15 July 2019

Jacob Bernoulli - Collected Quotes

"But here it seems to me that we are at a loss, since one is at liberty to do this only just in very few cases, and indeed one may hardly succeed else where other than in games of chance, the first inventors of which, doing their best to bring about fairness, arranged things for themselves in such a way that the numbers of cases in which gain or loss ought to follow, might be definite and known, and that all these cases might happen with equal facility. For in most other situations depending either on the working of nature or on the judgement of men, this is by no means the case." (Jacob Bernoulli, "Ars Conjectandi" ["The Art of Conjecturing"], 1713)

"But indeed, another way is open to us here by which we may obtain what is sought; and what you cannot deduce a priori, you can at least deduce a posteriori - i.e. you will be able to make a deduction from the many observed outcomes of similar events. For it may be presumed that every single thing is able to happen and not to happen in as many cases as it was previously observed to have happened or not to have happened in like circumstances." (Jacob Bernoulli, "Ars Conjectandi" ["The Art of Conjecturing"], 1713)

"Further, it cannot escape anyone that for judging in this way about any event at all, it is not enough to use one or two trials, but rather a great number of trials is required. And sometimes the stupidest man|by some instinct of nature per se and by no previous instruction (this is truly amazing)| knows for sure that the more observations of this sort that are taken, the less the danger will be of straying from the mark." (Jacob Bernoulli, "Ars Conjectandi" ["The Art of Conjecturing"], 1713)

"If thus all events through all eternity could be repeated, by which we would go from probability to certainty, one would find that everything in the world happens from definite causes and according to definite rules, and that we would be forced to assume amongst the most apparently fortuitous things a certain necessity, or, so to say, FATE." 
(Jacob Bernoulli, "Ars Conjectandi" ["The Art of Conjecturing"], 1713)

"It seems that to make a correct conjecture about any event whatever, it is necessary to calculate exactly the number of possible cases and then to determine how much more likely it is that one case will occur than another." (Jacob Bernoulli, "Ars Conjectandi" ["The Art of Conjecturing"], 1713))

"Probability is a degree of certainty and it differs from certainty as a part from a whole." (Jacob Bernoulli, "Ars Conjectandi" ["The Art of Conjecturing"], 1713)

"[…] probability as a measurable degree of certainty; necessity and chance; moral versus mathematical expectation; a priori an a posteriori probability; expectation of winning when players are divided according to dexterity; regard of all available arguments, their valuation, and their calculable evaluation; law of large numbers […]" (Jacob Bernoulli, "Ars Conjectandi" ["The Art of Conjecturing"], 1713)

"The art of measuring, as precisely as possible, probabilities of things, with the goal that we would be able always to choose or follow in our judgments and actions that course, which will have been determined to be better, more satisfactory, safer or more advantageous." (Jacob Bernoulli, "Ars Conjectandi" ["The Art of Conjecturing"], 1713)

"The sum of an infinite series whose final term vanishes perhaps is infinite, perhaps finite." (Jacob Bernoulli, "Ars Conjectandi" ["The Art of Conjecturing"], 1713)

"Verily to be sure, another way is open to us here, by which we may obtain that which is sought; & what it is not granted to find out a priori, it will at any rate be permitted to extract a posteriori, that is, from a result perceived many times in similar instances; since it ought to be assumed that every single thing is able to happen and not to happen in future in as many cases as it will have been observed formerly in similar circumstances to have occurred and not to have occurred." (Jacob Bernoulli, "Ars Conjectandi" ["The Art of Conjecturing"], 1713)

"We define the art of conjecture, or stochastic art, as the art of evaluating as exactly as possible the probabilities of things, so that in our judgments and actions we can always base ourselves on what has been found to be the best, the most appropriate, the most certain, the best advised; this is the only object of the wisdom of the philosopher and the prudence of the statesman." (Jacob Bernoulli, "Ars Conjectandi" ["The Art of Conjecturing"], 1713)

"Whence finally this singular result is seen to follow, that if observations of all events were to be continued through all eternity (the probability finally ending in complete certainty) all happenings in the world would be observed to occur in fixed [definite] ratios and according to a constant law of change; to such a degree that even in the most accidental and fortuitous happenings we would be bound to recognize [acknowledge] a sort of inevitability as it were and, so to say, a necessity ordained by fate." (Jacob Bernoulli, "Ars Conjectandi" ["The Art of Conjecturing"], 1713)

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