This volume covers many diverse topics related in varying degrees to
mathematics in mind including the mathematical and topological
structures of thought and communication. It examines mathematics in mind
from the perspective of the spiral, cyclic and hyperlinked structures of
the human mind in terms of its language, its thoughts and its various
modes of communication in science, philosophy, literature and the arts
including a chapter devoted to the spiral structure of the thought of
Marshall McLuhan. In it, the authors examine the topological structures
of hypertext, hyperlinking, and hypermedia made possible by the Internet
and the hyperlinked structures that existed before its emergence. It
also explores the cognitive origins of mathematical thinking of the
human mind and its relation to the emergence of spoken language, and
studies the emergence of mathematical notation and its impact on
education.
Topics addressed include:
- The historical context of any topic that involves how mathematical
thinking emerged, focusing on archaeological and philological evidence.
- Connection between math cognition and symbolism, annotation and other
semiotic processes.
- Interrelationships between mathematical discovery and cultural
processes, including technological systems that guide the thrust of
cognitive and social evolution.
- Whether mathematics is an innate faculty or forged in
cultural-historical context
- What, if any, structures are shared between mathematics and
language
