represent, is hotly debated in some circles. But is it practically important? To investigate this, I introduce new symbolic notation, capable of labelling object, brain-perception, and conscious representation. Simple physics-based reasoning argues against identity of object and representation (rejecting e.g., direct realism). Nevertheless, a pivotal concern of the direct-realism school remains: how do we have knowledge of the world, if it’s only experienced indirectly? I sketch an indirect-school response, and review recent theoretical results showing how it simply doesn’t work in the dynamically-conventional setting (which is the hallmark of modern mainstream science). After illustrating how dynamically-conventional dysfunctions affect the foundations of science itself, I point to an experimentally-based resolution of knowledge-problems (and of the direct/indirect debate itself). Because the foundational problems for science affect its standing in society (for example, in its conflict with postmodernist ‘post-Truth’), the object-representation debate does turn out to have a practical significance, far beyond its conventional, academic/abstract/technical, framing.

The history of the emergence of symbolic notation in mathematics in the 17th century and transformation of mathematical practice

The article analyzes the intellectual and cultural preconditions that made it possible to create symbolic notation in mathematics of the 17th century. It is shown that the reprints of Euclid’s Elements in the XVI century formed an intellectual and cultural background that allowed Viet and Stevens to transform the classical concept of arithmos into a symbolic concept of number, which made the creation of symbolic notation possible. It is argued that the development of symbolic notation is not a simple change in the way of notation, but significantly changed the mathematical practice, making it possible to introduce new objects and through symbolic transformations.

Do we have a sense for irrational numbers?

Number sense requires, at least, an ability to assess magnitude information represented by number symbols. Most educated adults are able to assess magnitude information of rational numbers fairly quickly, including whole numbers and fractions. It is to date unclear whether educated adults without training are able to assess magnitudes of irrational numbers, such as the cube root of 41. In a computerized experiment, we asked mathematically skilled adults to repeatedly choose the larger of two irrational numbers as quickly as possible. Participants were highly accurate on problems in which reasoning about the exact or approximate value of the irrational numbers’ whole number components (e.g., 3 and 41 in the cube root of 41) yielded the correct response. However, they performed at random chance level when these strategies were invalid and the problem required reasoning about the irrational number magnitudes as a whole. Response times suggested that participants hardly even tried to assess magnitudes of the irrational numbers as a whole, and if they did, were largely unsuccessful. We conclude that even mathematically skilled adults struggle with quickly assessing magnitudes of irrational numbers in their symbolic notation. Without practice, number sense seems to be restricted to rational numbers.

Methods of Assessing the Available Level of Symbolization in Communication in Children with Hearing and Sight and Multiple Disabilities

In this article, we describe a possible way of assessing the level of the means of communication in children with impaired sight and hearing in the structure of multiple developmental disorders. The method is designed for examination of children with complex and multiple disabilities. It is advisable to use a methodology for assessing the level of language development in children who do not enjoy the expanded verbal or sign language, especially in cases where the surrounding is difficult to assess what treatment and the extent to which the child understands. The proposed character level evaluation procedure, the child can understand, can be used for initial diagnosis, as well as for the dynamic tracking of language development in the learning process. This version of the method may be used with children who have a substantive vision. Addressing age: school-aged children. Stimulus material technique selected on the basis of the model of symbolic stairs (M. Skelly), according to which the first level of symbolization is the real object (the demonstration of an object becomes a permanent sign of the beginning of the corresponding event, such as a cap – a symbol of a walk), and the highest level of symbolization becomes concept language word. It includes 15 real objects, 5 items of clothing, 5 pieces of dishes and 5 educational supplies, pictures of these objects, realistic color images, as well as the outline of the image. In addition, the plates are attached to the printed names of the same things and pictures on their sign symbols. The procedure of conducting the survey and recording results are discribed. Evaluation protocol allows you to determine what level of symbolic notation of items most successful child acts and what is the maximum level of symbolization it is available. Examples of description and analysis of the results are presented.