Physicists From Scotland

"The human need for unity first created subjective religion, then objective analytical science; now it corrects the partiality of these attitudes by substituting one complete doctrine. (p. 251)"

"Faced by the dire nihilism of our time, we need a greater honesty... The Western search for unifying truth did not come to an end with Christianity, any more than with the physical theories of forty years ago."

"The Christian fog of self deception still does its damage: we either deceive ourselves by pretending to believe or overreact into a contempt of all religion. So, away with the fog!"

"There are good reasons to expect... a return to a concreteness of basic ideas, to simpler fundamentals easily understood, to principles that will bring exact science closer to the human perspective."

"There is no doubt of the need for an up-to-date, balanced, and comprehensive work on the history of atomism, drawing ideas, mathematics, and experiment together into a single story. When available, it should become required reading for all students of the exact sciences."

"The idea that time may be an active factor in causation has the mathematical significance that ' t ' (for the system in question) must appear explicitly in the formulation of the law. ...Such law may claim to express the fact of historic, irreversible duration."

"Discontinuity of its linguistic and logical terms is for the conscious analytical intellect psychologically and logically prior to notions of continuity. ...This functional priority... may not have been reflected in the history of the development of reason in all human communities. ...But it is relevant for the West that the Pythagoreans, with their discrete integers and point patterns, came before Euclid, with his continuous metrical geometry, and that physical atomism as a speculative philosophy preceded by some two thousand years the conception of a continuous physical medium with properties of its own."

"No one is so brilliant that he can afford to neglect what history can teach him."

"Two extreme interpretations of atomism have persisted through centuries: the näive assumption of objectively real indivisible pieces of matter, and the sophisticated view that "atom" is merely a name given to abstractions which it is convenient to assume in simplifying complex phenomena. The second perhaps stems from Ockham, who wrote in 1330 of "the fiction of abstract nouns"; from John Troland, who in 1704 interpreted material particles as mental fictions; and from countless others down to Ernst Mach, who after starting as a physical atomist came to regard atoms as "mental artifices" or "economical ways of symbolizing experience." Both views have advantages..."

"Theory confronts experiment, and both sides are a mixture of obscurity and clarity."

"The idea of the unconscious mental processes was, in many of its aspects, conceivable around 1700, topical around 1800, and became effective around 1900, thanks to the imaginative efforts of a large number of individuals of varied interests in many lands."

"I consider that Curie's Principle has two major consequences:- First: It shows that the class of processes which can be isolated for causal representation, not requiring the inference of external causes, is wider than the class of energetically closed systems. One-way processes in which the system loses energy can be isolable, in the sense that they can be given complete representation without taking their environment into account. Second: It suggests the possibility of a geometrical physics treating 3D spatial relations , i.e., angles or lengths, as primary. Just as statistical mechanics, the theory of crystal symmetry, and Group theory in quantum mechanics, are useful without assumptions about forces, so Curie's principle, with an appropriate model, can determine the path of a one-way process without such assumptions..."

"L. L. Whyte, in a short but prophetic essay, Archimedes or the Future of Physics, pointed out that in each of the two great new physical theories of this century the fundamental role was played by a particular constant of nature: in Relativity by c, the velocity of light in vacuo, and in Quantum Theory by h, Plank's constant. He suggested that the next great advance in our understanding of nature would be associated with a new fundamental constant, and he prophesied that this would be concerned with the flow of time."

"More comprehensive process than those of the conscious mind control human destiny. (p. 151)"

"The unitary system of thought has three main characteristics which distinguish it from many other systems: it deals with the form of systems rather than with their component parts; it recognizes a process of development as prior to the apparently static aspects of nature; and it is unitary, emphasizing one general form beneath all apparent dualism. (p. 21-22)"

"Thought is born of failure. When action satisfies there is no residue to hold the attention; to think is to confess a lack of adjustment which we must stop to consider. Only when the human organism fails to achieve an adequate response to its situation is there material for the process of thought, and the greater the failure the more searching they become. (p. 1)"

"The internal tendencies of every organism, if isolated, lead to its disintegration. But the processes of the wider system sustain and modify those internal tendencies by "nourishing" them and gradually increasing the mutual conformity of organism and environment. (p. 36)"

"The term dissociation is here used for a condition in which the organizing process in an individual fail to develop one characteristic form, and two or more mutually incompatible systems of behavior compete for control. (p. 62)"

"During the metamorphosis from ancient to European man, self-awareness, rationalism, monotheism, and morality all developed in parallel as expressions of the influence of a new form of social tradition on the organization of the individual. […] Europe forced the new mode of life till it produced a definite dissociation, for self-awareness did not then bring with it an adequate understanding of the self; religion could not offer a complete integration; the rational intellect knew nothing of its own origins, limitations or mode of operation; and morality necessarily failed to realize its aim. (p. 114)"

"The dissociation of the typical adult European is a consequence not of any universal human nature, a term that has no meaning, but of the influence of an inadequately organized tradition. (p. 124)"

"Man abhors the absence of integration. He demands integration, and will create religions, achieve heroic self-sacrifice, pursue mad ambitions, or follow the ecstasy of danger, rather than live without. If society refuses him this satisfaction in a constructive form he will seize a destructive principle to which he can devote himself and will take revenge on the society that thought his only demand was pleasure. (p. 188)"

"Goethe did not propose a return to the undifferentiated condition of Heraclitus. The development of man lead from undifferentiated unity with nature, through a differentiation achieved by separation, to a new organized unity. But this last state would be different from the first; it must contain within its recovered unity all the differentiated knowledge, all the specialized organs and faculties, of two thousands years of development. (p. 224)"

"Three centuries of increasingly intense application of the quantitative method had exhausted its guarantee of the progressive improvement of thought, because the regions where the method is adequate have already been explored. [...] It is scarcely possible to avoid the conclusion that a new method is now necessary to supplement the method of quantitative analysis. (p. 180)"

"It is impossible today to escape the need for a general awareness of the phasing of the historical process. In the past great cultures could be created unconsciously, the organic processes forming the new patterns without man's attention being drawn to their wider significance. But the unconscious phase of history is now past. The acceleration of social change which has resulted from the attention paid to specialized techniques can only be controlled by paying attention also to the general formative processes which in earlier times were unconscious. Consciousness of specialized technical methods must be balanced by consciousness of general developing forms. (p. 167)"

"The "marvellous Merchiston" (so he was known to the populace of his day) was born at Merchiston Castle in 1550. The period in which his birth and boyhood fell is the most momentous in the national history, and it determined and gave their peculiar character to his fundamental conceptions of human life and destiny. At the date of his birth the controversy had already begun which was eventually to cleave in twain the history of the Scottish people. The issue whether Roman Catholicism or Protestantism was to prevail was already joined. In 1546, four years before Napier was born, was condemned by the Church and burned as a heretic, and in the same year Cardinal Beaton, the principal agent in his death, was assassinated. In 1547 John Knox began his mission which, after an interval, he was to see crowned with success. During the first ten years of Napier's life the struggle between the two religions was virtually settled. Between the years 1550 and 1560 the country was distracted by civil war, one party being for the old religion and alliance with France, the other for Protestantism and alliance with England. The contest ended in the victory of the Protestant party, and in 1560 a Convention of the Estates set up Protestantism as the national religion. It is in youth that the strongest and most permanent prepossessions and prejudices are formed, and we may trace the origin of Napier's abiding horror of the Church of Rome to the air which he breathed in the opening years of his life. ...it came to be his burning conviction that the salvation of mankind was bound up with the overthrow of the Papacy."

"In 1563, the year of his mother's death, John was sent to the University of St. Andrews, the mother university of Scotland. He was only thirteen, but this was the usual age at which lads then entered the universities."

"What set Napier to work on creating tables which were to enable multiplication to be performed by a process of addition? What first gave him the idea of any such thing? ...there is a peculiarity in the form of his investigations which gives us a useful clue. He usually frames his propositions as though they applied exclusively or at all events specially to sines. Now it is evident that all that concerns logarithms must relate to numbers generally, and that their being sines has no bearing on the matter. Hence his confining his work to sines must indicate that he set out with the idea of working on them only, and that it was only at a later stage and perhaps incidentally that he realised that his results could with like advantage be applied to numbers generally. I conclude from this that his original idea was only to construct tables that would enable the product of two sines to be readily ascertained. If I am right in this, the suggestion may well have come to him from his familiarity with the well known trigonometrical formula:— \sin A \sin B = \frac{1}{2} ({\cos(A - B) - \cos(A + B)})"

"In the Descriptio the author published only so much of the reasoning on which his calculations rested as was necessary to enable the mathematical world to appreciate the nature and use of the tables which are to be found there. Indeed, we find Napier expressly stating in it that he does not propose to publish to the world the manner in which the tables were calculated until he finds that they have justified their existence by their acknowledged usefulness. The Descriptio therefore bears evidence of being written all at one time, to serve as an introduction and guide to the tables which were printed with it."

"The Constructio was evidently written at several different times. The order of its contents is peculiar, and there are to be seen in it evidences of different stages of the discovery. Its object was to explain fully the mode in which he had calculated the Tables and incidentally the reasoning on which they were based, but there are no historical references to the way in which he originally arrived either at the idea of a Table of Logarithms or at the method of constructing it."

"Writing about the middle of the eighteenth century, David Hume proclaimed John Napier of Merchiston as 'the person to whom the title of a great man is more justly due than to any other whom his country ever produced.' This judgment of Hume is the more remarkable, seeing he was himself naturally disposed to exalt literature above science. ...when he awarded the first place among his countrymen to Napier... it was doubtless from an enlivened conviction that his work had been of greater service to humanity."

"The invention of logarithms came on the world as a bolt from the blue. No previous work had led up to it, nothing had foreshadowed it or heralded its arrival. It stands isolated, breaking in upon human thought abruptly without borrowing from the work of other intellects or following known lines of mathematical thought. It reminds me of those islands in the ocean which rise up suddenly from great depths and which stand solitary with deep water close around all their shores. In such cases we may believe that some cataclysm has thrust them up suddenly with earth-rending force. But can it be so with human thought? Did this discovery come as a revelation to Napier, bursting on him as a light from Heaven, or was it the result of slow growth, the evidences of which are now obliterated, like those rocks whose abrupt sides are due, not to sudden and isolated disruption, but to the denudation which has carried away the neighbouring rocks, which, while they remained, testified to the gradual upheaval of the whole?"

"We have also taken care to have printed some Studies on the above-mentioned Propositions, and on the new kind of Logarithms, by that most excellent Mathematician Henry Briggs, public Professor at London, who for the singular friendship which subsisted between him and my father of illustrious memory, took upon himself, in the most willing spirit, the very heavy labour of computing this new Canon, the method of its creation and the explanation of its use being left to the Inventor. Now, however, as he has been called away from this life, the burden of the whole business would appear to rest on the shoulders of the most learned Briggs, on whom, too, would appear by some chance to have fallen the task of adorning this Sparta. Meanwhile (Reader) enjoy the fruits of these labours such as they are, and receive them in good part according to your culture. Farewell, Robert Napier, Son"

"The undoubted fact that Napier worked for some twenty years at the invention of logarithms before he published his first book relating to them is, to my mind, decisive upon this point. It must have been a slow and gradual evolution, even though that which remains furnishes so few traces of the earlier efforts. Is it then possible, out of what he has left us and out of the circumstances of the times, to read the history of this evolution to reconstitute the process of discovery by deciphering the half-effaced records of its growth?"

"All that Napier has left us on the subject of logarithms is contained in two short books, the one known as the Descriptio, published in 1614, and the other known as the Constructio, published after his death in 1619. Internal evidence as well as the distinct statement of his son, who published the Constructio, make it clear that it was in fact written many years before the Descriptio, and it represents in many passages an earlier stratum of thought. ...Napier saw and approved of a translation into English of the Descriptio, and about twenty-five years ago an excellent translation of the Constructio was published in Edinburgh."

"Many computing devices have been used since the invention of the abacus. These include , sector compasses, slide rules, calculators, and computers."

"Napier, in 1614, ...employed the idea of the fluxion of a quantity to picture by means of lines the relation between logarithms and numbers."

"Let our judgment not be too harsh. The period under consideration is too near the Middle Ages to admit of complete emancipation from mysticism even among scientists. Scholars like Kepler, Napier, Albrecht Duerer, while in the van of progress and planting one foot upon the firm ground of truly scientific inquiry, were still resting with the other foot upon the scholastic ideas of preceding ages."

"Napier, the explorer of the secrets of nature, passed among his countrymen for a trafficker with Satan. Even to-day a certain mystery surrounds the figure of the Laird of Merchiston. ...In Scotland, as in other countries, the universities were exclusive centres of intellectual activity, and the studies at the universities were under the sole dominion of the Church, which naturally laid its ban on investigations that might imperil its own teaching. By his isolation Napier is thus wrapped in a certain mystery, and the mystery is deepened by the fact that we know so little of him, and what we know is at times strangely incongruous with the main preoccupations of his life."

"He was distant and isolated from the great arena of letters; cooped up within the narrow limits of desolate Scotland, and encircled with savage sights and sounds of civil discord, above which the name of God was howled by those whose hands were red with murder. When we regard his times, and observe the influence that for so long a period of his life, the war of religion exercised over his intellectual exertions, the wonder is, not that his great contemporaries of the continent became distinguished before him, but that after all he should have extricated his mind from so many toils, and have placed himself by a single effort—though one like the spring of a roused lion—at the side of the astonished demi-gods of science, who had been unconscious of their rival."

"The invention of logarithms, without which many of the numerical calculations which have constantly to be made would be practically impossible, was due to Napier of Merchiston. The first public announcement of the discovery was made in his Mirifici Logarithmorum Canonis Descriptio, published in 1614, and of which an English translation was issued in the following year; but he had privately communicated a summary of his results to Tycho Brahe as early as 1594. In the work Napier explains the nature of logarithms by a comparison between corresponding terms of an arithmetical and geometrical progression. He illustrates their use, and gives tables of the logarithms of the sines and tangents of all angles of the first quadrant, for differences of every minute, calculated to seven decimal places. His definition of the logarithm of a quantity n was what we should now express by 10^7 \log_{e} \!\left( \frac{10^7}{n} \right). This work... is the first valuable contribution to the progress of mathematics which was made by any British writer."

"He was born in the year 1550, at Merchiston, the seat of his forefathers, near Edinburgh; four years after the birth of Tycho, fourteen before Galileo, and twenty one before Kepler."

"The Church of Scotland was planted by such noblemen as Argyle and Glencairn; such barons as Tullibardine and Grange. It was rendered popular, and thus greatly aided, by such preachers as Knox and Goodman; and it became dignified in the eyes of Protestant Europe by its first and greatest theologian, John Napier."

"It may surprise the reader to find this honour claimed for the Inventor of Logarithms, who has hitherto been regarded only on his throne of science, and that by the limited number capable of appreciating his genius. The celebrated historian and philosopher [David Hume] who pronounced him to be the greatest man his country ever produced, founded, probably, none of that estimate upon his theological merits; and more recent authors, ranking high among the historians of Christianity and theological learning in Scotland, have omitted to illustrate their subject with the most efficient example they could have found."

"That his invention was the greatest boon genius could bestow upon a Maritime Empire is a truth universally felt, and which no person is better qualified to appreciate than your Majesty. It is a proud reflection for Britain, that she does not owe to a stranger the creation of that intellectual aid which renders your Majesty's Fleets as free and fearless in Navigation as they have ever been in battle."

"The method by which the logarithms were calculated was explained in the Constructio, a posthumous work issued in 1619: it seems to have been very laborious, and depended either on direct involution and evolution, or on the formation of geometrical means. The method by finding the approximated value of a convergent series was introduced by Newton, Cotes, and Euler. Napier had determined to change the base to one which was a power of 10, but died before he could effect it"

"Even the sagacity of their author did not see the immense fertility of the principle he had discovered; he calculated his tables merely to facilitate arithmetical, and chiefly trigonometrical computation, and little imagined that he was at the same time constructing a scale whereon to measure the density of the strata of the atmosphere, and the heights of mountains; that he was actually computing the areas and the lengths of innumerable curves, and was preparing for a calculus which was yet to be discovered, many of the most refined and most valuable of its resources. Of Napier, therefore, if of any man, it may safely be pronounced, that his name will never be eclipsed by any one more conspicuous, or his invention superseded by any thing more valuable."

"It is no exaggeration to say that the invention of logarithms "by shortening the labours doubled the life of the astronomer." Logarithms were invented by John Napier, Baron of Merchiston, in Scotland. It is one of the greatest curiosities of the history of science that Napier constructed logarithms before exponents were used. To be sure, Stifel and Stevin made some attempts to denote powers by indices, but this notation was not generally known,—not even to Harriot, whose algebra appeared long after Napier's death. That logarithms flow naturally from the exponential symbol was not observed until much later. It was Euler who first considered logarithms as being indices of powers. What then was Napier's line of thought?"

"You have then (kind Reader) in this little book most amply unfolded the theory of the construction of logarithms, (here called by him artificial numbers, for he had this treatise written out beside him several years before the word Logarithm was invented,) in which their nature, characteristics, and various relations to their natural numbers, are clearly demonstrated."

"Napier, Lord of Merchiston, hath set my head and hands at work with his new and admirable Logarithms. I hope to see him this Summer, if it please God, for I never saw a book [Mirifici Logarithmorum Canonis Descriptio] which pleased me better, and made me more wonder."

"From every line of his descent talent seems to have flowed in upon John Napier."