James Clerk Maxwell Quotes

Thoroughly conscious ignorance is the prelude to every real advance in science.

That feeling in your heart: it’s called mono no aware. It is a sense of the transience of all things in life. The sun, the dandelion, the cicada, the Hammer, and all of us: we are all subject to the equations of James Clerk Maxwell, and we are all ephemeral patterns destined to eventually fade, whether in a second or an eon.

It is of great advantage to the student of any subject to read the original memoirs on that subject, for science is always most completely assimilated when it is in the nascent state...

One scientific epoch ended and another began with James Clerk Maxwell.

This change in the conception of reality is the most profound and the most fruitful that physics has experienced since the time of Newton. {Referring to James Clerk Maxwell's contributions to physics}

statistical laws are not necessarily used as a result of our ignorance. statistical laws can reflect how things really are. there are matters that can only be treated statistically.

Almighty God, Who hast created man in Thine own image, and made him a living soul that he might seek after Thee, and have dominion over Thy creatures, teach us to study the works of Thy hands, that we may subdue the earth to our use, and strengthen the reason for Thy service;

Very few of us can now place ourselves in the mental condition in which even such philosophers as the great Descartes were involved in the days before Newton had announced the true laws of the motion of bodies.

By the time I began my study of physics in the early 1970s, the idea of unifying gravity with the other forces was as dead as the idea of continuous matter. It was a lesson in the foolishness of once great thinkers. Ernst Mach didn’t believe in atoms, James Clerk Maxwell believed in the aether, and Albert Einstein searched for a unified-field theory. Life is tough.

It is a good thing to have two ways of looking at a subject, and to admit that there are two ways of looking at it.

Francis Galton, whose mission it seems to be to ride other men's hobbies to death, has invented the felicitous expression 'structureless germs'.

By the study of Boltzmann I have been unable to understand him. He could not understand me on account of my shortness, and his length was and is an equal stumbling block to me.

DOES THE PROGRESS OF PHYSICAL SCIENCE TEND TO GIVE ANY ADVANTAGE TO THE OPINION OF NECESSITY (OR DETERMINISM) OVER THAT OF THE CONTINGENCY OF EVENTS AND THE FREEDOM OF THE WILL? NO. - ESSAY FOR THE ERANUS CLUB ON SCIENCE AND FREE WILL

The vast interplanetary and interstellar regions will no longer be regarded as waste places in the universe, which the Creator has not seen fit to fill with the symbols of the manifold order of His kingdom. We shall find them to be already full of this wonderful medium; so full, that no human power can remove it from the smallest portion of space, or produce the slightest flaw in its infinite continuity.

A molecule of hydrogen....whether in Sirius or in Arcturus, executes its vibrations in precisely the same time. Each molecule therefore throughout the universe bears impressed upon it the stamp of a metric system as distinctly as does the metre of the Archives at Paris, or the double royal cubit of the temple of Karnac. No theory of evolution can be formed to account for the similarity of molecules, for evolution necessarily implies continuous change, and the molecule is incapable of growth or decay, of generation or destruction.... We are therefore unable to ascribe either the existence of the molecules or the identity of their properties to any of the causes which we call natural.

Willard Gibbs did for statistical mechanics and for thermodynamics what Laplace did for celestial mechanics and Maxwell did for electrodynamics, namely, made his field a well-nigh finished theoretical structure.

That small word “Force,” they make a barber's block, Ready to put on Meanings most strange and various, fit to shock Pupils of Newton.... The phrases of last century in this Linger to play tricks— Vis viva and Vis Mortua and Vis Acceleratrix:— Those long-nebbed words that to our text books still Cling by their titles, And from them creep, as entozoa will, Into our vitals. But see! Tait writes in lucid symbols clear One small equation; And Force becomes of Energy a mere Space-variation.

Happy is the man who can recognize in the work of to-day a connected portion of the work of life and an embodiment of the work of Eternity. The foundations of his confidence are unchangeable, for he has been made a partaker of Infinity. He strenuously works out his daily enterprises because the present is given him for a possession. Thus ought man to be an impersonation of the divine process of nature, and to show forth the union of the infinite with the finite, not slighting his temporal existence, remembering that in it only is individual action possible, nor yet shutting out from his view that which is eternal, knowing that Time is a mystery which man cannot endure to contemplate until eternal Truth enlighten it.

I think a strong claim can be made that the process of scientific discovery may be regarded as a form of art. This is best seen in the theoretical aspects of Physical Science. The mathematical theorist builds up on certain assumptions and according to well understood logical rules, step by step, a stately edifice, while his imaginative power brings out clearly the hidden relations between its parts. A well constructed theory is in some respects undoubtedly an artistic production. A fine example is the famous Kinetic Theory of Maxwell. ... The theory of relativity by Einstein, quite apart from any question of its validity, cannot but be regarded as a magnificent work of art.

One of the things Maxwell learned from his reading was the fallibility of men's efforts to understand the world. All of the great scientists had made mistakes. He was acutely aware of his own tendency to make errors in calculation.

Accordingly, we find Euler and D'Alembert devoting their talent and their patience to the establishment of the laws of rotation of the solid bodies. Lagrange has incorporated his own analysis of the problem with his general treatment of mechanics, and since his time M. Poinsot has brought the subject under the power of a more searching analysis than that of the calculus, in which ideas take the place of symbols, and intelligent propositions supersede equations.

Michael Faraday and James Clerk Maxwell's explanation of electricity and magnetism paved the way for the illumination of our cities and gave us powerful electric motors and generators as well as instantaneous communication via TV and radio.

So many of the properties of matter, especially when in the gaseous form, can be deduced from the hypothesis that their minute parts are in rapid motion, the velocity increasing with the temperature, that the precise nature of this motion becomes a subject of rational curiosity. Daniel Bernoulli, John Herapath, Joule, Krönig, Clausius, &c., have shewn that the relations between pressure, temperature and density in a perfect gas can be explained by supposing the particles move with uniform velocity in straight lines, striking against the sides of the containing vessel and thus producing pressure. (1860)

Most creative scientists, even the most prolific and versatile, produce one theory per subject. When that theory has run its course they move on to another topic, or stop inventing. Maxwell was unique in the way he could return to a topic and imbue it with new life by taking an entirely fresh approach.

Qu'une goutee de vin tombe dans un verre d'eau; quelle que soit la loi du movement interne du liquide, nous verrons bientôt se colorer d'une teinte rose uniforme et à partir de ce moment on aura beau agiter le vase, le vin et l'eau ne partaîtront plus pouvoir se séparer. Tout cela, Maxwell et Boltzmann l'ont expliqué, mais celui qui l'a vu plus nettement, dans un livre trop peu lu parce qu'il est difficile à lire, c'est Gibbs dans ses principes de la Mécanique Statistique. Let a drop of wine fall into a glass of water; whatever be the law that governs the internal movement of the liquid, we will soon see it tint itself uniformly pink and from that moment on, however we may agitate the vessel, it appears that the wine and water can separate no more. All this, Maxwell and Boltzmann have explained, but the one who saw it in the cleanest way, in a book that is too little read because it is difficult to read, is Gibbs, in his Principles of Statistical Mechanics.

...only one man lived who could understand Gibbs's papers. That was Maxwell, and now he is dead.

But it is evident that all analogies of this kind depend on principles of a more fundamental nature; and that, if we had a true mathematical classification of quantities, we should be able at once to detect the analogy between any system of quantities presented to us and other systems of quantities in known sciences, so that we should lose no time in availing ourselves of the mathematical labors of those who had already solved problems essentially the same. [...] At the same time, I think that the progress of science, both in the way of discovery, and in the way of diffusion, would be greatly aided if more attention were paid in a direct way to the classification of quantities. - Remarks on the mathematical classification of physical quantities Proceedings of the London Mathematical Society, 1871

Some people gain their understanding of the world by symbols and mathematics. Others gain their understanding by pure geometry and space. There are some others that find an acceleration in the muscular effort that is brought to them in understanding, in feeling the force of objects moving through the world. What they want are words of power that stir their souls like the memory of childhood. For the sake of persons of these different types, whether they want the paleness and tenuity of mathematical symbolism, or they want the robust aspects of this muscular engagement, we should present all of these ways. It’s the combination of them that give us our best access to truth

The bushy-bearded Scottish physicist James Clerk Maxwell (1831–1879) subsequently devised wonderful equations that specified, among other things, how changing electric fields create magnetic fields and how changing magnetic fields create electrical ones. A changing electric field could, in fact, produce a changing magnetic field that could, in turn, produce a changing electric field, and so on. The result of this coupling was an electromagnetic wave.

this determinism says that in every case the result is determined by the previous condition of the subject we are looking at. Our free will at the best is like that of Lucretius's atoms — which at quite uncertain times and places deviate in an uncertain manner from their course. the atoms can swerve so there’s always the small possibility even for air molecules of not being forced to follow the determined laws. - ESSAY FOR THE ERANUS CLUB ON SCIENCE AND FREE WILL

David Hume, the great eighteenth century Scottish philosopher, had put the cat among the pigeons with his notion of scepticism: that nothing can be proved, except in mathematics, and that much of what we take to be fact is merely conjecture.

The velocity of light is one of the most important of the fundamental constants of Nature. Its measurement by Foucault and Fizeau gave as the result a speed greater in air than in water, thus deciding in favor of the undulatory and against the corpuscular theory. Again, the comparison of the electrostatic and the electromagnetic units gives as an experimental result a value remarkably close to the velocity of light–a result which justified Maxwell in concluding that light is the propagation of an electromagnetic disturbance. Finally, the principle of relativity gives the velocity of light a still greater importance, since one of its fundamental postulates is the constancy of this velocity under all possible conditions.

Each time scientists have unraveled a new force, it has changed the course of civilization and altered the destiny of humanity. For example, Newton’s discovery of the laws of motion and gravity laid the groundwork for the machine age and the Industrial Revolution. Michael Faraday and James Clerk Maxwell’s explanation of electricity and magnetism paved the way for the illumination of our cities and gave us powerful electric motors and generators as well as instantaneous communication via TV and radio. Einstein’s E = mc2 explained the power of the stars and helped to unravel the nuclear force. When Erwin Schrödinger, Werner Heisenberg, and others unlocked the secrets of the quantum theory, they gave us the high-tech revolution of today, with supercomputers, lasers, the internet, and all the fabulous gadgets in our living rooms. Ultimately, all the wonders of modern technology owe their origin to the scientists who gradually discovered the fundamental forces of the world.

Therein lies the key, I think, to Einstein’s brilliance and the lessons of his life. As a young student he never did well with rote learning. And later, as a theorist, his success came not from the brute strength of his mental processing power but from his imagination and creativity. He could construct complex equations, but more important, he knew that math is the language nature uses to describe her wonders. So he could visualize how equations were reflected in realities—how the electromagnetic field equations discovered by James Clerk Maxwell, for example, would manifest themselves to a boy riding alongside a light beam. As he once declared, “Imagination is more important than knowledge.”6

In despair, I offer your readers their choice of the following definitions of entropy. My authorities are such books and journals as I have by me at the moment. (a) Entropy is that portion of the intrinsic energy of a system which cannot be converted into work by even a perfect heat engine.—Clausius. (b) Entropy is that portion of the intrinsic energy which can be converted into work by a perfect engine.—Maxwell, following Tait. (c) Entropy is that portion of the intrinsic energy which is not converted into work by our imperfect engines.—Swinburne. (d) Entropy (in a volume of gas) is that which remains constant when heat neither enters nor leaves the gas.—W. Robinson. (e) Entropy may be called the ‘thermal weight’, temperature being called the ‘thermal height.’—Ibid. (f) Entropy is one of the factors of heat, temperature being the other.—Engineering. I set up these bald statement as so many Aunt Sallys, for any one to shy at. [Lamenting a list of confused interpretations of the meaning of entropy, being hotly debated in journals at the time.]

Natural causes, as we know, are at work, which tend to modify, if they do not at length destroy, all the dimensions of the earth and the whole solar system. But though in the course of ages catastrophes have occurred and may yet occur in the heavens, though ancient systems may be dissolved and new systems evolved out of their ruins, the molecules out of which these systems are built-the foundation stones of the material universe-remain unbroken and unworn. They continue this day as they were created-perfect in number and measure and weight, and form the innefaceable characters impressed on them we may learn that those aspirations after accuracy in measurement, truth in statement, and justice in action, which we reckon among our noblest attributes as men, are ours because they are essential constituents of the image of Him who in the beginning created, not only the heaven and the earth, but the materials which heaven and earth consist.

He that would enjoy life and act with freedom must have the work of the day continually before his eyes. Not yesterday's work, lest he fall into despair, nor to-morrow's, lest he become a visionary,--nor that which ends with the day, which is a worldly work, nor yet that only which remains to eternity, for by it he cannot shape his actions. Happy is the man who can recognize in the work of To-day a connected portion of the work of life, and an embodiment of the work of Eternity. The foundations of his confidence are unchangeable, for he has been made a partaker of Infinity. He strenuously works out his daily enterprises, because the present is given him for a possession. Thus ought Man to be an impersonation of the divine process of nature, and to show forth the union of the infinite with the finite, not slighting his temporal existence, remembering that in it only is individual action possible, nor yet shutting out from his view that which is eternal, knowing that Time is a mystery which man cannot endure to contemplate until eternal Truth enlighten it.

James Clerk Maxwell helped to enshrine this wave theory when he successfully conjectured a connection between light, electricity, and magnetism. He came up with equations that described the behavior of electric and magnetic fields, and when they were combined they predicted electromagnetic waves. Maxwell found that these electromagnetic waves had to travel at a certain speed: approximately 186,000 miles per second.* That was the speed that scientists had already measured for light, and it was obviously not a mere coincidence.4 It became clear that light was the visible manifestation of a whole spectrum of electromagnetic waves. This includes what we now call AM radio signals (with a wavelength of 300 yards), FM radio signals (3 yards), and microwaves (3 inches). As the wavelengths get shorter (and the frequency of the wave cycles thus increases), they produce the spectrum of visible light, ranging from red (25 millionths of an inch) to violet (14 millionths of an inch). Even shorter wavelengths produce ultraviolet rays, X-rays, and gamma rays. When we speak of “light” and the “speed of light,” we mean all electromagnetic waves, not just the ones that are visible to our eyes.

He wrote up the mathematics and everything fitted together. James had shown how the electrical and magnetic forces which we experience could have their seat not in physical objects like magnets and wires but in energy stored in the space between and around the bodies. Electrostatic energy was potential energy, like that of a spring; magnetic energy was rotational, like that in a flywheel, and both could exist in empty space. And these two forms of energy were immutably linked: a change in one was always accompanied by a change in the other. The model demonstrated how they acted together to produce all known electromagnetic phenomena.

Maxwell's greatest work shows two unique characteristics which stem from his philosophical insight. The first is the way he could return to a subject, often after a gap of several years and take it to new heights using an entirely fresh approach. He did this twice with electromagnetism. The second is even more remarkable. His electromagnetic theory embodied the notion that things we can measure directly, like mechanical force, are mery the outward manifestations of deeper processes, involving entities like electric field strength, which are beyond our powers of visualization. This presages the view that twentieth century scientists came to. As Banesh Hoffmann puts it in The Strange Story of the Quantum: "There is simply no way at all of picturing the fundamental atomic processes of nature in terms of space, time and causality.

The reason [James Clerk] Maxwell's Demon cannot exist is that it does take resources to perform an act of discrimination. We imagine computation is free, but it never is. The very act of choosing which particle is cold or hot itself becomes an energy drain and a source of waste heat. The principle is also known as "no free lunch." We do our best to implement Maxwell's Demon whenever we manipulate reality with our technologies, but we can never do so perfectly; we certainly can't get ahead of the game, which is known as entropy. All the air conditioners in a city emit heat that makes the city hotter overall. While you can implement what seems to be a Maxwell's Demon if you don't look too far or too closely, in the big picture you always lose more than you gain. Every bit in a computer is a wannabe Maxwell's Demon, separating the state of "one" from the state of "zero" for a while, at a cost. A computer on a network can also act like a wannabe demon if it tries to sort data from networked people into one or the other side of some imaginary door, while pretending there is no cost or risk involved.

To prove to an indignant questioner on the spur of the moment that the work I do was useful seemed a thankless task and I gave it up. I turned to him with a smile and finished, 'To tell you the truth we don't do it because it is useful but because it's amusing.' The answer was thought of and given in a moment: it came from deep down in my mind, and the results were as admirable from my point of view as unexpected. My audience was clearly on my side. Prolonged and hearty applause greeted my confession. My questioner retired shaking his head over my wickedness and the newspapers next day, with obvious approval, came out with headlines 'Scientist Does It Because It's Amusing!' And if that is not the best reason why a scientist should do his work, I want to know what is. Would it be any good to ask a mother what practical use her baby is? That, as I say, was the first evening I ever spent in the United States and from that moment I felt at home. I realised that all talk about science purely for its practical and wealth-producing results is as idle in this country as in England. Practical results will follow right enough. No real knowledge is sterile. The most useless investigation may prove to have the most startling practical importance: Wireless telegraphy might not yet have come if Clerk Maxwell had been drawn away from his obviously 'useless' equations to do something of more practical importance. Large branches of chemistry would have remained obscure had Willard Gibbs not spent his time at mathematical calculations which only about two men of his generation could understand. With this trust in the ultimate usefulness of all real knowledge a man may proceed to devote himself to a study of first causes without apology, and without hope of immediate return.

Everything passes, Hiroto,” Dad said. “That feeling in your heart: It’s called mono no aware. It is a sense of the transience of all things in life. The sun, the dandelion, the cicada, the Hammer, and all of us: We are all subject to the equations of James Clerk Maxwell and we are all ephemeral patterns destined to eventually fade, whether in a second or an eon.

In 1862, the Scottish mathematician James Clerk Maxwell developed a set of fundamental equations that unified electricity and magnetism. On his deathbed, he coughed up a strange sort of confession, declaring that “something within him” discovered the famous equations, not he. He admitted he had no idea how ideas actually came to him—they simply came to him. William Blake related a similar experience, reporting of his long narrative poem Milton: “I have written this poem from immediate dictation twelve or sometimes twenty lines at a time without premeditation and even against my will.” Johann Wolfgang von Goethe claimed to have written his novella The Sorrows of Young Werther with practically no conscious input, as though he were holding a pen that moved on its own.

little of the work of Faraday and others on electricity and magnetism had yet fed through to practical application. In short, science was a splendid hobby for a gentleman but a poor profession.

Maxwell was not only one of the most brilliant and influential scientists who ever lived but an altogether fine and engaging man. And

First, electric charges attract or repel one another with a force inversely proportional to the square of the distance between them: unlike charges attract, like ones repel. Second, magnetic poles attract or repel one another in a similar way but always come in pairs: every north pole is yoked to a south pole7. Third,

His faith was the guiding principle of his life but it was an intensely reflective personal faith which could not be contained within the rules of a sect. Institutional politics, whether of the church, the state or the university, was a topic that never engaged his interest.

Demolishes your demons, even if they are as fearsome as that of James Clerk Maxwell, remember that just as Josiah Willard Gibbs turned to his angel, you too will not be in science alone".

I know the tendency of the human mind is to do anything rather than think. But mental labour is not thought, and those who have with labour acquired the habit of application, often find it much easier to get up a formula than to master a principle.

... I think that the results which each man arrives at in his attempts to harmonise his science with his Christianity ought not to be regarded as having any significance except to the man himself, and to him only for a time, and should not receive the stamp of a society. For it is in the nature of science, especially those branches of science which are spreading into unknown regions, to be continually changing e.

Goodness knows what Maxwell would make of our current relish for watching people indulging in histrionic self-exposure on television. He would certainly have a wry smile at the irony of the fact that his own electromagnetic theory provides the means of bringing such unwholesome displays into our homes.

His electromagnetic theory embodied the notion that things we can measure directly, like mechanical force, are merely the outward manifestations of deeper processes, involving entities like electric field strength, which are beyond our powers of visualisation. This

Mathematical theories have sometimes been used to predict phenomena that were not confirmed until years later. For example, Maxwell's equations, named after physicist James Clerk Maxwell, predicted radio waves. Einstein's field equations suggested that gravity would bend light and that the universe is expanding. Physicist Paul Dirac once noted that the abstract mathematics we study now gives us a glimpse of physics in the future. In fact, his equations predicted the existence of antimatter, which was subsequently discovered. Similarly, mathematician Nikolai Lobachevsky said that "there is no branch of mathematics, however abstract, which may not someday be applied to the phenomena of the real world.

Several major and significant discoveries in science occurred in the 19th and 20th century through the works of scientists who believed in God. Even in just the last 500 years of modern scientific enterprise, a great many scientists were religious including names like Isaac Newton, Nicholas Copernicus, Johannes Kepler, Robert Boyle, William Thomson Kelvin, Michael Faraday, James Clerk Maxwell, Louis Pasteur and Nobel Laureate scientists like: 1.Max Planck 2.Guglielmo Marconi 3.Robert A. Milikan 4.Erwin Schrodinger 5.Arthur Compton 6.Isidor Isaac Rabi 7.Max Born 8.Dererk Barton 9.Nevill F. Mott 10.Charles H. Townes 11.Christian B. Anfinsen 12.John Eccles 13.Ernst B. Chain 14.Antony Hewish 15.Daniel Nathans 16.Abdus Salam 17.Joseph Murray 18.Joseph H. Taylor 19.William D. Phillips 20.Walter Kohn 21.Ahmed Zewail 22.Aziz Sancar 23.Gerhard Etrl Thus, it is important for the torchbearers of science to know their scope and highlight what they can offer to society in terms of curing diseases, improving food production and easing transport and communication systems, for instance. To mock faith and faithful, the scientists who do not believe in God do not just hurt the faithful people who are non-scientists, but a great many of their own colleagues who are scientists, but not atheists.

I was at first almost frightened when I saw such mathematical force made to bear upon the subject, and then wondered to see that the subject stood it so well. [Letter to James Clerk Maxwell, 25 March 1857, commenting on Maxwell's paper titled "On Faraday's Lines of Force"]

Happy is the man who can recognise in the work of Today a connected portion of the work of life, and an embodiment of the work of Eternity ...

James was generous with his time to any friend who needed it—as well as to some, like Lawson, who did not! When one friend had eye trouble and could not read, James spent an hour each evening reading out his bookwork for the next day. He bucked up fellow students when they were depressed and on several occasions nursed others who were sick. He helped freshmen who were having trouble with their studies. He also found time to keep up a lively correspondence with his father, Aunt Jane, Lewis Campbell and others.

By 1860, a great deal was known about electricity and magnetism. Magnets could be used to make electric currents flow, and flowing electric currents could deflect compass needles in the same way that magnets could. There was clearly a link between these two phenomena, but nobody had come up with a unified description. The breakthrough was made by the Scottish physicist James Clerk Maxwell, who, in a series of papers in 1861 and 1862, developed a single theory of electricity and magnetism that was able to explain all of the experimental work of Faraday, Ampère and others. But Maxwell’s crowning glory came in 1864, when he published a paper that is undoubtedly one of the greatest achievements in the history of science. Albert

James Clerk Maxwell and his theory of electromagnetism. Born in 1831 in Edinburgh, Maxwell, the son of a Scottish landowner, was destined to become the greatest theoretical physicist of the nineteenth century. At the age of fifteen, he wrote his first published paper on a geometrical method for tracing ovals.

These transient facts, These fugitive impressions. Must be transformed by mental acts, To permanent possessions. Then summon up your grasp of mind, Your fancy scientific, Till sights and sounds with thought combined Become of truth prolific

The remarkable Scottish physicist James Clerk Maxwell worked out in the early 1860s that light was an interaction between electricity and magnetism. And this meant that in principle, you could have an electric wave creating a magnetic wave, creating an electric wave and so on, hauling itself through empty space by its own bootstraps without any material medium required – it is the electromagnetic field that acts as the material.

He that would enjoy life and act with freedom must have the work of the day continually before his eyes. Not yesterday's work, lest he fall into despair, not to-morrow's, lest he become a visionary not that which ends with the day, which is a worldly work, nor yet that only which remains to eternity, for by it he cannot shape his action. Happy is the man who can recognize in the work of to-day a connected portion of the work of life, and an embodiment of the work of eternity. The foundations of his confidence are unchangeable, for he has been made a partaker of Infinity. He strenuously works out his daily enterprises, because the present is given him for a possession.

we are obliged to admit that the undulations are those of an ethereal substance, and not of the gross matter,

24 JAMES CLERK MAXWELL 1831-1879

James Clerk Maxwell had proven mathematically that light was electromagnetic radiation—electricity that was vibrating at an extremely high frequency.

Leo Szilard, in 1929, showed that the very act of acquiring information about a system increases its entropy in proportion to the amount of information gathered. As the entropy increases, less of the system's total heat energy is available for doing work. To gather enough information to work the shutter effectively we would have to use up, or render inaccessible, an amount of energy at least equal to the work output of any machine that we could drive from the system. So we will never be clever enough to create perpetual motion. Through the work of Szilard and others, Maxwell's demon helped to spark the creation of information theory, now an essential part of the theoretical basis of communications and computing.

The E and H waves always travel together: neither can exist alone. They vibrate at right angles to each other and are always in phase.

His system of equations worked with jewelled precision. Its construction had been an immense feat of sustained creative effort in three stages spread over 9 years. The whole route was paved with inspired innovations but from a historical perspective one crucial step stands out-the idea that electric currents exist in empty space. It is these displacement currents that give the equations their symmetry and make the waves possible. Without them the term @E/@t in equation (4) becomes zero and the whole edifice crumbles.

In the Treatise James made an important new prediction from his electromagnetic theory-that electromagnetic waves exert a radiation pressure. Bright sunlight, he calculated, presses on the earth's surface with a force of around 4 pounds per square mile, equivalen to 7 grams per hectare. This was too tiny a value to be observable in everyday life and its detection posed a challenge to experimenters. Eventually, in 1900, the Russian physicist Pyotr Lebedev succeeded, and confirmed James' prediction. Although small on an earthly scale, radiation pressure is one of the factors that shape the universe. Without it there would be no stars like our sun-it is internal radiation pressure that stops them from collapsing under their own gravity. James' discovery also helped to explain a phebomenon that had puzzled astronomers for centuries-why comets' tails point away from the sun.

He had made a discovery of the first magnitude. It opened up an entirely new approach to physics, which led to statistical mechanics, to a proper understanding of thermodynamics and to the use of probability distributions in quantum mechanics. If he had done nothing else, this breakthrough would have been enough to put him among the world's great scientists.

The new law that he predicted seemed to defy common sense. It was that the viscosity of a gas-the internal frictional that causes drag on a body moved through it-is independent of its pressure. One might expect a more compressed gas to exert a greater drag; even James was surprised at first that the theory said otherwise. But further thought showed that, at higher pressure, the effect on a moving body of being surrounded by more molecules is exactly counteracted by the screening effect they provide: each molecule travels, on average, a shorter distance before it collides with another one. A few years later, James and Katherine themselves did the experiment which showed the prediction to be correct.

In fact, confusion over units was not confined to electricity and magnetism. When two people spoke of a quantity like 'force' or 'power' you could not be sure that they meant the same thing. James saw a prime opportunity to straighten out the muddle. He went beyond his brief for the paper and proposed a systematic way of defining all physical quantities in terms of mass, length and time, symbolised by the letters M, L and T. For example, velocity was defined L/T, acceleration L/T^2, and force ML/T^2, since, by Newton's second law, force=mass x acceleration. His method is used in exactly this form today. Called dimensional analysis, it seems to us so simple and so natural a part of all physical science that almost nobody wonders who first thought of it.

Most creative scientists, even the most prolific and versatile, produce one theory per subject. When that theory has run its course they move on to another topic, or stop inventing. Maxwell was unique in the way he could could return to a topic and imbue it with new life by taking an entirely fresh approach. To the end of his life there was not one subject in which his well of inventiveness showed signs of exhaustion. With each new insight he would strengthen the foundations of the subject and trim away any expendable superstructure. In his first paper on elctromagnetism he had used the analogy of fluid flow to describe static electric and magnetic effects. In the second he had invented a mechanical model of rotating cells and idle wheels to explain all known electromagnetic effects and to predict two new ones, displacement current and waves. Evem the most enlightened of his contemporaries thought that the next step should be to refine the model, to try to find the true mechanism. But perhaps he was already sensing that the ultimate mechanisms of nature may be beyond our powers of comprehension. He decided to put the model on one side and build the theory afresh, using only the principles of dynamics: the mathematical laws which govern matter and motion.

It sometimes happens that mathematical methods conceived in the abstract turn out later to be so well suited to a particular application that they might have been written especially for it. When he was wrestling with the problems of general relativity, Albert Einstein came across the tensor calculus, invented 50 years earlier by Curbastro Gregorio Ricci and Tullio Levi-Civita, and saw that it was exactly what he needed. James enlisted a method that had been created in the mid-eighteenth century by Joseph-Louis Lagrange.

Ultimately, no amount of opposition could stifle Tesla’s creative powers. Enthused by his discoveries with X-rays, he devoted his energies to the realm of high-frequency electricity. Two decades earlier, James Clerk Maxwell had proven mathematically that light was electromagnetic radiation—electricity that was vibrating at an extremely high frequency. In 1888, Heinrich Hertz had confirmed that an electric spark emits electromagnetic waves. Tesla knew that this unexplored territory would yield astounding

The true logic of this world is to be found in the theory of probability.