"Riemann's third proposition that space is an "n-fold extended multiple" or a "multiply extended aggregate"... The term "Mannigfaltigkeit," as here employed, is a standing puzzle to the readers of Riemann's essay. ...Riemann adopted the term from Gauss, who was probably the originator of its employment for the designation of "space in general" (as distinguished from "flat space," in the metageometrical sense). Gauss, in turn, took the expression no doubt from Herbart... whose philosophy is to a great extent a sort of reproduction of the old Eleatic quandaries about "The One and the Many." Herbart, in fine, had obtained it from Kant, whose disciple he was, or believed himself to be, and whose phrase 'Mannigfaltigkeiten der Empfindung'is variously found... in... his followers. ...space is not a "multiple" or "aggregate" at all, but... its very essence is continuity. This... follows from its conceptual nature as well as from its relativity. ...space itself is not in any intelligible sense a quantity."
Quote Details
Added by wikiquote-import-bot
Unverified quote
0 likes
Original Language: English
Available Languages (1)
Sources
Imported from EN Wikiquote
https://en.wikiquote.org/wiki/Bernhard_Riemann
Revision History
No revisions have been submitted for this quote.
Categories
Bernhard Riemann
Georg Friedrich Bernhard Riemann (September 17, 1826 – July 20, 1866) was an influential German mathematician who made lasting and revolutionary contributions to analysis, number theory, and differential geometry.
69 quotes on TrueQuotesView all quotes by Bernhard Riemann →
Related Quotes
"As is known, scientific physics dates its existence from the discovery of the differential calculus. Only when it was…"
"Magnitude-notions are only possible where there is an antecedent general notion which admits of different specialisat…"
"Definite portions of a manifoldness, distinguished by a mark or by a boundary, are called Quanta. Their comparison wi…"
"If in the case of a notion whose specialisations form a continuous manifoldness, one passes from a certain specialisa…"
"Measure-relations can only be studied in abstract notions of quantity, and their dependence on one another can only b…"
"For Space, when the position of points is expressed by rectilinear co-ordinates, ds = \sqrt{ \sum (dx)^2 }; Space is …"
"Let us imagine that from any given point the system of shortest lines going out from it is constructed; the position …"
"With every simple act of thinking, something permanent, substantial, enters our soul. This substantial somewhat appea…"
"Mind-masses entering the soul appear to us as ideas, the quality of the latter depending on the inner state of the fo…"
"Nevertheless, it remains conceivable that the measure relations of space in the infinitely small are not in accordanc…"