Ernst Mach

Knowledge and Error

Living beings have reached equilibrium with their surroundings by means of adaptation that is partly innate and permanent, partly acquired and temporary. However, a mode of organization and behaviour that is biologically beneficial under certain circumstances may become detrimental under changed conditions and even end up by destroying life itself. A bird is organized for life in air, and a fish for life in water, but not the other way round. A frog snatches at flying insects that are his food but falls victim to this habit if he gets hold of a piece of moving cloth and is caught on the hook attached to it. Moths that fly towards light and colour for the sake of self-preservation, may in the course of this generally appropriate behaviour finish up on the painted flowers on wallpaper, which do not nourish; or in a flame, which kills. Any animal caught in a trap or by another beast thereby shows that its psychophysical organization is appropriate only up to a point. In the simplest animals stimulus and response may lie in attack and flight, so regularly linked that the observed facts would not cause us to imagine that sensation, ideas, moods and will intervene between the two, were it not that this is strongly suggested by analogy with processes we observe in ourselves. Here, stimuli work directly and actively, as in a reflex movement, say of tendons, of which we do not learn until after it has happened.

On Thought Experiments

Man collects experiences by observing changes in his surroundings. However, the most interesting and instructive changes for him are those that he can influence through his own intervention and deliberate movements. As regards such changes he need not remain purely passive, he can actively adapt them to his own requirements; besides, they are for him of the highest economic, practical and intellectual importance. That is what makes experiments so valuable. If we observe how a child in the first stages of independence examines the sensitivity of his own limbs, how he is surprised by his mirror image or by his shadow in sunlight and tries out how they behave by making movements, how he practises hitting a target we are driven to conclude that man has an innate tendency towards experiment, and that without much looking about he finds within himself the basic experimental method of variation. If the adult temporarily loses these treasures so that he must as it were discover them afresh, the explanation is that his social upbringing narrows his circle of interests and confines him to it while at the same time he acquires a large number of ready opinions, not to say prejudices, that he supposes not to be in need of examination.

The Economy of Science

I have shown at length in other writings1 that the scientific and methodical presentation of a domain of facts has the advantage over an accidental and unsystematic view of the same domain in a more sparing or more economical utilisation of our mental powers. I would not return to this subject here if various objections which have been made against this thesis did not drive me to give some further explanations.

Names and Numbers

A domain of knowledge like physics is possessed, in its control of experiences, of a constant and efficacious means of refining its doctrines. After the results of the foregoing investigations psychological analyses, and logical analyses which are founded on them, will not be considered as quite superfluous even in this domain. We will, then, now discuss some questions particularly of the latter kind which, treated at length, would have only disturbed the connection of the previous inquiry. The significance of names and numbers — what they have in common, and in what way they differ from one another — has made itself felt in our consideration of thermometric scales. What are names? What are numbers?

Number and Measure

Scientific knowledge arises from finding the connection between certain reactions or groups of reactions A and B in an object or a relatively stable complex of sensible elements. If for example we find that a species of plants systematically determined by a certain shape and position of leaves and flowers and so on (reaction A) shows in addition certain stimulated motions, geotropic and heliotropic phenomena (reaction B), this constitutes a finding in natural science. Fixing such knowledge in communicable form by a description that excludes misinterpretation remains an awkward business in spite of the development of a simplifying classificatory terminology. The same awkwardness repeats itself in the description of the behaviour of a closely related species of plant, which will again have many peculiarities that must be specially noted. What is even more difficult in view of these individual features, is to fix a wider group of insights in a comprehensive description. For a group of viviparous mammals it remains possible to demonstrate common physiological and anatomical reactions such as higher blood temperature, breathing through lungs, double circulatory systems and so on.

On the Determination of High Temperatures

Reference must here be made, in connection with our discussions of the conception of temperature, to “pyrometric” methods or means of determining high temperatures. Newton1 was the first to devise a method of this kind, and we shall simply state his ideas without at present making any critical comment.

Memory. Reproduction and Association

On a walk through the streets I meet a man whose face, frame, gait and speech provoke in me a lively idea of such a set of charateristics in different surroundings. I recognize X who stands before me as a sense experience to be the same as forms a part of my memories from the other setting. Recognition and identification would be senseless unless X were given twice over. Soon I recall previous conversations with him in the other surroundings, joint excursions and so on. Similar situations are observed in the most varied circumstances, and we may gather them under a rule: a sense experience, consisting of ABCD, revives the memory of an earlier one consisting of AKLM, thus reproducing it as an idea. Since KLM is not generally reproduced by BCD, we naturally take it that the common element A starts the process. First A is reproduced, and then follow KLM which were directly experienced with it or with other simultaneous features already reproduced. All processes in this field can be subsumed under this one law of association.

The Exuberance of the Imagination

The development of the imaginative process brings with it advantages for organic life, especially the vegetative kind. However, if ideas outbalance sensation too far, drawbacks may result: the soul becomes a parasite on the body, consuming the oil of life (Herbart’s phrase). This is evident in view of the chance events that may affect the associations on which adaptation of thought to facts depends, as was illustrated earlier. If favourable circumstances guide the imagination in such a way that it follows or anticipates facts, we gain knowledge. However, unfavourable circumstances can direct the attention on to inessentials, promoting thought connections that do not correspond to the facts but mislead. Thoughts repeatedly tested and found to correspond to the facts will always be constructive rules for action; but if in special circumstances one adopts untested chance connections as generally corresponding to fact, serious error will result, and disastrous practical consequences if one acts on them. Some examples from the history of culture illustrate the point.

Similarity and Analogy as a Leading Feature of Enquiry

Similarity is partial identity: the characteristics of similar objects are in part identical and in part different. Not a single observable mark of one object need coincide with a mark of the other, and yet the marks of the one may be interrelated in exactly the same way as those of the other. Jevons2 calls analogy a more deep-seated similarity; one might say, an abstract similarity. Analogy may in some circumstances remain quite concealed from direct sense observations and reveal itself only through comparison of conceptual interconnections between the marks of one object with the corresponding connections in the other. Maxwell3 not only defines analogy but also underlines those features of it that are most important for scientific enquiry, when he describes analogy as that partial similarity between the laws in one field and those in another, so that each illustrates the other. However, we shall see that Maxwell’s approach is not different from ours. Hoppe4 regards the concept of analogy as superfluous, since as with similarity in general it is merely a matter of conceptual agreement of certain marks in the objects between which analogy is found. Although this is correct, there are good grounds for taking analogy as a special case of similarity and distinguishing it from the general concept. Above all, it is the enquirer into nature who is driven to this view, since taking notice of analogies greatly furthers his work.

Development of Individuality in a Natural and Cultural Habitat

Severed from the parent body, the animal organism begins a life of its own. Its only inheritance is a set of reflex actions to help it over its immediate needs. By adapting this set to the special surroundings, modifying and extending it and gaining experience, the animal grows into a physical and mental individual. The human young here behave exactly like the chick running off with its eggshell and pecking at everything, or like the young alligator1 still dragging the shell attached to the umbilical cord while already snarling with open jaws and pouncing on any object brought near. The human young is less mature and less well furnished when it becomes a separate organism from its mother, whose physical and mental powers must long continue to make up for the child’s lack of independence.