An early stage in the evolution of Aristotle's physics

Aristotle's Physics V and VI deal with the same concepts: motion, change and continuity. The two books, however, employ altogether different approaches to the study of these concepts, thus presenting different orders of conceptualization. Abraham Edel (1982, 42) claims that Aristotle is a systematic philosopher “not in the sense of [i] one who pursues a deductive system … but in the sense of [ii] one who has a well-constructed and fairly clearly analyzed conceptual network that he uses with considerable power in field after field of human inquiry.” Truly, [ii] is more typical of Aristotle, but in the Physics both approaches are present. Books VI and V (respectively) are good examples. It is commonly taken for granted that Physics V prepares for VI, because of the order in which they appear in the corpus, and because V includes the definitions of the main concepts that are used in VI. A closer look at the texts, however, reveals that the definitions of V are not used in VI. I argue that the definitions of V were not only unknown when VI was written, but are actually incompatible with the spirit of Physics VI and with the main thesis underlying it. Physics VI is close in method, conceptual basis and in its radical formal approach to the Posterior Analytics, and a part of it (the early stratum) looks like a mathematical exercise. The mathematical-logical approach was abandoned, and gave way to the more mature Aristotelian style, which is already dominant in Physics V.     

Das Parallelenproblem im Corpus Aristotelicum

Summary In the Corpus Aristotelicum are numerous items suggesting that the assertion of the fifth postulate in Euclid's Elements had been preceded by attempts to demonstrate this postulate itself, or some equivalent fundamental proposition, within the rigorous frame of Absolute Geometry in Bolyai's sense. Thus geometers contemporary with Aristotle tried to solve the problem which became known commonly in later centuries as the Problem of Parallels.Probably these geometers first attempted a direct solution. Only one text at our disposal supports this hypothesis: (1) Anal. Prior. 65 a 4–7. My analysis below in Chapter I shows that a mathematical meaning can be read from this somewhat obscure text only if it is interpreted as an allusion by Aristotle to those geometers who believe they are demonstrating, obviously in an absolute way, the proposition Elem. I 29, equivalent to the fifth postulate, but do not realize that in the process they are using lemmas which result themselves from the proposition to be demonstrated. Such a lemma would assert the uniqueness of the parallels, existence of which was shown in an absolute way in Elem. I 27. My conjecture and reconstruction afford a natural explanation for an inconsequence singular for Book I of the Elements, namely, the presence of the proposition Elem. I 31 in the purely Euclidean part of the book, in spite of the fact that the assertion merely repeats the absolute proposition Elem. I 27 without explicitly containing any Euclidean element.It is probable that the failure of these direct attempts led to an indirect approach to the problem through reductio ad absurdum of some hypothesis contrary to what was to become Postulate V or to some equivalent proposition. Numerous texts survive from which it is clear that geometers contemporary with Aristotle followed fairly far the consequences of an hypothesis contrary to the fifth postulate, obtaining important results which are partly identical with some theorems of Saccheri. Some of these texts attest first of all that what Saccheri called the Hypothesis of the Obtuse Angle had been stated in an independent and explicit way and that the fundamental result, identical with Prop. 14 of Saccheri's Euclides ab omni naevo vindicatus (1733), had been obtained, namely, that within Bolyai's Absolute Geometry this hypothesis leads to the remarkable formal contradiction that parallels intersect. This conclusion followed from two different formulations of the Obtuse Angle Hypothesis: (2) Anal. Prior. 66a 11–14, if the exterior angle (formed by a secant which intersects two parallel straight lines) is smaller than the interior angle (opposite and situated on the same side of the secant), and (3) 66a 14–15, if the sum of the angles in a triangle is greater than 2R. Finally, an item in (4) Ethica ad Eudemum 1222b 35–36 shows us that by investigating the Obtuse Angle Hypothesis, the Greek geometers also discovered the quadrilateral in which the sum of the angles is equal to 8R; this quadrilateral, which does not appear even in Saccheri's book, is the maximal quadrilateral of the Riemann geometry, a quadrilateral degenerated into a straight line closed upon itself (Chapter IV 20).Nowhere in the Corpus does the Hypothesis of the Acute Angle appear in an independent formulation. Nevertheless in (5) Anal. Poster. 90a 33–34 this Hypothesis is mentioned along with the other two: namely, Aristotle states that the essence of the triangle consists in the sum of its angles' being equal to, greater than or less than 2R (Chapter V 27). The formulation of the fifth postulate in the Elements allows greater probability to the conjecture of independent existence of the Acute Angle Hypothesis as well. Indeed, in its original formulation the fifth postulate is redundant, since it unnecessarily specifies in which of the half-planes (bounded by the secant) the intersection of the two straight lines occurs; this specification is itself a theorem. The Acute Angle Hypothesis must have been formulated not only symmetrically to (3) Anal. Prior. 66 a 14–15, that is, the sum of the angles of the triangle is less than 2R, as results from (5) Anal. Poster. 90 a 33–34, but also symmetrically to (2) Anal. Prior. 66 a 11–14. In the latter case the following final conclusion should have been reached in order to reduce to absurdity the Acute Angle Hypothesis: Two straight lines cut by a secant are incident if the sum of the interior angles (on the same side of the secant) is smaller than 2R, and the incidence occurs on that side of the secant where the sum of the angles is less than 2R. In the frame of the Acute Angle Hypothesis, this end conclusion is relevant only if this final specification (concerning the half-plane where the incidence occurs) is explicitly emphasised. According to my conjecture, it was precisely the practical impossibility of reaching this conclusion as a theorem of Absolute Geometry that later determined Euclid to transpose this decisive end conclusion from the Acute Angle Hypothesis, without changing its wording, and to include it among the postulates (Chapter II 13).A queer passage of Proklos (In primum Euclidis Elementorum, ed. Friedlein p. 368, 26–369, 1) in which the Acute Angle Hypothesis is presented in the form of a Zenonian paradox reinforces the conjecture that this hypothesis was studied independently by the ancient geometers (Chapter VI 33). Thus failure to solve the Problem of Parallels preceded not only the later Non-Euclidean geometry but also Euclidean geometry itself.The general undifferentiated Contra-Euclidean Hypothesis appears in the following form in all the other texts examined: The sum of the angles in the triangle is not equal to 2R. This hypothesis is nowhere qualified by Aristotle as being absurd or impossible: On the contrary, he takes it always as being just as much justified a priori as is the Euclidean theorem Elem. I 32 which contradicts it. For instance in (6) Anal. Poster. 93 a 33–35 Aristotle puts the problematical alternative: Which of the two propositions is right (or, which of the two constitutes the Logos, the raison d'être of the triangle), the one that states that the sum of the angles in the triangle is equal to 2R, or on the contrary, the one that states that the sum of the angles in the triangle is not equal to 2R (Chapter V 28)?In a number of texts the theorem Elem. I 32 itself and the general Contra-Euclidean Hypothesis are treated as being a sort of principle, and stress is laid on the idea that the logical consequences of each of these items invariantly preserve its specific (Euclidean or non-Euclidean) geometrical content [(7) 1187 a 35–38 (Chapter IV 18); (8) 1222 b 23–26 (Chapter IV 19); (9) 1187 b 1–2 (Chapter IV 18); (10) 1222 b 41–42 Chapter IV 21); (11) 1187 b 2–4 (Chapter IV 18)]; (12) Physica 200 a 29–30: If the sum of the angles in the triangle is not equal to 2R, then the principles of geometry cannot remain the same (Chapter V 25); (13) Metaph. 1052 a 6–7: It is impossible that the sum of the angles in the triangle be sometimes equal to 2R and sometimes not equal to 2R (Chapter V 24). Finally, the most important item of this sort is to be found in (14) De Caelo 281 b 5–7: If we accept as a starting hypothesis that it is impossible for the sum of the angles in the triangle to be equal to 2R, then the diagonal of the square is commensurable with its side (Chapter III).Another group of texts reveal Aristotle's attitude as regard these Contra-Euclidean theorems: (15) 1222 b 38–39 (Chapter IV 20); (16) 200 a 16–19 (Chapter VI 30); (17) 402 b 18–21 (Chapter VI 31); (18) 171 a 12–16 (Chapter VI 32); (19) 77 b 22–26 (Chapter V 26); (20) 101 a 15–17 (Chapter VI 31); (21) 76 b 39–77 a 3 (Chapter VI 31). These passages reveal Aristotle's conviction that these paradoxical Contra-Euclidean propositions (which cannot be annihilated by reductio ad absurdum) are nevertheless inacceptable as bad, probably because their graphical construction requires curved lines for representing the concept of straight lines.Finally, another group of texts show that Aristotle sensed in a way the necessity of adding to the foundations of Geometry a new postulate, from which the proposition Elem. I 32 should follow rigorously.

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Aram Frenkian zum Gedächtnis

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Vorgelegt von J. E. Hofmann     

Demonstration of vascular dopamine receptors in membranes from rabbit renal artery using3H-spiroperidol binding

Summary Binding of³H-spiroperidol to membranes branes from rabbit renal artery was found to be saturable and of high affinity. Dopamine receptor antagonists inhibited binding much more potently thana-adrenergic antagonists and dopamine was much more potent than noradrenaline, indicating that³H-spiroperidol labels vascular dopamine receptors in rabbit renal artery.The skilful technical assistance of Mrs Doris Petermeyer and Miss Ulrike Jansen is gratefully acknowledged.     

A novel cannabinoid containing a 1,8-cineol moiety

Summary The synthesis of a novel cannabinoid containing a 1,8-cineol moiety (1) is described. It is much less biologically active than ¹-tetrahydrocannabinol.Acknowledgment. This work was supported by NIDA (grant No. DA-00574-01).     

The problem of the invariance of dimension in the growth of modern topology,part II

Summary This work examines the historical origins of topological dimension theory with special reference to the problem of the invariance of dimension. Part I, comprising chapters 1–4, concerns problems and ideas about dimension from ancient times to about 1900. Chapter 1 deals with ancient Greek ideas about dimension and the origins of theories of hyperspaces and higher-dimensional geometries relating to the subsequent development of dimension theory. Chapter 2 treatsCantor's surprising discovery that continua of different dimension numbers can be put into one-one correspondence and his discussion withDedekind concerning the discovery. The problem of the invariance of dimension originates with this discovery. Chapter 3 deals with the early efforts of 1878–1879 to prove the invariance of dimension. Chapter 4 sketches the rise of point set topology with reference to the problem of proving dimensional invariance and the development of dimension theory. Part II, comprising chapters 5–8, concerns the development of dimension theory during the early part of the twentieth century. Chapter 5 deals with new approaches to the concept of dimension and the problem of dimensional invariance. Chapter 6 analyses the origins ofBrouwer's interest in topology and his breakthrough to the first general proof of the invariance of dimension. Chapter 7 treatsLebesgue's ideas about dimension and the invariance problem and the dispute that arose betweenBrouwer andLebesgue which led toBrouwer's further work on topology and dimension. Chapter 8 offers glimpses of the development of dimension theory afterBrouwer, especially the development of the dimension theory ofUrysohn andMenger during the twenties. Chapter 8 ends with some concluding remarks about the entire history covered. Dedicated to Hans Freudenthal     

Laccase production byPolyporus sanguineus under different nutritional and environmental conditions

Summary Laccase production was higher in malt extract medium than in lignin, andPolyporus sanguineus appears to be better thanPolyporus versicolor andTrametes hirsuta (syn.Polyporus hirsutus) for enzyme production. Phenolic compounds, of which resorcinol was the most active, induced enzyme production; while sugars repressed it. A temperature of 37°C, pH 3 and indulin AT at a concentration of 0.2% gave the best enzyme yield.A part of Ph. D. thesis of D.S. Arora.Acknowledgments. We thank Westvaco Chemical Division, USA, and Dr P.S. Rehill, Forest Research Institute, Dehradun, India for providing lignin samples and the fungal strain, respectively. D.S. Arora further thanks University Grants Commission, New Delhi for financial assistance.     

The Curie's Lab and its Women (1906–1934) Le laboratoire Curie et ses Femmes (1906–1934)

When Bouvet discovered the relationship between the binary arithmetic of Leibniz and the hexagrams of the I ching—in reality only a purely formal correspondence—he sent to Leibniz a woodcut diagram of the Fu-Hsi arrangement, which provides the key to the analogy. This diagram, in a re-drawn version, was first published by Gorai Kinzō in a study of Leibniz's interpretation of the I ching and Confucianism which has been influential in providing, indirectly, the principal source for the accounts of Wilhelm and Needham. Yet this pioneering study of Leibniz's interpretation of the hexagrams is virtually unknown. Even the account of Needham, who saved it from complete obscurity, contains one or two inaccuracies about it and these are repeated by Zacher in his otherwise excellent monograph on Leibniz's binary arithmetic.     

Inter-theory relations in quantum gravity: Correspondence,reduction, and emergence

Relationships between current theories, and relationships between current theories and the sought theory of quantum gravity (QG), play an essential role in motivating the need for QG, aiding the search for QG, and defining what would count as QG. Correspondence is the broad class of inter-theory relationships intended to demonstrate the necessary compatibility of two theories whose domains of validity overlap, in the overlap regions. The variety of roles that correspondence plays in the search for QG are illustrated, using examples from specific QG approaches. Reduction is argued to be a special case of correspondence, and to form part of the definition of QG. Finally, the appropriate account of emergence in the context of QG is presented, and compared to conceptions of emergence in the broader philosophy literature. It is argued that, while emergence is likely to hold between QG and general relativity, emergence is not part of the definition of QG, and nor can it serve usefully in the development and justification of the new theory.     

Mechanisms of self-incompatibility in flowering plants

Self-incompatibility is a widespread mechanism in flowering plants that prevents inbreeding and promotes outcrossing. The self-incompatibility response is genetically controlled by one or more multi-allelic loci, and relies on a series of complex cellular interactions between the self-incompatible pollen and pistil. Although self-incompatibility functions ultimately to prevent self-fertilization, flowering plants have evolved several unique mechanisms for rejecting the self-incompatible pollen. The self-incompatibility system in the Solanaceae makes use of a multi-allelic RNase in the pistil to block incompatible pollen tube growth. In contrast, the Papaveraceae system appears to have complex cellular responses such as calcium fluxes, actin rearrangements, and programmed cell death occurring in the incompatible pollen tube. Finally, the Brassicaceae system has a receptor kinase signalling pathway activated in the pistil leading to pollen rejection. This review highlights the recent advances made towards understanding the cellular mechanisms involved in these self-incompatibility systems and discusses the striking differences between these systems. Received 10 May 2001; received after revision 20 June 2001; accepted 20 June 2001     

On the verge of <Emphasis Type="Italic">Umdeutung</Emphasis> in Minnesota: Van Vleck and the correspondence principle. Part two

This is the second installment of a two-part paper on developments in quantum dispersion theory leading up to Heisenberg’s Umdeutung paper. In telling this story, we have taken a 1924 paper by John H. Van Vleck in The Physical Review as our main guide. In this second part we present the detailed derivations on which our narrative in the first part rests. The central result that we derive is the Kramers dispersion formula, which played a key role in the thinking that led to Heisenberg’s Umdeutung paper. We derive classical formulae for the dispersion, emission, and absorption of radiation and use Bohr’s correspondence principle to construct their quantum counterparts both for the special case of a charged harmonic oscillator (Sect. 5) and for arbitrary non-degenerate multiply-periodic systems (Sect. 6). We then rederive these results in modern quantum mechanics (Sect. 7). This paper was written as part of a joint project in the history of quantum physics of the Max Planck Institut für Wissenschaftsgeschichte and the Fritz-Haber-Institut in Berlin. The authors gratefully acknowledge support from the Max Planck Institute for History of Science. The research of Anthony Duncan is supported in part by the National Science Foundation under grant PHY-0554660.     

The biologically active conformation of ergot alkaloids

Summary Molecular mechanics and NMR studies of the D ring conformation of ergot alkaloids demonstrate that both D₁ and D₂ forms may exist in solution. The comparison of the geometric parameters defining the spatial relations between the aromatic moieties and the basic nitrogen of conformationally restricted dopamine analogs, and that of ergolene, shows the D₁ conformation to be the bioactive one.     

Initial transdetermination in the first leg discs of differentDrosophila species

Initial transdetermination leads from lateral and medial halves of male first leg imaginal discs almost exclusively to structures of the base and the spread (blade) of the wing. Mesonotum never appeared. The frequency of transdetermination is species-specific and most probably cell-autonomous. Medial halves transdetermine more frequently than lateral halves. Under the influence of an equivalent amount of blastema growthD. nigromelanica transdetermine with a much higher frequency thanD. virilis.     

Galilean argumentation and the inauthenticity of the Cigoli letter on painting vs. sculpture

This essay is partly a case study of the role of logic in historiography. It is also partly a test case for the thesis of a Galilean correspondence between aesthetic attitude and scientific thought, advanced by Panofsky, Koyré, and Heilbron. Intrinsically, it is a discussion of the authenticity of the letter to Cigoli dated 26 June 1612, widely attributed to Galileo, containing argumentation about the relative aesthetic merits of painting and sculpture. I undertake a systematic analysis of the letter’s method of argument, comparing and contrasting it with Galileo’s. I argue that the letter does have some Galilean characteristics: critical reasoning; ad hominem argumentation, in the seventeenth-century sense; and appeal to experimentation. However, the letter falls short of the typical Galilean open-mindedness, fair-mindedness, and clarity; crucially, it uses several illative terms which Galileo never uses, and does not use the one he uses most often. The latter features outweigh the former. Moreover, I discuss some aspects of the letter’s substantive content, primarily a theory of vision that disregards the dynamics of perspective and the faculty of binocularity, which Galileo understood and exploited very well. My novel argument vindicates an old judgment of Favaro, who doubted the letter’s authenticity.     

The morphology of the lateral line system in 3 species of Pacific cottoid fishes occupying disparate habitats

Summary The superficial neuromasts inLeptocottus armatus (Pacific staghorn sculpin) andOligocottus maculosus (tidepool sculpin) are depressed below the rim of an epidermal collar, whereas the superficial neuromasts inPsychrolutes paradoxus (tadpole sculpin) are surrounded by a pair of hillocks. The lateral line canal system appears identical across these species, whereas the system of superficial neuromasts shows some intraspecific variation. The sand-livingLeptocottus has a more highly developed system of superficial neuromasts thanOligocottus, which lives in a rocky habitat. The present results support the correlation between lateral line system morphology and habitat features previously postulated by Dijkgraaf.     

Peace with nature,or plants as indicators to the loss of humanity

Summary 1)Peace with nature means that human relations with other beings are controlled constitutionally within a community to which not only mankind belongs. Constitutionally restricted and in this sense non-violent, human domination is legitimate. 2) What we are allowed to do depends on who we are. Mankind is the species in which nature emerges to express herself in language, art and reason, and in doing so she moves herself forward with us. 3) How we should relate ourselves to nature also depends on our understanding of nature. Nature basically is acting nature, or creative power, and in this sense equally is the nature of the beings of nature. 4) Some artifacts are more natural and correspond to peace with nature better than others which are unnatural and violate peace with nature. Also in our fellow world, and even apart from man's influence, nature is whatought to be. 5) The technologically less advanced countries should not repeat the mistakes of the industrialized countries. The traditional pattern of industrial economy cannot be generalized to all peoples and violates peace with nature. 6) Plants are not only most sensitive indicators to environmental pollution but to the loss of humanity as well.     

Unterschiedliche Empfindlichkeit verschiedener Angiotensinderivate gegen Abbau durch Plasma oder Nierenhomogenat

Summary -Asp¹-Angiotensin II had a more pronounced action on the blood pressure of nephrectomized rats than the corresponding-compound.-Asp¹-Angiotensins were more slowly destroyed by rat serum, rat kidney homogenate, and human plasma than-compounds, especially-Asp¹-Angiotensin II amide.     

Les tests microbiologiques pour la détermination des vitamines

Summary The growth factors for microorganisms are nothing else than the vitamines known in animal physiology. Some microorganisms, like animals, have lost the possibility of synthetising these factors, which must be added to the culture medium. The action of the vitamine is quantitative and specific. These properties enable the auxo-heterotrophic microorganism, having lost the possibility of synthesis for a determined vitamine, to be used for a quantitative determination of this factor. The Phycomyces test for thiamine (vitamine B₁) and its different practical applications are discussed.