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A philosophical essay on probabilities, by Pierre Simon Laplace
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A philosophical essay on probabilities. 234 Pages.
- Sales Rank: #566559 in eBooks
- Published on: 2013-02-02
- Released on: 2013-02-02
- Format: Kindle eBook
Language Notes
Text: English (translation)
Original Language: French
About the Author
Pierre Simon is Charge de recherche, CNRS, at Universite Lyon 1, France. He completed his PhD at Universite Paris-Sud, Orsay under the supervision of Elisabeth Bourscaren. His thesis, 'Ordre et stabilite dans les theories NIP', received the 2012 Sacks Prize for the best thesis in logic that year as well as the Perrissin-Pirasset/Schneider prize from the Chancellerie des Universites de Paris.
Most helpful customer reviews
25 of 25 people found the following review helpful.
Probability theory is nothing but common sense reduced to calculation
By Peter Norvig
This is an awesome book. It is hard to believe Laplace wrote this in 1816; it seems so modern. If you've ever worked on problems like "take two urns, A and B, the first containing four
white and two black balls ..." you'll be interested to know these problems all go back to this book. Laplace said "Probability theory is nothing but common sense reduced to calculation", and he shows it here. I like the discussion of how many judges should be assigned to a case, and what proportion of them should be required to vote guilty for a guilty verdict to be returned. Laplace shows how to minimize expected loss on this problem (although he, somewhat unrealistically, assumes that each judge's opinion is independent of the others).
2 of 2 people found the following review helpful.
Always read The Classics
By Frank Grange
Popularly misidentified as a frequentist, Laplace was really the original "Bayesian" as we use the term today. Unlike Bayes, over-credited by anglophiles or francophobes, Laplace really defined the useful methods that created modern Bayesian inference and analysis. (Re)reading Laplace is worthwhile for any practicing or academic toiler in probability, statistics, modeling and simulation.
While I haven't French, the translation flows well, so I assume the translator and editor were knowledgeable and careful.
1 of 1 people found the following review helpful.
THE FAMED MATHEMATICIAN LOOKS AT “THE MOST IMPORTANT QUESTIONS OF LIFE” FROM A PROBABILISTIC PERSPECTIVE
By Steven H Propp
Pierre-Simon, marquis de Laplace (1749-1827) was a French mathematician and astronomer whose work was pivotal to the development of mathematical astronomy and statistics. He wrote in the Introduction to this 1812 book, “This philosophical essay is the development of a lecture on probabilities which I delivered in 1795 to the normal schools whither I had been called… as professor of mathematics with Lagrange… I present here without the aid of analysis the principles and general results of this theory, applying them to the most important questions of life, which are indeed for the most part only problems of probability… nearly all our knowledge is problematical; and… even in the mathematical sciences themselves … are based on probabilities; so that the entire system of human knowledge is connected with the theory set forth in this essay… in considering, even in the eternal principles of reason, justice, and humanity, only the favorable changes which are constantly attached to them, there is a great advantage in following these principles and serious inconvenience in departing from them.” (Pg. 1-2)
He suggests, "We ought then to regard the present state of the universe as the effect of its anterior state and as the cause of the one which is to follow. Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective situation of the beings who compose it---an intelligence sufficiently vast to submit these data to analysis---it would embrace in the same formula the movements of the greatest bodies of the universe and those of the lightest atom; for it, nothing would be uncertain and the future, as the past, would be present to its eyes." (Pg. 4)
He notes, “the transcendent results of calculus are, like all the abstractions of the understanding, general signs whose true meaning may be ascertained only by repassing by metaphysical analysis to the elementary ideas which have led to them; this often presents great difficulties, for the human mind tries still less to transport itself into the future than to retire within itself. The comparison of infinitely small differences with finite differences is able similarly to shed great light upon the metaphysics of infinitesimal calculus.” (Pg. 44)
He observes, “Amid the variable and unknown causes which we comprehend under the name ‘chance,’ and which render uncertain and irregular the march of events, we see appearing, in the measure that they multiply, a striking regularity which seems to hold to a design and which has been considered as a proof of Providence. But in reflecting upon this we soon recognize that this regularity is only the development of the respective possibilities of simple events which ought to present themselves more often when they are probable.” (Pg. 60)
Concerning jury trials, he points out, “In a jury of twelve members, if the plurality demanded for the condemnation is eight of twelve votes, the probability of the error to be feared is … a little more than one eighth, it is almost 1/22nd if this plurality consists of nine votes. In the case of unanimity the probability of the error to be feared is … more than a thousand times less than in our juries. This supposes that the unanimity results only from proofs favorable or contrary to the accused… the probability of the decision is too feeble in our juries, and I think that in order to give a sufficient guarantee to innocence, one ought to demand at least a plurality of nine votes in twelve.” (Pg. 139)
He comments, “[Leibnitz] imagined, since God can be represented by unity and nothing by zero, that the Supreme Being had drawn from nothing all beings, as unity with zero expresses all the numbers in this system of arithmetic. This idea was so pleasing to Leibnitz that he communicated it to the Jesuit Grimaldi… in the hope that this emblem of creation would convert to Christianity the emperor there who particularly loved the sciences. I report this incident only to show to what extent the prejudices of infancy can mislead the greatest men.” (Pg. 169)
He suggests, “Man, made for the temperature which he enjoys, and for the element which he breathes, would not be able, according to all appearance, to live upon the other planets. But ought there not to be an infinity of organization relative to the various constitutions of the globes of this universe? If the single difference of the elements and of the climates make so much variety in terrestrial productions, how much greater the difference ought to be among those of the various planets and of their satellites! The most active imagination can form no idea of it; but their existence is very probable.” (Pg. 181)
This book will be of interest not just to students of the history of science, but to students of probability and related areas.
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