'this transitory existence, no doubt destined to be effaced'.
The calculus allows integration by parts with random variables ; this operation is used in mathematical finance to compute the sensitivities of financial derivatives . The calculus has applications for example in stochastic filtering .
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By Nagarjuna's lifetime, scholastic Buddhism had become much more than merely an institution which charged itself with the handing on of received scripture, tradition and council-established orthodoxy; it had grown into a highly variegated, inwardly and outwardly engaged set of philosophical positions. These schools took it upon themselves not merely to represent Buddhist teaching or make the benefits of its practice available, but also to explain Buddhism, to make it not only a reasonable philosophical discourse, but the most supremely reasonable of them all. The ultimate goal of life, liberation from rebirth, though in general shared by all soteriologies in Brahmanism, Jainism and Buddhism, was represented uniquely by Buddhists as the pacification of all psychological attachments through the extinguishing ( nirvana ) of desires, which would lead to a consequent extinguishing of karma and the prevention of rebirth. One particularly unique doctrine of Buddhism in its attempt to thematize these issues was the theory of no-self or no-soul ( anatman ) and what implications it carried. In the empirical sense, the idea of no-self meant that not only persons, but also what are normally considered the stable substances of nature are not in fact fixed and continuous, that everything from one's sense of personal identity to the forms of objects could be analyzed away, as it were, into the atomic parts which were their bases. In the ultimate metaphysical sense, it meant that no one, upon release from rebirth, will live eternally as a spiritual, self-conscious entity ( atman ), but that the series of births caused by inherited karma will simply terminate, reducing, as its cash-value, the total amount of suffering in the world. These theories prompted sharp and deep questions and criticisms, such as, "if the things and persons of the world are nothing more than atoms in constant flux, how can a person have an orderly experience of a world of apparent substances?", "if there is no enduring identity or self, who is it that practices Buddhism and is liberated?", and "how should we account for the differences between enlightened beings like the Buddha and unenlightened ones, like ourselves?" Answering such questions intelligibly for the inquiring minds of the philosophical community were a number of distinct schools which came collectively to be known as schools involved with the "analysis of elements" ( abhidharma ). Nagarjuna received his philosophical training in the texts, vocabulary and debates of the Abhidharmikas.