دانلود کتاب تئوری شیف از طریق مثال ها

In many cases, events and objects are given to observation as extended through time and space, and so the data about these is local and distributed in some fashion. For now, we can think of this situation in terms of the data being indexed by, or attached to, given delimited regions or domains of some sensors. In a very general and rough way, by local we typically understand that something is being compared to what is around or nearby it; this is as opposed to the global, generally understood to mean compared to everything or across an entire domain of interest. Satisfying a property at a local level does not necessarily entail that the same will obtain at the global level. In saying that the data is local, we just mean that it holds throughout, or is defined for, a certain limited region; that is, its validity is restricted to a prescribed region or partial domain or reference context. We also use this language of locality to describe a way of evaluating a property or data ascribed to a part or point of its extended domain in terms of what that property or data looks like viewed from its immediate surroundings—that is, whenever it holds somewhere, it should also hold nearby. We collect temperature and pressure readings and thus form a notion of ranges of possible temperatures and pressures over certain geographical regions; we record the fluctuating stockpile of products in a factory over certain business cycles; we accumulate observations or images of certain patches of the sky or the earth; we gather testimonies or accounts about particular events understood to have unfolded over a certain region of space-time; we build up a collection of test results concerning various parts of the human body; we amass collections of memories or recordings of our distinct interpretations of a certain piece of music; we develop observations about which ethical and legal principles or laws are respected throughout a given region or network of human actors; we form a concept of our kitchen table via various observations and encounters, assigning certain attributes to those regions of space-time delimiting our various encounters with the table, where we expect that the ascribed properties or attributes are present throughout the entirety of a region of their extension. Even if certain phenomena are not intrinsically local, frequently their measurement or the method employed in data collection may still be local. But even the least scrupulous person does not merely accumulate or amass local or partial data points. From an early age, we try to understand the various modes of connections and cooperations between the data, to patch these partial pieces together into a larger whole whenever possible, to resolve inconsistencies among the various pieces, to go on to build coherent and more global visions out of what may have been given to us only in pieces. As informed citizens or as scientists, we look at the data given to us on arctic sea-ice melting rates, on temperature changes in certain regions, on concentrations of greenhouse gases at various latitudes and various ocean depths, and so on, and we build a more global vision of the changes to our entire planet on the basis of the connections and feedbacks between these various data. As investigators of a crime, we must piece together a complete and consistent account of the events from the partial accounts of various witnesses. As doctors, we must infer a diagnosis and a plan of action from the various individual test results concerning the parts of a patient’s body. We take our many observations concerning the behavior of certain networks of human actors and try to form global ethical guidelines or principles to guide us in further encounters. Yet sometimes information is simply not local in nature. Roughly, one might think of such nonlocality in terms of how, as perceivers, certain attributes of a space may appear to us in a particular way but then cease to manifest themselves in such a way over subparts of that space, in which case one cannot really think of the perception as being built up from local pieces. For a different example: in the game of ScrabbleTM, one considers the assignment of letters, one by one, to the individual squares in a lattice of squares, with the aim of building words out of such assignments.