On Topology IV (More on Topology)

"The young mathematical disciple 'topology' might be of some help in making psychology a real science." (Kurt Lewin, Principles of topological psychology, 1936)

"Topology provides the synergetic means of ascertaining the values of any system of experiences. Topology is the science of fundamental pattern and structural relationships of event constellations." (R Buckminster Fuller, "Operating Manual for Spaceship Earth", 1969)

"Topology is not ‘designed to guide us’ in structure. It is this structure." (Jacques Lacan, "L’Étourdit", 1972)

"No other theory known to science [other than superstring theory] uses such powerful mathematics at such a fundamental level. […] because any unified field theory first must absorb the Riemannian geometry of Einstein’s theory and the Lie groups coming from quantum field theory. […] The new mathematics, which is responsible for the merger of these two theories, is topology, and it is responsible for accomplishing the seemingly impossible task of abolishing the infinities of a quantum theory of gravity." (Michio Kaku, "Hyperspace", 1995)

"Topology makes it possible to explain the general structure of the set of solutions without even knowing their analytic expression." (Michael I. Monastyrsky, "Riemann, Topology, and Physics" 2nd Ed., 2008)

"At the basis of the distance concept lies, for example, the concept of convergent point sequence and their defined limits, and one can, by choosing these ideas as those fundamental to point set theory, eliminate the notions of distance." (Felix Hausdorff)

"In every subject one looks for the topological and algebraic structures involved, since these structures form a unifying core for the most varied branches of mathematics." (K Weise and H Noack, "Aspects of Topology")

"Mathematicians do not study objects, but relations between objects. Thus, they are free to replace some objects by others so long as the relations remain unchanged. Content to them is irrelevant: they are interested in form only." (Henri Poincaré)

"Poetry and code - and mathematics - make us read differently from other forms of writing. Written poetry makes the silent reader read three kinds of pattern at once; code moves the reader from a static to an active, interactive and looped domain; while algebraic topology allows us to read qualitative forms and their transformations." (Stephanie Strickland)

"Topology is the study of the modal relations of spatial figures and the laws of connectivity, mutual position, and ordering of points, lines, surfaces, and solids and their parts independently of measure and magnitude relations." (Johann B Listing)