Kenneth E. Iverson: Notation

Kenneth E. Iverson was Canadian computer scientist. Explore interesting quotes on notation.
Kenneth E. Iverson: 24 quotes0 likes

“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.”

Kenneth E. Iverson

§1.4
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

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

“I was appalled to find that the mathematical notation on which I had been raised failed to fill the needs of the courses I was assigned, and I began work on extensions to notation that might serve. In particular, I adopted the matrix algebra used in my thesis work, the systematic use of matrices and higher-dimensional arrays (almost) learned in a course in Tensor Analysis rashly taken in my third year at Queen’s, and (eventually) the notion of Operators in the sense introduced by Heaviside in his treatment of Maxwell’s equations.”

Kenneth E. Iverson

"Kenneth E. Iverson" http://keiapl.info/rhui/autobio.htm, autobiographical sketch from an unfinished work (ca. 2004), on his experience at Harvard with "a Masters program in Automatic Data Processing in 1955; in effect, the first computer science program."

“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

§5
Notation as a Tool of Thought (1979)

“The precision provided (or enforced) by programming languages and their execution can identify lacunas, ambiguities, and other areas of potential confusion in conventional [mathematical] notation.”

Kenneth E. Iverson

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

“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

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

“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

§0
Notation as a Tool of Thought (1979)

“The initial motive for developing APL was to provide a tool for writing and teaching. Although APL has been exploited mostly in commercial programming, I continue to believe that its most important use remains to be exploited: as a simple, precise, executable notation for the teaching of a wide range of subjects.”

Kenneth E. Iverson

"A Personal View of APL", IBM Systems Journal, 30 (4), 1991

“It is important to distinguish the difficulty of describing and learning a piece of notation from the difficulty of mastering its implications. […] Indeed, the very suggestiveness of a notation may make it seem harder to learn because of the many properties it suggests for exploration.”

Kenneth E. Iverson

§5.2
Notation as a Tool of Thought (1979)

“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

§1.1
Notation as a Tool of Thought (1979)