University of Cambridge alumni

2767 quotes found

"No man holding a strong belief on one side of a question, or even wishing to hold a belief on one side, can investigate it with such fairness and completeness as if he were really in doubt and unbiased; so that the existence of a belief not founded on fair inquiry unfits a man for the performance of this necessary duty. Nor is it that truly a belief at all which has not some influence upon the actions of him who holds it. He who truly believes that which prompts him to an action has looked upon the action to lust after it, he has committed it already in his heart. If a belief is not realized immediately in open deeds, it is stored up for the guidance of the future. It goes to make a part of that aggregate of beliefs which is the link between sensation and action at every moment of all our lives, and which is so organized and compacted together that no part of it can be isolated from the rest, but every new addition modifies the structure of the whole. No real belief, however trifling and fragmentary it may seem, is ever truly insignificant; it prepares us to receive more of its like, confirms those which resembled it before, and weakens others; and so gradually it lays a stealthy train in our inmost thoughts, which may someday explode into overt action, and leave its stamp upon our character for ever."

- William Kingdon Clifford

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"Belief, that sacred faculty which prompts the decisions of our will, and knits into harmonious working all the compacted energies of our being, is ours not for ourselves but for humanity. It is rightly used on truths which have been established by long experience and waiting toil, and which have stood in the fierce light of free and fearless questioning. Then it helps to bind men together, and to strengthen and direct their common action. It is desecrated when given to unproved and unquestioned statements, for the solace and private pleasure of the believer; to add a tinsel splendour to the plain straight road of our life and display a bright mirage beyond it; or even to drown the common sorrows of our kind by a self-deception which allows them not only to cast down, but also to degrade us. Whoso would deserve well of his fellows in this matter will guard the purity of his beliefs with a very fanaticism of jealous care, lest at any time it should rest on an unworthy object, and catch a stain which can never be wiped away. It is not only the leader of men, statesmen, philosopher, or poet, that owes this bounden duty to mankind. Every rustic who delivers in the village alehouse his slow, infrequent sentences, may help to kill or keep alive the fatal superstitions which clog his race. Every hard-worked wife of an artisan may transmit to her children beliefs which shall knit society together, or rend it in pieces. No simplicity of mind, no obscurity of station, can escape the universal duty of questioning all that we believe. It is true that this duty is a hard one, and the doubt which comes out of it is often a very bitter thing. It leaves us bare and powerless where we thought that we were safe and strong. To know all about anything is to know how to deal with it under all circumstances. We feel much happier and more secure when we think we know precisely what to do, no matter what happens, than when we have lost our way and do not know where to turn. And if we have supposed ourselves to know all about anything, and to be capable of doing what is fit in regard to it, we naturally do not like to find that we are really ignorant and powerless, that we have to begin again at the beginning, and try to learn what the thing is and how it is to be dealt with — if indeed anything can be learnt about it. It is the sense of power attached to a sense of knowledge that makes men desirous of believing, and afraid of doubting."

- William Kingdon Clifford

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"A bad action is always bad at the time when it is done, no matter what happens afterwards. Every time we let ourselves believe for unworthy reasons, we weaken our powers of self-control, of doubting, of judicially and fairly weighing evidence. We all suffer severely enough from the maintenance and support of false beliefs and the fatally wrong actions which they lead to, and the evil born when one such belief is entertained is great and wide. But a greater and wider evil arises when the credulous character is maintained and supported, when a habit of believing for unworthy reasons is fostered and made permanent. If I steal money from any person, there may be no harm done from the mere transfer of possession; he may not feel the loss, or it may prevent him from using the money badly. But I cannot help doing this great wrong towards Man, that I make myself dishonest. What hurts society is not that it should lose its property, but that it should become a den of thieves, for then it must cease to be society. This is why we ought not to do evil, that good may come; for at any rate this great evil has come, that we have done evil and are made wicked thereby. In like manner, if I let myself believe anything on insufficient evidence, there may be no great harm done by the mere belief; it may be true after all, or I may never have occasion to exhibit it in outward acts. But I cannot help doing this great wrong towards Man, that I make myself credulous. The danger to society is not merely that it should believe wrong things, though that is great enough; but that it should become credulous, and lose the habit of testing things and inquiring into them; for then it must sink back into savagery."

- William Kingdon Clifford

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"In what cases, then, let us ask in the first place, is the testimony of a man unworthy of belief? He may say that which is untrue either knowingly or unknowingly. In the first case he is lying, and his moral character is to blame; in the second case he is ignorant or mistaken, and it is only his knowledge or his judgment which is in fault. In order that we may have the right to accept his testimony as ground for believing what he says, we must have reasonable grounds for trusting his veracity, that he is really trying to speak the truth so far as he knows it; his knowledge, that he has had opportunities of knowing the truth about this matter; and his judgment, that he has made proper use of those opportunities in coming to the conclusion which he affirms. However plain and obvious these reasons may be, so that no man of ordinary intelligence, reflecting upon the matter, could fail to arrive at them, it is nevertheless true that a great many persons do habitually disregard them in weighing testimony. Of the two questions, equally important to the trustworthiness of a witness, "Is he dishonest?" and "May he be mistaken?" the majority of mankind are perfectly satisfied if one can, with some show of probability, be answered in the negative. The excellent moral character of a man is alleged as ground for accepting his statements about things which he cannot possibly have known."

- William Kingdon Clifford

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"Upon Clifford's death the labour of revision and completion was entrusted to Mr. R. C. Rowe, then Professor of Pure Mathematics at University College, London. ...On the sad death of Professor Rowe, in October 1884, I was requested... to take up the task of editing... For the latter half of Chapter III. and for the whole of Chapter IV. ...I am alone responsible. Yet whatever there is in them of value I owe to Clifford; whatever is feeble or obscure is my own. ...With Chapter V. my task has been by no means light. ...Without any notice of mass or force it seemed impossible to close a discussion on motion; something I felt must be added. I have accordingly introduced a few pages on the laws of motion. I have since found that Clifford intended to write a concluding chapter on mass. How to express the laws of motion in a form of which Clifford would have approved was indeed an insoluble riddle to me, because I was unaware of his having written anything on the subject. I have accordingly expressed, although with great hesitation, my own views on the subject; these may be concisely described as a strong desire to see the terms matter and force, together with the ideas associated with them, entirely removed from scientific terminology—to reduce, in fact, all dynamic to kinematic. I should hardly have ventured to put forward these views had I not recently discovered that they have (allowing for certain minor differences) the weighty authority of Professor Mach, of Prag. But since writing these pages I have also been referred to a discourse delivered by Clifford at the Royal Institution in 1873, some account of which appeared in Nature, June 10, 1880. Therein it is stated that 'no mathematician can give any meaning to the language about matter, force, inertia used in current text-books of mechanics.' This fragmentary account of the discourse undoubtedly proves that Clifford held on the categories of matter and force as clear and original ideas as on all subjects of which he has treated; only, alas! they have not been preserved."

- William Kingdon Clifford

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"We may... be treating merely as physical variations effects which are really due to changes in the curvature of our space; whether, in fact, some or all of those causes which we term physical may not be due to the geometrical construction of our space. There are three kinds of variation in the curvature of our space which we ought to consider as within the range of possibility. (i) Our space is perhaps really possessed of a curvature varying from point to point, which we fail to appreciate because we are acquainted with only a small portion of space, or because we disguise its small variations under changes in our physical condition which we do not connect with our change of position. The mind that could recognise this varying curvature might be assumed to know the absolute position of a point. For such a mind the postulate of the relativity of position would cease to have a meaning. It does not seem so hard to conceive such a state of mind as the late Professor Clerk-Maxwell would have had us believe. It would be one capable of distinguishing those so-called physical changes which are really geometrical or due to a change of position in space. (ii) Our space may be really same (of equal curvature), but its degree of curvature may change as a whole with the time. In this way our geometry based on the sameness of space would still hold good for all parts of space, but the change of curvature might produce in space a succession of apparent physical changes. (iii) We may conceive our space to have everywhere a nearly uniform curvature, but that slight variations of the curvature may occur from point to point, and themselves vary with the time. These variations of the curvature with the time may produce effects which we not unnaturally attribute to physical causes independent of the geometry of our space. We might even go so far as to assign to this variation of the curvature of space 'what really happens in that phenomenon which we term the motion of matter.'"

- William Kingdon Clifford

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"With the new views advocated by Riemann... the texture, structure or geometry of space is defined by the metrical field, itself produced by the distribution of matter. Any non-homogeneous distribution of matter would then entail a variable structure of geometry for space from place to place. ... Riemann's exceedingly speculative ideas on the subject of the metrical field were practically ignored in his day, save by the English mathematician Clifford, who translated Riemann's works, prefacing them to his own discovery of the non-Euclidean Clifford space. Clifford realised the potential importance of the new ideas and suggested that matter itself might be accounted for in terms of these local variations of the non-Euclidean space, thus inverting in a certain sense Riemann's ideas. But in Clifford's day this belief was mathematically untenable. Furthermore, the physical exploration of space seemed to yield unvarying Euclideanism. ...it was reserved for the theoretical investigator Einstein, by a stupendous effort of rational thought, based on a few flimsy empirical clues, to unravel the mystery and to lead Riemann's ideas to victory. (In all fairness to Einstein... he does not appear to have been influenced directly by Riemann.) Nor were Clifford's hopes disappointed, for the varying non-Euclideanism of the continuum was to reveal the mysterious secret of gravitation, and perhaps also of matter, motion, and electricity. ... Einstein had been led to recognize that space of itself was not fundamental. The fundamental continuum whose non-Euclideanism was fundamental was... one of Space-Time... possessing a four-dimensional metrical field governed by the matter distribution. Einstein accordingly applied Riemann's ideas to space-time instead of to space... He discovered that the moment we substitute space-time for space (and not otherwise), and assume that free bodies and rays of light follow geodesics no longer in space but in space-time, the long-sought-for local variations in geometry become apparent. They are all around us, in our immediate vicinity... We had called their effects gravitational effects... never suspecting that they were the result of those very local variations in the geometry for which our search had been in vain....the theory of relativity is the theory of the space-time metrical field."

- William Kingdon Clifford

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"Students of Spinoza will easily trace the connection between his theory of mind and matter and the doctrine set forth in Clifford's essays on "Body and Mind," and "The Nature of Things-in themselves. … Briefly put, the conception is that mind is the one ultimate reality; not mind as we know it in the complex forms of conscious feeling and thought, but the simpler elements out of which thought and feeling are built up. The hypothetical ultimate element of mind, or atom of mind-stuff, precisely corresponds to the hypothetical atom of matter, being the ultimate fact of which the material atom is the phenomenon. Matter and the sensible universe are the relations between particular organisms, that is, mind organized into consciousness, and the rest of the world. This leads to results which would in a loose and popular sense be called materialist. But the theory must, as a metaphysical theory, be reckoned on the idealist side. To speak technically, it is an idealist monism. Indeed it is a very subtle form of idealism, and by no means easy of apprehension at first sight. Nevertheless there are distinct signs of a convergence towards it on the part of recent inquirers who have handled philosophical problems in a scientific spirit, and particularly those who have studied psychology on the physiological side. Perhaps we shall be told that this proves the doctrine to be materialism in disguise; but it is hardly worth while to dispute about names while more serious things remain for discussion. And the idea does require much more working out; involving, as it does, extensive restatement and rearrangement of metaphysical problems. It raises not only several questions, but preliminary (and really fundamental) problems as to what questions are reasonable."

- William Kingdon Clifford

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"Apart from a few Crown appointments, like the Christ Church and Trinity Headships, Oxford and Cambridge had ever since the Revolution enjoyed a very complete immunity from Royal and Ministerial interference—an academic liberty that held in it the seeds of intellectual freedom for the whole country, as compared to the practice in many other lands down to our own time. The quarrel of James II with the Universities was constantly in the recollection of the dons, who, whether Whig or Tory, would never, in his daughter's reign, permit the least interference with their internal government by royal mandate or request. Any such attempt was promptly met by expressions of the hope that Queen Anne would "reflect upon what was done in Magdalen College in her father's time." Meanwhile politics swayed College elections, as in the case of poor "Mr. Entwissle's pretensions" to a Fellowship at Brazennose, for the young man was found to be a Whig, "which was against the present humour of the College." Such an incident in 1711 is not surprising, but it is a remarkable proof of academic freedom from government control that Oxford was permitted to continue such practices and to remain Tory, and largely Jacobite, under the Hanoverian kings and their Whig governments. Academic and scholastic freedom, which is a necessary condition of intellectual and political freedom, was established as against the State in Eighteenth Century England. In a great part of Europe it does not exist to-day. It is one of the island blessings we have inherited from our Whig and Tory ancestors."

- G. M. Trevelyan

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"The investigation of the form and brightness of the rings or rays surrounding the image of a star as seen in a good telescope, when a diaphragm bounded by a rectilinear contour is placed upon the object-glass, though sometimes tedious is never difficult. The expressions which it is necessary to integrate are always sines and cosines of multiples of the independent variable, and the only trouble consists in taking properly the limits of integration. Several cases of this problem have been completely worked out, and the result, in every instance, has been entirely in accordance with observation. These experiments... have seldom been made except by those whose immediate object was to illustrate the undulatory theory of light. There is however a case of a somewhat different kind; which in practice recurs perpetually, and which in theory requires for its complete investigation the value of a more difficult integral; I mean the usual case of an object-glass with a circular . The desire of submitting to mathematical investigation every optical phænomenon of frequent occurrence has induced me to procure the computation of the numerical values of the integral that presents itself in this inquiry: and I now beg leave to lay before the Society the calculated table, with a few remarks upon its application."

- George Biddell Airy

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"Newton pointed out and assigned generally, not only the nature and the magnitude of the periodical forces which are concerned in producing the tides, but likewise indicated their true character as undulations, in one very remarkable proposition, as well as in a special explanation of... the tides of the Port of Batsha. The equilibrium theory of Daniel Bernoulli adopted the first part of Newton's views but altogether neglected the second. ...Professor Airy ...has pronounced the theory proposed by La Place in the Mécanique Céleste,—if viewed with reference to the boldness and comprehensive character of its design rather than to the success of its execution—"as one of the most splendid works of the greatest mathematician of the past age." The problem, however, was not considered by [La Place] in the most general form which it is capable of receiving. He assumed the earth to be entirely covered by water, and its depth to be uniform, at least throughout the same parallel of latitude, and he neglected the resistance both of the particles of the fluid amongst each other, and of that which arises from the irregular surfaces in the channels over which the tide is transmitted. He was consequently obliged to omit the consideration of the tides in canals, rivers, and narrow seas, which constitute some of the most interesting, and by no means the most unmanageable, of the problems which later, and even in some respects more simple, investigations of the oscillations of the sea have brought within the control of analysis. Imperfect, however, as the results of this theory were as it came from the hand of its author, their importance cannot easily be estimated too highly. Dr. Young adopted the general principles which they involved, though he has subjected them to a totally different treatment; and Professor Airy, who has materially simplified the investigations which it contains, by rejecting some conditions which they included, such as the density of the sea, by which they were made needlessly difficult and complicated, has not only verified the more remarkable of the conclusions at which La Place arrived, but has also made important use of his methods in his own theory of waves and tides, which is by far the most complete and comprehensive that has ever yet appeared."

- George Biddell Airy

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"He eagerly... mastered the Physical Astronomy in the most thorough manner, as was evidenced by his Papers collected in his "Mathematical Tracts," his investigation of the Long Inequality of the Earth and Venus, and many other works. As Plumian Professor he had charge of the small Observatory at Cambridge, where he did a great deal of the observing and reduction work himself, and became thoroughly versed in the practical working of an Observatory. The result of this was immediately seen in the improved methods which he introduced at Greenwich, and which were speedily imitated at other Observatories. Optics and the Undulatory Theory of Light had been very favourite subjects with him, and he had written and lectured frequently upon them. In the construction of the new and powerful telescopes and other optical instruments required from time to time this knowledge was very essential, for in its instrumental equipment the Greenwich Observatory was entirely remodelled during his tenure of office. And in many of the matters referred to him, as for instance that of the Lighthouses, a thorough knowledge of Optics was most valuable. He had made a great study of the theory and construction of clocks, and this knowledge was invaluable to him at Greenwich in the establishment of new and more accurate astronomical clocks, and especially in the improvement of chronometers. He had carefully studied the theory of pendulums, and had learned how to use them in his experiments in the Cornish mines. This knowledge he afterwards utilized very effectively at the Harton Pit in comparing the density of the Earth's crust with its mean density; and it was very useful to him in connection with geodetic surveys and experiments on which he was consulted. And his mechanical knowledge was useful in almost everything."

- George Biddell Airy

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"I passed by a corner office in which an employee was typing up a document relating to brand performance. … Something about her brought to mind a painting by Edward Hopper which I had seen several years before at the Museum of Modern Art in Manhattan. In New York Movie (1939), an usherette stands by the stairwell of an ornate pre-war theatre. Whereas the audience is sunk in semidarkness, she is bathed in a rich pool of yellow light. As often in Hopper’s work, her expression suggests that her thoughts have carried her elsewhere. She is beautiful and young, with carefully curled blond hair, and there are a touching fragility and an anxiety about her which elicit both care and desire. Despite her lowly job, she is the painting’s guardian of integrity and intelligence, the Cinderella of the cinema. Hopper seems to be delivering a subtle commentary on, and indictment of, the medium itself, implying that a technological invention associated with communal excitement has paradoxically succeeded in curtailing our concern for others. The painting’s power hangs on the juxtaposition of two ideas: first, that the woman is more interesting that the film, and second, that she is being ignored because of the film. In their haste to take their seats, the members of the audience have omitted to notice that they have in their midst a heroine more sympathetic and compelling than any character Hollywood could offer up. It is left to the painter, working in a quieter, more observant idiom, to rescue what the film has encouraged its viewers not to see."

- Alain de Botton

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"He was reminded of a Dutch book whose moral he often returned to: De Schoonheid van hoogspanningslijnen in het Hollandse landschap, written by a couple of academics in Rotterdam University, Anne Kieke Backer and Arij de Boode. The Beauty of Electricity Pylons in the Dutch Landscape was a defence of the contribution of transmission engineering to the visual appeal of Holland, referencing the often ignored grandeur of the towers on their march from power stations to cities. Its particular interest for Ian, however, lay in its thesis about the history of the Dutch relationship to windmills, for it emphasised that these early industrial objects had originally been felt to have all the pylons’ threateningly alien qualities, rather than the air of enchantment and playfulness now routinely associated with them. They had been denounced from pulpits and occasionally burnt to the ground by suspicious villagers. The re-evaluation of the windmills had in large part been the work of the great painters of the Dutch Golden Age, who, moved by their country’s dependence on the rotating utilitarian objects, gave them pride of place in their canvases, taking care to throw their finest aspect into relief, like their resilience during storms and the glint of their sails in the late afternoon sun. … It would perhaps be left to artists of our own day to teach us to discern the virtues of the furniture of contemporary technology."

- Alain de Botton

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"What struck me at the League was the prestige in which our Government and our Prime Minister are held. What has struck hon. Members who have listened to this Debate is the fact that public opinion in the dictator countries has conceived a profound admiration for our Prime Minister and our country. Our country, therefore, is the country which is in a priceless position for securing the future of peace...It seems to me that we have two choices either to settle our differences with Germany by consultation, or to face the inevitability of a clash between the two systems of democracy and dictatorship. In considering this, I must emphatically give my opinion as one of the younger generation. War settles nothing, and I see no alternative to the policy upon which the Prime Minister has so courageously set himself—the construction of peace, with the aid which I have described. There is no other country which can achieve this, and I ask hon. and right hon. Gentlemen opposite sincerely to believe that in our efforts to understand, to consult with and, if possible, to get friendship with Germany, we do not abandon by one jot or tittle the democratic beliefs which are the very core of our whole being and system. In conclusion, I must gratify the right hon. Gentleman the Member for Wakefield by quoting Shakespeare. The right hon. Gentleman will remember the little poem "Under the Greenwood Tree"—"Here shall he see" "No enemy," "But winter and rough weather". We have the winter before us, and we have a great deal of political rough weather, but in that rough weather, do not let us forget the joint idea of peace which animates us all."

- Rab Butler

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"Some would hail Rab Butler as beyond question the most important and the greatest Conservative of his generation; and certainly his continuous record as a minister or shadow minister from 1932 to 1964 is a tribute to his endurance. Helped by his young lieutenants he rebuilt the Tory Party; he taxed his countrymen's income less than any other chancellor; he abolished wartime controls; and under him began the prosperity for which Macmillan claimed the credit. His admirers thought the title he chose for his memoirs exemplified his exact understanding of politics: The Art of the Possible. And yet for all his reputation among us as a liberal Conservative who had re-educated his party after 1945 as Peel did after 1832, for all his patronage of a generation of clever young Conservatives in Central Office, for all his amusing deviousness, afraid to strike yet willing, well, not to wound but to scratch, he was so cautious, so much a man of Munich that few major initiatives came from the succession of departments where he presided. He had a record that looked fine as home secretary, chancellor and foreign secretary and, of course, as minister for education: hardly a foot put wrong. But, then, some of us considered, his feet had not moved all that far. If you stride you may put a foot wrong, and Butler failed to stride into the European Community. He and Eden reinforced each other's scepticism. "Whenever I met Anthony, the sort of conversation was, 'Simply nothing doing, you know.'" On major issues he hardly ever questioned the wisdom of his advisers. The paradox remains. He could have won the 1964 election for the Tories but was the only contender for the leadership towards whom his colleagues felt lukewarm."

- Rab Butler

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"Since the belief in transmission of acquired adaptations arose from preconception rather than from evidence, it is worth observing that, rightly considered, the probability should surely be the other way. For the adaptations relate to every variety of exigency. To supply themselves with food, to find it, to seize and digest it, to protect themselves from predatory enemies whether by offence or defence, to counter-balance the changes of temperature, or pressure, to provide for mechanical strains, to obtain immunity from poison and from invading organisms, to bring the sexual elements into contact, to ensure the distribution of the type; all these and many more are accomplished by organisms in a thousand most diverse and alternative methods. Those are the things that are hard to imagine as produced by any concatenation of natural events; but the suggestions that organisms had had from the beginning innate in them a power of modifying themselves, their organs and their instincts so as to meet these multifarious requirements does not materially differ from the more overt appeals to supernatural intervention. The conception, originally introduced by Hering and independently by S. Butler, that adaptation is a consequence or product of accumulated memory was of late revived by Semon and has been received with some approval, especially by F. Darwin. I see nothing fantastic in the notion that memory may be unconsciously preserved with the same continuity that the protoplasmic basis of life possesses. That idea, though purely speculative and, as yet, incapable of proof or disproof contains nothing which our experience of matter or of life at all refutes. On the contrary, we probably do well to retain the suggestion as a clue that may some day be of service. But if adaptation is to be the product of these accumulated experiences, they must in some way be translated into terms of physiological and structural change, a process frankly inconceivable."

- William Bateson

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"Much of the skill of the true mathematical physicist and of the mathematical astronomer consists in the power of adapting methods and results carried out on an exact mathematical basis to obtain approximations sufficient for the purposes of physical measurements. It might perhaps be thought that a scheme of Mathematics on a frankly approximative basis would be sufficient for all the practical purposes of application in Physics, Engineering Science, and Astronomy, and no doubt it would be possible to develop, to some extent at least, a species of Mathematics on these lines. Such a system would, however, involve an intolerable awkwardness and prolixity in the statements of results, especially in view of the fact that the degree of approximation necessary for various purposes is very different, and thus that unassigned grades of approximation would have to be provided for. Moreover, the mathematician working on these lines would be cut off from the chief sources of inspiration, the ideals of exactitude and logical rigour, as well as from one of his most indispensable guides to discovery, symmetry, and permanence of mathematical form. The history of the actual movements of mathematical thought through the centuries shows that these ideals are the very life-blood of the science, and warrants the conclusion that a constant striving toward their attainment is an absolutely essential condition of vigorous growth. These ideals have their roots in irresistible impulses and deep-seated needs of the human mind, manifested in its efforts to introduce intelligibility in certain great domains of the world of thought."

- E. W. Hobson

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"The actual evolution of mathematical theories proceeds by a process of induction strictly analogous to the method of induction employed in building up the physical sciences; observation, comparison, classification, trial, and generalisation are essential in both cases. Not only are special results, obtained independently of one another, frequently seen to be really included in some generalisation, but branches of the subject which have been developed quite independently of one another are sometimes found to have connections which enable them to be synthesised in one single body of doctrine. The essential nature of mathematical thought manifests itself in the discernment of fundamental identity in the mathematical aspects of what are superficially very different domains. A striking example of this species of immanent identity of mathematical form was exhibited by the discovery of that distinguished mathematician . . . Major MacMahon, that all possible Latin squares are capable of enumeration by the consideration of certain differential operators. Here we have a case in which an enumeration, which appears to be not amenable to direct treatment, can actually be carried out in a simple manner when the underlying identity of the operation is recognised with that involved in certain operations due to differential operators, the calculus of which belongs superficially to a wholly different region of thought from that relating to Latin squares."

- E. W. Hobson

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"A new point is determined in Euclidean Geometry exclusively in one of the three following ways: Having given four points A, B, C, D, not all incident on the same straight line, then (1) Whenever a point P exists which is incident both on (A,B) and on (C,D), that point is regarded as determinate. (2) Whenever a point P exists which is incident both on the straight line (A,B) and on the circle C(D), that point is regarded as determinate. (3) Whenever a point P exists which is incident on both the circles A(B), C(D), that point is regarded as determinate. The cardinal points of any figure determined by a Euclidean construction are always found by means of a finite number of successive applications of some or all of these rules (1), (2) and (3). Whenever one of these rules is applied it must be shown that it does not fail to determine the point. Euclid's own treatment is sometimes defective as regards this requisite. In order to make the practical constructions which correspond to these three Euclidean modes of determination, correponding to (1) the ruler is required, corresponding to (2) both ruler and compass, and corresponding to (3) the compass only. ...it is possible to develop Euclidean Geometry with a more restricted set of postulations. For example it can be shewn that all Euclidean constructions can be carried out by means of (3) alone..."

- E. W. Hobson

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"The first period embraces the time between the first records of empirical determinations of the ratio of the circumference to the diameter of a circle until the invention of the Differential and Integral Calculus, in the middle of the seventeenth century. This period, in which the ideal of an exact construction was never entirely lost sight of, and was occasionally supposed to have been attained, was the geometrical period, in which the main activity consisted in the approximate determination of π by the calculation of the sides or the areas of regular polygons in- and circum-scribed to the circle. The theoretical groundwork of the method was the Greek method of Exhaustions. In the earlier part of the period the work of approximation was much hampered by the backward condition of arithmetic due to the fact that our present system of numerical notation had not yet been invented; but the closeness of the approximations obtained in spite of this great obstacle are truly surprising. In the later part of this first period methods were devised by which the approximations to the value of π were obtained which required only a fraction of the labour involved in the earlier calculations. At the end of the period the method was developed to so high a degree of perfection that no further advance could be hoped for on the lines laid down by the Greek Mathematicians; for further progress more powerful methods were required."

- E. W. Hobson

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"The second period, which commenced in the middle of the seventeenth century, and lasted for about a century, was characterized by the application of the powerful analytical methods provided by the new Analysis to the determination of analytical expressions for the number π in the form of convergent series, products, and continued fractions. The older geometrical forms of investigation gave way to analytical processes in which the functional relationship as applied to the trigonometrical functions became prominent. The new methods of systematic representation gave rise to a race of calculators of π, who, in their consciousness of the vastly enhance means of calculation placed in their hands by the new Analysis, proceeded to apply the formulae to obtain numerical approximations to π to ever larger numbers of places of decimals, although their efforts were quite useless for the purpose of throwing light upon the true nature of that number. At the end of this period no knowledge had been obtained as regards the number π of the kind likely to throw light upon the possibility or impossibility of the old historical problem of the ideal construction; it was not even definitely known whether the number is rational or irrational. However, one great discovery, destined to furnish the clue to the solution of the problem, was made at this time; that of the relation between the two numbers π and e, as a particular case of those exponential expressions for the trigonometrical functions which form one of the most fundamentally important of the analytical weapons forged during this period."

- E. W. Hobson

0 likesMathematicians from EnglandUniversity of Cambridge alumniUniversity of Cambridge facultyFellows of the Royal Society
"In the third period, which lasted from the middle of the eighteenth century until late in the nineteenth century, attention was turned to critical investigations of the true nature of the number π itself, considered independently of mere analytical representations. The number was first studied in respect of its rationality or irrationality, and it was shown to be really irrational. When the discovery was made of the fundamental distinction between algebraic and transcendental numbers, i.e. between those numbers which can be, and those numbers which cannot be, roots of an algebraical equation with rational coefficients, the question arose to which of these categories the number π belongs. It was finally established by a method which involved the use of some of the most modern of analytical investigation that the number π was transcendental. When this result was combined with the results of a critical investigation of the possibilities of a Euclidean determination, the inferences could be made that the number π, being transcendental, does not admit of a construction either by a Euclidean determination, or even by a determination in which the use of other algebraic curves besides the straight line and the circle are permitted. The answer to the original question thus obtained is of a conclusive negative character; but it is one in which a clear account is given of the fundamental reasons upon which that negative answer rests."

- E. W. Hobson

0 likesMathematicians from EnglandUniversity of Cambridge alumniUniversity of Cambridge facultyFellows of the Royal Society
"It would seem at first sight as if the rapid expansion of the region of mathematics must be a source of danger to its future progress. Not only does the area widen but the subjects of study increase rapidly in number, and the work of the mathematician tends to become more and more specialized. It is, of course, merely a brilliant exaggeration to say that no mathematician is able to understand the work of any other mathematician, but it is certainly true that it is daily becoming more and more difficult for a mathematician to keep himself acquainted, even in a general way, with the progress of any of the branches of mathematics except those which form the field of his own labours. I believe, however, that the increasing extent of the territory of mathematics will always be counteracted by increased facilities in the means of communication. Additional knowledge opens to us new principles and methods which may conduct us with the greatest ease to results which previously were most difficult of access; and improvements in notation may exercise the most powerful effects both in the simplification and accessibility of a subject. It rests with the worker in mathematics not only to explore new truths, but to devise the language by which they may be discovered and expressed; and the genius of a great mathematician displays itself no less in the notation he invents for deciphering his subject than in the results attained.... I have great faith in the power of well-chosen notation to simplify complicated theories and to bring remote ones near and I think it is safe to predict that the increased knowledge of principles and the resulting improvements in the symbolic language of mathematics will always enable us to grapple satisfactorily with the difficulties arising from the mere extent of the subject"

- James Whitbread Lee Glaisher

0 likesMathematicians from EnglandAstronomers from EnglandPeople from LondonUniversity of Cambridge alumniUniversity of Cambridge faculty
"Quite distinct from the theoretical question of the manner in which mathematics will rescue itself from the perils to which it is exposed by its own prolific nature is the practical problem of finding means of rendering available for the student the results which have been already accumulated, and making it possible for the learner to obtain some idea of the present state of the various departments of mathematics.... The great mass of mathematical literature will be always contained in Journals and Transactions, but there is no reason why it should not be rendered far more useful and accessible than at present by means of treatises or higher text-books. The whole science suffers from want of avenues of approach, and many beautiful branches of mathematics are regarded as difficult and technical merely because they are not easily accessible.... I feel very strongly that any introduction to a new subject written by a competent person confers a real benefit on the whole science. The number of excellent text-books of an elementary kind that are published in this country makes it all the more to be regretted that we have so few that are intended for the advanced student. As an example of the higher kind of text-book, the want of which is so badly felt in many subjects, I may mention the second part of Prof. Chrystal’s “Algebra” published last year, which in a small compass gives a great mass of valuable and fundamental knowledge that has hitherto been beyond the reach of an ordinary student, though in reality lying so close at hand. I may add that in any treatise or higher text-book it is always desirable that references to the original memoirs should be given, and, if possible, short historic notices also. I am sure that no subject loses more than mathematics by any attempt to dissociate it from its history."

- James Whitbread Lee Glaisher

0 likesMathematicians from EnglandAstronomers from EnglandPeople from LondonUniversity of Cambridge alumniUniversity of Cambridge faculty
"Mathematics is the fruitful Parent of, I had almost said all, Arts, the unshaken Foundation of Sciences, and the plentiful Fountain of Advantage to Human Affairs. In which last Respect, we may be said to receive from the Mathematics, the principal Delights of Life, Securities of Health, Increase of Fortune, and Conveniences of Labour: That we dwell elegantly and commodiously, build decent Houses for ourselves, erect stately Temples to God, and leave wonderful Monuments to Posterity: That we are protected by those Rampires from the Incursions of the Enemy; rightly use Arms, skillfully range an Army, and manage War by Art, and not by the Madness of wild Beasts: That we have safe Traffick through the deceitful Billows, pass in a direct Road through the tractless Ways of the Sea, and come to the designed Ports by the uncertain Impulse of the Winds: That we rightly cast up our Accounts, do Business expeditiously, dispose, tabulate, and calculate scattered 248 Ranks of Numbers, and easily compute them, though expressive of huge Heaps of Sand, nay immense Hills of Atoms: That we make pacifick Separations of the Bounds of Lands, examine the Moments of Weights in an equal Balance, and distribute every one his own by a just Measure: That with a light Touch we thrust forward vast Bodies which way we will, and stop a huge Resistance with a very small Force: That we accurately delineate the Face of this Earthly Orb, and subject the Oeconomy of the Universe to our Sight: That we aptly digest the flowing Series of Time, distinguish what is acted by due Intervals, rightly account and discern the various Returns of the Seasons, the stated Periods of Years and Months, the alternate Increments of Days and Nights, the doubtful Limits of Light and Shadow, and the exact Differences of Hours and Minutes: That we derive the subtle Virtue of the Solar Rays to our Uses, infinitely extend the Sphere of Sight, enlarge the near Appearances of Things, bring to Hand Things remote, discover Things hidden, search Nature out of her Concealments, and unfold her dark Mysteries: That we delight our Eyes with beautiful Images, cunningly imitate the Devices and portray the Works of Nature; imitate did I say? nay excel, while we form to ourselves Things not in being, exhibit Things absent, and represent Things past: That we recreate our Minds and delight our Ears with melodious Sounds, attemperate the inconstant Undulations of the Air to musical Tunes, add a pleasant Voice to a sapless Log and draw a sweet Eloquence from a rigid Metal; celebrate our Maker with an harmonious Praise, and not unaptly imitate the blessed Choirs of Heaven: That we approach and examine the inaccessible Seats of the Clouds, the distant Tracts of Land, unfrequented Paths of the Sea; lofty Tops of the Mountains, low Bottoms of the Valleys, and deep Gulphs of the Ocean: That in Heart we advance to the Saints themselves above, yea draw them to us, scale the etherial Towers, freely range through the celestial Fields, measure the Magnitudes, and determine the Interstices of the Stars, prescribe inviolable Laws to the Heavens themselves, and confine the wandering Circuits of the Stars within fixed Bounds: Lastly, that we comprehend the vast Fabrick of the Universe, admire and contemplate the wonderful Beauty of the Divine 249 Workmanship, and to learn the incredible Force and Sagacity of our own Minds, by certain Experiments, and to acknowledge the Blessings of Heaven with pious Affection."

- Isaac Barrow

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"These Disciplines [mathematics] serve to inure and corroborate the Mind to a constant Diligence in Study; to undergo the Trouble of an attentive Meditation, and cheerfully contend with such Difficulties as lie in the Way. They wholly deliver us from a credulous Simplicity, most strongly fortify us against the Vanity of Scepticism, effectually restrain from a rash Presumption, most easily incline us to a due Assent, perfectly subject us to the Government of right Reason, and inspire us with Resolution to wrestle against the unjust Tyranny of false Prejudices. If the Fancy be unstable and fluctuating, it is to be poised by this Ballast, and steadied by this Anchor, if the Wit be blunt it is sharpened upon this Whetstone; if luxuriant it is pared by this Knife; if headstrong it is restrained by this Bridle; and if dull it is roused by this Spur. The Steps are guided by no Lamp more clearly through the dark Mazes of Nature, by no Thread more surely through the intricate Labyrinths of Philosophy, nor lastly is the Bottom of Truth sounded more happily by any other Line. I will not mention how plentiful a Stock of Knowledge the Mind is furnished from these, with what wholesome Food it is nourished, and what sincere Pleasure it enjoys. But if I speak farther, I shall neither be the only Person, nor the first, who affirms it; that while the Mind is abstracted and elevated from sensible Matter, distinctly views pure Forms, conceives the Beauty of Ideas, and investigates the Harmony of Proportions; the Manners themselves are sensibly corrected and improved, the Affections composed and rectified, the Fancy calmed and settled, and the Understanding raised and excited to more divine Contemplation. All which I might defend by Authority, and confirm by the Suffrages of the greatest Philosophers."

- Isaac Barrow

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"J. M. Child... has made a searching study of Barrow and has arrived at startling conclusions on the historical question relating to the first invention of the calculus. He places his conclusions in italics in the first sentence as follows Isaac Barrow was the first inventor of the Infinitesimal Calculus... Before entering upon an examination of the evidence brought forth by Child it may be of interest to review a similar claim set up for another man as inventor of the calculus... Fermat was declared to be the first inventor of the calculus by Lagrange, Laplace, and apparently also by P. Paul Tannery, than whom no more distinguished mathematical triumvirate can easily be found. ...Dinostratus and Barrow were clever men, but it seems to us that they did not create what by common agreement of mathematicians has been designated by the term differential and integral calculus. Two processes yielding equivalent results are not necessarily the same. It appears to us that what can be said of Barrow is that he worked out a set of geometric theorems suggesting to us constructions by which we can find lines, areas and volumes whose magnitudes are ordinarily found by the analytical processes of the calculus. But to say that Barrow invented a differential and integral calculus is to do violence to the habit of mathematical thought and expression of over two centuries. The invention rightly belongs to Newton and Leibniz."

- Isaac Barrow

0 likesMathematicians from EnglandTheologians from EnglandUniversity of Cambridge alumniUniversity of Cambridge facultyFellows of the Royal Society
"In a 1967 article, “Virgin Birth,” Leach astutely foreshadowed the reflexivity of the late 1970’s and 1980’s, calling attention to the fact that anthropologists call their own practice religion but assert that other peoples practice magic. In the present volume he presents the dramatic case of the fabrication of the Aryan invasion, which shows how profoundly the seemingly objective academic endeavors are af­ fected by the mentalité of the culture to which they belong. Leach de­ scribes how cherished but erroneous assumptions in linguistics and anthropology were accepted without question. If the mentalité of the academic culture was in part responsible for the fabrication, geo­ politics was even more responsible for upholding the Aryan invasion as history. The theory fit the Western or British vision of their place in the world at the time. The conquest of Asian civilization needed a mythical charter to serve as the moral justification for colonial ex­ pansion. Convenient, if not consciously acknowledged, was the Aryan invasion by a fair-skinned people, speaking the so-called Proto-Indo-European language, militarily conquering the dark- skinned, peasant Dasa (Dasyu), who spoke a non-European language and with whom the conquerors lived, as Leach puts it, in a “system of sexual apartheid.” The first civilization in India, thus, was built by the Aryan invaders. A remarkable case of Orientalism indeed."

- Edmund Leach

0 likesAnthropologists from EnglandFellows of the British AcademyUniversity of Cambridge alumniUniversity of Cambridge faculty
"[T]he best packings in up to eight dimensions belong to families A_n, D_n and E_n, and the corresponding s turn up in apparently unrelated areas... [I]n 24 dimensions the \Lambda_{24} has... connections with , s, and the Monster simple group... [O]ne day someone will write an article on "The Ubiquity of the Leech lattice." ...There are applications of... packings to number theory... [e.g.,] solving s, and to "the "... There are... applications of sphere packings... in digital communications... a typical question from... spread-spectrum communications for mobile radio... how many spheres of radius 0.25 can be packed in a sphere of radius 1 in 100-dimensional space? ...Two and three-d... packings... circles in a two-d... packing may represent s... in... a cable. Three-d... packings have applications in chemistry and physics... biology... antenna design... choosing directions for X-ray tomography... and... statistical analysis on spheres... n-dimensional packings may be used in... numerical evaluation of integrals... on the surface of a sphere in \R^n or in its interior. ...A related application ...n-dimensional search or approximation problems ...[I]n physics... dual theory and superstring theory... have involved the E_8 and \Lambda_{24} lattices and the related Lorentzian lattices in dimensions 10 and 26..."

- John Horton Conway

0 likesMathematicians from EnglandAtheists from EnglandPeople from LiverpoolUniversity of Cambridge alumniUniversity of Cambridge faculty
"The linguistic designation of a category of “Indo-European/Aryan” languages is not the question here. However, the historical, and prevailing, use of the language designation is the issue. For two centuries, scholars concentrating on the South Asian data have described an Indo-European/Aryan migration/invasion into South Asia to explain the formation of Indian civilization. The conflating of language, people/culture, “race” to maintain the “myth of the Aryan invasion” continues, perhaps, as Leach so cogently notes, due to the academic prestige at stake. The distinguished scholar Colin Renfrew (1987) opts to distort the archaeological record rather than to challenge it. Failing to identify archaeological evidence for such a migration in the European post-Neolithic periods, Renfrew argues instead for an Indo-European/Aryan human migration associated with the spread of food production economies from Anatolia. In doing so, he ignores critical archaeological data from Southwest Asia and South Asia. The South Asian archaeological data reviewed here does not support Renfrew’s position nor any version of the migration/invasion hypothesis describing western population movement into South Asia. Rather, the physical distribution of prehistoric sites and artifacts, stratigraphic data, radio- metric dates, and geological data describing the prehistoric/proto-historic environment perhaps can account, in some degree, for the Vedic oral tradition describing a cultural discontinuity of what was an indigenous population movement in the Indo-Gangetic region."

- Colin Renfrew

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"A space containing electric currents may be regarded as a field where energy is transformed at certain points into the electric and magnetic kinds by means of batteries, dynamos, thermoelectric actions, and so on, while in other parts of the field this energy is again transformed into heat, work done by electromagnetic forces, or any form of energy yielded by currents. Formerly a current was regarded as something travelling along a conductor, attention being chiefly directed to the conductor, and the energy which appeared at any part of the circuit, if considered at all, was supposed to be conveyed thither through the conductor by the current. But the existence of induced currents and of electromagnetic actions at a distance from a primary circuit from which they draw their energy, has led us, under the guidance of Faraday and Maxwell, to look upon the medium surrounding the conductor as playing a very important part in the development of the phenomena. If we believe in the continuity of the motion of energy, that is, if we believe that when it disappears at one point and reappears at another it must have passed through the intervening space, we are forced to conclude that the surrounding medium contains at least a part of the energy, and that it is capable of transferring it from point to point."

- John Henry Poynting

0 likesAcademics from the United KingdomPhysicists from EnglandPeople from ManchesterUniversity of Cambridge alumniFellows of the Royal Society
"This passage was cited by Thomas W. Arnold in his Preaching of Islam to support his contention that the most important agents in the spread of Islam in the Deccan were peaceful Muslim saints. While Arnold's general argument may have a good deal of valid- an argument that will be explored in greater depth in the present study, it would seem that in the case of Pir Ma‘bari he ‘chose the wrong example to illustrate it. For the question arises: why did Arnold cite a tradition, the 1884 Bombay Gazetteer, which presented only one side, the “peaceful missionary” side, of Pir Marais life? One possibility is that the hagiographic traditions such a the one quoted above were unknown to Arnold and that he had available to him only the Gazetteer version. Another possibility is that Arnold was aware of the Sufi’ militancy in the hagiographic traditions but chose to ignore it, an interpretation that would accord with the general effort in his books to revise the simplistic nineteenth-century image of Islam as religion of the sword. But it does not suffice to correct one distorted view by presenting an equally distorted, if opposite, view. If the Sufis peaceful character can be supported by both ‘written and oral traditions, so can his militancy. In view of the tendency of both oral and written traditions to extol or even fabricate the pious qualities of Sufis, it is most likely that Pir ‘Matbari like Sufi Sarmast, was in reality a militant Sufi and only acquired the reputation of peaceful missionary through generations of oral transmission of his life story."

- Thomas Walker Arnold

0 likesAcademics from EnglandNon-fiction authors from EnglandHistorians from EnglandOrientalistsUniversity of Cambridge alumni
"It seems, moreover, that my argument has some relevance to choices we must make even now. There are some species of large predatory animals, such as the Siberian tiger, that are currently on the verge of extinction. If we do nothing to preserve it, the Siberian tiger as a species may soon become extinct. The number of extant Siberian tigers has been low for a considerable period. Any ecological disruption occasioned by their dwindling numbers has largely already occurred or is already occurring. If their number in the wild declines from several hundred to zero, the impact of their disappearance on the ecology of the region will be almost negligible. Suppose, however, that we could repopulate their former wide-ranging habitat with as many Siberian tigers as there were during the period in which they flourished in their greatest numbers, and that that population could be sustained indefinitely. That would mean that herbivorous animals in the extensive repopulated area would again, and for the indefinite future, live in fear and that an incalculable number would die in terror and agony while being devoured by a tiger. In a case such as this, we may actually face the kind of dilemma I called attention to in my article, in which there is a conflict between the value of preserving existing species and the value of preventing suffering and early death for an enormously large number of animals."

- Jeff McMahan (philosopher)

0 likesAcademics from the United StatesPhilosophers from the United StatesUniversity of Oxford alumniUniversity of Cambridge alumniUniversity of Oxford faculty
"It has been traditional in British historiography to trace industrial growth and technological innovation to the sturdy virtues of bourgeois individualism, and especially to the individualism of Protestant-democratic England... [T]he example of Japan in our time refutes the necessity of any such connection, for Japan has demonstrated the possible industrial dynamism of a highly deferential society, indeed a society which has only recently masked the values and practices of a divine-right monarchy. It is perhaps possible in the changed climate of the 1980s to re-emphasise the extent to which England's commercial and industrial achievement in the eighteenth and nineteenth centuries rested not only on success in war, averting revolution and eliminating French competition, but also on the virtues of loyalty, diligence, discipline, subordination and obedience in the work-place, whether factory, mine or office (indeed the British economy was eventually overtaken by others which practised these virtues to a higher degree). But such practices had already been elevated to the status of social ideals within the Anglican-aristocratic nexus; and it was the military elite, not the nation of shopkeepers, which won the wars. The values of nineteenth-century industrial society owed far more to the values of the ancien regime than the Victorians were prepared to admit."

- J. C. D. Clark

0 likesHistorians from the United KingdomUniversity of Cambridge alumniUniversity of Cambridge facultyUniversity of Oxford faculty
"In an epoch-making study entitled English Society 1688–1832: Ideology, Social Structure and Political Practice during the Ancien Regime, published in 1985, he forcefully argued that eighteenth-century England, its policy based on a close alliance between the monarchy, the aristocracy and the church, was an "ancien regime", indistinguishable from contemporary France, for instance, or even Spain. What it was not was some sort of forward-looking experiment in constitutional monarchy and representative government. Thus the final collapse of this ancien regime was heralded not by the parliamentary Reform Act of 1832 but by the repeal of the Test and Corporation Acts in 1830 [sic], when England ceased to be a confessional state. In the same way he argued for the close identification of political radicalism with religious nonconformity, in contradiction to E. P. Thompson's Tawneyesque The Making of the English Working Class, published in 1963 and well established as a classic. Clark's theories have provoked a great deal of opposition, not eased by his confrontational technique and acerbity of manner, but he has to be taken seriously, and it must be rare indeed for a scholar of his age (born in 1951) to have two major historical conferences and two issues of different professional journals entirely devoted to a discussion of his theories. We must never forget that his work runs in parallel with the excellent but more conventional work of John Cannon, Ian Christie, Paul Langford and others, but there is no doubt that he has put a new spin on British eighteenth-century studies, and it is safe to say that they will never be the same again."

- J. C. D. Clark

0 likesHistorians from the United KingdomUniversity of Cambridge alumniUniversity of Cambridge facultyUniversity of Oxford faculty
"The situation of the Muslims of China was very different. They were geographically remote from the Muslim heartlands— in contrast to the Muslims of India, whose contacts were so close that to a large extent they transacted their affairs in Persian... The result was the appearance of a Muslim literature in Chinese that pressed the argument that Confucian and Muslim values were fully compatible, if not identical. Thus an inscription purportedly dating from 742, but likely to have been forged by Chinese Muslims in the Ming period, says of Confucius and Muḥammad that “their language differed, yet their principles agreed.”... Nor is Islamic-­Confucian syncretism likely to have cut much ice with the Chinese elite. One prominent Chinese Muslim author was able to persuade some Confucian scholars to write laudatory prefaces for his books, and the title of his heavily Confucianized work on Muslim ritual found a place in an imperial compendium of 1773–­1782. But the work was placed in the company of books that “contained little that was praiseworthy and much that was contemptible,” and an editorial comment, while conceding that the author’s literary style “is actually rather elegant,” maintained that “the clever literary ornamentation does him no good” for the simple reason that “Islam is fundamentally far-­fetched and absurd.”"

- Michael Cook (historian)

0 likesHistorians from the United KingdomUniversity of Cambridge alumniPrinceton University facultyMembers of the American Philosophical SocietyFellows of the British Academy
"Russia perceives NATO as an enemy — fair enough: NATO perceives Russia as an enemy — and is determined to prevent major countries on Russia’s borders from becoming members of NATO. Russia, in this way, I have to say, is no different from the United States. Your previous segment was about the history of U.S. coups in Honduras and other parts of Latin America to ensure that this area remains in American sphere of influence, or at the very least that external powers are excluded from that region. It’s called the Monroe Doctrine, right? Russia is no different in that regard. It doesn’t mean that Putin hopes for a new Soviet Union, but he does certainly want to keep NATO out of that region and is prepared to fight, as he’s shown in the past, to stop that happening. The problem about NATO is that it talks the talk, but, I mean, no serious person thinks that European countries, with the possible exception of Poland, will go to war for Ukraine. So, this, as well as the gas dependence, which you mentioned, is, in the end, a major card in Russia’s hand, that — in the very last resort. I’m not saying that the Putin government wants war, but it is prepared to go to war in the very last resort, and NATO almost certainly is not... Zelensky is extremely unpopular now for the failure to improve the economic situation — worsened by COVID, of course — and continued very high levels of corruption."

- Anatol Lieven

0 likesHistorians from EnglandUniversity of Cambridge alumniNon-fiction authors from EnglandAcademics from EnglandPeople from London
"Being earnest to press on his Errand he came for, the Ambassador sent to Narun Gi Pundit to know what was transacted in the Articles; but was returned for Answer. The Rajah stopt his Ears to all Affairs, declaring he had granted all the Demands, except those two Articles, expressing, Our Money shall go current in his Dominions, and his on Bombaim; and that he shall restore whatever Wrecks may happen on his Coasts belonging to the English, and Inhabitants of Bombaim. The first he accounted unnecessary to be inserted, because he forbids not the passing of any manner of Coins; nor on the other side, can he force his Subjects to take those Monies, whereby they shall be Losers; but if our Coin be as fine an Allay, and as weighty as the Moguls, and other Princes, he will not prohibit it. To the other he says, that it is against the Laws of Conchon to restore any Ships, Vessels, or Goods, that are driven ashore by Tempest, or otherwise; and that should he grant us that Privilege, the French, Dutch, and other Merchants, would claim the same Right; which he could not grant without breaking a Custom has lasted many Ages: The rest of our Desires he willingly conceded embracing with much satisfaction our Friendship, promising to himself and Country much Happiness by our Settlement and Trade: Notwithstanding Narun Gi Pundit did not altogether despair of obtaining our Wrecks, because we enjoyed the same Privilege in the Mogul, and Duccan Country."

- John Fryer (travel writer)

0 likesTravel writersUniversity of Cambridge alumniUniversity of Cambridge facultyFellows of the Royal SocietyPhysicians from England
"Near a Month after they had been here, Narun Gi Pundit sent word, That to Morrow about Seven or Eight in the Morning, the Rajah Seva Gi intended to ascend his Throne; and he would take it kindly if they came to congratulate him thereon; that it was necessary to present him with some small thing, it not being the Custom of the Eastern Parts to appear before a Prince empty-handed. The Ambassador sent him word, according to his Advice; he would wait on the Rajah at the prescribed time. Accordingly next Morning he and his Retinue went to Court, and found the Rajah seated on a Magnificent Throne, and all his Nobles waiting on him in Rich Attire; his Son Samba Gi Rajah, Peshuah Mora Pundit, and a Brachmine of Great Eminence, seated on an Ascent under the Throne; the rest, as well Officers of the Army as others, standing with great Respect. The English made their Obeisance at a distance; and Narun Sinai held up the Diamond Ring that was to be presented him: He presently took notice of it, and ordered their coming nearer, even to the Foot of the Throne, where being Vested, they were desired to retire; which they did not so soon, but they took notice on each side of the Throne there hung (according to the Moors manner) on heads of Gilded Launces many Emblems of Dominion and Government; as on the Right-hand were two great Fishes Heads of Gold, with very large Teeth; on the Left, several Horses Tails, a Pair of Gold Scales on a very high Launce’s head, equally poized, an Emblem of Justice and as they returned, at the Palace Gate stood two small Elephants on each side, and two fair Horses with Gold Trappings, Bridles, and Rich Furniture, which made them admire how they brought them up the Hill, the Passage being both difficult and hazardous. Two days after this, the Rajah was married to a Fourth Wife, without State; and doth every day bestow Alms on the Brachmines…"

- John Fryer (travel writer)

0 likesTravel writersUniversity of Cambridge alumniUniversity of Cambridge facultyFellows of the Royal SocietyPhysicians from England
"Was I ever discriminated against? There are two kinds of discrimination: explicit and implicit. For the most part, explicit discrimination did not affect me much. However, in retrospect, implicit discrimination—for example, the fact that I was so isolated as a postdoc because I could not share in college life—as well as my own internalized misogyny, did have a significant effect, though I hardly noticed this at the time. Another important factor, and one that I was aware of, was pervasive but not overt: it was very rare that women became professional scientists in Britain at the time, largely because science (and particularly “hard” as opposed to “life” science) was considered such a very unfeminine thing to do. ... These days, when most of the obvious barriers to women’s participation in mathematics have been removed, there still remain very strong and insidious internal barriers, shown in such phenomena as stereotype threat or imposter syndrome. The prejudices that lead to people accepting as completely normal that women should not get degrees at Cambridge (they first could get Cambridge degrees in 1948) are very strong and do not disappear immediately when the external barrier is removed. ... In the 1960s there were, of course, very visible manifestations of the idea that academic life is not for women. At the time, most Ivy League universities in the States did not admit women, and in Britain almost all the colleges at the most prestigious universities (Oxford and Cambridge) were single sex."

- Dusa McDuff

0 likesAcademics from EnglandFellows of the Royal SocietyMathematicians from EnglandUniversity of Cambridge alumniWomen mathematicians
"For the ungodly talie and ymagin thus amonge themselves (but not right:) The tyme of oure life is but short and tedious, and when a man is once gone, he hath nomore joye ner pleasure, nether knowe we eny man that turneth agayne from death: for we are borne of naught, and we shal be herafter as though we had never bene. For oure breth is as a smoke in oure nostrels, and the wordes as a sparck to move oure herte. As for oure body, it shalbe very asshes that are quenched, and oure soule shal vanish as the soft ayre. Oure life shall passe awaye as the trace of a cloude, and come to naught as the myst that is dryven awaye with the beames of the Sonne, and put downe with the heate therof. Oure name also shalbe forgotten by litle and litle, and no man shal have oure workes in remembraunce.For oure tyme is a very shadow that passeth awaye, and after oure ende there is no returnynge, for it is fast sealed, so that no man commeth agayne. Come on therfore, let us enjoye the pleasures that there are, and let us soone use the creature like as in youth. We wil fyll oure selves with good wyne and oyntment, there shal no floure of the tyme go by us. We wil crowne oure selves with roses afore they be wythered. There shal be no fayre medowe, but oure lust shal go thorow it. Let every one of you be partaker of oure volupteousnes. Let us leave some token of oure pleasure in every place, for that is oure porcion, els gett we nothinge. ...Soch thinges do the ungodly ymagin, and go astraye, for their owne wickednes hath blynded them. As for the misteries of God, they understonde them not : they nether hope for the rewarde of righteousnesse, ner regarde the worshipe that holy soules shall have. For God created man to be undestroied, yee after the ymage of his awne licknesse made he him. Neverthelesse thorow envye of the devell came death in to the worlde, and they that holde of his syde, do as he doth.But the soules of the righteous are in the hande of God, and the payne of death shal not touch them. In the sight of the unwyse they appeare to dye, and their ende is taken for very destruccion. The waye of the righteous is judged to be utter destruccion, but they are in rest. And though they suffre payne before men, yet is their hope full of immortalite."

- Myles Coverdale

0 likesUniversity of Cambridge alumniTheologians from EnglandAnglican bishopsAnglicans from the United KingdomTranslators from England
"My research is in the field of spectral geometry, the study of how the shape of an object affects the modes in which it can resonate. A famous question in the field is, Can one hear the shape of a drum? Spectral geometry bridges different branches of science, including engineering and physics, as well as a number of different fields of mathematics. However, quite different sorts of questions are studied within each discipline. I am a mathematical analyst, which gives me an appreciation for the infinite and the infinitesimal. At the moment, one of the things I am working on understanding is the total wavelength of a surface like a sphere or something of greater complexity, such as the surface of a bagel or a pretzel. What is this total wavelength? If you strike a surface it can resonate at any one of a list of frequencies, and the wavelength of the sound produced by the vibration is inversely proportional to the frequency. In the mathematically idealized model, there are infinitely many possible wavelengths. The total wavelength should be the sum of all of these individual wavelengths except that this infinite sum equals infinity. Fortunately, a finite number can be assigned to it by a slightly elusive process called regularization. (This process is also used in mathematical physics to mysteriously obtain true answers from formulas which do not really make sense!) I first became interested in the total wavelength as a model related to a question which can be roughly stated as, can one hear the shape of the universe? However, the total wavelength shows up in many quite different areas of mathematics and I am finding these connections intriguing."

- Kate Okikiolu

0 likesMathematicians from EnglandWomen academics from EnglandUniversity of Cambridge alumniUniversity of California, Los Angeles alumniPrinceton University faculty
"I am a mathematical analyst, and most of my research is in the area of spectral geometry. Problems in spectral geometry are also studied by various kinds of geometers, number theorists, applied mathematicians, mathematical physicists, and others. What is Spectral geometry? Spectral geometry most usually means the study of how the geometry of an object is related to the natural frequencies of the object. These are the frequencies at which the object can vibrate. A vibrating object often produces a sound, and the frequencies can be heard as the dominant tone and the overtones of the sound. The well-known question highlighting what spectral geometry is all about is the question "Can one hear the shape of a drum?" I am a mathematical analyst, and most of my research is in the area of spectral geometry. Problems in spectral geometry are also studied by various kinds of geometers, number theorists, applied mathematicians, mathematical physicists, and others. In mathematical terms, the natural frequencies of an object (or rather their squares) are the eigenvalues of a partial differential operator called the Laplacian. This Laplacian takes each function defined on the object and differentiates it twice to give a new function. The eigenvalues of the Laplacian form an infinite sequence of numbers tending to infinity. In spectral geometry we study how these numbers depends on the shape of the object. For people who like to know the full story, I should mention that many spectral geometers (including me) who work on the Laplacian on smooth manifolds study the whole sequence of eigenvalues of the Laplacian. Now the low eigenvalues can give accurate values for the frequencies at which a real-life object vibrates, but the very high eigenvalues do not correspond to genuine physical vibrations of the object because of molecular forces and damping. These effects are not included in the model where the vibration is driven by the Laplacian alone. This means that my research is rather different from that of an engineer who wishes to model precisely the vibrations of a real-life object. In actual fact the questions I work on are more closely related to mathematics arising in quantum physics and string theory. In addition, I don't always study the Laplacian, but also the eigenvalues of other operators, which might represent other physical quantities than the frequencies of vibration. I mostly study spectral geometry for nice smooth objects such as spheres and tori, but some people work on rough objects and even discrete objects like graphs. In the last eight years, I have worked mostly on the spectral zeta function, which is an infinite sum of powers of the eigenvalues. In particular, I have worked on the zeta-regularised determinant, which is used in topology, quantum field theory, and string theory. Recently, I have been very interested in the sum of squares of the wavelength of a surface, which is related to all kinds of different things including vortex theory."

- Kate Okikiolu

0 likesMathematicians from EnglandWomen academics from EnglandUniversity of Cambridge alumniUniversity of California, Los Angeles alumniPrinceton University faculty
"It remained for Alfred Cobban to play the role of Copernicus and point out the emperor-theory's nakedness. At least his writings of some twenty years ago constitute the most apparent landmark of the revisionist school. Cobban's main points were that the French bourgeoisie of the eighteenth century — he did not question its existence — was neither (a) capitalist or industrial, (even in intent), nor (b) revolutionary. Rather than being a class of "industrial entrepreneurs and financiers of big business," the bourgeoisie was composed of "land-owners, rentiers, and officials." Itself a class deeply involved in privileges, it abhorred the thought of revolution. Moreover, this bourgeoisie was, he thought, not rising but declining. Cobban recognized the confusions in the situation and called for new, freshly directed research. He was sure that historians had imposed on the Old Regime a "sociological theory" drawn from a later age, one that did not fit that earlier epoch. They had looked into the mirror of their own age rather than into the past, and they had seen Rockefeller and Lenin rather than the real Necker and Voltaire, thus misreading the whole code. Cobban further noted the obvious fact that so far as France was concerned, the Revolution did not usher in a triumphant capitalism but in fact had impeded modernization, industrialization, technological innovation for a century or more. He added that when historians construed the Parisian sans culottes of the Revolution as an incipient proletariat they also mistook reality by importing later ideas, a point others had already made."

- Alfred Cobban

0 likesUniversity of Cambridge alumniHistorians from EnglandUniversity College London faculty
"Who was the most famous female mathematician? ...Emmy Noether, [was an] excellent... fantastic mathematician, but if I went into the street, who would know Emmy Noether? ...Even more famous than Marie Curie. Films have been made about this woman. Ada Lovelace... famous, but not as famous as this one. I've seen films, books have been written about her. Hugely famous, most children would know her name. I'm going to put her picture up and it's going to surprise you. ...Florence Nightingale's an incredibly famous woman because... she basically founded modern nursing. ...The story ...she was sent to Crimea and... set up hospitals... which saved huge number of lives, and when she went back to England she developed modern nursing and her practice... are used all over the world, and everyone thinks she's a nurse, but... she was a . She was one of the first members of the and was a really good statistician... [T]he way she cured people wasn't so much through medical care. It's through the... more modern approach, which was to try to work out what was causing people to be ill. ...[S]he gathered loads and loads of data on this and... produced graphs of this data... essentially to convey what she was doing to politicians, because politicians then and sadly now, don't know what numbers are... [S]o she did this through graphical information and she developed... rose diagrams which are very like pie charts... [S]o she not only developed ... she also developed graphical presentation of data, which is universal, and she's incredibly famous, but noone knows she was a mathematician. ...The Royal Statistical Society ...building is called the Nightingale building, after her."

- Christopher Budd (mathematician)

0 likesAcademics from the United KingdomEducators from the United KingdomMathematicians from the United KingdomUniversity of Cambridge alumni
"[[w:Recreational mathematics|[R]ecreational math]] is a huge... subject... [A] particular favorite of mine... s and labyrinths, which were originally recreational. One of the earliest examples... involves... the ... the product of a between the queen of King and... Zeus, dressed up as a bull... turned into a bull, or whatever they do. The product... was the Minotaur... half man and half bull... [H]e was... ferocious and... lived in the center of a labyrinth underneath the palace of King Minos. ...Theseus... said I will go with the 9 young men and 9 young women and... attempt to kill the Minotaur. So when he went to Crete he was met by one of my heroes... ... the first female mathematician... recorded in the classical literature. ...[S]he gave him a sword. By the way she fell in love with him. ...[S]he also said ..."I will give you an algorithm for cracking the labyrinth ...and using this algorithm, he went into the labyrinth, found ...[and] killed the Minotaur, got out of the labyrinth and took the young men and... women back to Greece... [O]n the way he stopped off at an island... where they had a great party... and only after they had sailed off did they realize they'd left Ariadne behind, and she died of a broken heart and turned into a spider... [T]he real hero of the story is the labyrinth. ...[T]his design, although they've found it everywhere in the ancient culture, is universal. There are clear examples of Native American populations in the U.S. having essentially discovered the same design."

- Christopher Budd (mathematician)

0 likesAcademics from the United KingdomEducators from the United KingdomMathematicians from the United KingdomUniversity of Cambridge alumni
"Different media of publication—textbooks, monographs, quarterlies, abstracts, and ‘review letters’—have been introduced, one after another, to meet new professional needs; and the historically changing operations of a scientific profession are reflected once more in the transfer of influence from one medium to another. The ‘s’ of seventeenth-century Europe were initially linked by the circulated correspondence of men like Henry Oldenburg. With the foundation of national academies, emphasis shifted to their Transactions and to treatises such as Newton’s Principia, which were published under their auspices. In subsequent centuries, the balance has again shifted several times: to quarterlies, to twice-monthly periodicals, weeklies, and even shorter-term publications. The proliferation of journals and the acceleration of publication are effects, in part of the fragmentation of sub-disciplines, in part of the sharpened competition for priority; but they are associated also with a great decentralization of scientific authority. Where no one can hope to master all the available concepts and theories, scientific professions were bound to move towards a pluralistic pattern of authority. On the very frontiers of research, indeed, we are now back not only with ‘invisible colleges’ but with a multiplicity of Oldenburgs, who circulate duplicated ‘prepublication’ material in highly specialized subjects to an international circle of equally specialized devotees. In the more self-consciously original branches of science—it has even been suggested—only out-of-date ideas ever actually get into print!"

- Stephen Toulmin

0 likesPhilosophers from EnglandPeople from LondonUniversity of Cambridge alumniNew York University facultyStanford University faculty
"The importance of status is vividly illustrated by perhaps the most celebrated summit in German history: the meeting at Canossa in 1077 between Pope Gregory VII and Holy Roman Emperor Henry IV. In German this is known as der Canossagang, the journey to Canossa; more aptly in Italian as l’umiliazione di Canossa, for it was truly a humiliation. In the Investiture Controversy—the power struggle between pope and emperor over the right to appoint bishops—Henry had renounced Gregory as pope, only to find himself excommunicated. This papal edict not only imperilled Henry’s immortal soul, it also laid him open to revolt by the German nobility. He sought a meeting with Gregory who, fearing violence, retreated to the castle of Canossa, in safe territory south of Parma. This forced the emperor to come to him. What exactly happened is shrouded in legend, but supposedly Henry arrived in the depths of winter, barefoot and in a pilgrim’s hair shirt, only to be kept waiting by Gregory for three days. When he was finally admitted to the castle on January 28, 1077, the emperor knelt before the pope and begged forgiveness. He was absolved and the two most powerful figures in Christendom then shared the Mass. The reconciliation was short-lived. After being excommunicated a second time Henry crossed the Alps with his army and replaced Gregory with an “antipope” of his own. But the events themselves matter less than the myth that grew up around them. During the German Reformation Henry was lionized as the defender of national rights and the scourge of the Catholic pope, often being dubbed “the first Protestant.” And during Chancellor Otto von Bismarck’s struggle to rein in the Catholic church, he famously declared in the Reichstag on May 14, 1872: “We will not go to Canossa, neither in body nor in spirit.” He was voicing the new German Reich’s resolve to accept no outside interference in its affairs—political or religious. As a result Henry IV shivering outside the gates of Canossa became a familiar figure in late-nineteenth-century German art; the phrase “to go to Canossa” (nach Canossa gehen) entered the language as a synonym for craven surrender—almost the equivalent of "Munich" to the British and Americans."

- David Reynolds

0 likesHistorians from the United KingdomUniversity of Cambridge facultyHarvard University facultyUniversity of Cambridge alumniTelevision presenters
"Throughout history, security as much as status has been an obstacle to summitry. In 1419 France was in turmoil from war with the English and a power struggle provoked by the periodic insanity of King Charles VI. On September 10 the dauphin, Charles’ son, conferred on a bridge near Rouen with their archrival, John, Duke of Burgundy. Both men were well attended by guards and a barrier had been erected in the middle, with a wicket gate bolted on either side to allow passage only by mutual consent. During the conference Duke John was persuaded to come through the gate—only to be cut down by the dauphin’s bodyguard. The dauphin, inheriting the throne as Charles VII, recovered much of France from the English. When his son, Louis XI, met the Yorkist king Edward IV at Picquigny near Amiens in 1475 to conclude a peace treaty, the fate of Duke John was much in mind. The chronicler Philippe de Commines tells how this conference was held on a bridge over the Somme. Louis insisted that across the middle of the bridge and along its sides his carpenters should build "a strong wooden lattice, such as lions’ cages are made with, the hole between each bar being no wider than to thrust in a man’s arm." The two kings somehow managed to embrace between the holes and conducted their meeting in secure cordiality."

- David Reynolds

0 likesHistorians from the United KingdomUniversity of Cambridge facultyHarvard University facultyUniversity of Cambridge alumniTelevision presenters
"Although by about 1500 several strong national states had emerged in Europe, they remained greatly dependent on their monarchs. This kind of personalized power is at the heart of summitry. One of the most famous encounters took place on the so-called Field of the Cloth of Gold in June 1520, bringing together Henry VIII of England and François I of France. The young English monarch, whose titles still included "King of France," had resumed the old struggle in 1512. But his advisor Cardinal Thomas Wolsey secured a truce and then arranged a summit to consummate an enduring peace. It took place on the edge of Calais, the last English enclave in France, in a shallow dip known as the Val d’Or. Both sides of the valley were carefully reshaped to ensure that neither party enjoyed a height advantage. A special pavilion was constructed for the meeting and festivities, surrounded by thousands of tents and a three-hundred-foot-square timber castle for the rest of those attending. Henry’s entourage alone numbered more than five thousand, while the French crown needed ten years to pay off its share of the cost. [...] At the appointed hour on June 7, 1520, the Feast of Corpus Christi, the two monarchs with their retinues in full battle array appeared on the opposite sides of the valley. There was a moment of tense silence—each side feared an ambush by the other. Then the two kings spurred their horses forward to the appointed place marked by a spear in the ground and embraced. The ice was broken. They dismounted and went into the pavilion arm in arm to talk. Then began nearly two weeks of jousting, feasting and dancing that culminated in a High Mass in the open air. Choirs from England and France accompanied the mass and there was a sermon on the virtues of peace. In both choreography and cost, the Field of the Cloth of Gold resembles contemporary summits. In a further similarity, style was more important than substance: by 1521 the two countries were at war again. In many ways they were natural rivals, whereas Henry was bound—by marriage and interest—to France’s enemy Charles V, king of Spain. Both before and after the Cloth of Gold Henry met Charles for discussions of much greater diplomatic magnitude. And although Wolsey hoped the meeting of the British and French elites might build bridges, this soon proved an illusion. As the Cloth of Gold demonstrated, egos were everything in these summits, with each side alert to any hint of advantage gained summits by the other. Commines was implacably opposed to such meetings for this very reason. It was, he said, impossible "to hinder the train and equipage of the one from being finer and more magnificent than the other, which produces mockery, and nothing touches any person more sensibly than to be laughed at.""

- David Reynolds

0 likesHistorians from the United KingdomUniversity of Cambridge facultyHarvard University facultyUniversity of Cambridge alumniTelevision presenters
"[A]t the time praise was showered on Chamberlain for brokering the deal. On his return from Locarno, he received a special welcome at Victoria Station and, in further similarity to Disraeli in 1878, was immediately made a Knight of the Garter. Prime Minister Stanley Baldwin praised him for resolving an issue that had "so far defied the efforts of every statesman since the war." One of Baldwin’s predecessors, Lord Arthur Balfour, said that Chamberlain’s name would be "indissolubly associated” with this probable "turning point in civilisation." A few months later Chamberlain was awarded the Nobel Peace Prize. For a politician who had grown up in the shadow of his famous father, "Radical Joe," it was an intoxicating apotheosis. “I am astonished and a little frightened by the completeness of my success and by its immediate recognition everywhere,” Chamberlain told his sister. On October 22, 1925, he dined alone with his younger half-brother Neville, who noted in his diary that Austen "talked almost without stopping from 8 till 11.00 on Locarno. Very naturally, perhaps, the rest of the world does not exist for him...Looking back he felt that no mistake had been made from beginning to end." Neville found it hard to conceal his envy at Austen’s success. Nor, as we shall see, did he forget it."

- David Reynolds

0 likesHistorians from the United KingdomUniversity of Cambridge facultyHarvard University facultyUniversity of Cambridge alumniTelevision presenters
"And then the English Ministrels blew aloud their Trumpets, and sounded their Pipes, and other Instruments of Martial Musick, and Marched furiously to meet the Scots. Now to each Battail of English, were two Wings of chosen Archers, who shot this day so thick, and so home, that the Scots could by no means maintain their Order: So that the Englishmen of Arms and Footmen enter'd in among them, and beat them down by Heaps. Yet still the Scots fought valiantly; and while the Lord Archibald Douglas liv'd, kept the Field with great Courage; tho' much to their Loss: But when they saw him struck thro' the Body with a Spear, they began to flee for safeguard of their Lives, tho' to very little purpose. For when the Scotch Valets and Pages saw the Discomfiture, they ran away upon the Spur, with their Masters' Horses to save themselves, taking no Care for their Masters. But when the English men of Arms saw that, they leap'd on their Horses, and follow'd the Chace with great Fury; then were the Scotch men trodden down on all sides, their display'd Banners fell'd to the Ground, all torn and hack'd in pieces; and many a good Habergeon bathed in the Owners' Blood. Yet frequently did the Scots gather together in Companies to dispute the point with their Pursuers; but still they were discomfited. And thus, says my Author (M.S. vet. Ang. in Bibl. C.C.C. c. 224), it befell as God would, that the Scots had that day no more Power nor Might against the English, than twenty Sheep would have against five Wolves."

- Joshua Barnes

0 likesClassical scholarsAuthors from EnglandHistorians from EnglandUniversity of Cambridge alumniUniversity of Cambridge faculty
"These paradigms of ‘race’ and ‘progress’ and their corollaries of ‘racial purity’, and the notion that the only beneficial conquests were those of ‘master races’ over subject ones, could not tolerate the Ancient Model. Thus Müller’s refutations of the legends of Egyptian colonization in Greece were quickly accepted. The Aryan Model—which followed his success—was constructed within the new paradigms. It was encouraged by a number of factors: the discovery of the Indo-European language family with the Indo-Europeans or Aryans soon seen as a ‘race’, the plausible postulation of an original Indo-European homeland in central Asia, and the need to explain that Greek was fundamentally an Indo-European language. Moreover at precisely the same period, the early 19th century, there was intense historical concern with the Germanic overwhelming of the Western Roman Empire in the 5th century AD, and the Aryan conquests in India in the 2nd millennium BC. The application of the model of northern conquest to Greece was thus obvious and very attractive: vigorous conquerors were supposed to have come from a suitably stimulating homeland to the north of Greece, while the ‘Pre-Hellenic’ aborigines had been softened by the undemanding nature of their homeland. And although the large number of non-Indo-European elements in Greek culture could not be reconciled with the ideal of complete Aryan Hellenic purity, the notion of a northern conquest did make the inevitable ‘racial’ mixing as painless as possible. Naturally the purer and more northern Hellenes were the conquerors, as befitted a master race. The Pre- Hellenic Aegean populations, for their part, were sometimes seen as marginally European, and always as Caucasian; in this way, even the natives were untainted by African and Semitic ‘blood’."

- Martin Bernal

0 likesHistorians from EnglandUniversity of Cambridge alumniUniversity of Cambridge facultyCornell University facultyJews from the United Kingdom
"The upholders of conventional wisdom have been...disconcerted by Hellenosemitica, a major work by...Michael Astour, which first appeared in 1967. Hellenosemitica, a series of studies of striking parallels between West Semitic and Greek mythology, showed connections of structure and nomenclature that were far too close to be explained away as similar manifestations of the human psyche. Apart from the challenge posed by this basic theme, Astour made three other fundamental attacks. First, the fact of his writing the book at all upset the academic status quo. While it was permissible for a Classicist, coming from the dominant discipline, to discuss the Middle East in its relation to Greece and Rome, the converse did not hold true. A Semitist was felt to have no right to write about Greece. Secondly, Astour questioned the absolute primacy of archaeology over all other sources of evidence about prehistory—myth, legend, language and names—thus threatening the ‘scientific’ status of ancient history. Thirdly, he sketched out a sociology of knowledge for Classics, indicating links between developments in scholarship and those in society. He even implied a connection between anti-Semitism and hostility to the Phoenicians and cast doubt on the notion of steady accumulative progress of learning. But the worst threat came from his basic message that the legends of Danaos and Kadmos contained a factual kernel."

- Martin Bernal

0 likesHistorians from EnglandUniversity of Cambridge alumniUniversity of Cambridge facultyCornell University facultyJews from the United Kingdom
"After the 1780s, the intensification of racism and the new belief in the central importance of ‘ethnicity’ as a principle of historical explanation became critical for perceptions of Ancient Egypt. The Egyptians were increasingly detached from the noble Caucasians, and their ‘black’ and African nature was more and more emphasized. Thus the idea that they were the cultural ancestors of the Greeks – the epitome and pure childhood of Europe – became unbearable. There was also a new crisis between Egyptian mythology and Christianity with the works of Dupuis, which represented the ideological or theological counterpart of the French Revolution’s attack on European social order. It is only with this background that one can make sense of the tormented career of Champollion during the years of reaction between 1815 and 1830. Although Champollion was an avowed revolutionary and an enthusiastic Bonapartist, one of his earliest discoveries discredited some of the theories of Dupuis’s supporters, and he and his decipherment were therefore welcomed by the Church and the Restoration nobility. On the other hand, his championing of Egypt over Greece combined with his political beliefs to infuriate Hellenist and Indianist scholars, who continued to do all they could to block his academic career."

- Martin Bernal

0 likesHistorians from EnglandUniversity of Cambridge alumniUniversity of Cambridge facultyCornell University facultyJews from the United Kingdom
"Why was Astour’s work considered so...offensive? First, it offended at a formal level, because it challenged the academic hierarchy; this was a reflection of the relative power of the two disciplines. Although Classicists had previously discussed Eastern parallels to Hellenic mythology, it was entirely different and unacceptable for Orientalists to pronounce on Greece.There were also fundamental objections to the content of Astour’s work. Scholars like Fontenrose and Walcot had made broad sweeps of world mythology – including India, Iran and so on – and they gave preference, if possible, to the less offensive sources. By contrast, Astour’s derivation of Greek names from Semitic not only poached on the sacred ground of language, but also made the connections between West Semites and Greeks disturbingly close and specific. Furthermore, two of the myth cycles he treated – those of Kadmos and Danaos – were concerned with Near Eastern colonization in Greece, and he made a plausible case for their having a historical kernel of truth. The fourth section of Hellenosemitica was even more provocative in that it went into the sociology of knowledge, and its sketch of the history and ideology of Classics and Classical archaeology has been the basis of all later writings on this subject, this volume included. In doing this Astour injected relativism into subjects that had previously been impervious to the forces of probabilism and uncertainty that have transformed other disciplines since the 1890s."

- Martin Bernal

0 likesHistorians from EnglandUniversity of Cambridge alumniUniversity of Cambridge facultyCornell University facultyJews from the United Kingdom
"For the safeguard of your country, if you be called to the wars, grutch [complain] not nor groan at it. Go with good wills and lusty courages to meet them in the field rather than to tarry till they come home to you and hang you at your own gates. Play not the milksops in making curtsy who shall go first, but Show yourselves true Englishmen in readiness, courage, and boldness. And be ashamed to be the last. Fear neither French nor Scot. For first you have God and all his army of angels on your side [a marginal note observes "God is English"]. You have right and truth, and seek not to do them wrong but to defend your own right. Think not that God will suffer you to be foiled at their hands, for your fall is his dishonor. If you lose the victory, he must lose the glory. For you fight not only in the quarrel of your country but also and chiefly in defense of his true religion and of his dear son Christ....What people be they with whom we shall match. Are they giants? Are they conquerors or monarchs of the world? No, good Englishman, they be effeminate Frenchmen, stout in brag but nothing in deed. They be such as you have always made to take to their heels..., saving that William of Normandy crept in among us through the civil war of two brethren, Harold and Tostig. And yet, what did he? He left his posterity to reign which were rather by time turned to be English than the noble English to become French, as our tongue and manners at this day declareth, which differeth very little from our ancestors the Saxons....Thus have we nothing to dismay us but all things to encourage us. God to fight for us, the strength of our land, the courage of our men, the goodness of our soil....Now, therefore, it is our duties to be in every wise obedient....Do you not hear how lamentably your natural mother, your country of England, calleth upon you for obedience?...I have been and am glad of you. I delight and rejoice in you above all over nations. In declaration whereof I have always spued out and cast from me Danes, French, Norwegians, and Scots. I could brook none of them for the tender love that I bare unto you, of whom I have my name. I never denied to minister to you by my singular commodities which God hath lent me for you, as corn and cattle, land and pasture, wool and cloth, lead and tin, flesh and fish, gold and silver, and all my other treasures. I have poured them out among you and enriched you above all your neighbors....Besides this, God hath brought forth in me the greatest and excellentest treasure that he hath for your comfort and all the world’s. He would that out of my womb should come that servant of his, your brother John Wyclif, who begat [John] Hus, who begat [Martin] Luther, who begat truth. What greater honor could you or I have than it pleased Christ, as it were in a second birth, to be born again of me among you? [A marginal note comments: "Christ's second birth in England"]. And will you now suffer me, or rather by your disobedience purchase me, to be a mother without my children?...Stick to your mother as she sticketh to you. Let me keep in quiet and feed, as I have done, your wives, your children, and your kinsfolks. Obey your mistress and mine which God hath made lady [queen] over us, both by nature and law. You cannot be my children, if you be not her subjects....?Thus good, truehearted Englishmen, speaketh your country unto you, not in word but in deed. Wherefore give no dull ear to hear, nor hearken to any vain blasts or voices which may draw you from the love of your country and the defense of your sovereign...."

- John Aylmer (bishop)

0 likesAnglican bishopsTheologians from EnglandNon-fiction authors from EnglandUniversity of Cambridge alumni
"I will boldly say, that England...hath more fallow dear than all Europe that I have seen. No kingdom in the world hath so many dove-houses...The English husbandmen eat barley and rye brown bread, and prefer it to white bread as abiding longer in the stomach, and not so soon disgested with their labour; but citizens and gentlemen care eat most pure white bread, England yielding...all kinds of corn in plenty...The English have abundance of white meats, of all kinds of flesh, fowl and fish and of all things good for food...The oysters of England were of old carried as far as Rome, being more plentiful and savoury than in any other part...In the seasons of the year the English eat fallow deer plentifully, as bucks in summer and does in winter, which they bake in pasties, and this venison pasty is a dainty, rarely found in any other kingdom. Likewise brawn is a proper meat to the English, not known to others...In general, the English cooks, in comparison with other nations, are most commended for roasted meats...But the Italian Sansovine is much deceived, writing, that in general the English eat and cover the table at least four times in the day; for howsoever those that journey, and some sickly men staying at home, may perhaps take a small breakfast, yet in general the English eat but two meals (of dinner and supper) each day, and I could never see him that useth to eat four times in the day."

- Fynes Moryson

0 likesNon-fiction authors from EnglandUniversity of Cambridge alumniUniversity of Cambridge faculty