Hegel’s Exposition of Goethe’s Theory of Colour

Logic, mathematics, physics: from a loose thread to the close link: Or what gravity is for both logic and mathematics rather than only for physics

“…Then, the relevant analogue of the Fifth Postulate also being equivalent to its "flatness" (regardless of "concaveness") would state, that there exists only a single spherical symmetry able to transform a certain spherical manifold belonging to the light cone into another determined by any point of the light cone belonging to the transformed spherical manifold. The analogue of the Fifth Postulate relevant to Minkowski space can be visualized by concentric balls in Euclidean space and the statement that if a certain ball and a certain point not belonging to its surface are given in advance, there exists only a single ball concentric to the given one such that the given point belongs to Engelhardt 1993;Falkenburg 1993;Fleischhacker 1993;Garrison 1993;Gjertsen 1993;Gower 1993;Grattan-Guinness 1993;Ihmig 1993;Illetterati 1993;Kluit 1993;Melica 1993;Miller 1993;Morretto 1993;Petry 1993;Pozzo 1993;Priest 1993;Snelders 1993;Toth 1993a;Wahsnerin 1993;Wandschneider 1993;Wehrle 1993;Weinstock 1993;Wolf-Gazo 1993. One can further trace Lobachevsky's approach applied to Minkowski space by rejecting the afore-formulated analogue of the Fifth postulate similarly allowing for either no concentric symmetry to exist (accordingly, following rather Riemann), on the one hand, or more than one concentric symmetry to exist (thus following Lobachevsky and his hyperbolic counterpart of Euclidean geometry literally), on the other hand. Next, a parameter analogical to Riemann's space curvature can be introduced so that each "non-Minkowski" (i.e., replacing "non-Euclidean") geometry us featured unambiguously by a single real value of the parameter at issue.…”

Logic, mathematics, physics: from a loose thread to the close link: Or what gravity is for both logic and mathematics rather than only for physics

“…Then, the relevant analogue of the Fifth Postulate also being equivalent to its "flatness" (regardless of "concaveness") would state, that there exists only a single spherical symmetry able to transform a certain spherical manifold belonging to the light cone into another determined by any point of the light cone belonging to the transformed spherical manifold. The analogue of the Fifth Postulate relevant to Minkowski space can be visualized by concentric balls in Euclidean space and the statement that if a certain ball and a certain point not belonging to its surface are given in advance, there exists only a single ball concentric to the given one such that the given point belongs to Engelhardt 1993;Falkenburg 1993;Fleischhacker 1993;Garrison 1993;Gjertsen 1993;Gower 1993;Grattan-Guinness 1993;Ihmig 1993;Illetterati 1993;Kluit 1993;Melica 1993;Miller 1993;Morretto 1993;Petry 1993;Pozzo 1993;Priest 1993;Snelders 1993;Toth 1993a;Wahsnerin 1993;Wandschneider 1993;Wehrle 1993;Weinstock 1993;Wolf-Gazo 1993. One can further trace Lobachevsky's approach applied to Minkowski space by rejecting the afore-formulated analogue of the Fifth postulate similarly allowing for either no concentric symmetry to exist (accordingly, following rather Riemann), on the one hand, or more than one concentric symmetry to exist (thus following Lobachevsky and his hyperbolic counterpart of Euclidean geometry literally), on the other hand. Next, a parameter analogical to Riemann's space curvature can be introduced so that each "non-Minkowski" (i.e., replacing "non-Euclidean") geometry us featured unambiguously by a single real value of the parameter at issue.…”

Logic, mathematics, physics: from a loose thread to the close link. Or what gravity is for both logic and mathematics rather than only for physics

“…Then, the relevant analogue of the Fifth Postulate also being equivalent to its "flatness" (regardless of "concaveness") would state, that there exists only a single spherical symmetry able to transform a certain spherical manifold belonging to the light cone into another determined by any point of the light cone belonging to the transformed spherical manifold. The analogue of the Fifth Postulate relevant to Minkowski space can be visualized by concentric balls in 42 Hegel's dialectics though interpreted by himself as the natural ontology of the world and thus as natural philosophy (for which it has been often criticized for being scholastic, metaphysical and antiscientific) can be anyway rehabilitated partly in the present context as a continuation of Newton's implicit ontomathematics, however, realized as universal ontology in the talweg of the philosophical tradition; some papers which may be cited are: Borzeszkowski 1993; Buchdahl 1993;Burbidge 1993;Buttner 1993;Drees 1993;Engelhardt 1993;Falkenburg 1993;Fleischhacker 1993;Garrison 1993;Gjertsen 1993;Gower 1993;Grattan-Guinness 1993;Ihmig 1993;Illetterati 1993;Kluit 1993;Melica 1993;Miller 1993;Morretto 1993;Petry 1993;Pozzo 1993;Priest 1993;Snelders 1993;Toth 1993a;Wahsnerin 1993;Wandschneider 1993;Wehrle 1993;Weinstock 1993; Wolf-Gazo 1993.…”