I offer a new objectivist theory of the contents of color language and color experience, intended especially as an account of what normal intersubjective variation in color perception and classification shows about those contents. First I explain an abstract account of the contents of color and other gradable adjectives; on the account, these contents are certain objective properties constituted in part by contextually intended standards of application, which are in turn values in the dimensions of variation associated with the adjectives. (...) Then I propose an explanation of normal variations in linguistic color classification; these are postulated to be effects of differences in intended standards for the color adjectives appearing in the classifying predicates. Next, I consider a potential objection to this explanation, based on the suggestion that contextual content should be more accessible than the explanation predicts. In reply, I point out that contextual content is occasionally opaque to unsophisticated reflection. Finally, I present a companion account of the contents of color experiences on which these represent an object as lying on certain salient intervals in the chromatic dimensions, and I show how the account accommodates intersubjective variation in color perception. (shrink)

It is shown constructively that a strongly extensional function of bounded variation on an interval is regulated, in a sequential sense that is classically equivalent to the usual one.

One of the major adaptations during the evolution of Homo sapiens was an increase in brain size. Here we present evidence that a significant and substantial proportion of variation in brain size may be related to changes in temperature. Based on a sample of 109 fossilized hominid skulls, we found that cranial capacities were highly correlated with paleoclimatic changes in temperature, as indexed by oxygen isotope data and sea-surface temperature. Indeed, as much as 52% of the variance in the cranial (...) capacity of these skulls could be accounted for by temperature variation at 100 ka intervals. As an index of more short-term seasonal fluctuations in temperature, we examined the latitude of the sites from which the crania originated. More than 22% of the variance in cranial capacity of these skulls could be accounted for by variation in equatorial distance. (shrink)

Objective: To analyse the time variation of topics in bioethical publications as a proxy of the relative importance.Methods: We searched the Medline database for bioethics publications using the words “ethics or bioethics”, and for 360 specific topics publications, associating Medical Subject Heading topic descriptors to those words. We calculated the ratio of bioethics publications to the total publications of Medline, and the ratio of each topic publications to the total bioethics publications, for five-year intervals, from 1970 to 2004. We calculated (...) the time variation of ratios, dividing the difference between the highest and lowest ratio of each topic by its highest ratio. Four topics were described, selected to illustrate different patterns of variation: “Induced Abortion”, “Conflict of Interest”, “Acquired Immunodeficiency Syndrome”, “Medical Education.”Results: The ratio of bioethics publications to total Medline publications increased from 0.003 to 0.012. The variation of the topic’s ratios was higher than 0.7 for 68% of the topics. The Induced Abortion ratios decreased from 0.12 to 0.02. Conflict of Interest ratios increased from zero to 0.07. The Acquired Immunodeficiency Syndrome ratios were nearly zero in the first three intervals, had a peak of 0.06 during 1985–9, followed by a decrease to 0.01. Medical Education ratios varied few, from 0.04 to 0.03.Conclusions: There was an increase of bioethical publications in the Medline database. The topics in bioethics literature have an important time variation. Some factors were suggested to explain this variation: current legal cases, resolution of the issue, saturation of a discussion and epidemiologic importance. (shrink)

In his book on P max [7], Woodin presents a collection of partial orders whose extensions satisfy strong club guessing principles on ω | . In this paper we employ one of the techniques from this book to produce P max variations which separate various club guessing principles. The principle (+) and its variants are weak guessing principles which were first considered by the second author [4] while studying games of length ω | . It was shown in [1] (...) that the Continuum Hypothesis does not imply (+) and that (+) does not imply the existence of a club guessing sequence on ω | . In this paper we give an alternate proof of the second of these results, using Woodin's P max technology, showing that a strengthening of (+) does not imply a weakening of club guessing known as the Interval Hitting Principle. The main technique in this paper, in addition to the standard P m a x machinery, is the use of condensation principles to build suitable iterations. (shrink)

The aim of this study was to test red - green dichromats' ability to discriminate between illuminant and surface-reflectance changes in natural scenes. Stimuli were simulations of natural scenes presented on a colour monitor with 10-bit resolution per gun. The natural scenes were obtained with a fast hyperspectral imaging system. Six different scenes (including rocks, foliage, and buildings) were tested. In each trial, two images were presented in sequence, each for 1 s, with no interval. The images differed in (...) the phase of daylight on the scene: first with correlated colour temperature 25 000 K, then 6 700 K. The spectral reflectance of a region in the second image was changed randomly, consistent with a local change in daylight. The observer's task was to decide whether a particular surface in the successive images was the same (pure illuminant change) or different (illuminant change with a surface-reflectance change). The performance of four deuteranopes and five protanopes varied considerably across the scenes tested, with mean colour constancy indices (± 1 SEM) of 0.48 (± 0.13) and 0.19 (± 0.10), respectively (1.0 representing ideal performance). Deuteranopes seemed less disadvantaged than protanopes, performing close to normal with some scenes. (shrink)

A very weak omniscience principle is formulated, related omniscience principlesare considered, and the theorem that a function of bounded variation is the difference of two increasing functions is shown to be equivalent to the omniscience principle WLPO. It is a so shown that an arbitrary function with located variation on an interval is the difference of two increasing functions.

Research on the perception of silence has led to insights regarding its positive effects on individuals. We conducted a series of studies during which individuals were exposed to several minutes of silence in different contexts. Participants were introduced to different social and environmental settings, either in a seminar room at a university or in a city garden, alone or in a group. Instructions across studies varied, as participants were exposed to real waiting situations, were asked to just think and to (...) explicitly experience the time interval without further instructions or following a session of Depth Relaxation Music Therapy (DRMT)/ Hypnomusictherapy (HMT). Silence was judged to significantly increase relaxation, improve mood states, and alter the perception of time and the orientation towards the present moment. We controlled for influences of trait variables, such as impulsivity, mindfulness, daydreaming, and time perspective. Findings empirically demonstrate that exposure to silence can be effective in therapeutic and educational contexts to promote relaxation and well-being. (shrink)

The problem of generalizing the power option-pricing model to incorporate more empirical features becomes an urgent and necessary event. A new power option pricing method is designed for the financial market uncertainty that simultaneously involves randomness and fuzziness. The randomness in market uncertainty is modeled by a time-fractional diffusion model, which describes trend memory in underlying asset prices. The fuzziness in market uncertainty is characterized by a triangular interval type-2 fuzzy numbers, which better captures the fuzziness of underlying asset (...) prices. Considering the decision-maker’s subjective judgment, we show the price mean value with the possibility-necessity weight and pessimistic-optimistic index under the type-2 fuzzy environment. We develop the power option pricing model with the time-fractional diffusion model and the triangular interval type-2 fuzzy numbers. Furthermore, the analytic solutions of pricing call power option and put power option are obtained and verified by the variational iterative reconstruction method. Our study shows that power option pricing, which adopts the time-fractional model and the triangular interval type-2 fuzzy numbers, can better capture the trend memory and double fuzziness of the real market. In addition, a numerical example is provided to illustrate that the power option means the value is decreasing with respect to the pessimistic-optimistic index and is fluctuating with respect to the possibility-necessity weight index. (shrink)

Understanding the functional mechanisms underlying genetic signals associated with complex traits and common diseases, such as cancer, diabetes and Alzheimer's disease, is a formidable challenge. Many genetic signals discovered through genome‐wide association studies map to non‐protein coding sequences, where their molecular consequences are difficult to evaluate. This article summarizes concepts for the systematic interpretation of non‐coding genetic signals using genome annotation data sets in different cellular systems. We outline strategies for the global analysis of multiple association intervals and the in‐depth (...) molecular investigation of individual intervals. We highlight experimental techniques to validate candidate (potential causal) regulatory variants, with a focus on novel genome‐editing techniques including CRISPR/Cas9. These approaches are also applicable to low‐frequency and rare variants, which have become increasingly important in genomic studies of complex traits and diseases. There is a pressing need to translate genetic signals into biological mechanisms, leading to prognostic, diagnostic and therapeutic advances. (shrink)

This paper consists of three main parts. First, we give an introduction to Hill’s assumption A (n) and to theory of interval probability, and an overview of recently developed theory and methods for nonparametric predictive inference (NPI), which is based on A (n) and uses interval probability to quantify uncertainty. Thereafter, we illustrate NPI by introducing a variation to the assumption A (n), suitable for inference based on circular data, with applications to several data sets from the literature. (...) This includes attention to comparison of two groups of circular data, and to grouped data. We briefly discuss such inference for multiple future observations. We end the paper with a discussion of NPI and objective Bayesianism. (shrink)

It is shown that in any model of constructive mathematics in which a certain omniscience principle is false, for strongly extensional functions on an interval the distinction between sequentially continuous and regulated disappears. It follows, without the use of Markov's Principle, that any recursive function of bounded variation on a bounded closed interval is recursively sequentially continuous.

This paper is the third of a multi-part examination of the Babylonian mathematical lunar theories known as Systems A and B. Part I (Britton, AHES 61:83–145, 2007) addressed the development of the empirical elements needed to separate the effects of lunar and solar anomaly on the intervals between syzygies, accomplished in the construction of the System A lunar theory early in the fourth century B.C. Part II (Britton, AHES 63:357–431, 2009) examines the accomplishment of this separation by the construction of (...) a successful theory depicting the variations due to lunar anomaly in System A and its subsequent adaptation in System B. The present paper examines the introduction of the uniform zodiac, necessary for any theory depicting variations depending on the position of syzygy. It addresses three questions: (1) In light of all available evidence, what is the magnitude of the constant term in the expression Δλ* = C − 1.3828°Y, describing the difference between the Babylonian sidereal longitudes and modern tropical longitudes? (2) What considerations governed the placement of the Babylonian sidereal zodiac relative to the fixed stars? (3) When was the uniform zodiac introduced? To the first question it finds C = 3.20° ± 0.1°, scarcely different from Huber’s (Centaurus 5:192–208, 1958) estimate of 3.08°, essentially confirming Huber’s result obtained from much less data. For the second it shows that accommodating the three asterisms comprising Taurus limited the placement of the zodiac to within 3°, while the prominence of half sign multiples among the measured intervals between prominent Normal Stars led irresistibly to the choice adopted. Finally, it finds that the zodiac was introduced between −408 and −397 and probably within a very few years of −400. (shrink)

In On Local Motion in the Two New Sciences, Galileo distinguishes between ‘time’ and ‘quanto time’ to justify why a variation in speed has the same properties as an interval of time. In this essay, I trace the occurrences of the word quanto to define its role and specific meaning. The analysis shows that quanto is essential to Galileo’s mathematical study of infinitesimal quantities and that it is technically defined. In the light of this interpretation of the word quanto, (...) Evangelista Torricelli’s theory of indivisibles can be regarded as a natural development of Galileo’s insights about infinitesimal magnitudes, transformed into a geometrical method for calculating the area of unlimited plane figures. (shrink)

Injuries in professional soccer are a significant concern for teams, and they are caused amongst others by high training load. This cohort study describes the relationship between workload parameters and the occurrence of non-contact injuries, during weeks with high and low workload in professional soccer players throughout the season. Twenty-one professional soccer players aged 28.3 ± 3.9 yrs. who competed in the Iranian Persian Gulf Pro League participated in this 48-week study. The external load was monitored using global positioning system (...) and the type of injury was documented daily by the team's medical staff. Odds ratio and relative risk were calculated for non-contact injuries for high- and low-load weeks according to acute, chronic, acute to chronic workload ratio, and AW variation values. By using Poisson distribution, the interval between previous and new injuries were estimated. Overall, 12 non-contact injuries occurred during high load and 9 during low load weeks. Based on the variables ACWR and Δ-AW, there was a significantly increased risk of sustaining non-contact injuries during high-load weeks for ACWR, and Δ-AW. Finally, the expected time between injuries was significantly shorter in high load weeks for ACWR [1.25 vs. 3.33, rate ratio time ] and Δ-AW respectively, compared to low load weeks. The risk of sustaining injuries was significantly larger during high workload weeks for ACWR, and Δ-AW compared with low workload weeks. The observed high OR in high load weeks indicate that there is a significant relationship between workload and occurrence of non-contact injuries. The predicted time to new injuries is shorter in high load weeks compared to low load weeks. Therefore, the frequency of injuries is higher during high load weeks for ACWR and Δ-AW. ACWR and Δ-AW appear to be good indicators for estimating the injury risk, and the time interval between injuries. (shrink)

Body expression and dance are activities that contribute to the integral well-being of people. In an educational context, the process of evaluating our students implies variations in their moods. This study tackles the states of mind that students perceive before and after the evaluation of a practice in the subject ofBody expression and dance, developed through choreographies, that were, previously rehearsed, and later presented to the rest of the class in a specific session. Our main interest was the obtention (...) of information on the states of mind of the students prior to the evaluation of their choreographies, and again once they had been performed. The study design consisted of two phases: two different choreographies separated by an interval of 2 months. The students were asked about their moods before and after performing their choreographies, which were evaluated. The participants, 167 in total, 35 women and 132 men, aged 18 to 22 years old, filled out a POMS questionnaire, before and after the evaluation of each occasion. Differences were found in the stress-anxiety, vigor-activity, fatigue-immobility scales and the total mood score. In all of them, except for the fatigue-immobility scale, we found a decrease in scores after the performance, compared to scores before. For the Stress-Anxiety factor, lower values were observed in the post-tests in comparison to the pre-tests, and also lower values in the pre- and post-test scores regarding the second choreography. We conclude that the practical evaluation of the subject through choreography modifies the mood states of the students, favoring their well-being after its execution, which is why evaluation through practice is considered a positive element in the educational process. (shrink)

The notion of Nash equilibrium in static oligopoly games is based on the assumption that each firm knows its entire demand curve (and, therefore, its entire profit function). It is much more likely, however, that firms only have some idea of the outcome of small price variations within some relatively small interval of prices. This is because firms can only learn their demand functions through price experiments and if they are risk-averse and/or have a low discount factor, they (...) will be unwilling to engage in extensive price experiments involving large variations in price. We can therefore expect firms to experiment through small price variations and stop when they reach a price such that no small deviation.. (shrink)

Continuous functions on the unit interval are relatively tame from the logical and computational point of view. A similar behaviour is exhibited by continuous functions on compact metric spaces equipped with a countable dense subset. It is then a natural question what happens if we omit the latter ‘extra data’, i.e., work with ‘unrepresented’ compact metric spaces. In this paper, we study basic third-order statements about continuous functions on such unrepresented compact metric spaces in Kohlenbach’s higher-order Reverse Mathematics. We (...) establish that some (very specific) statements are classified in the (second-order) Big Five of Reverse Mathematics, while most variations/generalisations are not provable from the latter, and much stronger systems. Thus, continuous functions on unrepresented metric spaces are ‘wild’, though ‘more tame’ than (slightly) discontinuous functions on the reals. (shrink)

Recent research has shown that mind wandering recruits executive resources away from the external task towards inner thoughts. No studies however have determined whether executive functions are drawn away in a unitary manner during mind wandering episodes, or whether there is variation in specific functions impacted. Accordingly, we examined whether mind wandering differentially modulates three core executive functions—response inhibition, updating of working memory, and mental set shifting. In three experiments, participants performed one of these three executive function tasks and reported (...) their attentional state as either on-task or mind wandering at random intervals. We found that mind wandering led to poorer performance in the response inhibition and working memory tasks, but not the set-shifting task. These findings suggest that mind wandering does not recruit executive functions in a monolithic manner. Rather, it appears to selectively engage certain executive functions, which may reflect the adaptive maintenance of ongoing task performance. (shrink)

In this series of papers, I attempt to provide an answer to the question how the Babylonian scholars arrived at their mathematical theory of planetary motion. Paper I (de Jong in Arch Hist Exact Sci 73:1–37, 2019) was devoted to a study of system A theory of the outer planets. In this second paper, I will study system A theory of the planet Venus. All presently known ephemerides of Venus appear to have been written after 200 BC so that the (...) development of system A theory of Venus may have been a late development. On the other hand, there are several earlier texts in which the motion of Venus, going from one synodic phenomenon to the next one, is parametrized in quite some detail. At least six computational systems of Venus are known of which only two, systems A0 and A3, are genuine type-A systems. Both are based on the hypothesis that in exactly 1151 years Venus experiences 720 synodic phenomena of the same kind and that after this period of 1151 years Venus returns to exactly the same position in the sky. This period relation was probably derived from the observational fact that after 8 years Venus returns to a position in the zodiac that falls on average 2.5° short of its previous position. The study of the Babylonian planetary theory of Venus presented here will be primarily based on the system A3 theory of Venus because it is the most complete of the two systems. The parameters of the four step functions characterizing the system A3 model of the first and last appearances of Venus are known from previous studies of tablet BM 32599 (ACT 1050). Based on a database of synthetic observations of the first and last appearances (morning first, morning last, evening first and evening last) and the two stationary points (morning station and evening station) of Venus between 315 BC and 50 BC, I first discuss the observational material from the point of view of a Babylonian astronomer. This involves deriving synodic time intervals and synodic arcs from the observed dates and longitudes of Venus. Both vary with the position of Venus in the zodiac. This variation shows up most purely in the synodic arcs and synodic time intervals of Venus at its stations. The variation pattern of the synodic arcs and of the synodic time intervals at the first and last appearances of Venus differ considerably because they are strongly affected by atmospheric extinction and by the ecliptic latitude of Venus. A comparison of predictions of the first and last appearances of Venus computed according to system A3 with observations in the synthetic database shows that the models provide fairly accurate fits to the observations of evening last and morning first with typical standard deviations of about 2° but rather poor fits to the observations of morning last and evening first with typical standard deviations of about 7° and 4°. Quite surprisingly, it turns out that the morning first A3 model fits the observed longitudes of Venus at its stations almost perfectly, with standard deviations of about 1°. This suggests that observations of the stations of Venus must have been available to the Babylonian astronomer(s) who constructed the system A3 model of Venus and who computed the longitudes of Venus at its first and last appearances preserved in tablet BM 32599. This is quite puzzling because observations of the stations of Venus were definitely not part of the standard observing program of the Babylonian astronomers as we know it from the Astronomical Diaries. To resolve this problem, I propose that observations could have been made by some individual astronomer for his own use but that these observations never became part of the tradition of what was regularly observed and recorded in the Astronomical Diaries. It turns out that 25 years of observations of Venus (here illustrated for the years 203 BC to 178 BC) is sufficient for the construction of a system A model that perfectly fits the variation of the synodic arcs of Venus at its stations. By combining observed time intervals and known velocities of Venus, observations over this limited timespan can also be used to construct longitudes of Venus at its first and last appearances from previous known positions of Venus based on Normal Stars passages or from known positions at its stations. This is the only way in which positions of Venus at its first and last appearances can be determined because at its first and last appearances the sky is too bright for Normal Stars to be visible. I propose that the Babylonian system A3 models of Venus were based on longitudes constructed in this way. I finally suggest that the tablet, of which BM 32599 is the remainder, was filled line by line starting with a set of initial values in the bottom left-hand corner of the tablet and that the choice of these initial values was based on an observation of Venus at its evening station when it was exceptionally close to the Normal Star η Piscium in February 179 BC. Based on this choice of initial conditions, the tablet covers the years 403 BC to 170 BC and it may have been composed around 170 BC. It was probably computed with the purpose of creating a raster of longitudes with mazes of about 2.5° that could be used to predict future positions of Venus at its first or last appearance once a position at a previous first or last appearance was available. (shrink)

This paper is the second of a multi-part examination of the creation of the Babylonian mathematical lunar theories known as Systems A and B. Part I (Britton 2007) addressed the development of the empirical elements needed to separate the effects of lunar and solar anomaly on the intervals between syzygies. This was accomplished in the construction of the System A lunar theory by an unknown author, almost certainly in the city of Babylon and probably early in the 4th century B.C. (...) The present paper focuses mainly on System A and the likely process of its construction. The first three sections are largely descriptive – first of the basic concepts which underlie the theory; then of the component schemes comprising the theory; and finally of two distinctive texts which suggest how the theory was constructed. The crux of the paper is Sect. 4, which describes how the theory seems likely to have been constructed. Here the crucial insight in separating the effects of lunar and solar anomaly appears to have been recognizing that – of all the measurable intervals bounded by eclipses – only 235 months exhibits a variation due solely to lunar anomaly, and that by means of an elegant mathematical model the amplitudes of 223 and 12 months could be deduced from its amplitude. The rest of the section describes the likely details of the derivation of the Φ ~ Λ scheme, and the extension of the methodology to the other components of the theory. It concludes with a demonstration that Φ and its dependent schemes were anchored through the Φ ~ W scheme to the syzygy on –403 Aug 18 (GN 7391) which concluded the shortest 6-month interval in the first 24 saros cycles since –746 (and in fact in the 900 years separating Nabonassar and Ptolemy). The next three sections address a number of largely technical details and amplifications of the theory, beginning with the schemes describing the variation of lunar velocity (column F) in Sect. 5. Section 6 addresses issues concerning the interpretation of Φ and the so-call Saros Text (BM 36705), while Sect. 7 discusses System B’s corresponding treatment of the effects of lunar anomaly, illustrating both its derivative nature and mathematically less rigorous structure. Section 8 examines the accuracy of the two theories, showing that the System A theory was both remarkably accurate and superior to System B. The final section offers some brief remarks on the power and elegance of the mathematical treatment of the problem by the author of System A. (shrink)

Cross-cultural studies have revealed broad quantitative associations between subsistence practice and demographic parameters for preindustrial populations. One explanation is that variationin the availability of suitable weaning foods influenced the frequency and duration of breastfeeding and thus the length of interbirth intervals and the probability of child survival (the “weaning food availability” hypothesis). We examine the available data on weaning age variation in preindustrial populations and report results of a cross-cultural test of the predictions that weaning occurred earlier in agricultural and (...) pastoral populations because dairy and cereal production increased the availability of easily digestible, nutrientrich foods appropriate for weaning. We found that, contrary to predictions, supplementation with liquid foods other than breast milk was delayed in agricultural populations relative to less agriculturally dependent ones and complementary feeding with solid foods was delayed in pastoral populations relative to those less dependent on herding. Although the duration of breastfeeding was longer in populations dependent on hunting, there was no qualitative evidence that such populations lacked foods appropriate for weaning. The patterns observed suggest that the relationships between demography and subsistence observed among preindustrial societies cannot be explained by the “weaning food availability” hypothesis. We discuss the implications for understanding the mechanisms underlying prehistoric human demography, subsistence shifts, allocation to parenting and mating effort, and the evolutionary implications of tradeoffs between diet and disease. (shrink)

Investigation of the 4 th order dynamic systems characteristic polynomials behavior in conditions of the interval parametric uncertainties is carried out on the basis of root locus portraits. The roots behavior regularities and corresponding diagrams for the root locus parameter distribution along the asymptotic stability bound are specified for the root locus portraits of the systems. On this basis the stability conditions are derived, graphic-analytical method is worked out for calculating intervals of variation for the polynomial family parameters ensuring (...) its robust stability. The discovered regularities of the system root locus portrait behavior allow to extract hurwitz sub-families from the non-hurwitz families of interval polynomials and to determine whether there exists at least one stable polynomial in the unstable polynomial family. (shrink)

The great revolutions of modern times have been analysed from various angles, but their civilizational aspects and contexts have on the whole been neglected. More specifically, the major 20th-century revolutions can be seen as particularly important cases of intercivilizational encounters. They represent different responses to the ascendant and challenging civilization of the West. The Western civilizational trajectory (or set of trajectories), based on a shift from fideism to empiricism and on multiple social dynamics fuelled by this cultural reorientation (such as (...) those of the capittalist economy and the one-nation-state), is selectively appropriated by non-Western societies which at the same time reject the less adaptable parts of the West in the name of traditional or invented alternatives. Russia, China, Turkey and Iran are analysed as variations of this recurrent pattern. At one end of the spectrum, the Russian revolution aspired to transcend Western models on the basis of a more radical interpretation of their own principles; at the other, the Iranian revolution, made up of several episodes with intervals in between, has been characterized by an exceptionally tenacious - and in some ways inventive - defence of a pre-existing civilizational identity. (shrink)

It has been recognized in the literature of the calculus of variations that the classical statement of the principle of least action (Hamilton's principle for conservative systems) is not strictly correct. Recently, mathematical proofs have been offered for what is claimed to be a more precise statement of Hamilton's principle for conservative systems. According to a widely publicized version of this more precise statement, the action integral for conservative systems is a minimum for discrete systems for small time intervals (...) only and is never minimum for continuous systems. In this paper, two contradictions to this “more precise” statement are demonstrated, one for a discrete system and one for a continuous system. (shrink)

Animals depleting one patch of resources must decide when to leave and switch to a fresh patch. Foraging theory has predicted various decision mechanisms; which is best depends on environmental variation in patch quality. Previously we tested whether these mechanisms underlie human decision making when foraging for external resources; here we test whether humans behave similarly in a cognitive task seeking internally generated solutions. Subjects searched for meaningful words made from random letter sequences, and as their success rate declined, they (...) could opt to switch to a fresh sequence. As in the external foraging context, time since the previous success and the interval preceding it had a major influence on when subjects switched. Subjects also used the commonness of sequence letters as a proximal cue to patch quality that influenced when to switch. Contrary to optimality predictions, switching decisions were independent of whether sequences differed little or widely in quality. (shrink)

The paper is a comparative study of the methodologies of Malthus and Ricardo. Its claims are: (i) economic laws almost always admit of exceptions for Malthus; for Ricardo even contingent predictions allow no exception apart from random temporary variations; (ii) both rely on the prestigious Newtonian paradigm, while interpreting it according to two distinct methodological traditions (the one deriving from MacLaurin, the other from Priestley); (iii) the choice of stressing what happens during intervals or in permanent states leads to (...) opposing definitions of the main problem of economic science in so far as equilibrium is always already given for Ricardo and is never given for Malthus; (iv) their use of the ambiguous notion of "tendency" leaves unclear for both the degree of predictive power with which theories are endowed; (v) what both share is the idea of a natural order and this idea is the source of both shortcomings and endless disagreement. -/- . (shrink)

Maintenance of proper health and prevention of diseases of civilization are now significant public health problems. Nutrition is an important factor in the development of youth, as well as the current and future state of health. The aim of the study was to show the benefits of the application of cluster analysis to assess the dietary habits of high school students. The survey was carried out on 1,631 eighteen-year-old students in seven randomly selected secondary schools in Bialystok using a self-prepared (...) anonymous questionnaire. An evaluation of the time of day meals were eaten and the number of meals consumed was made for the surveyed students. The cluster analysis allowed distinguishing characteristic structures of dietary habits in the observed population. Four clusters were identified, which were characterized by relative internal homogeneity and substantial variation in terms of the number of meals during the day and the time of their consumption. The most important characteristics of cluster 1 were cumulated food ration in 2 or 3 meals and long intervals between meals. Cluster 2 was characterized by eating the recommended number of 4 or 5 meals a day. In the 3rd cluster, students ate 3 meals a day with large intervals between them, and in the 4th they had four meals a day while maintaining proper intervals between them. In all clusters dietary mistakes occurred, but most of them were related to clusters 1 and 3. Cluster analysis allowed for the identification of major flaws in nutrition, which may include irregular eating and skipping meals, and indicated possible connections between eating patterns and disturbances of body weight in the examined population. (shrink)

Can the theory of conceptual spaces developed by Peter Gärdenfors and others be applied to moral issues? Martin Peterson argues that several moral principles can be construed as regions in a shared similarity space, but Kristin Shrader-Frechette and Gert-Jan Lokhorst question Peterson’s claim. They argue that the moral similarity judgments used to construct the space are underspecified and subjective. In this paper, we present new data indicating that moral principles can indeed be construed as regions in a multidimensional conceptual space (...) on the basis of moral similarity judgments. Four hundred and seventy-five students taking a course in engineering ethics completed a survey in which they were presented with ten cases featuring ethical issues related to technology and engineering. Participants were asked to judge the moral similarity of each pair of cases and to select which moral principle they believed should be applied for resolving the case. We used interval multidimensional scaling as well as individual differences scaling for analyzing the moral similarity judgments. Despite noteworthy individual variations in the judgments, the five moral principles included in the study were discernable in the aggregate multidimensional spaces, even for participants with no previous exposure to the principles. Participants tended to apply the same moral principles to cases rated as morally similar. Our overall conclusion is that moral similarity judgments, and their representation in multidimensional spaces, can help us identify moral principles that are relevant for assessing difficult moral choice situations. (shrink)

This paper presents a theoretical framework of the circular shift network coding system through the study of nonmultiple clustered interval music performance style conversion and the analysis of music conversion by using circular shift topology, and a series of basic research results of circular shift network coding is obtained under this framework. It reveals the essential connection between scalar network coding based on finite domain and cyclic shift network coding, designs a solution construction algorithm for cyclic shift network coding (...) under multicast network, and portrays the multicast capacity of cyclic shift network coding. It overcomes the problem that the piano roll-curtain representation cannot distinguish between a single long note and multiple consecutive notes of the same pitch, describes musical information more comprehensively, extracts musical implicit style from the note matrix based on autoencoder, and better eliminates the potential influence of musical content on musical performance style. A two-way recurrent neural network based on the gated recurrent unit is used to extract a sequence of note feature vectors of different styles, and a one-dimensional convolutional neural network is used to predict the intensity of the extracted note feature vector sequence for a specific style, which better learns the intensity variation of different styles of MIDI music. (shrink)

Objective Our objective was to evaluate whether those individuals with previous involvement with formal clinical ethics processes differ in their attitudes towards the resolution of prototypical clinical ethics cases than general health care professionals. We hypothesized that those individuals with previous participation in ethics consultation would have significantly different attitudes on the appropriate role of ethics committees in the assessment and resolution of clinical ethical dilemmas than those who have not. Methods We conducted a case-based survey of health care professionals (...) at six US hospitals. We administered the survey to health care professionals in a variety of clinical roles at each center and further sub-categorized these by respondents reporting or not reporting their membership on an ethics committee or participation as an ethics consultant/requestor of ethics consult services. Using the analysis of variance test, we present the variation in attitudes using a 5-point Likert scale with 95% confidence intervals and significance set at p ≤ 0.05. Results A total of 240 respondents completed the survey (response rate: 63.6%) from all six surveyed centers (128 respondents with involvement with ethics consultation, 112 respondents without). Health care professionals not previously involved with formal clinical ethics processes were less likely to view the ethics committee as having a role in resolving the presented clinical ethical dilemmas ( p = 0.01 for analysis of variance comparison). Conclusion In this multi-center survey study, health care providers without previous involvement with formal clinical ethics processes were less likely than those with previous involvement to support a role for ethics committees aiding in ethical case resolution. (shrink)

In 1969 the American avant-garde filmmaker Ken Jacobs gained wide recognition with a two-hour long interpretation of a 1905 silent short film. Ever since, the artist has kept on revisiting the same material, each time with a different technological approach. Originally hailed as a prime example of structural filmmaking, Jacobs’ more recent variations on the theme of Tom Tom the Piper’s Son beg for a broader understanding of his methods and the meanings implied. To gain a deeper insight in (...) this on-going mise-en-abyme, this essay expands comments by the artist himself with concepts taken from animation, media-archaeology and Warburg’s Mnemosyne atlas. Rereading a filmic text with minute attention, remediating it from an analogue to an electronic format, and reanimating the original action by adding a variety of intervals: all Jacobs’ strategies are aimed at demonstrating the afterlife of Tom Tom in a contemporary cultural context. (shrink)

Epidemiological studies have confirmed that long-term exposure to road traffic noise can cause cardiovascular diseases, and when noise exposure reaches a certain level, the risk of related CDs significantly increases. Currently, a large number of Chinese residents are exposed to high noise exposure, which could greatly increase the risk of cardiovascular disease. On the other hand, relevant studies have found that people with high noise sensitivity are more susceptible to noise. And it is necessary to pay more attention to the (...) high noise-sensitive people. This study investigated the acute physiological effect of different noise-sensitive groups by indoor-level noise stimulus experiments under laboratory conditions, by observing heart rate variability indicators, including standard deviation of NN intervals, low frequency/high frequency, and heart rate. The results showed that there was no significant difference in HRV between the high-sensitive group and the low-sensitive group at the physiological baseline and the different stimulating noise levels. Then, based on the theory of cumulative effect of noise proposed by WHO Regional Office for Europe, non-significant but observable differences between groups were further discussed. By analyzing differences of the variation trends and the within-group significant changes of SDNN and HR between the two groups, the results tended to show that the high-sensitive group is more affected by road traffic noise. In addition, the values of SDNN and HR showed observable between-group differences at 55 dB and 65 dB which corresponding to the SPL associated with a significantly increased risk of cardiovascular disease concerned by epidemiological studies. According to the cumulative effect theory, these differences in HRV caused by short-term noise stimulation may have the potential to produce physiological response and lead to between-groups differences in prevalence after long-term recurrent effect, and deserve attention and further research. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:323 A DEFENSE OF HUME ON IDENTITY THROUGH TIME A durable complaint against Hume is that he blatantly begs the question in his Treatise account of our acquisition of the idea of identity through time. Green and Grose made the accusation in 1878; one hundred years later Stroud echoed the same accusation, its force and liveliness seemingly undiminished. I suggest that this accusation is based on a tempting but (...) unwarranted assumption about Humean perceptions. It is unwarranted despite Price's arguments for it. When the assumption is corrected Hume is exonerated. This defense prepares the way for a new understanding of Hume's subtle and important theory of identity. Clarifying his theory is the goal; defending him is the means. I will merely summarize the Green and Grose interpretation, saving detailed examination for Stroud's. Stroud's version seems more tightly argued for and spares one the problems of interpreting commentators from a different philosophical tradition. Green and Grose run together Hume's account of the acquisition of the idea of identity, with his account of the application of that idea to a succession of related perceptions. This fully intended confusion can be explained by their understanding of Hume's claim that "impressions are... perishing existences." (T 194) They assume that for Hume no perception (impression or idea) is a unity if it exists at an interval of time composed of a succession of times. Rather the perception is really a succession of perceptions. Their assumed interpretation makes Hume seem to them to beg the question as follows: To acquire the idea of identity through time is to acquire the idea of something 324 which is unitary and exists at a succession of times. But any impression which might give this idea is really a succession of related impressions. A succession of related impressions can convey the idea of identity only by being confused with a unitary impression which exists at a succession of times. Such confusion would be possible only for someone who already had the idea of something unitary which exists at a succession of times. So the idea of 2 identity can be acquired only if it is already had. In other words, Hume claims that an impression had for a relatively long time gives the idea of identity. Any long impression is really a succession. A succession can give the idea of identity only if it is confused with something that has identity. That confusion requires the idea of identity already. So Hume begs the question. There are gaps in this argument. But its influence has been important and its structure is clear: If we assume that perceptions are exceedingly brief, then Hume begs the question. (I will call the assumption 'the prosecution's assumption.') Stroud's argument that Hume begs the question has the same structure, or so I will argue. The role of the prosecution's assumption is not immediately apparent, but it is a crucial role. Stroud's accusation is as follows: By Hume's definition, identity is the invariableness and uninterruptedness of an object through a supposed change in time. (T 201) However, on Hume's account of acquiring the concept of identity, the acquisition involves imagining a change in time without any variation or interruption in an object. But that just ¿s, by definition, to imagine the object's identity through the change in time. So acquiring the concept of identity requires an act of imagination involving the 325 concept of identity. So, Stroud concludes, on Hume's account the concept of identity can be acquired only 3 if it is had. Hume's account begs the question. I think it is usually unwise to attribute blunders to subtle thinkers. I will not do it to Hume, nor to his commentators. I will argue that what Hume presupposes in explaining identity through time is a little different from identity through time. Thus the presupposition is not question-begging. More specifically, I will argue that Hume distinguishes three technical concepts, three ways to take up time: (i) merely occupying an interval of time, (ii) having duration for an interval of time, and (iii) being identical through an interval of time. Concept (iii... (shrink)

We consider two scenarios of the Hotelling–Downs model of spatial competition. This setting has typically been explored using pure Nash equilibrium, but this paper uses point rationalizability (Bernheim, Econometrica J Economet Soc 52(4):1007–1028, 1984) instead. Pure Nash equilibrium imposes a correct beliefs assumption, which may rule out perfectly reasonable choices in a game. Point rationalizability does not have this correct beliefs assumption, which makes this solution concept more natural and permissive. The first scenario is the original Hotelling–Downs model with an (...) arbitrary number of agents. Eaton and Lipsey (Rev Econ Stud 42(1):27–49, 1975) used pure Nash equilibrium as their solution concept for this setting. They showed that with three agents, there does not exist a pure Nash equilibrium. We characterize the set of point rationalizable choices for any number of agents and show that as the number of agents increases, the set of point rationalizable choices increases as well. In the second scenario, agents have limited attraction intervals (Feldman et al. Variations on the Hotelling–Downs model. In: Thirtieth AAAI Conference on Artificial Intelligence, pp 496–501, 2016). We show that the set of point rationalizable choices does not depend on the number of agents, apart from this number being odd or even. Furthermore, the set of point rationalizable choices shrinks as the attraction interval increases. (shrink)

In this series of papers, I attempt to provide an answer to the question how the Babylonian scholars arrived at their mathematical theory of planetary motion. Paper I (de Jong in Arch Hist Exact Sci 73:1–37, 2019) was devoted to a study of system A theory of the outer planets. In this second paper, I will study system A theory of the planet Venus. All presently known ephemerides of Venus appear to have been written after 200 BC so that the (...) development of system A theory of Venus may have been a late development. On the other hand, there are several earlier texts in which the motion of Venus, going from one synodic phenomenon to the next one, is parametrized in quite some detail. At least six computational systems of Venus are known of which only two, systems A0 and A3, are genuine type-A systems. Both are based on the hypothesis that in exactly 1151 years Venus experiences 720 synodic phenomena of the same kind and that after this period of 1151 years Venus returns to exactly the same position in the sky. This period relation was probably derived from the observational fact that after 8 years Venus returns to a position in the zodiac that falls on average 2.5° short of its previous position. The study of the Babylonian planetary theory of Venus presented here will be primarily based on the system A3 theory of Venus because it is the most complete of the two systems. The parameters of the four step functions characterizing the system A3 model of the first and last appearances of Venus are known from previous studies of tablet BM 32599 (ACT 1050). Based on a database of synthetic observations of the first and last appearances (morning first, morning last, evening first and evening last) and the two stationary points (morning station and evening station) of Venus between 315 BC and 50 BC, I first discuss the observational material from the point of view of a Babylonian astronomer. This involves deriving synodic time intervals and synodic arcs from the observed dates and longitudes of Venus. Both vary with the position of Venus in the zodiac. This variation shows up most purely in the synodic arcs and synodic time intervals of Venus at its stations. The variation pattern of the synodic arcs and of the synodic time intervals at the first and last appearances of Venus differ considerably because they are strongly affected by atmospheric extinction and by the ecliptic latitude of Venus. A comparison of predictions of the first and last appearances of Venus computed according to system A3 with observations in the synthetic database shows that the models provide fairly accurate fits to the observations of evening last and morning first with typical standard deviations of about 2° but rather poor fits to the observations of morning last and evening first with typical standard deviations of about 7° and 4°. Quite surprisingly, it turns out that the morning first A3 model fits the observed longitudes of Venus at its stations almost perfectly, with standard deviations of about 1°. This suggests that observations of the stations of Venus must have been available to the Babylonian astronomer(s) who constructed the system A3 model of Venus and who computed the longitudes of Venus at its first and last appearances preserved in tablet BM 32599. This is quite puzzling because observations of the stations of Venus were definitely not part of the standard observing program of the Babylonian astronomers as we know it from the Astronomical Diaries. To resolve this problem, I propose that observations could have been made by some individual astronomer for his own use but that these observations never became part of the tradition of what was regularly observed and recorded in the Astronomical Diaries. It turns out that 25 years of observations of Venus (here illustrated for the years 203 BC to 178 BC) is sufficient for the construction of a system A model that perfectly fits the variation of the synodic arcs of Venus at its stations. By combining observed time intervals and known velocities of Venus, observations over this limited timespan can also be used to construct longitudes of Venus at its first and last appearances from previous known positions of Venus based on Normal Stars passages or from known positions at its stations. This is the only way in which positions of Venus at its first and last appearances can be determined because at its first and last appearances the sky is too bright for Normal Stars to be visible. I propose that the Babylonian system A3 models of Venus were based on longitudes constructed in this way. I finally suggest that the tablet, of which BM 32599 is the remainder, was filled line by line starting with a set of initial values in the bottom left-hand corner of the tablet and that the choice of these initial values was based on an observation of Venus at its evening station when it was exceptionally close to the Normal Star η Piscium in February 179 BC. Based on this choice of initial conditions, the tablet covers the years 403 BC to 170 BC and it may have been composed around 170 BC. It was probably computed with the purpose of creating a raster of longitudes with mazes of about 2.5° that could be used to predict future positions of Venus at its first or last appearance once a position at a previous first or last appearance was available. (shrink)

From the end of the First World War, a broad discussion took place within the framework of the revived German constitutional teaching on the question of the physical normality of man. The founder of the so-called statistical concept of normality, which preceded the still widespread normal (reference) interval concept, is H. Rautmann, who gave it the character of a tool for discriminating between health and disease. Among some of his successors (Bauer, Borchardt, Günther), however, it was considered more a (...) means of establishing a type, without supposing any precise relation between the frequency of a character in the population and the probability of the occurrence of disease. The concept of a statistical norm as a certain region of the variation range of a character determined by the parameters of Gaussian distribution was criticized both by the supporters of the ideal norm (Hildebrandt) and those who were in favour of a ‘personal’ norm (Grote). The underlying motifs of these three conceptions of normality influenced German constitutional doctrine until after the end of the Second World War, but without a satisfactory solution to the diagnosis of physical normality being found. Since the 1950s, world medicine has moved more and more in the direction of prevention, with the emphasis on a study of individual dispositions to disease and its precursors. In this connection a new view of health has gained importance whereby it is considered a smoothly gradated condition, not sharply distinguished from disease (‘continual’ model of health and disease as opposed to the previous ‘alternative’ model). The purpose of diagnostic characters is no longer merely to place patients in clearly defined categories as healthy or affected by one disease or another, but has taken on the function of indices of the disposition to disease among those who exhibit ‘gross normality’. Discrimination between the alternative and continuous models allows a clarification to be made of the sources of the confusion in which the pre-war concept of statistical normality had found itself. Today many exceptions are known to the rule that the functional optimum lies in the region of the population mean, both for the population as a whole and for individuals; and immense variability has been found in the manner in which individuals in the population attain health. Thus a distinction between health and disease by statistical means alone (such as establishing some sort of species design) is not possible at all. The ideal of a personal norm is pursued today through the concept of a multivariate norm backed up by modern data processing methods, though it was anticipated in principle by Kaup even in the 1920s. CiteULike Connotea Del.icio.us What's this? (shrink)

continent. 1.2 (2011): 78-91. This article consists of three parts. First, I will review the major themes of Quentin Meillassoux’s After Finitude . Since some of my readers will have read this book and others not, I will try to strike a balance between clear summary and fresh critique. Second, I discuss an unpublished book by Meillassoux unfamiliar to all readers of this article, except those scant few that may have gone digging in the microfilm archives of the École normale (...) supérieure. The book in question is Meillassoux’s revised doctoral dissertation L’Inexistence divine (or The Divine Inexistence ), with its seemingly bizarre vision of a God who does not yet exist but might exist in the future. Without literally accepting this view, I will claim that it is philosophically interesting in ways that even a hardened sceptic might be able to appreciate. Third and finally, I will speculate on the possible future of Meillassoux’s speculative materialism itself. And here I mean its future development not by Meillassoux, but by those readers who might be inspired by his book. Plato could never have predicted the emergence of Aristotle’s philosophy, despite the obvious debt of the latter to the former. Nor could Descartes have predicted Spinoza and Leibniz, nor Kant the German Idealists, and neither could Husserl in 1901 have foreseen the later emergence of Heidegger. How are the works of interesting philosophers transformed by later thinkers of comparable importance? While it may seem that there are countless ways to do this, I think there are only two basic ways in which this happens: you can radicalize your predecessors, or you can reverse them. I will close this article with a few words about these two methods, and try to imagine how Meillassoux might be radicalized or reversed by some future admirer. My view is that the more important thinkers are, the easier they are to radicalize or reverse. This helps explain why the great philosophers of the West have so often appeared in clusters, succeeding one another at relatively brief intervals during periods of especial ferment. 1. After Finitude After Finitude is unusually short for such an influential book of philosophy: running to just 178 pages in the original French, and an even more compact 128 pages in the English version, despite the introduction of roughly eight pages of new material for the English edition. Rather than summarizing Meillassoux’s book in the order he intended, I will focus on six points that strike me as the pillars of his debut book. Along the way, I will offer a few criticisms as well. The first pillar of the book is Meillassoux’s own term “correlationism.”1 Although he introduces this term as the name for an enemy, it is striking that Meillassoux remains impressed by correlationism much more than his fellow speculative realists are. This continued appreciation for his great enemy influences the shape of his own ontology. Is there a world outside our thinking of it, or does the world consist entirely in being thought? Traditionally, this dispute between realism and idealism has been dismissed in continental philosophy as a “pseudo-problem,” in a strategy pioneered by Husserl and extended by Heidegger. We cannot be realists, since following Kant we have no direct access to things-in-themselves. But neither are we idealists, since the human being is always already outside itself, aiming at objects in intentional experience, deeply engaged with practical implements, or stationed in some particular world-disclosing mood. The centuries-old dispute between realism and idealism is dissolved by saying that we cannot think either real or ideal in isolation from the other. There is neither human without world nor world without human, but only a primordial correlation or rapport between the two. This is what “correlationism” means: philosophy trapped in a permanent meditation on the human-world correlate, trying to find the best model of the correlate: is it language, intentionality, embodiment, or some other form of correlation between human and world? Among other problems, this generates some friction between philosophy and the literal meaning of science. When cosmologists say that the universe originated 13.5 billion years ago, they do not mean “13.5 billion years ago for us ,” but literally 13.5 billion years ago, well before conscious life existed, and thus at a time when there was no such thing as a correlate. Meillassoux also coins the term “ancestrality” (10) for the reality that predated the correlate, and later expands this term to “dia-chronicity,” (112) to refer to events occurring after the extinction of human beings no less than to those occurring before we existed. Up to this point, Meillassoux’s focus on ancestral entities existing prior to consciousness might seem like a straightforward realist who wants to unmask correlationism as just another form of idealism. Yet Meillassoux also admires the correlationist maneuver, which can obviously be traced back to Kant. Unlike a thinker such as Whitehead, Meillassoux feels no nostalgia for the pre-critical realism that came before Kant: “we cannot but be heirs of Kantianism,” he says (29). What impresses Meillassoux about correlationism is something both simple and familiar. If we attempt to think a tree outside thought, this is itself a thought . Any form of realism which thinks it can simply and directly address the world the way it is fails to escape the correlational circle, since the attempt to think something outside of thought is itself nothing other than a thought, and thereby collapses back into the very human-world correlate that it pretends to escape. For Meillassoux this step, suggested by Kant but first refined by the ensuing figures of German Idealism, marks decisive forward progress in the history of philosophy that must not be abolished. Any attempt to break free from the correlate must first acknowledge its mighty intellectual power. Realist though he may seem, Meillassoux’s works are filled with praise of such figures as Fichte and Hegel, not of so-called “naïve realists.” It is also the case that for Meillassoux, not all correlationisms are the same. The second pillar of his book is a distinction between various positions that I have termed “Meillassoux’s Spectrum,” though of course he is never so immodest as to name it after himself. He distinguishes between at least six different possible positions, and perhaps we could add even subtler variations if we wished. But in its simplest form, Meillassoux’s Spectrum allows for just four basic outlooks on the question of realism vs. anti-realism. Three of these are easy to understand, since we have already been discussing them. At one extreme is so-called “naïve realism,” which holds that a world exists outside the mind, and that we can know this world. Meillassoux rejects this naïve realism as having been overthrown by Kant’s critical philosophy. At the other extreme is subjective idealism, in which nothing exists outside the mind. For to think a dog outside thought immediately turns it into a thought, and therefore there cannot be anything outside; the very notion is meaningless. In between these two is what we have called correlationism. And here comes a crucial moment for Meillassoux, since he distinguishes between the two forms of “weak” and “strong” correlationism, and chooses the strong form as the launching pad for his own philosophy. Weak correlationism is easy to explain, since we all know it from the philosophy of Kant. The things-in-themselves can be thought but not known. They certainly must exist, since there cannot be appearances without something that appears. And we can think about them, which idealism holds to be impossible. They are simply unknowable due to the finitude of human thought. Strong correlationism is the new position introduced by Meillassoux (though he sees it at work in numerous twentieth century thinkers), midway between weak correlationism and subjective idealism. The major difference between the three positions is as follows. Weak correlationism says: “The things-in-themselves exist, but we cannot know them.” The subjective idealist says: “This is a contradiction in terms, since when we think the things-in-themselves, we already turn them into thoughts.” But the strong correlationist says: “Just because ‘things-in-themselves’ is a meaningless notion does not mean that they cannot exist. No one has ever traveled to the world-in-itself and come back to make a report on it. Thus, the fact that we cannot think things-in-themselves without contradiction does not prove that they do not exist anyway. There may be things-in-themselves, we simply are not capable of thinking them without contradiction form within the correlational circle.” This step is crucial for Meillassoux, since strong correlationism is the position he attempts to radicalize into his own new standpoint: speculative materialism. As I see it, this step of the argument fails. Strong correlationism cannot avoid collapsing into subjective idealism, since the statements of the strong correlationist are rendered meaningless from within. All three of the other positions in the Spectrum make perfectly good sense even for those who disagree with them. The naïve realist says that things-in-themselves exist and we can know them; the meaning of this statement is clear. The weak correlationist can say that things-in-themselves exist but lie forever beyond our grasp; this too makes perfect sense, even though the German Idealists try to show a contradiction at work here. We can also understand the claim of the subjective idealist that to think anything outside thought turns it into a thought, and that for this reason we cannot think the unthought. The strong correlationist, alone among the four, speaks nonsense . This person says “I cannot think the unthought without turning it into a thought, and yet the unthought might exist anyway.” But notice that the final phrase “the unthought might exist anyway” is fruitless for this purpose. For we have already heard that to think any unthought turns it into a thought. But now the strong correlationist wants to do two incompatible things simultaneously with this unthought. On the one hand, he neutralizes the unthought by showing that it instantly changes into just another thought. But on the other hand, he wants to appeal to the unthought as a haunting residue that might exist outside thought, thereby undercutting the absolute status of the human-world correlate found in idealism. But this is impossible. If you accept the argument that thinking the unthought turns it into a thought, you cannot also add “but maybe there is something outside that prevents this conversion from being absolutely true,” because this “something outside” is immediately converted into nothing but a thought for us. In short, Meillassoux here seems to be offering a kind of Zen koan: his “strong correlationism” is reminiscent of the gateless gate, or the sound of one hand clapping, or the command to punch Hegel in the jaw when meeting him on the road. We cannot at the same time both destroy the realist challenge of the things-in-themselves in order to undercut realism and reintroduce that very realist sense in order to undercut idealism. In a world where everything is instantly converted into thought, we cannot claim that there might be something extra-mental anyway, because this “might be something” is itself converted into a thought by the same rules that condemned dogs, trees, and houses to the idealist prison. This brings us to the third pillar of Meillassoux’s argument, which is the key to all the rest: the necessity of contingency. His strategy is to transform our supposed ignorance of things-in-themselves into an absolute knowledge that they exist without reason, and that the laws of nature can change at any time for no reason at all. In this way the cautious agnosticism of Kantian philosophies is avoided, but so is the collapse of reality into thought as found in German Idealism. Meillassoux does try to prove the existence of things-in-themselves existing outside thought; he simply holds that they must be proven after passing through the rigors of the correlationist challenge, not just arbitrarily decreed to exist in the manner of naïve realism. As he puts it, “Everything could actually collapse: from trees to stars, from stars to laws, from physical laws to logical laws; and this not by virtue of some superior law whereby everything is destined to perish, but by virtue of the absence of any superior law capable of preserving anything, no matter what, from perishing” (53). If idealism thinks that the human-world correlate is absolute, for Meillassoux it is the facticity of the correlate that is absolute. He tries to show this with a nice brief dialogue between five separate characters (55-59) which is covered in detail in my forthcoming book,2 but which I will simplify here for reasons of time. In this simplified version, we first imagine a dogmatic realist arguing with a dogmatic idealist. The realist says that we can know the truth about the things-in-themselves; the idealist counters that we can only the truth about thought, since all statements about reality must be turned into statements concerning our thoughts about reality. Here the correlationist enters and proclaims that both of these positions are equally dogmatic. For although we have access to nothing but thoughts, we cannot be sure that these thoughts are all that exist; there could be a reality outside thought, there is simply no way to know for sure. And this latter position is the one that Meillassoux attempts to transform from an agnostic, skeptical point into an ontological claim about the contingency of everything. Consider it this way. How does the correlationist defeat the idealist? The idealist holds that the existence of anything outside thought is impossible. The correlationist, by contrast, holds that something might exist outside the human-world correlate. But this “something might” has to be an absolute possibility. It cannot mean that “something outside thought might exist for thought ,” because that is what the idealist already says. No, the correlationist must mean that something might exist outside thought quite independently of thought. In other words, the correlationist says that idealism might be wrong, and this means it is absolutely true that idealism might be wrong. Thus, correlationism is no longer just a skeptical position. It holds that all the possibilities of the world are absolute possibilities. We have absolute knowledge that any of the possibilities about the existence or non-existence of things-in-themselves might be true, and this means that correlationism flips into Meillassoux’s own position: speculative materialism. As Meillassoux sees it, there are only two options here. Option A is to absolutize the human-world correlate, which is what the idealist does: there absolutely cannot be anything outside thought. Option B, by contrast, is to absolutize the facticity of the correlate: its character of simply being given to us, without any inherent necessity. The correlationist cannot have it both ways by saying: “there absolutely might be something outside thought, yet maybe this is absolutely impossible.” In other words, once we escape dogmatism we can only be idealists or speculative materialists, not correlationists. The human-world correlate is merely a fact, not an absolute necessity. But this facticity itself cannot be merely factical: it must be absolute. Here Meillassoux coins the French neologism factualité , which has been suitably translated into the English neologism “factiality.” (7, 122-3) Factialty means that for everything that exists, it is absolutely possible that it might be otherwise, not just that we cannot know whether or not it might be otherwise. Just as Kant transformed philosophy into a meditation on the categories governing human finitude, Meillassoux wishes to turn philosophy into a meditation on the necessary conditions of factiality, which he calls “figures”—a new technical term for him. (80) One such figure is that the law of non-contradiction must be true, and for an unusual reason. Since everything is proven to be contingent, nothing that exists can be contradictory, for whatever is contradictory has no opposite into which it might be transformed, and thus contingency would be impossible.3 Another such figure is that there must be something rather than nothing: for since contingency exists, something must exist in order to be contingent. It is a daring high-wire act, one that sacrifices realism to the correlational circle in order to rebuild it from out of its own ashes. Some might conclude that the lack of reason in things is a byproduct of the ignorance of finite humans, Meillassoux is making precisely the opposite point. For in fact, the doctrine of finitude usually leads directly to belief in a hidden reason. The fact that it lies beyond human comprehension merely increases our belief in this arbitrarily chosen concealed ground. By defending anew the concept of absolute knowledge Meillassoux evacuates the world of everything hidden. The reason for things having no reason is not that the reason is hidden, but that no reason exists. Thus, even while insisting on the necessity of non-contradiction, he rejects the other Leibnizian principle: sufficient reason. Everything simply is what it is, in purely immanent form, without deeply hidden causes. Or as Meillassoux puts it: “There is nothing beneath or beyond the manifest gratuitousness of the given—nothing but the limitless and lawless power of its destruction, emergence, or persistence” (63).The world is a “hyper-chaos”(64). But this is not the same thing as flux. For the chaos of the world is such that stability might occur just as easily as constant, turbulent change. Let’s now digress a bit, and return to the question of ancestrality, which Meillassoux transforms later in the book into “dia-chronicity.” Correlationism holds that all talk of a world outside the correlate is immediately recuperated by the correlate. The phrase “13.5 billion years ago” becomes “13.5 billion years ago for us ,” and the phrase “the universe following the extinction of humans” becomes “the universe following the extinction of humans for humans .” But notice that whether we talk about the world before or after humans, in both cases it is time that is used to challenge the correlate. Meillassoux has no interest in challenges that might be posed by space. For example, what about a vase in a lonely country house that topples to the floor and smashes when no one is there to watch it? Isn’t this also a challenge to correlationism, no less than the Big Bang or the heat death of the universe long after humans have vanished? In an eight-page supplement to the English translation of After Finitude ,4 possibly in response to my own 2007 review of the French original,5 Meillassoux bluntly denies that space is of any relevance to the question. Spatial distance is a merely harmless challenge to the human-world correlate. After all, even though no one is there in the lonely country house to witness the shattering of the vase, we can say that had there been an observer , that observer would have witnessed the toppling and destruction of the vase. For this event still occurs in a world in which the human-world correlate already exists, whereas the diachronicity of events both before and after the existence of humans makes it impossible to say that had there been an observer they would have witnessed the Big Bang occurring in such and such a fashion. However, it seems to me that Meillassoux merely asserts that the temporal simultaneity of our existence with that of the vase in the lonely country house is enough to render it harmless. It is true that the house does not exist prior to the correlate, but nonetheless it exists outside the correlate, and that is enough to make the same challenge. It is difficult to see why the “had there been an observer” maneuver succeeds in the case of a vase in the countryside in April 2011 but fails in the case of the Big Bang. This is not just a matter of nitpicking Meillassoux’s argumentative style: the fact that he bases his argument on time has at least two important consequences for his position. For in the first place, even though Meillassoux insists that the laws of nature are absolutely contingent, this turns out to be true only in a temporal sense. That is to say, it is a paradoxical feature of Meillassoux’s philosophy that he does allow for the existence of laws of nature, and simply believes that they can change at any moment without reason. Within any given moment, laws of nature do exist. He never suggests that different parts of the universe can have different laws at the same time, nor does he have any interest in the laws of part/whole composition that take place within any given instant. Could it be the case that rather than being made of gold atoms, a small chunk of gold could be made of silver atoms, cotton, horses, or that this same small piece of gold could be made of gigantic vaults filled with even more gold? These are not topics that draw Meillassoux’s attention, since he is focused solely on how the laws of nature might change or endure from one moment to the next . Another implication for Meillassoux’s system is that his concept of things-in-themselves turns out to be to be inadequate. For when he proves that things-in-themselves can exist without humans, this turns out to be true only in a temporal sense as well. Namely, things-in-themselves existed ten billion years ago, and they will continue to exist after all humans have succeeded in exterminating themselves. However, being able to exist before our births and after our deaths is just one small part of what it means to be a thing-in-itself. The more important part is that even if a thing is sitting on a table right now, in front of me, even if I stroke it lovingly or press my face up against it directly, I am still dealing only with a phenomenal version of the thing; the thing-in-itself continues to withdraw from all access. Yet no such thing is acknowledged by Meillassoux. For him finitude is a disaster, and absolute knowledge is in fact possible. Meillassoux’s thing-in-itself exists in independence only of the human lifespan , not of human knowledge. The fifth pillar of Meillassoux’s argument is his use of Cantor’s transfinite mathematics to show that even if the laws of nature are contingent, they need not be unstable, and thus we cannot use the apparent stability of nature to disprove his metaphysics of absolute contingency. What Cantor showed is that there are different sizes of infinity, and that all these infinities cannot be totalized in a single infinite number of infinities. Meillassoux sees this as crucial, since it allows him to discredit any “probabilistic” argument against his theory. The probabilistic argument (as defended quite clearly by Jean-René Vernes)6 would say this: given that the laws of nature seem so stable, it it is extremely improbable that there is no hidden reason for their remaining so stable. As Meillassoux sees it, probability is of value only when we can index an accessible total of cases. These can even be infinite: for example, there are an infinite number of points where a rope can break when stretched tight, but this does not stop us from calculating probabilities for various sections of the rope to break. By contrast, there is no way to sum up the number of possible laws of nature. For here there is no way to totalize; we cannot stand outside of nature and calculate the possible number of laws so as to determine the probabilities that any one of them might change. Therefore, although we can speak of probability when dealing with intraworldly events such as elections, horse races, and coin-flips, we cannot use the words “probable” or “improbable” when describing alterations at the level of nature as a whole. Rather than commenting on the validity of this argument and its use of Cantor, let me simply note that it once again creates a dualistic ontology. We already saw that Meillassoux treats time differently from space. In analogous fashion, he now treats the level of world differently from that of intraworldly events. The emergence of worlds is purely contingent and virtual and governed by no probability at all, while events within the world necessarily follow laws (even if these laws can change at any moment without reason), and thus their probabilities can be calculated. It is a strategy deeply reminiscent of Badiou’s (2005) own dualism between the normal “state of the situation” and the rare and intermittent “event.” The sixth and final pillar of Meillassoux’s book can be dealt with briefly, since we have already touched on it elsewhere. It comes at the very beginning of the book, when Meillassoux says that we must revive the distinction between primary and secondary qualities, and that the primary qualities are the ones that can be mathematized. He admits that he has not yet published a proof of this idea, though in fact it is already known as one of his primary doctrines. And here we encounter the familiar problem with Meillassoux’s inadequate conception of things-in-themselves. “Primary qualities” refers to those qualities that a thing has independently of its relations with us or anything else. But if the primary qualities can be mathematized, this means that they are not entirely independent of us, since our knowledge can get right to the bottom of them. The mathematized qualities of things are independent of us only in Meillassoux’s sense that they will still have those qualities even when all humans are dead. But to repeat, autonomy from the human lifespan is not the same as autonomy from human access. Here once more Meillassoux is concerned only with independence from the human-world correlate across time, not in any given instant. 2. L’Inexistence divine In 1997, the same year in which he turned thirty years old, Meillassoux earned his doctorate at the École normale supériuere with a brazen dissertation entitled L’Inexistence divine ( The Divine Inexistence ). The work was substantially revised in 2003. But even then, with typical fastidiousness, Meillassoux decided that the work was not yet ready for press. It has now been scrapped in favor of some future, multi-volume work bearing the same title. While writing my book on Meillassoux for Edinburgh University Press, I was permitted to translate excerpts from this unpublished work for use as an appendix in my own book; in total, the appendix contains approximately twenty percent of Meillassoux’s 2003 manuscript, the first time any of it will be published in any language. Nonetheless, a portion of the argument was already tested in the article “Spectral Dilemma,” published in English in the journal Collapse (2008: 261-75). There the philosophical motives for the virtual God are already made clear. What troubles us most are early deaths, brutal deaths, deaths of especial injustice– the sorts of deaths in which the brutal twentieth century was so abundant. And here, neither the atheist nor the believer can help us. The atheist can offer nothing but a sad and cynical resignation when reflecting on the victims of these terrible crimes. The believer does little better, being unable to explain how God could have allowed such things to happen, due to the famous intractability of the problem of evil. The solution offered to this dilemma by Meillassoux is bold, and all the more so given that he emerges from such a deeply Leftist, materialist, and unreligious background. His solution is that God does not yet exist, and therefore is not blameworthy for these catastrophes. Given that everything is contingent in Meillassoux’s philosophy, this God and divine justice might never exist, but they can at least exist as an object of hope. Let’s begin by jumping to the end of L’Inexistence divine , where the alternatives are laid out so nicely. There are four basic attitudes that humans can have towards God, Meillassoux says. First, we can believe in God because he exists. This is the classical theist attitude, rejected for the simple reason that it would be amoral and blasphemous to believe in a God who allows children to be eaten by dogs, to use Dostoevsky’s example. Second, we can disbelieve in God because he does not exist: the classical atheist attitude. But this leads to sadness, cynicism, and a sneering contempt for the greatness of human capacity. The third option, rather more complex, is to disbelieve in God because he does exist: in other words, to exist in rebellion against God as the one who must be blamed for the evils of the earth. The examples here might range from Lucifer himself, to the more human figure of Captain Ahab in Melville’s Moby-Dick , to Werner Herzog’s even more recent catchphrase, “Every man for himself, and God against all.” That leaves only the fourth option: believing in God because he does not exist. Meillassoux closes his book by saying that the fourth option has now been tried (namely, in the course of his own book), and that now that all four have been specified, we must choose. The first reaction to this theory of the inexistent God will be laughter. Few readers will ever be literally convinced by it, and probably none will immediately be convinced by it. But if we ask ourselves why we laugh, the answer is because it sounds so improbable that an inexistent God might suddenly emerge and resurrect the dead. It obviously sounds more like a gullible theology than a rigorous piece of philosophical work. Yet two things need to be kept in mind. First, Meillassoux’s theories are hardly more unlikely than those of great philosophers of the past such as Plato, Plotinus, Avicenna, Malebranche, Spinoza, Leibniz, Nietzsche, or Whitehead. We read the great philosophers not because their systems are plausible in commonsense terms that can be measured by the laws of probability. Instead, we read them precisely because they shatter the existing framework of common sense and open up new window on the universe. Second, and even more importantly, Meillassoux has already rejected probability as a valid measuring stick in philosophy. Or rather, he accepts probability in the intra-worldly realm (where it is linked with potentiality), and rejects it at the level of the world itself (where potentiality is replaced with what he calls virtuality). The virtual God can appear at any moment for no reason at all, just as any other new configuration of laws of nature can appear: in a manner that the laws of probability cannot calculate. Responding to those who might ridicule the idea of a sudden emergence of God and a resurrection of the dead, Meillassoux cites Pascal, who asserts that the resurrection of the dead would be far less incredible than the fact that we were born in the first place. This shifts philosophy onto new ground. Rather than concerning ourselves with what is likely to happen in the world as we know it, we focus instead on the most important things that could happen. For this reason, the expected objection that a virtual God is no more likely to appear than a virtual unicorn or a virtual flying spaghetti monster misses the point. Unicorns and spaghetti monsters could also appear, just like any other non-contradictory thing. But these would just be novel bizarre entities among others, not the heralds of completely new worlds. For Meillassoux, the emergence of matter, life, and thought have been the three truly amazing advents of the world so far, each of them dependent on the advent(s) preceding them. As he sees it, there can be no greater intraworldly entity than the human beings who already exist, since nothing in the world is better than the absolute knowledge of which humans alone are capable. This means that the next great advent must be something that perfects human beings rather than superseding them. And this can only be the world of justice, in which the dead are resurrected and their horrible deaths partially cancelled (Meillassoux never considers the possibility of a God who would literally erase the pre-divine past so that it never happened at all). The only immortality worth having is an immortality of this life, not an existence in some ill-defined afterworld. Human existence, he holds, must always be governed by a “symbol” that gives us the “immanent and comprehensible inscription of values in a world.” And just as cosmic history made the three great contingent leaps of matter, life, and thought, with a leap to justice as the only one still to come, a similar structure occurs within human culture and its symbols, which consist so far of the cosmological, naturalistic, and historical symbols, with a “factial” symbol still to come. We can review each of these symbols briefly. The cosmological symbol refers to the ancient dualism between the terrestrial and celestial spheres. Here below everything is conflict, corruption, and decay; but in the heavens nothing is perishable, all movement is circular, and everything is arranged in mutual harmony. This symbol is ended by modern physics when Galileo discovers such blemishes as sunspots and craters on the moon, and when Newton integrates both celestial and terrestrial movement into a single gravitational law. Next comes the naturalistic or romantic symbol, in which perfection comes not from the sky but from nature itself. The world is filled with pretty flowers (Meillassoux claims that the ancients never discussed the beauty of flowers until Plotinus in the third century) and with living creatures naturally moved by pity, at least until society corrupts them. This symbol collapses in the face of reality as we know it, since pity is no more common than war, corruption, and violence. This brings us to the historical symbol, which only now is passing away. Bad things may happen, but history has an inner logic of its own, such that everything works out in the end. The ultimate form of the historical symbol is the economic symbol, whether in a Marxist or neo-liberal form. Just as the Marxist holds that the inner economic logic of the capitalists will inexorably lead them to self-destruction, the neo-liberal assumes that the sum total of individual selfish actions will lead, in the long run, to the greatest possible good. We worship the economy and let it guide history for us, just as the ancients worshipped celestial bodies and held them to be free from blemish. The final remaining symbol is the factial symbol, which Meillassoux hopes will now emerge. Factiality, we recall, is his term for the absolute contingency of everything that exists. Once we have grasped this absolute contingency, we are free to expect the dramatic advent of the coming fourth World: the world of justice, inaugurated by a virtual God and even mediated by a messianic human figure. There is the added feature, however, that this messiah must abandon all claims to special status once the messianic realm of justice is achieved. The messianic figure will then be no more special than any person on the street, since a reign of human equality will have arisen. Although this focus on human being might seem like a return to standard humanism, Meillassoux holds that human pre-eminence has never truly been maintained. Previously, humans have been treated as special only because they contemplate the Good, because they resemble their omnipotent creator, or because they happen to be the temporary victors in a cruel Darwinian death-match between millions of living species. For Meillassoux, by contrast, humans have value because they know the eternal. But it is not the eternal that is important, since this merely represents the blind, anonymous contingency of each thing. What is important is not knowledge of the eternal , but knowledge of the eternal. We should not admire Prometheus for stealing fire from the gods; Prometheus is simply as bad as all the gods, no matter how much he increased our power. Feuerbach and Marx were wrong to say that God is a projection of the human essence, since for Meillassoux the usual concept of God represents the degradation of the human essence. If the traditional God was allowed to inflict plagues and tsunamis on the human race, the Promethean human of the twentieth century simply assumes the right to inflict death camps and atomic fireballs instead. In this respect, we have simply begun to imitate the degradation of humanity that was formerly invested in an omnipotent and arbitrary God. In response to charges that absolute contingency might lead to political quietism, Meillassoux counters that the World of justice would mean nothing unless we had already hoped for it beforehand. A World of justice that came along at random would merely be an improved third World of thought: indeed, a perfect one. But it would have satisfied no craving, and would therefore have no redemptive power. For this reason, we must actively hope for the fourth World of justice for such a fourth World ever to arise. Not only justice, but beauty is dependent on such hope: for Meillassoux, who is here somewhat dependent on Kant, beauty means an accord between our human symbolization and the actual world, which could never be present in a World of the blessed any more than justice could. And just as a messianic figure is needed to incarnate our hope and then abandon power once the World of justice is realized, it is the figure of the child whose fragile contingency shows us a dignity and a demand for justice beyond all power. 3. Meillassoux Radicalized or Reversed Given the promising reception of Meillassoux’s first book, it would not be groundless to engage in early speculation about what it might take to earn him a place in the history of philosophy. Maybe this will never happen—who knows?—but quite possibly it will: his lucid argumentative methods and sheer philosophical imagination at least make him a good candidate to be read well into the future, especially following further elaboration in print of his mature system. Philosophy is often practiced as thought it were nothing more than the amassing of “knockdown arguments.” But this is no more insightful than saying that good architecture is the amassing of steal beams. It is true that poorly constructed building cannot stand for long, but sound construction is merely the first, indispensable step in building. In fact, I am inclined to say that what really makes a philosopher important is not being right, but being wrong . I mean this in a very specific sense. I once heard the interesting remark about twentieth century culture that “you have to remember that the sixties really happened in the seventies.” That is to say, it was in the 1970’s rather than the more honored 1960’s that civil rights, free love, long hair, and the rock and roll drug culture really took root. With respect to the history of philosophy, we might just as easily say: “you have to remember that Plato really happened in Aristotle,” that “Kant really happened in Hegel” or “Hume really happened in Kant,” or that “Husserl’s phenomenology first achieved its truth in Heidegger.” One becomes an important philosopher not by being right, but by attracting rebellious admirers who tell you that you are wrong , even as their own careers silently orbit around your own. To recruit faithful disciples may be comforting and flattering, but the greatest thinkers have generally had to experience refutation at the hands of their most talented heirs. For this reason, I would propose that we size up the magnitude of living thinkers not by deciding how many times they are right and wrong, but by asking instead: who would take the trouble to refute this author? For this reason I do not ask: “Is Meillassoux right?”, since I do not believe in the virtual God myself, nor am I convinced by any important aspect of Meillassoux’s philosophy. Instead, I ask if there are interesting ways to overturn him. Only by being overturned, by no longer remaining a contemporary, does one become a classic. Let’s begin with a simple model of refutation, which can be refined further at a later date once the basic point is established. One kind of refutation simply consists in saying: “This author is a complete idiot.” The refuter now walks away in celebration, and no link between the present and the future is built; all is reduced to rubble. But this sort of mediocre triumphalism is generally practiced by those who achieve little of their own, and is not especially interesting. Much more interesting is the sort of refutation that does not take its target to be a complete idiot. I would like to suggest that there are just two basic ways in which this can be done: radicalization and reversal . It has not escaped my notice that this is a fairly good match for the Deleuzian distinction between irony and humor. Whereas irony critiques and adopts the opposite principle of what it attacks, humor accepts what it confronts but pushes it into highly exaggerated form. The ironist is like the worker who sows chaos by rebeling and contradicting the boss, while the humorist is like the worker who follows orders to an absurdly literal degree, with equally chaotic results. Let’s start with a few examples. In Aristotle’s treatment of Plato, and Heidegger’s of Husserl, we find reversal. Plato’s eidei are transformed by Aristotle into mere secondary substances, and the individual worldly things despised by Plato become what is primary. For Husserl what is primary is whatever is present to consciousness, while for Heidegger this is precisely what is secondary, since the primary stuff of the world withdraws from any form of presence at all. As for radicalization, it is most easily found in the transformation of Kant by German Idealism: “Kant was right to wall off the things-in-themselves from human access, and simply should have realized that the thought of the Ding an sich is also a thought, and thereby the noumena are just special cases of the phenomena,” with much following from this discovery. It would also be easy to read Spinoza as a radicalizer of Descartes, and Berkeley and Hume as radicalized versions of Locke. Perhaps the distinction is now sufficiently clear. Admiring refutations are not those that say “Professor X is an idiot,” which is merely the flip side of the eager disciple’s fruitless “Professor X got everything right.” Instead, it will be some variant of one of the following two options: “Professor X is important, but got it backwards,” or “Professor X is important, but didn’t push things far enough.” In the history of philosophy these two latter cases have often been painful in purely human terms: Aristotle expresses sadness at refuting Plato, Kant is openly annoyed at Fichte, and Husserl feels betrayed and used by Heidegger. Rude handling from later figures almost seems to be the sine qua non of being a great philosopher. Now, it has already been claimed that Meillassoux is an emerging philosopher of the first importance, and by no less a figure than Alain Badiou: “It would be no exaggeration to say that Quentin Meillassoux has opened up a new path in the history of philosophy…” (Preface, vii). But rather than taking Badiou’s word for it, or rejecting his word, we might experiment by asking how Meillassoux could be radicalized or reversed. Are there interesting ways of doing this that might launch whole new schools of philosophy, unexpected or even condemned by Meillassoux himself? While no one can see the future, the present is poor when it is not riddled with virtual futures. The relation between philosophers and their predecessors and successors is always somewhat complicated, of course. But generally there is one central divergence at stake, which might be taken as the key to all the others. On this basis we could say that new thinkers primarily radicalize or primarily reverse the main ideas of their chief philosophical forerunner. There may be specific historical conditions and perhaps even personality traits connected with these two types, but this question can be left aside for now. More important for us is that radicalizers will generally be followed by reversers, and vice versa. Consider the textbook example of a reversal in the history of philosophy: Kant’s Copernican Revolution, which inverts the so-called dogmatic tradition that addresses the world itself, and makes the world revolve instead around the conditions by which it is known. While it is not completely impossible that Kant’s successors might have re-reversed this principle back into a new and stronger dogmatic realism, conditions were premature for such a move. Anyone doing this too early would likely have been an angry anti-Kantian reactionary rather than an original thinker in command of a genuinely new realist principle. The far more likely outcome is the one that actually happened: Kant’s reversal of his predecessors was viewed as incomplete, or as retaining lamentable bits of the traditional view, which despite his admirable breakthrough he was unable to shake off. This was the view of German Idealism, anyway. In similar fashion, Spinoza could also be viewed as a radicalizer of Descartes, who is equally accused of preserving various Scholastic dogmas in an otherwise radical project of philosophical reversal. The point is this: reversals in the history of thought tend to be followed soon thereafter by radicalizations of those reversals. The same may hold true in reverse: radicalizations might generally be followed by reversals, given that it is not always possible to be more radical than the radicals have already been. Consider the case of Husserl, who radicalizes Brentano’s early vagueness about what lies beyond immanent objectivity, and Twardowski’s assertion that there must be an external object lying outside the intentional content, by collapsing everything into the intentional sphere: there is no difference between the Berlin in my consciousness and the actual Berlin that is home to millions of people. It is difficult to see how one could be even more radical than Husserl’s idealist turn here. And thus the road is paved to Heidegger’s reversal of classical phenomenology, in which the key point is what lies deeper than any presence to consciousness: the Sein whose power and obscurity cannot be made exhaustively present, but only sends itself in historical epochs. In similar fashion we might also read Leibniz as a reverser of Spinoza’s radicalization, retrieving a strong sense of individual substance and a certain validity of what the Scholastics had said. Returning to Meillassoux, we might ask which kind of philosopher he is: a radicalizer or a reverser? At present, Meillassoux looks to me like a radicalizer (though for now his future remains shrouded in mist). He takes the correlationist tradition, which allows us to speak only of the relation between human and world, and tries to raise it into an even more extreme claim about the absolute contingency of everything. But whereas German Idealism did this by trying to collapse the distinction between thought and world entirely into the “thought” side, Meillassoux does it by trying to shift the non-absolute contingency of the thought-world correlate from epistemology to ontology. It is no longer a question of the inability of human knowledge to know what lies outside the correlate, but the inability of reality itself to be rooted in any definite laws. Furthermore, if we look at the various features of Meillassoux’s philosophy identified earlier tonight, all but one are already so radical that there is no obvious way to push them further. The one exception would be his claim that the world as a whole can change for no reason at any moment, coupled with the inconsistent claim that within a given world there are laws of nature that everything must follow. If gravitational attraction between all masses is a current law in our world, then for Meillassoux there can be no exceptions to this law for as long as it remains in force. A toppled vase will fall to the floor every time for sure,unless there is a cosmic change by which the laws of nature as a whole have altered. (This is reminiscent of the late medieval distinction between the absolute and ordained power of God, according to which God has the power to set or change the laws of nature, but not to contravene those laws locally once they are set.) On this point, to radicalize Meillassoux would simply be to say: there are no laws of nature even in the local sense. Everything that happens, even in the world here and now, is purely contingent and not governed by even a trace of law. And while this would be a more consistent development of Meillassoux’s thoughts on contingency, it is difficult to see how it could lead to a new philosophy. Instead, the admiring successors of Meillassoux are more likely to reverse one of his already sufficiently radical points. At least four candidates come to mind: *First, we have seen that Meillassoux thinks correlationism is challenged by a time before or after consciousness, but not by a space lying outside it. Perhaps this could be reversed into saying that spatial exteriority is the really crucial point. The arguments on this point are perhaps the least convincing in After Finitude (and do not even occur in the original French edition), and therefore it might be a candidate for the “blind spot” of which no philosopher is ever free. *Second, Meillassoux uses Cantor to claim that the contingency of laws of nature would not entail that they are unstable. A successor of Meillassoux might claim that it does make them unstable, and celebrate this fact. This person would then have to explain why common sense seems to encounter a relatively stable world despite its truly rampant instability. Whereas Meillassoux’s problem is to show how stability might exist despite contingency, this successor’s problem would be slightly different: to show why actual, full-blown instability might have the appearance of stability. *Third, Meillassoux claims that the primary qualities of things are those that can be mathematized. He might be reversed by a successor who says the opposite: the mathematizable qualities are the secondary ones, and the primary ones are those that elude symbolic formulation. While this is a perfectly valid possible objection to Meillassoux, it is one that is made in advance by some of his predecessors and is still made by some of his peers, making it less interesting for futurology than some of his other points. *Fourth and finally, whereas Meillassoux claims that God does not exist but might exist in the future, a successor might argue even more bizarrely that God has always existed but might vanish in the future. Let’s arbitrarily select the first of these possibilities, and imagine briefly where it might lead, if pursued in the future by admiring detractors. Meillassoux comes from the circle of Badiou, and some of Badiou’s most ardent admirers are found in Latin America. So, let’s imagine that towards mid-century some ingenious reversers of Meillassoux emerge in that portion of the Spanish-speaking world. Just for fun, let’s call them Castro and Chávez. And in order to avoid any confusion with the present-day politicians of those names, we will stipulate that Meillassoux’s great successors are both women. The philosopher Castro (we will suppose she comes from Peru) reverses Meillassoux’s argument that the ancestral or diachronic are what most threaten the human-world correlate. Instead, she claims that the diachronic does not threaten the correlate at all, and that we must instead look at space as what ruins the correlate and demands a strange new realism. What would such a philosophy look like? In order to determine this, we might ask what price Meillassoux pays for doing it the opposite way. As I see it, he pays in two separate ways. One is that laws of nature for him are contingent over time . The laws of nature apply to the universe as a whole at any given moment, and would be changed globally if they are ever changed at all. The second price he pays is that Meillassoux has no mereology , or theory of parts and wholes. Everything for him is on the level of the given, or immanent in experience, with the sole proviso that the laws governing this immanence might change without notice at any given moment. In reversing Meillassoux, Castro makes the following claims in the preface to her stunning debut book of 2045, The Cosmos and its Neighborhoods , rapidly translated from Spanish into all the languages of the world: Despite his brilliant analysis of the contingency of laws of nature over time, Meillassoux gets two important assumptions wrong. First, he allows for only one set of contingent laws to govern nature as a whole. Second, he allows laws to govern only the world that is immanent in experience, and thereby fails to explore the contingency among part-whole relations. In this book I will argue, first, that the laws of nature vary in any given instant between one region of the universe and the next; and second, that the world is made up of layers of parts and wholes that are also contingent with respect to one another. Those are the words of Castro. This may sound like a hopeless free-for-all of chaos, yet the book somehow succeeds in drawing some compelling deductions about how laws must vary from one place or level in the world to the next. Trapped in the limited horizon of 2011, and not yet inspired by the heavily balkanized political and technological situation of 2050 that somehow lends additional credence to Castro’s vision, we can only vaguely grasp what such a philosophy might look like. After this reversal of Meillassoux by Castro, the usual pattern leads us to expect a radicalization by Chávez, a young Argentine student of Castro. How could the already strange theories of Castro be radicalized? Perhaps as follows, in a disturbing new book entitled The Implosion of the Neighborhoods , which argues as follows: Castro was right to shift the Meillassouxian framework of contingency from time to space. However, in this respect she retained a surprisingly traditional opposition between the two. In this book I will show that time and space collapse into one another. This may sound too much like the discredited four-dimensional block universe of twentieth century physics and philosophy. However, the four-dimensional universe is a model biased in favor of space, merely adding an extra dimension to the commonsense spatial continuum while stipulating that the serial passage of time is an illusion. In this book I will argue instead for a one-dimensional space-time modeled after our experience of time, in which there is no simultaneous co-existence at all between different parts of the universe, or ‘neighborhoods’ as my esteemed teacher Castro has called them. Instead, the various portions of the universe link to one another by succession rather than by coexistence. Buenos Aires, New York, and Amsterdam do not exist simultaneously in the same landscape, but one after the other in the mind of some observer, and this observer can only be an observer much larger than any human. Against Meillassoux’s notion of a virtual God that does not exist now but might exist in the future, I will argue for an actual God that surveys the universe in sequence, thereby generating the illusion of spatial diversity and even the illusion of individual minds located within that diversity. Once this divine observer dies, the universe as a whole must perish. Again, these ideas are so bizarre that we of 2011 can barely comprehend them, just as Aristotle would have had a difficult time grasping the theories of Descartes. We could then perhaps imagine a further reversal of this theory, emanating from the intellectually resurgent Philippines of the twenty-second century. The Filipino School might argue that the universe is already dead, given the collapse of its spatial richness into the serial observations of a flimsy and mortal God. The virtual universe does not yet exist, but might exist in fully spatial form in the future, and this would require the death of God and the resulting liberation of God’s succession of images as independent, spatially situated realities. With a bit of sharpening, we might be able to make all of these imaginary thinkers more intuitively clear. Along with the history of philosophy, there might arise a new discipline generating imaginary futures for philosophy. The richness of Meillassoux’s system comes not from the fact that he is plausibly right about so many things, but because his philosophy offers such a treasury of bold statements ripe for being radicalized or reversed. He is a rich target for many still-unborn intellectual heirs, and this is what gives him the chance to be an important figure. NOTES 1. Quentin Meillassoux, After Finitude . Trans. R Brassier. (London: Continuum, 2008.) Page 5. The word “correlationism” does not appear in his doctoral thesis. As Meillassoux informed me in an email of February 8, 2011, he first coined this term in 2003 or 2004, while editing for publication a lecture he had given at the École normale supérieure on a day devoted to the theme of “Philosophy and Mathematics,” an event including Alain Badiou as one of the participants. 2. Graham Harman, Quentin Meillassoux: Philosophy in the Making . (Edinburgh: Edinburgh University Press, forthcoming 2011). 3. In an email of December 6, 2010, Meillassoux clarifies that in After Finitude he only deduces the impossibility of a “universal contradiction,” not of a determinate contradiction. In the same email he suggests that he can also prove the latter, though the proof is somewhat lengthier than the one found in After Finitude . 4. After Finitude (18-26), in the passage falling between the two sets of triple asterisks. These pages were sent by Meillassoux to translator Ray Brassier (in French) during the translation process, and do not appear in the original French version of the book. 5. Graham Harman, “Quentin Meillassoux: A New French Philosopher.” Philosophy Today 51.1 (2007): Pages 104-117. The passage where I raise the question of space can be found in the first column of page 107. 6. Vernes is first cited on p. 95 of After Finitude . See Jean-René Vernes, Critique de la raison aléatoire, ou Descartes contra Kant . (Paris: Aubier, 1982).  . (shrink)

The lodestone is an extremely rare form of the mineral magnetite that occurs naturally as a permanent magnet. It therefore attracts metallic iron as well as fragments of ordinary ‘inert’ magnetite. This ‘magic’ property was known to many ancient cultures, and a powerful lodestone has always commanded a high price. By the eleventh century AD the Chinese had discovered that a freely suspended elongated lodestone would tend to set with its long axis approximately north–south, and utilized this property in the (...) magnetic compass. They also appear to have discovered that this invaluable characteristic could be handed‐on to a steel needle if the latter were contacted with, or stroked by, a lodestone.The magnetism of the lodestone was scientifically investigated by William Gilbert in the sixteenth century, when he defined its ‘poles' and the well‐known rule that ‘like poles repel, unlike attract’. He also studied ‘inclination’ and ‘variation’, and means to aid the preservation of magnetic power. How to concentrate it by ‘arming’ the lodestone with caps or pole‐pieces of soft iron was discovered in the same century. These methods have been repeated, confirmed, and improved. The lodestone occupies a vital place in the history of magnetism, but little beyond Gilbert's work can be reached by historical studies because vastly improved steel or alloy permanent magnets, and electromagnets, replaced it before quantitative measurements were developed. These techniques have therefore been applied retrospectively to both museum specimens and contemporary natural lodestones. A good source of the latter was found to be the igneous complex known as Magnet Cove, Arkansas, and this material has been used as the ‘type example’. All specimens were discrete, well‐rounded, rusty brown pebbles found near the surface. Their unweathered interiors were black titanomagnetite. No significant trace element or crystallographic differences could be found between the lodestones and the magnetically inert material that always accompanied them. The magnetic moment per unit volume of the ‘as‐found’ Magnet Cove lodestones varied between 6.5 and 11.6 emu cm−3, which compares poorly with the hundreds of units characteritzing modern permanent magnets. Hysteresis loops gave a saturation intensity of 27–51 emu cm−3, suggesting that intensity has diminished since formation. This agrees with general experience of magnets, especially in the absence of a ‘keeper’. The initial volume susceptibility of Magnet Cove magnetite was about 0.18 for low fields, and always remained <1. This means that a normal terrestrial magnetic field with a maximum vector <1 Oe is unable to induce even the low magnetic moments we see today, while a field approaching 1000 Oe is required for saturation. These parameters, and the rare occurrence of lodestones as near‐surface fragments, support suggestions that they are the product of a lightning strike upon an exposure of a suitable magnetite. Transient currents averaging 30 000 A have been measured. This would give rise to a zone of potential magnetic saturation at least 12 cm in diameter, to which some of the ejected fragments would be exposed. An attempt to determine the period elapsed since formation of the Magnet Cove lodestone was made by annealing magnetically saturated specimens at temperatures up to 500°C, and measuring J v at weekly intervals for 100 days. The decay curves visually resembled exponential functions, but mathematical tests proved that they were not strictly so. Interpretation was therefore difficult, but a pragmatic procedure involving excessive extrapolation suggested an ‘age’ of about 3500 years. (shrink)

This introduction to fictional “fertility dystopias” presents literary examples of the rapid expansion or collapse of populations through the manipulation of fertility or the fraught inability or decision not to. Additionally, these fictions are periodized with their extraliterary social contexts, revealing roughly three intervals: pronatalism dominant before the 1950s, antinatalism ascendant from the 1950s to the early 1970s, and, beginning in the middle 1970s to the present, contestation between pronatalism and antinatalism. Despite the ascendance of antinatalism, fertility dystopias in the (...) middle interval reveal antinatalist assumptions but with accompanying anxiety rather than complete endorsement. Today, tracking with global variations in local fertility rates and development levels, both antinatalist and pronatalist messages are expressed with equal vigor. (shrink)