therefore unobservable, it "virtually disappears from the physical world, having no inter- action with it." It takes Professor Lovejoy seven pages of his Freedom and the Modern Physical World Picture 839 The Revolt against Dualism to explain why this does not make sense to him. I can only subscribe fervently to the proposition that it doesn't, but I am intrigued by the readiness with which the application of Heisenberg's Uncertainty Principle from cosmic to human values was made by men of distinction in the field of physical science. Schottky and Nernst were among the first ex- pressly to cast doubt, on the basis of the new light-quantum theory, upon the ideas of causality hitherto generally accepted. Born and Eddington are convinced that the final abandonment of strict cau- sality of all happening is really the last word. Haas in the following words: "If a precise description of atomic events in the classical sense is impossible in itself, the causal principle naturally loses its meaning for physics." Schroedinger himself appears of late inclined towards this interpretation. At any rate, he has expressly assented to the radical doubt concerning the traditional concepts of causality. And Bernhard Bavink now regards the feelings of freedom and the need for causality as "obviously only two sides of one and the same set of facts." If many have welcomed the new outlook as a settlement of the old conflict between freedom and determinism, others are strenu- ously opposed to such an idea. With C. G. Darwin they contend that the question is a philosophic one outside the region of the thought of physics. They point out that, if an experiment is carried out with a thousand electrons, what was a probability for one becomes nearly a certainty in the case of the larger mass. Now, to find room for free will within the realm governed by physical science, we have to suppose that the motions of our own bodies are in some way not free to obey the inexorable commands of the older mechanics. But even if laws have only the value of statistical statements, it is evident that the millions of electrons in our bodies will behave with extreme regularity and that any uncertainty would have to wait for a time fantastically longer than the estimated age of the universe. Sir Arthur Eddington, however, believes that the difficulty is not insuperable and that any break- down of determinism in the world will open the door slightly for indeterminism also in human psychology. To conclude this section of our study: Heisenberg's principle does not indeed affect the problem of freedom in a direct or causal way. There is no connection between the freedom within the atom and that within the human mind. However, the last word has been spoken regarding necessity in the physical world, and the entire burden of proof now rests on the determinist position. The argu- ment against free will based on man's inclusion in a closed system of cause and effect has now taken revenge from the mechanistic scheme from which it originated. 840 Freedom and the Modern Physical World Picture III The new physical world picture brings a number of emergences, advances from lower to higher levels, parallel with an increasing complexity, which J >lds some relation to the problem of freedom. I am not speaking now of those emergences to which we have become accustomed in the discussion of evolution: life, conscious- ness, the backbone, he nourishing breast, mind, personality. I am thinking of the ad ance in complexity which at certain points insensibly passes in ',) a new integration, governed by a new prin- ciple which with rel ~rences to the preceding stage must be termed transcendental. I aLil thinking of the impossibility of defining the boundary between emulsions and true solutions. I am thinking of the fact that the law of entropy can no longer be assumed to hold in the neighborhood of absolu~e zero. I am thinking of the well-known fact that out of existing units on a lower plane units on a higher plane are formed, from atoms molecules, from molecules micellae, from these the chromomeres and other constituents of the cells, from these the cells themselves, from them the multi- cellular organism, from these again symbioses, associations, etc., and in the case of human beings, finally, families, states, and alliances, which are all (to use Driesch's expression) "more than the SlL'11 of their p 's." From the atom . P ~ ~d stars, from amoeba to humanity, there is an almost uninterrupted series of steps in the formation of ever higher and more comprehensive wholes. And now there is an end to the physical domain. Always as man has delved deeper and deeper into the universe's struc- ture, he has found finer and more detailed construction. Atoms showed their electrons, but now the bottom has dropped out. Schroedinger and Heisenberg have spoken. There is an end to knowledge not because of a limit to endeavor but because of the nature of knowledge itself, Before the infinitesimal is reached, meaning ceases. As one who has not been professionally engaged in modern physical research, I may confess that nothing so intrigues me in the study of Philosophy of Science as the magnitude of results achieved with experimentation on values so extremely refined as to leave the imagination helpless in their presence. We have long known that in the more recent speculation on the nature of the physical world the quantity defined as the product of two con- jugated coordinates p and q was given the namE; action. We are also given to understand that the first form in which the quantum theory was stated implied that this quantity, the action, was atomic, i. e., that it could be transferred only in units of finite size. But we were not prepared to hear that thib radical change in our pic- ture of the physical world was produced by calculations dealing Freedom and the Modern Physical World Picture 841 with almost infinitely small particles. Prof. F. A. Lindemann of Oxford, addressing the British Institute of Philosophy in 1932, ex- plained that an oscillation of the balance-wheel of a watch in- volves some 1025 atoms of action. He goes on to say that the number of drops of water in the oceans of the world is of the order 1025• Yet it is in these regions of almost pure thought that quantum mechanics operates with its non,- commutative algebra. Within the atom the electron is thirty-eight times ten bil- lionths of a millimeter. I am well aware of the fact that, of course, according to the newest physics, all such measurements can be understood only if we employ a mathematical scheme which no longer operates by the ordinary rules of arithmetic. It is im- possible to see how a particle of the mass of an electron could be confined to a region of space as minute as a nucleus. This difficulty cannot be resolved on the basis of the older theories. They were developed to describe the properties of an atom in which the regions of space involved are of the order of, say, one billionth of an inch; they become meaningless when applied to phenomena confined to regions of space a thousand times smaller in extent, such as those required for a nucleus. It is a startling fact but pertinent to our investigation that, when nature is arranged in film.s of one millimicron, they suddenly possess other properties than those which it had in thicker layers. Referring to the quantum theory, General J . C. Smuts in 1931 said: "Even in physics, organization is becoming more important than the somewhat nebulous entities which enter into matter. The partial truth of mechanism is always subtended by the deeper truth of organicity, or holism. The emergence of this organic view of nature from the domain of physics is a matter of first- rate importance and must have very far-reaching repercussions for our eventual world-view." We are obviously only a short distance away from the goal of a final unified summary of all physical knowledge, and the question as to whether this goal will be the expression of a necessary or an indeterminate "thusness" is obvious and inevitable. This, of course, is eminently true as we pass upward from the crystal to the cell. There is an immense increase in complexity as we enter the domain of living matter. We can form mathe- matical representations of it, but our thought processes falter long before we reach the truth. Consider only that of carbohydrate molecules. Many varieties have one hundred to two hundred atoms each. Now, the smallest cell is one ten thousandth of a millimeter in diameter. It may have ten thousand protein molecules (Errera), and each molecule contains hundreds, some contain thousands, of atoms, and these are as real as cannon balls. Laid one layer deep, 842 Freedom and the Modern Physical World Picture it requires one thousand billion to complete one square inch. In weight the smallest cell is 1.6 times one sextillionth of a milligram, and a sextillionth gives you a figure with twenty-one zeros. According to recent investigations by American biochemists, the molecular weight of an enzyme gene is 50,000. Dr. Ralph Wyckoff of the Rockefeller Institute, who has estimated the molecular weight of the virus of the mosaic disease in the tobacco plant, places it at the tremendous figure of about 17,000,000, and with this com- plexity go functions as little related to the mere multiplying of atoms as the simple multiplying of bits of steel makes a type- writer. Prof. Hans Spemann of the University of Freiburg has reported the discovery of certain enzymelike substances whose chief function seems to be the guidance of simple cells into the formation of physical organs. Under their mysteriously operating influence the cells shape themselves into stomach, liver, ear, eye, brain, or whatever may be needed to complete the animal structure. Between the various levels of reality with which we deal in natural science, - I am not dealing with the philosophical levels of reality, such as sensation, ethical values, esthetics, etc., - there is something of the relation which exists between a regular polygon, inscribed in a circle, whose sides are being constantly doubled in number, so that the perimeter of the polygon will constantly ap- proach the circumference of the circle as its limit. In the case of a regular hexagon inscribed in a circle it is evident that as the number of the sides is increased by the ratio 2 in geometrical progression, we shall have the series 6, 12, 24, 48, 96, . . . ? That is to say, the number of sides will increase indefinitely toward the limit - infinity; and simultaneously - with every step in the pro- gression - each side of the hexagon will be diminished by one half its length, thus forming an inverse series progressing steadily to the limit - zero. To wit: 1, 1/2, %, lfs, ;.).6 .. • 0. The limit of the entire development, then, will be represented by the expression ? by 0, which signifies that the polygon will never attain its limit until the number of its sides becomes infinite and the length of each zero; which means again that this limit will not be attained until the polygon as such has been completely annihilated. In its place we have a figure totally different in kind therefrom, the circle. In short, the circle does not differ from the polygon in degree but in kind; it is not a polygon developed to an immense number of (finite) degrees, - i. e., a polygon developed to "the nth degree,"- not a "highly developed polygon" ; but an altogether different kind of entity. However, it is obvious that the greater the number of its sides, the more "circular" or "circlelike" does the inscribed polygon appear, and a polygon of a thousand sides (could we construct it) would doubtless be indistinguishable to the eye from a true circle, Freedom and the Modern Physical World Picture 843 though differing fundamentally therefrom. It is just this deception of mere appearances which we notice, for instance, in the grand spectrum of electromagnetic waves, in which the visible band of light rays is but a small fraction. It is this deceptive continuity that causes us to overlook the emergence of new processes at certain stages of diminishing wave-length. There are here subdivisions that belong to altogether distinct categories , or orders of existence. And as each new category arises, there is a closer approach to freedom. This is noticeable even in the case of the lowest one-cell or- ganism, the amoeba. Once the behavior of amoeba, stentor, and paramaecium were described exclusively in mechanistic terms (such as "tropisms"). Today we know that their activities involve the same characteristics as the behavior of higher animals. The amoeba seeks food and endeavors to escape from its enemies, in- cluding its cannibal fellow-amoebae. From here on upward, organic life is characterized by a kind of behavior which the word spontaneity defines more accurately than the phrase mechanical necessity. At the organic level factors enter upon the scene which we speak of as interests. And now, as we pass through higher levels of life, Nature seems to be struggling to free itself from the mechanistic chains. Means and end take the place of cause and effect. Determinism is not disproved; it is simply transcended. It has been pointed out by L . T. More of Cincinnati that the very idea of energy changes as we pass from the crystal to the celL The phrase "vital energy" is irritating to a physicist, and rightly so. Ordinary chemical laws no longer apply. This is the borderland between physical and psychical laws. As the structures become more complicated, a new method of calculation is needed, probably a Gestalt mathematics. For elementary psychical structures do not unite additively (as do physical forces in parallelogram of force), but the lower Gestalt merges into the higher. This demand for a new Gestalt mathematics for the discussion of biological prob- lems has actually been made by Friedman and by Bavink. The conception of causal activity common to the sciences which study inorganic nature cannot be transferred without further criticism to the examination of life and mind. An astronomer, we are told, given three good positions of a comet, can with reasonable accuracy predict its appearance a thousand years hence. This same astronomer, given three good positions of a robin on the lawn, cannot predict the direction of its movement a second hence. From chance combinations the living cell is distinguished as being a true biological whole; it really forms a Gestalt in Kohler's sense, that is, a system in which each part contributes towards the existence of the whole. As we proceed from the cell to the 844 Freedom and the Modern Physical World Picture thinking mind, we observe the emergence of new integrations passing through the biological field into the spher e of human action. The beginnings of all human faculties are to be found in animals, but in order to turn such a faculty into the power of a human being, a certain something must be added. This some- thing is what is usually termed mind. It is obviously related to the low physical life of animals in the same way that the organic is related to the inorganic. One does not exclude the other but includes it and brings it into a higher and more comprehensive region. In other ' words, we have here a new emergent, charac- terized by self- consciousness (the ego) and the feeling of pos- sessing freedom of will. As complexity increases, calculability decreases. For man there is not only the extremely complicated body structure but also the fact that his environmen t is not only his world, as the animal, but the world. Thence, by another evolution of the polygon into a circle, the field of values - the free moral agent and the lover of beauty. On yet a higher level, the spiritual, and with it the liberty of the children of God. "There is something" - wrote, not a dreamer and poet, not a mystic theologian, but a hard-headed physicist, Professor More of Cin- cinnati, less than ten years ago, - "There is something that is not dust at all, though as in all things else it is found therein ; something that is the Order of the Cosmos and the Beauty of the World; that lives in all things living and dwells in the mind and soul of man; something not fulfilled in physics, which vivifies the dust and makes the dry bones live. You can call it entelechy, you may call it the Harmony of the World, you may call it the elan vital, you may call it the Breath of Life. Or you may call it, as it is called in the Story-book of Creation and in the hearts of men - you may call it the Spirit of God." St. Louis, Mo. TH. GRAEBNER