A classic of science, this famous essay by "the Newton of France" introduces lay readers to the concepts and uses of probability theory. It is of especial interest today as an application of mathematical techniques to problems in social and biological sciences. Generally recognized as the founder of the modern phase of probability theory, Laplace here applies the principles A classic of science, this famous essay by "the Newton of France" introduces lay readers to the concepts and uses of probability theory. It is of especial interest today as an application of mathematical techniques to problems in social and biological sciences. Generally recognized as the founder of the modern phase of probability theory, Laplace here applies the principles and general results of his theory "to the most important questions of life, which are, in effect, for the most part, problems in probability." Thus, without the use of higher mathematics, he demonstrates the application of probability to games of chance, physics, reliability. of witnesses, astronomy, insurance, democratic government and many other areas. General readers will find it an exhilarating experience to follow Laplace's nontechnical application of mathematical techniques to the appraisal, solution and/or prediction of the outcome of many types of problems. Skilled mathematicians, too, will enjoy and benefit from seeing how one of the immortals of science expressed so many complex ideas in such simple terms.

# A Philosophical Essay on Probabilities

A classic of science, this famous essay by "the Newton of France" introduces lay readers to the concepts and uses of probability theory. It is of especial interest today as an application of mathematical techniques to problems in social and biological sciences. Generally recognized as the founder of the modern phase of probability theory, Laplace here applies the principles A classic of science, this famous essay by "the Newton of France" introduces lay readers to the concepts and uses of probability theory. It is of especial interest today as an application of mathematical techniques to problems in social and biological sciences. Generally recognized as the founder of the modern phase of probability theory, Laplace here applies the principles and general results of his theory "to the most important questions of life, which are, in effect, for the most part, problems in probability." Thus, without the use of higher mathematics, he demonstrates the application of probability to games of chance, physics, reliability. of witnesses, astronomy, insurance, democratic government and many other areas. General readers will find it an exhilarating experience to follow Laplace's nontechnical application of mathematical techniques to the appraisal, solution and/or prediction of the outcome of many types of problems. Skilled mathematicians, too, will enjoy and benefit from seeing how one of the immortals of science expressed so many complex ideas in such simple terms.

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4out of 5Jake–“Probability is a (some people would say *the*) logical calculus of uncertainty.” ~ David Braber Often times we’re not in control of the provenance of our data. When we try to model the world from our data in some way, it should arise from our beliefs and irregularities we observe from the universe. The simplest model we often use, linear regression, is easily resolved with just two data points. When you think about Newton’s physics, it’s simply put, a simple regression model with high validation “Probability is a (some people would say *the*) logical calculus of uncertainty.” ~ David Braber Often times we’re not in control of the provenance of our data. When we try to model the world from our data in some way, it should arise from our beliefs and irregularities we observe from the universe. The simplest model we often use, linear regression, is easily resolved with just two data points. When you think about Newton’s physics, it’s simply put, a simple regression model with high validation accuracy. Easily resolved with two data points, but doesn’t generalize properly when you start dealing with smaller masses and more data points. But it’s a useful model if you just care about where your starting place, ending place are and you assume masses are large I bring up Newton because LaPlace was a colleague to Newton. LaPlace would be the one who did the grunt work of generalizing mechanics and that was used as a framework for thinking about probabilities in this book. It’s quite odd that so many people think LaPlace thought the world was deterministic. In the chapter where he brings up what would later be referred to as LaPlace’s Demon, it’s literally titled Sur Les Probabilities or “On the Probabilities.” LaPlace was setting up his demon as a straw-man so that he could later tear it down. From here on out I’ll take snippets of this chapter and talk about them. “We out the to regard the present state of the universe as the effect of its anterior state and as the cause of one which is to follow.” That’s Markov’s principle in action, which is to say, if a recursive algorithm cannot fail to converge, then it converges. This would lead to Church’s thesis, which connects the abstract mathematics to the real world consequences and limitations of computability. This was a conjecture by LaPlace 100 years ahead of the formal proof. “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...” Boltzmann would become depressed sixty years after this because no one believed him when he spoke of atoms, yet LaPlace states it as an inevitability. That formula he’s speaking of is Bayes’ rule, which really should be called LaPlaces’ Rule because he was the one responsible for its formalization and how we use it. We have a predilection for rewarding the first to discover an idea, and not the first to make it usable. This in my view is a mistake. “... for it, nothing would be uncertain and the future, as the past, would be present to its eyes.” This is the bit that people quote as if LaPlace were an idiot. Holding it up as the sign that he thought the world was deterministic. He would go onto later say, “The curve described by a simple molecule of air or vapor is regulated in a manner just as certain as the planetary orbits; the only difference between them is that which comes from our ignorance...Probability is relative in part to this ignorance, and in part to our knowledge.” Aside from this thinking being sixty years ahead of its time, he’s stating in simple terms that probability encodes our uncertainty. If there was any doubt to what LaPlace thought he would go onto say: “In this state of indecision it is impossible for us to announce their occurrence with certainty.” If we do not have knowledge, we cannot predict with certainty. Now that we’re here, how do we deal with this uncertainty? He would go onto propose the use of what is now known as latent variables, although he did not use this language. Noise as it is referred to today is what we observe in terms of our data about the world that departs from what we say in our model, which we deal with with a probability distribution. We don’t know how this will happen, and this is what LaPlace talks about in terms of our ignorance. It was this thinking that would lead him to be the first to formally prove the central limit theorem which was the justification for the Gaussian density. The real point that LaPlace was trying to make is that, effectively aleatoric uncertainty is just epistematic uncertainty. That is to say, uncertainty from lack of knowledge is the same as uncertainty arising from something which can be modeled as a stochastic system. The real difference between the two is just the depth to which our knowledge is limited by the scope and size of the problem. “I think if it were true that P=NP or if we had no limitations on memory and computation, AI would be a piece of cake. We could just brute-force any problem. We could go "full Bayesian" on everything (no need for learning anymore. Everything becomes Bayesian marginalization). But the world is what it is.” ~ Yann LeCun

5out of 5Roberto Rigolin F Lopes–We are in 1812, Laplace is educating us on probability calculus. He warms up pointing out that probability is one of the most important human developments from the 17th century. Probability is defined simply as: "The ratio of the number of favorable cases to that of all possible cases". Then he goes keenly through applications such as: decisions in assemblies and judgments, mean duration of life, illusions estimating probabilities and so on. It "probably" bursted lots of superstitions within hum We are in 1812, Laplace is educating us on probability calculus. He warms up pointing out that probability is one of the most important human developments from the 17th century. Probability is defined simply as: "The ratio of the number of favorable cases to that of all possible cases". Then he goes keenly through applications such as: decisions in assemblies and judgments, mean duration of life, illusions estimating probabilities and so on. It "probably" bursted lots of superstitions within human endeavors.

5out of 5Bastian Greshake Tzovaras–Skip the introductory parts to probability if you've ever sat in a course on the topic. The later parts on applying probabilities to all sciences and everyday life are nicer. Skip the introductory parts to probability if you've ever sat in a course on the topic. The later parts on applying probabilities to all sciences and everyday life are nicer.

4out of 5David Owen–If you believe that, at least in principle, science can answer every question, t'hen this is the book for you. He was a brilliant French mathematician and polymath whose most famous quote involves an entity called 'Laplace's Demon'. A must read if you like science and philosophy - it will make your mind soar! If you believe that, at least in principle, science can answer every question, t'hen this is the book for you. He was a brilliant French mathematician and polymath whose most famous quote involves an entity called 'Laplace's Demon'. A must read if you like science and philosophy - it will make your mind soar!

4out of 5Nick Black–GT Barnes & Noble, 2009-06-08, spontaneous purchase. I was looking at the Dover Math+Science section (two shelves now, and growing! w00t!), overwhelmed by all the mathematical goodness, and suffered some crosstalk of titles; for a second, I thought I'd spied "Recreations in Cohomology Operations and Homotopy Theory". Before realizing my error, I blinked, and said aloud, "I don't want to meet the motherfucker who's like, hey, instead of going to Vail this year I'd like to do a week of recreationa GT Barnes & Noble, 2009-06-08, spontaneous purchase. I was looking at the Dover Math+Science section (two shelves now, and growing! w00t!), overwhelmed by all the mathematical goodness, and suffered some crosstalk of titles; for a second, I thought I'd spied "Recreations in Cohomology Operations and Homotopy Theory". Before realizing my error, I blinked, and said aloud, "I don't want to meet the motherfucker who's like, hey, instead of going to Vail this year I'd like to do a week of recreational homotopy theory. Maybe fight a few cops and see if I can catch some recreational gonorrhea, you know, piss some recreational kidney stones, steal some fat girl's diet pills so i can stay awake working on cohomology operation theory, maybe playfully throw myself and loved ones into a chemical fire and make a game of who can drink the most white phosphorus or hell just call it a Steenrod Square Party and spike drain-o directly into my pee-hole," but then I grokked they were two different books. I sheepishly grabbed Laplace, rendered tender, and got out. You expect to run a business this way? A pox, mssrs Barnes and Nobel, on both your houses.

4out of 5Tim Clouse–One of the fundamental texts on subjective probability and Bayes' Theorem. Contains Laplace's Rule of Succession, which has bedeviled thinkers in probability for the past 200 years. Appears to be a translation from 1901, but is understandable. One of the fundamental texts on subjective probability and Bayes' Theorem. Contains Laplace's Rule of Succession, which has bedeviled thinkers in probability for the past 200 years. Appears to be a translation from 1901, but is understandable.

5out of 5Pamela–some interesting bits written in antiquated style.. helpful.

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