Bertrand Russell quote: “The rules of logic are to mathematics what those of structure are to architecture.”

“(Game theory is) essentially a structural theory. It uncovers the logical structure of a great variety of conflict situations and describes this structure in mathematical terms. Sometimes the logical structure of a conflict situation admits rational decisions; sometimes it does not.”

Anatol Rapoport (1911–2007) Russian-born American mathematical psychologist

Source: 1960s, Prisoner's dilemma: A study in conflict and cooperation (1965), p. 196

“I lose faith in mathematics, logical and rigid. What with those that even zero doesn’t accept?”

Dejan Stojanovic (1959) poet, writer, and businessman

"I and I," p. 30
The Shape (2000), Sequence: “Happiness of Atoms”

“The presence of an enterprise reference architecture aids an enterprise in its ability to understand its structure and processes. Similar to a computer architecture, the enterprise architecture is comprised of several views. The enterprise architecture should provide activity, organizational, business rule (information), resource, and process views of an organization.”

Donald H. Liles (1947) American engineer

Joseph Sarkis, Adrien Presley and Donald H. Liles (1995) "The management of technology within an enterprise engineering framework." in: Computers & industrial engineering.

“The bottom line for mathematicians is that the architecture has to be right. In all the mathematics that I did, the essential point was to find the right architecture. It's like building a bridge. Once the main lines of the structure are right, then the details miraculously fit. The problem is the overall design.”

Freeman Dyson (1923) theoretical physicist and mathematician

"Freeman Dyson: Mathematician, Physicist, and Writer". Interview with Donald J. Albers, The College Mathematics Journal, vol 25, no. 1, (January 1994)

“The term architecture is used here to describe the attributes of a system as seen by the programmer, i. e., the conceptual structure and functional behavior, as distinct from the organization of the data flow and controls, the logical design, and the physical implementation. i. Additional details concerning the architecture”

Gene Amdahl (1922–2015) American physicist

Gene Amdahl, Gerrit Blaauw, and Fred Brooks (1964) " Architecture of the IBM System http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.72.7974&rep=rep1&type=pdf." in: IBM Journal of Research and Development Vol 8 (2) p. 87-101

“The term architecture is used here to describe the attributes of a system as seen by the programmer, i. e., the conceptual structure and functional behavior, as distinct from the organization of the data flow and controls, the logical design, and the physical implementation. i. Additional details concerning the architecture”

Fred Brooks (1931) American computer scientist

Gene Amdahl, Gerrit Blaauw, and Fred Brooks (1964) "Architecture of the IBM System." in: IBM Journal of Research and Development Vol 8 (2) p. 87-101.

“So much of modern mathematical work is obviously on the border-line of logic, so much of modern logic is symbolic and formal, that the very close relationship of logic and mathematics has become obvious to every instructed student. The proof of their identity is, of course, a matter of detail: starting with premisses which would be universally admitted to belong to logic, and arriving by deduction at results which as obviously belong to mathematics, we find that there is no point at which a sharp line can be drawn, with logic to the left and mathematics to the right. If there are still those who do not admit the identity of logic and mathematics, we may challenge them to indicate at what point, in the successive definitions and deductions of Principia Mathematica, they consider that logic ends and mathematics begins. It will then be obvious that any answer must be quite arbitrary.”

Bertrand Russell (1872–1970) logician, one of the first analytic philosophers and political activist

Source: 1910s, Introduction to Mathematical Philosophy (1919), Ch. 18: Mathematics and Logic

“There is a logic of language and a logic of mathematics.”

Thomas Merton (1915–1968) Priest and author

The Secular Journal of Thomas Merton (1959)
Context: There is a logic of language and a logic of mathematics. The former is supple and lifelike, it follows our experience. The latter is abstract and rigid, more ideal. The latter is perfectly necessary, perfectly reliable: the former is only sometimes reliable and hardly ever systematic. But the logic of mathematics achieves necessity at the expense of living truth, it is less real than the other, although more certain. It achieves certainty by a flight from the concrete into abstraction. Doubtless, to an idealist, this would seem to be a more perfect reality. I am not an idealist. The logic of the poet — that is, the logic of language or the experience itself — develops the way a living organism grows: it spreads out towards what it loves, and is heliotropic, like a plant.

“I became aware that in Hank's recorded songs were the archetype rules of poetic songwriting. The architectural forms are like marble pillars and they had to be there. Even his words - all of the syllables are divided up so they make perfect mathematical sense. You can learn a lot about the structure of songwriting by listening to his records.”

Hank Williams (1923–1953) American country music singer

Bob Dylan, Chronicles: Volume One (2004)
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“Many formal organizational structures arise as reflections of rationalized institutional rules. The elaboration of such rules in modern states and societies accounts in part for the expansion and increased complexity of formal organizational structures. Institutional rules function as myths which organizations incorporate, gaining legitimacy, resources, stability, and enhanced survival prospects. Organizations whose structures become isomorphic with the myths of the institutional environment-in contrast with those primarily structured by the demands of technical production and exchange-decrease internal coordination and control in order to maintain legitimacy. Structures are decoupled from each other and from ongoing activities. In place of coordination, inspection, and evaluation, a logic of confidence and good faith is employed.”

John W. Meyer (1935) Sociologist and professor at Stanford University

Meyer, John W., and Brian Rowan. " Institutionalized organizations: Formal structure as myth and ceremony http://www.sasse.se/akademiska/310/meyer%20rowan.pdf." American journal of sociology (1977): 340-363.

“The rules of logic are to mathematics what those of structure are to architecture.”

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