“The concept of centroid as sum led me to examine Möbius' Barycentrische Calcul, a work of which until then I knew only the title; and I was not little pleased to find here the same concept of the summation of points to which I had been led in the course of the development. This was the first, and… the only point of contact which my new system of analysis had with the one that was already known.”

— Hermann Grassmann

Ausdehnungslehre (1844)

Adopted from Wikiquote. Last update Sept. 27, 2023. History

Help us to complete the source, original and additional information

Do you have more details about the quote "The concept of centroid as sum led me to examine Möbius' Barycentrische Calcul, a work of which until then I knew only …" by Hermann Grassmann?

Hermann Grassmann 10

German polymath, linguist and mathematician 1809–1877

Related quotes

“The concept of rotation led to geometrical exponential magnitudes, to the analysis of angles and of trigonometric functions, etc. I was delighted how thorough the analysis thus formed and extended, not only the often very complex and unsymmetric formulae which are fundamental in tidal theory, but also the technique of development parallels the concept.”

Hermann Grassmann (1809–1877) German polymath, linguist and mathematician

Ausdehnungslehre (1844)

“I am now profoundly convinced of what I had only hinted at before, namely, that the struggle between the advocates of a free society and the advocates of the socialist system is not a moral but an intellectual conflict. Thus socialists have been led by a very peculiar development to revive certain primitive instincts and feelings which in the course of hundreds of years had been practically suppressed by commercial or mercantile morals, which by the middle of the last century had come to govern the world economy.”

Friedrich Hayek (1899–1992) Austrian and British economist and Nobel Prize for Economics laureate

" The Moral Imperative of the Market https://mises.org/library/moral-imperative-market", in The Unfinished Agenda: Essays on the Political Economy of Government Policy in Honour of Arthur Seldon (1986)
1980s and later

“As I was reading the extract from your paper in the geometric sum and difference… I was struck by the marvelous similarity between your results and those discoveries which I made even as early as 1832…
I conceived the first idea of the geometric sum and difference of two or more lines and also of the geometric product of two or three lines in that year (1832). This idea is in all ways identical to that presented in your paper. But since I was for a long time occupied with entirely different pursuits, I could not develop this idea. It was only in 1839 that I was led back to that idea and pursued this geometrical analysis up to the point where it ought to be applicable to all mechanics. It was possible for me to apply this method of analysis to the theory of tides, and in this I was astounded by the simplicity of the calculations resulting from this method.”

Hermann Grassmann (1809–1877) German polymath, linguist and mathematician

Letter to Saint-Venant (1845) as quoted by Michael J. Crowe, A History of Vector Analysis: The Evolution of the Idea of a Vectorial System (1967)

“A work on tidal theory… led me to Lagrange's Mécanique analytique and thereby I returned to those ideas of analysis. All the developments in that work were transformed through the principles of the new analysis in such a simple way that the calculations often came out more than ten times shorter than in Lagrange's work.”

Hermann Grassmann (1809–1877) German polymath, linguist and mathematician

the "ideas of analysis" to which he returned, are those quoted above.
Ausdehnungslehre (1844)

“Theoretical psychology in its present state must try to develop a system of concepts which shows all the characteristics of a Gestalt, in which any part depends upon every other part. As we do not yet have the knowledge of facts which really suffices to determine this system of concepts and as, on the other hand, this knowledge of "facts" cannot be acquired without developing this system of concepts, there seems to be only one way open: to proceed slowly by tentative steps, to make decisions rather reluctantly, to keep in view always the whole field of psychology, and to stay in closest contact with the actual work of psychological research.”

Kurt Lewin (1890–1947) German-American psychologist

Source: 1930s, Principles of topological psychology, 1936, p. viii.

“I believe our only hope for the future is to adopt a new conception of human ecology, one in which we start to reconstitute our concept of the richness in human capacity.”

Ken Robinson (1950) UK writer

“I was a new person then, I knew things I had not known before, I knew things that you can know only if you have been through what I had just been through.”

Jamaica Kincaid (1949) Antiguan-American novelist, essayist, gardener, and gardening writer

Source: The Autobiography of My Mother

“During the 1950s and 1960s most of the work which was called cybernetics tended to focus on control systems in engineering or on applications of the concept of feedback in fields ranging from mathematics to sociology. At the 1970 meeting of the American Society for Cybernetics in Philadelphia Heinz von Foerster sought to redirect attention to the original interests which had led to the founding of the field of cybernetics. In a paper titled "Cybernetics of Cybernetics" he made a distinction between first order cybernetics, the cybernetics of observed systems, and second order cybernetics, the cybernetics of observing systems.”

Stuart A. Umpleby (1944) American scientist

Stuart A. Umpleby (1991) "Strategies for Winning Acceptance of Second Order Cybernetics." In George E. Lasker, et al. (eds.) Advances in Human Systems and Information Technologies. Windsor, Canada: International Institute for Advanced Studies in Systems Research and Cybernetics, 1992. pp. 97-196. (paper)

“Blessed be the hour in which I was first led to inquire into my own spiritual nature and destination! All my doubts are removed; I know what I can know, and have no fears for what I cannot know. I am satisfied; perfect clearness and harmony reign in my soul, and a new and more glorious existence begins for me. My entire destiny I cannot comprehend; what I am to become, exceeds my present power of conception. A part, which is concealed from me, is visible to the father of spirits. I know only that it is secure, everlasting and glorious. That part of it which is confided to me I know, for it is the root of all my other knowledge.”

Johann Gottlieb Fichte book The Vocation of Man

Jane Sinnett, trans 1846 p.120
The Vocation of Man (1800), Faith

“At fifteen years of age, when first my parents settled down in London (temporarily as they thought) I had never been in England, never had an English friend or English governess, or English tuition of any sort or kind. I did not speak one word of English. Then how did it all come about? Neo-Victorians and Neo-Georgians will put it down to destiny; others to predestination. I, in my humble way, put it down to the Will of God. And looking back on my long life and its many changes I can trace the links of my chain of life that began on the great plains of Hungary, continued through the heart of London, and find me now at this hour of writing this book in Monte Carlo jotting down all that I can remember of those links which led me one by one to the conception of my first literary work. If any one of those links had not been, if any turn of event in my life had been different, I would probably have ended my days in the country of my birth and known nothing of the happiness which comes from love, from the affection of friends (such as one meets in England) and from success in the work to which I devoted so many years of my life.”

Emma Orczy (1865–1947) Hungarian-British author of "The Scarlet Pimpernel"

Source: Links in the Chain of Life (1947), Ch. 1

Help us to complete the source, original and additional information

Hermann Grassmann 10

Related quotes

Related topics