Nakayamas Lemma Quotes

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Quotes About Nakayamas Lemma

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Furious, the beast writhed and wriggled its iterated integrals beneath the King's polynomial blows, collapsed into an infinite series of indeterminate terms, then got back up by raising itself to the nth power, but the King so belabored it with differentials and partial derivatives that its Fourier coefficients all canceled out (see Riemann's Lemma), and in the ensuing confusion the constructors completely lost sight of both King and beast. So they took a break, stretched their legs, had a swig from the Leyden jug to bolster their strength, then went back to work and tried it again from the beginning, this time unleashing their entire arsenal of tensor matrices and grand canonical ensembles, attacking the problem with such fervor that the very paper began to smoke. The King rushed forward with all his cruel coordinates and mean values, stumbled into a dark forest of roots and logarithms, had to backtrack, then encountered the beast on a field of irrational numbers (F1) and smote it so grievously that it fell two decimal places and lost an epsilon, but the beast slid around an asymptote and hid in an n-dimensional orthogonal phase space, underwent expansion and came out, fuming factorially, and fell upon the King and hurt him passing sore. But the King, nothing daunted, put on his Markov chain mail and all his impervious parameters, took his increment Δk to infinity and dealt the beast a truly Boolean blow, sent it reeling through an x-axis and several brackets - but the beast ~ Stanisław Lem
Nakayamas Lemma quotes by Stanisław Lem
Stoic ethics is a species of eudaimonism. Its central, organizing concern is about what we ought to do or be to live well - to flourish. That is, we make it a lemma that all people ought to pursue a good life for themselves as a categorical commitment second to none. It does not follow from this that they ought to pursue any one particular version of the good life, or to cling tenaciously to the one they are pursuing. …

Living virtuously is the process of creating a single, spatiotemporal object - a life. A life has a value as an object, as a whole. It is not always the case that its value as an object will be a function of the value of its spatiotemporal parts considered separately. But it is always the case that an evaluation of the parts will be incomplete until they are understood in the context of the whole life. What seems so clearly valuable (or required or excellent) when we focus on a thin temporal slice of a life (or a single, long strand of a life) may turn out to be awful or optional or vicious when we take a larger view. And it is the life as a whole that we consider when we think about its value in relation to other things, or its value as a part of the cosmos.

… In our view, a focus on the parts of a life, or on the sum of its parts, obscures some important features of ethical inquiry. One such feature is the extent to which an agent's own estimate of the value of his life is necessarily inconclusive: others will have to judge his life as ~ Lawrence C. Becker
Nakayamas Lemma quotes by Lawrence C. Becker
One day Shizuo Kakutani was teaching a class at Yale. He wrote down a lemma on the blackboard and announced that the proof was obvious. One student timidly raised his hand and said that it wasn't obvious to him. Could Kakutani explain?

After several moments' thought, Kakutani realized that he could not himself prove the lemma. He apologized, and said that he would report back at their next class meeting.

After class, Kakutani, went straight to his office. He labored for quite a time and found that he could not prove the pesky lemma. He skipped lunch and went to the library to track down the lemma. After much work, he finally found the original paper. The lemma was stated clearly and succinctly. For the proof, the author had written, 'Exercise for the reader. ~ Steven G. Krantz
Nakayamas Lemma quotes by Steven G. Krantz
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