Fellows Of The Royal Society

"I yield to authority. I think the practice of the Court of Chancery for more than one hundred years, and the authority of Judges of very great eminence, establish such a course of practice and such a chain of authority, that I do not think I am at liberty to assume that either the Court or those very learned Judges were in error as to their powers and jurisdiction."

"I should regard it as certainly a novelty in our jurisprudence if the regular order of a learned Judge could be affected, or qualified, or altered in the slightest degree by what some subordinate officer of the Court thought proper to say in writing about it, even though in so doing he committed this additional irregularity—that to that private correspondence he affixed the seal of the Court."

"We should treat with great respect the opinion of eminent American lawyers on points which arise before us, but the practice, which seems to be increasing, of quoting American decisions as authorities, in the same way as if they were decisions of our own Courts, is wrong. Among other things it involves an inquiry, which often is not an easy one, whether the law of America on the subject in which the point arises is the same as our own."

"The last thirty years [1925 to 1955] have seen an enormous improvement in the position of geometry as a branch of mathematics, or, rather, have seen the re-integration of geometry into the main fabric of mathematics. Indeed, one can go further and say that with the restoration of geometry to its rightful place in the mathematical scheme the process of fragmentation which had been doing so much harm to mathematics has been reversed, and we may look forward to the day in which there are no longer analysts, algebraists, geometers and so on, but simply mathematicians. Mathematical research has two aspects, motivation and technique, and when the latter gains control the result is apt to be excessive specialisation. The revolution of geometrical thought, and the reinstatement of geometry as one of the major mathematical disciplines, have helped to bring about a unification of mathematics which we may justly regard as one of the major contributions of the last quarter century to the subject."

"Hodge's work was in the great tradition of Riemann and Poincaré but his more immediate inspiration came from the work of Lefschetz, for whom he had a tremendous admiration."

"Conway made a fortuitous match for a Ph.D. adviser in Harold Davenport, considered the leader of the internationally respected British school of number theory. And while politically and socially speaking Conway was a radical, Davenport was a conservative. “All changes are for the worse,” he'd say. And looking back upon his career and his charges, he said: “I had 2 very good students. Baker”—Alan Baker, later a Fields Medalist—“to whom I would give a problem and he would return with a very good solution. And Conway, to whom I would give a problem and he would return with a very good solution to another problem.”"

"Mathematicians are extremely lucky, they are paid for doing what they would by nature have to do anyway. One should not have a non-teaching fellowship too long, there comes a time when one must make a contribution to society. Great mathematics is achieved by solving difficult problems not by fabricating elaborate theories in search of a problem."

"It is not, I think, going too far to say, that every fact connected with the human organization goes to prove, that man was originally formed a frugivorous animal … This opinion is principally derived from the formation of his teeth and digestive organs, as well as from the character of his skin, and the general structure of his limbs. It is not my intention now to go further into the discussion of this subject, than to observe, that if analogy be allowed to have any weight in the argument, it is wholly on that side of the question which I have just taken. Those animals, whose teeth and digestive apparatus most nearly resemble our own, namely, the apes and monkeys, are undoubtedly frugivorous."

"The year which has passed has not, indeed, been marked by any of those striking discoveries which at once revolutionize, so to speak, the department of science on which they bear."

"Physiologists have usually represented that our species holds a middle rank, in the masticatory and digestive apparatus, between the flesh-eating and the herbivorous animals; — a statement which seems rather to have been deduced from what we have learned by experience on this subject, than to result fairly from an actual comparison of man and animals. … The teeth of man have not the slightest resemblance to those of the carnivorous animals, except that their enamel is confined to the external surface. He possesses, indeed, teeth called canine, but they do not exceed the level of the others, and are obviously unsuited to the purposes which the corresponding teeth execute in carnivorous animals. … Thus we find that, whether we consider the teeth and jaws, or the immediate instruments of digestion, the human structure closely resembles that of the simiæ; all of which, in their natural state, are completely herbivorous."

"Every man has some peculiar train of thought which he falls back upon when he is alone. This, to a great degree, moulds the man."

"THE prejudice which is commonly entertained against metaphysical speculations seems to arise chiefly from two causes: First, from an apprehension that the subjects about which they are employed, are placed beyond the reach of the human faculties; and, secondly, from a belief that these subjects have no relation to the business of life."

"What we commonly call sensibility, depends, in a great measure, on the power of imagination. Point out two men, any object of compassion; --a man, for example, reduced by misfortune from easy circumstances to indigence. The one feels merely in proportion to what he perceives by his senses. The other follows, in imagination, the unfortunate man to his dwelling, and partakes with him and his family in their domestic distresses.... As he proceeds in the painting, his sensibility increases, and he weeps, not for what he sees, but for what he imagines. It will be said, that it was his sensibility which originally aroused his imagination; and the observation is undoubtedly true; but it is equally evident, on the other hand, that the warmth of his imagination increases and prolongs his sensibility."

"Nothing, in truth, has such a tendency to weaken not only the powers of invention, but the intellectual powers in general, as a habit of extensive and various reading without reflection."

"As all our knowledge of the material world is derived from the information of our senses, natural philosophers have, in modern times, wisely abandoned to metaphysicians, all speculations concerning the nature of that substance of which it is composed; concerning the possibility or impossibility of its being created; concerning the efficient causes of the changes which take place in it; and even concerning the reality of its existence, independent of that of percipient beings: and have confined themselves to the humbler province of observing the phenomena it exhibits, and of ascertaining their general laws."

"With the respectability of the senses and feelings established, textbooks written by the Scottish philosophers began to include such topics as perception, memory, imagination, association, attention, language, and thinking. Such a textbook was written by Dugald Stewart (1753–1828), titled Elements of the Philosophy of the Human Mind (1792), and was used at Yale University in 1824."

"Among the various subjects of the inquiry, however, which, inconsequence of the vague use of language, are comprehended under the general title of metaphysics, there are some, which are essentially distinguished from the rest, both by the degree of evidence which accompanies their principles, and by the relation which they bear to the useful sciences and arts: and it has unfortunately happened, that these have shared in that general discredit, into which the other branches of metaphysics have fallen. To this circumstance is probably to be ascribed, the little progress which has hitherto been made in the PHILOSOPHY OF THE HUMAN MIND; a science, so interesting in its nature, and so important in its applications, that it could scarcely have failed, in these inquisitive and enlightened times, to have excited a very general attention, if it had not accidentally been classed, in the public opinion with the vain and unprofitable disquisitions of the schoolmen."

"International law, like the moral law, is part of the law of England, but only to the extent that the Courts will not help those that break it."

"Arguments from the American statute are not of much force, because Englishmen are not bound to know it."

"The rule is this: that wherever there is a decision of a Court of concurrent jurisdiction, the other Courts will adopt that as the basis of their decision, provided it can be appealed from. If it cannot be appealed from, then they will exercise their own judgment."

"Judges are philologists of the highest order."

"In criminal cases you always begin by proving the corpus delicti, and then connect the prisoner with it."

"Circumstantial evidence only raises a probability."

"In a perfectly new case—a case altogether primae impressionis—I think the Judges are bound to hold fast to the principles of the common law—to remember the maxim, "Salus reipublicae suprema lex," and if the condition be really in principle against the public good, to pronounce it in their judgment void."

"You have no right, for the purpose of justifying a libel, to inquire into a man's life and opinions."

"You need not cite cases that are familiar."

"The Crown cannot ever be prejudiced by the misconduct or negligence of any of its officers."

"I remember Lord Eldon saying to counsel, " You have told us how far the cases have gone, will you now tell us where they are to stop?" I think it is now time that we should say where the cases are to stop."

"The Dutch Company, actuated solely by the spirit of gain, and viewing their [Javan] subjects, with less regard or consideration than a West India planter formerly viewed a gang upon his estate, because the latter had paid the purchase money of human property, which the other had not, employed all the existing machinery of despotism to squeeze from the people their utmost mite of contribution, the last dregs of their labor, and thus aggravated the evils of a capricious and semi-barbarous Government, by working it with all the practised ingenuity of politicians, and all the monopolizing selfishness of traders."

"You cannot do physics or cosmology without an assumed philosophical basis. You can choose not to think about that basis: it will still be there as an unexamined foundation of what you do."

"Attempts to explain values in terms of neuroscience or evolutionary theory in fact have nothing whatever to say about what is good or bad. That is a philosophical or religious question (scientists trying to explain ethics from these kinds of approaches always surreptitiously introduce some unexamined concept of what is a good life by the back door)."

"Above all he believes that these mathematically based speculations solve thousand year old philosophical conundrums, without seriously engaging those philosophical issues. The belief that all of reality can be fully comprehended in terms of physics and the equations of physics is a fantasy."

"THE ETERNAL TRUTHS OF MATHEMATICS -- https://www.whyarewehere.tv/people/george-ellis/"

""On the limits of quantum theory: Contextuality and the quantum–classical cut", Annals of Physics 327 (2012) 1890–1932"

"Actually philosophical speculations have led to a great deal of good science. Einstein’s musings on Mach’s principle played a key role in developing general relativity. Einstein’s debate with Bohr and the EPR paper have led to a great of deal of good physics testing the foundations of quantum physics. My own examination of the Copernican principle in cosmology has led to exploration of some great observational tests of spatial homogeneity that have turned an untested philosophical assumption into a testable – and indeed tested - scientific hypothesis. That’ s good science."

"MORAL REALITY AND MORAL FACTS -- https://www.whyarewehere.tv/people/george-ellis/"

"WHAT IS FINE-TUNING? -- https://www.whyarewehere.tv/people/george-ellis/"

"TOP-DOWN CAUSATION -- https://www.whyarewehere.tv/people/george-ellis/"

"I have separated arithmetical from symbolical algebra, and I have devoted the present volume entirely to the exposition of the principles of the former science and their application to the theory of numbers and of arithmetical processes: the second volume, which is now in the press, will embrace the principles of symbolical algebra: it will be followed, if other and higher duties should allow me the leisure to complete them, by other works, embracing all the more important departments of analysis, with the view of presenting their principles in such a form, as may make them component parts of one uniform and connected system."

"In arithmetical algebra we consider symbols as representing numbers, and the operations to which they are submitted as included in the same definitions as in common arithmetic; the signs + and - denote the operations of addition and subtraction in their ordinary meaning only, and those operations are considered as impossible in all cases where the symbols subjected to them possess values which would render them so in case they were replaced by digital numbers; thus in expressions such as a + b we must suppose a and b to be quantities of the same kind; in others, like a - b, we must suppose a greater than b and therefore homogeneous with it; in products and quotients, like ab and \frac{a}{b} we must suppose the multiplier and divisor to be abstract numbers; all results whatsoever, including negative quantities, which are not strictly deducible as legitimate conclusions from the definitions of the several operations must be rejected as impossible, or as foreign to the science."

"This work... was designed in the first instance to be a second edition of a Treatise on Algebra, published in 1830, and which has been long out of print; but I have found it necessary, in carrying out the principles developed in that work, to present the subject in so novel a form, that I could not with propriety consider it in any other light than as an entirely new treatise."

"Symbolical algebra adopts the rules of arithmetical algebra, but removes altogether their restrictions: thus symbolical subtraction differs from the same operation in arithmetical algebra in being possible for all relations of value of the symbols or expressions employed... all the results of arithmetical algebra which are deduced by the application of its rules, and which are general in form, though particular in value, are results likewise of symbolical algebra, where they are general in value as well as in form: thus the product of a^{m} and a^{n}, which is a^{m+n} when m and n are whole numbers, and therefore general in form though particular in value, will be their product likewise when m and n are general in value as well as in form: the series for (a+b)^{n}, determined by the principles of arithmetical algebra, when n is any whole number, if it be exhibited in a general form, without reference to a final term, may be shewn, upon the same principle, to the equivalent series for (a+b)^n, when n is general both in form and value."

"I assure you that I shall never cease to exert myself to the utmost in the cause of reform, and that I will never decline any office which may increase my power to effect it. I am nearly certain of being nominated to the office of Moderator in the year 1818-1819, and as I am an examiner in virtue of my office, for the next year I shall pursue a course even more decided than hitherto, since I shall feel that men have been prepared for the change, and will then be enabled to have acquired a better system by the publication of improved elementary books. I have considerable influence as a lecturer, and I will not neglect it. It is by silent perseverance only, that we can hope to reduce the many-headed monster of prejudice and make the University answer her character as the loving mother of good learning and science."

"It is now more than twenty years since I somewhat rashly undertook to write the Life of Dr. Young. For many years, however, after making this engagement, I found myself so much occupied by the duties of a very laborious college office, that I had no leisure to commence the work; and when the possession of leisure would have enabled me to have done so, my health became so seriously deranged that I felt myself unequal to any continued and severe literary labour. The undertaking was consequently abandoned, and it was proposed to transfer it to other hands; but it was not found easy to secure the services of a person who possessed sufficient scientific knowledge to enable him to write the life of an author whose works were so various in their character and not unfrequently so difficult to understand and analyse, as those of Dr. Young."

"I have endeavoured... to present the principles and applications of Symbolical, in immediate sequence to those of Arithmetical, Algebra, and at the same time to preserve that strict logical order and simplicity of form and statement which is essential to an elementary work. This is a task of no ordinary difficulty, more particularly when the great generality of the language of Symbolical Algebra and the wide range of its applications are considered, and this difficulty has not been a little increased, in the present instance, by the wide departure of my own views of its principles from those which have been commonly entertained."

"I Gladly avail myself of the opportunity of inscribing to you, for a second time, a work of mine on Algebra, as a sincere tribute of my respect, affection and gratitude. I trust that I shall not be considered as derogating from the higher duties which, (in common with you), I owe to my station in the Church, if I continue to devote some portion of the leisure at my command, to the completion of an extensive Treatise, embracing the more important departments of Analysis, the execution of which I have long contemplated, and which, in its first volume I now offer to the public, under the auspices of one of my best and dearest friends."

"This principle, which is thus made the foundation of the operations and results of Symbolical Algebra, has been called "The principle of the permanence of equivalent forms", and may be stated as follows: "Whatever algebraical forms are equivalent, when the symbols are general in form but specific in value, will be equivalent likewise when the symbols are general in value as well as in form.""

"As proposals for estimating the social scarcity prices of natural resources remain contentious, economic accountants ignore them and governments remain wary of doing anything about them."

"In the quantitative models that appear in leading economics journals and textbooks, nature is taken to be a fixed, indestructible factor of production. The problem with the assumption is that it is wrong: nature consists of degradable resources."

"Now, the Priests who belonged to the Temples, scorn'd to use the same Customs in common with these Gypsies; for they thought themselves to be a nobler and graver sort of Fortune-tellers; which makes a mighty difference, I'll assure you, in this great affair."