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Automatic Mathematician

  • 1 Heuristics

       [A]t one point AM [Automatic Mathematician] had some notions of sets, set-operations, numbers, and simple arithmetic. One heuristic rule it knew said " If F is an interesting relation, then look at its inverse". This rule fired after AM had studied "multiplication" for a while. The r.h.s. of the rule then directed AM to define and study the relation "divisors-of" (e.g. divisors-of (12) {1,2,3,4,6,12}. Another heuristic rule that later fired said " If f is a relation from A into B, then it's worth examining those members of A which map into extremal members of B." In this case, f was matched to "divisors-of", A was "numbers", B was "sets of numbers", and an extremal member of B might be, e.g., a very small set of numbers. Thus this heuristic rule caused AM to define the set of numbers with no divisors, the set of numbers with only 1 divisor, with only 2 divisors, etc. One of these sets (the last [ sic] mentioned) turned out subsequently to be quite important; these numbers are of course the primes. (Lenat & Harris, 1978, p. 30)
       Extraordinarily rapid progress during the early stages of an attack on a new problem area is a rather common occurrence in AI research; it merely signifies that the test cases with which the system has been challenged are below the level of difficulty where combinatorial explosion of the number of pathways in the problem space sets in.... It is the goal of AI research to move that threshold higher and higher on the scale of problem complexity through the introduction of heuristics-heuristics to reduce the rate of growth of the solution tree, heuristics to guide the development of the tree so that it will be rich in pathways leading to satisfactory problem solutions, and heuristics to direct the search to the "best" of these pathways. (Gelernter, quoted in Barr & Feigenbaum, 1982, pp. 139-140)

    Historical dictionary of quotations in cognitive science > Heuristics

  • 2 Flügge-Lotz, Irmgard

    SUBJECT AREA: Aerospace
    [br]
    b. 1903 Germany
    d. 1974 USA
    [br]
    German/American aeronautical engineer, specializing inflight control.
    [br]
    Both her father, a mathematician, and her mother encouraged Flügge-Lotz in her desire, unusual for a woman at that time, for a technical education. Her interest in aeronautics was awakened when she was a child, by seeing zeppelins (see Zeppelin, Ferdinand, Count von) being tested. In 1923 she entered the Technische Hochschule in Hannover to study engineering, specializing in aeronautics; she was often the only woman in the class. She obtained her doctorate in 1929 and began working in aeronautics. Two years later she derived the Lotz Method for calculating the distribution in aircraft wings of different shapes, which became widely used. Later, Flügge-Lotz took up an interest in automatic flight control of aircraft, notably of the discontinuous or "on-off" type. These were simple in design, inexpensive to manufacture and reliable in operation. By 1928 she had risen to the position of head of the Department of Theoretical Aerodynamics at Göttingen University, but she and her husband, Wilhelm Flügge, an engineering academic known for his anti-Nazi views, felt themselves increasingly discriminated against by the Hitler regime. In 1948 they emigrated to the USA, where Flügge was soon offered a professorship in engineering, while his wife had at first to make do with a lectureship. But her distinguished work eventually earned her appointment as the first woman full professor in the Engineering Department at Stanford University.
    She later extended her work on automatic flight control to the guidance of rockets and missiles, earning herself the description "a female Werner von Braun ".
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    Principal Honours and Distinctions
    Society of Women Engineers Achievement Award 1970. Fellow, Institution of Aeronautics and Astronautics.
    Bibliography
    Flügge-Lotz was the author of two books on automatic control and over fifty scientific papers.
    Further Reading
    A.Stanley, 1993, Mothers and Daughters of Invention, Meruchen, NJ: Scarecrow Press, pp. 899–901.
    LRD

    Biographical history of technology > Flügge-Lotz, Irmgard

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