Gustav Theodor Fechner

Recently, in examining Bernard Riemann's influences from his philosophical fragments, I came upon the work of Fechner. Today, Fechner is almost exclusively remembered as the father of the field of "psychophysics." In particular, his logarithmic function for the threshold of conscious perceptions. However, Riemann was very much captivated by Fechner's writing on Zend Avesta. It is quite remarkable that Riemann's work on sonic shockwave propagation predated the actual demonstration of the said phenomena by some decades. The reason for this is, I believe that the principle involved actually transcends the narrow application that Riemann gave it in that instance, i.e. of pressure and the speed of sound . That is that given a wave being propagated beyond the speed at which the medium is capable of accepting a shockwave aggregates perforce. As this continues over time the shockwave can be thought of as a negatively curved horn surface. This idea immediately links to Riemann's habilitation thesis wherein he details the non Euclidian geometries as the basis of choice for metric for physical space. It is the moving over from positively curved propagation to a negatively curved time series that is there in germ form in that thesis of Riemann. And I believe that likewise Fechner in the Zend Avesta evinces the germ of autowave phenomenology when he states (in English translation from the German): "Our future spheres of existence, though all incorporated in the same great body, the earth, will not disturb, confuse or efface each other. Even here our spheres of existence necessarily cross and intersect each other, as the means of mutual intercourse, which in the here after will only increase in intimacy, variety and consciousness; and in our brain the material changes connected with our reminiscences cross and intersect each other, leaving them nevertheless undisturbed and uneffaced." (my emphasis added) I believe that this is a remarkable instance of how a method for viewing interconnectedness of physical and psychological phenomena leads to a correct hypothesis of neurological characteristics before any experimental apparatus is available.