James Clerk Maxwell (1831-1879)

Transcript (PDF)

The 19th Century
Presentation 12 of 13

James Clerk Maxwell (1831-1879)
A Treatise on Electricity and Magnetism (3rd Ed. 1981, Oxford).
The Preparation of Einstein.
Presented by Roger Weir
Tuesday, February 21, 1984

Transcript:

From one voice and one mind. Some overview of history but not history in a textbook sense of moving from event-to-event, or complication-to-complication, but history from a standpoint of moving from person-to-person. If you look back over the series, they are always focused on a person. Our only guarantee of veracity is to be able to put ourselves in the other person’s shoes. The old American Indian prayer speaks eloquently of this: “Let me not criticize my fellow man until I have walked a mile in his moccasins.” We can empathize. We have the ability, believe it or not, to project ourselves in sympathy to another person completely. It is a phenomenon known as love. And there are many ways in which love manifests itself. And the great mystery of love is the truth that we may displace our own selves with the care and love of another. And this exchange of cells is the mystery of love and the dynamic of the universe. The willingness to do this is our only guarantee of survival. Our agreeing to these conditions of life and having understood that this is the only real dynamic there is, is the only guarantee we have that we may continue.

So I have tried to place an overview of history in terms of people, moving person-to-person and grouping the persons according to what used to be called epochs or ages or periods of history. Actually the patterns that I’ve been cutting out are the result of many years of study, not just on myself, or just my teachers – even though they were some of the best in the world – but of many prize individuals over a long time. There are histories of history now. We have meta histories. We have ideas about philosophies of history that go far beyond what anyone might have ever understood or known before. And so the way in which I have cut out these patterns, cut out these groupings, is not in terms of aggregation so much as in terms of what in higher mathematics would be called matrixes. And I have arranged the individuals within the matrixes so as to present a dynamic. The dynamic line of development being in all cases the– what would be taken as the meaning in a vector analysis of the dynamic of that matrix leading to the next set of conditions.

We’re going to talk a little bit about vector analysis today and about its origins in the 19th century. But in tracing over the last four years this kind of matrix history moving person-to-person I have sought to engender again a vector line of meaning which we would call development from a static standpoint but which yields a purposefulness when finally understood in terms of its direction, its intensity, its culmination. We at every moment of this present inherit the responsibility of that meaningfulness of that purposefulness. And frankly from the standpoint of someone who understands a great deal of this, nothing is being done currently in our time to accept this burden. The only reason that we could not continue is that this condition of non-acceptance would become apparent to the universe. If it does we will not last. Not because of something in ourselves, not because of a flaw or a compulsion in ourselves, but because of a failure to meet the basic essential conditions of intelligent purposeful life.

The world is not dead. The universe is quite alive and we are constantly on stage in terms of the meaningfulness. Meaning is the movement of truth. Just as Plato said that time is the moving image of eternity. Meaning is the moving understanding of truth. The universe manifests truth as a basic condition of integrity. Only by keeping the meaningfulness intact do we continue. Without that there will indeed be nothing for us. So there is a rather somber undertone. There is a contrapuntal percussion, perhaps not always visible, but I draw it out because with the lecture today and the lecture next week we will have come within view of our own time.

I have brought the lecture series, the progression of matrixes, up to the 20th century, where we find ourselves, marooned as it were (post-historical man we were once called in the 40s when the condition was first beginning to be noticed), but I have left out several major connections which I am filling in and will fill in the rest of the year.

One major connection is the transition at the so-called Elizabethan period, the transition from Cortez to Leibniz focusing on the fulcrum of Cervantes and Shakespeare. I’m currently doing that at the Philosophical Research Society. The next transition is what was called the Age of Revolution which will take the turn of the 1700s to the 1800s, the period of the French Revolution, the period of Napoleon, of Beethoven, of Shelley, Goethe. And that will be taken at the Philosophical Research Society, April, May, and June of this year. The third transition is the one to our own time. That is from the 19th century to the 20th century. And that requires a matrix all of its own because the individuals in that matrix lead on a vector of revelation which was only apparent in our own time in that matrix in that group in that lecture series – which will be July, August, and September of this year – I will take persons like Madame Blavatsky, persons like Nietzsche, Schopenhauer, Strindberg, Ibsen, the individuals like Rilke who led to the 20th century, Cézanne. We’ll, we’ll take the major figures – Einstein – we will come into the 20th century late this year in the summer. But to complement this forward movement, because there’s always wisdom, as we will see Clark Maxwell was quite aware of the fact, whenever anyone moves powerfully in one direction you must also move comprehensively in the other direction.

We may not step forward with impunity in terms of wholeness without having also a sense of moving backwards. This is not simply a choreography applicable to Tai Chi movements. It’s simply an understanding of wisdom and experience in these dynamics. So as I move forward in that I’m going to also on the Tuesday night series move back in time move back in large notions of duration and will present the Dark Age series for six months and then we’ll move further back in time and present the Alexandrian Matrix – the first thousand years of Alexandria – take in one of the most fruitful eras in human history probably more fruitful even than our own so far because the mind and spirit which we have today were formed both East and West in that time period from 350 BC to roughly about 500 AD. That will be also a six month course.

At the end of that series I will bring the Thursday and Tuesday nights together. In that I will focus the dynamic of the whole five years of effort on understanding the American tradition and I will take again the person to person history but develop it in large. I will take a whole quarter on Benjamin Franklin. A whole quarter on Thomas Jefferson. A whole quarter on Emerson. A whole quarter on William James. A whole quarter on John Dewey. And a whole quarter on William Faulkner. And try and bring the American tradition through, not as some other addition to the European aggregate but as a cross section of the world of all time and all peoples moving progressively closer and closer to a disclosure of its universal nature.

The problem we have in this country which the Soviets do not understand is that we are not a European country. We are not a Christian country. We are in fact a very strange interpenetration of all traditions and all countries and therefore the Soviets do not see us at all. We are invisible to them, just as they are misunderstood by us. And the tragedy of our time is that power politics and a global scale is played for the wrong reasons, with players who do not understand what moves the other person will make and what moves they will make in response. This condition of course is a rather dangerous one similar to someone gambling without knowing the rules of the game. All of this hopefully will be of some use and of some value.

And as the conditions become more rounded, that is, as the tape series in the lecture series come to some sense of closure along the end of 1986 I will try to transpose what I can to print from it. I don’t know how long that will take but at some effort that needs to be done. I didn’t start this until I was more than forty years of age, and I kept hoping someone else would do it. No one else has done it, so I have shouldered the load simply by default out of default. Which brings us to the 19th century.

The 19th century as we have seen is a case in point. It is totally misunderstood both East and West, that the major figures of the 19th century are quite different from what they are supposed to be. They are in fact illustrative of a dynamic line of meaning which when revealed discloses to us a tragic posture of trying to grasp firmly the material world and measure it, codify it, and have it, or to express it in some form which one could have, and measure, codify, and have, or some artful expression or some literary expression or some scientific expression that there must be some way in which man can tell himself a in a descriptive capacity what this world is and have it and be certain that he does have it and that progressively in the 19th century as this was undertaken time and again by individual after individual of genius in their genius and in their attempts they found continuously successively cumulatively that it could not be done.

And so the last figure in the series is a man who realized that his own time had lived through a tragic nightmare and that waking up from it in the 20th century man would find that he was not only empty handed but what little clothing he had been bequeathed by history was now in shreds and tatters and he would have to go naked in the world all over again and learn all over again. And this psychological archetypal penetration of the return to the primitive condition is what powered the vision of art in the early part of the 20th century. That the return to the primitive is the only way by which we may verify that the cycle of frustration is over, and some new beginnings can at least commence. This deep-seated need in the 20th century as we will see produces incredible results. The return to nature, the return to the primordial, will be glamorized with all the slurs and blurs of the mistakes and flaws of the past so that we may not even understand our rebirth. But that’s for another course.

Tonight we have James Clerk Maxwell, who was called Clerk Maxwell. He was Scottish. He was born in Edinburgh about 1831. His father bought a beautiful estate, a rather large estate, in the south of Scotland near a place called New Galloway and it’s in that section of Scotland that’s sort of midway between Ireland and Edinburgh. It’s a peninsula of Scotland that juts out into the Irish Sea above the Isle of Man and it goes by the Scottish name of Kirkcudbrightshire – Kirkcudbright. It is a kind of a barren landscape with mountainous hilly heather regions and a lot of lakes. The young Clerk Maxwell was moved there very young and spent the first years of his life probably, until he was eight or nine years old, in the carefree countryside of Scotland in the fresh air, the pure water, and this condition made of Clerk Maxwell what it does for all little Scottish country boys, absolutely basic honest human being who relates to life in a straightforward straight on regard. The kind of person who would require clear water and unadulterated oatmeal for breakfast.

This personality of Clerk Maxwell was to stand him in stead, and even though he lived only forty-eight years, he was to revolutionize science, to revolutionize mathematics, and revolutionize the whole approach to mentality. There are other figures who contribute to this. We should in a more detailed and comprehensive matrix also take into consideration the man who came before him and the man who came after him. The man who came before him was Michael Faraday. The man who came after him was J. J. Thompson. But it is Clerk Maxwell who is the fulcrum of the issue, who personifies the exquisite results of a country Scottish boy who looked straight into the universe and is fitted with a language enabling him to describe exactly what he experiences, what he sees.

He was entered into Cambridge. At first he was entered in a matriculated to Peterhouse College in Cambridge but very soon went over to Trinity College. And Trinity College was the great tradition of science and mathematics. It was the College of Isaac Newton and in fact Clerk Maxwell was compared to Isaac Newton at least until Einstein came along. He was considered second only to Newton. There at Trinity College Cambridge, Maxwell’s great intellectual clarity stood him in great stead and when he graduated in 1854 he was already a capable competent individual. He had, in fact, already written a number of papers, which had been published, and one of them concerned the motion of double refraction in viscous liquids under stress. That is to say if you take a liquid in a volume and subject it to a stress, along the line of stress there will be a double fracturing, each side of the– of the stress will reflect an occurrence.

This balance appealed to Clerk Maxwell. The fact that nature should disclose a symmetry in its gut nature seemed absolutely right to the mind of Clerk Maxwell. In fact, it began to penetrate to his imagination that perhaps the basic notion of what we called energy – electricity – would operate with the same symmetry, same forthrightness. He had made the acquaintance at Trinity College Cambridge with Michael Faraday whose great works were highly readable, probably because they were not couched in mathematical terms. Faraday was not a mathematician and because he was not a mathematician most of his scientific writings are in the form of notes and diaries, journals, series of experiments which he would go record, and his observations. And it’s these eight volumes of Faraday’s Experiments and Journals that form the basis of Faraday’s genius. But it’s apparent in reading through Faraday that his accumulated experience in the world, in the physics of electricity and magnetism, in the world of force and energy were not tied into the expressive exact precise world of science because they were not mathematically expressed.

The young mathematical genius Clark Maxwell began to take it upon himself to translate Faraday into mathematics. That is to say, he first thought of himself as a translator, a Confucius of science, not someone who is pioneering something new, but someone who was conserving the past by bringing the best elements together into a series, order, and form, and translating it into a compatible language into a pattern of expression that would key into, tie into, the world of applicability. Because mathematics is the applicable world from mathematics science becomes technology. Through the language of mathematics, science in its experimental phase transmutes and becomes technology in its structural phase. And if the 20th century is anything at all, it’s a technological fantasy.

So we have to understand Clark Maxwell because he’s very important in this whole progression of how this fantasy came to be. He was appointed, very soon after coming out of Cambridge with his degree to a little college in Aberdeen Marischal College, and for four years he held this post as a professor there. He in fact seemed to settle down. He liked the home life very much. He thought to himself that the best thing that he could do would be to teach decently and live decently. He married. He married a woman named Mary Dewar, like the Dewar Scotch, who was the daughter of the principal of Marischal College. He had inherited the estate named Glen Ayre. It seemed to him that life was very satisfying, very direct. He had no more druthers.

But four years went by and in 1860 the University of Aberdeen was founded; Marischal College was folded into the structure and Clerk Maxwell was left out. He applied at Edinburgh and was turned down but he was accepted at the University of London. It’s one of those events that in retrospect we think to ourselves some divine wise hand has planned all this because London was the perfect place for Clark Maxwell. And for eight years in the 1860s – from 1860 to 1868 – that is in the period when the Civil War was ravaging the United States, in England, in London, in the mind of Clark Maxwell the modern scientific world was being formed. That is to say, that Clerk Maxwell’s direct Scottish bright-eyed mind was structuring out a worldview that would eventually obtain and become the world order in the 20th century with some emendations. All this was happening while the Civil War was going on.

By 1868 Clerk Maxwell’s capacity to understand electricity and magnetism had ballooned to proportions that were unheard of. That is to say he had found himself in a capacity of synthesis wherein the synthesis had transcended completely all of the implications that had been thought possible previously. So he retired; he went back to Glen Eyre with his wife and he devoted all of his time to writing. And what he wrote there was his great Treatise on Electricity and Magnetism, which would be published in 1873 in two volumes – that is, the first edition would be.

But while he was there while he was working on this great monumental work, this classic of the new age, he was gaining fame throughout Europe, and especially throughout England, for the brilliancy of his mathematical mind of his capacity to order large structures of endeavor. And so the University of Cambridge sent for him in 1871. They were going to set up a new laboratory. It was to be built with all the latest equipment. It was to have a large endowment in terms of funds, in terms of staffing. It was to commemorate a physicist, a British physicist named Henry Cavendish, who had died in 1810 – he’d lived from 1731 about 100 years before Maxwell and died in 1810. And Cavendish was extremely famous. His estate and a number of friends had left considerable funds and by this time, 1871, had matured and so they brought Clerk Maxwell to Cambridge to design and set up the Cavendish Laboratory, which would become the alchemical crucible in which modern physics would be born.

There were only eight years remaining to Clerk Maxwell’s life, but he applied himself. He set up and structured the Cavendish Laboratory, its library, its staff, its functioning with the incredible genius of his mind. He made the Cavendish Laboratory the first real instrument for high level physics. And it was done all in the 1870s. All of the labs that we find in the 20th century, the research capacity, the energizing of design and intent, the arrangement of investigative personnel and equipment, and the dovetailing of all these facilities together owe a great deal to Clerk Maxwell. My own sense of design of what an education would be has largely been formulated through acquaintance with this kind of a structuring technique.

He made the Cavendish Laboratory the most outstanding area of research in thought in the 19th century. The man who would become the director of the Cavendish at the end of the 19th century into the 20th would be the great physicist J. J. Thompson who finally took electricity and magnetism and the experimental science of the laboratory completely into the 20th century. It became the prototype of the kind of laboratories– well there’s an example: the laboratory that Oppenheimer set up to develop the atomic bomb, was based in its structure and intent personnel and equipment on this kind of a design. So that Clerk Maxwell’s mind made in and shaped an investigating tool which was a high energy physics lab where the mathematical work could be keyed into the experimental work and where the interplay of minds and equipment, processes of discovery and recovery, of publishing and retrospect, all could be brought into a wholesome mixture where it could influence each other and produce the kind of quality manifestation that is needed for the human mind to penetrate through the mysteries of matter.

The external phenomenon was the laboratory. The internal phenomenon was the Treatise on Electricity and Magnetism. It is a thousand pages. It is largely mathematical. It is filled with complex equations. Einstein, when he wrote The Evolution of Physics from Early Concepts to Relativity and Quanta, with his friend Leopold Infeld, writes in here under the chapter, “Field, Relativity” – “Field, Relativity”:

“During the second half of the nineteenth century new and revolutionary ideas were introduced into physics; they opened the way to a new philosophical view, differing from the mechanical one. The results of the work of Faraday, Maxwell, and Hertz led to the development of modern physics, to the creation of new concepts, forming a new picture of reality.”

And he will want to discuss in here the development of Maxwell’s part. And he will say here that one of the most important developments which occurred first in the mind of Faraday but was unusable in the way in which Faraday expressed it so that Maxwell, understanding its primordial utility, translated it into the usable form of mathematics. The notion in Faraday’s mind was that we have got to stop looking at the world as things. We have got to stop thinking of electricity and magnetism as movements of things. That in fact the only way to understand the phenomena of electricity and magnetism and even gravity and all the basic powers of the universe is to conceive of them as fields. And that when we conceive of them as field phenomena we then have the right mentality to address ourselves intelligently to the phenomenon.

The problem with Faraday is that he could not detail this into a mathematical language so that it could be translated into action. It couldn’t be dealt with. It is Clerk Maxwell who took this field notion and honed it sharp so that it became an implement, and carved out the technological world.

Let me shift over here to a book called The Evolution of Scientific Thought from Newton to Einstein by d’Abro published in Dover Paperbacks and on page 126 we find d’Arbo finally getting around to Maxwell. He writes in here, “Faraday was the first scientist to realise the enormous importance of the electromagnetic field. He saw in it a reality of a new category differing from matter. [He was capable of transmitting effects from place.] It was capable of transmitting effects from place to place, and was not to be likened to a mere mathematical fiction such as the gravitational field was then to be assumed.”

Now at that time most of the work that was being done in physics, in mathematics, assumed a principle of action at a distance that the efficacy of force and energy resided within things and moved from thing to thing. But Faraday, through his experiments, had conceived of the idea that it– the reality of energy resided not in things but in a field. He used the term aether. He couldn’t find the right term and so he used the term aether rather like a midwestern Housewives use the term Tao in the 20th century. It meant a vague something or other. You couldn’t really think of it. This aether Faraday decided must carry an impress through itself, like a wave, and that this is the way in which electromagnetic energy is transmitted through the universe but that the carrying medium was the ultimate contradiction. It could receive impressions of fantastic force and yet was seemingly nothing material in itself.

What could this be? He couldn’t understand. 37:22 It seemed to him a mystery. In other words, according to Faraday, when a current was flowing along a wire the most important aspect of the phenomenon lay not in the current itself but in the fields of electric and magnetic force distributed throughout space in the currents vicinity. Don’t look at the wire but also don’t look at the current in the wire. Conceive instead the obverse, the negative of things: the field of current generated by the current; the field of force around it. That it has the shaping power. In this elevation of the field to a position of preeminence it is often called the pure physics of the field or field physics. Maxwell took this notion from Faraday – Faraday gave it to him – knew Maxwell. Maxwell toyed with this. And in toying with this, in addressing himself to the field, he realized that just as he had dealt with symmetry in the [inaudible] of viscous liquids – and this is true in solids too – that there is a symmetry of the lines of force that develop. That the same principle would have to affect itself in terms of the energy field in the universe.

That is to say, when he was developing the mathematical equation – E is for the energy; H is for magnetism – in the first equation there– there are two equations for electricity and there are two equations for magnetics. I’m tempted to give you the derivation of these terms as Maxwell does at the very beginning of his book, but I’ll come back to that. Let’s stick with the equations. The first equation has a little mathematical notation – DIV – and it simply indicates a mathematical arrangement, a statement that div E = 0 – that this condition of– let this condition of electricity equal zero. The next function is called a “curl”. The curl of electricity equals – and this is where the equation becomes a little iffy since we don’t have a blackboard, but let me give it to you again. It’s in d’Abro page 126: curl – the curl function of electricity equals -1 over C and dH over dt (t being time, c being a velocity) – curl E = -1/c dH/dt

This equation, when it came to magnetism, had been assumed by Faraday to just apply to electricity, but Maxwell’s sense of symmetry made him write the same kind of equation for magnetism. So that he then had two sets of equations and in these equations one more operation was applied which brought an apparent revelation to Maxwell’s mind that electricity and magnetism were for all intents and purposes polar energies. They converted into each other. That a magnetic field will create electricity, but an electric field will create magnetism. But they are related. And the way in which they are related, in the equations, has to do with the three fundamental aspects of what used to be called matter and now we’re being transposed into relational phenomenon of a field form. The three basic factors being length, time, and mass. And in fact now we have to go to Maxwell’s book.

I don’t want to get too far afield from what you can go to. This is a Dover edition.

Maxwell in his enormous treatise gives us a 30 page preliminary. And in this preliminary he gives us all that we need to know to understand the shift of frame of reference which he is endeavoring to bring into manifestation by writing this book. He at the very beginning in the preface tells us some interesting little points that we’ve all forgotten. That the word electric, electron in Greek, refers to amber because it was the experiments with amber that first produced the phenomenon of electricity. So electron just means– is the Greek word for amber. That is, it takes place because of the maneuvering of this element. Magnetic comes from the Greek word magnes because the lodestone was found in a section of Greece in Thessaly – Thessaly Magnesia. So it was called– So magnetism and electricity and words come from the Greek which relate to the things in which they were first found.

This is– this is characteristic of Maxwell’s great comprehension that he takes everything back to the beginning. He– he follows the mathematician’s penchant to find some coordinate system and to establish the origin of the coordinate system so that whenever he establishes any point in an argument he can connect any point in the argument with the origin of the coordinate system and thereby given, when asked at any time, a meaningful line of development between every single iota of the argument and the conditions, the intellectual structure, under which it occurs. This is new. This is a revolution in thought. This is an unbelievably capable individual.

Now this had been done in absolutist terms by the geniuses of yoga-like Patanjali, or the geniuses of mystical insight like Plotinus, but it had never been done in terms of a reductive language of applicability that could come back to the world of material and express it exactly in this term. So that Maxwell’s thought here is extremely sophisticated, making possible an accuracy of conception which in one generation would produce the theory of relativity. But the accuracy of this mentality is so difficult to entertain. It is– It is like trying to stand on tiptoes and then realizing that one’s toes have nothing to do with one’s height.

I have to give you a little vignette here. There was a mathematician, an Irishman from Dublin, about this time. And his name in fact is Hamilton – William Rowan Hamilton. He had become an extremely capable mathematician but he had set himself an incredible problem. He had taken up the issue of trying to understand three-dimensional space in terms of equations. He had solved most of the basic expressive problems that were in terms of area, two-dimensional space – planes – where you have to have a special kind of a mathematic that brings in imaginary numbers. It’s expressed A + bI. I being an imaginary number. That is where there’s a set, a parallel set of two numbers, so that any point or any expression in the equations actually is made up of two parallel locations at the same time. It’s like applying double vision to an intellectual conception. You can’t think of any one thing but you have to think in terms of pairs constantly and accurately and keep them parallel and straight all the time. And the way to do this is through the mathematics of this plane, this kind of algebra, algebraic formulation, which then keyed into calculus.

When it came to three-dimensional space. There was a problem. The equations wouldn’t solve. Nothing would happen. Hamilton tried using the very sophisticated three triplets and nothing would happen. You couldn’t solve anything. He was hung up for years. And one day he was walking along the Grand Canal in Dublin and it hit him all of a sudden. And Hamilton, so distracted, he ran to one of the posts of Brown Bridge and carved the equations in the post of the bridge – and they’re still there in Dublin. He realized that when you deal with three-dimensional space you can’t deal with it in terms of triplets but you have to have fours. You have to have four numbers. You have to have four expressions for every point in three-dimensional space. The reason being is that the whole plane shifts in three-dimensional space. So you have to have coordinates to describe the one plane and then you have to have another pair to describe the plane within the other dimension.

So this discovery by Hamilton – this is 1843 – did two things. It freed up mathematics from its shackling to the old arithmetic common sense flaw. One of the first things that had to be given up was the commutative laws of multiplication. That is, it had been assumed since time immemorial that A×B is the same as B×A. It is not true in three-dimensional space. It is not necessarily true and rarely is exactly true. That the commutative laws of multiplication had to be given up was hard enough, but the fact was is that the mentality involved in sustaining a mathematical analysis of this complexity. Hamilton’s quadrillions were– were phenomenally difficult. The expression, in fact, was so long and so cumbersome that it was used only by the real intellectual elite until a man named J. Willard Gibbs came along and simplified the whole process. And it was from Gibbs that we have vector analysis. But this mentality meant that there were certain persons freed up finally to envision cubes. One could deal in equations confidently, exactly, precisely, not only with squares c squared but one could deal with cubes – C cubed (C3) – and on a three-dimensional level with a three-dimensional model available for exacting mathematical analysis. When you take a look at a field phenomenon you can finally make sense of it in terms of the mathematical language which you’re seeking to speak to write. You can go to the blackboard and you can with quite a certainty describe what it is that you’re saying.

But Maxwell, to whom all kudos, because he is the one that put all this in operation – but Maxwell was the one who then delivered the message. We have three basic measurements available to us for reality: We have length; we have mass; we have time. That in framing any mathematical system that is going to be descriptively accurate then, we have to be rigorous in terms of these three measurements, these three quantities. At the very first page, the first paragraph of his treatise, he writes,

“Every expression of a Quantity consists of two factors or components. One of these is the name of a certain known quantity of the same kind as the quantity to be expressed, which is taken as a standard of reference. The other component is the number of times the standard is to be taken in order to make up the required quantity. The standard quantity is technically called the Unit, and the number is called the Numerical Value of the quantity.”

And now all of our direction is going to shift away from numerical value to the unit, because the unit must be dependable and the unit can only be thought of in terms of the highest rigorousness. Now we’re dealing with a three-dimensional model now, because we’ve got these three elements that are– that are in it. These are what are– these are what were called the– the dimensions.

He says, “in all scientific studies [hence] it is of the greatest importance to employ units belonging to a properly defined system, and to know the relations of these units to the fundamental units, so that we may be able at once to transform our results from one system to another.”

In other words, in order to have a technology, we have to have this mathematical transmutational fulcrum. And it has to be exact because we’re going to be required to read out from our mathematical thought structure in terms of calling out the tuned to the phenomenal world and reshaping it.

The first is length, the first of the three fundamental units, and all three have to be inter-defined so that they form a unity. He talks about length. He talks about how a foot is this or that or how in astronomy there’s a distance between the Earth and the sun and so forth. But then he says:

“In the present state of science the most universal standard of length which we could assume would be the wave length in vacuum of a particular kind of light, emitted by some widely diffused substance such as sodium, which has well-defined lines in its spectrum. Such a standard would be independent of any changes in the dimension of the earth, and should be adopted by those who expect their writings to be more permanent than that body.”

Maxwell’s little Scottish sense of humor saying that we’re dealing with something that is now no longer colloquial in any sense of the term but universal in every sense of the term. One of the basic constituents, elements, of the universe – sodium – and its– the wavelength in a vacuum of a particular kind of light emitted from it will be our sense of length. Then you can denote this he says. You can use L, now, and it will have a meaningfulness, an exactness. But what about time? And he talks about how the standard unit of time around countries is always a rotation of the earth on its axis so forth and that the unit of time adopted in all physical research searches is usually one second of mean solar time. But he says here in astronomy a year is sometimes used as a unit of time but a more universal unit of time might be found by taking the periodic time of vibration of the particular kind of light whose wavelength is the unit of length.

In other words we’re going to take now for time, the vibration, the periodic time of vibration of that particular kind of light whose wavelength was the unit of length. Light comes out in a wavelength. So the length of that wave is our length. But it occurs in a periodicity. And the periodicity now is our sense of time. So they’re related.

Third is mass. And he talks about the pound and how seven thousand grains make a pound. And he says that these weights for the pound are in London. And he talks about a different kind of a metric measurement and how the standards for this are in Paris. And he says we need a different mass; we need a different understanding. He says the accuracy with which the masses of bodies can be compared by weighing is far greater than that hitherto attained in the measurement of lengths so that all masses ought, if possible, to be compared directly with the standard and not deduced from experiments on water. So he says we will denote in descriptive astronomy the mass of the sun or that of the earth is sometimes taken as a unit. But in the dynamical theory of astronomy the unit of mass is deduced from the units of time and length combined with the fact of universal gravitation. The astronomical unit of mass is that mass which attracts another body placed at the unit of distance so as to produce in that body a unit of acceleration. So that we now have in mass bound up in it already intrinsic with it the notion of acceleration; the notion of length; the notion of periodicity in time. The– The description of this is all bound up together.

In these equations, once we have these three – length, time, and mass – in this arrangement we may then derive all the rest of the phenomena that we need to deal with. In the first derived unit that Maxwell had was velocity. And of course, because he was dealing with a length of light from sodium and because he was dealing with the periodicity of its vibration for time and then mass compounded from those the first derived unit of velocity read out of course in terms of light that is to say one of the quandaries which modern physics finds itself in was built into a conundrum in the first place in the whole structure of thought that made this available expressively.

The– all the other derived units– and I’ll skip over them; I don’t want to tire you on this, but Maxwell was proceeding rather like Euclid proceeded with his geometry moving from step to step leaving nothing out, assiduously covering every aspect. There were sections in the– all this is preliminary. There were sections on physical continuity and discontinuity. There were sections on discontinuity of a function of more than one variable. There were periodic and multiple functions. The relation of physical quantities to directions in space. And then he came to intense intensities and fluxes.

And all the time he is distinguishing, he is saying we have two distinct ways of looking at phenomena. We can see them in terms of what used to be called from object to object. This influence, where there is a line of development, a line of force or we can see them in terms of the field which encompasses the objects in which case we’re looking at something called a field. And in order to understand the field phenomenon we need a cross section of the field which is in. area a square phenomenon such and such – K square (K2). Or if we want to get into a three-dimensional cross section we can use some kind of a cube –K cube (K3). So that we have two distinct ways of looking at reality. We may look at it in terms of some kind of a line development or in some kind of an area development. That is the key to understanding. The one is to move in terms of line and the key in the other is to understand a passage of energy through a certain area or a certain volume and that either way we enjoy a capacity to then measure the effects of force and phenomena in the universe and coordinate all of our experiments together into this one master language.

And with this transformative three-dimensional capacity we can then translate that accumulated understanding into a technical application in the world. So the man who designed the Cavendish Laboratory was also designing the intellectual room, the mental space, where modern physics would be born. This is one of the great– great events of all time that this could this could actually happen. He goes into the different kinds of integrals – line integrals. He goes into potentials. He talks about how all the various great discoveries that had been discounted before. Not understood how he’s bringing them all back together. A man named Green had done an essay that had been neglected by mathematicians; discoveries by Gauss on the continent and so forth that in fact all of this would be brought together in this treatise.

And then, he takes us, after the preliminary, into part one – which is Electrostatics – and he takes us back to experiment. After this preliminary, where he started from just the very basics and developed a whole algebra a whole geometry of expression. The first part of the book takes us back to “Experiment 1”:

“Let a piece of glass and a piece of resin, neither of which exhibits any electrical properties, be rubbed together and left with the rubbed surfaces in contact. They will still exhibit no electrical properties. Let them be separated. They will now attract each other.”

So that Maxwell is following his plan all over again. But what he has described on sort of the structural sub-basement, foundational level in the preliminary, he now will go through that whole structure rigorously in terms of collating all of the experiments up to his own time. Bringing all of them together just as a master mathematician will bring all the various elements that are needed for a full equation and bring them into his equation. Maxwell will proceed over the next thousand pages to bring all of the basic experiments that have actually been done. And all the basic mathematical insight that has already been done. But what has not been done is the correlation of all of them together in one master pattern. And when he did that it finally stood as one of those great achievements that for all time other men can use. Even though it went through a revised second edition, after his death, a couple of years later Maxwell had rewritten the first nine chapters of the Treatise on Electricity and Magnetism.

He died at age forty-eight in 1879, Cambridge. And his fellow workers brought the revised nine chapters and the rest of– of the work in the reprint brought it out. In 1891, J. J. Thompson the great director of the Cavendish Laboratory brought out a third edition in which some basic footnotes were put in trying to bring everything up current but there was so much that had become fruitful because of Maxwell by 1891 that he brought out a supplemental volume, a third volume, which Dover did not reprint. Unfortunately, I have to find a copy from the 1891 printing of it.

It was that third edition of the Treatise on Electricity and Magnetism with the J. J. Thomson third volume that Einstein read that everybody was reading in the world of physics. Because what had been done for them is that this great laboratory of the mind with its expressive capacity to translate into actual three-dimensional mathematical mentality. The correlation of all the experiments and all the thought that had been done up until that time and then gave a transmitted way of applying that to the physical world. So that an ecology of mind and world was set in motion where the rigorous application of man’s certainty of measurement was not so much applied to the world, but applied to his mind because the veracity of the higher mathematics of nuclear physics is applicable because we have a mental control upon it. It is our yoga. It is the yoga that technology is based upon. That if we order our minds in this way and can measure the world through this area so described, this volume so described in our minds, then we can order the world in accordance with it. Such is the tragic flaw that 20th century man labors under daily.

Well next week we’ll see some man who may not have been able to read Maxwell’s book but who received the message in the fullness of his spirit – Leo Tolstoy – who was the master spirit of the whole century. With that we’ll close out the series and this lecture here; turn the place over to the Kabbalists.