laplacean

Example Sentences

• "The object of this paper is to set forth briefly to what extent the principles proposed by Laplace in his Mécanique Céleste, tome 1, livre 2, may be made available in practice for the derivation of preliminary orbits of comets, minor planets, and satellites. […] Before proceeding to a discussion of the difficulties referred to above as having been encountered by various investigators in attempting to formulate practical orbit methods on the basis of Laplace's principles, and before demonstrating the advantages of the methods which I have termed "Short Methods," it is necessary to state that in emphasizing the practical value of the Laplacean principles I do not intend to detract in the least from their great but astronomically less important theoretical value. I shall therefore first consider in brief the general theoretical value of the Laplacean principles by means of a summary of their essential features. […] The direct solution which has just been outlined corresponds to the so-called first hypothesis of other methods. It is evident that the accuracy of Laplace's direct solution depends upon the accuracy of the fundamental observational data for which we have chosen α, δ; α′, δ′; α″, δ″. If the epoch is chosen to coincide with the date of one of the observations, then α, δ are fixed numbers, and the accuracy of the Laplacean solution depends upon the accuracy of the adopted values of their velocities and accelerations or, which is an equivalent statement, upon the accuracy of their first and second differential coefficients. In practically all other methods the accuracy of the solution depends upon the accuracy of the adopted values of the ratios of the triangles."
• "What does Freud oppose to the view that the future is already written? It is in so far as chance does exist in the physical, as opposed to mental world, that Freud distinguishes himself from a superstitious person. Yet the analyst never takes a chance event at face value. Everything mental — that is speakable — is determined. This sense of determination, the famous determinism that Freud is rebuked for, is in truth more of a parody of nineteenth century Laplacean determinism than its extension. From the dream in The interpretation of dreams, we derive the simple formula that dreams foretell the future insofar as the future is a perfect likeness of the past. This model seems to be akin to the Laplacean determinism of the nineteenth century, the view that, given knowledge of initial conditions, of the present state of forces and elements in the universe, the entire history of a system can be predicted, both forward, into the future, and backwards, into the past. This determinism is broken up, we are told, by twentieth-century physics. But this Laplacean future is the future invoked by the dream; the real future, if such a thing can be allowed to escape the clutches of the Augustinian paradoxes, is a very different thing. One simple index of Freud's avoidance of the Laplacean denial of a difference between past and future is the fact that the question of chance and coincidence bulks so large in discussions of foretelling the future. In a sense, the future is the privileged domain of the miraculous for psychoanalysis. And yet, psychoanalysis itself essays to enter into the domain of the future by undoing the Laplacean determinations the patient constructs for him or herself."
• "Laplace had owned Bayes’ rule in all but name since 1781. The formula, the method, and its masterful utilization all belong to Pierre Simon Laplace. He made probability-based statistics commonplace. By transforming a theory of gambling into practical mathematics, Laplace’s work dominated probability and statistics for a century. “In my mind,” Glenn Shafer of Rutgers University observed, “Laplace did everything, and we just read stuff back into Thomas Bayes. Laplace put it into modern terms. In a sense, everything is Laplacean.” If advancing the world’s knowledge is important, Bayes’ rule should be called Laplace’s rule or, in modern parlance, BPL for Bayes-Price-Laplace. Sadly, a half century of usage forces us to give Bayes’ name to what was really Laplace’s achievement."