Manifoldness Quotes
The ultimate "causes of price" - to use a Classical term - lie deeply embedded in the psychology and techniques of mankind and his environment, and are as manifold as the sands of the sea. All economic analysis is an attempt to classify these manifold causes, to sort them out into categories of discourse that our limited minds can handle, and so to perceive the unity of structural relationship which both unites and separates the manifoldness. Our concepts of "demand" and "supply" are such broad categories. In whatever sense they are used, they are not ultimate determinants of anything, but they are convenient channels through which we can classify and describe the effects of the multitude of determinants of the system of economic magnitude.
Kenneth Boulding
Definite portions of a manifoldness, distinguished by a mark or by a boundary, are called Quanta. Their comparison with regard to quantity is accomplished in the case of discrete magnitudes by counting, in the case of continuous magnitudes by measuring. Measure consists in the superposition of the magnitudes to be compared; it therefore requires a means of using one magnitude as the standard for another. In the absence of this, two magnitudes can only be compared when one is a part of the other; in which case also we can only determine the more or less and not the how much. The researches which can in this case be instituted about them form a general division of the science of magnitude in which magnitudes are regarded not as existing independently of position and not as expressible in terms of a unit, but as regions in a manifoldness.
Bernhard Riemann
With every simple act of thinking, something permanent, substantial, enters our soul. This substantial somewhat appears to us as a unit but (in so far as it is the expression of something extended in space and time) it seems to contain an inner manifoldness; I therefore name it "mind-mass."
Bernhard Riemann
Magnitude-notions are only possible where there is an antecedent general notion which admits of different specialisations. According as there exists among these specialisations a continuous path from one to another or not, they form a continuous or discrete manifoldness; the individual specialisations are called in the first case points, in the second case elements, of the manifoldness.
Bernhard Riemann
