# Mathematics Severed from Human Experience: The Birth of Modern Science

## GA 326 — 27 December 1922, Dornach

### Lecture IV

In the last lecture, I spoke of a former view of life from which the modern scientific view has evolved. It still combined the qualitative with the form-related or geometrical elements of mathematics, the qualitative with the quantitative. One can therefore look back at a world conception in which the triangle or another geometrical form was an inner experience no matter whether the form referred to the surface of a given body or to its path of movement. Geometrical and arithmetical forms were intensely qualitative inner experiences. For example, a triangle and a square were each conceived as emerging from a specific inward experience.

This conception could change into a different one only when men lost their awareness that everything quantitative—including mathematics—is originally experienced by man in direct connection with the universe. It changed when the point was reached where the quantitative was severed from what man experiences. We can determine this moment of separation precisely. It occurred when all concepts of space that included man himself were replaced by the schematic view of space that is customary today, according to which, from an arbitrary starting point, the three coordinates are drawn. The kind of mathematics prevalent today, by means of which man wants to dominate the so-called phenomena of nature, arose in this form only after it had been separated from the human element. Expressing it more graphically, I would say in a former age man perceived mathematics as something that he experienced within himself together with his god or gods, whereby the god ordered the world. It came as no surprise therefore to discover this mathematical order in the world. In contrast to this, to impose an arbitrary space outline or some other mathematical formula on natural phenomena—even if such abstract mathematical concepts can be identified with significant aspects in these so-called natural phenomena—is a procedure that cannot be firmly related to human experiences. Hence, it cannot be really understood and is at most simply assumed to be a fact. Therefore in reality it cannot be an object of any perception. The most that can be said of such an imposition of mathematics on natural phenomena is that what has first been mathematically thought out is then found to fit the phenomena of nature. But why this is so can no longer be discovered within this particular world perception.

Think back to the other worldview that I have previously described to you, when all corporeality was regarded as image of the spirit. One looking at a body found in it the image of spirit. One then looked back on oneself, on what—in union with one's own divine nature—one experienced as mathematics through one's own bodily constitution. As a work of art is not something obscure but is recognized as the image of the artist's ideas, so one found in corporeal nature the mathematical images of what one had experienced with one's own divine nature. The bodies of external nature were images of the divine spiritual. The instant that mathematics is separated from man and is regarded only as an attribute of bodies that are no longer seen as a reflection of spirit, in that instant agnosticism creeps into knowledge.

Take a concrete example, the first phenomenon that confronts us after the birth of scientific thinking, the Copernican system. It is not my intention today or in any of these lectures to defend either the Ptolemaic or the Copernican system. I am not advocating either one. I am only speaking of the historical fact that the Copernican system has replaced the Ptolemaic. What I say today does not imply that I favor the old Ptolemaic system over the Copernican. But this must be said as a matter of history. Imagine yourself back in the age when man experienced his own orientation in space: above-below, right-left, front-back. He could experience this only in connection with the earth. He could, for example, experience the vertical orientation in himself only in relation to the direction of gravity. He experienced the other two in connection with the four compass points according to which the earth itself is oriented. All this he experienced *together* with the earth as he felt himself standing firmly on it. He thought of himself not just as a being that begins with the head and ends a the sole of the feet. Rather, he felt himself penetrated by the force of gravity, which had something to do with his being but did not cease at the soles of his feet. Hence, feeling himself within the nature of the gravitational force, man felt himself one with the earth. For his concrete experience, the starting point of his cosmology was thus given by the earth. Therefore he felt he Ptolemaic system to be justified.

Only when man severed himself from mathematics, only then was it possible also to sever mathematics from the earth and to found an astronomical system with its center in the sun. Man had to lose the old experience-within-himself before he could accept a system with its center outside the earth. The rise of the Copernican system is therefore intimately bound up with the transformation of civilized mankind's soul mood. The origin of modern scientific thinking cannot be separated from the general mental and soul condition, but must be viewed in context with it.

It is only natural that statements like this are considered absurd by our contemporaries, who believe in the present world view far more fervently than the sectarians of olden days believed in their dogmas. But to give the scientific mode of thinking its proper value, it must be seen as arising inevitably out of human nature and evolution. In the course of these lectures, we shall see that by doing this we are actually assigning far greater value to science than do the modern agnostics.

Thus the Copernican world conception came into being, the projection of the cosmic center from the earth to the sun. Fundamentally, the whole cosmic thought edifice of Giordano Bruno,[^1] who was born in 1548 and burned at the stake in Rome in 1600, was already contained in the Copernican world view. It is often said that Giordano Bruno glorifies the modern view of nature, glorifies Copernicanism. One must have deep insight into the inner necessity with which this new cosmology arose if one is to have any feeling at all for the manner and tone in which Giordano Bruno speaks and writes. Then one sees that Giordano Bruno does not sound like the followers of the new view or like the stragglers of the old view. He really does not speak about the cosmos mathematically so much as lyrically. There is something musical in the way Giordano Bruno describes the modern conception of nature. Why is that? The reason is that Giordano Bruno, though he was rooted with his whole soul in a bygone world perception, told himself with his outward intellect: The way things have turned out in history, we cannot but accept the Copernican world picture. He understood the absolute necessity that had been brought about by evolution. This Copernican world view, however, was not something he had worked out for himself. It was something given to him, and which he found appropriate for his contemporaries. Belonging as he did to an older world conception, he could not help but experience inwardly what he had to perceive and accept as knowledge. He still had the faculty of inner experience, but he did not have scientific forms for it. Therefore although he described them so wonderfully, he did not follow the Copernican directions of thought in the manner of Copernicus, Galileo, Kepler, or Newton.[^2] Instead, he tried to experience the cosmos in the old way, the way that was suitable when the world cosmos was experienced within one's being. But in order to do this, mathematics would have had to be also mysticism, inward experience, in the way I described yesterday. This it could not be for Giordano Bruno. The time for it was past. Hence, his attempt to enter the new cosmology through living experience became an experience, not of knowledge but of poetry, or at least partially so. This fact lends Giordano's works their special coloring. The atom is still a monad; in his writings, it is still something alive. The sum of cosmic laws retains a soul quality, but not because he experienced the soul in all the smallest details as did the ancient mystics, and not because he experienced the mathematical laws of the cosmos as the intentions of the spirit. No, it was because he roused himself to wonder at this new cosmology and to glorify it poetically in a pseudo-scientific form. Giordano Bruno is truly something like a connecting link between two world conceptions, the present one and the ancient one that lasted into the fifteenth century. Man today can form scarcely any idea of the latter. All cosmic aspects were then still experienced by man, who did not yet differentiate between the subject within himself and the cosmic object outside. The two were still as one; man did not speak of the three dimensions in space, sundered from the orientation within his own body and appearing as above-below, right-left, and forward-backward.

Copernicus tried to grasp astronomy with abstract mathematical ideas. On the other hand, Newton shows mathematics completely on its own. Here I do not mean single mathematical deductions, but mathematical thinking in general, entirely divorced from human experience. This sounds somewhat radical and objections could certainly be made to what I am thus describing in broad outlines, but this does not alter the essential facts. Newton is pretty much the first to approach the phenomena of nature with abstract mathematical thinking. Hence, as a kind of successor to Copernicus, Newton becomes the real founder of modern scientific thinking.

It is interesting to see in Newton's time and in the age that followed how civilized humanity is at pains to come to terms with the immense transformation in soul configuration that occurred as the old mathematical-mystical view gave way to the new mathematical-scientific style. The thinkers of the time find it difficult to come to terms with this revolutionary change. It becomes all the more evident when we look into the details, the specific problems with which some of these people wrestled. See how Newton, for instance, presents his system by trying to relate it to the mathematics that has been severed from man. We find that he postulates time, place, space, and motion. He says in effect in his *Principa*: I need not define place, time, space, and motion because everybody understands them.[^3] Everybody knows what time is, what space, place, and motion are, hence these concepts, taken from common experience, can be used in my mathematical explanation of the universe. People are not always fully conscious of what they say. In life, it actually happens seldom that a person fully penetrates everything he says with his consciousness. This is true even among the greatest thinkers. Thus Newton really does not know why he takes place, time, space, and motion as his starting points and feels no need to explain or define them, whereas in all subsequent deductions he is at pains to explain and define everything. Why does he do this? The reasons is that in regard to place, time, motion, and space all cleverness and thinking avail us nothing. No matter how much we think about these concepts, we grow no wiser than we were to begin with. Their nature is such that we experience them simply through our common human nature and must take them as they come. A successor of Newton's, Bishop Berkeley,[^4] took particular notice of this point. He was involved in philosophy more than Newton was, but Berkeley illustrates the conflicts taking place during the emergence of scientific thinking. In other respects, as we shall presently hear, he was not satisfied with Newton, but he was especially struck by the way that Newton took these concepts as his basis without any explanation, that he merely said: I start out from place, time, space, and motion; I do not define them; I take them as premises for my mathematical and scientific reflections. Berkeley agrees that one must do this. One must take these concepts in the way they are understood by the simplest person, because there they are always clear. They become unclear not in outward experience, but in the heads of metaphysicians and philosophers. Berkeley feels that when these four concepts are found in life, they are clear; but they are always obscure when found in the heads of thinkers.

It is indeed true that all thinking about these concepts is of no avail. One feels this. Therefore, Newton is only beginning to juggle mathematically when he uses these concepts to explain the world. He is juggling with ideas. This is not meant in a derogatory way; I only want to describe Newton's abilities in a telling manner. One of the concepts thus utilized by Newton is that of space. He manipulates the idea of space as perceived by the man in the street. Still, a vestige of living experience is contained therein. If, on the other hand, one pictures space in terms of Cartesian mathematics, without harboring any illusions, it makes one's brain reel. There is something undefinable about this space, with its arbitrary center of coordinates. One can, for example, speculate brilliantly (and fruitlessly) about whether Descartes’ space if finite or infinite. Ordinary awareness of space that is still connected with the human element really is not at all concerned with finiteness or infinity. It is after all quite without interest to a living world conception whether space can be pictured as finite or infinite. Therefore one can say that Newton takes the trivial idea of space just as he finds it, but then he begins to mathematize. But, due to the particular quality of thinking in his age, he already has the abstracted mathematics and geometry, and therefore he penetrates spatial phenomena and processes of nature with abstract mathematics. Thereby he sunders the natural phenomena from man. In fact, in Newton's physics we meet for the first time ideas of nature that have been completely divorced from man. Nowhere in earlier times were conceptions of nature so torn away from man as they are in Newtonian physics.

Going back to a thinker of the fourth or fifth century A.D.—though people of that period can hardly be called “thinkers,” because their inner life was far more alive than the mere life in thoughts—we would find that he held the view: “I live; I experience space along with my God, and orient myself in space up-and-down, right-left, and forward-backward, but I dwell in space together with my God. He outlines the directions and I experience them.” So it was for a thinker of the third or fourth century A.D. and even later; indeed, it only became different in the fourteenth century. Thinking geometrically about space, man did not merely draw a triangle but was conscious of the fact that, while he did this, God dwelled within him and drew along with him. His experience was qualitative; he drew the qualitative reality that God Himself had placed within him. Everywhere in the outer world, whenever mathematics was observed, the intentions of God were also observed.

By Newton's time mathematics has become abstracted. Man has forgotten that originally he received mathematics as an inspiration from God. And in this utterly abstract form, Newton now applies mathematics to the study of space. As he writes his Principia, he simply applies this abstracted mathematics, this idea of space (which he does not define,) because he has a dim feeling that nothing will be gained by trying to define it. He takes the trivial idea of space and applies his abstract mathematics to it, thus severing it from any inward experiences. This is how he speaks of the principles of nature.

Later on, interestingly enough, Newton goes somewhat deeper. This is easy to see if one is familiar with his works. Newton becomes ill at ease, as it were, when he contemplates his own view of space. He is not quite comfortable with this space, torn as it is out of man and estranged completely from the spirit. So he defines it after all, saying that space is the sensorium of God. It is most interesting that at the starting point of modern science the very person who was the first to completely mathematize and separate space from man, eventually defines space as God's sensorium,[^5] a sort of brain or sense organ of God. Newton had torn nature asunder into space and man-who-experiences-space. Having done this, he feels inwardly uneasy when he views this abstract space, which man had formerly experienced in union with his god. Formerly, man had said to himself: What my human sensorium experiences in space, I experience together with my god. Newton becomes uneasy, now that he has torn space away form the human sensorium. He has thereby torn himself away from his permeation with the divine-spiritual. Space, with all is mathematics, was not something external. So, in later life, Newton addresses it as God's sensorium, though to begin with he had torn the whole apart, thus leaving space devoid of Spirit and God. But enough feeling remained in Newton that he could not leave this externalized space devoid of God. So he deified it again.

Scientifically, man tore himself loose from his god, and thus from the spirit; but outwardly he again postulated the same spirit. What happened here explains why a man like Goethe found it impossible[^6] to go along with Newton on any point. Goethe's Theory of Color is one particularly characteristic point. This whole procedure of first casting out the spirit, separating it from man, was foreign to Goethe's nature. Goethe always had the feeling that man has to experience everything, even what is related to the cosmos. Even in regard to the three dimensions Goethe felt that the cosmos was only a continuation of what man had inwardly experienced. Therefore Goethe was by nature Newton's adversary.

Now let us return to Berkeley, who was somewhat younger than Newton, but still belonged to the period of conflict that accompanied the rise of the scientific way of thinking. Berkeley had no quarrel with Newton's accepting the trivial ideas of place, space, time, and motion. But he was not happy with this whole science that was emerging, and particularly not with its interpretations of natural phenomena. It was evident to him that when nature is utterly severed from man it cannot be experienced at all, and that man is deceiving himself when he imagines that he is experiencing it.

Therefore, Berkeley declared that bodies forming the external basis for sense perceptions do not really exist. Reality is spiritual through and through. The universe, as it appears to us—even where it appears in a bodily form—is but the manifestation of an all-pervading spirit. In Berkeley, these ideas appear pretty much as mere assertions, for he no longer had any trace of the old mysticism and even less of the ancient pneumatology. Except for his religious dogma, he really had no ground at all for his assertion of such all-pervading spirituality. But assert it he did, and so vigorously that all corporeality become for him no more than a revelation of the spirit. Hence it was impossible for Berkeley to say: I behold a color and there is vibrating movement back of it that I cannot see—which is what modern science justifiably states. Instead, Berkeley said: I cannot hypothetically assume that there is anything possessing any corporeal property such as vibratory movement. The basis of the physical world of phenomena must be spiritually conceived. Something spiritual is behind a color perception as its cause, which I experience in myself when I know myself as spirit. Thus Berkeley is a spiritualist in the sense in which this term is used in German philosophy.

For dogmatic reasons, but with a certain justification, Berkeley makes innumerable objections against the assumption that nature can be comprehended by mathematics that has been abstracted from direct experience. Since to Berkeley the whole cosmos was spiritual, he also viewed mathematics as having been formed together with the spirit of the cosmos. He held that we do in fact experience the intentions of the cosmic spirit insofar as they have mathematical forms, for that we cannot apply mathematical concepts in an external manner to corporeal objects.

In accordance with this point of view, Berkeley opposed what mathematics had become for both Newton and Leibnitz,[^7] namely differential and integral calculus. Please, do not misunderstand me. Today's lecture must be fashioned in such a way that it cannot but provoke many objections in one who holds to the views prevailing today. But these objections will fade away during the ensuring lectures, if one is willing to keep an open mind. Today, however, I want to present the themes that will occupy us in a rather radical form.

Berkeley became an opponent of the whole infinitesimal calculus[^8] to the extent that it was then known. He opposed what was beyond experience. In this regard, Berkeley's feeling for things was often more sensitive than his thoughts. He felt how, to the quantities that the mind could conceive, the emergence of infinitesimal calculus added other quantities; namely, the differentials, which attain definition only in the differential coefficient. Differentials must be conceived in such a way that they always elude our thinking, as it were. Our thinking refuses to completely permeate them. Berkeley regarded this as a loss of reality, since knowledge for him was only what could be experienced. Therefore he could not approve of mathematical ideas that produced the indetermination of the differentials.

What are we really doing when we seek differential equations for natural phenomena? We are pointing to something that eludes our possible experience. I realize, of course, that many of you cannot quite follow me on these points, but I cannot here expound the whole nature of infinitesimal calculus. I only want to draw attention to some aspects that will contribute to our study of the birth of modern science.

Modern science set out to master the natural phenomena by means of a mathematics detached from man, a mathematics no longer inwardly experienced. By adopting this abstract mathematical view and these concepts divorced from man, science arrived at a point where it could examine only the inanimate. Having taken mathematics out of the sphere of live experience, one can only apply it to what is dead. Therefore, owing to this mathematical approach, modern science is directed exclusively to the sphere of death. In the universe, death manifests itself in disintegration, in atomization, in reduction to microscopic parts—putting it simply, in a crumbling into dust. This is the direction taken by the present-day scientific attitude. With a mathematics detached from all living experience, it takes hold of everything in the cosmos that turns to dust, that atomizes. From this moment onward it becomes possible to dissipate mathematics itself into differentials. We actually kill all living forms of thought, if we try to penetrate them with any kind of differential equation, with any differential line of thought. To differentiate is to kill; to integrate is to piece the dead together again in some kind of framework, to fit the differentials together again into a whole. But they do not thereby become alive again, after having been annihilated. One ends up with dead specters, not with anything living.

This is how the whole perspective of what was opening up through infinitesimal calculus appeared to Berkeley. Had he expressed himself concretely, he might well have said: First you kill the whole world by differentiating it; then you fit its differentials together again in integrals, but you no longer have a world, only a copy, an illusion. With regard to its content, every integral is really an illusion, and Berkeley already felt this to be so. Therefore, differentiation really implies annihilation, while integration is the gathering up of bones and dust, so that the earlier forms of the slain beings can be pieced together again. But this does not bring them back to life; they remain no more than dead replicas.

One can say that Berkeley's sentiments were untimely. This they certainly were, for the new way of approach had to come. Anyone who would have said that infinitesimal calculus should never have been developed would have been called not a scientific thinker but a fool. On the other hand, one must realize that at the outset of this whole stream of development, feelings such as Berkeley's were understandable. He shuddered at what he thought would come from a infinitesimal study of nature and had to do with the process of birth but a study of all dying aspects in nature.

Formerly this had not been observed, nor had there been any interest in it. In earlier times, the coming-into-being, the germinating, had been studied; now, one looked at all that was fading and crumbling into dust. Man's conception was heading toward atomism, whereas previously it had tended toward the continuous, lasting aspects of things. Since life cannot exist without death and all living things must die, we must look at and understand all that is dead in the world. A science of the inanimate, the dead, had to arise. It was absolutely necessary. The time that we are speaking about was the age in which mankind was ready for such a science. But we must visualize how this went against the grain of somebody who, like Berkeley, still lived completely in the old view.

The after-effects of what came into being then are still very much with us today. We have witnessed the triumphs of just those scientific labors that made Berkeley shudder. Until they were somewhat modified through the modern theory of relativity,[^9] Newton's theories reigned supreme, Goethe's revolt against them made no impression. For a true comprehension of what went on we must go back to Newton's time and see the shuddering of thinkers who still had a vivid recollection of earlier views and how they clung to feelings that resembled the former ones.

Giordano Bruno shrank from studying the dead nature that was now to be the object of study. He could not view it as dead in a purely mathematical manner of thought, so he animated the atoms into monads and imbued his mathematical thinking with poetry in order to retain it in a personal sphere. Newton at first proceeded from a purely mathematical standpoint, but then he wavered and defined space (which he has first completely divorced from man through his external mathematics) as God's sensorium. Berkeley in his turn rejected the new direction of thinking altogether and with it the whole trend towards the infinitesimal.

Today, however, we are surrounded and overwhelmed by the world view that Giordano Bruno tried to turn into poetry, that Newton felt uncomfortable about, and that Berkeley completely rejected. Do we take what Newton said—that space is a sensorium of God—seriously when we think in the accepted scientific sense today? People today like to regard as great thinkers those men who have said something or other that they approve. But if the great men also said something that they do not approve, they feel very superior and think: Unfortunately, on this point he wasn’t as enlightened as I am. Thus many people consider Lessing[^10] a man of great genius but make an exception for what he did toward the end of his life, when he became convinced that we go through repeated earth lives.

Just because we must in the present age come to terms with the ideas that have arisen, we must go back to their origin. Since mathematics has once and for all been detached from man, and since nature has been taken hold of by this abstract mathematics that has gradually isolated us from the whole of nature, we must now somehow manage to find ourselves in this nature. For we will not attain a coherent spiritual knowledge until we once again have found the spirit in nature.

Just as it is a matter of course that every living man will sooner or later die, so it was a matter of course that sooner or later in the course of time a conception of death had to emerge from the former life-imbued world view. Things that can only be learned from a corpse cannot be learned by a person who is unwilling to examine the corpse. Therefore certain mysteries of the world can be comprehended only if the modern scientific way of thinking is taken seriously.

Let me close with a somewhat personal remark.[^11] The scientific world view must be taken seriously, and for this reason I was never an opponent of it; on the contrary, I regarded it as something that of necessity belongs to our time. Often I had to speak out against something that a scientist, or so-called scientist, had made of the things that were discovered by unprejudiced investigation of the sphere of death. It was the misinterpretation of such scientific discoveries that I opposed. On this occasion let me state emphatically that I do not wish to be regarded as in any way an opponent of the scientific approach. I would consider it detrimental to all our anthroposophical endeavors if a false opposition were to arise between what anthroposophy seeks by way of spiritual research and what science seeks—and must of necessity seek in its field—out of the modern attitude.

I say this expressly, my dear friends, because a healthy discussion concerning the relationship between anthroposophy and science must come to pass within our movement. Anything that goes wrong in this respect can only do grave harm to anthroposophy and should be avoided.

I mention this here because recently, in preparing these lectures, I read in the anthroposophical periodical *Die Drei* that atomism was being studied in a way in which no progress can be made. Therefore, I want to make it clear that I consider all these polemics in *Die Drei* about atomism as something that only serves to stultify the relations between anthroposophy and science.

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[^1]: Giordano Bruno: Nola 1548–1600 Rome. Dominican, 1563–1576, a great traveler. Main works developed at the English court at the time of Elizabeth I. After he returned to Italy he was imprisoned because of heretical teachings, and was burned in Rome after 8 years in prison. See *Riddles of Philosophy*, and *The Spiritual Guidance of Man*, by Rudolf Steiner.

[^2]: Isaac Newton, Sir: Woolsthorpe, Lincolnshire 1642–1727 Kensington, London. Born as a dwarf-like child. Grew up on a farm and went to village and small town schools until 1661. After he was accepted at the University he was of medium talent until his “flaming” as a genius physicist, astronomer, mathematician 1663–1664. Professor in Cambridge 1669–1701, member of the Royal Society London 1662 and from 1703 until his death, its President. Main work: *Law of Gravitation, Mathematically Adapted to the Law of Motion from Kepler*, developed 1666, published 1687 in *Philosophiae Naturalis Principa Mathematica.* The idea of an infinitesimal mathematics came from Newton in 1663; three years later he had developed his differential mathematics. His *Optics*, 1704, put forth the division of light in color as well as emission theory.

 Later Newton lost all interest in physics, mathematics, and also in the destiny and consequences of his works. He turned towards chemical and alchemical experiments and studies of their old traditions. In his old age he was interested in religious-speculative studies. Before his death he compared his life with a day, in which a child is playing with sand and mussels and is not aware anymore of the cosmos at his back. Literature: J.W.N. Sullivan, *Isaac Newton 1642–1727* (London 1938).

[^3]: In Newton's second edition of his *Philosophiae Naturalis Principa Mathematica* of 1713 the definition is “But I do not define, because it is well known to all of us.”

[^4]: George Berkeley: Desert Castle, Thomastown, Ireland 1685–1753 Oxford. English philosopher and Anglican missionary, Bishop from 1734. Main works: *Treatise Concerning the Principle of Human Knowledge*, 1710; *Alciphron*, about ethics and free thinkers, 1732; *Siris*, concerning metaphysical questions. See: *Riddles of Philosophy*.

 Berkeley said: “One has to do it in such a way”: e.g., as in Paragraph 113 of *Principles of Human Knowledge.* In the writing *De Motu* ( *From Motion*) is written in Paragraph 43: “Motion, even though perceived clearly by the senses, was darkened, but not because of its own being, but far more through commentaries by learned philosophers.”

[^5]: In the work *Optice* by Newton, which is the Latin translation of his *Optics* (1704), published by Samuel Clarke in 1706 and approved with additions made by Newton, the formula appears only at the end of the book at the so-called 28th Problem: “If these questions are answered in the right way, could we then not ascertain the phenomenon that there is a being, unbodily, intelligent, which can perceive the endless universe as it were with its sense organs, and which seems to look into the innermost and is surrounding it with its all-embracing presence, while that in us that is usually feeling and thinking are only handed-down pictures in which we then perceive and observe our organs?” This thought seems not only to be Newton's, but was also presented in a similar way by Henry More, the Platonist from Cambridge who was a friend of Newton.

[^6]: For his polemic concerning Newton's color theory, see Rudolf Steiner, *Goethe the Scientist* (New York: Anthroposophic Press, 1950), especially the Introduction, “Goethe, Newton and the Physicists”; see also the forthcoming book, Heinrich O. Proskauer, *The Rediscovery of Color* (Spring Valley, NY: Anthroposophic Press).

[^7]: Leibnitz: Leipzig 1646–1716 Hanover. Philologist, mathematician, physicist, lawyer, statesman, priest. Mostly living at princely courts, traveling a lot. Discoverer of the Infinitesimal Calculus 1686, independently of Newton.

[^8]: In his writing *The Analyst* ( *The Analyst*, 1734, included in the book *Writings about the Origin of Mathematics and Physics*) the Table of Contents is in the form of 50 theses. No. 7, for example, is as follows: “Objections against the Secrets of Belief Which are Made Unfairly by Those who Admit Them in Science;” or No. 13: “The Rule for the Flux of Potency is Achieved through Unfair Reasoning;” and No. 22: “With the Help of a Double Mistake Analysts Come to their Truth, but not to Science, in which They do not even Know How They Came to Their Own Conclusions.” From the *Polemic Dispute*, which follows *The Analyst*, an example is: “No big name on this earth will ever cause me to take unclear things for clear ones. They think of one as if it were a crime to think one could see further than Sir Isaac Newton, even above him. I am convinced though that they speak for the feelings of many others. But there are also some ... who think and feel it unfair to copy some great man's shortcomings, and who see no crime in wanting to see further than Sir Isaac Newton, but further than the whole of mankind.”

[^9]: Prepared by Mach and Lorentz, developed by Einstein, *Special Theory of Relativity* 1905, *Common Theory of Relativity* 1916. Made it necessary to revise Newton's Mechanics with the help of non-Euclidean Geometry. See also *Riddles of Philosophy* and Georg Unger, *Von Bidden, Physicalischer Begriffe*, Part 3 (Stuttgart: 1967), pages 100–122.

[^10]: Lessing, Gottfried Ephraim: Kamenz/Lausitz 1729–1781 Brunswick. Dramatist, essayist, critic. Opens a new epoch in German literature and an. His last writing, “The Education of the Human Race,” (1780) finds it necessary to postulate reincarnation for the sake of the development of the human race. See *Riddles of Philosophy*.

[^11]: The reason was a controversy in the magazine *Die Drei* of 1921–1922, pages 1107 and 1114, as well as in the following years publication (see pages 172–330 about the reality of atoms). See Rudolf Steiner's *First Scientific Lecture Course: Light Course* (Forest Row, England: Steiner Schools Fellowship, 1977).