"Beholding beauty with the eye of the mind, he will be enabled to bring forth, not images of beauty, but realities (for he has hold not of an image but of a reality) [...]." (Plato, "The Symposium", cca. 385–370 BC)
"We must make a threefold distinction and think of that which becomes, that in which it becomes, and the model which it resembles." (Plato, "Timaeus", 360 BC)
"[Imagination is] that in virtue of which we say that an image occurs to us and not as we speak of it metaphorically." (Aristotle, "De Anima" III, cca. 350 BC)
"For imagination is different from either perceiving or discursive thinking, though it is not found without sensation, or judgement without it. That this activity is not the same kind of thinking as judgement is obvious. For imagining lies within our own power whenever we wish (e.g. we can call up a picture, as in the practice of mnemonics by the use of mental images), but in forming opinions we are not free: we cannot escape the alternative of falsehood or truth." (Aristotle, "De Anima", cca. 350 BC)
"Since it seems that there is nothing outside and separate in existence from sensible spatial magnitudes, the objects of thought are in the sensible forms, viz. both the abstract objects and all the states and affections of sensible things. Hence no one can learn or understand anything in the absence of sense, and when the mind is actively aware of anything it is necessarily aware of it along with an image; for images are like sensuous contents except in that they contain no matter. Imagination is different from assertion and denial; for what is true or false involves a synthesis of thoughts. In what will the primary thoughts differ from images? Must we not say that neither these nor even our other thoughts are images, though they necessarily involve them?" (Aristotle, "De Anima", cca. 350 BC)
"The intellectual capacity thinks the forms in the phantasmata (mental images) […] And for the following reason, as without having perceptual awareness no one could either learn or understand anything, so when one engages in intellectual activity one must at that time do so by means of a phantasma. For, phantasmata are just as perceptual states (aisthemata) are [in actual external perception] but without matter." (Aristotle, "De Anima" III, cca. 350 BC)
"Thinking is different from perceiving and is held to be in part imagination, in part judgement: we must therefore first mark off the sphere of imagination and then speak of judgement. If then imagination is that in virtue of which an image arises for us, excluding metaphorical uses of the term, is it a single faculty or disposition relative to images, in virtue of which we discriminate and are either in error or not? The faculties in virtue of which we do this are sense, opinion, knowledge, thought." (Aristotle, "De Anima", cca. 350 BC)
"Now for the thinking soul images take the place of direct perceptions; and when it asserts or denies that they are good or bad, it avoids or pursues them. Hence the soul never thinks without a mental image." (Aristotle, "De Anima" , cca. 350 BC)
"As regards the question, therefore, what memory or remembering is, it has now been shown that it is the having of an image, related as a likeness to that of which it is an image; and as to the question of which of the faculties within us memory is a function, it has been shown that it is a function of the primary faculty of sense-perception, i.e. of that faculty whereby we perceive time." (Aristotle, "De Memoria et Reminiscentia" ["On Memory and Recollection"], 4th century BC)
"But since we have, in our work on the soul, treated of imagination, and the faculty of imagination is identical with that of sense-perception, though the being of a faculty of imagination is different from that of a faculty of sense-perception; and since imagination is the movement set up by a sensory faculty when actually discharging its function, while a dream appears to be an image (for which occurs in sleep - whether simply or in some particular way - is what we call a dream): it manifestly follows that dreaming is an activity of the faculty of sense-perception, but belongs to this faculty qua imaginative." (Aristotle, "On Dreams", 4th century BC)
"For according to the arguments from the existence of the sciences there will be Forms of all things of which there are sciences, and according to the argument that there is one attribute common to many things there will be Forms even of negations, and according to the argument that there is an object for thought even when the thing has perished, there will be Forms of perishable things; for we can have an image of these." (Aristotle, "Metaphysics", 4th century BC)
"It is obvious then, that memory belongs to that part of the soul to which imagination belongs. […] Just as the picture painted on the panel is at once a picture and a portrait, and though one and the same, is both, yet the essence of the two is not the same, and it is possible to think of it both as a picture and as a portrait, so in the same way we must regard the mental picture within us both as an object of contemplation in itself and as a mental picture of something else […]. Insofar as we consider it in relation to something else, e.g. as a likeness, it is also an aid to memory." (Aristotle, "De Memoria et Reminiscentia" [On Memory and Recollection], 4th century BC)
"He [Simonides] inferred that persons desiring to train this faculty [of memory] must select places and form mental images of the things they wish to remember and store those images in the places, so that the order of the places will preserve the order of the things, and the images of the things will denote the things themselves, and we shall employ the places and images respectively as a wax writing-tablet and the letters written on it." (Marcus Tullius Cicero [cited in Yates 1966], "De Oratore", 55 BC)
"As infinite kinds of almost identical images arise continually from the innumerable atoms and flow out to us from the gods, so we should take the keenest pleasure in turning and bending our mind and reason to grasp these images, in order to understand the nature of these blessed and eternal beings." (Marcus Tullius Cicero, "De Natura Deorum" ["On the Nature of the Gods"], 45 BC)
"In the same way as regards the soul, when that kind of thing in us which mirrors the images of thought and intellect is undisturbed, we see them and know them in a way parallel to sense-perception, along with the prior knowledge that it is intellect and thought that are active. But when this is broken because the harmony of the body is upset, thought and intellect operate without an image, and then intellectual activity takes place without a mind-picture." (Plotinus, "Enneads", cca. 270 AD)
"[...] so external sensation is the image of this perception of the soul, which is in its essence truer and is a contemplation of forms alone without being affected. From these forms, from which the soul alone receives its lordship over the living being, come reasonings, and opinions and noetic acts; and this is precisely where ‘we’ are." (Plotinus, "Enneads", cca. 270 AD)
"We both are, and know that we are, and delight in our being, and our knowledge of it. Moreover, in these three things no true-seeming illusion disturbs us; for we do not come into contact with these by some bodily sense, as we perceive the things outside of us of all which sensible objects it is the images resembling them, but not themselves which we perceive in the mind and hold in the memory, and which excite us to desire the objects. But, without any delusive representation of images or phantasms, I am most certain that I am, and that I know and delight in this." (Aurelius Augustinus, "The City of God", early 400s)
"We invoke the imagination and the intervals that it furnishes, since the form itself is without motion or genesis, indivisible and free of all underlying matter, though the elements latent in the form are produced distinctly and individually on the screen of imagination. What projects the images is the understanding; the source of what is projected is the form in the understanding; and what they are projected in is this 'passive nous' that unfolds in revolution about the partlessness of genuine Nous." (Proclus Lycaeus, "A Commentary on the First Book of Euclid’s Elements", cca 5th century)
"[…] the mind orders nothing by its own motions, but lies merely receptive under the impressions of bodies, reflecting empty images in a mirror in place of reality." (Anicius Manlius Severinus Boethius, "The Consolation of Philosophy", cca. 524)
"An image is, after all, a reminder; it is to the illiterate what a book is to the literate, and what the word is to the hearing, the image is to sight. All this is the approach through the senses: but it is with the mind that we lay hold on the image." (John of Damascus, cca. 8th century)
"[…] reason is the thing without which our state would be the state of wild beasts, of children and lunatics; it is the thing whereby we picture our intellectual acts before they become manifest to the senses, so that we see them exactly as though we had sensed them; then we represent these pictures in our sensual acts so that they correspond exactly with what we have represented and imagined." (Rhazes [Abu Bakr Muhammad Ibn Zakariyya Al-Razi], "Spiritual Physick", cca 10th century)
"The faculty which grasps such concepts acquires intelligible forms from sense-perception by force of an inborn disposition, so that forms, which are in the form-bearing faculty and the memorizing faculty, are made present to [the rational soul] with the assistance of the imaginative and estimative [faculties]." (Avicenna Latinus [Ibn Sina], "A Compendium on the Soul", cca. 996-997)
"It seems that all perception is but the grasping of the form of the perceived object in some manner. If, then, it is a perception of some material object, it consists in an apprehension of its form by abstracting it from matter in some way. But the kinds of abstraction are different and their degrees various. This is because, owing to matter, the material form is subject to certain states and conditions which do not belong to [the form] by itself insofar as it is this form. So sometimes the abstraction from matter is effected with all or some of these attachments, and sometimes it is complete in that the concept is abstracted from matter and from the accidents it possesses on account of the matter."(Avicenna Latinus [Ibn Sina], "Liber De anima", cca. 1014-1027)
"The animal faculties assist the rational soul in various ways, one of them being that sense-perception brings to it particulars, from which four things result in [the rational soul]: One of them is that the mind extracts single universals from the particulars, by abstracting their concepts from matter and the appendages of matter and its accidents, by considering what is common in it and what different, and what in its existence is essential and what accidental. From this the principles of conceptualization come about [in] the soul: and this with the help of its employing imagination and estimation." (Avicenna Latinus [Ibn Sina], "Liber De Anima", cca. 1014-1027)
"When the intellectual faculty considers the particulars which are [stored] in imagination and the light of the above-mentioned active intellect shines upon them in us, then the [particulars] are transformed into something abstracted from matter and from the [material] attachments and get imprinted in the rational soul, but not in the sense that the particulars themselves are transferred from imagination to our intellect, nor in the sense that the concept buried in [material] attachments - which in itself and with regard to its essence is abstract - produces a copy of itself, but in the sense that looking at the particulars disposes the soul for something abstracted to flow upon it from the active intellect. (Avicenna Latinus [Ibn Sina], "Liber De Anima", cca. 1014-1027)
"Sometimes a thing is perceived [via sense-perception] when it is observed; then it is imagined, when it is absent [in reality] through the representation of its form inside, Sense-perception grasps [the concept] insofar as it is buried in these accidents that cling to it because of the matter out of which it is made without abstracting it from [matter], and it grasps it only by means of a connection through position [ that exists] between its perception and its matter. It is for this reason that the form of [the thing] is not represented in the external sense when [sensation] ceases. As to the internal [faculty of] imagination, it imagines [the concept] together with these accidents, without being able to entirely abstract it from them. Still, [imagination] abstracts it from the afore-mentioned connection [through position] on which sense-perception depends, so that [imagination] represents the form [of the thing] despite the absence of the form's [outside] carrier." (Avicenna Latinus [Ibn Sina], "Pointer and Reminders", cca. 1030)
"The multiplicity of the soul's occupations with sense-perceptible imaginable forms and connotational images, which are in the form-bearing and the remembering [faculties respectively], with the help of the estimative and cogitative faculty, makes the soul obtain a disposition for the reception of abstractions of them [i.e., of the imaginable forms and images] from the separate substance through some kind of relationship between the two. Observation and inspection of the issue verify this. These occupations [with imaginable forms and images] are those which give [the soul] a perfect disposition that is specific for [the reception of] each individual form, though an intellectual concept may [also] provide this specific [disposition] for [the reception of] another intellectual concept." (Avicenna Latinus [Ibn Sina], "Pointer and Reminders", cca. 1030)
"The employment of tropes, just as the use of schemata, is the exclusive privilege of the very learned. The rules governing tropes are also very strict, so that the latitude in which they may be used is definitely limited. For the rules teach that we may not extend figures. One who is studiously imitating the authors by using metaphors and figures, must take care to avoid crude figures that are hard to interpret. What is primarily desirable in language is lucid clarity and easy comprehensibility. Therefore schemata should be used only out of necessity or for ornamentation. Speech was invented as a means of communicating mental concepts; and figures [of speech] are admitted so far as they compensate by their utility for whatever they lack in conformity to the [rules of the grammatical] art." (John of Salisbury, "Metalogicon", 1159)
"There are also schemata, which we may translate as figures in wording or sense, and which comprise various forms of diction used to embellish speech. Barbarisms and metaplasms occur in single words; solecisms and schemata, not in individual words, but in the joining of a number of words." (John of Salisbury, "Metalogicon", 1159)
"In the foregoing you will discover a very remarkable thing. God reserved the truth of things, which is the supreme truth, for Himself, but He conceded to His image the formation of images of things at whatever time." (Richard of St. Victor, "Benjamin Major" [aka "The Mystical Ark"], cca 1162)
"Know that the figures employed by prophets are of two kinds: first, where every word which occurs in the simile represents a certain idea: and secondly, where the simile, as a whole, represents a general idea, but has a great many points which have no reference whatever to that idea: they are simply required to give to the simile its proper form and order, or better to conceal the idea: the simile is therefore continued as far as necessary, according to its literal sense." (Moses Maimonides, "The Guide for the Perplexed", 1190)
"Part of the functions of the imaginative faculty is, as you well know, to retain impressions by the senses, to combine them, and chiefly to form images." (Moses Maimonides, "Guide of the Perplexed", 1190 [translated by Michael Friedländer, 1904])
"All that is required between cognizer and cognized is a likeness in terms of representation, not a likeness in terms of an agreement in nature. For it's plain that the form of a stone in the soul is of a far higher nature than the form of a stone in matter. But that form, insofar as it represents the stone, is to that extent the principle leading to its cognition." (Thomas Aquinas, "Quaestiones disputatae de veritate", cca. 1256-1259)
"One who doesn't perceive the essence and quiddity of a thing, but only its image, can't know the thing. For one who has seen only a picture of Hercules doesn't know Hercules. A human being, however, perceives nothing of a thing, except only its image, that is, a species received through the senses, which is an image of the thing and not the thing itself. For not the stone but a species of the stone is in the soul." (Thomas Aquinas, "Summa Theologiae", cca. 1266-1273)
"[…] one ought to say that one may perceive the image of a thing in two ways. In one way, as the object of cognition. In this way it is true that one perceiving only the thing's image does not cognize the thing; for example, someone seeing the image of Hercules painted on a wall does not thereby either see or cognize Hercules. In another way, as the basis [ratio] of cognizing, and in this way the claim is not true. For through only a species perceived of a thing the thing is truly cognized - as a stone is truly seen through its sensible species alone, received in the eye, and is truly intellectively cognized through its intelligible species alone, received in intellect." (Thomas Aquinas, "Summa Theologiae", cca. 1266-1273)
"Phantasms don't have the same manner of existing that the human intellect has [...] and so they cannot through their own power make an impression on the possible intellect. But through the power of the agent intellect, a kind of likeness results in the possible intellect as a result of agent intellect's turning toward the phantasms […] And this is how intelligible species are said to be abstracted from phantasms. It's not that some form that is numerically the same is first in phantasms and then produced in the possible intellect."(Thomas Aquinas, "Summa Theologiae", cca. 1266-1273)
"Nor is it enough to say that the intelligible notions formed by the active intellect subsist somehow in the phantasmata (mental image), which are certainly intrinsic to us; for as we have already observed in treating the passive intellect, objects only become actually intelligible when abstracted from phantasmata; so that merely by way of the phantasmata, we cannot attribute the work of the active intellect to ourselves" (Thomas Aquinas, "De Anima" III, cca. 1268) [On Aristotle's phantasmata]
"The attention will tend toward the species either in such a way that it would not pass beyond so as to attend to the object, or in such a way that it would pass beyond. If in the first way, then the thing will not be seen in itself but only its image will be seen as if it were the thing itself." (Peter J Olivi, "Quaestiones in secundum librum Sententiarum", cca. 1280- 1282)
"Such an image or fictum was postulated for no other reason than to supposit for a thing in such a way that both a proposition might be composed out of it and it might be common to things. For these are denied of things." (William Ockham, "Expositio in librum Perihermenias", cca. 1321-1324)
"The thing represented needs to be cognized in advance - otherwise the representative would never lead to a cognition of the thing represented as to something similar." (William Ockham, "Expositio in librum Perihermenias", cca. 1321-1324)
"When the Soul wants to experience something she throws out an image in front of her and then steps into it." (Eckhart von Hochheim [aka Meister Eckhart] cca. 14th century)
"[…] the painter cannot produce any form or figure […] if first this form or figure is not imagined and reduced into a mental image (idea) by the inward wits. And to paint, one needs acute senses and a good imagination with which one can get to know the things one sees in such a way that, once these things are not present anymore and transformed into mental images (fantasmi), they can be presented to the intellect. In the second stage, the intellect by means of its judgement puts these things together and, finally, in the third stage the intellect turns these mental images […] into a finished composition which it afterwards represents in painting by means of its ability to cause movement in the body." (Romano Alberti, "Della nobiltà della Pittura" ["The Nobility of Painting"], 1585)
"[W]hatsoever the Philosopher saith should be done, [the poet] gives a perfect picture of it by some one, by who he presupposeth it was done, so as he coupleth the generall notion with the particuler example. A perfect picture I say, for hee yeeldeth to the powers of the minde an image of that whereof the Philosopher bestoweth but a wordish description, which doth neither strike, pearce, nor possesse the sight of the soule so much, as that other doth." (Sir Philip Sidney, "Defence of Poesie", 1595)
"That faculty which perceives and recognizes the noble proportions in what is given to the senses, and in other things situated outside itself, must be ascribed to the soul. It lies very close to the faculty which supplies formal schemata to the senses, or deeper still, and thus adjacent to the purely vital power of the soul, which does not think discursively […] Now it might be asked how this faculty of the soul, which does not engage in conceptual thinking, and can therefore have no proper knowledge of harmonic relations, should be capable of recognizing what is given in the outside world. For to recognize is to compare the sense perception outside with the original pictures inside, and to judge that it conforms to them." (Johannes Kepler, "Harmonices Mundi" ["Harmony of the World"] , 1619)
"The entire method consists in the order and arrangement of the things to which the mind's eye must turn so that we can discover some truth." (René Descartes, "Rules for the Direction of the Mind", 1628)
"Certainly a phantasm is that in which the understanding knows a singular, and yet a phantasm is not a formal sign, since it does not inhere in nor inform the understanding; nor is it an instrumental sign, since it does not lead to a significate from a preexisting cognition, but immediately represents that significate; for the understanding does not need first to know the phantasm as a thing known, in order to have a knowledge of singulars. [...] If, nevertheless, the understanding were to respect the phantasm as a knowable thing and attain the singular by means of it, the understanding would be using the phantasm as a known object manifesting another and consequently as an instrumental sign. But this will be through a reflex cognition upon the entity of the phantasm." (John of St. Thomas, "Tractatus de signis", 1632)
"From all this I am beginning to have a rather better understanding of what I am. But it still appears - and I cannot stop thinking this - that the corporeal things of which images are formed in my thought, and which the senses investigate, are known with much more distinctness than this puzzling 'I' which cannot be pictured in the imagination." (René Descartes, "Meditations" II, 1641)
"An image (in the most strict signification of the word) is the Resemblance of some thing visible […] (Thomas Hobbes, "Leviathan", 1651)
"For after the object is removed, or the eye shut, we still retain an image of the thing seen, though more obscure than when we see it. And this is it the Latins call imagination, from the image made in seeing, and apply the same, though improperly, to all the other senses. But the Greeks call it fancy, which signifies appearance, and is as proper to one sense as to another. IMAGINATION, therefore, is nothing but decaying sense; and is found in men and many other living creatures, as well sleeping as waking." (Thomas Hobbes, "Leviathan: The Matter, Form and Power of a Commonwealth Ecclesiastical and Civil", 1651)
"For the Mind feels those things that it conceives in understanding no less than those it has in the memory. For the eyes of the mind, by which it sees and observes things, are demonstrations [descriptions] themselves." (Baruch Spinoza, "Ethics, Demonstrated in Geometrical Order", 1677)
"[...] in ordering our thoughts and images, we must always attend to those things which arc good in each thing so that in this way we are always determined to acting from an affect of joy." (Baruch Spinoza, "Ethics", 1677)
"The idea of any mode in which the human body is affected hy external bodies must involve the nature of the human body and at the same rime the nature of the external body." (Baruch Spinoza, "Ethics", 1677)
"The images of things are affections of the human body whose ideas represent external bodies as present to us. […] the affections of the human body whose ideas present external bodies as present to us, we shall call things, though they do not reproduce [external] figures of things. And when the mind regards bodies in this way, we shall say that it imagines." (Baruch Spinoza, "Ethics", 1677)
"It is also only by virtue of the continual action of God upon us that we have in our soul the ideas of all things; that is to say, since every effect expresses its cause, the essence of our soul is a certain expression, imitation or image of the divine essence, thought, and will and of all the ideas which are comprised in God." (Gottfried W Leibniz, "Discourse on Metaphysics", 1686)
"As in a block of marble all possible figures are potentially contained in it, and can be drawn out of it by the movement or by the action of the chisel, so in the same way all intelligible figures are potentially in intelligible extension and are discovered in it according to the different ways in which this extension is represented to the mind, as a consequence of the general laws which God has established according to which he continuously acts in us. " (Nicolas Malebranche , "Dialogues On Metaphysics And Religion", 1688)
"A spirit is one simple, undivided, active being: as it perceives ideas, it is called the understanding, and as it produces or otherwise operates about them, it is called the will. Hence there can be no idea formed of a soul or spirit: for all ideas whatever, being passive and inert, vide, they cannot represent unto us, by way of image or likeness, that which acts." (George Berkeley, "Principles of Human Knowledge", 1710)
"That an idea which is inactive, and the existence whereof consists in being perceived, should be the image or likeness of an agent subsisting by itself, seems to need no other refutation, than barely attending to what is meant by those words. But perhaps you will say, that though an idea cannot resemble a spirit, in its thinking, acting, or subsisting by itself, yet it may in some other respects: and it is not necessary that an idea or image be in all respects like the original."(George Berkeley, "Principles of Human Knowledge", 1710)
"The ideas imprinted on the senses by the Author of Nature are called real things: and those excited in the imagination being less regular, vivid and constant, are more properly termed ideas, or images of things, which they copy and represent. But then our sensations, be they never so vivid and distinct, are nevertheless ideas, that is, they exist in the mind, or are perceived by it, as truly as the ideas of its own framing. The ideas of sense are allowed to have more reality in them, that is, to be more strong, orderly, and coherent than the creatures of the mind; but this is no argument that they exist without the mind. They are also less dependent on the spirit, or thinking substance which perceives them, in that they are excited by the will of another and more powerful spirit: yet still they are ideas, and certainly no idea, whether faint or strong, can exist otherwise than in a mind perceiving it." (George Berkeley, "Principles of Human Knowledge", 1710)
"Thoughts are the images of things, words are of thoughts; and we all know that images and pictures are only so true as they are true representations men and things. […] For poets as well painters think it their business to take likeness of things from their appearance."(Joseph Trapp, "Lectures on Poetry", 1711)
"It is your opinion, the ideas we perceive by our senses are not real things, but images, or copies of them. Our knowledge therefore is no farther real, than as our ideas are the true representations of those originals. But as these supposed originals are in themselves unknown, it is impossible to know how far our ideas resemble them; or whether they resemble them at all. We cannot therefore be sure we have any real knowledge." (George Berkeley, "Three Dialogues", 1713)
"To speak the truth, Philonous, I think there are two kinds of objects, the one perceived immediately, which are likewise called ideas, the other are real things or external objects perceived by the mediation of ideas, which are their images and representations. Now I own, ideas do not exist without the mind; but the latter sort of objects do." (George Berkeley, "Three Dialogues", 1713)
"[...] things which do not now exist in the mind itself, can only be perceived, remembered, or imagined, by means of ideas or images of them in the mind, which are the immediate objects of perception, remembrance, and imagination. This doctrine appears evidently to be borrowed from the old system; which taught, that external things make impressions upon the mind, like the impressions of a seal upon wax; that it is by means of those impressions that we perceive, remember) or imagine them; and that those impressions must resemble the things from which they are taken. When we form our notions of the operations of the mind by analogy, this way of conceiving them seems to be very natural, and offers itself to our thoughts: for as every thing which is felt must make some impression upon the body, we are apt to think, that every thing which is understood must make some impression upon the mind." (Thomas Reid, "An Inquiry into the Human Mind", 1734)
"All the perceptions of the human mind resolve themselves into two distinct kinds, which I shall call impressions and ideas. The difference betwixt these consists in the degrees of force and liveliness, with which they strike upon the mind, and make their way into our thought or consciousness. Those perceptions, which enter with most force and violence, we may name impressions; and under this name I comprehend all our sensations, passions and emotions, as they make their first appearance in the soul. By ideas I mean the faint images of these in thinking and reasoning. I believe it will not be very necessary to employ many words in explaining this distinction." (David Hume, "A Treatise of Human Nature", 1738)
"But to form the idea of an object, and to form an idea simply is the same thing; the reference of the idea to an object being an extraneous denomination, of which in itself it bears no mark or character. Now as it is impossible to form an idea of an object, that is possessed of quantity and quality, and yet is possessed of no precise degree of either; it follows, that there is an equal impossibility of forming an idea, that is not limited and confined in both these particulars. Abstract ideas are therefore in themselves individual, however they may become general in their representation. The image in the mind is only that of a particular object, though the application of it in our reasoning be the same, as if it were universal." (David Hume, "Treatise of Human Nature", 1738)
"Nay farther, even with relation to that succession, we cou'd only admit of those perceptions, which are immediately present to our consciousness, nor cou'd those lively images, with which the memory presents us, be ever receiv'd as true pictures of past perceptions. The memory, senses, and understanding are, therefore, all of them founded on the imagination, or the vivacity of our ideas."(David Hume, "A Treatise of Human Nature A Treatise of Human Nature", 1738)
"It seems evident, that men are carried, by a natural instinct or prepossession, to repose faith in their senses; and that, without any reasoning, or even almost before the use of reason, we always suppose an external universe, which depends not on our perception, but would exist, though we and every sensible creature were absent or annihilated. […] It seems also evident, that, when men follow this blind and powerful instinct of nature, they always suppose the very images, presented by the senses, to be the external objects." (David Hume, "An Enquiry Concerning Human Understanding", 1748)
"Our mental vision or conception of ideas is nothing but a revelation made to us by our Maker. When we voluntarily turn our thoughts to any object, and raise up its image in the fancy, it is not the will which creates that idea: It is the universal Creator, who discovers it to the mind, and renders it present to us." (David Hume, "An Enquiry Concerning Human Understanding", 1748)
"Wit, you know, is the unexpected copulation of ideas, the discovery of some occult relation between images in appearance remote from each other." (Samuel Johnson, "The Rambler", 1750)
"Things which do not now exist in the mind itself, can only be perceived, remembered, or imagined, by means of the ideas or images in the mind, which are the immediate objects of perception, remembrance, and imagination." (Thomas Reid, "An Inquiry into the Human Mind on the Principles", 1764)
"Invention, strictly speaking, is little more than a new combination of those images which have been previously gathered and deposited in the memory: nothing can come of nothing." (Joshua Reynolds, "Discourses on Art", [discourse] 1769)
"Men always fool themselves when they give up experience for systems born of the imagination. Man is the work of nature, he exists in nature, he is subject to its laws, he can not break free, he can not leave even in thought; it is in vain that his spirit wants to soar beyond the bounds of the visible world, he is always forced to return." (Paul-Henri T d’Holbach, "Système de la Nature", 1770)
"This formal and pure condition of sensibility to which the employment of the concept of understanding is restricted, we shall entitle the schema of the concept. The procedure of understanding in these schemata we shall entitle the schematism of pure understanding.
The schema is in itself always a product of imagination. Since, however, the synthesis of imagination aims at no special intuition, but only at unity in the determination of sensibility, the schema has to be distinguished from the image." (Immanuel Kant," Critique of Pure Reason", 1781)
"This schematism of our understanding, in its application to appearances and their mere form, is an art concealed in the depths of the human soul, whose real modes of activity nature is hardly likely ever to allow us to discover, and to have open to our gaze." (Immanuel Kant, "Critique of Pure Reason", 1781)
"Conceiving as well as projecting or resolving, are what the schoolmen called immanent acts of the mind, which produce nothing beyond themselves. But painting is a transitive act, which produces an effect distinct from the operation, and this effect is the picture. Let this therefore be always remembered, that what is commonly called the image of a thing in the mind, is no more than the act or operation of the mind in conceiving it." (Thomas Reid, "Essays on the Intellectual Powers of Man", 1785)
"Language is the express image and picture of human thoughts; and, from the picture, we may often draw very certain conclusions with regard to die original. " [...] if there were really such images in the mind, or in the brain, they could not be general, because every thing that really exists is an individual. Universals are neither acts of the mind, nor images in the mind." (Thomas Reid, "Essays on the Intellectual Powers of Man", 1785)
"There are conceptions which may be called fancy pictures. They are commonly called creatures of fancy, or of imagination. They are not the copies of any original that exists, but are originals themselves […]. They were conceived by their creators, and may be conceived by others, but they never existed. We do not ascribe the qualities of true or false to them, because they are not accompanied with any belief, nor do they imply any affirmation or negation." (Thomas Reid,"Essays on the Intellectual Powers of Man", 1785)
"Everything possible to be believed is an image of truth." (William Blake, "The Marriage of Heaven and Hell" , 1790)
"The impossibility of separating the nomenclature of a science from the science itself is owing to this, that every branch of physical science must consist of three things: the series of facts which are the objects of the science, the ideas which represent these facts, and the words by which these ideas are expressed. Like three impressions of the same seal, the word ought to produce the idea, and the idea to be a picture of the fact." (Antoine L Lavoisier, "Elements of Chemistry in a New Systematic Order", 1790)
"The imagination is an eye where images remain forever." (Joseph Joubert, [Letter to Revd. Dr. Trusler] 1799)
"One says of a person who has travelled much, that he has seen the world. to the knowledge of the world than just seeing it. Whoever wants to must draw up a plan beforehand and must not just regard the world senses." (Immanuel Kant "Physische Geographie" [Physical Geography], 1802)
"Former ages thought in terms of images of the imagination, whereas we moderns have concepts. Formerly the guiding ideas of life presented themselves in concrete visual form as divinities, whereas today they are conceptualized. The ancients excelled in creation; our own strength lies rather in destruction, in analysis." (Johann Wolfgang von Goethe, 1806)
"Taste is the intermediate faculty which connects the active with the passive powers of our nature, the intellect with the senses; and its appointed function is to elevate the images of the latter, while it realizes the ideas of the former."(Samuel T Coleridge, "On the Principles of Genial Criticism", 1814)
"The imagination […] that reconciling and mediatory power, which incorporating the reason in images of the sense and organizing (as it were) the flux of the senses by the permanence and self-circling energies of the reason, gives birth to a system of symbols, harmonious in themselves, and consubstantial with the truths of which they are the conductors." (Samuel T Coleridge, "The Statesman's Manual", 1816)
"It seems to be like taking the pieces of a dissected map out of its box. We first look at one part, and then at another, then join and dove-tail them; and when the successive acts of attention have been completed, there is a retrogressive effort of mind to behold it as a whole. The poet should paint to the imagination, not to the fancy; and I know no happier case to exemplify the distinction between these two faculties." (Samuel T Coleridge," Biographia Literaria", 1817)
"Theories usually result from the precipitate reasoning of an impatient mind which would like to be rid of phenomena and replace them with images, concepts, indeed often with mere words." (Johann Wolfgang von Goethe, "Maxims and Reflections", 1833)
as is sufficiently evident in the case of metaphors and similes. So from all time what was said or sung inwardly to the ear had to be presented equally to the eye. And so in childish days we see word and picture in continual balance; in the book of the law and in the way of salvation, in the Bible and in the spelling-book. When something was spoken which could not be pictured, and something pictured which could not be spoken, all went well; but mistakes were often made, and a word was used instead of a picture; and thence arose those monsters of symbolical mysticism, which are doubly an evil." (Johann Wolfgang von Goethe, "Maxims and Reflections", 1833)
"Every presentation of philosophy, whether oral or written, is to be taken and can only be taken in the sense of a means. Every system is only an expression or image of reason, and hence only an object of reason, an object which reason - a living power that procreates itself in new thinking beings - distinguishes from itself and posits as an object of criticism. Every system that is not recognized and appropriated as just a means, limits and warps the mind for it sets up the indirect and formal thought in the place of the direct, original and material thought." (Ludwig Feuerbach, "Towards a Critique of Hegel’s Philosophy", 1839)
"The eye of the intellect 'sees in all objects what it brought with it the means of seeing'" (Thomas Carlyle, [probably quoting Varnhagen von Ense] 1839)
"Logicians may reason about abstractions. But the great mass of men must have images." (Thomas B Macaulay, Critical and Miscellaneous Essays, 1840)
"A line, as defined by geometers, is wholly unconceivable. We can reason about a line as if it had no breadth; because we have a power, which is the foundation of all the control we can exercise over the operations of our minds; the power, when a perception is present to our senses, or a conception to our intellects, of attending to a part only of that perception or conception, instead of the whole. But we cannot conceive a line without breadth: we can form no mental picture of such a line: all the lines which we have in our minds are lines possessing breadth." (John S Mill, "System of Logic ratiocinative and inductive, being a connected view of the principles of evidence and the methods of scientific investigation", 1843)
"A human being, what is a human being? Everything and nothing. Through the power of thought it can mirror everything it experiences. Through memory and knowledge it becomes a microcosm, carrying the world within itself. A mirror of things, a mirror of facts. Each human being becomes a little universe within the universe!" (Guy de Maupassant, [in "The Journal of a Madman"] 1851)
"When I have before my eyes a pair of stereoscopic drawings which are hard to combine, it is difficult to bring the lines and points that correspond, to cover each other, and with every little motion of the eyes they glide apart. But if I chance to gain a lively mental image (Anschauungsbild) of the represented solid form (a thing that often occurs by lucky chance), I then move my two eyes with perfect certainty over the figure without the picture separating again." (Hermann von Helmholtz, "Tonempfindungen" ["Sensations of Tone"], 1863)
"By reducing imagination to the power of forming images, and by insisting that no image can be formed except out of the elements furnished by experience, I do not mean to confound imagination with memory; indeed, the frequent occurrence of great strength of memory with comparative feebleness of imagination, would suffice to warn us against such a conclusion." (George H Lewes, "The Principles of Success in Literature", 1865)
"However rapid and remote their flight of thought, it is a succession of images, not of abstractions. The details which give significance, and which by us are seen vaguely as through a vanishing mist, are by them seen in sharp outlines. The image which to us is a mere suggestion, is to them almost as vivid as the object. And it is because they see vividly that they can paint effectively." (George H Lewes, "The Principles of Success in Literature", 1865)
"The degree in which each mind habitually substitutes signs for images will be, CETERIS PARIBUS [with other conditions remaining the same], the degree in which it is liable to error. This is not contradicted by the fact that mathematical, astronomical, and physical reasonings may, when complex, be carried on more successfully by the employment of signs; because in these cases the signs themselves accurately represent the abstractness of the relations. Such sciences deal only with relations, and not with objects; hence greater simplification ensures greater accuracy. But no sooner do we quit this sphere of abstractions to enter that of concrete things, than the use of symbols becomes a source of weakness. Vigorous and effective minds habitually deal with concrete images." (George H Lewes, "The Principles of Success in Literature", 1865)
"Thus representations of the external world are images of the lawlike temporal succession of natural events, and if they are correctly formed in accordance with the laws of our thinking, and we are able correctly to translate them back again into actuality through our actions, then the representations that we have are also the uniquely true [ones] for our faculty of thought; all others would be false." (Hermann von Helmholtz, "Handbuch der physiologischen Optik" Vol. 3, 1867)
"Therefore, the great business of the scientific teacher is, to imprint the fundamental, irrefragable facts of his science, not only by words upon the mind, but by sensible impressions upon the eye, and ear, and touch of the student, in so complete a manner, that every term used, or law enunciated, should afterwards call up vivid images of the particular structural, or other, facts which furnished the demonstration of the law, or the illustration of the term." (Thomas H Huxley, "Lay Sermons, Addresses and Reviews", 1870)
"You cannot crown the edifice by this abstraction. The scientific imagination, which is here authoritative, demands as the origin and cause of a series of ether waves a particle of vibrating matter quite as definite, though it may be excessively minute, as that which gives origin to a musical sound. Such a particle we name an atom or a molecule. I think the imagination when focused so as to give definition without penumbral haze, is sure to realise this image at last." (John Tyndall, "The Scientific Use of the Imagination", 1870)
"When a mental image, as such, is the object of my apprehension, there is no meaning in seeking to distinguish its existence in my consciousness (in me) from its existence out of my consciousness (in itself) ; for the object apprehended is, in this case, one which does not even exist, as the objects of external perception do, in itself outside of my consciousness. It exists only within me." (Friedrich Ueberweg, "System of Logic and History of Logical Doctrines", 1871)
"Thus the man who is responsive to artistic stimuli reacts to the reality of dreams as does the philosopher to the reality of existence; he observes closely, and he enjoys his observation: for it is out of these images that he interprets life, out of these processes that he trains himself for life." (Friedrich Nietzsche," The Birth of Tragedy", 1872)
"Everything which distinguishes man from the animals depends upon this ability to volatilize perceptual metaphors in a schema, and thus to dissolve an image into a concept. For something is possible in the realm of these schemata which could never be achieved with the vivid first impressions: the construction of a pyramidal order according to castes and degrees, the creation of a new world of laws, privileges, subordinations, and clearly marked boundaries - a new world, one which now confronts that other vivid world of first impressions as more solid, more universal, better known, and more human than the immediately perceived world, and thus as the regulative and imperative world." (Friedrich Nietzsche, "On Truth and Lie in an Extra-Moral Sense", 1873)
"Ideas are substitutions which require a secondary process when what is symbolized by them is translated into the images and experiences it replaces; and this secondary process is frequently not performed at all, generally only performed to a very small extent. Let anyone closely examine what has passed in his mind when he has constructed a chain of reasoning, and he will be surprised at the fewness and faintness of the images which have accompanied the ideas." (George H Lewes "Problems of Life and Mind", 1873)
"If we wish to form a mental representation of what is going on among the molecules in calm air, we cannot do better than observe a swarm of bees, when every individual bee is flying furiously, first in one direction, and then in another, while the swarm, as a whole, either remains at rest, or sails slowly through the air." (James C Maxwell, "Molecules", Nature, 1873)
"That immense framework and planking of concepts to which the needy man clings his whole life long in order to preserve himself is nothing but a scaffolding and toy for the most audacious feats of the liberated intellect. And when it smashes this framework to pieces, throws it into confusion, and puts it back together in an ironic fashion, pairing the most alien things and separating the closest, it is demonstrating that it has no need of these makeshifts of indigence and that it will now be guided by intuitions rather than by concepts. There is no regular path which leads from these intuitions into the land of ghostly schemata, the land of abstractions. There exists no word for these intuitions; when man sees them he grows dumb, or else he speaks only in forbidden metaphors and in unheard - of combinations of concepts. He does this so that by shattering and mocking the old conceptual barriers he may at least correspond creatively to the impression of the powerful present intuition." (Friedrich Nietzsche, "On Truth and Lie in an Extra-Moral Sense", 1873)
"The leading characteristic of algebra is that of operation on relations. This also is the leading characteristic of Thought. Algebra cannot exist without values, nor Thought without Feelings. The operations are so many blank forms till the values are assigned. Words are vacant sounds, ideas are blank forms, unless they symbolize images and sensations which are their values. Nevertheless it is rigorously true, and of the greatest importance, that analysts carry on very extensive operations with blank forms, never pausing to supply the symbols with values until the calculation is completed; and ordinary men, no less than philosophers, carry on long trains of thought without pausing to translate their ideas (words) into images." (George H Lewes "Problems of Life and Mind", 1873)
"The imagination is one of the highest prerogatives of man. By this faculty he unites, independently of the will, former images and ideas, and thus creates brilliant and novel results […] The value of the products of our imagination depends of course on the number, accuracy, and clearness of our impressions; on our judgment and taste in selecting or rejecting the involuntary combinations, and to a certain extent on our power of voluntarily combining them. (Charles Darwin, "The Descent of Man:", 1874)
"With every simple act of thinking, something permanent, substantial, enters our soul. This substantial somewhat appears to us as a unit but (in so far as it is the expression of something extended in space and time) it seems to contain an inner manifoldness; I therefore name it ‘mind-mass’. All thinking is, accordingly, formation of new mind masses." (Bernhard Riemann, "Gesammelte Mathematische Werke", 1876)
"You may read any quantity of books, and you may be almost as ignorant as you were at starting, if you don’t have, at the back of your minds, the change for words in definite images which can only be acquired through the operation of your observing faculties on the phenomena of nature." (Thomas H Huxley, "Science and Education", 1877)
"As long as the training of a naturalist enables him to trace the action only of a particular material system, without giving him the power of dealing with the general properties of all such systems, he must proceed by the method so often described in histories of science - he must imagine model after model of hypothetical apparatus, till he finds one which will do the required work. If this apparatus should afterwards be found capable of accounting for many of the known phenomena, and not demonstrably inconsistent with any of them, he is strongly tempted to conclude that his hypothesis is a fact, at least until an equally good rival hypothesis has been invented." (James C Maxwell, "Tait’s Thermodynamics", Nature Vol. XVII (431), 1878)
"For of an image one requires some kind of sameness with the pictured object, of a statue sameness of form, of a delineation sameness of perspective projection in the visual field, of a painting also sameness of color." (Heinrich Hertz, "The Facts in Perception", 1878)
"There are great differences in the power of forming pictures of objects in the mind's eye; in other words of visualising them. In some persons the faculty of perceiving these images is so feeble that they hardly visualise at all. […] Other persons perceive past scenes with a distinctness and an appearance of reality that differ little from actual vision. Between these wide extremes I have met with a mass of intermediate cases extending in an unbroken series." (Francis Galton, "Mental imagery", 1880)
"There is a kind, I might almost say, of artistic satisfaction, when we are able to survey the enormous wealth of Nature as a regularly ordered whole - a kosmos, an image of the logical thought of our own mind." (Hermann von Helmholtz, "Popular Lectures on Scientific Subjects", 1881)
"A visual image is the most perfect form of mental representation wherever the shape, position, and relations of objects in space are concerned. It is of importance in every handicraft and profession where design is required." (Francis Galton, "Mental Imagery" [in "Inquiries into Human Faculty and Development"] 1883)
"In the highest minds a descriptive word is sufficient to evoke crowds of shadowy associations, each striving to manifest itself. When they differ so much from one another as to be unfitted for combination into a single idea, there will be a conflict, each being prevented by the rest from obtaining sole possession of the field of consciousness. There could, therefore, be no definite imagery so long as the aggregate of all the pictures that the word suggested of objects presenting similar aspects, reduced to the same size, and accurately superposed, resulted in a blur; but a picture would gradually evolve as qualifications were added to the word, and it would attain to the distinctness and vividness of a generic image long before the word had been so restricted as to be individualised. If the intellect be slow, though correct in its operations, the associations will be few, and the generalised image based on insufficient data. If thevisualising power be faint, the generalised image will be indistinct." (Francis Galton, "Mental Imagery" [in "Inquiries into Human Faculty and Development"] 1883)
"The place where the image appears to lie, differs much. Most persons see it in an indefinable sort of way, others see it in front of the eye, others at a distance corresponding to reality. There exists a power which is rare naturally, but can, I believe, be acquired without much difficulty, of projecting a mental picture upon a piece of paper, and of holding it fast there, so that it can be outlined with a pencil." (Francis Galton, "Mental Imagery" [in "Inquiries into Human Faculty and Development"] 1883)
"While all that we have is a relation of phenomena, a mental image, as such, in juxtaposition with or soldered to a sensation, we can not as yet have assertion or denial, a truth or a falsehood. We have mere reality, which is, but does not stand for anything, and which exists, but by no possibility could be true. […] the image is not a symbol or idea. It is itself a fact, or else the facts eject it. The real, as it appears to us in perception, connects the ideal suggestion with itself, or simply expels it from the world of reality. […] you possess explicit symbols all of which are universal and on the other side you have a mind which consists of mere individual impressions and images, grouped by the laws of a mechanical attraction." (Francis H Bradley, "Principles of Logic", 1883)
"If the second principle [the context principle] is not observed, one is almost forced to take as the meanings of words mental pictures or acts of the individual mind, and so to offend against the first principle as well." (Gottlob Frege, "The Foundations of Arithmetic", 1884)
"The steps to scientific as well as other knowledge consist in a series of logical fictions which are as legitimate as they are indispensable in the operations of thought, but whose relations to the phenomena whereof they are the partial and not unfrequently merely symbolical representations must never be lost sight of." (John Stallo, "The Concepts and Theories of Modern Physics", 1884)
"The traditional psychology talks like one who should say a river consists of nothing but pailsful, spoonsful, quartpotsful, barrelsful, and other moulded forms of water. Even were the pails and the pots all actually standing in the stream, still between them the free water would continue to flow. It is just this free water of consciousness that psychologists resolutely overlook. Every definite image in the mind is steeped and dyed in the free water that flows round it. With it goes the sense of its relations, near and remote, the dying echo of whence it came to us, the dawning sense of whither it is to lead." (William James, "On Some Omissions of Introspective Psychology", Mind, 1884)
"The unimaginability of the content of a word is no reason, then, to deny it any meaning or to exclude it from usage. That we are nevertheless inclined to do so is probably owing to the fact that we consider words individually and ask about their meaning [in isolation], for which we then adopt a mental picture. Thus a word for which we are lacking a corresponding inner picture will seem to have no content. However, we must always consider a complete sentence. Only in [the context of] the latter do the words really have a meaning. The inner pictures which somehow sway before us (in reading the sentence) need not correspond to the logical components of the judgment. It is enough if the sentence as a whole has a sense; by means of this its parts also receive their content." (Gottlob Frege, "The Foundations of Arithmetic" , 1884)
"[…] deduction consists in constructing an icon or diagram the relations of whose parts shall present a complete analogy with those of the parts of the object of reasoning, of experimenting upon this image in the imagination, and of observing the result so as to discover unnoticed and hidden relations among the parts." (Charles S Peirce, 1885)
"Mental states of every kind - sensations, feelings, images - which were at one time present in consciousness and then have disappeared from it - have not with their disappearance absolutely ceased to exist. Although the inwardly - turned look may no longer be able to find them, nevertheless they have not been utterly destroyed and annulled, but in a certain manner they, continue to exist, stored up to speak, in the memory." (Hermann Ebbinghaus, "Memory: A contribution to experimental psychology", 1885)
"The great basic thought that the world is not to be comprehended as a complex of ready-made things, but as a complex of processes, in which the things apparently stable no less than their mind-images in our heads, the concepts, go through an uninterrupted change of coming into being and passing away, in which, in spite of all seeming accidents and of all temporary retrogression, a progressive development asserts itself in the end - this great fundamental thought has, especially since the time of Hegel, so thoroughly permeated ordinary consciousness that in this generality it is scarcely ever contradicted." (Friedrich Engels," Ludwig Feuerbach and the Outcome of Classical German Philosophy", 1886)
"The theory most prevalent among teachers is that mathematics affords the best training for the reasoning powers; […] The modem, and to my mind true, theory is that mathematics is the abstract form of the natural sciences; and that it is valuable as a training of the reasoning powers, not because it is abstract, but because it is a representation of actual things." (Truman H Safford, "Mathematical Teaching and Its Modern Methods", 1886)
"The mathematical theory of potential and the like has -insured safe and certain progress, and enables mathematicians to dispense for the time being with theories of electricity and with mental imagery. Few, however, are the minds strong enough thus to dispense with all but the most formal and severe of mental aids; and none, I believe, to whom some mental picture of the actual processes would not be a help if it were safely available." (Oliver J Lodge, "Modern Views of Electricity", 1889)
"[...] the task of the theory consists in constructing a picture of the external world that exists purely internally and must be our guiding star in all thought and experiment; that is in completing, as it were, the thinking process and carrying out globally what on a small scale occurs within us whenever we form an idea." (Ludwig E Boltzmann, "On the Significance of Theories", 1890)
"Every definite image in the mind is steeped and dyed in the free water that flows around it. With it goes the sense of its relations, near and remote, the dying echo of whence it came to us, the dawning sense of whither it is to lead. The significance, the value, of the image is all in this halo or penumbra that surrounds and escorts it, - or rather that is fused into one with it and has become bone of its bone and flesh of its flesh; leaving it, it is true, an image of the same thing it was before, but making it an image of that thing newly taken and freshly understood. […] Great thinkers have vast premonitory glimpses of schemes of relations between terms, which hardly even as verbal images enter the mind, so rapid is the whole process. We all of us have this permanent consciousness of whither our thought is going." (William James, "The Principles of Psychology", 1890)
" […] as a general rule, that in selecting a particular case for constructing a model the first prerequisite is regularity. By selecting a symmetrical form for the model, not only is the execution simplified, but what is of more importance, the model will be of such a character as to impress itself readily on the mind." (Felix Klein, 1893)
"The mechanism of thought consists in combinations, separations, and recombinations of representative images or symbols […] the object of thought is adaptation to environment." (Paul Carus, "Le probeme de la conscience du moi", 1893)
"It is a common and necessary feature of human intelligence that we can neither conceive of things nor define them conceptually without adding attributes to them that simply do not exist. This applies not only to every thought and imagination of ordinary life, even the sciences do not proceed otherwise. Only philosophy seeks and finds the difference between things that exist and things that we perceive, and also sees the necessity of this difference. […] What we add are therefore not incorrect conceptions but the conditions for such conceptions in general. We cannot simply remove them and replace them with better ones; either we must add them, or we must abstain from all conceptions of this kind." (Heinrich Hertz, "Die Prinzipien der Mechanik in neuem Zusammenhange dargestellt", 1894)
"It is now known that as the physical basis of any word, be it noun or verb, there is a series of mental images acquired through different senses, located in different regions of the gray cortex of the brain, and joined together in a unit by a series of association-tracts which pass in the white matter under the cortex. The word ‘concept’ long used by psychologists to denote congeries of mental images making up an idea conveyed by a single word may be adopted by the pathologist to indicate this collection of mental images. To be complete, such a concept must have all its parts intact and the connections between those parts also intact." (Anon, "Aphasia", Psychological Review Vol. I (1), 1894)
"[…] we cannot a priori demand from nature simplicity, nor can we judge what in her opinion is simple. But with regard to images of our own creation we can lay down requirements. We are justified in deciding that if our images are well adapted to the things, the actual relations of the things must be represented by simple relations between the images. And if the actual relations between the things can only be represented by complicated relations, which are not even intelligible to an unprepared mind, we decide that those images are not sufficiently well adapted to the things. Hence our requirement of simplicity does not apply to nature, but to the images thereof which we fashion ; and our repugnance to a complicated statement as a fundamental law only expresses the conviction that, if the contents of the statement are correct and comprehensive, it can be stated in a simpler form by a more suitable choice of the fundamental conceptions." (Heinrich Hertz, "The Principles of Mechanics Presented in a New Form", 1894)
"We form ourselves images or symbols of external objects; and the form which we give them is such that the necessary consequents of the images in thought are always the images of the necessary consequents in nature of the things pictured. In order that this requirement may be satisfied, there must be a certain conformity between nature and our thought." (Heinrich Hertz," Die Prinzipien der Mechanik in neuem Zusammenhange dargestellt", 1894)
"The first step, whenever a practical problem is set before a mathematician, is to form the mathematical hypothesis. It is neither needful nor practical that we should take account of the details of the structure as it will exist. We have to reason about a skeleton diagram in which bearings are reduced to points, pieces to lines, etc. and [in] which it is supposed that certain relations between motions are absolutely constrained, irrespective of forces. Some writers call such a hypothesis a fiction, and say that the mathematician does not solve the real problem, but only a fictitious one. That is one way of looking at the matter, to which I have no objection to make: only, I notice, that in precisely the same sense in which the mathematical hypothesis is 'false', so also is this statement 'false', that it is false. Namely, both representations are false in the sense that they omit subsidiary elements of the fact, provided that element of the case can be said to be subsidiary which those writers overlook, namely, that the skeleton diagram is true in the only sense in which from the nature of things any mental representation, or understanding, of the brute existent can be true. For every possible conception, by the very nature of thought, involves generalization; now generalization omits, means to omit, and professes to omit, the differences between the facts generalized." (Charles S Peirce, "Report on Live Loads", cca. 1895)
"Deduction is that mode of reasoning which examines the state of things asserted in the premises, forms a diagram of that state of things, perceives in the parts of the diagram relations not explicitly mentioned in the premises, satisfies itself by mental experiments upon the diagram that these relations would always subsist, or at least would do so in a certain proportion of cases, and concludes their necessary, or probable, truth." (Charles S Peirce, "Kinds of Reasoning", cca. 1896)
"It is a mistake to reduce mater to the perception which we have of it, a mistake also to make of it a thing able to produce in us perceptions, but in itself is of another nature than they. Matter, in our view, is an aggregate of ‘images’. And by ‘image‘ we mean a certain existence which is more than that which the idealist calls a representation, but less than that which the realist calls a thing - an existence placed ha!fway between the ‘thing‘ and the ‘representation’. This conception of matter is simply that of common sense. [...] For common sense, then, the object exists in itself, and, on the other hand, the object is, in itself, pictorial, as we perceive it image it is, but a self-existing image." (Henri Bergson,"Matter and Memory", 1896)
"Memory-images, it is true, cannot be directly aroused through external sense impressions, but follow them after a longer or shorter interval. Still, it is obvious that their attributes, and especially their relation to the primary ideas through direct impressions, can be most accurately be learned, not by waiting for their chance arrival, but by using such memory-ideas as may be aroused in a systematic, experimental way, through immediately preceding impressions." (Wilhelm M Wundt, "Outlines of Psychology", 1897)
"Intellectual work is an act of creation. It is as if the mental image that is studied over a period of time were to sprout appendages like an ameba - outgrowths that extend in all directions while avoiding one obstacle after another - before interdigitating with related ideas." (Santiago Ramón y Cajal, "Reglas y Consejos sobre InvestigacÃon Cientifica: Los tónicos de la voluntad", 1897)
"All our ideas and concepts are only internal pictures, or if spoken, combinations of sounds. The task of our thinking is so to use and combine them that by their means we always most readily hit upon the correct actions and guide others likewise. In this, metaphysics follows the most down-to-earth and practical point of view, so that extremes meet. The conceptual signs that we form thus exist only within us, we cannot measure external phenomena by the standard of our ideas. We can therefore pose such formal questions as whether only matter exists and force is a property of it, or whether force exists independently of matter or conversely whether matter is a product of force but none of these questions are significant since all these concepts are only mental pictures whose purpose is to represent phenomena correctly." (Ludwig Boltzmann, 1899)
"[…] no theory can be objective, actually coinciding with nature, but rather that each theory is only a mental picture of phenomena, related to them as sign is to designatum. From this it follows that it cannot be our task to find an absolutely correct theory but rather a picture that is, as simple as possible and that represents phenomena as accurately as possible. One might even conceive of two quite different theories both equally simple and equally congruent with phenomena, which therefore in spite of their difference are equally correct." (Ludwig Boltzmann, "On the development of the methods of theoretical physics", 1899)
"[…] we must have imagination. I do not mean mere fancy, which creates unreal images and impossible monsters, but imagination, the power of making pictures or images in our mind of that which is, though it is invisible to us." (Arabella B Buckley, "The Fairy-Land of Science", 1899)
"This is the greatest degree of impoverishment; the image, deprived little by little of its own characteristics, is nothing more than a shadow. It has become that transitional form between image and pure concept that we now term ‘generic image’, or one that at least resembles the latter. The image, then, is subject to an unending process of change, of suppression and addition, of dissociation and corrosion.
This means that it is not a dead thing; it is not at all like a photographic plate with which one may reproduce copies indefinitely. Being dependent on the state of the brain, the image undergoes change like all living substance, - it is subject to gains and losses, especially losses. But each of the foregoing three classes has its use for the inventor. They serve as material for different kinds of imagination - in their concrete form, for the mechanic and the artist; in their schematic form, for the scientist and for others." (Théodule-Armand Ribot, "Essay on the Creative Imagination", 1900)
"We imagine cases, place mental diagrams before our mind's eye, and multiply these cases, until a habit is formed of expecting that always to turn out the case, which has been seen to be the result in all the diagrams. To appeal to such a habit is a very different thing from appealing to any immediate instinct of rationality. That the process of forming a habit of reasoning by the use of diagrams is often performed there is no room for doubt. It is perfectly open to consciousness." (Charles S Peirce, "Fallibility of Reasoning and the Feeling of Rationality", cca. 1902)
"An icon is a representamen of what it represents and for the mind that interprets it as such, by virtue of its being an immediate image, that is to say by virtue of characters which belong to it in itself as a sensible object, and which it would possess just the same were there no object in nature that it resembled, and though it never were interpreted as a sign. It is of the nature of an appearance, and as such, strictly speaking, exists only in consciousness, although for convenience in ordinary parlance and when extreme precision is not called for, we extend the term icon to the outward objects which excite in consciousness the image itself." (Charles S Peirce, "On Existential Graphs, Euler's Diagrams, and Logical", 1903)
"But surely it is self-evident that every theory is merely a framework or scheme of concepts together with their necessary relations to one another, and that the basic elements can be constructed as one pleases." (Gottlob Frege, [in "On the Foundations of Geometry and Formal Theories of Arithmetic" 1971] cca. 1903-1909)
"Chemistry and physics are experimental sciences; and those who are engaged in attempting to enlarge the boundaries of science by experiment are generally unwilling to publish speculations; for they have learned, by long experience, that it is unsafe to anticipate events. It is true, they must make certain theories and hypotheses. They must form some kind of mental picture of the relations between the phenomena which they are trying to investigate, else their experiments would be made at random, and without connection." (William Ramsay, "Radium and Its Products", Harper’s Magazine, 1904)
"The mind of man, learning consciously and unconsciously lessons of experience, gradually constructs a mental image of its surroundings - as the mariner draws a chart of strange coasts to guide him in future voyages, and to enable those that follow after him to sail the same seas with ease and safety." (William C Dampier, "The Recent Development of Physical Science" , 1904)
"A mental image gives you a framework upon which to work. It is like the drawing of the architect, or the map of the explorer. Think over this for a few moments until you get the idea firmly fixed in your mind." (William W Atkinson, "Practical Mental Influence and Mental Fascination", 1908)
"Materialism is the recognition of 'objects in themselves' , or outside the mind; ideas and sensations are copies of images of those objects." (Vladimir Lenin, "Materialism and Empirio-Criticism", 1908)
"The scientific worker has elected primarily to know, not do. He does not directly seek, like the practical man, to realize the ideal of exploiting nature and controlling life – though he makes this more possible; he seeks rather to idealize – to conceptualize – the real, or at least those aspects of reality that are available in his experience. He thinks more of lucidity and formulae than of loaves and fishes. He is more concerned with knowing Nature than with enjoying her. His main intention is to describe the sequences in Nature in the simplest possible formulae, to make a working thought-model of the known world. He would make the world translucent, not that emotion may catch the glimmer of the indefinable light that shines through, but for other reasons – because of his inborn inquisitiveness, because of his dislike of obscurities, because of his craving for a system – an intellectual system in which phenomena are at least provisionally unified." (Sir John A Thomson," Introduction to Science", 1911)
"For a long time it has been known that the first systems of representations with which men have pictured to themselves the world and themselves were of religious origin. There is no religion that is not a cosmology at the same time that it is a speculation upon divine things. If philosophy and the sciences were born of religion, it is because religion began by taking the place of the sciences and philosophy." (Emile Durkheim, "The Elementary Forms of the Religious Life", 1912)
"Psychology tells us that the habit of forming clear images is an important one, and that all the higher forms of knowledge depend upon the accuracy with which concepts are formed." (Edith M Buell, "Word pictures as a means of mental development", American Annals of the Deaf yuVol. 57 (5), 1912)
"For thought raised on specialization the most potent objection to the possibility of a universal organizational science is precisely its universality. Is it ever possible that the same laws be applicable to the combination of astronomic worlds and those of biological cells, of living people and the waves of the ether, of scientific ideas and quanta of energy? .. Mathematics provide a resolute and irrefutable answer: yes, it is undoubtedly possible, for such is indeed the case. Two and two homogenous separate elements amount to four such elements, be they astronomic systems or mental images, electrons or workers; numerical structures are indifferent to any element, there is no place here for specificity." (Alexander Bogdanov, "Tektology: The Universal Organizational Science" Vol. I, 1913)
"Would it be possible for a 'mental image' , perception or idea, to correspond to a 'physical object', if the parts of the former were not combined in the same order as the parts of the latter? […] The more fully the similarity of two mental images is 'recognized' , i.e., the more elements of both images are brought to identity in the consciousness, the greater the extent they are associated 'by similarity'." (Alexander Bogdanov, "Tektology: The Universal Organizational Science" Vol. I, 1913)
"Acting is the physical representation of a mental picture and the projection of an emotional concept." (Laurette Taylor, "The Quality You Need Most", Green Book Magazine, 1914)
"I call the combination of a concept and a sound-image a sign, but in current usage the term generally designates only a sound-image, a word, for example (arbor, etc.). One tends to forget that arbor is called a sign only because it carries the concept ‘tree’, with the result that the idea of the sensory part implies the idea of the whole." (Ferdinand de Saussure, "Course in General Linguistics", 1915)
"The conception of lines of force was introduced by Faraday to form a mental picture of the processes going on in the electric field. To him these lines were not mere mathematical abstractions. He ascribed to them properties that gave them a real physical significance." (Hendrik van der Bijl, "The Thermionic Vacuum Tube and Its Applications", 1920)
"A geometrical-physical theory as such is incapable of being directly pictured, being merely a system of concepts. But these concepts serve the purpose of bringing a multiplicity of real or imaginary sensory experiences into connection in the mind. To ‘visualise’ a theory, or bring it home to one's mind, therefore means to give a representation to that abundance of experiences for which the theory supplies the schematic arrangement" (Albert Einstein, "Geometry and Experience", 1921)
"The continuing effects of mental images and ideas that, later, emerge in memory actually take place in the sphere of our feelings. […] Our life of feelings – with its joys, pains, pleasures, displeasures, tensions, and relaxations – is the actual vehicle for the enduring qualities of the ideas and mental images that we can recall at a later stage." (Rudolf Steiner, "Education for Adolescents", 1921)
"The logical picture of the facts is the thought. […] A picture is a model of reality. In a picture objects have the elements of the picture corresponding to them. The fact that the elements of a picture are related to one another in a determinate way represents that things are related to one another in the same way." (Ludwig Wittgenstein, "Tractatus Logico-Philosophicus", 1922)
"Thinking in pictures is, therefore, only a very incomplete form of becoming conscious. In some way, too, it stands nearer to unconscious processes than does thinking in words, and it is unquestionably older than the latter both ontogenetically and phylogenetically." (Sigmund Freud, "The Ego And The Id", 1923)
"The sciences bring into play the imagination, the building of images in which the reality, of the past is blended with the ideals for the future, and from the picture there springs the prescience of genius." (William J Mayo, "Contributions of Pure Science to Progressive Medicine", The Journal of the American Medical Association Vol. 84 (20), 1925)
"The identifying ourselves with the visual image of ourselves has become an instinct; the habit is already old. The picture of me, the me that is seen, is me." (David H Lawrence, "Art and Morality", 1925)
"This is the reason why mechanical explanations are better understood than stories, even though they are more difficult to reproduce. The exposition, even if it is faulty, excites analogous schemas already existing in the listener’s mind; so that what takes place is not genuine understanding, but a convergence of acquired schemas of thought. In the case of stories, this convergence is not possible, and the schemas brought into play are usually divergent." (Jean Piaget, "The Language and Thought of the Child", 1926)
"We wish to obtain a representation of phenomena and form an image of them in our minds. Till now, we have always attempted to form these images by means of the ordinary notions of time and space. These notions are perhaps innate; in any case they have been developed by our daily observations. For me, these notions are clear, and I confess that I am unable to gain any idea of physics without them. […] I would like to retain this ideal of other days and describe everything that occurs in this world in terms of clear pictures." (Hendrik A Lorentz, [Fifth Solvay Conference] 1927)
"At first sight the assimilative tendency shown by thought seems sufficient to secure stability in judgments. To assimilate, in psychology as in biology, is to reproduce oneself by means of the external world; it is to transform perceptions until they are identical with one’s own thought, i.e. with previous schemas. Assimilation is therefore preservation and, in a certain sense, identification." (Jean Piaget, "Judgement and Reasoning in the Child", 1928)
"In the presence of certain objects of thought or of certain affirmations the child, in virtue of previous experiences, adopts a certain way of reacting and thinking which is always the same, and which might be called a schema of reasoning. Such schemas are the functional equivalents of general propositions, but since the child is not conscious of these schemas before discussion and a desire for proof have laid them bare and at the same time changed their character, they cannot be said to constitute implicit general propositions. They simply constitute certain unconscious tendencies which live their own life but are submitted to no general systematization and consequently lead to no logical exactitude. To put it in another way, they form a logic of action but not yet a logic of thought." (Jean Piaget, "Judgement and Reasoning in the Child", 1928)
"Imagery is not past but present. It rests with what we call our mental processes to place these images in a temporal order." (George H Mead, 1929)
"Thought is prior to language and consists in the simultaneous presentation to the mind of two different images." (Thomas E Hulme, "Notes on Language and Style", 1929)
"It has become increasingly evident in recent times, however, that nature works on a different plan. Her fundamental laws do not govern the world as it appears in our mental picture in any very direct way, but instead they control a substratum of which we cannot form a mental picture without introducing irrelevancies." (Paul A M Dirac, "The Principles of Quantum Mechanics", 1930)
"It is not surprising that our language should be incapable of describing the processes occurring within the atoms, for, as has been remarked, it was invented to describe the experiences of daily life, and these consist only of processes involving exceedingly large numbers of atoms. Furthermore, it is very difficult to modify our language so that it will be able to describe these atomic processes, for words can only describe things of which we can form mental pictures, and this ability, too, is a result of daily experience. Fortunately, mathematics is not subject to this limitation, and it has been possible to invent a mathematical scheme - the quantum theory - which seems entirely adequate for the treatment of atomic processes; for visualisation, however, we must content ourselves with two incomplete analogies - the wave picture and the corpuscular picture" (Werner K Heisenberg, "The Physical Principles of the Quantum Theory", 1930)
"It seems that the human mind has first to construct forms independently, before we can find them in things. Kepler’s marvelous achievement is a particularly fine example of the truth that knowledge cannot spring from experience alone, but only from the comparison of the inventions of the intellect with observed fact." (Albert Einstein, 1930)
"The final truth about phenomena resides in the mathematical description of it; so long as there is no imperfection in this, our knowledge is complete. We go beyond the mathematical formula at our own risk; we may find a [nonmathematical] model or picture that helps us to understand it, but we have no right to expect this, and our failure to find such a model or picture need not indicate that either our reasoning or our knowledge is at fault." (James Jeans, "The Mysterious Universe", 1930)
"The methods of progress in theoretical physics have undergone a vast change during the present century. The classical tradition has been to consider the world to be an association of observable objects (particles, fluids, fields, etc.) moving about according to definite laws of force, so that one could form a mental picture in space and time of the whole scheme. This led to a physics whose aim was to make assumptions about the mechanism and forces connecting these observable objects, to account for their behaviour in the simplest possible way. It has become increasingly evident in recent times, however, that nature works on a different plan. Her fundamental laws do not govern the world as it appears in our mental picture in any very direct way, but instead they control a substratum of which we cannot form a mental picture without introducing irrelevancies. (Paul A M Dirac, "The Principles of Quantum Mechanics", 1930)
"The solution of the difficulty is that the two mental pictures which experiment lead us to form - the one of the particles, the other of the waves - are both incomplete and have only the validity of analogies which are accurate only in limiting cases." (Werner Heisenberg,"On Quantum Mechanics", 1930)
"In this way things, external objects, are assimilated to more or less ordered motor schemas, and in this continuous assimilation of objects the child's own activity is the starting point of play. Not only this, but when to pure movement are added language and imagination, the assimilation is strengthened, and wherever the mind feels no actual need for accommodating itself to reality, its natural tendency will be to distort the objects that surround it in accordance with its desires or its fantasy, in short to use them for its satisfaction. Such is the intellectual egocentrism that characterizes the earliest form of child thought." (Jean Piaget, "The Moral Judgment of the Child", 1932)
"'Schema' refers to an active organisation of past reactions, or of past experiences, which must always be supposed to be operating in any well-adapted organic response. That is, whenever there is any order or regularity of behavior, a particular response is possible only because it is related to other similar responses which have been serially organised, yet which operate, not simply as individual members coming one after another, but as a unitary mass. Determination by schemata is the most fundamental of all the ways in which we can be influenced by reactions and experiences which occurred some time in the past. All incoming impulses of a certain kind, or mode, go together to build up an active, organised setting: visual, auditory, various types of cutaneous impulses and the like, at a relatively low level; all the experiences connected by a common interest: in sport, in literature, history, art, science, philosophy, and so on, on a higher level." (Frederic C Bartlett, "Remembering: A study in experimental and social psychology", 1932)
"[T]he sudden inventions characteristic of the sixth stage [of infant development] are in reality the product of a long evolution of schemata and not only of an internal maturation of perceptive structures. [..] This is revealed by the existence of a fifth stage, characterized by experimental groping. […] What does this mean if not that the practice of actual experience is necessary in order to acquire the practice of mental experience and that invention does not arise entirely preformed despite appearances? (Jean Piaget, "The origin of intelligence in children" 1936)
"In perception, a knowledge forms itself slowly; in the [mental] image the knowledge is immediate. We see now that the image is a synthetic act which unites a concrete, nonimagined, knowledge to elements which are more actually representative. The image teaches nothing: it is organized exactly like the objects which do produce knowledge, but it is complete at the very moment of its appearance. […] Thus, the object presents itself in the image as having to be apprehended in a multiplicity of synthetic acts. Due to this fact, and because its content retains a sensible opacity, like a phantom, because it does not involve either essences or generating laws but only an irrational quality, it gives the impression of being an object of observation: from this point of view the image appears to be more like a perception than a concept." (Jean-Paul Sartre, "The Psychology of Imagination", 1940)
"[…] the image is an act which envisions an absent or non-existent object as a body, by means of a physical or mental content which is present only as an "analogical representative" of the object envisioned." (Jean-Paul Sartre, "The Psychology of Imagination", 1940)
"If the organism carries a ‘small-scale model’ of external reality and of its possible actions within its head, it is able to try out various alternatives, conclude which is the best of them, react to future simulations before they arise, utilize the knowledge of past events in dealing with the present and the future, and in every way to react in a much fuller, safer, and more competent manner to the emergencies which face it." (Kenneth Craik, "The Nature of Explanation", 1943)
"My hypothesis then is that thought models, or parallels, reality - that its essential feature is not ‘the mind’, ‘the self’, ‘sense-data’, nor propositions but symbolism, and that this symbolism is largely of the same kind as that which is familiar to us in mechanical devices which aid thought and calculation." (Kenneth Craik, "The Nature of Explanation", 1943)
"While the stuff from which our world picture is build is yielded exclusively from the sense organs as organs of the mind, so that every man's world picture is and always remains a construct of his mind and cannot be proved to have any other existence […]" (Erwin Schrodinger, "What is Life?", 1944)
"The words of the language, as they are written or spoken, do not seem to play any role in any mechanism of thought. The physical entities which seem to serve as elements in thought are certain signs and more or less clear images which can be 'voluntarily' reproduced or combined. […] But taken from a psychological viewpoint, this combinatory play seems to be the essential feature in productive thought - before there is any connection with logical construction in words or other kinds of signs which can be communicated to others. The above-mentioned elements are, in my case, of visual and some of muscular type. Conventional words or other signs have to be sought for laboriously only in a secondary stage, when the mentioned associative play is sufficiently established and can be reproduced at will." (Albert Einstein, [letter to Hadamard, in (Jacques Hadamard, "The Psychology of Invention in the Mathematical Field, 1945)])
"[…] learning consists not in stimulus-response connections but in the building up in the nervous system of sets which function like cognitive maps […] such cognitive maps may be usefully characterized as varying from a narrow strip variety to a broader comprehensive variety." (Edward C Tolman, "Cognitive maps in rats and men", 1948)
"What now is the answer to the question as to the bridge between the perception of the senses and the concepts, which is now reduced to the question as to the bridge between the outer perceptions and those inner image-like representations. It seems to me one has to postulate a cosmic order of nature - outside of our arbitrariness- to which the outer material objects are subjected as are the inner images […] The organizing and regulating has to be posited beyond the differentiation of physical and psychical […] I am all for it to call this ‘organizing and regulating’ ‘archetypes’. It would then be inadmissible to define these as psychic contents. Rather, the above-mentioned inner pictures (dominants of the collective unconscious, see Jung) are the psychic manifestations of the archetypes, but which would have to produce and condition all nature laws belonging to the world of matter. The nature laws of matter would then be the physical manifestation of the archetypes." (Wolfgang Pauli, [Letter to Markus Fierz], 1948)
"When one analyzes the pre-conscious step to concepts, one always finds ideas which consist of 'symbolic images'. The first step to thinking is a painted vision of these inner pictures whose origin cannot be reduced only and firstly to the sensual perception but which are produced by an 'instinct to imagining' and which are re-produced by different individuals independently, i. e. collectively [...] But the archaic image is also the necessary predisposition and the source of a scientific attitude. To a total recognition belong also those images out of which have grown the rational concepts." (Wolfgang Pauli, [Letter to Markus Fierz] 1948)
"Man tries to make for himself in the fashion that suits him best a simplified and intelligible picture of the world; he then tries to some extent to substitute this cosmos of his for the world of experience, and thus to overcome it. This is what the painter, the poet, the speculative philosopher, and the natural scientist do, each in his own way." (Albert Einstein, "The World as I See It", 1949)
"The crucial problem is that of describing what is ‘seen in the mind’s eye’ and what is ‘heard in one’s head’. What are spoken of as ‘visual images’, ‘mental pictures’ […] are commonly taken to be entities which are genuinely found existing and found existing elsewhere than in the external world. So minds are nominated for their theaters." (Gilbert Ryle, "The Concept of Mind" , 1949)
"The solution of the difficulty is that the two mental pictures which experiment lead us to form - the one of the particles, the other of the waves - are both incomplete and have only the validity of analogies which are accurate only in limiting cases." (Werner Heisenberg, "The Physical Principles of the Quantum Theory", 1949)
"To see is one thing; to picture or visualise is another. A person can see things, only when his eyes are open, and when his surroundings are illuminated; but he can have pictures in his mind’s eye, when his eyes are shut and when the world is dark." (Gilbert Ryle, "The Concept of Mind", 1949)
"The more the schemata are differentiated, the smaller the gap between the new and the familiar becomes, so that novelty, instead of constituting an annoyance avoided by the subject, becomes a problem and invites searching." (Jean Piaget, "The Construction Of Reality In The Child", 1950)
"Accommodation of mental structures to reality implies the existence of assimilatory schemata apart from which any structure would be impossible." (Jean Piaget, "The Construction Of Reality In The Child", 1950)
"What in fact is the schema of the object? In one essential respect it is a schema belonging to intelligence. To have the concept of an object is to attribute the perceived figure to a substantial basis, so that the figure and the substance that it thus indicates continue to exist outside the perceptual field. The permanence of the object seen from this viewpoint is not only a product of intelligence, but constitutes the very first of those fundamental ideas of conservation which we shall see developing within the thought process." (Jean Piaget, "The Psychology of Intelligence", 1950)
"A conceptual scheme is never discarded merely because of a few stubborn facts with which it cannot be reconciled; a conceptual scheme is either modified or replaced by a better one, never abandoned with nothing left to take its place."(James B Conant, "Science and Common Sense", 1951)
"Common sense […] may be thought of as a series of concepts and conceptual schemes which have proved highly satisfactory for the practical uses of mankind. Some of those concepts and conceptual schemes were carried over into science with only a little pruning and whittling and for a long time proved useful. As the recent revolutions in physics indicate, however, many errors can be made by failure to examine carefully just how common sense ideas should be defined in terms of what the experimenter plans to do." (James B Conant, "Science and Common Sense", 1951)
"As our mental eye penetrates into smaller and smaller distances and shorter and shorter times, we find nature behaving so entirely differently from what we observe in visible and palpable bodies of our surroundings that no model shaped after our large-scale experiences can ever be ‘true’. A complete satisfactory model of this type is not only practically inaccessible, but not even thinkable. Or, to be precise, we can, of course, think of it, but however we think it, it is wrong; not perhaps quite as meaningless as a ‘triangular circle’, but more so than a ‘winged lion’." (Erwin Schrödinger, "Science and Humanism", 1952)
"The process of understanding in nature, together with the joy that man feels in understanding, i.e., in becoming acquainted with new knowledge, seems therefore to rest upon a correspondence, a coming into congruence of preexistent internal images of the human psyche with external objects and their behavior. […] the place of clear concepts is taken by images of strongly emotional content, which are not thought but are seen pictorially, as it were, before the minds eye." (Wolfgang Pauli, "Der Einfluss archetypischer Vorstellungen auf die Bildung naturwissenschaftlicher Theorien bei Kepler", 1952)
"As an empiricist I continue to think of the conceptual scheme of science as a tool, ultimately, for predicting future experience in the light of past experience. Physical objects are conceptually imported into the situation as convenient intermediaries - not by definition in terms of experience, but simply as irreducible posits comparable, epistemologically, to the gods of Homer." (Willard v O Quine, "From a Logical Point of View", 1953)
"A symbol, therefore, may have no effect and indeed ordinarily will have no effect on the image of the immediate future around one. It does produce an effect, however, of what might be called the image of the image, on the image of the future, on the image of the past, on the image of the potential or even of the image of the possible." (Kenneth E Boulding, "The Image: Knowledge in life and society", 1956)
"I have suggested that one of the basic theorems of the theory of the image is that it is the image which in fact determines what might be called the current behavior of any organism […] The image acts as a field. The behavior consists in gravitating toward the most highly valued part of the field." (Kenneth E Boulding, "The Image: Knowledge in life and society", 1956)
"Nature is more subtle, more deeply intertwined and more strangely integrated than any of our pictures of her - than any of our errors. It is not merely that our pictures are not full enough; each of our pictures in the end turns out to be so basically mistaken that the marvel is that it worked at all." (Jacob Bronowski, "Science and Human Values", 1956)
"The problem of the transformation of images is of great importance in the theory of economic development. […] The problem here is that of the initiation and imitation of superior processes. Both these phenomena require transformation of the image; a new process always starts as a new image, as a new idea. The process itself is merely a form of transcription of the new image." (Kenneth E Boulding, "The Image: Knowledge in life and society", 1956)
"While the stuff from which our world picture is built is yielded exclusively from the sense organs as organs of the mind, so that every man's world picture is and always remains a construct of his mind and cannot be proved to have any other existence, yet the conscious mind itself remains a stranger within that construct, it has no living space in it, you can spot it nowhere in space." (Erwin Schrödinger, „Mind and Matter: the Tarner Lectures", 1956)
"Within the confines of my abstraction, for instance, it is clear that the problem of truth and validity cannot be solved completely, if what we mean by the truth of an image is its correspondence with some reality in the world outside it. The difficulty with any correspondence theory of truth is that images can only be compared with images. They can never be compared with any outside reality. The difficulty with the coherence theory of truth, on the other hand, is that the coherence or consistency of the image is simply not what we mean by its truth." (Kenneth E Boulding, "The Image: Knowledge in life and society", 1956)
"The ultimate origin of the difficulty lies in the fact (or philosophical principle) that we are compelled to use the words of common language when we wish to describe a phenomenon, not by logical or mathematical analysis, but by a picture appealing to the imagination. Common language has grown by everyday experience and can never surpass these limits. Classical physics has restricted itself to the use of concepts of this kind; by analysing visible motions it has developed two ways of representing them by elementary processes; moving particles and waves. There is no other way of giving a pictorial description of motions - we have to apply it even in the region of atomic processes, where classical physics breaks down." (Max Born, "Atomic Physics", 1957)
"Just as the eye sees details that are not there if they fit in with the sense of the picture, or overlooks them if they make no sense, so also very little inherent certainty will suffice to secure the highest scientific value to an alleged fact, if only it fits in with a great scientific generalization, while the most stubborn facts will be set aside if there is no place for them in the established framework of science." (Michael Polanyi, "Personal Knowledge", 1958)
"The reason why new concepts in any branch of science are hard to grasp is always the same; contemporary scientists try to picture the new concept in terms of ideas which existed before." (Freeman J Dyson, "Innovation in Physics" , Scientific American, 1958)
"It follows that if our ideas and mental images concerning ourselves are distorted or unrealistic, then our reaction to our environment will likewise be inappropriate. […] The aim of self-image psychology is not to create a fictitious self which is all-powerful, arrogant, egoistic, all-important. Such an image is as inappropriate and unrealistic as the inferior image of self. Our aim is to find the ‘real self’, and to bring our mental images of ourselves more in line with ‘the objects they represent’." (Maxwell Maltz, "Psycho-Cybernetics", 1960)
"Mental pictures offer us an opportunity to practice new traits and attitudes, which otherwise we could not do. This is possible because again - your nervous system cannot tell the difference between an actual experience and one that is vividly imagined." (Maxwell Maltz, "Psycho-Cybernetics", 1960)
"Once we give serious consideration to the hypothesis of the unconscious, it follows that our view of the world can be but a provisional one; for if we effect so radical an alteration in the subject of perception and cognition as this dual focus implies, the result must be a world view very different from any known before." (Carl Gustav Jung, "The Structure And Dynamics Of The Psyche", 1960)
"This other world is the so-called physical world image; it is merely an intellectual structure. To a certain extent it is arbitrary. It is a kind of model or idealization created in order to avoid the inaccuracy inherent in every measurement and to facilitate exact definition." (Max Planck, "The Philosophy of Physics", 1963)
"Science begins with the world we have to live in, accepting its data and trying to explain its laws. From there, it moves toward the imagination: it becomes a mental construct, a model of a possible way of interpreting experience. The further it goes in this direction, the more it tends to speak the language of mathematics, which is really one of the languages of the imagination, along with literature and music." (Northrop Frye, "The Educated Imagination", 1963)
"They [archetypes] are, at the same time, both images and emotions. One can speak of an archetype only when these two aspects are simultaneous. When there is merely the image, then there is simply a word picture of little consequence. But by being charged with emotion, the image gains numinosity (or psychic energy); it becomes dynamic, and consequences of some kind must flow from it." (Carl G Jung, "Man and His Symbols", 1964)
"This language controls by reducing the linguistic forms and symbols of reflection, abstraction, development, contradiction; by substituting images for concepts. It denies or absorbs the transcendent vocabulary; it does not search for but establishes and imposes truth and falsehood." (Herbert Marcuse, "One-Dimensional Man", 1964)
"Thus a word or an image is symbolic when it implies something more than its obvious and immediate meaning. It has a wider ‘unconscious’ aspect that is never precisely defined or fully explained. […] As the mind explores the symbols it is led to ideas that lie beyond the grasp of reason." (Carl G Jung, "Man and His Symbols", 1964)
"As perceivers we select from all the stimuli falling on our senses only those which interest us, and our interests are governed by a pattern-making tendency, sometimes called a schema. In a chaos of shifting impressions each of us constructs a stable world in which objects have recognisable shapes, are located in depth and have permanence." (Mary Douglas, "Purity and Danger", 1966)
"The direct task of our cognitive apparatus is the formation of invariants, and namely invariants of perception, thinking and motives. […] Still, in the first place, exactly these invariants are, cybernetically speaking, enabling a stabilization of the relationship between humans and their environment and between humans themselves." (Georg Klaus, "Kybernetik und Erkenntnistheorie" ["Cybernetics and Epistemology"], 1966)
"The symbol is the tool which gives man his power, and it is the same tool whether the symbols are images or words, mathematical signs or mesons." (Jacob Bronowski, "The Reach of Imagination", 1967)
"To imagine means to make images and to move them about inside one's head in new arrangements." (Jacob Bronowski, "The Reach of Imagination", 1967)
"A thought that is born within thought, an act of thought engendered within its own genealogy, neither given through innateness, nor presupposed in reminiscence, is a thought without image." (Gilles Deleuze, "Difference and Repetition" , 1968)
"We realize, however, that all scientific laws merely represent abstractions and idealizations expressing certain aspects of reality. Every science means a schematized picture of reality, in the sense that a certain conceptual construct is unequivocally related to certain features of order in reality […]" (Ludwig von Bertalanffy, "General System Theory", 1968)
"Visual thinking calls, more broadly, for the ability to see visual shapes as images of the patterns of forces that underlie our existence - the functioning of minds, of bodies or machines, the structure of societies or ideas." (Rudolf Arnheim, "Visual Thinking", 1969)
"Each of us uses models constantly. Every person in his private life and in his business life instinctively uses models for decision making. The mental image of the world around you which you carry in your head is a model. […] A mental image is a model. All our decisions are taken on the basis of models." (Jay W Forrester, "Counter-Intuitive Behaviour of Social Systems", Technological Review 73, 1971)
"The image of the world around us, which we carry in our head, is just a model. Nobody in his head imagines all the world, government or country. He has only selected concepts, and relationships between them, and uses those to represent the real system." (Jay W Forrester, "Counter-Intuitive Behaviour of Social Systems", Technological Review 73, 1971)
"But metaphor is an indispensable tool of thought and expression - a characteristic of all human communication, even of that of the scientist. The conceptual models of cybernetics and the energy theories of psycho-analysis are, after all, only labeled metaphors." (Gregory Bateson, "Steps to an Ecology of Mind", 1972)
"[…] conceptual models, even when incorrect, are useful to the extent that criticism of the model may point to new theoretical developments." (Gregory Bateson, "Steps to an Ecology of Mind", 1972)
"Everything we think we know about the world is a model. Every word and every language is a model. All maps and statistics, books and databases, equations and computer programs are models. So are the ways I picture the world in my head – my mental models. None of these is or ever will be the real world. […] Our models usually have a strong congruence with the world. That is why we are such a successful species in the biosphere. Especially complex and sophisticated are the mental models we develop from direct, intimate experience of nature, people, and organizations immediately around us." (Donella Meadows, "Limits to Growth", 1972)
"Images apparently occupy a curious position somewhere between the statements of language, which are intended to convey a meaning, and the things of nature, to which we only can give a meaning." (Ernst Gombrich, "Symbolic Images", 1972)
"There are two subcategories of holist called irredundant holists and redundant holists. Students of both types image an entire system of facts or principles. Though an irredundant holist's image is rightly interconnected, it contains only relevant and essential constitents. In contrast, redundant holists entertain images that contain logically irrelevant or overspecific material, commonly derived from data used to 'enrich' the curriculum, and these students embed the salient facts and principles in a network of redundant items. Though logically irrelevant, the items in question are of great psychological importance to a 'redundant holist', since he uses them to access, retain and manipulate whatever he was originally required to learn." (Gordon Pask, "Learning Strategies and Individual Competence", 1972)
"What a lost person needs is a map of the territory, with his own position marked on it so he can see where he is in relation to everything else. Literature is not only a mirror; it is also a map, a geography of the mind. Our literature is one such map, if we can learn to read it as our literature, as the product of who and where we have been. We need such a map desperately, we need to know about here, because here is where we live. For the members of a country or a culture, shared knowledge of their place, their here, is not a luxury but a necessity. Without that knowledge we will not survive." (Margaret Atwood, "Survival: A Thematic Guide to Canadian Literature", 1972)
"A person is changed by the contingencies of reinforcement under which he behaves; he does not store the contingencies. In particular, he does not store copies of the stimuli which have played a part in the contingencies. There are no 'iconic representations' in his mind; there are no 'data structures stored in his memory'; he has no 'cognitive map' of the world in which he has lived. He has simply been changed in such a way that stimuli now control particular kinds of perceptual behavior." (Burrhus F Skinner, "About behaviorism", 1974)
"Your experience in the world of physical matter flows outward from the center of your psyche. Then you perceive this experience. exterior events, circumstances and conditions are meant as a kind of living feedback. Altering the state of the psyche automatically alters the physical circumstances. There is no other valid way of changing physical events. It might help if you imagine an inner living dimension within yourself in which you create, in miniature psychic form, all the exterior conditions that you know. Simply put, you do exactly this. Your thoughts, feelings and mental pictures can be called incipient exterior events, for in one way or another, each of these is materialized into physical reality." (Jane Roberts, "The Nature of Personal Reality", 1974)
"Imagination is the outreaching of mind […] the bombardment of the conscious mind with ideas, impulses, images and every sort of psychic phenomena welling up from the preconscious. It is the capacity to ‘dream dreams and see visions’" (Rollo May, "The Courage to Create", 1975)
"Models are not intended to either reflect or construct a single objective reality. Rather, their purpose is to simulate some aspect of a possible reality. In NLP, for instance, it is not important whether or not a model is 'true' , but rather that it is 'useful' . In fact, all models can be perceived as symbolic or metaphoric, as opposed to reflective of reality. Whether the description being used is metaphorical or literal, the usefulness of a model depends on the degree to which it allows us to move effectively to the next step in the sequence of transformations connecting deeper structures and surface structures. Instead of 'constructing' reality, models establish a set of functions that serve as a tool or a bridge between deep structures and surface structures. It is this bridge that forms our 'understanding' of reality and allows us to generate new experiences and expressions of reality." (Richard Bandler & John Grinder, "The Structure of Magic", 1975)
"The most pervasive paradox of the human condition which we see is that the processes which allow us to survive, grow, change, and experience joy are the same processes which allow us to maintain an impoverished model of the world - our ability to manipulate symbols, that is, to create models. So the processes which allow us to accomplish the most extraordinary and unique human activities are the same processes which block our further growth if we commit the error of mistaking the model of the world for reality." (Richard Bandler & John Grinder," The Structure of Magic", 1975)
"The conception of the mental construction which is the fully analysed proof as being an infinite structure must, of course, be interpreted in the light of the intuitionist view that all infinity is potential infinity: the mental construction consists of a grasp of general principles according to which any finite segment of the proof could be explicitly constructed." (Michael Dummett, "The philosophical basis of intuitionistic logic", 1975)
"Imagining is not perceiving, but images are indeed derivatives of perceptual activity. In particular, they are the anticipatory phases of that activity, schemata that the perceiver has detached from the perceptual cycle for other purposes. […] The experience of having an image is just the inner aspect of a readiness to perceive the imagined object." (Ulrich Neisser, "Cognition and reality" 1976)
"The model of the natural world we build in our minds by such a process will forever be inadequate, just a little cathedral in the mountains. Still it is better than no model at all." (Timothy Ferris, "The Red Limit: The Search for the Edge of the Universe", 1977)
"We never have any understanding of any subject matter except in terms of our own mental constructs of ‘things’ and ‘happenings’ of that subject matter." (Douglas T Ross, "Structured analysis (SA): A language for communicating ideas", IEEE Transactions on Software Engineering Vol. 3 No. 1, 1977)
"Imagination is our means of interpreting the world, and it also is our means of forming images in the mind. The images themselves are not separate from our interpretations of the world; they are our way of thinking of the objects in the world. We see the forms in our mind’s eye and we see these very forms in the world. We could not do one of these things if we could not do the other" (Mary Warnock, "Imagination", 1978)
"We may not speak of the image as a thing, like a canvas only in our heads. But we may say that in thinking with images we are thinking analogically, or by means of representations, just as we are when we look at somebody’s portrait rather than at himself. […] The image is our attempt to reach the non-existent or absent object in our thoughts as we concentrate on this or that aspect of it, its visible appearance, its sound, its smell. […] The images themselves are not separate from our interpretations of the world; they are our way of thinking of objects in the world." (Mary Warnock, "Imagination", 1978)
"[...] it seems (to many) that we cannot account for perception unless we suppose it provides us with an internal image (or model or map) of the external world, and yet what good would that image do us unless we have an inner eye to perceive it, and how are we to explain its capacity for perception? It also seems (to many) that understanding a heard sentence must be somehow translating it into some internal message, but how will this message be understood: by translating it into something else? The problem is an old one, and let’s call it Hume’s Problem, for while he did not state it explicitly, he appreciated its force and strove mightily to escape its clutches. (Daniel Dennett, "Brainstorms: Philosophical essays on mind and psychology", 1978)
"The evolutionary vision is agnostic in regard to systems in the universe of greater complexity than those of which human beings have clear knowledge. It recognizes aesthetic, moral, and religious ideas and experiences as a species, in this case of mental structures or of images, which clearly interacts with other species in the world's great' ecosystem." (Kenneth Boulding," Ecodynamics: A New Theory of Societal Evolution", 1978)
"Information is recorded in vast interconnecting networks. Each idea or image has hundreds, perhaps thousands, of associations and is connected to numerous other points in the mental network." (Peter Russell, "The Brain Book: Know Your Own Mind and How to Use it", 1979)
"A mental image occurs when a representation of the type created during the initial phases of perception is present but the stimulus is not actually being perceived; such representations preserve the perceptible properties of the stimulus and ultimately give rise to the subjective experience of perception." (Stephen Kosslyn, "Image and Mind", 1980)
"A schema, then is a data structure for representing the generic concepts stored in memory. There are schemata representing our knowledge about all concepts; those underlying objects, situations, events, sequences of events, actions and sequences of actions. A schema contains, as part of its specification, the network of interrelations that is believed to normally hold among the constituents of the concept in question. A schema theory embodies a prototype theory of meaning. That is, inasmuch as a schema underlying a concept stored in memory corresponds to the meaning of that concept, meanings are encoded in terms of the typical or normal situations or events that instantiate that concept." (David E Rumelhart, "Schemata: The building blocks of cognition", 1980)
"Once we have accepted a configuration of schemata, the schemata themselves provide a richness that goes far beyond our observations. […] In fact, once we have determined that a particular schema accounts for some event, we may not be able to determine which aspects of our beliefs are based on direct sensory information and which are merely consequences of our interpretation." (David E Rumelhart, "Schemata: The building blocks of cognition", 1980)
"These organizational processes result in our perceptions being structured into units corresponding to objects and properties of objects. It is these larger units that may be stored and later assembled into images that are experienced as quasi-pictorial, spatial entities resembling those evoked during perception itself [...] It is erroneous to equate image representations with mental photographs, since this would overlook the fact that images are composed from highly processed perceptual encodings." (Stephen Kosslyn, "Image and Mind", 1980)
"What is in the present is what the image ‘represents‘, but not the image itself which, in cinema as in painting, is never to be confused with what it represents. The image itself is the system of the relationships between its elements, that is, a set of relationships from which the variable present only flows. […] What is specific in the image, as soon as it is creative, is to make perceptible, to make visible, relationships of time which cannot be seen in the represented object and do not allow them - selves to be reduced to the present." (Gilles Deleuze, "Cinema 2: The Time-Image" , 1980)
"Mathematics associates new mental images with […] physical abstractions; these images are almost tangible to the trained mind but are far removed from those that are given directly by life and physical experience." (Yuri I Manin, "Mathematics and Physics", 1981)
"The ‘eyes of the mind’ must be able to see in the phase space of mechanics, in the space of elementary events of probability theory, in the curved four-dimensional space-time of general relativity, in the complex infinite dimensional projective space of quantum theory. To comprehend what is visible to the ‘actual eyes’, we must understand that it is only the projection of an infinite dimensional world on the retina." (Yuri I Manin, "Mathematics and Physics", 1981)
"Mental schemas are not rigid. By lasting and laborious processes the mental schemas accommodate themselves, in the long run, to the features of real situations and become progressively more fit to manage them and to solve the problems with which we are faced. Each period of mental development is characterized by a system. of basic mental schemas which determine the capacity of the child to learn, to interpret, and to use the information he gets." (Efraim Fischbein, "Intuition and Proof", For The Leaning of Mathematics 3 (2), 1982)
"Myths and science fulfill a similar function: they both provide human beings with a representation of the world and of the forces that are supposed to govern it. They both fix the limits of what is considered as possible." (François Jacob, "The Possible and the Actual", 1982)
"Vision is a process that produces from images of the external world a description that is useful to the viewer and not cluttered with irrelevant information." (David Marr, "Vision", 1982)
"In the consideration of mental models we need really consider four different things: the target system, the conceputal model of that target system, the user’s mental model of the target system, and the scientist's conceptualization of that mental model. The system that the person is learning or using is, by definition, the target system. A conceptual model is invented to provide an appropriate representation of the target system, appropriate in the sense of being accurate, consistent, and complete." (Donald A Norman, "Some Observations on Mental Models" [in "Mental Models", Ed. Dedre Gentner & Albert L Stevens], 1983)
"Myth is the system of basic metaphors, images, and stories that in-forms the perceptions, memories, and aspirations of a people; provides the rationale for its institutions, rituals and power structure; and gives a map of the purpose and stages of life." (Sam Keen, "The Passionate Life", 1983)
"People’s views of the world, of themselves, of their own capabilities, and of the tasks that they are asked to perform, or topics they are asked to learn, depend heavily on the conceptualizations that they bring to the task. In interacting with the environment, with others, and with the artifacts of technology, people form internal, mental models of themselves and of the things with which they are interacting. These models provide predictive and explanatory power for understanding the interaction." (Donald A Norman, "Some observations on Mental Models", 1983)
"Since mental models can take many forms and serve many purposes, their contents are very varied. They can contain nothing but tokens that represent individuals and identities between them, as in the sorts of models that are required for syllogistic reasoning. They can represent spatial relations between entities, and the temporal or causal relations between events. A rich imaginary model of the world can be used to compute the projective relations required for an image. Models have a content and form that fits them to their purpose, whether it be to explain, to predict, or to control." (Philip Johnson-Laird, "Mental models: Toward a cognitive science of language, inference, and consciousness", 1983)
"The thing and the perception of the thing are one amid the same thing, one and the same image, but related in one or other of two systems of reference. The thing is the image as it is in itself, as it is related to all the other images to whose action it completely submits and on which it reacts immediately. But the perception of the thing is the same image related to another special image which frames it, and which only retains a partial action from it, and only reacts to it mediately." (Gilles Deleuze, "Cinema 1: The Movement Image", 1983)
"The purpose of a mental model is to allow the person to understand and to anticipate the behavior of a physical system. This means that the model must have predictive power, either by applying rules of inference or by procedural derivation (in whatever manner these properties may be realized in a person); in other words, it should be possible for people to ' run' their models mentally. This means that the conceptual mental model must also include a model of the relevant human information processing and knowledge structures that make it possible for the person to use a mental model to predict and understand the physical system." (Donald A Norman, "Some Observations on Mental Models" [in "Mental Models"], 1983)
"Concepts are inventions of the human mind used to construct a model of the world. They package reality into discrete units for further processing, they support powerful mechanisms for doing logic, and they are indispensable for precise, extended chains of reasoning. […] A mental model is a cognitive construct that describes a person's understanding of a particular content domain in the world." (John Sown, "Conceptual Structures: Information Processing in Mind and Machine", 1984)
"Mental models are the mechanisms whereby humans are able to generate descriptions of system purpose and form, explanations of system functioning and observed system states, and predictions of future system states." (William B Rouse & Nancy M Morris, "On looking into the black box: Prospects and limits in the search for mental models", Psychological Bulletin (3), 1986)
"The basic idea is that schemata are data structures for representing the generic concepts stored in memory. There are schemata for generalized concepts underlying objects, situations, events, sequences of events, actions, and sequences of actions. Roughly, schemata are like models of the outside world. To process information with the use of a schema is to determine which model best fits the incoming information. Ultimately, consistent configurations of schemata are discovered which, in concert, offer the best account for the input. This configuration of schemata together constitutes the interpretation of the input. (David E Rumelhart, Paul Smolensky, James L McClelland & Geoffrey E Hinton, "Schemata and sequential thought processes in PDP models", 1986)
"The reinvention of daily life means marching off the edge of our maps." (Bob Black, "The Abolition of Work and Other Essays", 1986)
"A mental model is a data structure, in a computational system, that represents a part of the real world or of a fictitious world. It is assumed that there can be mental models of abstract realms, such as that of mathematics, but little more will be said about them. A model-theoretic semanticist is free to think of the entities in his model as actual items in the world. [...] Mental model is an appropriate term for the mental representations that underlie everyday reasoning about the world. To understand the everyday world is to have a theory of how it works." (Alan Granham, "Mental Models as Representations of Discourse and Text", 1987)
"The mapping from linguistic inputs to mental models is not a one-one mapping. So semantic properties of sentences may not be recoverable from a mental model. Reading or listening is typically for content not for form. People want to know what is being said to them, not how it is being said. [...] A mental model is a representation of the content of a text that need bear no resemblance to any of the text's linguistic representations. Its structure is similar to the situation described by the text." (Alan Granham, "Mental Models as Representations of Discourse and Text", 1987)
"[…] a mental model is a mapping from a domain into a mental representation which contains the main characteristics of the domain; a model can be ‘run’ to generate explanations and expectations with respect to potential states. Mental models have been proposed in particular as the kind of knowledge structures that people use to understand a specific domain […]" (Helmut Jungermann, Holger Schütz & Manfred Thuering, "Mental models in risk assessment: Informing people about drugs", Risk Analysis 8 (1), 1988)
"Each of us has many, many maps in our head, which can be divided into two main categories: maps of the way things are, or realities, and maps of the way things should be, or values. We interpret everything we experience through these mental maps. We seldom question their accuracy; we're usually even unaware that we have them. We simply assume that the way we see things is the way they really are or the way they should be." (Stephen Covey, "The 7 Habits of Highly Effective People", 1989)
"The more aware we are of our basic paradigms, maps, or assumptions, and the extent to which we have been influenced by our experience, the more we can take responsibility for those paradigms, examine them, test them against reality, listen to others and be open to their perceptions, thereby getting a larger picture and a far more objective view." (Stephen Covey, "The 7 Habits of Highly Effective People", 1989)
"A mental model is a knowledge structure that incorporates both declarative knowledge (e.g., device models) and procedural knowledge (e.g., procedures for determining distributions of voltages within a circuit), and a control structure that determines how the procedural and declarative knowledge are used in solving problems (e.g., mentally simulating the behavior of a circuit)." (Barbara Y White & John R Frederiksen, "Causal Model Progressions as a Foundation for Intelligent Learning Environments", Artificial Intelligence 42, 1990)
"Images are defined to be information structures, with different kind of images representing different kind of information about what the actor is doing, why and how, and what kind of progress is being made." (Terence R. Mitchell & Lee R Beach, "Organizational behavior and human decision processes", 1990)
"’Mental models’ are deeply ingrained assumptions, generalizations, or even pictures or images that influence how we understand the world and how we take action. Very often, we are not consciously aware of our mental models or the effects they have on our behavior. […] Mental models focus on the openness needed to unearth shortcomings in our present ways of seeing the world. [...] Mental models are deeply held internal images of how the world works, images that limit us to familiar ways of thinking and acting. Very often, we are not consciously aware of our mental models or the effects they have on our behavior." (Peter Senge, "The Fifth Discipline", 1990)
"Perceptual interpretive processes are applied to mental images in much the same way that they are applied to actual physical objects. In this sense, imagined objects can be 'interpreted' much like physical objects." (Ronald A. Finke, "Creative Imagery", 1990)
"Hard though the scientists of mental imagery try, they cannot get around the fact that the representations they deal with are like pictures. […] The methods have to assume, and the experiments continually corroborate, that having imagery is somehow like perceptual seeing, and that it is somehow like seeing pictures. […] The minimal reason for this assumption is that people do naturally talk of seeing pictures before their mind’s eye." (Eva T H Brann, "The World of Imagination", 1991)
"Many people would accept that we do not really have knowledge of the world; we have knowledge only of our representations of the world. Yet we seem condemned by our constitution to treat these representations as if they were the world, for our everyday experience feels as if it were of a given and immediate world." (Francisco Varela, "The Embodied Mind", 1991)
"Philosophy, art, and science are not the mental objects of an objectified brain but the three aspects under which the brain becomes subject." (Gilles Deleuze, What is Philosophy?", 1991)
"The most persuasive positive argument for mental images as objects is [that] whenever one thinks one is seeing something there must be something one is seeing. It might be an object directly, or it might be a mental picture. [This] point is so plausible that it is deniable only at the peril of becoming arbitrary. One should concede that the question whether mental images are entities of some sort is not resolvable by logical or linguistic analysis, and believe what makes sense of experience." (Eva T H Brann, "The World of Imagination", 1991)
"The strangest and most wonderful constructions in the whole animal world are the amazing, intricate constructions made by the primate Homo sapiens. Each normal individual of this species makes a self. Out of its brain it spins a web of words and deeds, and, like the other creatures, it doesn't have to know what it's doing; it just does it. This web protects it, just like the snail's shell. […] As such, it plays a singularly important role in the ongoing cognitive economy of that living body, because, of all the things in the environment an active body must make mental models of, none is more crucial than the model the agent has of itself." (Daniel Dennett, "Consciousness Explained", 1991)
"We construct mental models that provide us with situations in which we can interact with mental objects that represent objects, properties and relations and that behave in ways that simulate the objects, properties and relations that our models represent. […] The concepts and principles that a person understands, in this sense, are embedded in the kinds of objects that he or she includes in mental models and in the ways in which those objects behave, including how they combine and separate to form other objects." (James G Greeno, "Number sense as situated knowing in a conceptual domain", Journal for Research on Mathematics Education Vol. 22 No. 3, 1991)
"[For] us to be able to speak and understand novel sentences, we have to store in our heads not just the words of our language but also the patterns of sentences possible in our language. These patterns, in turn, describe not just patterns of words but also patterns of patterns. Linguists refer to these patterns as the rules of language stored in memory; they refer to the complete collection of rules as the mental grammar of the language, or grammar for short." (Ray Jackendoff, "Patterns in the Mind", 1994)
"People have amazing facilities for sensing something without knowing where it comes from (intuition); for sensing that some phenomenon or situation or object is like something else (association); and for building and testing connections and comparisons, holding two things in mind at the same time (metaphor). These facilities are quite important for mathematics. Personally, I put a lot of effort into ‘listening’ to my intuitions and associations, and building them into metaphors and connections. This involves a kind of simultaneous quieting and focusing of my mind. Words, logic, and detailed pictures rattling around can inhibit intuitions and associations." (William P Thurston, "On proof and progress in mathematics", Bulletin of the American Mathematical Society Vol. 30 (2), 1994)
"[...] images are probably the main content of our thoughts, regardless of the sensory modality in which they are generated and regardless of whether they are about a thing or a process involving things; or about words or other symbols, in a given language, which correspond to a thing or process. Hidden behind those images, never or rarely knowable by us, there are indeed numerous processes that guide the generation and deployment of those images in space and time. Those processes utilize rules and strategies embodied in dispositional representations. They are essential for our thinking but are not a content of our thoughts." (Antonio R Damasio, "Descartes' Error. Emotion, Reason, and the Human Brain", 1994)
"We all depend on models to interpret our everyday experiences. We interpret what we see in terms of mental models constructed on past experience and education. They are constructs that we use to understand the pattern of our experiences." (David Bartholomew, "What is Statistics?", 1995)
"I do not know that my view is more correct; I do not even think that ‘right’ and ‘wrong’ are good categories for assessing complex mental models of external reality - for models in science are judged [as] useful or detrimental, not as true or false." (Stephen Jay Gould, "Dinosaur in a Haystack: Reflections in Natural History", 1995)
"The term mental model refers to knowledge structures utilized in the solving of problems. Mental models are causal and thus may be functionally defined in the sense that they allow a problem solver to engage in description, explanation, and prediction. Mental models may also be defined in a structural sense as consisting of objects, states that those objects exist in, and processes that are responsible for those objects’ changing states." (Robert Hafner & Jim Stewart, "Revising Explanatory Models to Accommodate Anomalous Genetic Phenomena: Problem Solving in the ‘Context of Discovery’", Science Education 79 (2), 1995)
"A mental model is not normally based on formal definitions but rather on concrete properties that have been drawn from life experience. Mental models are typically analogs, and they comprise specific contents, but this does not necessarily restrict their power to deal with abstract concepts, as we will see. The important thing about mental models, especially in the context of mathematics, is the relations they represent. […] The essence of understanding a concept is to have a mental representation or mental model that faithfully reflects the structure of that concept. (Lyn D. English & Graeme S. Halford, "Mathematics Education: Models and Processes", 1995)
"The mental model, in turn, can be considered as a syntactic language of thought whose semantic interpretation is provided by the actual world. In this sense, a person's beliefs are true to the extent that they correspond to the world." (William J Rapaport, "Understanding Understanding: Syntactic Semantics and Computational Cognition", Philosophical Perspectives Vol. 9, 1995)
"When we visually perceive the world, we do not just process information; we have a subjective experience of color, shape, and depth. We have experiences associated with other senses (think of auditory experiences of music, or the ineffable nature of smell experiences), with bodily sensations (e.g., pains, tickles, and orgasms), with mental imagery (e.g., the colored shapes that appear when one tubs one's eyes), with emotion (the sparkle of happiness, the intensity of anger, the weight of despair), and with the stream of conscious thought." (David Chalmers, "The Puzzle of Conscious Experience", Scientific American, 1995)
"If we are to have meaningful, connected experiences; ones that we can comprehend and reason about; we must be able to discern patterns to our actions, perceptions, and conceptions. Underlying our vast network of interrelated literal meanings (all of those words about objects and actions) are those imaginative structures of understanding such as schema and metaphor, such as the mental imagery that allows us to extrapolate a path, or zoom in on one part of the whole, or zoom out until the trees merge into a forest." (William H Calvin, "The Cerebral Code", 1996)
"It [system dynamics] focuses on building system dynamics models with teams in order to enhance team learning, to foster consensus and to create commitment with a resulting decision […] System dynamics can be helpful to elicit and integrate mental models into a more holistic view of the problem and to explore the dynamics of this holistic view […] It must be understood that the ultimate goal of the intervention is not to build a system dynamics model. The system dynamics model is a means to achieve other ends […] putting people in a position to learn about a messy problem [...] create a shared social reality […] a shared understanding of the problem and potential solutions [...] to foster consensus within the team [..]" (Jac A M Vennix, "Group Model Building: Facilitating Team Learning Using System Dynamics", 1996)
"Our mental model of the way the world works must shift from images of a clockwork, machinelike universe that is fixed and determined, to the model of a universe that is open, dynamic, interconnected, and full of living qualities." (Joseph Jaworski, "Synchronicity: The Inner Path of Leadership", 1996)
"People build practical, useful mental models all of the time. Seldom do they resort to writing a complex set of mathematical equations or use other formal methods. Rather, most people build models relating inputs and outputs based on the examples they have seen in their everyday life. These models can be rather trivial, such as knowing that when there are dark clouds in the sky and the wind starts picking up that a storm is probably on the way. Or they can be more complex, like a stock trader who watches plots of leading economic indicators to know when to buy or sell. The ability to make accurate predictions from complex examples involving many variables is a great asset." (Joseph P Bigus, "Data Mining with Neural Networks: Solving business problems from application development to decision support", 1996)
"Perhaps our ultimate understanding of scientific topics is measured in terms of our ability to generate metaphoric pictures of what is going on. Maybe understanding is coming up with metaphoric pictures." (Per Bak, "How Nature Works: the science of self-organized criticality", 1996)
"The logic of the emotional mind is associative; it takes elements that symbolize a reality, or trigger a memory of it, to be the same as that reality. That is why similes, metaphors and images speak directly to the emotional mind." (Daniel Goleman, "Emotional Intelligence", 1996)
"The seemingly stable scene you normally see is really a mental model that you construct - the eyes are actually darting all around, producing a retinal image as jerky as an amateur video, and some of what you thought you saw was instead filled in from memory." (William H Calvin, "How Brains Think", 1996)
"Discourses are ways of referring to or constructing knowledge about a particular topic of practice: a cluster (or formation) of ideas, images and practices, which provide ways of talking about, forms of knowledge and conduct associated with, a particular topic, social activity or institutional site in society. These discursive formations, as they are known, define what is and is not appropriate in our formulation of, and our practices in relation to, a particular subject or site of social activity." (Stuart Hall, "Representation: Cultural Representations and Signifying Practices", 1997)
"[Schemata are] knowledge structures that represent objects or events and provide default assumptions about their characteristics, relationships, and entailments under conditions of incomplete information." (Paul J DiMaggio, "Culture and Cognition", Annual Review of Sociology 23, 1997)
"We are a people captivated by the power and romance of metaphor, forever seeking the invisible through the image of the visible." (Lewis H Lapham, "Waiting For The Barbarians", 1997)
"A model is an edited, distorted and generalised copy of the original and therefore there can never be complete. A model is not in any sense ‘true’: it can be judged only by whether it works or doesn’t work. If it works, it allows another person to get the same class of results as the original person from whom the model was taken." (Joseph O’Connor, "Leading With NLP: Essential Leadership Skills for Influencing and Managing People", 1998)
"Having a choice is better than not having a choice. Always try to have a map for yourself that gives you the widest and richest number of choices. Act always to increase choice. The more choices you have, the freer you are and the more influence you have." (Joseph O’Connor, "Leading With NLP: Essential Leadership Skills for Influencing and Managing People", 1998)
"Intuition isn't direct perception of something external. It's the effect in the mind/brain of manipulating concrete objects - at a later stage, of making marks on paper, and still later, manipulating mental images. This experience leaves a trace, an effect, in your mind/brain." (Reuben Hersh, "What Is Mathematics, Really?", 1998)
"Our brain is mapping the world. Often that map is distorted, but it's a map with constant immediate sensory input." (Edward O Wilson, [interview] 1998)
"Perhaps we all lose our sense of reality to the precise degree to which we are engrossed in our own work, and perhaps that is why we see in the increasing complexity of our mental constructs a means for greater understanding, even while intuitively we know that we shall never be able to fathom the imponderables that govern our course through life." (Winfried G Sebald, "The Rings of Saturn", 1998)
"Theories rarely arise as patient inferences forced by accumulated facts. Theories are mental constructs potentiated by complex external prods (including, in idealized cases, a commanding push from empirical reality)." (Stephen J Gould, "Leonardo's Mountain of Clams and the Diet of Worms" , 1998)
"A vision is a clear mental picture of a desired future outcome. If you have ever put together a large 1,000-piece jigsaw puzzle, the chances are you used the picture on the top of the puzzle box to guide the placement of the pieces. That picture on the top of the box is the end result or the vision of what you are trying to turn into a reality. It is much more difficult - if not impossible - to put the jigsaw puzzle together without ever looking at the picture." (Jane Flaherty & Peter B Stark, "The Manager's Pocket Guide to Leadership Skills", 1999)
"A collective mental map functions first of all as a shared memory. Various discoveries by members of the collective are registered and stored in this memory, so that the information will remain available for as long as necessary. The storage capacity of this memory is in general much larger than the capacities of the memories of the individual participants. This is because the shared memory can potentially be inscribed over the whole of the physical surroundings, instead of being limited to a single, spatially localized nervous system. Thus, a collective mental map differs from cultural knowledge, such as the knowledge of a language or a religion, which is shared among different individuals in a cultural group but is limited by the amount of knowledge a single individual can bear in mind." (Francis Heylighen, "Collective Intelligence and its Implementation on the Web", 1999)
"[A mental model] is a relatively enduring and accessible, but limited, internal conceptual representation of an external system (historical, existing, or projected) whose structure is analogous to the perceived structure of that system." (James K Doyle & David N Ford, "Mental models concepts revisited: Some clarifications and a reply to Lane", System Dynamics Review 15 (4), 1999)
"According to the representational format claim, images constitute a class of mental models that is particularly suited to represent visually perceptible information. More specifically, an image can be conceived of as a viewer centered projection of an underlying mental model which, in turn, represents spatiotemporal aspects of external objects or events. Unlike propositional or network representations, images depict, rather than describe, a particular state of affairs." (Gert Rickheit & Lorenz Sichelschmidt, „Mental Models: Some Answers, Some Questions, Some Suggestions", 1999)
"Cultural archetypes are the unconscious models that help us make sense of the world: they are the myths, narratives, images, symbols, and files into which we organize the data of our life experience" (Clotaire Rapaille, "Cultural Imprints", Executive Excellence Vol. 16 (10), 1999)
"Imagining the unseeable is hard, because imagining means having an image in your mind. And how can you have a mental image of something you have never seen? Like perception itself, the models of science are embedded inextricably in the current worldview we call culture." (K C Cole, "First You Build a Cloud and Other Reflections on Physics as a Way of Life", 1999)
"In broad terms, a mental model is to be understood as a dynamic symbolic representation of external objects or events on the part of some natural or artificial cognitive system. Mental models are thought to have certain properties which make them stand out against other forms of symbolic representations." (Gert Rickheit & Lorenz Sichelschmidt, "Mental Models: Some Answers, Some Questions, Some Suggestions", 1999)
"Simple observation generally gets us nowhere. It is the creative imagination that increases our understanding by finding connections between apparently unrelated phenomena, and forming logical, consistent theories to explain them. And if a theory turns out to be wrong, as many do, all is not lost. The struggle to create an imaginative, correct picture of reality frequently tells us where to go next, even when science has temporarily followed the wrong path." (Richard Morris, "The Universe, the Eleventh Dimension, and Everything: What We Know and How We Know It", 1999)
"The three basic mechanisms of averaging, feedback and division of labor give us a first idea of a how a CMM [Collective Mental Map] can be developed in the most efficient way, that is, how a given number of individuals can achieve a maximum of collective problem-solving competence. A collective mental map is developed basically by superposing a number of individual mental maps. There must be sufficient diversity among these individual maps to cover an as large as possible domain, yet sufficient redundancy so that the overlap between maps is large enough to make the resulting graph fully connected, and so that each preference in the map is the superposition of a number of individual preferences that is large enough to cancel out individual fluctuations. The best way to quickly expand and improve the map and fill in gaps is to use a positive feedback that encourages individuals to use high preference paths discovered by others, yet is not so strong that it discourages the exploration of new paths." (Francis Heylighen, "Collective Intelligence and its Implementation on the Web", 1999)
"What it means for a mental model to be a structural analog is that it embodies a representation of the spatial and temporal relations among, and the causal structures connecting the events and entities depicted and whatever other information that is relevant to the problem-solving talks. […] The essential points are that a mental model can be nonlinguistic in form and the mental mechanisms are such that they can satisfy the model-building and simulative constraints necessary for the activity of mental modeling." (Nancy J Nersessian, "Model-based reasoning in conceptual change", 1999)
"Because feeling does not have a form; it has to be treated like an inner sensation which can only be understood in terms of the images it triggers. These images do not, however, represent the feeling as such, for they are independently existing representations or fantasies that are merely associated at the moment of pleasure or pain." (Angelika Rauch, "The Hieroglyph of Tradition: Freud, Benjamin, Gadamer, Novalis, Kant", 2000)
"When we talk of seeing an image, either in front of us or visualised with closed eyes, we invoke a range of metaphors and ideas which highlight the relationship between perception and imagery. For those of us with unimpaired vision, to see with ‘the mind’s eye’ conjures up a picture of perception where there is not a great deal of difference between an external or internal image." (Michael Forrester," Psychology of the Image", 2000)
"A mental model is a representation of some domain or situation that supports understanding, reasoning, and prediction. Mental models permit reasoning about situations not directly experienced. They allow people to mentally simulate the behavior of a system. Many mental models are based on generalizations and analogies from experience." (D Gentner, "Psychology of Mental Models" [in "International Encyclopedia of the Social & Behavioral Sciences"], 2001)
"A symbol is a mental representation regarding the internal reality referring to its object by a convention and produced by the conscious interpretation of a sign. In contrast to signals, symbols may be used every time if the receiver has the corresponding representation. Symbols also relate to feelings and thus give access not only to information but also to the communicator’s motivational and emotional state. The use of symbols makes it possible for the organism using it to evoke in the receiver the same response it evokes in himself. To communicate with symbols is to use a language." (Lars Skyttner, "General Systems Theory: Ideas and Applications", 2001)
"In the definition of meaning, it is assumed that both the source and receiver have previously coded (and stored) signals of the same or similar referents, such that the messages may have meaning and relate to behaviour. That is, the used symbols must have the same signification for both sender and receiver. If not, the receiver will create a different mental picture than intended by the transmitter. Meaning is generated by individuals in a process of social interaction with a more or less common environment. It is a relation subsisting within a field of experience and appears as an emergent property of a symbolic representation when used in culturally accepted interaction. The relation between the symbolic representation and its meaning is random. Of this, however, the mathematical theory has nothing to say. If human links in the chain of communication are missing, of course no questions of meaning will arise." (Lars Skyttner, "General Systems Theory: Ideas and Applications", 2001)
"Our view of reality is like a map with which to negotiate the terrain of life. If the map is true and accurate, we will generally know how to get there. If the map is false and inaccurate, we generally will be lost." (M Scott Peck, "Wisdom from the Road Less Traveled", 2001)
"Science begins with the world we have to live in, accepting its data and trying to explain its laws. From there, it moves toward the imagination: it becomes a mental construct, a model of a possible way of interpreting experience. The further it goes in this direction, the more it tends to speak the language of mathematics, which is really one of the languages of the imagination, along with literature and music." (Northrop Frye, "The Educated Imagination", 2002)
"A person thinking in the nonverbal mode is actually thinking with the meaning of the language in the form of mental pictures of the concepts and ideas it contains. Nonverbal thought doesn't require literacy. An illiterate person can communicate without knowing what the symbols look like. ... Literacy, then, is established as the person learns how the symbols look and becomes able to recognize them as representing certain things or concepts." (Ronald D Davis & Eldon M Braun, "The Gift of Learning", 2003)
"Deep change in mental models, or double-loop learning, arises when evidence not only alters our decisions within the context of existing frames, but also feeds back to alter our mental models. As our mental models change, we change the structure of our systems, creating different decision rules and new strategies. The same information, interpreted by a different model, now yields a different decision. Systems thinking is an iterative learning process in which we replace a reductionist, narrow, short-run, static view of the world with a holistic, broad, long-term, dynamic view, reinventing our policies and institutions accordingly." (John D Sterman, "Learning in and about complex systems", Systems Thinking Vol. 3 2003)
"Eliciting and mapping the participant's mental models, while necessary, is far from sufficient [...] the result of the elicitation and mapping process is never more than a set of causal attributions, initial hypotheses about the structure of a system, which must then be tested. Simulation is the only practical way to test these models. The complexity of the cognitive maps produced in an elicitation workshop vastly exceeds our capacity to understand their implications. Qualitative maps are simply too ambiguous and too difficult to simulate mentally to provide much useful information on the adequacy of the model structure or guidance about the future development of the system or the effects of policies." (John D Sterman, "Learning in and about complex systems", Systems Thinking Vol. 3 2003)
"Science does not speak of the world in the language of words alone, and in many cases it simply cannot do so. The natural language of science is a synergistic integration of words, diagrams, pictures, graphs, maps, equations, tables, charts, and other forms of visual and mathematical expression. […] Science thus consists of] the languages of visual representation, the languages of mathematical symbolism, and the languages of experimental operations." (Jay Lemke, "Teaching all the languages of science: Words, symbols, images and actions", 2003)
"To form a mental picture of the event, the knowledge developer attempts to integrate his or her perception of the situation with the expert’s perception. That mental picture is then recorded. What happens is a continuous shuttle process; the knowledge developer mentally moves back and forth from the initial impression of the event to the later evaluation of the event. What is finally recorded is the evaluation made during this retrospective period. Because a time lapse can make details of a situation less clear, the information is not always valid." (Elias M Awad, "Knowledge Management", 2003)
"We start from vague pictures or ideas […] which we encapsulate by rules, and then we discover that those rules persuade us to modify our mental images. We engage in a dialog between our mental images and our ability to justify them via equations. As we understand what we are investigating more clearly, the pictures become sharper and the equations more elaborate. Only at the end of the process does anything like a formal set of axioms followed by logical proofs" (E Brian Davies, "Science in the Looking Glass", 2003)
"I often told the fanatics of realism that there is no such thing as realism in art: it only exists in the mind of the observer. Art is a symbol, a thing conjuring up reality in our mental image. That is why I don't see any contradiction between abstract and figurative art either." (Antoni TÃ pies, "TÃ pies, Werke auf Papier 1943 – 2003", 2004)
"A mental model is conceived […] as a knowledge structure possessing slots that can be filled not only with empirically gained information but also with ‘default assumptions’ resulting from prior experience. These default assumptions can be substituted by updated information so that inferences based on the model can be corrected without abandoning the model as a whole. Information is assimilated to the slots of a mental model in the form of ‘frames’ which are understood here as ‘chunks’ of knowledge with a well-defined meaning anchored in a given body of shared knowledge." (Jürgen Renn, "Before the Riemann Tensor: The Emergence of Einstein’s Double Strategy", "The Universe of General Relativity" Ed. by A.J. Kox & Jean Eisenstaedt, 2005)
"When a particular image appears in the mind's eye often enough it begins to connect apparently unrelated ideas leading to models and theories. […] Patterns experienced again and again become intuitions. […] Intuitive judgments are made by our use of imagery; intuition is the result of mental model building. […] The mental model used and the form of the intuition is dependent upon the question being answered." (Roger Frantz, "Two Minds", 2005)
"A conceptual model is a mental image of a system, its components, its interactions. It lays the foundation for more elaborate models, such as physical or numerical models. A conceptual model provides a framework in which to think about the workings of a system or about problem solving in general. An ensuing operational model can be no better than its underlying conceptualization." (Henry N Pollack, "Uncertain Science … Uncertain World", 2005)
"Patterns experienced again and again become intuitions. […] Intuitive judgments are made by our use of imagery; intuition is the result of mental model building. […] The mental model used and the form of the intuition is dependent upon the question being answered." (Roger Frantz, "Two Minds", 2005)
"[…] the human brain must work in models. The trick is to have your brain work better than the other person’s brain because it understands the most fundamental models: ones that will do most work per unit. If you get into the mental habit of relating what you’re reading to the basic structure of the underlying ideas being demonstrated, you gradually accumulate some wisdom." (Charles T Munger, "Poor Charlie’s Almanack", 2005)
"We must begin by distinguishing between visual mental imagery and visual perception: Visual perception occurs while a stimulus is being viewed, and includes functions such as visual recognition (i. e., registering that a stimulus is familiar) and identification (i. e., recalling the name, context, or other information associated with the object). Two types of mechanisms are used in visual perception: ‘bottom-up’ mechanisms are driven by the input from the eyes; in contrast, ‘top-down’ mechanisms make use of stored information (such as knowledge, belief, expectations, and goals). Visual mental imagery is a set of representations that gives rise to the experience of viewing a stimulus in the absence of appropriate sensory input. In this case, information in memory underlies the internal events that produce the experience. Unlike afterimages, mental images are relatively prolonged." (Stephen M Kosslyn, "Mental images and the brain", Cognitive Neuropsychology 22, 2005)
"You must know the big ideas in the big disciplines and use them routinely - all of them, not just a few. Most people are trained in one model - economics, for example - and try to solve all problems in one way. This is a dumb way of handling problems. […] What you need is a latticework of mental models in your head. And, with that system, things gradually get to fit together in a way that enhances cognition." (Charles T Munger, "Poor Charlie’s Almanack", 2005)
"A mental model represents a possibility, or, to be precise, the structure and content of the model capture what is common to the different ways in which the possibility could occur [...]" (Philip N Johnson-Laird, Mental Models, Sentential Reasoning, and Illusory Inferences, [in "Mental Models and the Mind"], 2006)
"According to mental model theory, human reasoning relies on the construction of integrated mental representations of the information that is given in the reasoning problem's premises. These integrated representations are the mental models. A mental model is a mental representation that captures what is common to all the different ways in which the premises can be interpreted. It represents in 'small scale' how 'reality' could be - according to what is stated in the premises of a reasoning problem. Mental models, though, must not be confused with images. A mental model often forms the basis of one or more visual images, but some of them represent situations that cannot be visualized. Instead, mental models are often likened to diagrams since, as with diagrams, their structure is analogous to the structure of the states of affairs they represent." (Carsten Held et al, "Mental Models and the Mind", 2006)
"From the processing view, the model theory distinguishes between three different operations. In the construction phase, reasoners construct the mental model that reflects the information from the premises. In the inspection phase, this model is inspected to find new information that is not explicitly given in the premises. In most variants of the model theory, the inspection process is conceptualized as a spatial focus that scans the model to find new information not given in the premises.. In the variation phase, reasoners try to construct alternative models from the premises that refute the putative conclusion. If no such model is found, the putative conclusion is considered true." (Carsten Held et al, "Mental Models and the Mind", 2006)
"Mental models are mental representations of a certain type. The main problem in the philosophy of mental representation is to characterize the relation between a mental representation and the represented object. Naively speaking, a mental representation is an entity that 'stands for' another—the represented object - , but here 'stands for' is just a metaphoric place-holder for 'represents', thus requires further explanation." (Carsten Held et al, "Mental Models and the Mind", 2006)
"Mental models can be literal representations of the external world (as they often are with visual imagery) or arbitrary representations (as they are with propositional, mathematical, or verbal models). In either case, they are explanatory or descriptive representations of the external world." (Gregory J Feist, "The Psychology of Science and the Origins of the Scientific Mind", 2006)
"Art is constructivist in nature, aimed at the deliberate refinement and elaboration of mental models and worldviews. These are the natural products of cognition itself, the outcome of the brain’s tendency to strive for the integration of perceptual and conceptual material over time. […] human culture is essentially a distributed cognitive system within which worldviews and mental models are constructed and shared by the members of a society. Artists are traditionally at the forefront of that process, and have a large influence on our worldviews and mental models." (Mark Turner, "The Artful Mind: Cognitive science and the riddle of human creativity", 2006)
"But because of the way in which depictions represent, there is a correspondence between parts and spatial relations of the representation and those of the object; this structural mapping, which confers a type of resemblance, underlies the way images convey specific content. In this respect images are like pictures. Unlike words and symbols, depictions are not arbitrarily paired with what they represent." (Stephen Kosslyn et al," The Case for Mental Imagery", 2006)
"Nothing resembles reality less than the photograph. Nothing resembles substance less than its shadow. To convey the meaning of something substantial you have to use not a shadow but a sign, not the limitation but the image. The image is a new and different reality, and of course it does not convey an impression of some object, but the mind of the subject; and that is something else again." (Thomas Merton, "Angelic Mistakes: The Art of Thomas Merton", 2006)
"The model theory postulates that mental models are parsimonious. They represent what is possible, but not what is impossible, according to assertions. This principle of parsimony minimizes the load on working memory, and so it applies unless something exceptional occurs to overrule it." (Philip N Johnson-Laird, Mental Models, Sentential Reasoning, and Illusory Inferences, [in "Mental Models and the Mind"], 2006)
"[…] the 'reality' that we perceive is based on mental models in which things don't usually change their shapes or disappear, despite their changing appearances. We mainly react to what we expect - and tend to represent the things that we see as though they remain the same as we move atomic." (Marvin Minsky, "The Emotion Machine: Commonsense thinking, artificial intelligence, and the future of the human mind", 2006)
"We all construct mental models that describe our various mental states, bodies of knowledge about our abilities, depictions of our acquaintances, and collections of stories about our pasts. Then, whenever we use our models of ourselves, we tend to use terms like conscious - when those reflections lead to choices we make, and we use unconscious or unintentional to describe those activities that we regard as beyond our control." (Marvin Minsky, "The Emotion Machine: Commonsense thinking, artificial intelligence, and the future of the human mind", 2006)
"We solve easy problems in routine ways, scarcely thinking about how we accomplish these - but when our usual methods don't work, we start to 'reflect' on what went wrong and find ourselves to be switching around in a network of 'models', each of which purports to represent some facet or aspect of ourselves, so that we end representing ourselves with a loosely connected collection of images, models, and anecdotes." (Marvin Minsky, "The Emotion Machine: Commonsense thinking, artificial intelligence, and the future of the human mind", 2006)
"Why must those models be simplifications? Each model must help us to focus on only those aspects that matter in some particular context; that's what makes a map more useful to us than seeing the entire landscape that it depicts. The same applies to what we store in our minds. Consider how messy our minds would become if we filled them up with descriptions of things whose details had too little significance. So instead, we spend large parts of our lives at trying to tidy up our minds - selecting the portions we want to keep, suppressing others we'd like to forget, and refining the ones we're dissatisfied with." (Marvin Minsky, "The Emotion Machine: Commonsense thinking, artificial intelligence, and the future of the human mind", 2006)
"All models (whether mental or those turned into computer maps/models) are developed using a particular lens of what we value - what we think is important to understand, or what performance we wish to develop or improve." (Peggy Holman et al, "The Change Handbook", 2007)
"[...] each of us frames, orders and/or organizes our experiences in terms of socially learned incomplete mental models or mind sets that shape our experiences perspectivally. These mental models are constitutive of all our experiences. They are the ways in which we make sense of our experiences [...]" (Patricia H Werhane "A Place for Philosophers in Applied Ethics and the Role of Moral Reasoning in Moral Imagination", Business Ethics Quarterly 16 (3), 2007)
"Just as physicists have created models of the atom based on observed data and intuitive synthesis of the patterns in their data, so must designers create models of users based on observed behaviors and intuitive synthesis of the patterns in the data. Only after we formalize such patterns can we hope to systematically construct patterns of interaction that smoothly match the behavior patterns, mental models, and goals of users. Personas provide this formalization." (Alan Cooper et al, "About Face 3: The Essentials of Interaction Design", 2007)
"Mental models reflect the beliefs, values, and assumptions that we personally hold, and they underlie our reasons for doing things the way we do." (Kambiz E Maani & Robert Y Cavana, "Systems Methodology", The Systems Thinker Vol. 18 No. 8, 2007)
"’Mental models’ are deeply ingrained assumptions, generalizations, or even pictures or images that influence how we understand the world and how we take action. Very often, we are not consciously aware of our mental models or the effects they have on our behavior. […] The discipline of working with mental models starts with turning the mirror inward; learning to unearth our internal pictures of the world, to bring them to the surface and hold them rigorously to scrutiny. It also includes the ability to carry on ‘learningful’ conversations that balance inquiry and advocacy, where people expose their own thinking effectively and make that thinking open to the influence of others." (Jossey-Bass Publishers, "The Jossey-Bass Reader on Educational Leadership", 2nd Ed. 2007)
"We tend to form mental models that are simpler than reality; so if we create represented models that are simpler than the actual implementation model, we help the user achieve a better understanding. […] Understanding how software actually works always helps someone to use it, but this understanding usually comes at a significant cost. One of the most significant ways in which computers can assist human beings is by putting a simple face on complex processes and situations. As a result, user interfaces that are consistent with users’ mental models are vastly superior to those that are merely reflections of the implementation model." (Alan Cooper et al, "About Face 3: The Essentials of Interaction Design", 2007)
"A mental model can be thought of as an internal picture that affects a leader's actions and relationships with others. Mental models are theories people hold about specific systems in the world and their expected behavior." (Richard Daft, "The Leadership Experience", 2008)
"Images and pictures […] have played a key role in shaping our scientific picture of the world. […] Carefully constructed families of pictures can act as a calculus all their own. Like any successful systems of symbols, with an appropriate grammar they enlarge the number of things that we can do without consciously thinking." (John D Barrow, "Cosmic Imagery: Key Images in the History of Science", 2008)
[mental models:] "Internal representations constructed on the spot when required by demands of an external task or by a self-generated stimulus. It enables activation of relevant schemata, and allows new knowledge to be integrated. It specifies causal actions among concepts that take place within it, and it can be interacted with in the mind." (Daniel Churchill, "Mental Models" [in "Encyclopedia of Information Technology Curriculum Integration"] , 2008)
"Each generation builds a mental picture that reflects their own understanding of this world. They construct mental tools that penetrate more and more deeply into it, so that they can explore aspects of it that were previously hidden." (Alain Connes, "The Princeton Companion to Mathematics", Ed. by Timothy Gowers et al, 2008)
"When the words are used without mental image or concrete objects, we label them as metaphor. […] While concepts are being internalised, language is not only appropriated but metaphorised." (Lynne Cameron, "Metaphor in the construction of a learning environment", 2008)
"Actually, around 80% of the data we use to make decisions is already in our heads before we engage with a situation. Our power to perceive is governed and limited by cognitive filters, sometimes termed our ‘mental model’. Mental models are formed as a result of past experience, knowledge and attitudes. They are deeply ingrained, often subconscious, structures that limit what we perceive and also colour our interpretation of supposed facts." (Robina Chatham & Brian Sutton, "Changing the IT Leader’s Mindset", 2010)
"Mental models are formed over time through a deep enculturation process, so it follows that any attempt to align mental models must focus heavily on collective sense making. Alignment only happens through a process of socialisation; people working together, solving problems together, making sense of the world together." (Robina Chatham & Brian Sutton, "Changing the IT Leader’s Mindset", 2010)
"Mental models and rules are intimately intertwined, since the models often suggest clear rules for societies to follow. Religions are more than theories; they are prescriptive moral codes that seek to enforce rules on their followers. They, like the rules they enjoin, are invested with considerable emotional meaning and therefore are believed for intrinsic reasons and not simply because they are accurate or useful. While religious beliefs cannot be verified, they are also difficult to falsify. All of this reinforces the fundamental conservatism of human societies, because mental models of reality once adopted are hard to change in the light of new evidence that they are not working." (Francis Fukuyama, "The Origins of Political Order", 2011)
"Once a myth becomes established, it forms part of our mental model of the world and alters our perception, the way our brains interpret the fleeting patterns our eyes pick up." (Jeremy Wade, "River Monsters: True Stories of the Ones that Didn't Get Away", 2011)
"To think one needs to use a mental model, but mental models are only an abstraction of reality and at best an oversimplification. Making them explicit is the only chance one has to learn and improve them." (Jamshid Gharajedaghi, "Systems Thinking: Managing Chaos and Complexity", 2011)
"A theory is a purely mental image of how something should be. In other words, the thought in the dark (with eyes closed) comes first, and the comparison with nature (eyes open) comes later. If the imagined agrees with the real, then the theory is correct." (Adrian Bejan, [interview] 2012)
"Effective communication is not possible unless there’s understanding of the mental model held by the person to whom you’re communicating. This is fundamental in communication. The only way to understand the mental models of the people is to be involved with the people." (Donald K Smith, "Make Haste Slowly", 2012)
"Mental models represent possibilities, and the theory of mental models postulates three systems of mental processes underlying inference: (0) the construction of an intensional representation of a premise’s meaning – a process guided by a parser; (1) the building of an initial mental model from the intension, and the drawing of a conclusion based on heuristics and the model; and (2) on some occasions, the search for alternative models, such as a counterexample in which the conclusion is false. System 0 is linguistic, and it may be autonomous. System 1 is rapid and prone to systematic errors, because it makes no use of a working memory for intermediate results. System 2 has access to working memory, and so it can carry out recursive processes, such as the construction of alternative models." (Sangeet Khemlania & P.N. Johnson-Laird, "The processes of inference", Argument and Computation, 2012)
"Also known as worldview, mental model, or mind-set, our perspective of the world is based on the sum total of our knowledge and experiences. It defines us, shaping our thoughts and actions because it represents the way we see ourselves and situations, how we judge the relative importance of things, and how we establish a meaningful relationship with everything around us." (Navi Radjou & Prasad Kaipa, "From Smart to Wise: Acting and Leading with Wisdom", 2013)
"Mental models bind our awareness within a particular scaffold and then selectively can filter the content we subsequently receive. Through recalibration using revised mental models, we argue, we cultivate strategies anew, creating new habits, and galvanizing more intentional and evolved mental models. This recalibration often entails developing a strong sense of self and self-worth, realizing that each of us has a range of moral choices that may deviate from those in authority, and moral imagination." (Patricia H Werhane et al, "Obstacles to Ethical: Decision-Making Mental Models, Milgram and the Problem of Obedience", 2013)
"Models are present in everything we do. One does not have a family or corporation in one's head. Instead, one has observations about those systems. Such observations and assumptions constitute mental models, which are then used as the basis for action. System dynamics models have little impact unless they change the way people perceive a situation. They must relate to and improve mental models if they are to fill an effective role." (Jay W. Forrester, "Modeling for What Purpose?", The Systems Thinker Vol. 24 (2), 2013)
"System dynamics models have little impact unless they change the way people perceive a situation. A model must help to organize information in a more understandable way. A model should link the past to the present by showing how present conditions arose, and extend the present into persuasive alternative futures under a variety of scenarios determined by policy alternatives. In other words, a system dynamics model, if it is to be effective, must communicate with and modify the prior mental models. Only people's beliefs - that is, their mental models - will determine action. Computer models must relate to and improve mental models if the computer models are to fill an effective role." (Jay W. Forrester, "Modeling for What Purpose?", The Systems Thinker Vol. 24 (2), 2013)
"These framing perspectives or mental models construe the data of our experiences, and it is the construed data that we call 'facts'. What we often call reality, or the world, is constructed or socially construed in certain ways such that one cannot get at the source of the data except through these construals." (Patricia H Werhane et al, "Obstacles to Ethical: Decision-Making Mental Models, Milgram and the Problem of Obedience", 2013)
"Various scientific methodologies are themselves mental models through which scientists discover, predict, and hypothesize about what we then call reality. In the social constructionist paradigm such mental models frame all our experiences. They schematize, and otherwise facilitate and guide the ways in which we recognize, react, and organize the world. How we define the world is dependent on such schema and thus all realities are socially structured. In the socially constructed paradigm, the multivariate mental models or conceptual schema are the means and mode through which we constitute our experiences." (Patricia H Werhane et al, "Obstacles to Ethical: Decision-Making Mental Models, Milgram and the Problem of Obedience", 2013)
"Learning is a process of modifying or completely changing our mental models based on new experiences or evidence." (Edward D Hess, "Learn or Die: Using Science to Build a Leading-Edge Learning Organization", 2014)
"Mental imagery is often useful in problem solving. Verbal descriptions of problems can become confusing, and a mental image can clear away excessive detail to bring out important aspects of the problem. Imagery is most useful with problems that hinge on some spatial relationship. However, if the problem requires an unusual solution, mental imagery alone can be misleading, since it is difficult to change one’s understanding of a mental image. In many cases, it helps to draw a concrete picture since a picture can be turned around, played with, and reinterpreted, yielding new solutions in a way that a mental image cannot. There are many models for problem solving and many of them will require teamwork." (James Schindler, "Followership", 2014)
"Design is the process of taking something that appears in the mind’s eye, modeling it in one or more of a number of ways, predicting how that thing will behave if it is made, and then making it, sometimes modifying the design as we make it. Design is what engineering is about. Furthermore, modeling is how engineering design is done. This includes mental models, mathematical models, computer models, plans and drawings, written language, and (sometimes) physical models." (William M Bulleit, "The Engineering Way of Thinking: The Idea", Structure [magazine], 2015)
"Fuzzy thinking can never be proven wrong. And only when we are proven wrong so clearly that we can no longer deny it to ourselves will we adjust our mental models of the world - producing a clearer picture of reality. Forecast, measure, revise: it is the surest path to seeing better." (Philip E Tetlock, "Superforecasting: The Art and Science of Prediction", 2015)
"One of the most powerful transformational catalysts is knowledge, new information, or logic that defies old mental models and ways of thinking. […] The key to transforming mental models is to interrupt the automatic responses that are driven by the old model and respond differently based on the new model. Each time you are able to do this, you are actually loosening the old circuit and creating new neural connections in your brain, often referred to as self-directed neuroplasticity." (Elizabeth Thornton, "The Objective Leader", 2015)
"We all have mental models: the lens through which we see the world that drive our responses to everything we experience. Being aware of your mental models is key to being objective." (Elizabeth Thornton, "Learn to Be an Objective Leader without Losing Everything", 2015)
"A mental representation is a mental structure that corresponds to an object, an idea, a collection of information, or anything else, concrete or abstract, that the brain is thinking about. […] Because the details of mental representations can differ dramatically from field to field, it’s hard to offer an overarching definition that is not too vague, but in essence these representations are preexisting patterns of information - facts, images, rules, relationships, and so on - that are held in long-term memory and that can be used to respond quickly and effectively in certain types of situations." (Anders Ericsson & Robert Pool," Peak: Secrets from the New Science of Expertise", 2016)
"In the classical deterministic scenario, a model consists of a few variables and physical constants. The relational structure of the model is conceptualized by the scientist via intuition gained from thinking about the physical world. Intuition means that the scientist has some mental construct regarding the interactions beyond positing a skeletal mathematical system he believes is sufficiently rich to capture the interactions and then depending upon data to infer the relational structure and estimate a large number of parameters." (Edward R Dougherty, "The Evolution of Scientific Knowledge: From certainty to uncertainty", 2016)
"So everyone has and uses mental representations. What sets expert performers apart from everyone else is the quality and quantity of their mental representations. Through years of practice, they develop highly complex and sophisticated representations of the various situations they are likely to encounter in their fields - such as the vast number of arrangements of chess pieces that can appear during games. These representations allow them to make faster, more accurate decisions and respond more quickly and effectively in a given situation. This, more than anything else, explains the difference in performance between novices and experts." (Anders Ericsson & Robert Pool," "Peak: Secrets from the New Science of Expertise" , 2016)
"A mathematician possesses a mental model of the mathematical entity she works on. This internal mental model is accessible to her direct observation and manipulation. At the same time, it is socially and culturally controlled, to conform to the mathematics community's collective model of the entity in question. The mathematician observes a property of her own internal model of that mathematical entity. Then she must find a recipe, a set of instructions, that enables other competent, qualified mathematicians to observe the corresponding property of their corresponding mental model. That recipe is the proof. It establishes that property of the mathematical entity." (Reuben Hersh," Mathematics as an Empirical Phenomenon, Subject to Modeling", 2017)
"A model may be defined as a substitute of any object or system. […] A mental image used in thinking is a model, and it is not the real system. A written description of a system is a model that presents one aspect of reality. The simulation model is logically complete and describes the dynamic behaviour of the system. Models can be broadly classified as (a) physical models and (b) abstract models [..] Mental models and mathematical models are examples of abstract models." (Bilash K Bala et al, "System Dynamics: Modelling and Simulation", 2017)
"Like all models, people’s mental models are an abstraction of reality. They may be complete and correct, or they may have gaps or inconsistencies that are consequential to effective decision making and action. A mental model is usually less complex than the real-world phenomenon involved and tends to lag in context or time and so can easily become out of date. In many cases, people may lack conscious, well-formed mental models on issues that they have not thoroughly considered in the past. This may be challenging for decision-makers as people’s responses may seem unpredictable or irrational." (Matthew D Wood, An Introduction to Mental Modeling, [in "Mental Modeling Approach: Risk Management Application Case Studies"], 2017)
"Mental Modeling enables discovery of people’s mental models in a structured, rigorous, respectful manner. Mental Modeling has been recognized as one of the premier methods for informing the development of strategies and communications that precisely address people’s current thinking, judgment, decision making, and behavior on complex issues , including risk issues. Broadly, Mental Modeling works from the 'inside out', starting with an in-depth understanding of people’s mental models, and then using that insight to develop focused strategies and communication that builds on where people are at in their thinking today, reinforcing what they know about a topic and addressing critical gaps. Broadly stated, the goal is to help people make well-informed decisions and take appropriate actions on the topic at hand." (Matthew D Wood, An Introduction to Mental Modeling, [in "Mental Modeling Approach: Risk Management Application Case Studies"], 2017)
"The crucial concept that brings all of this together is one that is perhaps as rich and suggestive as that of a paradigm: the concept of a model. Some models are concrete, others are abstract. Certain models are fairly rigid; others are left somewhat unspecified. Some models are fully integrated into larger theories; others, or so the story goes, have a life of their own. Models of experiment, models of data, models in simulations, archeological modeling, diagrammatic reasoning, abductive inferences; it is difficult to imagine an area of scientific investigation, or established strategies of research, in which models are not present in some form or another. However, models are ultimately understood, there is no doubt that they play key roles in multiple areas of the sciences, engineering, and mathematics, just as models are central to our understanding of the practices of these fields, their history and the plethora of philosophical, conceptual, logical, and cognitive issues they raise. "(Otávio Bueno, [in" Springer Handbook of Model-Based Science", Ed. by Lorenzo Magnani & Tommaso Bertolotti, 2017])
"Self-image is the mental image that we have about our self. […] We are therefore constantly on the road, straying from one mental image to the next, and identify with these images, and derive our identity from the images." (Frank M Wanderer, "Wake Up Consciousness: A Guide for Spiritual Seekers", 2018)
"Images are generally resistant to change and ignore messages that do not conform to their internal settings. Sometimes, however, they do react and can alter in an incremental or even revolutionary manner. Humans can talk about and share their images and, in the symbolic universe they create, reflect upon what is and what might be." (Michael C Jackson, "Critical Systems Thinking and the Management of Complexity", 2019)
"In signs, one sees an advantage for discovery that is greatest when they express the exact nature of a thing briefly and, as it were, picture it; then indeed, the labor of thought is wonderfully diminished” (Gottfried W Leibniz)
