Academics From France

"The archaism of the Gāthās would incline us to situate Zarathuštra in the very beginning of the first millennium BCE, if not even earlier."

"Diversity isn’t just having a black person here and there. It’s about where they can have some kind of influence and power, and have a say in how things should run."

"You are right to believe in the goodness of people. Keep doing what you do; working hard, loving, laughing, forgiving and doing your bit might not change the whole world, but it will change you for the best."

"The God of Indian devotion - bhakti who responds to the same eternal needs of the human heart as exists anywhere else, never detaches himself wholly from the immanence of the world. He is personal and endowed with feelings only in the eyes of popular piety; to thought he reveals himself both far beyond and within at the same time; he reveals it as much as he hides it; and each man is in himself in some sort a manifestation of God."

"Maybe the true purpose of my life is for my body, my sensations and my thoughts to become writing, in other words, something intelligible and universal, causing my existence to merge into the lives and heads of other people."

"The worst thing about shame is that we imagine we are the only ones to experience it."

"I love my life, I like to be cosmopolitan, I would like to visit the whole earth and love it all."

"I can no longer think of any way to change my life except by having a baby. I will never sink lower than that."

"I am beginning to reach the age when I say hello to the old women I meet in my neighborhood, anticipating the moment in life when I shall be one of them. When I was twenty I didn't notice them; they would be dead before my face had wrinkles."

"I am endowed by shame's vast memory, more detailed and implacable than any other, a gift unique to shame."

"C'est la prose qui donne l'empire à une Langue, parce qu'elle est tout usuelle; la poésie n'est qu'un objet de luxe."

"C'est un terrible luxe que l'incredulité."

"La certitude et le mystère sont pour le sentiment; la clarté et l'incertitude pour le raisonnement."

"L'être qui ne fait de sentir, ne pense pas encore; et l'être qui pense, sent toujours."

"Dieu est la plus haute mesure de notre incapacité; l'universe, l'espace lui-même, ne sont pas si inaccessibles."

"L'imagination est amie de l'avenir."

"Tout le monde a besoin de la France, quand l'Angleterre a besoin de tout le monde."

"La raison est historienne, mais les passions sont actrices."

"Le prince absolu peut être un Néron, mais il est quelquefois Titus ou Marc-Aurèle; le peuple est souvent Néron, et jamais Marc-Aurèl."

"Ce qui n'est pas clair n'est pas français."

"L'homme qui parle est … l'homme qui pense tout haut."

"Le langage est la peinture de nos idées."

"Les idées sont des fonds qui ne portent intérèt qu'entre les mains du talent."

"La politique est comme le sphinx de la fable, elle dévore tous ceux qui n'expliquent pas ses énigmes."

"La religion unit les hommes dans les mêmes dogmes, la politique les unit dans les mêmes principes, et la philosophie les renvoie dans les bois; c'est le dissolvant de la société."

"Le chat ne nous caresse pas, il se caresse à nous."

"In the social body as in every organized body — that is, one in which the parts are arranged in certain relationships to each other relative to a given end — the cessation of vital functions does not come from the annihilation of their parts, but from their displacement and the disturbances of their relationships."

"A nobleman is not only a subject, he is the most subordinate of all."

"Father, mother, child, which express both the union of the sexes and de production of the being, can only be considered dependently on one another, and relatively to one another. A woman could exist without the existence of a man; but there is no mother if there is no father, nor a child without both of them. Each one of these ways of being presumes and recalls the other two; that is to say, they are relative. Considered thus, they are called relationships, in Latin, ratio; father, mother, child are persons, and their union forms the family. The union of the sexes, which is the foundation of all these relationships, is called marriage."

"Marriage is therefore not an ordinary contract, since in terminating it, the two parties cannot return themselves to the same state they were in before entering into it. And if the contract is voluntary at the time it is entered into, it can no longer be voluntary, and almost never is, at the time of its termination, since the party which manifests the desire to dissolve it takes all liberty from the other party to refuse, and has only too many means to force its consent."

"Let us now consider toposes. ... Unlike schemes, toposes generate geometry without points. In fact, nothing prevents us from proposing an axiomatic framework for geometry in which points, lines, and planes would all be on the same footing. Thus we know axiomatic systems for projective geometry (George Birkhoff) in which the primitive notion is that of a plate (a generalization of lines and planes), and in which the fundamental relationship is that of incidence. In mathematics, we consider a class of partially ordered sets called lattices; each of these corresponds to a distinct geometry. ... In the geometry of a topological space, the lattice of open sets plays a starring role, while points are relatively minor. But Grothendieck’s originality was to reprise Riemann’s idea that multivalued functions actually live not on open sets of the complex plane, but on spread-out Riemann surfaces. The spread-out Riemann surfaces project down to each other and thus form the objects of a category. However, a lattice is a special case of a category, since it includes at most one transformation between two given objects. Grothendieck thus proposed replacing the lattice of open sets with the category of spread-out open sets. When adapted to algebraic geometry, this idea solves a fundamental difficulty, since there is no implicit function theorem for algebraic functions. Sheaves can now be considered as special functors on the lattice of open sets (viewed as a category), and can thus be generalized to étale sheaves, which are special functors of the étale topology. Grothendieck would successfully play many variations on this theme in the context of various problems of geometric construction (for example, the problem of modules for algebraic curves). His greatest success in this regard would be the étale “ℓ-adic” cohomology of schemes, the cohomological theory needed to attack the Weil conjectures."

"... Formal groups. This topic is by far the deepest and most imaginative creation of Dieudonné, realized when Dieudonné was nearing 50, supposedly the term for an active mathematical life. It can be seen as the creation of a differential calculus for groups over a field of characteristic p > 0 (possibly finite). The methods of calculus do not work, and one has to resort to pure algebra. There were a number of forerunners: a version of Taylor’s formula in characteristic p > 0 due to Dieudonn ́e himself, the ideas of Delsarte about convolution operators (as explained in Book IV, chapter 6 of Bourbaki’s Éléments), a definition of the Lie algebra of a Lie group and its enveloping algebra in terms of distributions on the group (by L. Schwartz). But the impetus came from the book by Chevalley, in 1951, about algebraic groups. Chevalley had developed a purely algebraic version of Lie theory, but restricted to fields of characteristic 0. The case of characteristic p > 0 was “terra incognito”. In a long series of papers, published between 1954 and 1958, later on collected into a book ... Dieudonné explored in depth this new world."

"Now one final remark on the term spectrum. In physics each type of atom or molecule possesses a characteristic spectrum formed by its emission or absorption lines. Quantum mechanics interprets these as the characteristic values of an operator, the Hamiltonian, acting on a certain Hilbert space. It is thus natural to speak of the discrete spectrum of the Hamiltonian. The emission or absorption bands correspond to a continuous spectrum. In the early 1930s von Neumann succeeded brilliantly in defining the concept of a self-adjoint (unbounded) operator H on a Hilbert space 𝔥 and its spectrums. The contribution of Gelfand in 1940 was in associating a commutative Banach algebra A with the operator H and an isomorphism of A onto C0(S;\mathbb{C}). From that point on the evolution of the meaning of the word spectrum can be understood. For Grothendieck the spectrum of a commutative ring consists of its prime ideals (as in the case of Dedekind)."

"We must continue evangelizing people’s beliefs with regard to angels, as the Church always did in the past. I think that our teaching about angels mustn’t occupy center stage but that it is important, since it reminds us of the spiritual dimension of existence. The simple fact to think of an angelic world, that is a purely spiritual world, would be a good way to fight the world’s underlying materialism and make people understand that there aren’t only material realities. The preaching about angels invites us to have a greater and more beautiful idea of God."

"Evolution is a tinkerer, not an engineer."

"The dream of every cell is to become two cells."

"Anyone who acts without paying attention to what he is doing is wasting his life. I'd go so far as to say life is denied by lack of attention, whether it be to cleaning windows or trying to write a masterpiece."

"There is absolutely not a shadow of a doubt that the Greeks knew all about Indian philosophy."

"Nothing, in the present state of archaeological research ... enables us to reconstruct convincingly invasions that could be clearly attributed to Aryan groups."

"‘This famous vacuum that was sometimes called Vedic night . . . has been filling up more and more thanks to numerous findings.’93 In his opinion, the considerable changes that followed the end of the Indus cities are to be understood ‘within the framework of a continuity with the preceding millennia, without any radical break of the sort too often proposed earlier’."

"To take a single example here, some scholars decided that the Pirak culture, which emerged around 1800 BCE in the plains of Baluchistan, is the best representative of the Aryan intrusion. However, Jarrige, who directed excavations in the region, found that none of the transformations happening there in the early second millennium BCE, including the introduction of summer crops such as rice and millets (especially sorghum or jowar, in addition to the traditional winter crops of wheat and barley), ‘can be explained in the context of invasions of semi-nomadic peoples coming from the [Central Asian] steppes. … How could this series of transformations be seriously attributed to Indo-Aryan invaders? … Nothing, in the present state of archaeological research … enables us to reconstruct convincingly invasions that could be clearly attributed to Aryan groups’ (Jarrige 1995, pp. 24, 21). Regrettably, such well-informed views have been brushed aside in the desperate but vain search for material traces of those ‘Aryan groups’."

"As the excavator of Pirak, the only well-preserved second millennium B.C.E. site from the area (which he dates from 1700 to 700 B.C.E.), Jarrige (1985) finds a "town" of some size with "elaborate architec- ture" and evidence of a more intense level of irrigation and cultivation than occurred in the third millennium B.C.E.: "Just the opposite of that which has been presumed on the basis of negative evidence" (46). In view of the fact that Pirak is widely accepted as her- alding the Indo-Aryans due to the discovery of the horse there, my previous remarks about Indo-Aryans and urban centers are reinforced. Those wishing to consider Pirak as evidence of nomad Indo-Aryan pastoralists must address the fact that it was "a town of some size with elaborate architecture" that increased the agricultural productivity of the area."

"Jarrige's study of continuity and change concludes that the people living in the Kachi plain during the second millennium B.C.E. undoubtedly experienced the major economic transformations of the time yet maintained significant elements of cultural continuity and conservatism from the early third millennium B.C.E. and earlier. He underscores the continuity aspect of the area by comparing the ancient ruins of residential buildings from the excavations at Pirak with the very recent ruins of a house deserted by Hindus at partition in the same district. The resemblance is striking, while the samples of cooking pots between the two periods seem almost identical. Regarding the transformations, he doubts whether every newly attested item in the Kachi archaeological record of the second millennium B.C.E. could be attributed to an influx of new peoples, "since the processes . . . are too complex to be attributed to the arrival of invaders who at the same time would have had to have introduced rice from the Ganges, sorghum from the Arabian Gulf, and camels and horses from Central Asia" (Jarrige 1983, 56)."

"Although basic similarities exist, linking Mehrgarh with comparable Levantine and Zagrosian aceramic neolithic groups, “...they are sufficiently general to discount straightforward diffusion among communities that otherwise preserved their own, highly individual characteristics” (Jarrige 1991: 40)."

"Another element of continuity between ceramics of the third millennium Baluchistan and those of the second millennium can be found in the decoration. While the geometric painted designs on pottery from Pirak may be quite different from those on Harappan pottery, they are very much in the older ‘Quetta-Amri’ tradition. In our report on Pirak we pointed out similarities which we feel are too close to be explained merely as a result of coincidence. We postulated that such traditional styles of decoration survived in regions which were at the periphery of the principal zone of Harappan influence... ...Should the origins for these transformations of the second millennium be sought in exogeneous events, in colonization of the area by new peoples, by a sudden influx of refugees bringing new crops and animals with them? Probably not, since the processes which I have briefly described are too complex to be attributed to the arrival of invaders who at the same time would have had to have introduced rice from the Ganges, sorghum from the Arabian Gulf, and camels and horses from Central Asia. It is also not likely that the newcomers, whether they be a ruling elite or refugees, would have had the impetus to change an agricultural system still capable of being intensified without the introduction of new crops and, for rice, new irrigation practices."

"Phoenix-like, the theory of the invaders, preferably Indo-Europeans, always rises from its ashes."

"Along the same lines, the antiquities discovered at Quetta in 1985, which are also sometimes connected with intruding Indo-Aryans (i.e., e.g. Allchin 1995), can also simply be viewed as reflecting "the economic dynamism of the area extending from South Central Asia to the Indus Valley." The fact that similar objects are also found in graves and deposits in northern Iran, eastern Iran, northwestern Afghanistan, South Turkmenia, and Baluchistan might simply indicate "a wide distribution of common beliefs and ritual practices" (Jarrige and Hassan (1985) 1989, 162-163). Jarrige and Hassan reject the idea that these finds were associated with invaders related to the Hissar III C complex, since "there is nothing in the Gorgan Plain and at Hissar to prove that northern Iran has been a relay station for invading people. The . . . grey ware can very well be explained within its local context" (163-164). Nor are these scholars partial to the northern steppe Andronov alternatives, since: We leave to the linguists the problem of whether Indo-European languages were introduced into the Middle Asian regions from a still unknown part of the Eurasian steppes in the course of the third millennium or if Indo-Iranian languages have been associated with these regions for a much longer period. As far as archaeology is concerned, we do think that it is increasingly necessary for specialists in Indo-lranian studies to pay attention to the . . . interrelated cultural entities of the late third and early second millennium in the regions between Mesopotamia and the Indus. It is a direction of research that is likely to be more fruitful than are traditional attempts to locate remains left by nomads from "the Steppes," attempts that were in fashion when the Indo-Iranian Borderlands were thought to be a cultural vacuum. (164)"

"Despite inviting linguists to reconsider the northern steppe hypothesis in favor of the southern route, it can be inferred from Jarrige and Hassan, as from the work of a number of archaeologists considering the problem of Indo-Aryan origins, that the Indo-Aryan- locating project exists solely due to linguistic exigencies: The development of original but closely interrelated cultural units at the end of the third and the beginning of the second millennium cannot be explained just by the wandering of a single group of invaders. The processes were obviously multidirectional in regions with strong and ancient cultural traditions. This does not preclude the fact that movement of population and military expeditions . . . may have played an important historical part but, as far as archaeology is concerned, there is nothing to substantiate a simplistic model of invasion to account for the complex economic and cultural phenomena manifest at the end of the third millennium in the regions between Mesopotamia and the Indus Valley. (164)"

"Jarrige (1985) specifically mentions that the existence of the Indo-Aryans has "so far only been deduced on the basis of linguistic evidence" (62; ). Otherwise, "what we see is a dynamic system of multidirectional contacts and 'influences' extending throughout a vast area from southern Central Asia to the Ganges valley and continuing from the beginning of the 2nd millennium into the 1st millennium BC" (62)."

"From the Neolithic time till almost today there has never been, in spite of spectacular changes in the course of time, a definite gap or break in the history of the subcontinent."