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Various End-reckonings, based on both the Talmud and the Zohar, led to the conclusion that the Messiah would appear in 5600 A.M. (the six-hundredth year of the sixth millennium), corresponding to 1840 C.E. The firmly entrenched belief appears in documents from throughout the Jewish world: Persia and Kurdistan, Morocco, the Land of Israel, Eastern Europe (Hasidic and non-Hasidic alike), and Western Europe. The documents are relatively few, given the Jews’ reluctance to discuss such matters in writing, but it appears as well in accounts by Christian missionaries of their conversations with Jews in most of those areas.

Opposed to impurity, corruption, suffering, and death are Purity, Sanctity, Happiness, and Immortality. Since “now” and “death” are the only certainties in human existence, withdrawal from everything that is between them for the sake of connection with them means the victory of life over dying. Two other certainties correspond to “now” and “death”—God and the Day of Reckoning. The contingency of everything in existence raises the question of conviction, lack of doubt, and certainty in knowledge. Knowledge that has any level of certainty may be acquired only through the observation of the mutuality between fullness and phenomena. The divergence indicated by the duality of the heavens and the earth, the invisible and the visible, the spirit and matter, as also the multitude of people, has its root in original oneness. Thus, the totality of existence corresponds to God's creative injunction willingly, since the beginning of everything lies in the proximity and clarity of His nature.

The hippocampus and associated structures are organized in multiple loops, with reciprocal connections to the neocortex. The most prominent collective pattern of hippocampal neurons is theta oscillation. In one-dimensional tasks, pyramidal cells fire maximally at particular positions, signifying the place field center. The assembly members that define the current location also contribute spikes to the representation of past and future positions in multiple theta cycles. Similarly, positional “distances” among items of an episodic list can be coded by the synaptic strengths between the cell assemblies. In two-dimensional environments, exploration leads to crossing the same positions from different directions. These junctions serve to establish a map and subsequent landmark (map-based) navigation. The hallmark of the cognitive map is the presence of omnidirectional place cells in the hippocampus and tessellating “grid cells” in the entorhinal cortex. Neuron members of an omnidirectional or explicit assembly collectively define or symbolize the semantic “meaning” of an item.

This chapter deals with sensory and motor systems that animals use to navigate. Navigation involves the registration of the direction and distance of sites beyond the range of sensory detectors. In one form of navigation, foraging animals use path integration to keep a record of the direction and distance of their movement from the home site. In true navigation, an animal registers the location of a distant site using information at a given location. For example, pigeons return to their loft from locations they have not visited previously. In celestial navigation, migrating animals are guided by the sun or the stars. It has been shown recently that some animals navigate by sensing the local direction of the Earth’s magnetic field.

This chapter investigates a range of languages which still retain some use of the traditional lunar month, mobile week, and ecological cycle. It considers the adaptability and effectiveness of these calendars, and the mindset which underlay them. It also examines the likelihood that they will disappear in the near future as languages vanish. It also tries to answer the question of what exactly will be lost as the language and the systems they contain are abandoned, and why the loss matters both to science and to humanity.

This chapter discusses the use of eras as well as dating by regnal years, which gained currency simultaneously in astronomy and cosmology. The use of regnal years as marker go back to the earliest historical inscriptions, the edicts of the Mauryan emperor Aśoka, issued in the third century BC. At the functional level, regnal years introduced more precise dating in official documents. More importantly, it helped separate cosmological time reckoning from the functional, although the former was not discarded. Official documents, biographies, and genealogiers, too, began to carry these dates. Among these documents are inscriptions which are in effect the annals of Indian history. Issued by individual rulers and by members of the ruling class in the main, they include votive records relating to grants and gifts as well as statements of events, especially those important to politics and administration.

This chapter considers an ethological approach to the investigation of path integration by exploring a laboratory homing task, on a holeboard maze, that mimics the natural foraging conditions of wild rats. It also raises the intriguing suggestion that the hippocampus has a specialized role in integrating vestibular signals with information coming from other sensory sources. In addition, it is proposed that dead reckoning is involved in the everyday behaviour of animals. It is shown that the hippocampus may be involved in dead reckoning. Data indicate that by providing a network for computing direction and distance, signals from other sensory systems could be coupled to a vestibular code to assist in dead reckoning and piloting. Moreover, it is believed that it is possible that dead reckoning can bridge new problem-solving that appears to depend upon piloting. In general, an ethological model of spatial behaviour in which dead reckoning plays a central role in allowing an animal to determine its present position, to return to a starting position, and to solve new spatial problems is proposed.

In Africa the literature on cultural models is rich in the analysis of the relationship between self, society and mind. A key concept that appear across Africa is ubuntu—the self as existing in relationship to the we. This and similar concepts are surveyed as they are employed as ways of conceptualizing the self in relationship to society as debated by African social scientists and particularly in the context of colonialism and outsider reports on ubuntu. Researchers are marked as outside researchers (those from Euro-American cultural area) and indigenous (African) scholars conducting research in Africa. Thus the colonial power dynamic is much in play in contemporary research on cultural models in Africa. Much of the earliest cultural model’s research was in Africa and this is presented as a baseline for the subsequent research. Studies of tribal groups and self-social-mind integration are presented. Issues of HIV/Aids and male and female prostitution are also examined in South Africa.

This chapter discusses the role played by Leonardo Fibonacci's Liber abbaci in introducing modern arithmetic to the West. In the prologue of Liber abbaci, Fibonacci says he learned the nine Indian numbers used in trade when traveling with his father, meeting merchants in Egypt, Syria, Greece, and Provence. He implies that the Indian numbers were new to the merchants and wrote that the “Latin race” was lacking knowledge of the Indian method of arithmetic. The question of who introduced and influenced the practice of reckoning with Indian numerals to Europe has no simple answer, but there is no doubt that it took place from the late tenth century onward. By the end of the eleventh century, news of the Indian number system was all over Europe in the form of counters of the Gerbertian abacus marked with Indian numerals.

This chapter calls to account the sentiment of liberated and liberating free-verse artistry through a reading of Stephen Crane's poetry that combines formal analysis (a counting or measurement) and ethical reckoning (a characterization of the lyric subject). More simply put, it is an effort to interpret, in the work of a very untraditional poet, his use of a very traditional poetic device—the refrain—to measure or mark out a timely sense of a depersonalized aesthetics. Timely, that is, not in terms of present critical anxieties about the aesthetic, but rather in terms of a late-nineteenth-century preoccupation, in literature, science, philosophy, and beyond, with the phenomenon of repetition, which is, of course, the precondition for any type of measurement and for any concept of the personal.

This chapter presents the author's reflections about her father. Born in China in 1928, her father had a wartime childhood that displaced him from Shanghai to Hong Kong, Burma, Yunnan, and Calcutta before arriving in the United States in 1945 at the age of sixteen. He was an intellectual historian and social theorist, who taught at several universities before settling into a career in the History Department at San Francisco State from 1968 until his retirement in 1992. Since he passed away in July 2009, a significant part of the author's mourning has involved thinking deeply about the questions of critique and inheritance, reckoning and responsibility. She now comprehends that her father's life and death as profoundly attentive, committed to this sense of critique, taking actions to resolve contradictions, even when those actions pronounced the realization of the impossibility of resolution.

This chapter explains how the star is used to find one's position on the Earth while in a ship at sea. Trigonometry was first used for navigation by fourteenth-century Venetian merchant ships. Several navigational techniques can be identified from navigators' personal notebooks, including the table of marteloio. Essentially an application of plane trigonometry, marteloio was part of a group of methods known today as “dead” reckoning. Between 1730 and 1759, a clockmaker by the name of John Harrison constructed a series of four chronometers that could keep remarkably accurate time, even on a ship tossed by waves. The chapter considers the use of the method of Saint Hilaire (also called intercept, cosine-haversine, or Davis's method) to determine three quantities of a star in an astronomical triangle: latitude, declination, and local hour angle. It also discusses the use of the Law of Cosines to solve the star's altitude.

Focusing on the very notion of a “sociology of time,” this chapter examines the fundamental components of what constitutes a distinctly non-physical, sociocultural perspective on temporality. It begins by introducing the notion of a pronouncedly artificial “sociotemporal order” consisting of social norms and traditions of measuring, reckoning, and organizing time. It then proceeds to discuss major ways of collectively experiencing time, such as the utilitarian view of time, the mathematical conception of time, and both the linear and circular views of temporality. The chapter concludes by examining both the semiotic and the political dimensions of the social organization of time.

This chapter explores the practice of reckoning. Reckoning is the process of engaging with media traces to better understand ourselves and the world around us. It examines the evidentiary nature of media traces. Drawing on Derrida's notion of the trace, it examines the ways in which media accounting allows us to both prove and improve ourselves. It discusses the ways that various media traces are used as evidence. The chapter draws on the GoPro camera and its community of YouTube users to demonstrate how everyday people create and share their videos to document and prove that something happened. It is also argued that reckoning comes from the aggregated nature of media accounting. The chapter examines various tensions that arise when our media traces do not align with our sense of selves and describes a reconciliation process that we engage in through media accounting.

The span of an international tribunal’s local impact is not the same as its operational life, as Germany’s evolved relationship with Nuremberg highlights. Recognizing that the ICTY’s impact in Bosnia and Serbia will continue to evolve after the Tribunal ends its work, this chapter considers the Tribunal’s future impact, focusing in particular on its potential to stimulate a future reckoning with Serbia’s wartime past. While recognizing myriad differences between post-Milošević Serbia and postwar Germany, this chapter explores factors behind the latter’s eventual emergence as a “model penitent” long after German society rejected the moral message the Allies hoped Nuremberg would impart. It suggests that, after an extended period of “transitional denial,” Nuremberg may have contributed to Germany’s far-reaching reckoning with the past through a process of delayed norm diffusion.

This chapter follows the story of calendar reform from the end of the twelfth to the end of the thirteenth century, showing how during this period the problem was popularized via two different categories of computus text: the pedagogically oriented ‘vulgar’ or ecclesiastical computus and the astronomically refined ‘philosophical’ computus. Authors whose contributions to the debate are looked at in greater detail include Alexander Neckam, John of Sacrobosco, Robert Grosseteste, Robert Holcot, Campanus of Novara, Giles of Lessines, and Roger Bacon, who is well known for having directed a reform appeal to Pope Clement IV (1265–8). Attention is also paid to an obscure group of Franciscan scholars active in the 1270s to 1290s, who are noteworthy for their knowledge of the Jewish calendar, and to an anonymous treatise of 1276, which contains the first fully developed proposal to restore the Roman calendar.

This chapter focuses on the first serious effort made within the medieval Latin Church to correct the calculation of Easter by legislative means. This effort took place at the court of Pope Clement VI in Avignon, who invited skilled astronomers such as Jean des Murs and Firmin de Beauval to assist him in a planned reform of the Golden Number. The chapter explores the background to this papal initiative and the contributions made by its various protagonists, focusing in particular on a recently discovered Expositio kalendarii novi written by the monk Johannes de Termis in 1345. It also takes a closer look at the parallel discussions that took place in the Byzantine East, where the prospect of a calendar reform was first raised by Nicephorus Gregoras in 1324.