“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

On the Hypotheses which lie at the Bases of Geometry (1873)

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Bernhard Riemann 43

German mathematician 1826–1866

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“If in the case of a notion whose specialisations form a continuous manifoldness, one passes from a certain specialisation in a definite way to another, the specialisations passed over form a simply extended manifoldness, whose true character is that in it a continuous progress from a point is possible only on two sides, forwards or backwards. If one now supposes that this manifoldness in its turn passes over into another entirely different, and again in a definite way, namely so that each point passes over into a definite point of the other, then all the specialisations so obtained form a doubly extended manifoldness. In a similar manner one obtains a triply extended manifoldness, if one imagines a doubly extended one passing over in a definite way to another entirely different; and it is easy to see how this construction may be continued. If one regards the variable object instead of the determinable notion of it, this construction may be described as a composition of a variability of n + 1 dimensions out of a variability of n dimensions and a variability of one dimension.”

Bernhard Riemann (1826–1866) German mathematician

On the Hypotheses which lie at the Bases of Geometry (1873)

“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 (1826–1866) German mathematician

On the Hypotheses which lie at the Bases of Geometry (1873)

“For Space, when the position of points is expressed by rectilinear co-ordinates, ds = \sqrt{ \sum (dx)^2 }; Space is therefore included in this simplest case. The next case in simplicity includes those manifoldnesses in which the line-element may be expressed as the fourth root of a quartic differential expression…. I restrict myself… to those manifoldnesses in which the line element is expressed as the square root of a quadric differential expression…. Manifoldnesses in which, as in the Plane and in Space, the line-element may be reduced to the form \sqrt{ \sum (dx)^2 }, are… only a particular case of the manifoldnesses to be here investigated; they require a special name, and therefore these manifoldnesses… I will call flat. In order now to review the true varieties of all the continua which may be represented in the assumed form, it is necessary to get rid of difficulties arising from the mode of representation, which is accomplished by choosing the variables in accordance with a certain principle.”

Bernhard Riemann (1826–1866) German mathematician

On the Hypotheses which lie at the Bases of Geometry (1873)

“Cartan developed a general scheme of infinitesimal geometry in which Klein's notions were applied to the tangent plane and not to the n-dimensional manifold M itself.”

Hermann Weyl (1885–1955) German mathematician

On the foundations of general infinitesimal geometry. Bull. Amer. Math. Soc. 35 (1929) 716–725 [10.1090/S0002-9904-1929-04812-2] (quote on p. 716)

“From the perspective of Buddhism, Sartre’s notion of Existence, according to which one must create oneself continually in order to maintain oneself within nothing, remains a standpoint of attachment to the self – indeed, the most profound form of this attachment – and as such is caught in the self-contradiction this implies.”

Keiji Nishitani (1900–1990) Japanese philosopher

Source: The Self-Overcoming of Nihilism (1990), p. 187

“A philosophy which emphasises the idea of the One, is generally a dualistic philosophy in which the conception of Second receives exaggerated attention: for this One (though of course involving the idea of First) is always the other of a manifold which is not one.”

Charles Sanders Peirce (1839–1914) American philosopher, logician, mathematician, and scientist

The Architecture of Theories (1891)
Context: The origin of things, considered not as leading to anything, but in itself, contains the idea of First, the end of things that of Second, the process mediating between them that of Third. A philosophy which emphasises the idea of the One, is generally a dualistic philosophy in which the conception of Second receives exaggerated attention: for this One (though of course involving the idea of First) is always the other of a manifold which is not one. The idea of the Many, because variety is arbitrariness and arbitrariness is repudiation of any Secondness, has for its principal component the conception of First. In psychology Feeling is First, Sense of reaction Second, General conception Third, or mediation. In biology, the idea of arbitrary sporting is First, heredity is Second, the process whereby the accidental characters become fixed is Third. Chance is First, Law is Second, the tendency to take habits is Third. Mind is First, Matter is Second, Evolution is Third.

“The concept of management as a specific body of knowledge and practice forming the basis of a specialised profession … Wherever human activities are carried out in an organised and co-operative form, there management must be found.”

Lyndall Urwick (1891–1983) British management consultant

Vol II, p. 216.
1940s, The Making Of Scientific Management, 1945

“In Marx the dialectical method aims at understanding society as a whole. Bourgeois thought concerns itself with objects that arise either from the process of studying phenomena in isolation, or from the division of labor and specialisation in the different disciplines.”

György Lukács book History and Class Consciousness

Source: History and Class Consciousness (1968), p. 28

“Whatever is formed of matter receives the most perfect form possible in that species of matter; in each individual case the defects are in accordance with that individual matter.”

Maimónides book The Guide for the Perplexed

Compare Gottfried Leibniz argument for the "best of all possible worlds" in his Essays on the Goodness of God, the Freedom of Man and the Origin of Evil
Ch.12
Guide for the Perplexed (c. 1190), Part III
Context: Galen, in the third section of his book, "The Use of the Limbs," says correctly that it would be in vain to expect to see living beings formed of the blood of menstruous women and the semen virile, who will not die, will never feel pain, or will move perpetually, or shine like the sun. This dictum of Galen is part of the following more general proposition:—Whatever is formed of matter receives the most perfect form possible in that species of matter; in each individual case the defects are in accordance with that individual matter.

“Several actual worlds without one another are not, therefore, impossible by the very concept, as Wolf hastily concluded from the notion of a complex or multiplicity which he deemed sufficient to a whole, as such, but only on condition that there exist but one necessary cause of all things. If several are admitted, several worlds without one another will be possible in the strictest metaphysical sense.”

Immanuel Kant (1724–1804) German philosopher

Kant's Inaugural Dissertation (1770), Section IV On The Principle Of The Form Of The Intelligible World

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Bernhard Riemann 43

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