Eudoxus, Callippus and the Astronomy of the Timaeus

Whether the astronomy of the Timaeus had any significant influence on Eudoxus' theory of homocentric spheres is a matter of contention. Some commentators deny any such influence.1 Here I argue for a view of the Timaeus' astronomy, and of Eudoxus' astronomy, whereby Eudoxus' work was as much a natural development of the Timaeus as Callippus' work was of Eudoxus. I also argue for an important interpretative principle. This is that Plato, Eudoxus and Callippus could not account for all the phenomena they were aware of, and were aware of that fact. If the Timaeus presents a prototype, Eudoxus can then be seen to develop this astronomy, making the model more sophisticated and complex while staying within the cosmological principles, and attempting to solve the key problems which were left unsolved by the Timaeus model. He does this in much the same way as Callippus made Eudoxus' model more complex and sophisticated, and attempted to solve the leading problems in that model. I also consider some further objections to a significant interaction between Plato and Eudoxus, based on supposed philosophical differences, dating, and the evidence of later commentators. I conclude that these provide no significant obstacle to considering there to be a fruitful liaison between Plato and Eudoxus

The Creation and Destruction of the World

Here we explore various ideas about the creation and destruction of the world, including theories posited by the Presocratics, Plato, Aristotle, Epicureans, Stoics, and the Neoplatonists

Magic, Curses and Healing

Magic and curses played a strong role in Greek popular culture. As I shall explain below, many Greeks believed themselves to live in an “extended world” where it was possible to have relations with both the living and the dead by magical means. Diseases could be caused by the gods or magical means and were susceptible to magical treatment. On one view this belief in magic was dispelled by the Presocratic philosophers, though, as we shall see, matters were not quite so straightforward. Here we shall clarify the nature and context of Greek and Roman magic and explore some of the issues involved in its study

Second-order structure function analysis of scatterometer winds over the Tropical Pacific

22 pages, 16 figures, 1 tableKolmogorov second-order structure functions are used to quantify and compare the small-scale information contained in near-surface ocean wind products derived from measurements by ASCAT on MetOp-A and SeaWinds on QuikSCAT. Two ASCAT and three SeaWinds products are compared in nine regions (classified as rainy or dry) in the tropical Pacific between 10°S and 10°N and 140° and 260°E for the period November 2008 to October 2009. Monthly and regionally averaged longitudinal and transverse structure functions are calculated using along-track samples. To ease the analysis, the following quantities were estimated for the scale range 50 to 300 km and used to intercompare the wind products: (i) structure function slopes, (ii) turbulent kinetic energies (TKE), and (iii) vorticity-to-divergence ratios. All wind products are in good qualitative agreement, but also have important differences. Structure function slopes and TKE differ per wind product, but also show a common variation over time and space. Independent of wind product, longitudinal slopes decrease when sea surface temperature exceeds the threshold for onset of deep convection (about 28°C). In rainy areas and in dry regions during rainy periods, ASCAT has larger divergent TKE than SeaWinds, while SeaWinds has larger vortical TKE than ASCAT. Differences between SeaWinds and ASCAT vortical TKE and vorticity-to-divergence ratios for the convectively active months of each region are large. © 2014. American Geophysical Union. All Rights ReservedThe ASCAT-12.5 and ASCAT-25 data used in this work can be ordered online from the EUMETSAT Data Centre (www.eumetsat.int) as SAF type data in BUFR or NetCDF format. They can also be ordered from PO.DAAC (podaac.jpl.nasa.gov) in NetCDF format only. The SeaWinds-NOAA and QuikSCAT-12.5 data are also available from PO.DAAC. The SeaWinds-KNMI data are available from the KNMI archive upon an email request to [email protected]. Rain-rates and sea surface temperatures were obtained from the Tropical Rainfall Measuring Mission's (TRMM) Microwave Imager (TMI) archive at the Remote Sensing Systems web site (www.ssmi.com). SeaWinds Radiometer (SRAD) rain-rates were obtained from the QuikSCAT 25 km L2B science data product that is available from PO.DAAC. This work has been funded by EUMETSAT in the context of the Numerical Weather Prediction Satellite Applications Facility (NWP SAF). The contribution of GPK has been supported by EUMETSAT as part of the SAF Visiting Scientists programmePeer Reviewe

William Harvey, Aristotle and Astrology

In this paper I argue that William Harvey believed in a form of astrology. It has long been known that Harvey employed a macrocosm–microcosm analogy and used alchemical terminology in describing how the two types of blood change into one another. This paper then seeks to examine a further aspect of Harvey in relation to the magical tradition. There is an important corollary to this line of thought, however. This is that while Harvey does have a belief in astrology, it is strongly related to Aristotle's views in this area and is quite restricted and attenuated relative to some contemporary beliefs in astrology. This suggests a more general thesis. While Harvey was amenable to ideas which we associate with the natural magic tradition, those ideas had a very broad range of formulation and there was a limit to how far he would accept them. This limit was largely determined by Harvey's adherence to Aristotle's natural philosophy and his Christian beliefs. I argue that this is also the case in relation to Harvey's use of the macrocosm–microcosm analogy and of alchemical terminology, and, as far as we can rely on the evidence, this informs his attitudes towards witches as well. Understanding Harvey's influences and motives here is important in placing him properly in the context of early seventeenth-century thought

Parmenides, Cosmology and Sufficient Reason.

Why Parmenides had a cosmology is a perennial puzzle, if, as the ‘truth’ part of his poem appears to claim, what exists is one, undifferentiated, timeless and unchanging.1 Indeed, not only does the cosmological part of the poem tell us how the cosmos is arranged, it also tells us how the cosmos, humans and animals all came into being. Although more of the truth has survived, the cosmology originally made up some 2/3 to 3/4 of the poem.2 The poem claims it will give the ‘complete ordering’ and Parmenides is perceived to have ‘completed all the phenomena’.3 Parmenides also seems to have made some important original contributions to cosmology.4 These I take to be important facts which any explanation of the nature of this cosmology must account for. The aim of this paper is to explore a new suggestion for the status of the cosmology, that it may be equalled but not surpassed by other cosmologies which are capable of accounting for all of the phenomena. Its function, I argue, is to raise sufficient reason issues about some fundamental questions in cosmogony and cosmology. I will also argue that we can find sufficient reason considerations relating to cosmogony and cosmology in the truth part of the poem. This opens the possibility that it is at least in part issues of sufficient reason that link the two parts of the poem. Finally I will argue that by paying close attention to what Parmenides has to say about signs, σήματα, we can see how he leaves open the possibility of making positive contributions to cosmology. I believe this gives us a richer account of Parmenides, places him more firmly in the debates of presocratic cosmology and cosmogony and gives him interesting relations to his predecessors and successors.5 These sufficient reason considerations may work both as a critique of contemporary cosmogony and cosmology and a challenge to any future cosmogony and cosmology

Leucippus and Democritus on Like to Like and ou mallon

he central issue for this paper is whether for Leucippus and Democritus, 1 the like to like principle, which is critical to cosmos formation once a vortex forms, operates outside of the vortices. Should we consider like to like in the early atomists to be akin to a ‘fundamental force’, with a universal application, as some commentators have suggested?3 Or should we rather consider it to be a sorting effect generated by certain types of motion, occurring only when those types of motion occur? As a matter of detail this is interesting in itself and it also bears on several important interpretive issues for Leucippus and Democritus. What are the intrinsic properties of atoms, if any, beyond their size and shape? Is the initial formation of a vortex a matter of necessity or a matter of chance? Is what happens in a cosmos a matter of necessity or chance? Although not immediately obvious, this will also raise issues concerning to what extent Leucippus and Democritus are committed to the principle of sufficient reason. I will argue that there are good theoretical and textual reasons to believe that like to like occurs only in the vortices. I will also argue that just as there are no preferred sizes and shapes for atoms for Leucippus and Democritus, no preferred distribution of the atoms in the void and there are no preferred times or places for vortex/cosmos formation either. This I suggest gives Leucippus and Democritus a coherent and interesting position relative to Parmenides. Where Parmenides denies multiplicity and raises sufficient reason issues about the time and place of cosmos formation, Leucippus and Democritus assert multiplicity but without preferred shapes and sizes of atoms and cosmogony without preferred times and places of cosmos formation. Of importance here will be an interesting paradox in cosmogony - if we begin with a uniform entity or uniform distribution of entities how does a non-uniform state such as a cosmos arise, while if we begin with a non-uniform entity or non-uniform distribution of entities how do we explain this non-uniformity

Field Theory for a Deuteron Quantum Liquid

Based on general symmetry principles we study an effective Lagrangian for a neutral system of condensed spin-1 deuteron nuclei and electrons, at greater-than-atomic but less-than-nuclear densities. We expect such matter to be present in thin layers within certain low-mass brown dwarfs. It may also be produced in future shock-wave-compression experiments as an effective fuel for laser induced nuclear fusion. We find a background solution of the effective theory describing a net spin zero condensate of deuterons with their spins aligned and anti-aligned in a certain spontaneously emerged preferred direction. The spectrum of low energy collective excitations contains two spin waves with linear dispersions -- like in antiferromagnets -- as well as gapped longitudinal and transverse modes related to the Meissner effect -- like in superconductors. We show that counting of the Nambu-Goldstone modes of spontaneously broken internal and space-time symmetries obeys, in a nontrivial way, the rules of the Goldstone theorem for Lorentz non-invariant systems. We discuss thermodynamic properties of the condensate, and its potential manifestation in the low-mass brown dwarfs.Comment: 19 LaTeX pages; v2: 2 refs added, JHEP versio