Kenneth E. Iverson quote: “The utility of a language as a tool of thought increases with the range of topics it can treat, but decreases with the …”

“The properties of executability and universality associated with programming languages can be combined, in a single language, with the well-known properties of mathematical notation which make it such an effective tool of thought.”

Kenneth E. Iverson (1920–2004) Canadian computer scientist

§5
Notation as a Tool of Thought (1979)

“Although mathematical notation undoubtedly possesses parsing rules, they are rather loose, sometimes contradictory, and seldom clearly stated. […] The proliferation of programming languages shows no more uniformity than mathematics. Nevertheless, programming languages do bring a different perspective. […] Because of their application to a broad range of topics, their strict grammar, and their strict interpretation, programming languages can provide new insights into mathematical notation.”

Kenneth E. Iverson (1920–2004) Canadian computer scientist

Source: Math for the Layman (1999), Ch. 10, §D

“The structural properties of the language are many and complex, but at least they are finite and fairly easy to identify: there are only so many sounds, letters, and grammatical constructions, and although there is a huge vocabulary, at least the units are determinate and manageable.”

David Crystal (1941) British linguist and writer

Source: The Cambridge Encyclopedia of the English Language, 1987, p. 286

“Most programming languages are decidedly inferior to mathematical notation and are little used as tools of thought in ways that would be considered significant by, say, an applied mathematician.”

Kenneth E. Iverson (1920–2004) Canadian computer scientist

§0
Notation as a Tool of Thought (1979)

“One of the most important axioms is, that as the quantity of any commodity, for instance, plain food, which a man has to consume, increases, so the utility or benefit derived from the last portion used decreases in degree. The decrease in enjoyment between the beginning and the end of a meal may be taken as an example.”

William Stanley Jevons (1835–1882) English economist and logician

William Stanley Jevons Letter to his brother (1 June 1860), published in Letters and Journal of W. Stanley Jevons (1886), edited by Harriet A. Jevons, his wife, p. 151 - 152.

“In proportion therefore, as the repulsiveness of the work increases, the wage decreases.”

Karl Marx book The Communist Manifesto

Source: The Communist Manifesto

“One of the most important axioms is, that as the quantity of any commodity, for instance, plain food, which a man has to consume, increases, so the utility or benefit derived from the last portion used decreases in degree. The decrease in enjoyment between the beginning and the end of a meal may be taken as an example. And I assume that on an average, the ratio of utility is some continuous mathematical function of the quantity of commodity. This law of utility has, in fact, always been assumed by political economists under the more complex form and name of the Law of Supply and Demand. But once fairly stated in its simple form, it opens up the whole of the subject.”

William Stanley Jevons (1835–1882) English economist and logician

Letter to his brother (1 June 1860), published in Letters and Journal of W. Stanley Jevons (1886), edited by Harriet A. Jevons, his wife, p. 151. https://archive.org/details/cu31924074297254/page/n168/mode/1up

“The structural tools developed by the profession – hierarchical classifications, facets, thesaural relations, topic maps, the predicates used in ontology – will still be of use, provided that they can in each case pass a test of utility.”

Brian Campbell Vickery (1918–2009) British information theorist

Source: Meeting the challenge (2009), p. xxvii.

“If it is to be effective as a tool of thought, a notation must allow convenient expression not only of notions arising directly from a problem, but also of those arising in subsequent analysis, generalization, and specialization.”

Kenneth E. Iverson (1920–2004) Canadian computer scientist

§1.1
Notation as a Tool of Thought (1979)

“With the computer and programming languages, mathematics has newly-acquired tools, and its notation should be reviewed in the light of them. The computer may, in effect, be used as a patient, precise, and knowledgeable "native speaker" of mathematical notation.”

Kenneth E. Iverson (1920–2004) Canadian computer scientist

Source: Math for the Layman (1999), Ch. 10, §D

“The utility of a language as a tool of thought increases with the range of topics it can treat, but decreases with the amount of vocabulary and the complexity of grammatical rules which the user must keep in mind. Economy of notation is therefore important.”

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