About the Work
This book presents the mature epistemological reflections of Ernst Mach, a physicist and philosopher of science who profoundly influenced the intellectual currents of the late nineteenth and early twentieth centuries. Written during his tenure at the University of Prague and revised after his move to the University of Vienna, the work represents a sustained inquiry into the foundations of human knowledge, grounded not in abstract speculation but in the concrete analysis of sensory experience. The text is presented as a series of interconnected essays and investigations, unified by a central thesis about the nature of perception and reality. Mach, identified as formerly Professor of Physics at Prague and then Professor of the History and Theory of Inductive Science at Vienna, brings the rigorous habits of the physicist to bear on questions traditionally reserved for philosophy and physiology. The book is compact in size but dense with argument, and the author himself notes that its matter is not proportioned to its dimensions, offering succinct expositions rather than exhaustive applications of his conclusions.
The work opens with prefatory material that situates it within ongoing scientific debates. Mach expresses his conviction that the foundations of physics, and of science generally, await elucidation from biology, particularly from the analysis of sensations. He acknowledges his debt to Gustav Fechner, whose work provided an initial stimulus, and to Ewald Hering, whose physiological investigations offered crucial assistance. Mach is careful to disclaim any formal title of physiologist or philosopher, suggesting instead that his value lies precisely in approaching these problems as a physicist unconstrained by the barriers of specialist disciplines. The book includes numerous illustrative figures and diagrams, and the edition contains additional notes and appendices that appeared in later German editions, reflecting the considerable interest the work generated. The translator notes that Mach has not entered into detailed applications of his conclusions but rather presents the essential ideas in a concentrated form, leaving readers to trace the broader implications.
Context
The intellectual environment in which Mach developed his ideas was characterized by a profound transformation in the relationship between physics and psychology. The remarkable success of physical science had elevated mechanical modes of thought to a position of dominance, and even the physiology of the senses had assumed an almost exclusively physical character. Mach saw this as a distortion of the proper order, since physics itself is but a portion of a larger collective body of knowledge that includes the facts of sensation and consciousness. He sought to demonstrate that the physiology of the senses could pursue its own development while simultaneously assisting physics to understand its own foundations more clearly. This was not a merely academic exercise but a response to what Mach perceived as fundamental confusions embedded in the language and habits of scientific thought.
The immediate background includes the work of Johannes Müller, whose doctrine of specific energies of the nerves had opened new avenues for understanding sensation, and the psychophysical research of Fechner, which attempted to establish quantitative relationships between stimulus and sensation. Mach’s own position develops out of and against these traditions. He criticizes the tendency, which he attributes to the influence of a great authority, to relegate the explanation of different sensation qualities to unknown domains while regarding all neural processes as qualitatively alike and only quantitatively different. Against this view, Mach insists that as many physico-chemical neural processes should be assumed as there are distinguishable qualities of sensation. This position, which he describes as a consistent, monistic conception of Müller’s principle, had been articulated in his own earlier lectures on psychophysics, where he argued that such a conception alone could lead to a profounder knowledge of sensations.
The book also engages with the evolutionary theories that were reshaping biological thought in this period. Mach draws on Darwinian concepts to illuminate the origins and functions of sensory and cognitive capacities, treating instinct, memory, and even superstition as products of adaptation. He was influenced by Herbert Spencer’s evolutionary psychology and by Hering’s conception of memory as a general function of organized matter. The work reflects a moment when the implications of evolution for psychology were just beginning to be explored systematically, and Mach positions himself as a contributor to this nascent synthesis. He also acknowledges the work of contemporaries such as Avenarius and various investigators in physiology and biology, situating his own contributions within a broader movement toward a naturalistic understanding of mind.
Structure of the Book
The book is organized as a series of investigations that move from general epistemological considerations to specific analyses of particular sense modalities. The opening sections present what Mach calls his antimetaphysical remarks, establishing the fundamental orientation of the entire work. These introductory considerations examine the nature of the ego, the relation between bodies and sensations, and the proper method for scientific investigation. Mach introduces his notation of elements—the complexes of colors, sounds, spaces, times, and other sensory constituents that make up experience—and argues that traditional distinctions between the physical and the psychical rest on a misunderstanding of these elements’ nature.
Following this general introduction, the book proceeds to examine the principle of complete parallelism between the psychical and physical, illustrating this principle through historical examples drawn from the study of color vision and audition. Mach discusses the theories of Helmholtz, Brewster, and Thomas Young, showing how their successes and failures illuminate the proper method for coordinating psychological analysis with physiological and physical investigation. This section also introduces considerations drawn from evolution theory, including observations on instinctive behavior and inherited habits that bear on the nature of sensory and cognitive functions.
The central portions of the book are devoted to detailed analyses of space-sensation and time-sensation. Mach investigates the physiological processes underlying our perception of spatial relations, drawing on experiments involving eye movements, head movements, and the coordination of visual with motor experience. He discusses the contributions of Hering, particularly the threefold innervation corresponding to the three dimensions of optical space, and explores phenomena such as the apparent motion of objects during voluntary and involuntary eye movements. The analysis extends to the perception of depth, the role of light and shadow in defining bodily form, and the peculiar phenomena associated with monocular perspective drawings. Throughout, Mach emphasizes the role of organic habits and inherited adaptations in shaping our spatial perceptions.
The treatment of time-sensation acknowledges its greater difficulty, since time accompanies every sensation and cannot be wholly separated from any. Mach examines the specific quality of temporal experience, its connection with attention and consciousness, and the phenomena of rhythm recognition and temporal perspective. The book then turns to the sensations of tone, analyzing the relationship between musical sounds, the physiology of hearing, and the psychological principles that govern our perception of pitch and harmony. The concluding portions return to the broader philosophical implications of the analysis, considering the relation of sensations to the physical world and the proper conception of scientific knowledge.
Inside the Book
The English Edition and Its Prefaces
The book opens with the publication details of this English translation by C. M. Williams, issued by The Open Court Publishing Company in Chicago and London. Ernst Mach is identified by his academic titles: formerly Professor of Physics at the University of Prague and now Professor of the History and Theory of Inductive Science at the University of Vienna. The edition contains 37 cuts and runs to 208 pages.
In his Preface to the English Edition, written in Vienna in September 1896, Mach expresses his gratitude to the publishers for translating his Beiträge zur Analyse der Empfindungen. He observes that psychology’s recent progress has come largely through the principle of association, stimulated by advances in neural anatomy and physiology. Mach then states his own conviction: that we should assume as many physico-chemical neural processes as there are distinguishable qualities of sensation. This idea, he argues, is a consistent, monistic extension of Johannes Müller’s principle of specific energies, though it runs counter to prevailing opinion. Under the influence of a great authority, it has become customary to treat all neural processes as qualitatively alike and only quantitatively different, relegating the explanation of different sensation qualities to unknown domains. Mach cites his 1863 Vorlesungen über Psychophysik, where he argued that such a conception cannot lead to deeper knowledge of sensations and is physically unjustifiable—one need only think of current passing through copper, sulphate of copper, or acidulated water. He notes that few inquirers, Hering among them, still uphold Müller’s doctrine in its original significance.
The Original Preface, dated Prague, November 1885, explains that Mach’s excursions into this province grew from his conviction that the foundations of science, particularly physics, await elucidation from biology, especially the analysis of sensations. He acknowledges contributing little, as his investigations were carried on only at odd moments with long interruptions. He thanks investigators including E. Hering, V. Hensen, and W. Preyer. Though he claims no title of physiologist or philosopher, he hopes his work by a physicist unconstrained by specialist barriers may have value. His stimulus came from Fechner’s Elemente der Psychophysik (1860), and his greatest assistance from Hering’s solutions of problems referenced on pages 35 and 81. He recommends that readers avoiding general discussions omit the first and last chapters, though for him the conception of whole and parts are intimately related.
The Translator’s Note, by C. M. Williams, Boston, December 1896, observes that the book’s matter is not proportioned to its size. The author has not entered into detailed application of his conclusions but gives succinct exposition. The German edition has attracted great interest. New matter appears in notes on several pages and in two Appendices. The manuscript and proofs were revised by T. J. McCormack, translator of Mach’s Science of Mechanics, who independently rendered the “Introductory Remarks” and Appendix I.
The Antimetaphysical View of Sensations
The Introductory Remarks begin with a section titled “Antimetaphysical.” Mach notes that physical science’s modern success has made physical ways of thinking prominent. The physiology of the senses, leaving paths opened by Goethe, Schopenhauer, and especially Johannes Müller, has assumed an almost exclusively physical character. This tendency seems improper, since physics is but a portion of a larger collective body of knowledge. The physiology of the senses can pursue its own development and assist physics. Colors, sounds, temperatures, pressures, spaces, and times are connected with moods, feelings, and volitions. Relatively fixed complexes receive special names and are designated bodies, but they are not absolutely permanent—a table remains “the table at which I daily write” despite changes; a friend remains the same despite altered coat or expression. The relatively permanent complex of memories and feelings joined to a body is denominated the “I” or “Ego,” also only of relative permanency. The ego’s apparent permanency consists in continuity and slow changes; Mach recounts mistaking his own mirror reflection for a stranger twice. The will impelled to examine changes first exhibits component parts as properties. Complexes are disintegrated into elements. The habit of designating permanent compounds by single names conflicts with isolating component parts, producing the “monstrous notion of a thing in itself, unknowable and different from its ‘phenomenal’ existence.” Thing, body, and matter are nothing apart from their complexes of colors, sounds, and so forth. A body is one and unchangeable only when details need not be considered—both earth and billiard-ball are spheres when precision is unnecessary. Man can consciously determine his point of view; animals are usually forced to theirs. The tangible part of bodies appears as a constant, durable nucleus, and mechanical physics ascribes higher reality to space and time than to colors, sounds, and odors.
The Ego and Its Pseudo-Problems
Mach proceeds to argue that spaces and times may appropriately be called sensations, just as colors and sounds are. The ego and the relation of bodies to the ego give rise to similar pseudo-problems. He introduces a schematic notation: complexes of colors and sounds commonly called bodies are designated ABC…; our own body (a part of the former) is KLM…; the complex of volitions, memory-images, and the rest is αβγ…. Usually the complex αβγ… KLM…, making up the ego, is opposed to ABC…, the world of substance; sometimes αβγ… alone is viewed as ego, with KLM… ABC… as world. At first ABC… appears independent of the ego, but this independence is only relative. Changes in αβγ… may pass through KLM… to ABC… and vice versa—powerful ideas bursting into acts, or environment changing our body. KLM… appears more intimately connected with both αβγ… and ABC… than the latter are with each other.
The precise view is that ABC… is always codetermined by KLM. A cube of wood looks large close up, small at a distance, different with each eye, sometimes double, invisible with closed eyes. Properties of a body appear conditioned by our own body. All that can be said is that with different KLM, different ABC… are associated. A footnote cites Mach’s 1868 article stating that “sense-illusion” shows we have not incorporated into ordinary language that the senses represent things neither wrongly nor correctly—under different circumstances they produce different sensations.
Mach illustrates with the visible point S and the prick. We see an object with point S; touching S brings a prick. We can see S without feeling the prick, but when we feel the prick we find S. The visible point becomes a permanent nucleus to which the prick is annexed as accidental. From frequent occurrences we regard all properties of bodies as “effects” from permanent nuclei conveyed to the ego through the body—these effects we call sensations. This operation deprives the imagined nuclei of sensory content, converting them into mere mental symbols. The assertion that the world consists only of our sensations is then correct; the assumption of nuclei or reciprocal action between them is idle and superfluous, suiting only half-hearted realism or philosophical criticism.
The ego can be extended to embrace the entire world. A footnote gives examples: the virtuoso’s mastery of his instrument, the orator controlling thoughts of audiences, the politician guiding his party; in depression the ego contracts, a wall seeming to separate it from the world. The ego is not sharply marked off; its limits are indefinite and arbitrarily displaceable. Metaphysical difficulties arise from failing to observe this and unconsciously narrowing or enlarging those limits. The unities “body” and “ego” are only makeshifts for provisional survey and practical ends—grasping bodies, avoiding pain. In profound scientific investigations we must abandon them. The antithesis of ego and world, sensation and thing, vanishes; we deal only with the connexion of elements αβγ… ABC… KLM…, which is the combination of these elements with time and space. Science must accept this connexion and get its bearings without explaining its existence.
The Homogeneity of Elements and Other Persons
On superficial examination αβγ… seems more evanescent than ABC… and KLM…, whose elements seem more stably connected to solid nuclei. On closer inspection all elements prove homogeneous, yet the old antithesis of body and spirit easily regains ascendancy. The philosophical spiritualist struggles to give solidity to his mind-created world of bodies; the materialist cannot endow matter with sensation. The monistic point of view is easily clouded by older, more powerful instinctive notions.
In ABC… we find not only our own body KLM… but also other persons’ (or animals’) bodies K′L′M′…, K″L″M″…
The Pigeon Experiment and Inherited Habits
The segment opens with the author reflecting on instinctive behaviors that operate entirely without consciousness. He recalls an experiment witnessed in 1865 involving pigeons whose brains had been removed. These decerebrated animals would drink whenever their feet were placed in cold liquid—whether water, mercury, or sulphuric acid. Since birds naturally wet their feet when drinking, the author interprets this as an inherited habit adapted to an end, triggered automatically by appropriate stimuli even in the absence of consciousness. He connects this to Goltz’s work on the frog’s nerve centers, which describes similar phenomena.
The Sparrow Anecdote (1873)
During his autumn vacation in 1873, the author’s young son brought him a few-days-old sparrow that had fallen from its nest. The bird refused to swallow and would have died from forced feeding. The author reasoned that whether or not Darwinian theory is correct, a newborn child would perish without inherited sucking organs and impulses activated automatically by appropriate excitation; something similar must exist for birds. He experimented by sticking a small insect on a sharp stick and swinging it rapidly around the bird’s head. Immediately the bird opened its bill, beat its wings, and devoured the food. As the animal grew stronger and greedier, it began snatching food, and after seizing an insect that fell to the table, ate independently thereafter. As its intellect developed, the required excitation decreased. Upon reaching independence, it acquired all characteristic sparrow behaviors without learning them. By day it was trustful; in the evening it grew timid, sought the highest places, and would only quiet when prevented by the ceiling from going higher—another inherited habit. At darkness, it ruffled its feathers, hissed, and showed terror—a fear with purpose for a creature normally preyed upon by monsters.
Innate Superstition
This observation strengthened the author’s opinion that his children’s superstition was innate, not derived from nursery tales, which were carefully excluded from their upbringing. One child feared an arm-chair in shadow; another avoided a coal-hod with a raised cover resembling open jaws. The author states that “the fear of spirits is the true mother of religions.” Neither scientific analysis nor David Strauss’s historical criticism of myths will quickly banish these things. Habits answering to economic needs—fear of worse, hope of better—persist in uncontrollable brain instincts. Just as birds on uninhabited islands learn fear of man over generations, humans will unlearn the “creeping of flesh” only after many generations. Every performance of Faust shows secret sympathy with witchcraft-age conceptions.
Silk-Worm Experiment
The author’s father, an enthusiastic Darwinian and land-proprietor in Carniola, raised silkworms, including yami-mai in oak woods. Domestic mulberry silkworms, raised indoors for generations, have become helpless. When the father omitted straw bundles for cocoon-spinning, most worms perished; only a small portion—”the geniuses” with the greatest adaptation—spun cocoons. The author’s sister believes that one generation’s experiences are utilized in the next, but this requires further investigation.
Theoretical Conclusions
The author derives no “mysticism of the Unconscious” from these phenomena; a memory reaching beyond the individual renders them intelligible. A Spencer-Darwinian psychology founded on evolution theory with positive investigation would yield richer results than previous speculation. These observations were written before Schneider’s Der thierische Wille (Leipzig, 1880); the author agrees with Schneider’s details almost throughout, though their fundamental conceptions differ—Schneider’s distinction between sensation-impulses and perception-impulses the author deems superfluous. Weismann’s Ueber die Vererbung (Jena, 1883) regards inheritance of acquired traits as highly improbable, finding factors in germ-elements and their selection. The author concedes Weismann’s arguments nearly compel assent, but notes that new races forming and transmitting traits show germ-elements altered by outer influences; some influence on germ-plasm by the enveloping body must occur, so individual life’s influence on descendants cannot be entirely excluded. A 1895 addition praises C. Lloyd Morgan’s works.
Teleological Conceptions
A footnote explains the utility of teleological conceptions: recognizing a visible object under varying illumination depends on ratios of illumination-intensities between object and surroundings, making intelligible the organic properties of the eye. Weber’s law and Fechner’s psycho-physical formula appear not as fundamental but as explicable results of organic adjustments; belief in their universal validity is relinquished. The author cites his own papers where he abandoned Fechner’s logarithmic metrical formula, proposing instead a proportionality between excitation and sensation. He disputes Hering’s claim that he everywhere takes the psycho-physical law as foundation.
Against Species-Preservation as Ultimate End
The author warns against supposing that discovering a function’s necessity for species survival constitutes “mechanically explaining” it. Darwin himself is free from this short-sighted conception. The physical means of function development remains a physical problem; voluntary adaptation’s mode and reason remains psychological. Species preservation is one actual, valuable point of departure but not the last or highest. Species have been destroyed and new ones arisen. The pleasure-seeking, pain-avoiding will directs beyond species preservation: it preserves species when advantageous, transforms when advantageous, destroys when continuance would not be advantageous. Were it directed merely to preservation, it would move in a vicious circle—the biological counterpart of physics’ “perpetual motion.”
The Will and Space-Sensation
The author begins a new chapter by stating that the topic of the preceding chapter has only been discussed in three of his own small works. He will describe his own methods for understanding the sensation of space, without claiming to cover what others, particularly Hering’s theory, have accomplished. He admits his knowledge of the literature is imperfect for exact references but will specifically notice what he regards as the most important point of Hering’s theory.
When we move our eyes freely and voluntarily, observed objects do not change position or form, although their images are displaced on the retina. If an object A is reflected on the retina at a point below the point of most distinct vision, it appears at a certain height. When he raises his eyes to fix on B, A retains its former height; it would appear lower if the image position alone determined the space-sensation. Thus, the physiological process conditioning voluntary eye-raising can take the place of the height-sensation, is homogeneous with it, and is algebraically summationable with it. If the eyeball is turned upward by finger pressure, the object appears to sink proportionately to the shortening of the arc. The same occurs with involuntary processes like a muscle cramp. Opticians’ experience shows that patients with paralysis of the rectus externus reach too far to the right when grasping objects, because they need a stronger will-impulse to fix their glance to the right. This suggests the will to look right determines the optical space-sensation “right.”
He describes his own experiment: with eyes turned left, press putty against the right side of each eyeball; attempting to glance right succeeds only imperfectly, and objects suffer a strong displacement to the right. Thus the mere will to look right imparts a larger “rightward value” to retinal images. Both facts—voluntary turning not displacing objects, and forced involuntary turning displacing them to the left—amount to the same thing. The will to perform eye movements, or the innervation to the act, is itself the space-sensation. He compares this to itching or pricking, where we grasp the spot with correct movement; similarly, we turn our eyes with correct exertion toward an object stimulating the retina. Through organic apparatus and exercise, we hit the exact degree of innervation needed.
He describes a peculiar phenomenon: in a dark room, fix eyes on light A, then suddenly look at lower light B; A appears to make a rapid upward sweep, an after-image entering consciousness on completion of the glance-movement with positional values corresponding to earlier innervations, not the later eye position. Similar phenomena occur with Holtz’s electrical machine—a spark during a downward glance appears high above the electrodes. These answer to astronomers’ “personal equation,” confined to sight.
Head and Body Movement
Moving the head without fixing the eyes leaves objects motionless, though another observer sees the eyes take no part in turning. Breuer observed that during continuous rotation about a vertical axis, the eyes turn about ten times per full revolution opposite the clock-hands with uniform motion, then jerk back. This is an automatic, unconscious, reflexively excited eye movement. A simple conception involves two antagonistic innervation organs, one giving a uniform stream, the other an impulse after a lapse, like an overturning rain-gauge. This compensational movement causes retention of object position during body turning. When voluntarily turning the eyes in the same direction while turning the head, we overcompensate the automatic innervation, needing the same innervation as if the eye alone described the whole angle. This explains why optical space appears continuous, not an aggregation of fields, and why objects remain stationary.
Visual Illusions and the Geometry of the Retina
Mach continues his analysis of spatial vision by examining experiments with linear drawings observed monocularly. When viewing a particular figure vertically with one eye, raising one line segment causes it to appear as if projecting forward from the plane of the drawing, while depressing it makes that segment retreat and another project toward the observer. From these observations, Mach generalizes a principle: the legs of acute angles appear to thrust out on different sides of the drawing’s plane, whereas the legs of obtuse angles appear on the same side. Crucially, all angles exhibit a tendency to become right angles in perception.
Mach identifies this phenomenon as essentially identical to what is known as Zöllner’s pseudoscopy. He dismisses superficial explanations, such as the suggestion that we are merely habituated to seeing right angles in our environment. He points out that we frequently encounter oblique-angled objects in daily life, yet we never see a motionless oblique liquid surface without artificial preparation, as in his earlier experiment. The eye, he argues, apparently prefers the perception of an oblique liquid surface to that of an oblique-angled solid body.
He attempted to explain these effects through the contrast of directions, drawing an analogy to color contrast, and also through the principle of economy of thought, but found both approaches unsatisfactory. The principle of probability offers more promise. By conceiving the retina as a perfect sphere with the eye fixed on an angle’s vertex, planes through the eye’s center project the angle onto the retina as a spherical segment. An infinite number of objective angles, ranging from zero to one hundred eighty degrees, can correspond to any constant seen angle. Calculation suggests that larger angles are the most probable for observed acute angles, and smaller angles for observed obtuse angles. However, Mach could not determine whether geometrically similar phenomena are physiologically identical—an essential question—and he found the conception itself somewhat artificial.
The Perception of Solid Bodies and Motion
Plane linear drawings observed monocularly often appear flat, but introducing variation in the angles and motion causes them to assume solid form, typically appearing as a rotating solid body. Lissajous’ acoustic figures, which appear on a revolving cylinder with phase variation, exemplify this phenomenon. Mach notes our habitual dealings with solid bodies, observing that solid bodies in revolution surround us constantly and that the material world is essentially a continuous solid body, without which we could never conceive geometrical space. We apprehend dimensions directly rather than noting the positions of individual points, which explains the difficulty unpracticed observers have with perspective drawing.
Children, accustomed to real dimensions, do not understand foreshortening and prefer simple contours. Mach recalls this mental state from his own experience, which enables him to comprehend ancient Egyptian drawings that press all body parts into the plane at their true dimensions, like pressed plants. Pompeian frescoes show a perceptible disinclination to foreshortening despite an emerging sense of perspective. The ancient Italians, once they mastered the subject, indulged in excessive and sometimes unbeautiful foreshortenings that demand considerable ocular exertion from the viewer.
Seeing solid bodies with unchanged salient-point distances is easier through habit than eliminating the marks of solidity, which requires deliberate analysis. Wherever a coherent mass, unified by common coloring, exhibits spatial alteration, the process appears preferably as the motion of a solid body. Mach finds this conception unsatisfactory, believing instead that an elemental habit of the sight organ—not originally acquired through individual conscious experience—antecedently facilitated the apprehension of solid-body movements. He hypothesizes that a diminution of transverse dimension in an attended optical sensation-mass tends to induce a corresponding augmentation of depth dimension, and vice versa, analogous to the conservation of energy. This simpler view adequately explains the phenomenon and clarifies how such an elemental habit could be acquired, expressed organically, and inherited.
A counterpart observation involves an egg or dull-surfaced ellipsoid rolled across a table without turning on its generation axis, performing jolting movements. Viewed binocularly, it appears as a liquid body or a large oscillating drop, an effect more noticeable when it rotates moderately rapidly about a vertical axis with a horizontal longitudinal axis. Marks on the surface whose movements can be followed immediately destroy this effect, and a rotating solid body is then seen. Mach acknowledges that his explanations are incomplete but hopes they will stimulate more exact study.
The Sensation of Time
Mach turns to the investigation of time-sensation, which proves more difficult than the study of space-sensation. Many sensations appear with space-sensation, and others without it, but time-sensation accompanies every sensation and cannot be wholly separated from any. The underlying physiological processes are less known, more radical, and more concealed than for other sensations, so analysis must confine itself chiefly to the psychological side. Mach references his earlier work on the time-sense of the ear, not re-entering those experiments begun in 1860.
A definite, specific time-sensation exists beyond doubt. Two musical measures that vary utterly in tone order but are rhythmically identical are immediately recognized as such—not through understanding or reflection but through sensation. Just as bodies of different colors can share a spatial form, two tonal entities that are acoustically different may share a temporal form, and we detect the identical temporal components immediately, just as we do with spatial components.
Hearing acoustically identical bell strokes, Mach can discriminate the first, second, and third. He rejects the idea that accompanying thoughts or accidental associations provide distinguishing marks, since such estimates would prove unreliable if the accidental background vanished from memory. He describes how, while reflecting, a clock strikes unnoticed; afterward he can count distinctly one, two, three, four strokes from memory, the reflection vanishing when he attends to the recollection. The supposed background is wanting. Each stroke connects with a special time-sensation that starts into consciousness alongside it. Similarly, he distinguishes a memory image from a fancy by a specific time-sensation that differs from that of the present moment.
Attention, Fatigue, and the Flow of Time
Since time-sensation is always present while we are conscious, it likely connects with the organic consumption associated with consciousness—we feel the work of attention as time. Severe attention makes time seem long; easy employment makes it short. In phlegmatic conditions, hours pass rapidly. Completely exhausted attention brings sleep, and dreamless sleep lacks time-sensation. Profound sleep connects yesterday to today only intellectually. The organ of consciousness fatigues continually during waking, and the labor of attention increases continually. Sensations connected with greater attention expenditure appear to happen later.
Consciousness serves as a bridge of communication between all sensations and memories. Mach proposes that alongside each specific energy of the organ of consciousness, there must exist another particular energy—the sensation of time—such that no specific energy could be excited without evoking this time-sensation. Should this new energy appear physiologically superfluous or invented ad hoc, he suggests assigning it an important physiological function: maintaining the flow of blood that nourishes the brain-parts in their work, guiding this current to its destination, and regulating it. This would provide a material basis for conceptions of attention and time-sensation. The fact that there is but one continuous time becomes intelligible, since the partial attention given to one sense is always drawn from the total attention and determined by it.
When listening to similar strokes from a bell, we can distinguish each from the others and count them in memory, provided they are few. With large numbers, we distinguish the last strokes from one another but not the first. To avoid mistakes, one must count them immediately upon sounding, consciously connecting with each stroke some ordinal symbol. This phenomenon has a perfect analogue in the space-sense. In walking forwards, we have a distinct sensation of moving away from a starting-point, but the physiological measure of this removal is not proportional to the geometrical. Similarly, elapsed physiological time is subject to perspective contraction, its single elements becoming less and less distinguishable.
Rhythm and the Recognition of Temporal Form
If a special time-sensation exists, the identity of two rhythms will be immediately recognized. However, two rhythms that are physically the same may appear very different physiologically, just as the same space-figure by change of position may give rise to different physiological space-forms. A rhythm represented by musical notation appears quite different according to which lines or dots are regarded as the bars. The reason is that attention, guided by accent, is discharged at different points—the sensations of time corresponding to successive beats are compared with different initial sensations. Two physical time-figures may be termed similar when all parts of one stand in the same relation to one another as homologous parts of the other. Physiological similarity appears only when attention is introduced at homologous points of time. Mach judges that we recognize the identity of time-ratios of two rhythms only when they are capable of representation by very small whole numbers. We notice immediately only the identity or non-identity of two times, recognizing ratios only when one part is exactly contained in the other. This explains why, in marking time, time is always divided into absolutely equal parts.
Sensations of Tone and Their Origins
Mach turns to tone-sensations, restricting himself mainly to psychological analysis.
The Sciences and Their Methods
The various sciences are distinguished not by any fundamental divide in reality but by their subject matter and their method. All science, Mach argues, aims to represent facts in thought, whether for practical ends or to relieve intellectual discomfort. Using his own terminology, science arises when the elements of the sense-given world are reproduced or mimicked by thoughts. Physics, for instance, reproduces the relations among sense-given facts with thoughts. The physiology and psychology of the senses reproduce the relations of these facts to the body’s nervous system, while physiology proper traces the relations of nervous processes to each other and back to the sense-given facts. When thoughts are used to reproduce other thoughts, we arrive at the psychological sciences proper. One might assume that concepts like atoms, forces, and laws are more important than the portrayal of the facts themselves, but unbiased reflection shows that all our needs are satisfied when thoughts can completely represent sense facts. Such representation is the true end of physics; atoms, forces, and laws are merely means to facilitate this end, valuable only for the help they afford.
The Completion of Knowledge
Knowledge of a phenomenon is complete when thoughts can marshal all the relevant sense-given facts before the mind, acting as a substitute for them. To understand an earthquake, for example, one must be able to imagine the subterranean thunders, the oscillation of the ground, the cracking walls, and the falling plaster. When these subterranean processes stand out in full sensuous reality, we have all the insight we can have or require. Auxiliary mathematical conceptions are valueless if they cannot lead to a graphic representation of the sense-given facts. Similarly, seeing a white beam of light pass through a prism and issue into a fan-shaped band of colors, predicting the appearance of Fraunhofer’s lines on a screen, and observing how these lines alter with the prism’s position constitutes all the required knowledge. Laws and formulae are merely quantitative norms that regulate sensory representation; the latter is the end, the former the means.
The Adaptation of Thoughts to Facts
The adaptation of thoughts to facts is the aim of all research, a process science pursues consciously that daily life does unconsciously. We find our thoughts already adjusted to facts, marshaling elements in groups that copy the sense-given order. But our limited mental elements cannot keep pace with experience, and new facts necessitate a new adaptation, which is expressed as a judgment. Mach illustrates this with his three-year-old child, who on first visiting a meadow said, “We are in a ball. The world is a blue ball.” The percept of “we” was broadened by union with the percept of a ball, and the image of the “world” was supplemented by an enveloping blue ball. A judgment is always a supplementing or amendment of the deficiencies of a sensuous percept. It enriches, extends, and supplements existing percepts. When the process is over and the image is familiar, it is memory, not judgment. This “intuitive knowledge,” as Locke called it, underlies all of natural science and mathematics. Examples include the spatial extension of a tree’s root, the correction of a hasty generalization that a frog has no claws, the temporal extension of a caterpillar becoming a butterfly, and the geometrical intuition that a cube has six surfaces and eight corners.
Generalization and Differentiation
Intuitive knowledge impresses itself on memory as recollections that supplement sense facts. Since facts differ, only their common elements are emphasized, yielding the principle of the broadest possible generalization or continuity. Memory must also conform to the principle of sufficient differentiation. Animals demonstrate this: soft, bright red or yellow fruits remind them of a sweet taste, while green, hard fruits suggest sourness. The insect-hunting monkey snatches at buzzing things but avoids the yellow and black wasp. Both ends are attained by selecting and emphasizing the determinative elements of sensuous perception. The physicist generalizes, stating that all transparent solids refract incident light towards the perpendicular, and differentiates, noting that amorphous bodies and isomeric crystals refract simply while the rest do so doubly.
Problems and Investigation
Much mental adaptation occurs unconsciously. When a fact runs violently counter to customary thought and we cannot discover the determinative factor, a problem arises. The novel acts as a stimulus, and practical considerations or intellectual discomfort engender volitional thought-adaptation, which is investigation. Observing a lever lifting a large weight with a small one, we seek the differentiating factor that is not immediately given. We compare instances, note the varying influences of weights and arms, and only after mastering the concepts of “moment” and “work” does the problem vanish. These concepts are the differentiating elements; once they are noted habitually, the problem ceases to exist.
On Abstraction and Concepts
One cannot represent a general man or a general triangle that is both right-angled and equilateral. The image accompanying a concept is not the concept itself. Words are designations for many percepts, not identical with concepts. A child who saw a black dog called a black beetle, pig, or sheep “dog,” applying the name based on any similarity of color, motion, form, or covering. Another child calls bird feathers “hairs” and cow horns “feelers.” Most adults do similarly, but less noticeably. The illiterate call a rectangle a square, and nations do likewise, as when the Marcomanni called lions “dogs” or the Ionians named Nile crocodiles after their own lizards. A concept is never a finished percept; a word denoting a concept is an impulse to perform a familiar sensory operation that yields a definite sensuous element.
Substance and Constancy
Thoughts adapt only to what is constant in facts, and the mental reconstruction of constant elements alone yields economic advantage. This is the ultimate ground for the effort toward continuity in thought. The unconditionally constant is termed “substance.” A body is seen when we turn our eyes toward it, and it can be seen without being touched or touched without being seen. Though the appearance of its component elements is joined to conditions, these conditions are so absolutely in hand that they go unappreciated. The body is regarded as always present, whether sensed or not, which yields a predictive advantage and avoids surprise. The same applies to chemical elements, which are regarded as unconditionally constant despite requiring outward aids that are left out of account once familiar. On a higher plane, entire provinces of facts—electricity, magnetism, light, heat—are ascribed constancy. Saying a body is “electric” evokes more memories and definite expectations than emphasizing single attractions. But this hypostasising has disadvantages, for it follows historical paths. There is no specific electrical fact; every such fact can be regarded as chemical or thermal, as all physical facts are ultimately made of the same sensuous elements. Really unconditioned constancy does not exist. Absolute constancy arises only by overlooking conditions. Only one constancy embraces all forms: the constancy of connexion, or relation. Scientific propositions express such constancies: a tadpole becomes a frog, bodies fall at a certain rate. Force is merely constancy of connexion—body A exerting force on B means that B, contraposed to A, receives acceleration relative to A. The illusion of substance as a constant vehicle of force is shattered by putting sense-organs in B’s place.
Causality and the Unity of Nature
Ideas have varying constancy, and we support weaker ideas by stronger ones. Newton conceived planets as projectiles and tides as attracted by the moon; we add air pressure to understand pumps and siphons. This need is called the “need of causality,” the spring of scientific explanation. Mechanical thoughts are preferred as the strongest and most testable, hence the authority of mechanical explanations. Mathematical thoughts have even higher authority. In the electric current example, one may imagine oneself as Ampère’s swimmer, with the north pole deflecting to the left, or lay a watch in the circuit’s plane. These inner and outward reactions would be impossible if a chasm existed between self and world—nature is a single whole. When elements in a complexus are replaced, one seeks a constancy surviving the change. J. R. Mayer first felt this need, enunciating “force” or “energy,” conceiving it as absolutely constant, a store or substance. His struggle with expressions shows an instinctive need, and his achievement came from adapting existing physical concepts to facts and needs.
Geometric Space and Physical Experience
The geometrician’s space is not composed solely of space-sensations from sight and touch, but consists largely of physical observations that take space-sensations as their starting point. When the geometrician regards space as constituted alike at all points and in all directions, he exceeds what sight and touch actually provide. Without physical experience, the geometrician would never have reached this conception. The fundamental propositions of geometry were acquired wholly through physical observations—specifically through the superposition of measures of length and angles and the application of rigid bodies to one another. Without propositions of congruence, there would be no geometry. When we feel compelled to imagine an isosceles triangle as having equal angles at its base, this compulsion arises from the remembrance of powerful past experiences.
The Index of the Work
The book concludes with a comprehensive index, an alphabetical listing of the topics, names, and concepts discussed throughout the text, along with their corresponding page references. This section serves as a practical guide for the reader, mapping the intricate network of ideas that Mach has woven together. It is a purely functional apparatus, devoid of narrative prose, but it offers a final, structured overview of the book’s central concerns.
Key Concepts and Their Locations
The index reveals the book’s core thematic architecture. Entries such as “Connexion of elements” are identified as the primary subject-matter of science, with the constancies of these connexions being the only true constancies and their permanences the only real existences. The “Ego” is noted for its unstable character and its complex relation to bodies and the world of sense, with its origin, character, and import traced to specific pages. The “Elements” themselves—the ABC…, KLM…, and aβγ… complexes—are listed as the results of analysis and the fundamental components of the world, which may be viewed as merely dependent on one another.
The Scientists and Philosophers Referenced
The index catalogues the numerous thinkers with whom Mach engages. Figures like Darwin, Fechner, Helmholtz, and Newton appear frequently, indicating the breadth of Mach’s dialogue with the scientific tradition. The entry for “Mach” himself points to the origin of his philosophical and psychological views, while Kant is referenced in a footnote, suggesting a critical engagement with his idealism. The presence of Mayer, J. R., and his concept of force highlights the importance of thermodynamics in Mach’s thinking.
The Structure of Sensation and Science
The index clarifies the book’s distinctions between various scientific domains. “Physical science” is defined by its character and its influence on other sciences, and it is distinguished from physiological and psychical science. The “Sensations” are repeatedly identified as the elements of the world and the basis of all the physicist’s work. Specific entries on “Space-sensations” and “Space and time” point to the extensive analysis of perception, with space-sensations being produced by the motor-apparatus of the eye and defined as will. The “Specific energies” of sensation, particularly in audition, are also listed, showing the book’s deep dive into the physiology of perception.
The Final Entries on Sensation
The index concludes its alphabetical journey with entries on “Sensation” and “Sensations,” reinforcing the central thesis that they are the fundamental elements of reality. It notes the distinction between sensation and understanding, and between sensation and thing. The entry on “Sense-organs” highlights their origin, evolution, and their own independent life, memory, and intelligence. The final entries on “Specific energies” mention their role in audition and note that there are only two, leaving the reader with a final pointer to the detailed arguments contained within the body of the work. This structured list serves as the book’s true conclusion, offering a final, organized map of its entire intellectual landscape.
Main Arguments
The central argument of the book concerns the nature of the elements that constitute experience and the proper way to understand their relations. Mach contends that colors, sounds, temperatures, pressures, spaces, and times are the ultimate elements of which the world is composed, and that what we call bodies or objects are merely relatively stable complexes of these elements. The apparent permanence of a table or a friend consists not in some underlying substance but in the continuity and slow change of the sensory complexes to which these names are attached. Similarly, the ego or self is not an absolute unity but a relatively permanent complex of memories, feelings, and volitions, whose boundaries are indefinite and arbitrarily displaceable. The traditional antithesis between the ego and the world, between sensation and thing, arises from a failure to recognize the conventional and provisional character of these distinctions.
Mach argues that the assumption of a “thing in itself,” unknowable and different from its phenomenal appearance, is a monstrous notion produced by the habit of designating permanent compounds by single names. Bodies do not produce sensations; rather, complexes of sensations make up bodies. The physicist who forgets this treats bodies as thought-symbols for complexes of sensations, and this forgetfulness leads to pseudo-problems that cannot be solved within the framework that generates them. The assertion that the world consists only of our sensations is correct, but it must be understood properly: the elements themselves form the real foundation, and the assumption of mysterious entities behind them is idle and superfluous. This view, Mach claims, is economical and tolerant, avoiding the difficulties that beset both materialism and spiritualism.
A second major argument concerns the complete parallelism between the psychical and physical. Mach proposes that the same sensation must always be associated with the same nerve-process, and that every observable change in sensation corresponds to a discoverable change in the underlying process. This principle follows almost as a matter of course from his fundamental conception, which recognizes no gulf between the psychical and physical provinces, but he also enunciated it earlier as a heuristic principle of research. The principle implies that when sensations are psychologically analysable into independent components, corresponding components must be found in the nervous processes. Mach illustrates this through the history of color theory, showing how Brewster’s errors arose from defective psychological analysis while Thomas Young’s corrections followed from recognizing the compatibility of unlimited physical light kinds with few fundamental color-sensations.
The book also advances arguments about the nature of scientific explanation and the role of teleology. Mach warns against supposing that discovering a function’s necessity for species survival constitutes mechanically explaining it. The pleasure-seeking, pain-avoiding will directs beyond species preservation: it preserves species when advantageous, transforms them when advantageous, and destroys them when continuance would not be advantageous. Were it directed merely to preservation, it would move in a vicious circle—the biological counterpart of physics’ perpetual motion. Teleological conceptions are acceptable as investigative aids, but they do not enhance comprehension of reality’s facts. Similarly, Mach argues that no point of view has absolute, permanent validity; the philosophical standpoint of the average man has a high claim to consideration as a product of nature, but science must provisionally abandon it for specific purposes.
Key Concepts
The concept of elements stands at the foundation of Mach’s analysis. Elements are the colors, sounds, temperatures, pressures, spaces, times, and other constituents that make up experience, and they are homogeneous in nature whether they appear in what is conventionally called the physical or the psychical realm. Mach designates complexes of elements with symbolic notation: bodies as ABC, our own body as KLM, and the complex of volitions, memory-images, and the rest as αβγ. The ego is the complex αβγ…KLM, while the world of substance is ABC. These designations are not meant to introduce new entities but to clarify the relations among elements that traditional language obscures.
The principle of continuity and the principle of sufficient determinateness govern the connection of elements in thought. The intellect connects two things in thought according to continuity, while sufficient determinateness requires that particular conditions be associated with particular consequences, as in the law of refraction where a particular angle of incidence is associated with a particular angle of refraction. These principles find their fullest expression in the complete parallelism of the psychical and physical, which requires that the same sensation be associated with the same nerve-process and that observable changes in sensation correspond to discoverable changes in the process.
Mach introduces the concept of the economy of thought, though he develops it more through example than explicit formulation. The visual sense never puts forth greater efforts than excitation demands, and it proceeds according to the principle of probability: functions most frequently excited together tend to appear together when only one is excited. These principles coincide in their results, explaining why certain perceptions are preferred over others. The straight line, for instance, represents minimum departure from mean depth-sensations and is seen with least effort; the visual sense acts with economy and probability in preferring straight lines.
The concept of inherited habits plays a crucial role in Mach’s account of perception and behavior. He describes experiments with decerebrated pigeons that drank whenever their feet were placed in cold liquid, interpreting this as an inherited habit adapted to an end, triggered automatically by appropriate stimuli even without consciousness. The young sparrow that opened its bill when an insect was swung rapidly around its head demonstrated that the required excitation for feeding behavior decreases as intellect develops. Mach extends this to superstition, arguing that the fear of spirits is innate and that his children’s superstitious fears arose without exposure to nursery tales. These inherited habits are not confined to the individual but represent adaptations of the species, and they explain phenomena that would otherwise require mysterious unconscious forces.
The concept of the organ of representation is developed to explain the difference between sensation and imagination. Mach describes the organ of representation as one susceptible, in diminished degree, to all specific energies of sense and motor organs, so that according to attention, now this, now that energy is excited. This organ is eminently qualified for physiological mediation between energies, and its development marks the emergence of higher intelligence. The distinction between representations and sensations is fundamental: Mach can vividly represent a hexagon on a blackboard but always distinguishes what he sees from what he represents, the difference being “as by a fourth co-ordinate.”
Themes
A recurring theme is the critique of metaphysical assumptions embedded in ordinary language and scientific practice. Mach traces the “monstrous notion of a thing in itself” to the habit of designating permanent compounds by single names, which conflicts with the isolation of component parts. The unities of body and ego are only makeshifts for provisional survey and practical ends, and in profound scientific investigations they must be abandoned. This critique extends to the treatment of the ego as an indiscerptible unity, which leads to absurd questions about the seat of the soul and how the percept of a large tree could fit in a small head. Mach’s antimetaphysical orientation is not a denial of the value of ordinary experience but an insistence that no point of view has absolute, permanent validity.
The theme of the unity of science emerges from Mach’s insistence that physics and psychology are not separate provinces but portions of a larger collective body of knowledge. The physiology of the senses can pursue its own development and assist physics, while physics provides methods and concepts that illuminate sensory processes. The complete parallelism of the psychical and physical is not an article of faith but a working principle that guides investigation and yields concrete results. This unity is not achieved by reducing one realm to the other but by recognizing the homogeneity of elements that appear in both.
The developmental and evolutionary theme runs throughout the book. Mach treats sensory and cognitive capacities as products of adaptation, shaped by the conditions of life and transmitted through inheritance. The visual sense acts according to habits acquired through adaptation to life-conditions of species and individual. The fear of spirits is the true mother of religions, and humans will unlearn the “creeping of flesh” only after many generations. This evolutionary perspective does not reduce everything to species preservation, which Mach criticizes as a vicious circle, but rather situates human cognition within the broader context of organic life.
The theme of the relation between the individual and the world receives explicit treatment in Mach’s discussion of the ego. The ego is not a definite, unalterable, sharply-bounded unity; continuity alone is important. This continuity is only a means of conserving the ego’s content, which is the principal thing. The content is not confined to the individual and remains preserved in others after death. Mach states that “the ego is unsavable,” and that the fear of this fact has led to pessimism, optimism, and religious and philosophical absurdities. He recommends renouncing individual immortality to arrive at a freer view that precludes disregard for other egos. This theme connects Mach’s epistemology with an ethical orientation, suggesting that the recognition of the ego’s conventional character has implications for how we live.
The Author’s Conclusions
Mach concludes that the world does not consist of mysterious entities producing sensations, but rather that colors, sounds, spaces, and times are the ultimate elements with which science must work. The antithesis of ego and world, sensation and thing, vanishes when we recognize that we deal only with the connexion of elements, which is the combination of these elements with time and space. Science must accept this connexion and get its bearings without explaining its existence. The assumption of nuclei behind sensations or of reciprocal action between them is idle and superfluous, suiting only half-hearted realism or philosophical criticism.
The principle of complete parallelism between the psychical and physical provides the guiding method for investigation. Mach concludes that the same sensation must always be associated with the same nerve-process, and that every observable change in sensation corresponds to a discoverable change in the underlying process. This principle, which follows from his fundamental conception recognizing no gulf between psychical and physical provinces, has proven its heuristic value in the history of science, from Thomas Young’s corrections in color theory to Hering’s discoveries in the physiology of vision.
Mach concludes that the analysis of sensations reveals the conventional and provisional character of our intellectual categories. The unities of body and ego are makeshifts for practical ends, and in profound scientific investigations they must be abandoned. The ego is not a real, absolute unity but an ideal mental-economical unity, and its apparent permanency consists in continuity and slow change. The fear of losing individual immortality has led to various absurdities, but a freer view that recognizes the ego’s conventional character precludes disregard for other egos and opens the way to a more rational orientation toward life.
The book concludes with the recognition that science originates in the adaptation of thought to experience, and that problems arise when the province of experience is enlarged. The fundamental view of sensations as elements is economical and tolerant, avoiding the difficulties of both materialism and spiritualism. No point of view has absolute, permanent validity, but the philosophical standpoint of the average man has a high claim to consideration as a product of nature. The purpose of the analysis is not to discredit this view but to show why and for what purpose we hold it and must provisionally abandon it in scientific investigation. The elements form the real foundation, and we must not be impeded by intellectual abridgments like body, ego, matter, or mind in our pursuit of knowledge.
Significance
The significance of this work lies in its attempt to provide a unified foundation for scientific knowledge grounded in the analysis of sensory experience. Mach’s insistence that the elements of experience are homogeneous whether they appear in physical or psychical contexts challenged the prevailing dualism of his era and anticipated later developments in philosophy of science and psychology. His critique of the thing in itself and his treatment of the ego as a practical unity rather than an absolute substance influenced subsequent thinkers who sought to free science from metaphysical assumptions.
The book’s method—applying the rigorous habits of the physicist to questions traditionally reserved for philosophy—exemplified a new style of epistemological investigation. Mach’s principle of complete parallelism between the psychical and physical provided a working hypothesis that guided research in the physiology of the senses, and his historical analyses of color theory and audition demonstrated how psychological analysis could illuminate physical problems. His treatment of space-sensation and time-sensation offered concrete investigations that connected abstract epistemological principles with detailed experimental observations.
The evolutionary perspective that pervades the work was significant for its attempt to integrate Darwinian concepts into the understanding of cognition. Mach’s treatment of inherited habits, instinctive behavior, and the development of intelligence anticipated later work in evolutionary psychology and ethology. His warning against treating species preservation as the ultimate end of organic functions, and his insistence that the pleasure-seeking, pain-avoiding will directs beyond mere preservation, offered a more nuanced view than simple adaptationism.
The work’s significance also lies in its ethical implications. Mach’s conclusion that the ego is unsavable, and that the fear of this fact has led to various absurdities, points toward a freer view that precludes disregard for other egos. By showing that the boundaries of the self are indefinite and arbitrarily displaceable, Mach undermined the metaphysical foundations of egoism while preserving the practical importance of individual continuity. The book thus connects epistemological analysis with a broader vision of human life, suggesting that clarity about the nature of experience can contribute to a more rational and humane orientation toward the world and others.
