In its original form Dirac's equations have been expressed by use of the γ-matrices γμ, μ=0, 1, 2, 3. They are elements of the matrix algebra M 4 (ℂ). As emphasized by Hestenes several times, the γ-matrices are merely a (faithful) matrix representation of an orthonormal basis of the orthogonal spaceℝ 1,3, generating the real Clifford algebra Cl 1,3 . This orthonormal basis is also denoted by γμ, μ=0, 1, 2, 3. The use of the matrix algebra M 4 (ℂ) (...) to represent Cl 1,3 has some unsatisfactory aspects. The γ-matrices contain imaginary numbers as entries whereas Cl 1,3 is real. Moreover, as a matrix algebra Cl 1,3 is M 2 (ℍ) but only a part of M 4 (ℂ). For that reason we investigate in this paper several forms of Dirac's equations in terms of M 2 (ℍ) instead of M 4 (ℂ). In Section1 we survey Dirac's equations describing the interaction of matter with electromagnetic, electroweak, and strong fields. Section2 deals with electromagnetic/weak interactions employing M 2 (ℍ). Finally, in Section3 we deal with Dirac's equations for strong interactions between quarks. In contrast to su(2) ⊕ u(1), the Lie algebra su(3) is not isomorphic to any subalgebra of Cl 1,3 . Therefore we do not give a description of strong interactions by use of M 2 (ℍ). Instead of such an approach we describe these interactions using the space of quadruples of bivector fields in Cl 1,3 . The thus obtained description has remarkable formal resemblance to the original Dirac equations using wave functions with values in the linear spaceℂ 4. (shrink)

The text of Euripides' Troades depends mainly upon the versions preserved in two manuscripts, viz. Palatinus 287 and Vaticanus 909 . Both these manuscripts are well known and have been several times collated. Their importance in relation to one another and to the other existing manuscripts for the study of the text of Euripides in general has been frequently discussed and is no longer a subject of major controversy. The notes which follow are designed to put on record a number (...) of corrections to the readings ascribed to P and V for the Troades in the apparatus criticus of Prinz-Wecklein and later editors; and to correct and amplify the general descriptions of P and to call attention to certain difficulties in the current views of its relationship to Laurentianus xxxii. (shrink)

The words I wish to delete in 48-9 spoil a ‘tricolon crescendo’ whose three members are clearly marked and whose verbs are perhaps deliberately varied in person and tense. The parataxis by means of hic is awkward, and the words seem to be a versified gloss. The Scholiast says : id est: to nobilis tantum et imperitus. nam de plebe, id est de humili familia, eloquentes exeunt, qui nobilium imperitorum causas defendunt; but that could be a paraphrase based on the (...) text as it stands in our manuscripts. (shrink)

Writing of Terence'sAndria(‘The Girl from Andros’) in 1952, Duckworth said: ‘In theAndriathe second love affair is unusual; Charinus’ love for a respectable girl whose virtue is still intact has been considered an anticipation of a more modern attitude towards love and sex. More frequently in Plautus and Terence the heroine, if of respectable parentage, has been violated before the opening of the drama (Aulularia, Adelphoe), or she is a foreigner, a courtesan, or a slave girl' (Duckworth (1952), p. 158). Perhaps (...) in 1993 it does not seem quite so ‘modern’ that Charinus is not only in love with a respectable virgin but wishes to marry her. (shrink)

Cicero's philosophical works are now exciting renewed interest, in part because he provides vital evidence of the views of the Greek philosophers of the Hellenistic age, and partly because of the light he casts on the intellectual life of first century Rome. This edition uses the 1997 Clarendon text by the acclaimed translator P.G. Walsh.

Starting from a connected, partially ordered set of events, it is shown that results of the measurement of time are elements of a partially ordered and filtering field, as used in a previous paper. Moreover, some relations between physical formulas and properties of the field are proved. Finally, some open problems and suggestions are pointed out. For the convenience of the reader not acquainted with elementary algebraic methods, proofs are given in detail.

A neurosurgical view of consciousness is presented. It is biased by our need to deal with coma. The concept of primary or neurosurgical consciousness is discussed, and the anatomy, physiology, pathology and clinical features described in a simple a way. It is suggested that the dynamic interaction between the reticular activating system and the cerebral cortex is the anatomic and physiologic basis for primary consciousness. It is emphasised that this in no way diminishes the role of the cortex in either (...) primary or higher-order consciousness. In essence, a presentation is made of the neurosurgical view of cortex-brainstem inter- relationships, and the importance of this interrelationship to consciousness. (shrink)