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April 10, 2026
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"My own introduction to quaternionics took place in quite a different manner. Maxwell exhibited his main results in quaternionic form in his treatise. I went to Prof Tait's treatise to get information, and to learn how to work them. I had the same difficulties as the deceased youth, but by skipping them, was able to see that quaternionics could be employed consistently in vectorial work. But on proceeding to apply quaternionics to the development of electrical theory, I found it very inconvenient. Quaternionics was in its vectorial aspects antiphysical and unnatural, and did not harmonise with common scalar mathematics. So I dropped out the quaternion altogether, and kept to pure scalar and vectors, using a very simple vectorial algebra in my papers from 1883 onward. The paper at the beginning of vol. 2 of my Electrical Papers may be taken as a developed specimen; the earlier work is principally concerned with the vector differentiator ∇ and its applications, and physical interpretations of the various operations. Up to 1888 I imagined that I was the only one doing vectorial work on positive physical principles; but then I received a copy of Prof. Gibbs's Vector Analysis (unpublished, 1881-4)."
"Mathematics is of two kinds, Rigorous and Physical. The former is Narrow: the latter Bold and Broad. To have to stop to formulate rigorous demonstrations would put a stop to most physico-mathematical inquiries. Am I to refuse to eat because I do not fully understand the mechanism of digestion?"
"We do not dwell in the Palace of Truth. But, as was mentioned to me not long since, "There is a time coming when all things shall be found out." I am not so sanguine myself, believing that the well in which Truth is said to reside is really a bottomless pit."
"Waves from moving sources: Adagio. Andante. Allegro moderato."
"However absurd it may seem, I do in all seriousness hereby declare that I am animated mainly by philanthropic motives. I desire to do good to my fellow creatures, even to the Cui bonos."
"The following story is true. There was a little boy, and his father said, “Do try to be like other people. Don’t frown.” And he tried and tried, but could not. So his father beat him with a strap; and then he was eaten up by lions. Reader, if young, take warning by his sad life and death. For though it may be an honour to be different from other people, if Carlyle’s dictum about the 30 million be still true, yet other people do not like it. So, if you are different, you had better hide it, and pretend to be solemn and wooden-headed. Until you make your fortune. For most wooden-headed people worship money; and, really, I do not see what else they can do. In particular, if you are going to write a book, remember the wooden-headed. So be rigorous; that will cover a multitude of sins. And do not frown."
"Electric and magnetic forces. May they live for ever, and never be forgot, if only to remind us that the science of electromagnetics, in spite of the abstract nature of its theory, involving quantities whose nature is entirely unknown at the present, is really and truly founded on the observations of real Newtonian forces, electric and magnetic respectively."
"Research is a matter of overcoming obstacles. That's what research is about. There are problems. There are difficulties. It's hard to make sense of a collection of information or whatever. Obstacles are the nature of research. Maybe that's why some people give up. There's always an obstacle. You overcome one to find there's another one."
"My object has been, first to discover correct principles and then to suggest their practical development."
"It was in the year 1843 that I read a paper "On the Calorific Effects of Magneto-Electricity and the Mechanical Value of Heat" to the Chemical Section of the British Association assembled at Cork. With the exception of some eminent men, among whom I recollect with pride Dr. Apjohn, the president of the Section, the Earl of Rosse, Mr. Eaton Hodgkinson, and others, the subject did not excite much general attention; so that when I brought it forward again at the meeting in 1847, the chairman suggested that, as the business of the section pressed, I should not read my paper, but confine myself to a short verbal description of my experiments. This I endeavoured to do, and discussion not being invited, the communication would have passed without comment if a young man had not risen in the section, and by his intelligent observations created a lively interest in the new theory. The young man was William Thomson, who had two years previously passed the University of Cambridge with the highest honour, and is now probably the foremost scientific authority of the age."
"If the water flow down by a gradual natural channel, its potential energy is gradually converted into heat by fluid friction, according to an admirable discovery made by Mr Joule of Manchester above twelve years ago, which has led to the greatest reform that physical science has experienced since the days of Newton. From that discovery, it may be concluded with certainty that heat is not matter, but some kind of motion among the particles of matter; a conclusion established, it is true, by Sir Humphrey Davy and Count Rumford at the end of last century, but ignored by even the highest scientific men during a period of more than forty years."
"Mr Joule... fully established the relations of equivalence among the energies of chemical affinity, of heat, of combination or combustion, of electrical currents in the galvanic battery, of electrical currents in magnetoelectric machines, of engines worked by galvanism, and of all the varied and interchangeable manifestations of calorific action and mechanical force which accompany them. These researches, with the theory of animal heat and motion in relation to the heat of combustion of the food, and the theory of the phenomena presented by shooting stars, due to the same penetrating investigator, have afforded to the author of the present communication the chief groundwork for his speculations."
"It must be confessed that the new quantum mechanics is far from satisfying the requirements of the layman who seeks to clothe his conceptions in figurative language. Indeed, its originators probably hold that such symbolic representation is inherently impossible. It is earnestly to be hoped that this is not their last word on the subject, and that they may yet be successful in expressing the quantum postulate in picturesque form."
"There are some great men of science whose charm consists in having said the first word on a subject, in having introduced some new idea which has proved fruitful; there are others whose charm consists perhaps in having said the last word on the subject, and who have reduced the subject to logical consistency and clearness. I think by temperament Lord Rayleigh belonged to the second group."
"The only merit of which I personally am conscious was that of having pleased myself by my studies, and any results that may be due to my researches were owing to the fact that it has been a pleasure for me to become a physicist."
"In science by a fiction as remarkable as any to be found in law, what once been published even though it be in the Russian language, is spoken of as known, and it is too often forgotten that the rediscovery in the library may be a more difficult and uncertain process than the first discovery in the laboratory."
"Without encroaching upon grounds appertaining to the theologian and the philosopher, the domain of natural sciences is surely broad enough to satisfy the wildest ambition of its devotees. In other departments of human life and interest, true progress is rather an article of faith than a rational belief; but in science a retrograde movements is, from the nature of the case, almost impossible. Increasing knowledge brings with it increasing power, and great as are the triumphs of the present century, we may well believe that they are but a foretaste of what discovery and invention have yet in store for mankind. … The work may be hard, and the discipline severe; but the interest never fails, and great is the privilege of achievement."
"The history of this paper suggests that highly speculative investigations, especially by an unknown author, are best brought before the world through some other channel than a scientific society, which naturally hesitates to admit into its printed records matter of uncertain value. Perhaps one may go further, and say that a young author who believes himself capable of great things would usually do well to secure the favourable recognition of the scientific world by work whose scope is limited, and whose value is easily judged, before embarking upon higher flights."
"Opinions derived from long experience are exceedingly valuable, and outweigh all others, while they are consistent with facts and with each other; but they are worse than useless when they lead, as in this instance, to directly opposite opinions."
"Every new discovery in science brings with it a host of new problems, just as the invention of the automobile brought with it gas stations, roads, garages, mechanics, and a thousand other subsidiary details."
"No longer was light analogous to the discharge of a blunderbuss, but rather to the pulsating flight of birds."
"Acid rain is a short-hand term that covers a set of highly complex and controversial environmental problems. It is a subject in which emotive and political judgements tend to obscure the underlying scientific issues which are fairly easily stated but poorly understood."
"The results suggest a helical structure (which must be very closely packed) containing 2, 3 or 4 co‐axial nucleic acid chains per helical unit, and having the phosphate groups near the outside."
"Science and everyday life cannot and should not be separated."
"What’s the use of doing all this work if we don't get some fun out of this?"
"Although many of the artifices employed in the works before mentioned are remarkable for their elegance, it is easy to see they are adapted only to particular objects, and that some general method, capable of being employed in every case, is still wanting."
"The properties of bodies were investigated by several distinguished French mathematicians on the hypothesis that they are systems of molecules in equilibrium. The somewhat unsatisfactory nature of the results... produced... a reaction in favour of the opposite method of treating bodies as if they were... continuous. This method, in the hands of Green, Stokes, and others, has led to results the value of which does not at all depend on what theory we adopt as to the ultimate constitution of bodies."
"Molecular movements strictly obey the law of conservation of energy, but what we call "law" is simply an expression of the direction along which a form of energy acts, not the form of energy itself. We may explain molecular and molar motions, and discover all the physical laws of motion, but we shall be far as ever from a solution of the vastly more important question as to what form of will and intellect is behind the motions of molecules, guiding and constraining them in definite directions along predetermined paths. What is the determining cause in the background? What combination of will and intellect outside our physical laws guides the fortuitous concourse of atoms along ordered paths culminating in the material world in which we live? In these last sentences I have intentionally used words of wide signification — have spoken of guidance along ordered paths. It is wisdom to be vague here, for we absolutely can not say whether or when any diversion may be introduced into the existing system of earthly forces by an external power."
"An omnipotent being could rule the course of this world in such a way that none of us should discover the hidden springs of action. He need not make the sun stand still upon Gibeon. He could do all that he wanted by the expenditure of infinitesimal diverting force upon ultra-microscopic modifications of the human germ."
"The clock runs down. I lift the weight by exerting the proper amount of energy, and in this action the law of conservation of energy is strictly obeyed. But now I have the choice of either letting the weight fall free in a fraction of a second, or, constrained by the wheelwork, in twenty-four hours. I can do which I like, and whichever way I decide, no more energy is developed in the fall of the weight. I strike a match; I can use it to light a cigarette or to set fire to a house. I write a telegram; it may be simply to say I shall be late for dinner, or it may produce fluctuations on the stock exchange that will ruin thousands. In these cases the actual force required in striking the match or in writing the telegram is governed by the law or conservation of energy; but the vastly more momentous part, which determines the words I use or the material I ignite, is beyond such a law. It is probable that no expenditure of energy need be used in the determination of direction one way more than another. Intelligence and free will here come into play, and these mystic forces are outside the law of conservation of energy as understood by physicists."
"I am impelled to one further reflection, dealing with the conservation of energy. We say, with truth, that energy is transformed but not destroyed, and that whenever we can trace the transformation we find it quantitatively exact. So far as our very rough exactness goes, this is true for inorganic matter and for mechanical forces. But it is only inferentially true for organized matter and for vital forces. We can not express life in terms of heat or of motion. And thus it happens that just when the exact transformation of energy will be most interesting to watch, we can not really tell whether any fresh energy has been introduced into the system or not. Let us consider this a little more closely."
"The production of motion, molar or molecular, is governed by physical laws, which it is the business of the philosopher to find out and correlate. The law of the conservation of energy overrides all laws, and it is a preeminent canon of scientific belief that for every act done a corresponding expenditure of energy must be transformed. No work can be effected without using up a corresponding value in energy of another kind. But to us the other side of the problem is even of more importance. Granted the existence of a certain kind of molecular motion, what is it that determines its direction along one path rather than another?"
"I see no good reason why any man of scientific mind should shut his eyes to our work or deliberately stand aloof from it. Our Proceedings are, of course, not exactly parallel to the Proceedings of a society dealing with a long-established branch of science. In every form of research there must be a beginning. We own to much that is tentative, much that may turn out erroneous. But it is thus, and thus only, that each science in turn takes its stand. I venture to assert that both in actual careful record of new and important facts, and in suggestiveness, our society's work and publications will form no unworthy preface to a profounder science both of man, of nature, and of "worlds not realized" than this planet has yet known."
"It may be objected that brain waves, like any other waves, must obey physical laws. Therefore, transmission of thought must be easier or more certain the nearer the agent and recipient are to each other, and should die out altogether before great distances are reached. Also it can be urged that if brain waves diffuse in all directions they should affect all sensitives within their radius of action, instead of impressing only one brain. The electric telegraph is not a parallel case, for there a material wire intervenes to conduct and guide the energy to its destination. These are weighty objections, but not, I think, insurmountable. Far be it from me to say anything disrespectful of the law of inverse squares, but I have already endeavored to show we are dealing with conditions removed from our material and limited conceptions of space, matter, form. Is it inconceivable that intense thought concentrated toward a sensitive with whom the thinker is in close sympathy may induce a telepathic chain of brain waves, along which the message of thought can go straight to its goal without loss of energy due to distance? And is it also inconceivable that our mundane ideas of space and distance may be superseded in these subtle regions of unsubstantial thought, where "near" and "far" may lose their usual meaning?"
"Let me specially apply this general conception of the impossibility of predicting what secrets the universe may still hold, what agencies undivined may habitually be at work around us. Telepathy, the transmission of thought and images directly from one mind to another without the agency of the recognized organs of sense, is a conception new and strange to science. To judge from the comparative slowness with which the accumulated evidence of our society penetrates the scientific world, it is, I think, a conception even scientifically repulsive to many minds. We have supplied striking experimental evidence; but few have been found to repeat our experiments, We have offered good evidence in the observation of spontaneous cases, — as apparitions at the moment of death and the like, — but this "evidence has failed to impress the scientific world in the same way as evidence less careful and less coherent has often done before. Our evidence is not confronted and refuted; it is shirked and evaded as though there were some great a priori improbability which absolved the world of science from considering it. I at least see no a priori improbability whatever. Our alleged facts might be true in all kinds of ways without contradicting any truth already known. I will dwell now on only one possible line of explanation, — not that I see any way of elucidating all the new phenomena I regard as genuine, but because it seems probable I may shed a light on some of those phenomena. All the phenomena of the universe are presumably in some way continuous; and certain facts, plucked as it were from the very heart of nature, are likely to be of use in our gradual discovery of facts which lie deeper still."
"Ordinarily we communicate intelligence to each other by speech. I first call up in my own brain a picture of a scene I wish to describe, and then, by means of an orderly transmission of wave vibrations set in motion by my vocal chords through the material atmosphere, a corresponding picture is implanted in the brain of anyone whose ear is capable of receiving such vibrations. If the scene I wish to impress on the brain of the recipient is of a complicated character, or if the picture of it in my own brain is not definite, the transmission will be more or less imperfect; but if I wish to get my audience to picture to themselves some very simple object, such as a triangle or a circle, the transmission of ideas will be well-nigh perfect, and equally clear to the brains of both transmitter and recipient. Here we use the vibrations of the material molecules of the atmosphere to transmit intelligence from one brain to another."
"If a possible — nay, reasonable — variation in only one of the forces conditioning the human race, that of gravitation, could so modify our outward form, appearance, and proportions as to make us to all intents and purposes a different race of beings; if mere differences of size can cause some of the most simple facts in chemistry and physics to take so widely different a guise; if beings microscopically small and prodigiously large would simply as such be subject to the hallucinations I have pointed out, and to others I might enlarge upon, is it not possible that we, in turn, though occupying, as it seems to us, the golden mean, may also by the mere virtue of our size and weight fall into misinterpretations of phenomena from which we should escape were we or the globe we inhabit either larger or smaller, heavier or lighter? May not our boasted knowledge be simply conditioned by accidental environments, and thus be liable to a large element of subjectivity hitherto unsuspected and scarcely possible to eliminate?"
"It is remarkable how much of the utilised information men possess has been derived from the observations of astronomers. The mechanism of the universe was known before Harvey discovered the circulation of the blood, or Watt constructed a steam engine. The astronomers seem to have been the pioneers of every branch of human knowledge. The Old and the New Testament open astronomically: "In the beginning God created the heaven and the earth" (Gen., i., I). "The wise men from the east came to Jerusalem, saying, where is He that is born King of Jews? for we have seen His star in the east" (Matt., ii., 2). It must be remembered that the science of astronomy in one important respect differs from all other sciences. Astronomers are observers only - they ascertain causes by watching effects. They cannot interfere with or alter the causes in operation."
"A view of the constitution of matter which recommended itself to Faraday as preferable to the one ordinarily held appears to me to be exactly the view I endeavor to picture as the constitution of spiritual beings. Centers of intellect, will, energy, and power, each mutually penetrable, while at the same time permeating what we call space, but each center retaining its own individuality, persistence of self, and memory. Whether these intelligent centers of the various spiritual forces which in their aggregate go to make up man's character or karma are also associated in any way with the forms of energy which, centered, form the material atom — whether these spiritual entities are material, not in the crude, gross sense of Lucretius, but material as sublimated through the piercing intellect of Faraday — is one of those mysteries which to us mortals will perhaps ever remain an unsolved problem. My next speculation is more difficult, and is addressed to those who not only take too terrestrial a view, but who deny the plausibility — nay, the possibility — of the existence of an unseen world at all. I reply we are demonstrably standing on the brink, at any rate, of one unseen world. I do not here speak of a spiritual or immaterial world. I speak of the world of the infinitely little, which must be still called a material world, although matter as therein existing or perceptible is something which our limited faculties do not enable us to conceive. It is the world — I do not say of molecular forces as opposed to molar, but of forces whose action lies mainly outside the limit of human perception, as opposed to forces evident to the gross perception of human organisms. I hardly know how to make clear to myself or to you the difference in the apparent laws of the universe which would follow upon a mere difference of bulk in the observer. Such an observer I must needs imagine as best I can."
"It can scarcely be denied that the fundamental phenomena which first led mankind into chemical inquiries are those of combustion. But, as we have just seen, minimized beings would be unable to produce fire at will, except by certain chemical reactions, and would have little opportunity of examining its nature. They might occasionally witness forest fires, volcanic eruptions, etc.; but such grand and catastrophic phenomena, though serving to reveal to our supposed Lilliputians the existence of combustion, would be ill suited for quiet investigation into its conditions and products. Moreover, considering the impossibility they would experience of pouring water from one test tube to another, the ordinary operations of analytical chemistry and of all manipulations depending on the use of the pneumatic trough would remain forever a sealed book."
"These rays, as generated in the vacuum tube, are not homogeneous, but consist of bundles of different wave-lengths, analogous to what would be differences of colour could we see them as light. Some pass easily through flesh, but are partially arrested by bone, while others pass with almost equal facility through bone and flesh. It seems to me that in these rays we may have a possible mode of transmitting intelligence which, with a few reasonable postulates, may supply a key to much that is obscure in psychical research. Let it be assumed that these rays, or rays even of higher frequency, can pass into the brain and act on some nervous center there. Let it be conceived that the brain contains a center which uses these rays as the vocal chords use sound vibrations (both being under the command of intelligence), and sends them out, with the velocity of light, to impinge on the receiving ganglion of another brain. In this way some, at least, of the phenomena of telepathy, and the transmission of intelligence from one sensitive to another through long distances, seem to come into the domain of law and can be grasped. A sensitive may be one who possesses the telepathic transmitting or receiving ganglion in an advanced state of development, or who, by constant practice, is rendered more sensitive to these high-frequency waves. Experience seems to show that the receiving and the transmitting ganglions are not equally developed; one may be active, while the other, like the pineal eye in man, may be only vestigial. By such an hypothesis no physical laws are violated; neither is it necessary to invoke what is commonly called the supernatural."
"Popular imagination presupposes spiritual beings to be utterly independent of gravitation, while retaining shapes and proportions which gravitation originally determined, and only gravitation seems likely to maintain. When and if spiritual beings make themselves visible either to our bodily eyes or to our inward vision, their object would be thwarted were they not to appear in a recognizable form; so that their appearance would take the shape of the body and clothing to which we have been accustomed. Materiality, form, and space, I am constrained to believe, are temporary conditions of our present existence. It is difficult to conceive the idea of a spiritual being having a body like ours, conditioned by the exact gravitating force exerted by the earth, and with organs which presuppose the need for food and necessity for the removal of waste products. It is equally difficult, hemmed in and bound round as we are by materialistic ideas, to think of intelligence, thought, and will existing without form or matter and untrammeled by gravitation or space."
"I am not disposed to bewail the limitations imposed by human ignorance. On the contrary, I feel ignorance is a healthful stimulant; and my enforced conviction that neither I nor anyone can possibly lay down beforehand what does not exist in the universe, or even what is not going on all round us everyday of our lives, leaves me with a cheerful hope that something very new and very arresting may turn up anywhere at any minute. … I shall try to utilize this temper of mind today by clearing away, so far as I can, certain presuppositions, on one side or on the other, which seem to me to depend upon a too hasty assumption that we know more about the universe than as yet we really can know."
"I will point out a curious, inveterate, and widespread illusion — the illusion that our earthly bodies are a kind of norm of humanity, so that ethereal bodies, if such there be, must correspond to them in shape and size. When we take a physical view of a human being in his highest form of development, he is seen to consist essentially of a thinking brain, the brain itself, among its manifold functions, being a transformer whereby intelligent will power is enabled to react on matter. To communicate with the external world, the brain requires organs by which it can be transported from place to place, and other organs by means of which energy is supplied to replace that expended in the exercise of its own special functions."
"The most helpful quality which has aided me in psychical problems and has made me lucky in physical discoveries (sometimes of rather unexpected kinds) has simply been my knowledge — my vital knowledge, if I may so term it — of my own ignorance. Most students of nature sooner or later pass through a process of writing off a large percentage of their supposed capital of knowledge as a merely illusory asset. As we trace more accurately certain familiar sequences of phenomena we begin to realize how closely these sequences, or laws, as we call them, are hemmed round by still other laws of which we can form no notion. With myself this writing off of illusory assets has gone rather far and the cobweb of supposed knowledge has been pinched (as some one has phrased) into a particularly small pill."
"Which was first, Matter or Force? If we think on this question, we shall find that we are unable to conceive of matter without force, or force without matter. When God created the elements of which the earth is composed, He created certain wondrous forces, which are set free and become evident when matter acts on matter."
"The task I am called upon to perform today is to my thinking by no means a merely formal or easy matter. It fills me with deep concern to give an address, with such authority as a president's chair confers, upon a science which, though still in a purely nascent stage, seems to me at least as important as any other science whatever. Psychical science, as we here try to pursue it, is the embryo of something which in time may dominate the whole world of thought. This possibility — nay, probability — does not make it the easier to me now. Embryonic development is apt to be both rapid and interesting; yet the Prudent man shrinks from dogmatizing on the egg until he has seen the chicken."
"The human creature represents the most perfect thinking and acting machine yet evolved on this earth, developing through countless ages in strict harmony with the surrounding conditions of temperature, atmosphere, light, and gravitation. The profound modifications in the human frame, which any important alteration in either of these factors would occasion, are strangely unconsidered. It is true there have been questionings as to the effects that might be occasioned by changes in temperature and atmospheric composition, but possible variations in gravitation seem almost to have escaped notice. The human body, which long experience and habit have taught us to consider in its highest development as the perfection of beauty and grace — "formed in the image of God " — is entirely conditioned by the strength of gravitation on this globe. So far as has been possible to ascertain, the intensity of gravity has not varied appreciably within those geologic ages covering the existence of animated thinking beings."
"I have raised a question which may be regarded as heretical. At the time when our modern conception of chemistry first dawned... the average chemist... accepted the elements as ultimate facts... absolutely simple, incapable of transmutation or decomposition, each a kind of barrier behind which we could not penetrate. ...[H]e said they were self-existent from all eternity ...But in our times... we cannot help asking what are the elements, whence do they come, what is their signification? ...These elements perplex us in our researches, baffle us in our speculations, and haunt us in our very dreams. They stretch like an unknown sea before us—mocking, mystifying and murmuring strange revelations and possibilities. If I venture to say that... elements are not simple and primordial... but have evolved from simpler matters—or... one sole kind of matter—I... give formal utterance to an idea... for some time "in the air" of science. Chemists, physicists, philosophers of the highest merit declare explicitly their belief that the seventy... elements of our text-books are not the which we must never hope to pass."
"It is curious that the popular conceptions of evil and malignant beings are of the type that would be produced by increased gravitation — toads, reptiles, and noisome creeping things — while the arch fiend himself is represented as perhaps the ultimate form which could be assumed by a thinking brain and its necessary machinery were the power of gravitation to be increased to the highest point compatible with existence — a serpent crawling along the ground. On the other hand, our highest types of beauty are those which would be common under decreased gravitation. The "daughter of the gods, divinely tall," and the leaping athlete, please us by the slight triumph over the earthward pull which their stature or spring implies."