Non Fiction Authors From England

"Any satisfactory reproduction of the Conics must fulfil certain essential conditions: (1) it should be Apollonius and nothing but Apollonius, and nothing should be altered either in the substance or in the order of his thought, (2) it should be complete, leaving out nothing of any significance or importance, (3) it should exhibit under different headings the successive divisions of the subject, so that the definite scheme followed by the author may be seen as a whole."

"There is perhaps no question that occupies, comparatively, a larger space in the history of Greek geometry than the problem of the Doubling of the Cube. The tradition concerning its origin is given in a letter from Eratosthenes of Cyrene to King Ptolemy Euergetes quoted by Eutocius... "Eratosthenes to King Ptolemy greeting. "There is a story that one of the old tragedians represented Minos as wishing to erect a tomb for Glaucus and as saying, when he heard that it was a hundred feet every way,Too small thy plan to bound a royal tomb. Let it be double; yet of its fair form Fail not, but haste to double every side.But he was clearly in error; for when the aides are doubled, the area becomes four times as great, and the solid content eight times as great. Geometers also continued to investigate the question in what manner one might double a given solid while it remained in the same form."

"Nesselmann observes that we can, as regards the form of exposition of algebraic operations and equations, distinguish three historical stages of development... 1. ...Rhetoric Algebra, or "reckoning by complete words." ...the absolute want of all symbols, the whole of the calculation being carried on by means of complete words, and forming... continuous prose. ...2. ...Syncopated Algebra... is essentially rhetorical and therein like the first in its treatment of questions, but we now find for often-recurring operations and quantities certain abbreviational symbols. ...3. ...Symbolic Algebra ...uses a complete system of notation by signs having no visible connection with the words or things which they represent, a complete language of symbols, which supplants entirely the rhetorical system, it being possible to work out a solution without using a single word of the ordinary written language, with the exception (for clearness' sake) of a conjunction here and there, and so on. Neither is it the Europeans posterior to the middle of the seventeenth century who were the first to use Symbolic forms of Algebra. In this they were anticipated many centuries by the Indians."

"In illustration of his entire preoccupation with his studies, we are told that he would forget all about his food and such necessities of life, and would be drawing geometrical figures in the ashes of the fire, or, when anointing himself, in the oil on his body."

"While then for a long time everyone was at a loss, Hippocrates of Chios was the first to observe that, if between two straight lines of which the greater is double of the less it were discovered how to find two mean proportionals in continued proportion, the cube would be doubled; and thus he turned the difficulty in the original problem into another difficulty no less than the former. Afterwards, they say, some Delians attempting, in accordance with an oracle, to double one of the altars fell into the same difficulty. And they sent and begged the geometers who were with Plato in the Academy to find for them the required solution. And while they set themselves energetically to work and sought to find two means between two given straight lines, Archytas of Tarentum is said to have discovered them by means of half-cylinders, and Eudoxus by means of the so-called curved lines. It is, however, characteristic of them all that they indeed gave demonstrations, but were unable to make the actual construction or to reach the point of practical application, except to a small extent Menaechmus and that with difficulty."

"The most probable view is that adopted by Nesselmann, that the works which we know under the three titles formed part of one arithmetical work, which was, according to the author's own words, to consist of thirteen Books. The proportion of the lost parts to the whole is probably less than it might be supposed to be. The Porisms form the part the loss of which is most to be regretted, for from the references to them it is clear that they contained propositions in the Theory of Numbers most wonderful for the time."

"It may be in some measure due to the defects of notation in his time that Diophantos will have in his solutions no numbers whatever except rational numbers, in [the non-numbers of] which, in addition to surds and imaginary quantities, he includes negative quantities. ...Such equations then as lead to surd, imaginary, or negative roots he regards as useless for his purpose: the solution is in these cases ὰδοπος, impossible. So we find him describing the equation 4=4x+20 as ᾰτοπος because it would give x=-4. Diophantos makes it throughout his object to obtain solutions in rational numbers, and we find him frequently giving, as a preliminary, conditions which must be satisfied, which are the conditions of a result rational in Diophantos' sense. In the great majority of cases when Diophantos arrives in the course of a solution at an equation which would give an irrational result he retraces his steps and finds out how his equation has arisen, and how he may by altering the previous work substitute for it another which shall give a rational result. This gives rise, in general, to a subsidiary problem the solution of which ensures a rational result for the problem itself. Though, however, Diophantos has no notation for a surd, and does not admit surd results, it is scarcely true to say that he makes no use of quadratic equations which lead to such results. Thus, for example, in v. 33 he solves such an equation so far as to be able to see to what integers the solution would approximate most nearly."

"Almost the whole of Greek science and philosophy begins with Thales."

"Diophantos lived in a period when the Greek mathematicians of great original power had been succeeded by a number of learned commentators, who confined their investigations within the limits already reached, without attempting to further the development of the science. To this general rule there are two most striking exceptions, in different branches of mathematics, Diophantos and Pappos. These two mathematicians, who would have been an ornament to any age, were destined by fate to live and labour at a time when their work could not check the decay of mathematical learning. There is scarcely a passage in any Greek writer where either of the two is so much as mentioned. The neglect of their works by their countrymen and contemporaries can be explained only by the fact that they were not appreciated or understood. The reason why Diophantos was the earliest of the Greek mathematicians to be forgotten is also probably the reason why he was the last to be re-discovered after the Revival of Learning. The oblivion, in fact, into which his writings and methods fell is due to the circumstance that they were not understood. That being so, we are able to understand why there is so much obscurity concerning his personality and the time at which he lived. Indeed, when we consider how little he was understood, and in consequence how little esteemed, we can only congratulate ourselves that so much of his work has survived to the present day."

"In geometry the following theorems are attributed to him [Thales]—and their character shows how the Greeks had to begin at the very beginning of the theory—(1) that a circle is bisected by any diameter (Eucl. I., Def. 17), (2) that the angles at the base of an isosceles triangle are equal (Eucl. I., 5), (3) that, if two straight lines cut one another, the vertically opposite angles are equal (Eucl. I., 15), (4) that, if two triangles have two angles and one side respectively equal, the triangles are equal in all respects (Eucl. I., 26). He is said (5) to have been the first to inscribe a right-angled triangle in a circle: which must mean that he was the first to discover that the angle in a semicircle is a right angle. He also solved two problems in practical geometry: (1) he showed how to measure the distance from the land of a ship at sea (for this he is said to have used the proposition numbered (4) above), and (2) he measured the heights of pyramids by means of the shadow thrown on the ground (this implies the use of similar triangles in the way that the Egyptians had used them in the construction of pyramids)."

"A 'popular libertarianism' might ... feel all that needs to be done to bring the world to justice is to institute the minimal state now, starting as it were from present holdings. On this view, then, libertarianism starts tomorrow, and we take the present possession of property for granted."

"Ronald Dworkin... argues that our law includes not only norms found in treaties, customs, constitutions, statutes, and cases, but also moral principles that provide the best justification for the norms found there.5 On his account, the things justified by moral."

"The year in Oxford was the philosophically most important for Rawls since 1941–42 (his first year as a philosophy student, under the influence of Malcolm). Through Urmson, he got to know Oxford’s most important philosophers. He attended a lecture course by H. L. A. Hart, who, freshly promoted to a professorship, was expounding some of the ideas he would later publish in The Concept of Law. Rawls was especially impressed with a seminar taught by Berlin and Hampshire, with Hart’s active participation, in the winter of 1953. This covered Condorcet, Rousseau’s Social Contract, John Stuart Mill’s "On Liberty," Alexander Herzen, G. E. Moore, and two essays by John Maynard Keynes. Rawls continued to think of this seminar as an exemplar of excellent teaching that he should seek to emulate."

"I did, and still do, think that New Classical Economics has quite a bit in common with the Austrians (so did Robert Lucas, and I am surprised to find that I did not refer to this in the early 1980s, so I was either careless or did not know about it until a bit later)."

"Roughly speaking, Lundberg argued that Gunnar Myrdal's work has been enormously important, and noted that there was local pressure on the Nobel Prize Committee to recognize him, but wondered how it would be received abroad if this was done. (Remember that the Prize was then rather new, and Lundberg had to be careful about its reputation.) Giersch's reply was that the quality of the work surely merited the award, but maybe the politics of it would be easier if there was a joint recipient who was neither Swedish nor shared Myrdal's views – what about Hayek? That's it – is this where Hayek's prize came from, or was he already high on the list, or what?"

"There is no inherent reason or necessity that all women should voluntarily choose to devote their lives to one animal function and its consequences. Numbers of women are wives and mothers only because there is no other career open to them, no other occupation for their feelings or activities. Every improvement in their education, and enlargement of their faculties, everything which renders them more qualified for any other mode of life, increases the number of those to whom it is an injury and an oppression to be denied the choice. To say that women must be excluded from active life because maternity disqualifies them for it, is in fact to say that every other career should be forbidden them, in order that maternity may be their only resource."

"if we look to the great majority of cases, the effect of women’s legal inferiority, on the character both of women and of men, must be painted in far darker colours. We do not speak here of the grosser brutalities, nor of the man’s power to seize on the woman’s earnings, or compel her to live with him against her will. We do not address ourselves to any one who requires to have it proved that these things should be remedied. We suppose average cases, in which there is neither complete union nor complete disunion of feelings and character; and we affirm, that, in such cases, the influence of the dependence on the woman’s side is demoralising to the character of both."

"To the beloved and deplored memory of her who was the inspirer, and in part the author, of all that is best in my writings – the friend and wife whose exalted sense of truth and right was my strongest incitement, and whose approbation was my chief reward – I dedicate this volume. Like all that I have written for many years, it belongs as much to her as to me ... Were I but capable of interpreting to the world one half the great thoughts and noble feelings which are buried in her grave, I should be the medium of a greater benefit to it, than is ever likely to arise from anything that I can write, unprompted and unassisted by her all but unrivaled wisdom."

"We deny the right of any portion of the species to decide for another portion what is and what is not their ‘proper sphere’. The proper sphere for all human beings is the largest and highest which they are able to attain to."

". . . if scientists could get rid of the mental block which prevents them investigating a vast subject right under their noses, they could soon learn a great deal more than my wife and I are capable of doing."

"On the whole, the scientist is better off if he collects his facts by accident, little by little, so he can study them before he tries to fit them into a jigsaw puzzle, This is how the late Tom Lethbridge came to arrive at his theories about other dimensions of reality. It is also how Guy Lyon Playfair came to develop his own theories about the nature of the poltergeist."

"I am reasonably certain of one thing. The unquestioning acceptance of the Copenhagen interpretation has served to hold back progress on the development of alternative approaches. Blind acceptance of the orthodox position cannot produce the challenges needed to push the theory eventually to its breaking point. And break it will, probably in a way nobody can predict, to produce a theory nobody can imagine. The arguments about reality will undoubtedly persist, but at least we will have a better theory. I have tried to argue that quantum theory is a difficult subject for modern students of physical science because its interpretation is so firmly rooted in philosophy. If, in arguing the case, I have only made the subject seem even more confusing, then I apologize. However, my most important message is a relatively simple one: quantum theory is rife with conceptual problems and contradictions, and its most common interpretation is anti-realist in nature. If you fine the theory difficult to understand, this is the theory's fault—not yours."

"It seems incredible that we should willingly trade certainty for quantum confusion and doubt. But, make no mistake, despite its simplicity, its appealing visual images and its resonance with our common understanding, classical physics failed. The quantum description was built amidst the ruins of the structure that preceded it, and it is therefore appropriate that we begin our journey from within this classical landscape."

"A scientist in the late nineteenth century could be forgiven for thinking that the major elements of physics were built on unshakeable foundations and effectively established for all time. The efforts of generations of scientists, philosophers, and mathematicians had culminated in Isaac Newton's grand synthesis in the late seventeenth century."

"The last century was defined by physics. From the minds of the world’s leading physicists there flowed a river of ideas that would transport man kind to the very pinnacle of wonder and to the very depths of despair. This was a century that began with the certainties of absolute knowledge and ended with the knowledge of absolute uncertainty. It was a century in which physicists developed theories that would deny us the possibility that we can ever properly comprehend the nature of physical reality. It was also a century in which they built weapons with the capacity utterly to destroy this reality."

"Years ago, when I toiled as a columnist for The Nation, Nick Clegg was my intern. (So, for that matter, was Edward Miliband, Gordon Brown’s minister for energy and climate change and brother of Brown’s most likely replacement, Foreign Secretary David Miliband.) I have done my best to trade on this mentoring relationship with power, to little avail. Clegg worked for me in the magazine’s New York offices while I was writing from Washington, so our direct contact was limited. What I chiefly remember, apart from his now-famous personal charm, was how “European” he was. His parentage was partly Dutch and partly Russian. He has since married a Spanish woman and has three children with Spanish names. And, of course, his party is the one most closely identified with the British aspiration to full British engagement in the European Union. This is the strength and the weakness of his position, and of his party."

"And what is the reaction of the British political class? Well the Lib Dems, still think that the Euro is a success! I don't quite think where Cleggy gets this from, I don't know. Perhaps he is considering an alternative career as a stand up comedian, once he's out of politics."

"[While deputy prime minister] He's there to serve a very important ceremonial function as David Cameron's lapdog-cum-prophylactic protection device for all the difficult things that David Cameron has to do that cheese off the rest of the ... [ending absent] He’s a kind of shield. He’s a lapdog who’s been skinned and turned into a shield to protect."

"An officer candidate being interviewed for a posting on the British general staff was once asked to define the role of cavalry in modern warfare. He replied that it was to lend some color and dash to what would otherwise be a somewhat dreary and sordid occasion. Nick Clegg, the leader of Britain’s Liberal Democrats, is the equivalent of the cavalry in the case of Thursday’s British general election. Until his eruption onto the scene, the muddy battlefield was a dull trench war between two heavily armored divisions, each of them wearily familiar with the tactics and strategy of the other."

"In politics, you live by the sword, and you die by the sword."

"If the people who ran Facebook were monsters, I wouldn’t have worked there."

"I see no way to secure liberalism by trying to put its core values beyond any but internal or consensual reasoning. The resulting slide into relativism leaves a disastrous parallel between 'liberalism for the liberals!' and 'cannibalism for the cannibals!'"

"I agree with Nick."

"[Leaving the EU would be a] terrible thing for the British economy"

"In 2007 after a night of disappointing election results for our party in Edinburgh, Alex Cole Hamilton said this: if his defeat was part-payment for the ending of child detention, then he accepted it with all his heart. Those words revealed a selfless dignity which is very rare in politics but common amongst Liberal Democrats. If our losses today are part payment for every family that is more secure because of a job we helped to create, every person with depression who is treated with a compassion they deserve, every child who does a little better in school, every apprentice with a long and rewarding career to look forward to, every gay couple who know that their love is worth no less than anyone else’s and every pensioner with a little more freedom and dignity in retirement then I hope at least our losses can be endured with a little selfless dignity too."

"If I was a Brexit voter, I would feel increasingly betrayed that I voted in the belief that all these Brexiteers knew what they were doing"

"The home secretary and the Home Office – they can try to make the case as many times as they like but this idea, which was the idea of the heart of the snooper's charter, that every single website that you visit and every single website that anyone visits in this country is logged somewhere, that's just not going to happen while I'm in government."

"Some philosophers – I am again thinking particularly of Martin Hollis – have objected that it will only be rational to hold such a belief if it was in turn rational to hold the core beliefs from which this specific item is said to follow. But this image of a rational bedrock strikes me as confused. What does it mean for a purportedly core belief to be rationally held? On the one hand, it can hardly mean that we are capable of giving good reasons for holding it. For in that case it would be a derivative rather than a core belief. But on the other hand, I cannot see – as I have already conceded – what else it can mean to describe a belief as being held in a rational way. I cannot see, in short, that Hollis’s proposal can be deployed in such a way as to set limits to the kind of holism I am trying to expound. Even in the most primitive perceptual cases, even in the face of the clearest observational evidence, it will always be reckless to assert that there are any beliefs we are certain to form, any judgements we are bound to make, simply as a consequence of inspecting the allegedly brute facts. The beliefs we form, the judgements we make, will always be mediated by the concepts available to us for describing what we have observed. But to employ a concept is always to appraise and classify our experience from a particular perspective and in a particular way. What we experience and report will accordingly be what is brought to our attention by the range of concepts we possess and the nature of the discriminations they enable us to make. We cannot hope to find any less winding a path from experience to belief, from observational evidence to any one determinate judgement."

"What people have dubbed the snooper's charter - I have to be clear with you, that's not going to happen."

"[I promise] real remedies for the way the world is today not dangerous fantasies about a bygone world that no longer exists. And that is why I'm going to do everything I can to make sure that we remain part of the European Union because that is how we protect the Britain we love."

"Whether we like it or not the single market, the biggest destination of our goods and services, is a market place of rules,"

"We would support the government by not voting for a referendum [on the Lisbon treaty]. We would vote against a referendum on the treaty and vote in accordance with our long-held position that the real referendum that needs to be had is whether we stay in the EU or not."

"Maybe he one day - perhaps we will have to wait for his memoirs - could account for his role in the most disastrous decision of all, which is the illegal invasion of Iraq."

"We don't believe that the expansion of civil nuclear power is the great panacea the government makes it out to be. For a start, all the experts agree that where there is going to be an energy crunch between supply and increasing demand, will be around... 2016 or so. By the most optimistic scenarios from the government itself, there's no way they are going to have new nuclear come on stream until 2021, 2022. So it's just not even an answer."

"If the legislation is passed I will lead a grassroots campaign of civil disobedience to thwart the identity cards programme ... I, and I expect thousands of people like me, will simply refuse ever to register."

"Human Rights Act are not, as some would have you believe, foreign impositions. These are British rights, drafted by British lawyers. Forged in the aftermath of the atrocities of the Second World War. Fought for by Winston Churchill. So let me say something really clear about the Human Rights Act. In fact I'll do it in words of one syllable: It is here to stay."

"Years of uncertainty caused by a future EU referendum would hit jobs and growth and this is not in the national interest"

"Once the major wants of mankind are satisfied by the machine process, our factory system must be on a basis of regular annual replacement instead of progressive expansion—not on a basis of premature replacement through debauched workmanship, adulterated materials, and grossly stimulated caprice. "The case," as Mr. J. A. Hobson again puts it, "is a simple one. A mere increase in the variety of our material consumption relieves the strain imposed upon man by the limits of the material universe, for such a variety enables him to utilize a larger proportion of the aggregate matter. But in proportion as we add to mere variety a higher appreciation of those adaptations of matter which are due to human skill, which we call Art, we pass outside the limit of matter and are no longer slaves of roods and acres and a law of diminishing returns." In other words: a genuine standard, once the vital physical wants are satisfied, tends to change the plane of consumption and therefore to limit, in a considerable degree, the extent of further mechanical enterprise."

"Not the least advantage of basic communism would be the fact that it would tend to put a brake upon industrial enterprise. But such a brake, instead of being in the form of capitalist sabotage, or in the shocking dislocation of a commercial crisis, would be a gradual lessening of the speed of individual parts and a gearing of the whole organization into a steady routine of productivity. Mr. J. A. Hobson has put this matter with his usual insight and wisdom: "Industrial progress would undoubtedly be slower under state-control, because the very object of such control is to divert a larger proportion of human genius and effort from these occupations in order to apply them in producing higher forms of wealth..." However forbidding such a prospect looks to the enterpriser of the old order, humanly speaking it would represent a tremendous gain."

"This practical condition, together with the failure of international-political theories to provide either convincing explanations or serviceable guidance for research, has provided adequate temptation to pursue reductionist approaches. The economic theory of imperialism developed by Hobson and Lenin is the best of such approaches. By "best" I mean not necessarily correct but rather most impressive as theory. The theory is elegant and powerful. Simply stated and incorporating only a few elements, it claims to explain the most important of international-political events-not merely imperialism but also most, if not all, modem wars-and even to indicate the conditions that would permit peace to prevail. The theory offers explanations and, unlike most theories in the social sciences, predictions as well. Moreover, it has successfully performed the other tasks that a good theory should accomplish: namely, stimulating and guiding research and· provoking counter-theories that claim to account for the same phenomena. All in all, the literature that can be attributed to the Hobson-Lenin theory of imperialism, both in support of the theory and against it, is as extensive and as sophisticated as the literature associated with any other school in the field of international politics."