“The results of a scrutiny of the materials of chemical science from a mathematical standpoint are pronounced in two directions. In the first we observe crude, qualitative notions”

— J. R. Partington

Introduction
Higher Mathematics for Chemical Students (1911)
Context: The results of a scrutiny of the materials of chemical science from a mathematical standpoint are pronounced in two directions. In the first we observe crude, qualitative notions, such as fire-stuff, or phlogiston, destroyed; and at the same time we perceive definite measurable quantities such as fixed air, or oxygen, taking their place. In the second direction we notice the establishment of generalizations, laws, or theories, in which a mass of quantitative data is reduced to order and made intelligible. Such are the law of conservation of matter, the laws of chemical combination, and the atomic theory.

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J. R. Partington38

British chemist 1886–1965

J. R. Partington (1886–1965) British chemist

Introduction
Higher Mathematics for Chemical Students (1911)

“[S]cience is often regarded as the most objective and truth-directed of human enterprises, and since direct observation is supposed to be the favored route to factuality, many people equate respectable science with visual scrutiny—just the facts ma'am, and palpably before my eyes. But science is a battery of observational and inferential methods, all directed to the testing of propositions that can, in principle, be definitely proven false. […] At all scales, from smallest to largest, quickest to slowest, many well-documented conclusions of science lie beyond the strictly limited domain of direct observation. No one has ever seen an electron or a black hole, the events of a picosecond or a geological eon.”

Stephen Jay Gould book Eight Little Piggies

"Muller Bros. Moving & Storage", pp. 200–201
Eight Little Piggies (1993)

“The earliest chemical theory was qualitative in the strictest sense”

J. R. Partington (1886–1965) British chemist

Introduction
Higher Mathematics for Chemical Students (1911)
Context: The earliest chemical theory was qualitative in the strictest sense; the so-called Aristotelean doctrine of the four elements assumed that air, water, earth, and fire, were qualities impressed on a primal matter; and the changes of material bodies were explained by the assumption that properties could be taken up by, and impressed upon, or removed from, the base-stuff. Transmutation as a possibility followed at once, and centuries of vain endeavour were required to impress the fact of its impossibility, leading to the true concept of element.

“As the prerogative of Natural Science is to cultivate a taste for observation, so that of Mathematics is, almost from the starting point, to stimulate the faculty of invention.”

James Joseph Sylvester (1814–1897) English mathematician

"A plea for the mathematician", Nature, Vol. 1, p. 261.

“Hitherto, the science of Man has been limited to researches… respecting some of its laws, to results deduced from single or insulated observations, and to theories often based on mere glimpses; and these constitute pretty nearly all the materials it possesses.”

Adolphe Quetelet (1796–1874) Belgian astronomer, mathematician, statistician and sociologist

Introductory
A Treatise on Man and the Development of His Faculties (1842)

“A physical theory, like an abstract science, consists of definitions and axioms as first principles, and of propositions, their consequences; but with these differences:—first, That in an abstract science, a definition assigns a name to a class of notions derived originally from observation, but not necessarily corresponding to any existing objects of real phenomena, and an axiom states a mutual relation amongst such notions, or the names denoting them; while in a physical science, a definition states properties common to a class of existing objects, or real phenomena, and a physical axiom states a general law as to the relations of phenomena; and, secondly,—That in an abstract science, the propositions first discovered are the most simple; whilst in a physical theory, the propositions first discovered are in general numerous and complex, being formal laws, the immediate results of observation and experiment, from which the definitions and axioms are subsequently arrived at by a process of reasoning differing from that whereby one proposition is deduced from another in an abstract science, partly in being more complex and difficult, and partly in being to a certain extent tentative, that is to say, involving the trial of conjectural principles, and their acceptance or rejection according as their consequences are found to agree or disagree with the formal laws deduced immediately from observation and experiment.”

William John Macquorn Rankine (1820–1872) civil engineer

Source: "Outlines of the Science of Energetics," (1855), p. 121; Second paragraph

“We took the elevator back down from the first observation level of the Eiffel Tower and started walking in he direction of the Taj Mahal”

D.J. MacHale The Soldiers of Halla

Source: The Soldiers of Halla

“Throughout the nineteenth century, apart from the division in theoretical sciences and arts, classifiers attempted to divide the sciences into two groups. Already they had before them the examples of Francis Bacon (speculative and descriptive) and Hobbes (quantitative and qualitative). For Coleridge, the sciences were either pure (Grammar, Logic, Rhetoric, Mathematics, Metaphysics) or mixed. Arthur Schopenhauer’s similar groups were called pure and empirical, Wilhelm Wundt in 1887 called them formal and empirical, Globot mathematical and theoretical, and the St. Louis Congress of Arts and Sciences (1904) normative and physical.”

Brian Campbell Vickery (1918–2009) British information theorist

Karl Pearson made similar division of the sciences into abstract and concrete
Source: Classification and indexing in science (1958), Other Chapters, p. 154.

“A student of history, who cares little for Greek or mathematics in particular, but who likes to watch how things grow, will be able to extract from these pages a notion of the whole history of mathematical science down to Newton's time…”

James Gow (scholar) (1854–1923) scholar

Preface
A Short History of Greek Mathematics (1884)

“Anything can become excusable when seen from the standpoint of the result”

Yukio Mishima book The Temple of the Golden Pavilion

Source: The Temple of the Golden Pavilion

“The results of a scrutiny of the materials of chemical science from a mathematical standpoint are pronounced in two directions. In the first we observe crude, qualitative notions”

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J. R. Partington38

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