In the third century b.c.e., Eratosthenes of Cyrene made a famous measurement of the circumference of the Earth. This was not the first such measurement, but it is the earliest for which significant details are preserved. Cleomedes gives a short account of Eratosthenes’ method, his numerical assumptions, and the final result of 250,000 stades. However, many ancient sources attribute to Eratosthenes a result of 252,000 stades. Historians have attempted to explain the second result by supposing that Eratosthenes later made better (...) measurements and revised his estimate or that the original result was simply rounded to 252,000 to have a number conveniently divisible by 60 or by 360. These explanations are speculative and untestable. However, Eratosthenes’ estimates of the distances of the Sun and Moon from the Earth are preserved in the doxographical literature. This essay shows that Eratosthenes’ result of 252,000 stades for the Earth’s circumference follows from a solar distance that is attributed to him. Thus it appears that Eratosthenes computed not only a lower limit for the size of the Earth, based on the assumption that the Sun is at infinity, but also an upper limit, based on the assumption that the Sun is at a finite distance. The essay discusses the consequences for our understanding of his program. (shrink)

Commentaries on the target article offer diverse perspectives on integrative experiment design. Our responses engage three themes: (1) Disputes of our characterization of the problem, (2) skepticism toward our proposed solution, and (3) endorsement of the solution, with accompanying discussions of its implementation in existing work and its potential for other domains. Collectively, the commentaries enhance our confidence in the promise and viability of integrative experiment design, while highlighting important considerations about how it is used.

This article analyzes the angular spacing of the degree marks on the zodiac scale of the Antikythera mechanism and demonstrates that over the entire preserved 88° of the zodiac, the marks are systematically placed too close together to be consistent with a uniform distribution over 360°. Thus, in some other part of the zodiac scale (not preserved), the degree marks have been spaced farther apart. By contrast, the day marks on the Egyptian calendar scale are spaced uniformly, apart from minor (...) errors. A solar equation of center is apparent which rises by nearly 2.7° over the preserved portion of the zodiac. The placement of the degree marks indicates that, in the preserved portion of the zodiac, the Sun was considered to run at a uniform pace of about 30° per synodic month, which is consistent with the Sun’s speed in the fast zone of the Babylonian solar theory of System A. (shrink)

The eclipse predictor (or Saros dial) of the Antikythera mechanism provides a wealth of astronomical information and offers practically the only possibility for a close astronomical dating of the mechanism. We apply a series of constraints, in a sort of sieve of Eratosthenes, to sequentially eliminate possibilities for the epoch date. We find that the solar eclipse of month 13 of the Saros dial almost certainly belongs to solar Saros series 44. And the eclipse predictor would work best if the (...) full Moon of month 1 of the Saros dial corresponds to May 12, 205 BCE, with the exeligmos dial set at 0. We also examine some possibilities for the theory that underlies the eclipse times on the Saros dial and find that a Babylonian-style arithmetical scheme employing an equation of center and daily velocities would match the inscribed times of day quite well. Indeed, an arithmetic scheme for the eclipse times matches the evidence somewhat better than does a trigonometric model. (shrink)

The following paper continues discussions within this journal about how the work of Delueze and Guattari can inform radical pedagogy. Building primarily on Noel Gough's 2004 paper, we take up the challenge to move towards a more creative form of 'becoming cyborg' in our teaching. In contrast to work that has focused on Deleuzian theories of the rhizome, we deploy Guattari's work on institutional schizoanalysis to explore the role of group creativity in radical pedagogy. The institutional therapies of Felix Guattari's (...) schizoanalytic practice in the 1950s and 1960s and, before him, the Francophone educationalist Celestin Freinet, who founded the Modern School Movement, are explored and used to illuminate examples of some of our own attempts to set the classroom up as a space for collective engagement. We conclude by exploring how this understanding of the class as subject group may be used to mobilise action and de-stabilise the coordinates of existing academic divisions of labour. (shrink)

This article explores the use of walking interviews as a research method. In spite of a wave of interest in methods which take interviewing out of the "safe," stationary environment, there has been limited work critically examining the techniques for undertaking such work. Curiously for a method which takes an explicitly spatial approach, few projects have attempted to rigorously connect what participants say with where they say it. The article reviews three case studies where the authors have used different techniques, (...) including GPS, for locating the interview in space. The article concludes by arguing that researchers considering using walking interviews need to think carefully about what kinds of data they wish to generate when deciding which approach to adopt. (shrink)

The dominant paradigm of experiments in the social and behavioral sciences views an experiment as a test of a theory, where the theory is assumed to generalize beyond the experiment's specific conditions. According to this view, which Alan Newell once characterized as “playing twenty questions with nature,” theory is advanced one experiment at a time, and the integration of disparate findings is assumed to happen via the scientific publishing process. In this article, we argue that the process of integration is (...) at best inefficient, and at worst it does not, in fact, occur. We further show that the challenge of integration cannot be adequately addressed by recently proposed reforms that focus on the reliability and replicability of individual findings, nor simply by conducting more or larger experiments. Rather, the problem arises from the imprecise nature of social and behavioral theories and, consequently, a lack of commensurability across experiments conducted under different conditions. Therefore, researchers must fundamentally rethink how they design experiments and how the experiments relate to theory. We specifically describe an alternative framework, integrative experiment design, which intrinsically promotes commensurability and continuous integration of knowledge. In this paradigm, researchers explicitly map the design space of possible experiments associated with a given research question, embracing many potentially relevant theories rather than focusing on just one. Researchers then iteratively generate theories and test them with experiments explicitly sampled from the design space, allowing results to be integrated across experiments. Given recent methodological and technological developments, we conclude that this approach is feasible and would generate more-reliable, more-cumulative empirical and theoretical knowledge than the current paradigm – and with far greater efficiency. (shrink)

By concentrating on abortion, the culture wars have avoided facing a crisis about the end of life. This paper explores four themes: (1) the technological transformation of birth and death into matters of decision, not matters of fact; (2) abortion as the nexus of Eros (sex) with Thanatos (death); (3) the real crisis, conveniently masked by our obsession with sex, looming at the end of life, not at its beginning; (4) the surplus-repression that protects us from assuming responsibility for choosing (...) between life and death. (shrink)

Introducing this issue’s triptych on algorithms and culture, this article argues that prevailing modes of analysis that focus on the prospects for algorithms “taking over” are no longer useful. It advocates the need for a new conceptual vocabulary, which recognizes that algorithmic and cultural reasoning processes are already enmeshed with each other. The introduction suggests a need for an enterprise of algorithmic epistemology attuned to the fine structure of the ways in which culture and code have interacted in the past (...) and continue to interact today. (shrink)