Adaptive Control and Identification: Conflict or Conflux? (J. W. Polderman)

within the power even of Divine Providence to erase the occurrence of an event which had already happened, so that Providence could not control the frequency ofoccurrence ofA when it was merely known that B, following A, had happened. One is tempted to go on at length with reflections prompted by Hald’s excellent work. It should have a very wide sale, since in addition to the appeal to anyone seriously concerned to learn about the early history of a most important concept, it could serve extremely well as a textbook for quite elementary classes in probability theory, giving as it does details ofthe essentially elementary arguments used by these 18th century mathematicians, and providing problems to serve as textbook exercises. One annoying defect is the absence of an index of notations. For example, the reader of his chapter on the Insurance Mathematics ofde Moivre and Simpson could easily fail to follow up Hald’s "see 9.3," and he would then wonder where he might find out what lx, Lx and so on stand for. An English reader familiar with the character ofJohn Bull may also wonder why the spelling of John Bull’s creator’s name is made to agree with that of his birthplace in spite of much testimony to the fact that he himself dropped a "t." And feminists, along with those of us who have a softer spot for Thomas Simpson than Hald appears to have, may quarrel with his suggestion that the Ladies Diary, which carried much of the early work on elliptic functions, devoted itself only to elementary mathematics. But these tiny points are mere specks of dust on a very solid achievement.