Polymaths

"Giving himself no manner of uneasiness as to what others might think of him, nor caring either to please or displease, he was uniformly without disguise; and, as he shewed himself on all occasions in the same colours, he at last subdued the prejudice, and forced the admiration of others to identify itself with his own."

"We came finally to regard him... as an ingot of pure gold, whose value could not be enhanced by the fashion of the artist."

"He possessed great powers of invention... Not possessing himself, and being in no condition to obtain the instruments necessary for making observations, or a single machine for the purposes of experimental philosophy, he contrived to supply that deficiency by making them of the most common materials that fell in his way; and the dexterity he came to employ in the management of them made amends for the imperfection of their construction."

"Mr. Lambert was a stranger to the three kingdoms of nature (He was however tolerably conversant in chemistry; he made various experiments on salts... the subject of different papers... in the academy.): he had never given his attention to individuals, nor to facts in that arrangement. All his points of view centered in the starry vault, in a straight line before him, and in the chamber of his brain, where he was continually immured, even when you thought you were with him, and fixed, or at least divided his attention. No divergency in him either to the right or to the left, always in the region of abstractions, objects in the order, of what are called concretes scarcely grazed his sphere."

"If in two ellipses having a common major axis we take two such arcs that their chords are equal, and that also the sums of the radii vectores, drawn respectively from the foci to the extremities of these arcs, are equal to each other, then the sectors formed in each ellipse by the arc and the two radii vectores are to each other as the square roots of the parameters of the ellipses."

"I define as a unit any magnitude that can serve for the numerical derivation of a series of magnitudes, and in particular I call such a unit an original unit if it is not derivable from another unit. The unit of numbers, that is one, I call the absolute unit, all others relative. Zero can never be a unit."

"It was natural that Grassmann chose to introduce his system, not by means of a paper, but rather by means of a long and complicated book. ...such ideas as Grassmann's form of the scaler (dot) and vector (cross) products... have counterparts in modern vector analysis."

"One may say without great exaggeration that Grassmann invented linear algebra and, with none at all, that he showed how properly to apply it to geometry. ...He ...anticipated in its most important aspects Peano's treatment of the natural numbers, published 28 years later. ...A feature of Grassmann's work, far in advance of the times, is the tendency towards the use of the implicit definition. ...The definition of a linear space (or vector space) came into mathematics, in the sense of becoming widely known, around 1920, when Hermann Weyl and others published formal definitions. ...Grassmann did not put down a formal definition—again, the language was not available—but there is no doubt that he had the concept."

"While I was pursuing the concept of geometrical product, as this idea was established by my father... I concluded that not only rectangles, but also parallelograms, may be viewed as products of two adjacent sides, provided that the sides are viewed not merely as lengths, but rather as directed magnitudes. When I joined this concept of geometrical product with the previously established idea of geometrical sum the most striking harmony resulted. Thus when I multiplied the sum of two vectors by a third coplaner vector, the result coincided (and must always coincide) with the result obtained by multiplying separately each of the two original vectors by the third... and adding together (with due attention to positive and negative values) the two products. [Thus A(B + C) = AB + AC.] From this harmony I came to see a whole new area of analysis was opening up which could lead to important results."

"A work on tidal theory... led me to Lagrange's Mécanique analytique and thereby I returned to those ideas of analysis. All the developments in that work were transformed through the principles of the new analysis in such a simple way that the calculations often came out more than ten times shorter than in Lagrange's work."

"It is clear... that the concept of space can in no wise be generated by thought. ...Whoever maintains the contrary must undertake to derive the dimensions of space from the pure laws of thought—a problem which is at once seen to be impossible of solution."

"The concept of centroid as sum led me to examine Möbius' Barycentrische Calcul, a work of which until then I knew only the title; and I was not little pleased to find here the same concept of the summation of points to which I had been led in the course of the development. This was the first, and... the only point of contact which my new system of analysis had with the one that was already known."

"The history of geometry may be conveniently divided into five periods. The first extends from the origin of the science to about A. D. 550, followed by a period of about 1,000 years during which it made no advance, and in Europe was enshrouded in the darkness of the middle ages; the second began about 1550, with the revival of the ancient geometry; the third in the first half of the 17th century, with the invention by Descartes of analytical or modern geometry; the fourth in 1684, with the invention of the differential calculus; the fifth with the invention of descriptive geometry by Monge in 1795. The quaternions of Sir William Rowan Hamilton the Ausdehnungslehre of Dr. Hermann Grassmann, and various other publications, indicate the dawn of a new period. Whether they are destined to remain merely monuments of the ingenuity and acuteness of their authors, or are to become mighty instruments in the investigation of old and the discovery of new truths, it is perhaps impossible to predict."

"The concept of rotation led to geometrical exponential magnitudes, to the analysis of angles and of trigonometric functions, etc. I was delighted how thorough the analysis thus formed and extended, not only the often very complex and unsymmetric formulae which are fundamental in tidal theory, but also the technique of development parallels the concept."

"The first impulse came from the consideration of negatives in geometry; I was accustomed to viewing the distances AB and BA as opposite magnitudes. Arising from this idea was the conclusion that if A, B, and C are points of a straight line, then in all cases AB + BC = AC, this being true whether AB and BC are directed in the same direction or in opposite directions (where C lies between A and B). In the latter case AB and BC were not viewed as merely lengths, but simultaneously their considered since they were oppositely directed, Thus dawned the distinction between the sum of lengths and the sum of distances which were fixed in direction. From this resulted the requirement for establishing this latter concept of sum, not simply for the case where the distances were directed in the same or opposite directions, but also for any other case. This could be done in the most simple manner, since the law that AB + BC = AC remains valid when A, B, and C do not lie on a straight line. This then was the first step which led to a new branch of mathematics... I did not however realize how fruitful and how rich was the field that I had opened up; rather that result seemed scarcely worthy of note until it was combined with a related idea."

"I feel entitled to hope that I have found in this new analysis the only natural method according to which mathematics should be applied to nature, and according to which geometry may also be treated, whenever it leads to general and to fruitful results."

"Geometry can in no way be viewed... as a branch of mathematics; instead, geometry relates to something already given in nature, namely, space. I... realized that there must be a branch of mathematics which yields in a purely abstract way laws similar to geometry."

"As I was reading the extract from your paper in the geometric sum and difference... I was struck by the marvelous similarity between your results and those discoveries which I made even as early as 1832... I conceived the first idea of the geometric sum and difference of two or more lines and also of the geometric product of two or three lines in that year (1832). This idea is in all ways identical to that presented in your paper. But since I was for a long time occupied with entirely different pursuits, I could not develop this idea. It was only in 1839 that I was led back to that idea and pursued this geometrical analysis up to the point where it ought to be applicable to all mechanics. It was possible for me to apply this method of analysis to the theory of tides, and in this I was astounded by the simplicity of the calculations resulting from this method."

"Grassmann's first publication of his new system was made in 1844 in a book entitled "Die Lineale Ausdehnungslehre Ein Neuer Zweig der Mathematik." His novel and fruitful ideas were however presented in a somewhat abstruse and unusual form, with the result, as the author himself states in the preface to the second edition issued in 1878, that scarcely any notice was taken of the book by Mathematicians. He was finally convinced that it would be necessary to treat the subject in an entirely different manner in order to gain the attention of the mathematical world. Accordingly in 1862 he published "Die Ausdehnungslehre vollständig und in strenger Form bearbeitet," in which the treatment is algebraic... Since that time his great work has been more fully appreciated, but not even yet, in the opinion of the writer, at its real value."

"As the great generality of Grassmann's processes—all results being obtained for n-dimensional space—has been one of the main hindrances to the general cultivation of his system, it has been thought best to restrict the discussion to space of two and three dimensions."

"The exchange theorem... is sometimes called the Steinitz exchange theorem after Ernst Steinitz... The result was first proved Hermann Günther Graßmann..."

"From the imputation of confounding axioms with assumed concepts Euclid himself, however, is free. Euclid incorporated the former among his postulates while he separated the latter as common concepts—a proceeding which even on the part of his commentators was no longer understood, and likewise with modern mathematicians, unfortunately for science, has met with little imitation. As a matter of fact, the abstract methods of mathematical science know no axioms at all."

"The wonderful and comprehensive system of Multiple Algebra invented by Hermann Grassmann, and called by him the Ausdehnungslehre or Theory of Extension, though long neglected by the mathematicians even of Germany, is at the present time coming to be more and more appreciated and studied. In order that this system, with its intrinsic naturalness, and adaptability to all the purposes of Geometry and Mechanics, should be generally introduced to the knowledge of the coming generation of English-speaking mathematicians, it is very necessary that a text-book should be provided, suitable for use in colleges and universities, through which students may become acquainted with the principles of the subject and its applications."

"Some of the groundbreaking work in the treatment of n-dimensional geometry—was carried out by Hermann Günther Grassmann. ...Grassmann was responsible for the creation of an abstract science of "spaces," inside which the usual geometry was only a special case. Grassmann published his pioneering ideas (originating a branch of mathematics known as linear algebra) in 1844, in a book commonly known as Ausdehnungslehre... Grassmann's suggestion that BA = -AB violates one of the sacrosanct laws of arithmetic... Grassmann faced up squarely to this disturbing possibility and invented a new consistent algebra (known as exterior algebra) that allowed for several processes of multiplication and at the same time could handle geometry in any number of dimensions."

"There is at Paris likewife another sort of fodder which they call la lucern which is not inferior, but rather preferred before sainfoin. Every day produces some new things concerning it, not only in other countries but in our own."

"If the national husbandry of this commonwealth be improved, we may hope, through god's blessing, to see better days, and be able to bear necessary and public burdens to more ease to ourselves, and benefit to human society, than hitherto we could attain to."

"Samuel Hartlib, a celebrated writer on husbandry in the last century, a gentleman much beloved and esteemed by Milton, in his preface to the work, commonly called his Legacy, laments greatly that no public director of husbandry was established in England By Authority; and that we had not adopted the Flemish custom of letting farms upon improvement... Cromwell, in consequence of this admirable performance, allowed Hartlib a pension of 100l. a year ; and Hartlib afterwards, the better to fulfil the intentions of his benefactor, procured Dr. Beati's excellent annotations on the Legacy, with other valuable pieces from bis numerous correspondents."

"Our investigative research into the origin and first major use of solid state diode detector devices led to the discovery that the first transatlantic wireless signal in Marconi’s world-famous experiment was received by Marconi using the iron-mercury-iron-coherer with a telephone detector invented by Sir J.C. Bose in 1898."

"Bose was a physicist and a physicist he remained in his outlook to the very end."

"Bose was the first Indian to be admitted in person to the sanctum sanctorum of English, thus western science."

"To bringing about the scientific renaissance (In India) Sir Jagadish had influentially contributed. Indians are justly proud of the possession of a few men who have gained world-wide reputation in their particular fields of activity, and this pride reacts strongly on public opinion. At the Research Institute a group Indian post-graduate students devote their lives to research. The published Transactions of the Institute show that under the leadership of this eminent Bengali, Indian research is making substantial contribution to scientific knowledge, that in this field there is no fundamental difference between the Western and the Eastern mind, as was assumed when Sir Jagadish began his work."

"The unique throb of life in all creation could seem only poetic imagery before your advent, Professor! A saint I once knew would never pluck flowers. 'Shall I rob the rosebush of its pride in beauty? Shall I cruelly affront its dignity by my rude divestment?' His sympathetic words are verified literally through your discoveries!""

"Then afterwards, when victory is yours, we too-all of us Bengalis-will share in the honour and the glory. We do not need to understand what is it that you have done. Or to have given you any thought, time or money, but the moment we hear the chorus or praises in The Times from the lips of the Englishmen we shall lap it up. Some important news papers in our country will observe we are not inferior men; and another paper will observe we are making discovery after discovery in science. Earlier we shall not have felt an iota of responsibility towards you, but when victory has been won and you return home bearing a crop of records, then you will be one of us. Soughing and ploughing you will do alone; reaping we shall do together. The victory you will find will be more ours than yours."

"The generally accepted interpretation of Jagadish Chandra’s scientific activities is that he had essentially the biologist’s conception of Nature; lack of opportunities for biological studies while as a student in Calcutta and later lack of any teaching post in biology, induced Jagadish Chandra to take up the post of teacher in physics."

"They would be our worst enemy who would wish us to live only on the glories of the past and die off from the face of the earth in sheer passivity. By continuous achievement alone we can justify our great ancestry. We do not honour our ancestors by the false claim that they are omniscient and had nothing more to learn."

"Ashoka’s emblem of the Amlaki will be seen on the cornices of the Institute, and towering above all is the symbol of thunderbolt. It was the RishiDadhichi, the pure and blameless, who offered his life that the divine weapon, the thunderbolt, might be fashioned out of his bones to smite evil and exalt righteousness. It is but half of the Amlaki that we can offer now. But the past shall be reborn in a yet nobler future. We stand here today and resume work tomorrow, so that by the efforts of our lives and our unshaken faith in the future we may all help to build the greater India yet to be."

"Capacity to endure through infinite transformation must be innate in that mighty civilization which has seen the intellectual culture of the Nile Valley of Assyria and of Babylon wax and wane and disappear, and which today gazes on the future with the same invincible faith with which it met the past."

"Sir J.C. Bose's pioneering works in quasi-optic millimeter wave research in Calcutta, India about 100 years back during 1890s are highlighted. He developed an elegant millimeter wave spark transmitter, self recovering coherer detector, wire grid polariser, cylindrical diffraction grating, dielectric lens and prism, rectangular waveguide, horn antenna and microwave absorber, for the studies of reflection, refraction, absorption and polarisation of millimeter waves and its application to wireless remote control for firing a gun. All these pioneering activities indicate that he was well ahead of his time and prompted us to call him the "Father of Radio Science"."

"O Hermit, call thou in the authentic words Of that old hymn called Sama; "Rise! Awake! Call to the man who boasts his shastric lore From vain pedantic wranglings profitless, Call to that foolish braggart to come forth Out on the face of nature, this broad earth, Send forth this call unto thy scholar band; Together round thy sacrifice of fire Let them all gather. So may our India, Our ancient land unto herself return O once again return to steadfast work, To duty and devotion, to her trance Of earnest meditation; let her sit Once more unruffled, greedless, strifeless, pure, O once again upon her lofty seat And platform, teacher of all lands."

"...the "Resonant Cardiograph," Bose then pursued extensive researches on innumerable Indian plants. An enormous unsuspected pharmacopoeia of useful drugs was revealed. The cardiograph is constructed with an unerring accuracy by which a one-hundredth part of a second is indicated on a graph. Resonant records measure infinitesimal pulsations in plant, animal and human structure. The great botanist predicted that use of his cardiograph will lead to vivisection on plants instead of animals."

"I have sought permanently to associate the advancement of knowledge with the widest possible civic and public diffusion of it; and this without any academic limitations, henceforth to all races and languages, to both men and women alike, and for all time coming."

"He (Bose) was modern India’s first physicist after all, one of her very first scientists. He was his motherland’s first active participant in the Galilean - Newtonian tradition. He had confounded the British disbeliever. He had shown that the Eastern mind was indeed capable of the exact and exacting thinking demanded by western science. He had broken the mould."

"From his (Karna’s) low caste came rejection, came every disadvantage; but he always played and fought fair! So his life, though a series of disappointments and defeats to the very end – his slaying by Arjuna– appealed to me as a boy as the greatest of triumphs. I still think of the tournament where Arjuna had been victor, and then of Karna coming as a stranger to challenge him. Questioned of name and birth, he replies, “I am my own ancestor! You do not ask the might Ganges from which of its many springs it comes: its own flow justifies itself, so shall my deeds me! [Further he wrote :] Like that of my boyhood’s hero Karna, my life has been ever one of combat and must be to the last. It is not for man to complain of circumstances, but bravely to accept, to confront, and to dominate them."

"His model of an electric eye which records with electric signals message received from outside world, his physical model of memory as a mechanism for storing information justified this being considered a precursor of the modern discipline of cybernetics."

"Not in matter but in thought, not in possessions nor even in attainments but in ideals, is to be found the seed of immortality. Not through material acquisition but in generous diffusion of ideas and ideals can the true empire of humanity be established. Thus to Asoka, to whom belonged this vast empire, bound by the inviolate seas, after he had tried to ransom the world by giving away to the utmost, there came a time when he had nothing more to give, except one half of an Amlaki fruit. This was his last possession, and his anguished cry was that since he had nothing more to give, let the half of the Amlaki be accepted as his final gift."

"Nothing can be more vulgar or more untrue than the ignorant assertion that the world owes its progress of knowledge of any particular race. The whole world is interdependent and a constant stream of thought has throughout ages enriched the common heritage of mankind. It is the realization of this mutual interdependence that has kept the mighty fabric bound together and ensured the continuity of permanence of civilization."

"I was educated at Cambridge. How admirable is the Western method of submitting all theory to scrupulous experimental verification! That procedure has gone hand in hand with the gift for introspection which is my Eastern heritage. Together they have enabled me to sunder the silences of natural realms long uncommunicative. The telltale charts of my crescograph 2 are evidence for the most skeptical that plants have a sensitive nervous system and a varied emotional life. Love, hate, joy, fear, pleasure, pain, excitability, r, and countless appropriate responses to stimuli are as universal in plants as in animals."

"The true laboratory is the mind, where behind illusions we uncover the laws of truth."

"I have recently returned from an expedition to scientific societies of the West. Their members exhibited intense interest in delicate instruments of my invention which demonstrate the indivisible unity of all life. The Bose crescograph has the enormity of ten million magnifications. The microscope enlarges only a few thousand times; yet it brought vital impetus to biological science. The crescograph opens incalculable vistas."

"[Science] was a human heritage] belonging neither to the East or the West."