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In his 1950 essay “Projected Verse”, Charles Olsen argues “ONE PERCEPTION MUST IMMEDIATELY AND DIRECTLY LEAD TO A FURTHER PERCEPTION.”1 It is worth noting how Olsen locates writer’s perception as existing in continuum, which seems to emphasize a more fluid reading of poetry.
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Fool Me Once: Can Indifference Vindicate Induction? Roger White (2015) sketches an ingenious new solution to the problem of induction. It argues on a priori grounds that the world is more likely to be inductionfriendly than inductionunfriendly. The argument relies primarily on the principle of indifference, and, somewhat surprisingly, assumes little else. If inductive methods could be vindicated in anything like this way, it would be quite a groundbreaking result. But there are grounds for pessimism about the envisaged approach. This paper shows that in the crucial test cases White concentrates on, the principle of indifference actually renders induction no more accurate than random guessing. It then diagnoses why the indifferencebased argument seems so intuitively compelling, despite being ultimately unsound. 1 An IndifferenceBased Strategy White begins by imagining that we are “apprentice demons” tasked with devising an inductionunfriendly world – a world where inductive methods tend to be unreliable. To simplify, we imagine that there is a single binary variable that we control (such as whether the sun rises over a series of consecutive days). So, in essence, the task is to construct a binary sequence such that – if the sequence were revealed one bit at a time – an inductive reasoner would fare poorly at predicting its future bits. This task, it turns out, is surprisingly difficult. To see this, it will be instructive to consider several possible strategies for constructing a sequence that would frustrate an ideal inductive predictor. Immediately, it is clear that we should avoid uniformly patterned sequences, such as: 00000000000000000000000000000000 or 01010101010101010101010101010101. 1 Sequences like these are quite kind to induction. Our inductive reasoner would quickly latch onto the obvious patterns these sequences exhibit. A more promising approach, it might seem, is to build an apparently patternless sequence: 00101010011111000011100010010100 But, importantly, while induction will not be particularly reliable at predicting the terms of this sequence, it will not be particularly unreliable here either. Induction would simply be silent about what a sequence like this contains. As White puts it, “ In order for... induction to be applied, our data must contain a salient regularity of a reasonable length” (p. 285). When no pattern whatsoever can be discerned, presumably, induction is silent. (We will assume that the inductive predictor is permitted to suspend judgment whenever she wishes.) The original aim was not to produce an inductionneutral sequence, but to produce a sequence that elicits errors from induction. So an entirely patternless sequence will not suffice. Instead, the inductionunfriendly sequence will have to be more devious, building up seeming patterns and then violating them. As a first pass, we can try this: 00000000000000000000000000000001 Of course, this precise sequence is relatively friendly to induction. While our inductive predictor will undoubtedly botch her prediction of the final bit, it is clear that she will be able to amass a long string of successes prior to that point. So, on balance, the above sequence is quite kind to induction – though not maximally so. In order to render induction unreliable, we will need to elicit more errors than correct predictions. We might try to achieve this as follows: 00001111000011110000111100001111 2 The idea here is to offer up just enough of a pattern to warrant an inductive prediction, before pulling the rug out – and then to repeat the same trick again and again. Of course, this precise sequence would not necessarily be the way to render induction unreliable: For, even if we did manage to elicit an error or two from our inductive predictor early on, it seems clear that she would eventually catch on to the exceptionless higherorder pattern governing the behavior of the sequence. The upshot of these observations is not that constructing an inductionunfriendly sequence is impossible. As White points out, constructing such a sequence should be possible, given any complete description of how exactly induction works (p. 287). Nonetheless, even if there are a few special sequences that can frustrate induction, it seems clear that such sequences are fairly few and far between. In contrast, it is obviously very easy to corroborate induction (i.e. to construct a sequence rendering it thoroughly reliable). So induction is relatively unfrustrateable. And it is worth noting that this property is fairly specific to induction. For example, consider an inferential method based on the gambler’s fallacy, which advises one to predict whichever outcome has occurred less often, overall. It would be quite easy to frustrate this method thoroughly (e.g. 00000000…). So far, we have identified a highly suggestive feature of induction. To put things roughly, it can seem that: * Over a large number of sequences, induction is thoroughly reliable. * Over a large number of sequences, induction is silent (and hence, neither reliable nor unreliable). * Over a very small number of sequences (i.e. those specifically designed to thwart induction), induction is unreliable (though, even in these cases, induction is still silent much of the time). 3 Viewed from this angle, it can seem reasonable to conclude that there are a priori grounds for confidence that an arbitrary sequence is not inductionunfriendly. After all, there seem to be far more inductionfriendly sequences than inductionunfriendly ones. If we assign equal probability to every possible sequence, then the probability that an arbitrary sequence will be inductionfriendly is going to be significantly higher than the probability that it will be inductionunfriendly. So a simple appeal to the principle of indifference seems to generate the happy verdict that induction can be expected to be more reliable than not, at least in the case of binary sequences. Moreover, as White points out, the general strategy is not limited to binary sequences. If we can show a priori that induction over a binary sequence is unlikely to be inductionunfriendly, then it’s plausible that a similar kind of argument can be used to show that we are justified in assuming that an arbitrary world is not inductionunfriendly. If true, this would serve to fully vindicate induction. 2 Given Indifference, Induction Is not Reliable However, there are grounds for pessimism about whether the strategy is successful even in the simple case of binary sequences. Suppose that, as a special promotion, a casino decided to offer Fair Roulette. The game involves betting $1 on a particular color – black or red – and then spinning a wheel, which is entirely half red and half black. If wrong, you lose your dollar; if right, you get your dollar back and gain another. If it were really true that induction can be expected to be more reliable than not over binary sequences, it would seem to follow that induction can serve as a winning strategy, over the long term, in Fair Roulette. After all, multiple spins of the wheel produce a binary sequence of reds and blacks. And all possible sequences are 4 equally probable. Of course, induction cannot be used to win at Fair Roulette – past occurrences of red, for example, are not evidence that the next spin is more likely to be red. This suggests that something is amiss. Indeed, it turns out that no inferential method – whether inductive or otherwise – can possibly be expected to be reliable at predicting unseen bits of a binary sequence, if the principle of indifference is assumed. This can be shown as follows. Let S be an unknown binary sequence of length n. S is to be revealed one bit at a time, starting with the first. S: ? ? ? ? ? ? … ? :S n bits Let f be an arbitrary predictive function that takes as input any initial subsequence of S and outputs a prediction for the next bit: ‘0’, ‘1’, or ‘suspend judgment’. A predictive function’s accuracy is measured as follows: +1 for each correct prediction; 1 for each incorrect prediction; 0 each time ‘suspend judgment’ occurs. (So the maximum accuracy of a function is n; the minimum score is –n.) Given a probability distribution over all possible sequences, the expected accuracy of a predictive function is the average of its possible scores weighted by their respective probabilities. Claim: If we assume indifference (i.e. if we assign equal probability to every possible sequence), then – no matter what S is – each of f’s predictions will be expected to contribute 0 to f’s accuracy. And, as a consequence of this, f has 0 expected accuracy more generally. Proof: For some initial subsequences, f will output ‘suspend judgment’. The contribution of such predictions will inevitably be 0. So we need consider only those cases where f makes a firm prediction (i.e. ‘0’ or ‘1’; not ‘suspend judgment’). Let K be a klength initial subsequence for which f makes a firm prediction about the bit in 5
This required more prompting than I thought it would, and it seems that students were indifferent to my questioning them about the exam.
After discussing this result, we then diagnose why the indifference-based argument seems so intuitively compelling, despite being ultimately unsound.
If you would like to make money giving this book away please click here for details INTRODUCTION It seems like you hear it all the time from nearly every one you know – “I’m SO stressed out!” Pressures abound in this world today.
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This required more prompting than I thought it would, and it seems that students were indifferent to my questioning them about the exam.
Towards an Urban Sublime: Expressing the Inexpressible in Urban Romantic Poetry As the industrial revolution brought about the rapid urbanization of cities throughout Europe, writers who were previously concerned with the aesthetics of nature and the countryside found themselves grappling with an entirely new set of poetic and philosophical concerns. The teeming crowds, towering structures and spectacular sights that they encountered in the novel environment of the city incited in them feelings of overwhelming terror and awe akin to those typically associated with the romantic “sublime.” However, as we look more closely at the cityfocused works of poets like Baillie, Wordsworth and Hood, we begin to see that there is a fundamental difference between the “natural” sublime of earlier romantic poetry and the “urban” sublime of the city poem. Whereas the poet’s sublime experience in nature is typically associated with some sort of catharsis or transcendence, forcing man to come to terms with the limitations of his own humanity, the urban sublime instead incites a feelings of wonder and disgust at the incredible potential of that humanity itself, or—as Anne Janowitz put it in her essay The Artifactual Sublime —it forces man to confront “the self as if it were not the self; to experience the madeness of the human world as if it were different stuff than the labour of persons.” While it is true that, as Janowitz notes, this “misrecognition” of the sublime object often resulted in the experience of “romantic alienation,” I argue that the use of sublime language and natural imagery also acted as a sort of coping mechanism for their writers. Through the experience of the “urban” sublime is of course intrinsically linked to feelings of terror and isolation, the fact that these poets were describing particularly urban experiences in terms of something formerly associated with nature helped them to bridge the gap between the urban world and the natural one. This technique, therefore, served the dual purpose of expressing the unfamiliarity of this new landscape and familiarizing it, allowing these poets to discover, as Wordsworth put it, that the underlying “spirit of Nature” was still upon them, even in this “vast receptacle.” In Thomas Hood’s delightfully erratic Moral Reflections on the Cross of Saint Paul’s , we find a perfect example of the struggle many poets faced to familiarize the sublimely overwhelming urban environment. Hood’s speaker—who is presumably a tourist visiting London for the first time—is hilariously unable to produce any original or insightful “reflections” about the complex cityscape he sees spread out before him, and resorts instead to stringing together a bizarre collection of references and metaphors that don’t seem to fit together into a cohesive vision. The speaker’s numerous allusions to “classic” works of literature suggest that he feels a longing to express the “profound” nature of the landscape he is viewing, but even these references come off as disjointed and confused. In the poem’s first stanza, the speaker compares the ball of Saint Paul’s cathedral to Mount Olympus, the home of the gods in Greek mythology. He then immediately moves on to reference a figure from Roman mythology, when he proclaims that he is sitting “Among the gods, by Jupiter!” The speaker’s thoughts turn again towards the literary in the third stanza, when—looking down at the city crowds beneath him—the speaker feels the need to question the nature of man. “What is life?” He asks himself, and answers with an apparent reference to a now cliche line from William Shakespeare's As You Like it : “And what is life? And all its ages— / There’s seven stages!” Before he is able to offer any sort of “real” philosophical inquiry into what he means by this, however, the speaker distracts himself by naming off the seven neighborhoods of London, and never returns to the subject. While this random misfiring of halfbaked references helps develop the speaker’s delightfully zany personality, it also gestures at the bewilderment he feels upon taking in the sprawling landscape of London from above. Though the speaker cannot adequately express the profound emotional impact of this landscape in his own words—and it is clear that he does not have the educational background to substantiate even an insightful literary comparison—he still feels the urge to grasp for images and analogies that he associates with grandiosity and power. This attempt—and failure—to express the inexpressible is a common struggle in the literature of the sublime, and in Joanna Baillie’s poem London —which was written around the same time as Hood’s piece—we are introduced to yet another speaker who cannot quite find the right words to describe the overwhelming urban landscape. The difference here is that Baillie’s speaker is more familiar with the concept of the natural sublime, and she uses the language associated with it to explore the ways that the experience of urban sublime is both related to and separate from the experience of the sublime in nature. The poem’s initial description of the city—in which we find the city viewed again from above, from the hills of Hampstead “through the clear air”—presents the urban space as a rather innocuous, almost quaint vision. The London skyline seems to the speaker a “goodly sight,” and its structures are rendered in relation to familiar human figures. The spires of St. Paul’s cathedral flank the structure “in kindred grace, like twain of sisters dear,” the “ridgy roofs” of the city’s buildings sit amicably “side by side.” The entire vision is “softly tinted” by the distance of the viewer, _____. However, as the air begins to grow denser, and “moistened winds” prevail, the city’s landscape transfigures into something far more menacing. The “thin soft haze” of the poem’s first section becomes a “grand panoply of smoke arrayed,” and the dome of St. Paul’s Cathedral—which is now surrounded not by quaint spires, but by “heavy” clouds that sail around its imposing dome—seems “a curtain gloom / Connecting heaven and earth,—a threatening sign of doom.” The shifting weather strips the humanity from the city’s landscape, and the language of the speaker quickly shifts to the language that references the natural sublime. The combination of almost ethereal However, this use of sublime language also allows the speaker to articulate the differences between the urban world and the natural one. Though the speaker seems compelled to compare the structure to prodigious natural figures (she states that the cathedral “might some lofty alpine peak be deemed”) it becomes apparent that these metaphors are not quite sufficient to describe the sight she is witnessing. Because its form reveals “man’s artful structure,” (and by extension the “artful structure” of man’s society), the cathedral cannot be viewed as totally natural. Instead, it is referred to as “more than natural,” and seems to transcend the boundaries of both humanity and nature as it first “connects heaven and hearth” and then, a few lines later seems “far removed from Earth.” This somewhat confused description demonstrates the speaker’s complex feelings about the urban landscape. Though she knows one thing for certain about this cathedral—“She is sublime”—the speaker cannot quite find the language she needs to describe the sense of the particularly “urban” sublime she is experiencing. She knows the cathedral is a product of mankind, and that the power that it is imbued with is intrinsically linked with the oppressive church that it represents and the often corrupt society that it is a part of. Part of the reason that the church looks seems to her so terrifying is certainly the fact that entering the streets of the city means succumbing to the dominance of the church, the government, and society as a whole. Language has always failed to fully express the sublime experience, however, and the speaker’s attempts to conflate the urban sublime of the city with the natural sublime simply demonstrates a desire to give a recognizable form to the terror she is experiencing—in order to truly become what Lyotard calls an “expressive witness to the inexpressible,” the speaker must carry thought and rationality to their logical conclusions, and for a romantic poet the world can best be rationalized and understood in terms of the rural. In contrast to Hood’s speaker, whose manic metaphorhopping was a symptom of a mind unprepared to grapple with the urban landscape’s complexities, Baillie’s speaker logically considers the unfamiliar in terms of her own experience, and makes the urban feel, in a way, like an extension of nature. This blending of the natural and the urban is epitomized in the final portion of Baillie’s poem, when the viewpoint shifts to the perspective of a “distant traveller.” From afar, this traveller is able to view the London in its entirety, and finds himself awestruck by the stars in the “luminous canopy” above the city that seem to be “cast up from myriads of lamps that shine / Along her streets in many a starry line.” The “flood of human life in motion” creates a noise that sounds to the traveller like the “voice of a tempestuous ocean,” and he finds his soul filled with a “sad but pleasing awe” upon hearing it. These magnificent sights, which seem at once human and natural, express the rich suggest that the city is capable of igniting in the human soul the same complex emotions that a sublime natural splendor might. Wordsworth took this idea to its ultimate conclusion as he navigated the bacchanalian chaos that is St. Bartholomew’s fair at the conclusion of The Prelude, Book Seven. In Wordsworth’s poem, we are not viewing London from above, but from the very trenches of the city, and the sublimity he is experiencing comes not from the contemplation of the urban
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