# Popular Science Monthly/Volume 5/May 1874/The Limits of our Knowledge of Nature

(1874)
The Limits of our Knowledge of Nature by Emil du Bois-Reymond

 LIMITS OF OUR KNOWLEDGE OF NATURE.

By Professor EMIL DU BOIS-REYMOND,[1]

OF THE UNIVERSITY OF BERLIN.

TRANSLATED FROM THE GERMAN, BY J. FITZGERALD, A. M.

JUST as a world-conqueror of ancient times, as he halts for a day in the midst of his victorious career, might long to see the boundaries of the vast territories he has subjugated more clearly defined, so that here he may levy tribute of some nation hitherto exempt, or that there he may discern some natural barrier that cannot be overcome by his horsemen, and which constitutes the true limit of his power, in like manner it will not be out of place, if Natural Science, the world-conqueror of our times, resting as on a festive occasion from her labor, should strive to define the true boundaries of her immense domain. And this undertaking I hold to be all the more legitimate, because I believe there exist two widely-diffused errors with regard to the limits of natural science, and because I think it possible that from the study of such a question, despite its apparent triviality, some advantage might be derived even by those who do not at all share in the errors of which I speak.

Hence I propose to investigate the limits of natural science; and first I must say what natural science is.

Natural science—or, more definitely, knowledge of the physical world with the aid of and in the sense of theoretical natural science—means the reduction of all change in the physical world to movements of atoms produced independently of time by their central forces; or, in other words, natural science is the resolution of natural processes into the mechanics of atoms. It is a fact of psychological experience that, where such a resolution is practicable, our desire of tracing things back to their causes is provisionally satisfied. The propositions of mechanics are mathematically presentable, and have in themselves the same apodictic certainty as the propositions of mathematics. As the changes of the physical world are reduced to a constant sum of potential and kinetic energy, which is inseparable from a constant quantity of matter, there remains in these changes themselves nothing further that needs explanation.

What Kant says in the introduction to his "Metaphysical Elements of Natural Science," viz., "that "in each special natural science the amount of science, properly so called, is equal to the amount of mathematics it contains"—must, therefore, be further narrowed down, and instead of mathematics we must read atomic mechanics. Plainly this was Kant's own meaning, when he withheld from chemistry the title of science, and relegated it among experimental sciences. It is not a little noteworthy that in our own times chemistry, being forced, by the discovery of the doctrine of substitution, to surrender electro-chemical dualism, has been apparently still further removed from the grade of a science, in this sense of the word.

If we were to suppose all changes in the physical world resolved into atomic motions, produced by constant central forces, then we should know the universe scientifically. The condition of the world at any given moment would then appear to be the direct result of its condition in the preceding moment, and the direct cause of its condition in the subsequent moment. Law and chance would be only different names for mechanical necessity. Nay, we may conceive of a degree of natural science wherein the whole process of the universe might be represented by one mathematical formula, by one infinite system of simultaneous differential equations, which should give the location, the direction of movement, and the velocity, of each atom in the universe at each instant. "A mind," says Laplace, "which at a given instant should know all the forces acting in Nature, as also the respective situation of the beings of which it consists, provided its powers were sufficiently vast to analyze all these data, could embrace in one formula the movements of the largest bodies in the universe, and those of the smallest atom; nothing would be uncertain for such a mind, and the future, like the past, would be present to its eyes. The human intellect offers, in the perfection to which it has brought astronomy, a faint idea of what such a mind would be."

Indeed, just as in lunar equations the astronomer need give but a negative value to time, in order to determine whether, when Pericles embarked for Epidaurus, the sun was eclipsed for the Piræus, so could the mind imagined by Laplace, by suitable application of its universal formula, tell us who was the Man in the Iron Mask, or how the President was lost. As the astronomer foretells the day whereon years hence a comet emerges again out of the depths of space into the heavens, so could that mind by its equations determine the day whereon the Greek cross shall glitter from the mosque of St. Sophia, or when England shall have consumed the last of her coals. If in his universal formula he set down t${\displaystyle =}$–∞, he could discover the mysterious primeval condition of all things. He would in the boundless space see matter already in motion, or unequally distributed, for, were the distribution equable, there could never be disturbance of equilibrium. Suppose he lets t grow ad infinitum in the positive sense, then he could tell whether Carnot's theorem threatens the universe with icy immobility in finite or only in infinite time. For such a mind the hairs of our heads would be numbered, and without his knowledge no sparrow could fall to the ground. Being a seer expert both in the past and the future, for him, as D'Alembert, in the Introduction to the Encyclopædia, expressed it, giving utterance to the germ of Laplace's thought, "the universe would be one single fact and one great truth."

In Leibnitz, too, we find Laplace's thought, and even better developed in some measure than in Laplace himself, inasmuch as Leibnitz conceives of this mind as being endowed with senses and with technical powers of corresponding perfection. Bayle brought against the doctrine of Preëstablished Harmony the objection that it supposes the human body to be like a vessel that makes for its harbor by means of its own forces; Leibnitz replied that this is not so impossible as Bayle holds it to be. "There is no doubt," says he, "that a man might construct a machine that could for some time move about in a city, and turn accurately at certain street-corners. An incomparably more perfect, though still finite mind, might foresee and obviate an incomparably greater number of obstacles. So true is this, that if the world is, as some suppose, only a compound of a finite number of atoms, which move in accordance with the laws of mechanics, it is certain that a finite mind might be elevated sufficiently to comprehend and to foresee with mathematical certitude whatsoever is to occur therein within a given time. And thus this mind could not only construct a ship capable of making a given port by itself, provided the proper force and direction were supplied, but it could even construct a body capable of imitating the actions of man."

It need not be said that the human mind will ever remain very remote from this degree of acquaintance with Nature. To show how far we are from even the beginnings of such knowledge, we need but make one observation. Before our differential equations could be brought into the universal formula, all natural facts would have to be reduced to the motions of a substantially undifferentiated and consequently property-less substratum of what appears to us as heterogeneous matter: in other words, all quality would have to be explained by the arrangement and the motion of this substratum.

This is entirely in accord with what we know of the senses. It is universally conceded that the sense-organs and the sense-nerves carry to their appropriate cerebral regions, or, as Job. Müller calls them, "sense-substances" (Sinnsubstantzen), a motion that is in all cases ultimately identical. As in the experiment suggested by Bidder and successfully made by Vulpian on the nerves of taste, and those of the muscles of the tongue, the sensory and motor nerves, on being cut across, so heal together that excitation of the one class of fibres is transmitted by the cicatrix to the other class; in like manner, were the experiment possible, fibres from different sets of nerves would blend perfectly together. With the nerves of vision and of hearing severed, and then crossed with each other, we should with the eye hear the lightning-flash as a thunder-clap, and with the ear we should see the thunder as a series of luminous impressions. Sense-perception, therefore, as such, has its rise in the "sense-substances." It is these substances that translate the identical excitation of all the nerves into sense-perceptions, each set, according to its own nature, acting as carriers of Joh. Müller's "specific energies," and so giving quality. The Mosaic dictum, "There was light," is physiologically false. Light first was when the first red eye-point of an infusorial animal for the first time distinguished light from darkness. In the absence of the sense-substance of sight and hearing, this bright, glowing, resonant world around us would be dark and voiceless.

And voiceless and dark in itself, i. e., property-less, as the universe is on subjective decomposition of the phenomena of sense, so is it also from the mechanical stand-point, gained by objective contemplation. Here, in place of sound and light, we have only the vibrations of a primitive, undifferentiated matter, which here has become ponderable, and there imponderable.

But, however well grounded these views may be in general, nothing, as we may say, has been done toward carrying them out in detail. The philosopher's stone that should transmute into one another the as yet unanalyzed elements, and produce them from a higher element, if not from primeval matter itself, must be discovered before the first conjecture as to the development of apparently heterogeneous, from actually homogeneous matter, becomes possible.

Though the human mind will ever remain very remote from the mind imagined by Laplace, yet this is only a matter of degree, in some measure like the difference between a given ordinate of a curve and another immeasurably greater, though still finite, ordinate of the same curve. We resemble this mind, inasmuch as we conceive of it. We might even ask whether a mind like that of Newton does not differ less from the mind imagined by Laplace, than the mind of an Australian or of a Fuegian savage differs from the mind of Newton. In other words, the impossibility of stating and integrating the differential equations of the universal formula, and of discussing the result, is not fundamental, but rests on the impossibility of getting at the necessary determining facts, and, even where this is possible, of mastering their boundless extension, multiplicity, and complexity.

Thus the knowledge of Nature possessed by the mind imagined by Laplace, represents the highest thinkable grade of our own natural science. Hence we may lay this down as the basis of our inquiry as to the limits of this science. Whatever would remain unknown to such a mind, must be perfectly hidden away from our minds, which are confined within much narrower bounds.

There are two positions where even the mind imagined by Laplace would strive in vain to press on farther, and where we have to stand stock-still.

In the first place we must observe that the knowledge of Nature already spoken of as provisionally satisfying our desire of tracing things to their causes, in reality does no such thing, and is not knowledge at all. The conception of the world as consisting of minute parts that have always existed, and that are indestructible, and whose central forces produce all motion, is only a sort of substitute for an explanation. As has been remarked, it reduces all changes in the physical world to a constant sum of forces and a constant quantity of matter, and thus leaves in the changes themselves nothing that requires explanation. Given the existence of this constant, we can, in our joy for this new insight, be content for a little while; but soon we long to penetrate deeper, and to comprehend it in its own substance. The result is, as all know, that within certain limits the atomic theory is serviceable, and even indispensable for our physicomathematical studies, but that when we overtax it, and make demands upon it that it is not intended to meet, then as a corpuscular philosophy it leads to interminable contradictions.

A physical atom, i. e., a mass which, as compared with bodies with which we are acquainted, is held to be infinitesimal, but yet, regardless of its name, ideally divisible, and to which properties or a state of motion is attributed, whereby the behavior of a mass consisting of countless such atoms is explained—such a notion is a fiction quite congruous in itself, and under certain conditions a useful fiction in mathematical physics. But, latterly, atoms have been as far as possible discarded in favor of volume-elements of bodies regarded as continuous.

A philosophical atom, on the other hand, i. e., a presumably indivisible mass of inert and inefficient substratum, from which proceed through vacant space efficient forces, is, on closer consideration, a chimera.

For, if this indivisible, inert, by itself ineffective, substratum is to have any actual existence, it must occupy a certain space, however small; and, in that case, we cannot see how it can be indivisible. Then, too, it can occupy space only on condition that it possesses perfect hardness, i. e., that it resists the intrusion into the same space of any other body, in virtue of a force exerted out to its own limits, though not overstepping them, which excludes all other bodies, and which must therefore be greater than any other given force. Not to mention any of the other difficulties which meet us here, we may observe that the substratum is thus represented as no longer inefficient.

But if with the dynamists we conceive of the substratum as being only the middle point of the central forces, then the substratum does not occupy space, for a point is the very negation of space in space. Hence we have nothing from which the central forces spring; nothing that could be inert, like matter.

The idea of forces operating at a distance through vacant space is unthinkable, nay, even self-contradictory; though, since Newton's day, owing to a misunderstanding of his doctrine, and in the face of his express warning, it has been a current conception among investigators of Nature. If with Descartes and Leibnitz we consider all space as occupied, and all motion produced by transfer to bodies in contact, the origin of motion is indeed reduced to a concept derived from our sense-experiences, but this view has also its difficulties. To mention only one of these, it is impossible in this hypothesis to explain the different densities of bodies from different combinations of a homogeneous original matter.

The origin of these contradictions is readily detected. They have their root in our incapacity to conceive of any thing save what we have experienced by either our external or our internal sense. In our endeavor to analyze the physical world, we start out from the divisibility of matter, the parts being to our eyes something simpler and more primitive than the whole. When in thought we carry on this division of matter ad infinitum, we act in perfect accordance with our sense-perceptions, and we meet with no obstacle in the process. But we make no advance whatever toward an understanding of things, since we, in fact, carry over into the region of the minute and the invisible the concepts we obtained in the region of the gross and the visible. Thus it is that we acquire the notion of the physical atom. If now we arbitrarily stop the process of dividing at some point where we are supposed to have reached philosophical atoms, that are indivisible, perfectly hard, and furthermore per se inefficient, being merely the carriers of the central forces, we are expecting that a matter which we think of under the concept of matter as known to us should, without the aid of any new principle of explication, develop new primordial properties, to explain the nature of bodies. Thus we commit the error which is manifested in the previously-mentioned contradictions.

No one, that has bestowed any thought on this subject, can fail to acknowledge the transcendental nature of the obstacles that face us here. However we try to evade them, we ever meet them in one form or another. From whatever side we approach them, or under whatsoever cover, they are ever found invincible. The ancient Ionian physical philosophers were no more helpless than we in presence of this difficulty. The natural sciences, with all the progress they have made, have availed naught against it, nor will their future progress be of any greater effect. We shall never know any better than we now do (to use the words of Paul Erman), "was hier im Raume spukt," the spectre that haunts the world of matter. For even the mind imagined by Laplace, exalted as it would be high above our own, would in this matter be possessed of no keener insight than ourselves, and hence we despairingly recognize here one of the limitations of our understanding.

But if we turn aside from this primordial limit, and postulate matter and force as understood, then, as we have said, the physical world is intelligible ideally. From the original condition of a revolving nebular sphere, the Kantian hypothesis, as further developed by Helmholtz with the aid of the mechanical theory of heat, leads to a conception of the origin of our planetary system. We first see our earth revolving in its orbit as a glowing fluid drop with an atmosphere of undefinable constitution. In the course of immeasurable intervals of time we see it become coated over with a crust of indurating primordial rock; sea and land are divided, eruptions of hot carbonic acid break up the granite, and give material for strata of alkaline earths, and finally the conditions arise under which life became possible.

Where and under what form life first appeared, whether at the bottom of the deep sea, as bathybius protoplasm, or whether with the cooperation of the still excessive ultra-violet solar rays, with still higher pressure of carbonic acid in the atmosphere, who can tell? But Laplace's Mind could tell, with the aid of the universal formula. For, when inorganic matter coalesces to form organic matter, there is only a question of motion, of the arrangement of molecules into states of more or less stable equilibrium, and of an exchange of matter produced partly by the tension of the molecules, and partly by motion from without. What distinguishes living from dead matter, the plant and the animal, as considered only in its bodily functions, from the crystal, is just this: in the crystal the matter is in stable equilibrium, while a stream of matter pours through the organic being, and its matter is in a state of more or less perfect dynamic equlibrium, the balance being now positive, again approaching zero, and again negative. Hence, without the interference of extraneous masses and forces, the crystal will remain forever what it is, whereas the organic being depends for its existence on certain exterior conditions, transforms potential into kinetic energy, and vice versa, and has a definite duration in time. Thus we see, that though there is no fundamental difference between the forces operating in the crystal and in the organized being, still the two are incommensurable, just as a simple building is incommensurable with a factory into which coal, water, and raw material pass, on this side, while at the other side carbonic acid, water, vapor, smoke, ashes, and the products of the machinery, are sent out. The building we may regard as so made up of parts, each resembling the total result, that, like the crystal, it is separable into like parts; the factory, like the organic being (if we abstract from the cellular constitution of the latter, and the divisibility of sundry organisms), is an Individual.

It is therefore an error to recognize, in the first appearance of living things on the earth, any thing supernatural, or any thing else save an exceedingly difficult mechanical problem. This is one of the two errors to wich I proposed to call attention. The other limit of natural science is not here, any more than in the fact of crystallization. Were we able to create the conditions under which organic beings had their rise, which we are not even able to do for all crystals, then, according to the principle of actualism, we could produce organic beings now in the same way that they were first produced. And even though we never could succeed in observing the original production of organisms—to say nothing of experimenting on it—that fact would constitute no absolute objection to our view. Were matter and force intelligible to us, the world would not cease to be so, even though we should conceive the earth to be covered with the most luxuriant growth of vegetable life, from its emerald equatorial girdle to the last lichen-gray cliffs of the pole; and it would remain equally so, whatever share in the formation of the vegetable world we might concede to the laws of organic development, or to natural selection.

But, for reasons which will readily appear, we must leave out of view, in the present consideration, the now well-known indispensable aid rendered by insects in the fertilization of plants. For the rest, the grandest picture ever sketched of a primeval forest in the tropics by Bernardin de St. Pierre, Von Humboldt, or Pöppig, offers to the view of theoretical science absolutely nothing but matter in motion. This, I think, is the new and very simple form that can be given to the argument against "life-force," in the sense of the vitalists.

But now there comes in, at some point in the development of life upon the earth which we cannot ascertain—the ascertainment of which does not concern us here—something new and extraordinary; something incomprehensible, again, as was the case with the essence of matter and force. The thread of intelligence, which stretches back into negatively-infinite time, is broken, and our natural science comes to a chasm across which is no bridge, over which no pinion can carry us: we are here at the other limit of our understanding.

This other incomprehensible is consciousness. I will now, conclusively as I believe, prove that not only is consciousness unexplainable by its material conditions in the present status of science, which every one will readily admit, but that, even in the nature of things, it never can be explained by these conditions. The contrary opinion, that we must not give up all hope of getting at consciousness from its material conditions, and that in the course of hundreds or thousands of years the mind of man, having invaded now unthought-of realms of knowledge, might succeed where we fail—this is the other error which I propose to combat here.

I use the term "consciousness" designedly, the question here being only as to the fact of an intellectual phenomenon, of any kind whatsoever, even of the lowest grade. There is no need to think of Watt, engrossed with his parallelogram, nor of Shakespeare, Raffaelle, or Mozart, engaged in producing their grand creations, in order to have an instance of a mental fact unexplainable by its material conditions. Just as the most powerful and best developed muscular performance of man or animal is in fact no more obscure than the simple-contraction of a single muscle—as the single secretory cell involves the whole problem of secretion—so the most exalted mental activity is no more incomprehensible in its material conditions than is the first grade of consciousness, i. e., sensation. With the first awakening of pleasure or pain, experienced on earth by some creature of the simplest structure, appeared that impassable gulf, and then the world became doubly incomprehensible.

Few subjects have been more perseveringly studied, more written about, or more hotly disputed, than that of the connection between body and soul in man. All the philosophical schools, as also the fathers of the Church, have had their own opinions upon this matter. The more recent philosophy is less concerned with this question; but its beginnings in the seventeenth century abounded in theories of the interaction of matter and mind.

Two hypotheses set up by Descartes shut off that philosopher from all possibility of understanding this interaction. First, he held that body and soul are two different substances, united by God's omnipotence, and that, since the soul has no extension, they can come into contact only at one point, to wit, in the so-called pineal gland of the brain. He held, secondly, that the quantity of motion in the universe is constant. The more clearly it seems to follow from this that the soul cannot produce motion in matter, the more amazed are we on seeing Descartes, in order to save free-will, represent the soul as simply producing motion in the pineal gland, in such a way that the animal spirits, or, as we would say, the nervous principle, may flow out to the appropriate muscles. Conversely, the animal spirits, excited by sense-impressions, give motion to the pineal gland, and then the soul, which is in association with the latter, notes the motion.

Descartes's immediate followers, Clauberg, Malebranche, Geulincx, endeavored to correct this patent error. They insist upon the impossibility of interaction between mind and matter, as being two distinct substances. But, in order to understand how the soul nevertheless moves the body, and is moved by it, they suppose that the soul's willing is the occasion for God each time moving the body in harmony with the soul's desire. Conversely, sense-impressions give occasion to God to modify the soul in conformity with themselves. The causa efficiens, therefore, of the changes in the body wrought by the soul, and vice versa, is always God, and the soul's willing and the sense-impressions are but the causæ occasionales of the perpetually-renewed interventions of Omnipotence.

Finally, Leibnitz explained this problem on the hypothesis, originated, as it would appear, by Geulincx, of body and soul resembling two watches, with synchronous movement. This, says he, may occur in three ways: 1. The two watches might so influence one another by means of oscillations, conveyed to a common attachment, that their movements should be synchronous, as was observed by Huyghens, and as was exemplified, in the beginning of the present century, by Breguet, in a contrivance for rendering the action of two watches more uniform. 2. One of the watches might be constantly regulated, so as to keep it uniform with the other. 3. The watchmaker might be so skillful as to be able to make both go together, though independent of one another. As between body and soul, the first contrivance is clearly impossible. The second, which agrees with the occasionalist doctrine, is unworthy of God, whom it employs as a Deus ex machina. The third then remains, and here we find again Leibnitz's peculiar doctrine of Preëstablished Harmony.

But these and all similar views are discredited by the more recent investigations of natural science, and are void of all influence in modern thought, by reason of the dualistic principle on which they rest, in conformity to their semi-theological origin. The propounders of these theories start out from the hypothesis of a spiritual substance absolutely diverse from the body, viz., the soul, and their study is to investigate its association with the body. They find that the coupling of these two substances is possible only by a miracle, and that even after this first miracle another association of the two cannot take place except by means of a fresh miracle, or of a continuous miracle, dating from creation. This consequence they give out as a new solution of the problem, though they never took sufficient pains to inquire whether they themselves have not attributed to the soul such a nature that mutual interaction between it and the body is unthinkable. In short, the most satisfactory demonstration of the impossibility of the interaction of soul and body leaves room to question whether the premises were not arbitrary, and whether consciousness may not be regarded as simply the effect of matter, and so perhaps understood. Hence, the student of natural science demands that the argument to show that mental phenomena are unintelligible from their material conditions shall have nothing to do with any hypothesis as to the origin of such phenomena.

Astronomical knowledge of a material system I call such a knowledge of all its parts, their respective positions and their motions, that their position and motion, at any given time, past or future, may be calculated with the same certainty as we calculate the position and motion of the heavenly bodies, by means of previous absolute accuracy of observation and perfection of theory. To get the differential equation whose integration will give the desired results, we need only have, as it were, three positions of the parts of the system; i. e., we must know the position of the parts of the system at three successive instants, separated by two differentials of time. From the difference of the courses run in the equal and infinitesimal periods of time between the three we deduce the forces acting upon the system and within it.

In our incapacity to comprehend matter and force, astronomical knowledge of a material system is the completest knowledge we can expect to acquire of it. With this our instinct of causality is wont to be satisfied, and this is the kind of knowledge that would be possessed even by the Mind imagined by Laplace, if it made due use of its universal formula.

Now, suppose we had such astronomical knowledge as this, with regard to a muscle, a gland, an electrical organ, or a luminiferous organ in the state of excitation; of a ciliary cell, a plant, an ovum in contact with the sperm, or of a fruit at some stage of its development. In that case we should possess the fullest possible knowledge of these material systems, and our instinct of causality would be so far satisfied that we should desire nothing more, save to know what matter and force themselves are. Muscular contraction, secretion by the gland, the shock of the electrical, and the shining of the luminiferous organ; ciliary action, growth and chemical action of the cell in the plant; impregnation and development of the egg—all these phenomena, now hopelessly obscure, would be as evident for us as the movements of the planets. On the contrary, if we make a like supposition of astronomical knowledge, with regard to the brain of man, or even the soul-organ of the lowest animal, whose mental activity may be restricted to the sensation of pleasure and pain, then, so far as all the material phenomena are concerned, our knowledge would be as perfect, and our instinct of causality as satisfied, as in the case of muscular contraction or secretion, provided we had astronomical knowledge of muscles or glands. The involuntary actions of the centres, and those not necessarily connected with sensation—reflex action, simultaneous action, respiratory movements, growth and decay of the brain and spinal cord—would be completely understood. Further, those phenomena which are always, and hence necessarily, simultaneous with mental phenomena, would also be perfectly understood. And it certainly were a great triumph of human knowledge if we were able to say that, on occasion of a given mental phenomenon, a certain definite motion of definite atoms would occur in certain definite ganglia and nerves. It would be profoundly interesting if we could thus, with the mind's eye, note the play of the brain-mechanism, in working out a problem in arithmetic, after the manner of a calculating-machine; or, even if we could say what play of the carbon, hydrogen, nitrogen, oxygen, phosphorus, and other atoms, corresponds to the pleasure we experience on hearing musical sounds; what whirl of such atoms answers to the climax of sensual enjoyment; and what molecular storm to the raging pain we feel when the trigeminus nerve is misused. The intellectual enjoyment afforded by Fechner's preliminary studies in psychophysics, and by Donders's measurements of the duration of simpler mental operations, gives reason to expect that such direct insight into the material conditions of mental phenomena would be highly instructive.

Still, as regards mental operations themselves, it is clear that, even with astronomical knowledge of the mind-organ, they would be as unintelligible as they are now. Were we possessed of such knowledge, they would still remain perfectly unintelligible. Astronomical knowledge of the brain—the highest grade of knowledge we can expect ever to have—discloses to us nothing but matter in motion. But we cannot, by means of any imaginable movement of material particles, bridge over the chasm between the conscious and the unconscious.

Motion can only produce motion, or be converted back into potential energy. Potential energy can only produce motion, maintain static equilibrium, or exert pressure or traction. The sum of energy, however, remains the same. Beyond this law nothing can go in the physical world, nor can any thing fall short of it; the mechanical cause passes completely into the mechanical effect. Hence the mental phenomena, which in the brain appear in company with material phenomena, are, so far as our understanding is concerned, void of sufficient basis. They lie beyond the law of causality, and hence are unintelligible, like a mobile perpetuum. But they are also unintelligible on other grounds.

True, on superficial observation, it looks as though certain mental operations and conditions might be intelligible to us, from a knowledge of the material phenomena of the brain. Among such mental phenomena I might reckon memory, association of ideas, habit, specific talents, etc. It needs but little reflection to show that this is an error. We should only be acquainted with certain inner conditions of the soul's life, which are of about equal import with the external conditions created by sense-impressions; but we should know nothing about the origin of mental life in virtue of these conditions.

What conceivable connection subsists between definite movements of definite atoms in my brain, on the one hand, and on the other hand such (for me) primordial, indefinable, undeniable facts as these: "I feel pain, or pleasure; I experience a sweet taste, or smell a rose, or hear an organ, or see something red," and the immediately-consequent certainty, "Therefore I exist?" It is absolutely and forever inconceivable that a number of carbon, hydrogen, nitrogen, oxygen, etc., atoms should not be indifferent as to their own position and motion, past, present, or future. It is utterly inconceivable how consciousness should result from their joint action. If their respective positions and their motion were not indifferent to them, they would have to be regarded as each possessed of a consciousness of its own, and as so many monads. But this would not explain consciousness in general, nor would it in the least assist us in understanding the unitary consciousness of the individual.

That it is and ever will remain utterly impossible to understand higher mental operations from the mechanics of the cerebral atoms (supposing them to be known), needs not to be proved. Yet, as has been already remarked, we need not consider the higher forms of mental activity, in order to add weight to our argument. But its force is intensified by contrasting the absolute ignorance wherein astronomical knowledge of the brain leaves us with regard to the origin of the lowest mental phenomena, and the complete solution of the highest problems of the physical world which we get from such knowledge. A brain that should, from one cause or another, be unconscious—for instance, one that should sleep without dreaming—would, had we astronomical knowledge of it, hold no secret; and, if we possessed astronomical knowledge of the rest of the body also, then the whole human machine, with its respiration, its heart-beats, its exchanges of materials, its heat, etc.—in short, every thing short of the essence of matter and force, would be fully deciphered. The dreamless sleeper is comprehensible to us, like the universe previous to consciousness. But, as, on the first awakening of consciousness, the world became doubly incomprehensible, so too is it with the sleeper, at the first appearance of a faint image in dreaming.

The irreconcilable conflict of the mechanical view of the universe with freedom of will, and hence indirectly with ethics, is no doubt a matter of high importance. The ingenuity of thinkers in all times has been exhausted in trying to reconcile them, and this question will afford exercise to the mind of man forever. To say nothing of the fact that free-will may be denied, whereas pleasure and pain are unquestionable; desire, which gives the impetus to exertion, and hence gives occasion to act, or not to act, is necessarily preceded by sense-impressions. Hence it is to the problem of sensation, and not, as I have once said, to that of free-will, that analytical mechanics leads.

And here is the other limit of our knowledge of Nature. It is no less absolute than the first limit. For two thousand years, despite all the advances made by natural science, mankind has made no substantial progress toward the understanding of matter and force, any more than toward the understanding of mental activity from its material conditions. And so will it ever be. Even the Mind imagined by Laplace, with its universal formula, would, in its efforts to overstep these limits, be like an aëronaut essaying to reach the moon. In its world of mobile atoms, the cerebral atoms are in motion indeed, but it is a dumb show. This Mind views their hosts, and sees them crossing each other's course, but does not understand their pantomime; they think not for him, and hence, as we have already seen, the world of this Mind is still meaningless.

In this Mind we have the measure of our own capacity, or rather our impotence. Our knowledge of Nature is thus shut up between two limits, the one forevermore determining our incapacity to comprehend matter and force, the other determining our inability to understand mental facts from their material conditions. Between these limits the man of science is lord and master; he dismembers and builds up, and no one durst say wherein his knowledge and his power are circumscribed. Beyond these limits he cannot now, nor can he ever, go.

But the more frankly the student of natural science acknowledges these appointed limits, and the more humbly he is reconciled to this ignorance, the more profoundly conscious is he of his right inductively to fashion his own views as to the relations between mind and matter, with perfect freedom, and untrammeled by myths, dogmas, or time-honored philosophies.

He sees material conditions in a thousand ways influencing mental life. To his unprejudiced mind there seems no reason to doubt that sense-impressions are really communicated to the so-called Soul. He sees the human mind grow with the brain as it were, and, according to the empiricists, he finds that the actual forms of his thought are constituted by means of external perceptions. In sleep, and in dreams, in fainting, in intoxication and narcosis, in the delirium of fever and in inanition, in mania, epilepsy, idiocy, microcephaly—in a thousand morbid states he sees the soul to be dependent on the constant or transient condition of the brain. No theological prejudice prevents him, as it did Descartes, from recognizing in the souls of animals the relatives of the human soul, and less perfect members of the same series of development. On the contrary, he sees that in the vertebrates those parts of the brain which physiological research and pathological experience prove to be the seat of the higher mental activities keep pace, in their comparative development, with the growth of these activities. Where mental capacity makes the immense leap from the anthropoid apes to man which is indicated by the power of speech, we find a corresponding leap in cerebral mass. The varied arrangement of similar elementary particles in the invertebrates instructs the investigator of Nature that here, as in other organs, there is question less of the general architecture than of the structural elements.

With awe and wonder he regards the microscopic molecule of nervous substance which is the seat of the laborious, constructive, orderly, loyal, dauntless soul of the ant. Finally, the development theory, coupled with the doctrine of natural selection, forces upon him the theory that the soul came into being as the result, gradually attained, of certain material combinations, and that probably, like other heritable endowments that are of use to the individual in the struggle for life, it has risen and perfected itself up to its present state through a countless series of generations.

Now, if the ancient thinkers found every interaction between body and soul unintelligible and impossible on their theories, and if their undoubted simultaneous cooperation is to be explained only by a Preestablished Harmony of the two substances, then the notion they formed of the soul, in conformity with their scholastic conceptions, must have been erroneous. The necessity of a scholastic conclusion so plainly in conflict with the reality, is, as it were, an apogogical demonstration of the falsity of their premises. In his simile of the two watches, Leibnitz, as has been well observed by Fechner, overlooked the fourth and simplest supposition, viz., that perhaps the watches, whose simultaneous action is to be accounted for, may be after all only one. Whether we shall ever understand mental phenomena from their material conditions is a very different question from that other, viz., whether these phenomena are the product of material conditions. The former question might be decided in the negative without in the least affecting the latter, to say nothing of negativing it.

In the passage we have already cited, Leibnitz asserts that a mind incomparably higher than the human mind, but yet finite, could, if it were possessed of senses and technical powers of like perfection, form a body capable of mimicking the actions of man. He does not say that a man could be formed, for in his view the automaton of flesh and bone, which he regards as soulless, even as Descartes regarded all animals, still lacks the mechanically-incomprehensible soul-monad. The difference between Leibnitz's point of view and our own becomes very evident here. Imagine all the atoms whereof Cæsar was made up at a given moment, say as he stood at the Rubicon, to be by mechanical power brought together, each in its own place, and possessed of its own velocity in its proper direction. In our view Cæsar would then be restored mentally as well as bodily. This artificial Cæsar would at the first instant have the same sensations, ambitions, imaginings, as his prototype on the Rubicon, and the same memories, the same inherited and acquired faculties, etc. Suppose several artificial figures of the same model to be simultaneously formed out of a like number of other carbon, hydrogen, etc., atoms. What would at the first moment be the difference between the new Cæsar and his duplicate, beyond the differences in the places where they were formed? But the mind imagined by Leibnitz, after fashioning the new Cæsar and his many Sosiæ, could never understand how the atoms he himself had disposed in order, and set into action with proper velocity, could give mental activity.

Take Carl Vogt's bold expression, which in 1850 introduced a sort of mental tournament: "All those capacities which we call mental activities are only functions of the brain; or, to use a rather homely expression, thought is to the brain what the bile is to the liver, or the urine to the kidneys." The unscientific world were shocked at the simile, considering it to be an indignity to compare thought with the secretion of the kidneys. Physiology knows no such aesthetic, discriminations of rank. In the view of physiology the kidney secretion is a scientific object of just the same dignity as the investigation of the eye, or the heart, or any so-called "nobler" organ. Nor is Vogt's expression worthy of blame on the ground that it represents mental activity as being the result of material conditions in the brain. Its faultiness lies in this, that it leaves the impression on the mind that the soul's activity is in its own nature as intelligible from the structure of the brain, as is the secretion from the structure of a gland.

Wherever the material conditions of mental activity in the shape of a nervous system are lacking, as is the case with plants, the scientist cannot admit the existence of soul-life; and here he but seldom finds his views controverted. But what answer is to be made him if he were to require, as the condition of his believing in a soul of the universe, that there should be shown to him somewhere in the world, bedded in neuroglia, and nourished with warm arterial blood under due pressure, a system of ganglia and nerves corresponding in extent to the mental power of such a soul?

Finally, the question arises whether the two limits of our knowledge of Nature are not perhaps identical, i. e., whether, supposing we understood the nature of matter and force, we should not also understand how the substance that underlies them could, under certain conditions, feel, desire, and think. Certainly this is the simplest hypothesis, and, according to well-known principles of scientific research, until it is disproved it must be preferred to that other hypothesis, which, as we have said, makes the universe doubly incomprehensible. But such is the nature of things that we cannot attain clearness of view with regard to this point, and it were idle to dwell upon it.

With regard to the enigma of the physical world the investigator of Nature has long been wont to utter his "Ignoramus" with manly resignation. As he looks back on the victorious career over which he has passed, he is upheld by the quiet consciousness that wherein he now is ignorant, he may at least under certain conditions be enlightened, and that he yet will know. But as regards the enigma what matter and force are, and how they are to be conceived, he must resign himself once for all to the far more difficult confession—

"Ignorabimus!"

1. An Address delivered at the Forty-fifth Congress of German Naturalists and Physicians at Leipsic.