The ‘Chemistry of Space’: The Sources of Hermann Grassmann's Scientific Achievements

Albert Lewis's article (Annals of Science, 1977) analysing the influence of Friedrich Schleiermacher on Hermann Grassmann, stimulated many different studies on the founder of n-dimensional outer algebra.

Following a brief outline of the various, sometimes diverging, analyses of Grassmann's creative thinking, new research is presented which confirms Lewis's original contribution and widens it considerably. It will be shown that:

i.?Grassmann, although a self-taught mathematician, was at the centre of a hitherto understated intellectual trend, which was defining for Germany. Initiated by Pestalozzi's concept of elementary mathematical education and culminating in the modern mathematics of the late 19th Century, it was reflected in the contributions of Grassmann, Riemann, Jacobi and Eisenstein.

ii.?Hermann Grassmann, his father Justus, and his brother Robert were all demonstrably influenced by Schleiermacher's dialectic; however the two brothers responded to it in very different ways.

iii.?Whilst the more philosophical parts of Hermann's 1844 Extension Theory are characterised by the influence of Schleiermacher and also by the mathematical knowledge of his father, the entire development of this work is the unfolding of a single idea based on the father's interpretation of combinatorial multiplication as a ‘chemical conjunction‘, which was developed largely dialectically by Hermann.     

Zur Frage der Markierung einzelner Nervenzellen durch Mikroelektroden

Summary A method of electrophoretical marking of individual neurons with methylene blue by means of a glass micropipette (used in electrophysiology) is described. In combination with a new histological crushing technique, cytochemical analysis of whole undamaged cells thus marked can be correlated with electrophysiological findings in the same neuron.     

Synthesis of Heterocyclic Ring Systems Using Organometallic Reagents

We developed novel synthetic routes to heterocyclic ring systems by using transition metal-mediated or -catalyzed reactions. A Lewis acid-promoted addition of the propargyl Grignard reagent 2 to the Schiff base 1 followed by a silvermediated oxidative cyclization of the homopropargylamine 3 provided the aryl-substituted pyrrole 4. Combined with a cherroseleetive hydrogenation of the pyrrole ring, this rnethod has been applied to the total synthesis of the biologically active fused indolizidine alkaloids （ ± ）-harmicine and （ ± ）-crispine A. See Fig. 1.     

Kreisende kortikale Potentialfelder beim epileptischen Anfall

Summary The circular movement of cortical potential fields during epileptic seizures of the rabbit, evoked by intracortical application of penicillin, is described.     

Generation of pluripotent stem cells from adult human testis

Human primordial germ cells and mouse neonatal and adult germline stem cells are pluripotent and show similar properties to embryonic stem cells. Here we report the successful establishment of human adult germline stem cells derived from spermatogonial cells of adult human testis. Cellular and molecular characterization of these cells revealed many similarities to human embryonic stem cells, and the germline stem cells produced teratomas after transplantation into immunodeficient mice. The human adult germline stem cells differentiated into various types of somatic cells of all three germ layers when grown under conditions used to induce the differentiation of human embryonic stem cells. We conclude that the generation of human adult germline stem cells from testicular biopsies may provide simple and non-controversial access to individual cell-based therapy without the ethical and immunological problems associated with human embryonic stem cells.