Not Athenian or a Stranger:The Veiled Critique of Aristotle in Plato’s Laws

Plato’s last dialogue,the Laws,occupies an anomalous position within his larger body of work.An individual identified as the“Athenian stranger”replaces Socrates and reverses key Socratic teachings,most notably by endorsing tyranny.Scholars conclude that Plato abandoned his earlier political recommendations in favor of a more pragmatic vision.In that case,the Laws should be treated as Plato’s definitive work,the ultimate statement of his thought,when in fact,much more attention is paid to earlier dialogues,particularly the Republic.The problem is resolved and the true significance of the Laws revealed when the text is read as Plato’s ironic critique of his brilliant-but-rebellious student,Aristotle.Reasoning from Aristotelian premises,the Athenian stranger arrives at conclusions that Platonists and Aristotelians alike would find unpalatable or absurd.The alleged rupture between Plato’s earlier and later work disappears.The esoteric writings that are thought to have been the product of Aristotle’s later career are shown to have emerged from ideas that Plato himself was familiar with and rejected.

A Hidden Telete:Mythological Images as Symbols of Initiation in Roman Wall Paintings and Mosaics

Initiation was one of the most substantial experiences undergone in Antiquity.The term Les rites de passage introduced by Arnold van Gennep,accommodates the multifaceted significance of initiation in the social structure.The two main aspects of initiation were defined as the social and that which belonged to the religious sphere;or,the profane and the sacred.Initiation or rites of passage in the social realm were intended to delineate the transition from childhood to adult status,while the sacred initiation was intended to promise eternal life and a merging with the divine.As van Gennep has indicated,however,acts of apprenticeship of any kind were enveloped in ceremonies,since no act was entirely free of the sacred.Sacred initiations were intended to remain secret in Antiquity,thus explicit depictions of sacred rituals are rare in ancient art.As this study will demonstrate,however,signifiers of such initiation can nonetheless be found in Roman wall paintings and mosaics depicting mythological protagonists.The point of departure here is that initiation is the main issue manifested metaphorically in the depictions under discussion,with the sacred initiation rather than the social mostly featuring in the visual images.The analysis is based on literary and philosophical sources,and focuses on four personalities:Narcissus,Endymion,and Achilles,who are represented in their mythological context on wall paintings from Pompeii,and Heracles,who is shown in Roman mosaics in a scene familiar as the“Drinking Contest between Heracles and Dionysus”.

利用计算机软件解决晶体结构精修时晶胞群转换问题

本文就单晶结构解析过程中出现的晶胞群指认错误问题并结合具体的实例,利用PLATON软件解决此类问题,并讨论了具有空间手型空间群晶体结构解析中一些需要注意的问题.

Ratio of In-Sphere Volume to Polyhedron Volume of the Great Pyramid Compared to Selected Convex Polyhedral Solids

The architecture of the Great Pyramid at Giza is based on fascinating golden mean geometry. Recently the ratio of the in-sphere volume to the pyramid volume was calculated. One yields as result RV = π ⋅ φ5, where is the golden mean. It is important that the number φ5 is a fundamental constant of nature describing phase transition from microscopic to cosmic scale. In this contribution the relatively small volume ratio of the Great Pyramid was compared to that of selected convex polyhedral solids such as the Platonic solids respectively the face-rich truncated icosahedron (bucky ball) as one of Archimedes’ solids leading to effective filling of the polyhedron by its in-sphere and therefore the highest volume ratio of the selected examples. The smallest ratio was found for the Great Pyramid. A regression analysis delivers the highly reliable volume ratio relation , where nF represents the number of polyhedron faces and b approximates the silver mean. For less-symmetrical solids with a unique axis (tetragonal pyramids) the in-sphere can be replaced by a biaxial ellipsoid of maximum volume to adjust the RV relation more reliably.

Murdoch on Eros

Love and moral are the main themes of Iris Murdoch' s literary works.As the combination of the two main themes,her Eros theory plays a significant role in her works.On the basis of her personal perception of Platonic Eros and Freudian Eros,Murdoch establishes her own Eros Theory.To unveil this important theory,this paper tries to trace the sources of Murdoch' s Eros theory from Platonic Eros and Freudian Eros.

The Mathematics of Harmony. Proclus’ Hypothesis and New View on Euclid’s Elements and History of Mathematics Starting since Euclid

We are discussing one of the most unlikely hypotheses in the history of mathematics—Proclus’ hypothesis, which overturns a traditional view on Euclid’s Elements and the history of mathematics, starting since Euclid. According to Proclus, the main goal of Euclid, when writing the Elements, was to build a complete geometric theory of Platonic solids (Book XIII), associated in the ancient philosophy (Pythagoras, Plato) with the Universe harmony. To construct this theory, Euclid introduced in Book II the problem of dividing a segment into extreme and mean ratio (the “golden section”). It follows from Proclus’ hypothesis that Euclid’s Elements are the first attempt to create the “Mathematical Theory of the Universe Harmony”, based on Platonic solids and the “golden section”.

Plato Revealed: Alexander of Aphrodisias and His Philosophical Historiography

Alexander of Aphrodisias’s Commentary on Aristotle’s Metaphysics is an important testimony to understand Plato’s philosophy.In fact,Alexander uses some lost Aristotelian books,especially a work On the Good,from which we learn that Plato’s metaphysics is adialectical metaphysics,founded on an original opposition of two principles that shapes the whole reality—these principles being the One and the indefinite Dyad.Sensible things participate in ideas(they receive their being from ideas)and the intermediate mathematical entities lie between these two realities.However,ideas can be traced back to ideal numbers and the principles of ideal numbers are the One and the indefinite Dyad.Thus,these principles constitute their metaphysical foundation of ideas and,through the ideas,of the whole reality.

Lattice Boltzmann simulation of fluid flow through random packing beds of Platonic particles: Effect of particle characteristics

The influence of particle characteristics,such as shape,size,and volume fraction,on the permeability of porous media was investigated by combining the randomly packed beds of Platonic particles with the lattice Boltzmann method.Quantitative solutions of the permeability as a function of these characteristic parameters in mono-sized particle packing structures were obtained.The D3Q19 model is presented here,which was tested by three simple benchmark tests.A series of packed beds of Platonic particles as well as spherical particles were generated in a random manner.Numerical studies on factors influencing the permeability of materials were carried out to comprehensively study their impacts.The results revealed that the permeability significantly increased with increasing equivalent diameter of the particles(or decreasing volume fraction).At a fixed size and volume fraction of particles,the permeability of the Platonic particle packing structures was also influenced by particle morphology:permeability significantly reduced as the particle sphericity decreased.The permeability of tetrahedral particle packing structures dropped by more than 40%compared with that of corresponding spherical particle systems.

On Orientably Regular Non-abelian Covering Maps of the Platonic Maps

We investigate the orientably regular non-abelian coverings of regular maps.A complete classification of dihedral coverings of the Platonic maps for branching over faces(or,dually,vertices)is given.As a result,we generalise the results of Jones and Surowski on regular cyclic coverings of the Platonic maps.