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Who said: “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
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Home > Category Index for Science Quotations > Category Index M > Category: Mental

Mental Quotes (179 quotes)

[Magic] enables man to carry out with confidence his important tasks, to maintain his poise and his mental integrity in fits of anger, in the throes of hate, of unrequited love, of despair and anxiety. The function of magic is to ritualize man's optimism, to enhance his faith in the victory of hope over fear. Magic expresses the greater value for man of confidence over doubt, of steadfastness over vacillation, of optimism over pessimism.
Magic, Science and Religion (1925), 90.
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[About describing atomic models in the language of classical physics:] We must be clear that when it comes to atoms, language can be used only as in poetry. The poet, too, is not nearly so concerned with describing facts as with creating images and establishing mental connections.
As quoted by Werner Heisenberg, as translated by Arnold J. Pomerans, in Physics and Beyond: Encounters and Conversations (1971), 41. The words are not verbatim, but as later recollected by Werner Heisenberg describing his early encounter with Bohr in 1920.
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Truth then seems to me, in the proper import of the Word, to signifie nothing but the joining or separating of Signs, as the Things signified by them do agree or disagree one with another; which way of joining or separating of Signs, we call Proposition. So that Truth properly belongs only to Propositions: whereof there are two sorts, viz. Mental and Verbal; as there are two sorts of Signs commonly made use of, viz. Ideas and Words.
In 'Truth in General', Essay Concerning Human Understanding (1690), book 4, ch. 5, sec. 2, 289.
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A fossil hunter needs sharp eyes and a keen search image, a mental template that subconsciously evaluates everything he sees in his search for telltale clues. A kind of mental radar works even if he isn’t concentrating hard. A fossil mollusk expert has a mollusk search image. A fossil antelope expert has an antelope search image. … Yet even when one has a good internal radar, the search is incredibly more difficult than it sounds. Not only are fossils often the same color as the rocks among which they are found, so they blend in with the background; they are also usually broken into odd-shaped fragments. … In our business, we don’t expect to find a whole skull lying on the surface staring up at us. The typical find is a small piece of petrified bone. The fossil hunter’s search therefore has to have an infinite number of dimensions, matching every conceivable angle of every shape of fragment of every bone on the human body.
Describing the skill of his co-worker, Kamoya Kimeu, who discovered the Turkana Boy, the most complete specimen of Homo erectus, on a slope covered with black lava pebbles.
Richard Leakey and Roger Lewin, Origins Reconsidered: In Search of What Makes Us Human (1992), 26.
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A great department of thought must have its own inner life, however transcendent may be the importance of its relations to the outside. No department of science, least of all one requiring so high a degree of mental concentration as Mathematics, can be developed entirely, or even mainly, with a view to applications outside its own range. The increased complexity and specialisation of all branches of knowledge makes it true in the present, however it may have been in former times, that important advances in such a department as Mathematics can be expected only from men who are interested in the subject for its own sake, and who, whilst keeping an open mind for suggestions from outside, allow their thought to range freely in those lines of advance which are indicated by the present state of their subject, untrammelled by any preoccupation as to applications to other departments of science. Even with a view to applications, if Mathematics is to be adequately equipped for the purpose of coping with the intricate problems which will be presented to it in the future by Physics, Chemistry and other branches of physical science, many of these problems probably of a character which we cannot at present forecast, it is essential that Mathematics should be allowed to develop freely on its own lines.
In Presidential Address British Association for the Advancement of Science, Sheffield, Section A, Nature (1 Sep 1910), 84, 286.
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A New Arithmetic: “I am not much of a mathematician,” said the cigarette, “but I can add nervous troubles to a boy, I can subtract from his physical energy, I can multiply his aches and pains, I can divide his mental powers, I can take interest from his work and discount his chances for success.”
Anonymous
In Henry Ford, The Case Against the Little White Slaver (1914), Vol. 3, 40.
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A well-chosen anthology is a complete dispensary of medicine for the more common mental disorders, and may be used as much for prevention as cure.
'The Use of Poetry', On English Poetry (1922), 85.
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After an honest day’s work a mathematician goes off duty. Mathematics is very hard work, and dons tend to be above average in health and vigor. Below a certain threshold a man cracks up; but above it, hard mental work makes for health and vigor (also—on much historical evidence throughout the ages—for longevity). I have noticed lately that when I am working really hard I wake around 5.30 a.m. ready and eager to start; if I am slack, I sleep till I am called.
In 'The Mathematician’s Art of Work' (1967), collected in Béla Bollobás (ed.), Littlewood’s Miscellany (1986), 195.
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Anyone of common mental and physical health can practice scientific research. … Anyone can try by patient experiment what happens if this or that substance be mixed in this or that proportion with some other under this or that condition. Anyone can vary the experiment in any number of ways. He that hits in this fashion on something novel and of use will have fame. … The fame will be the product of luck and industry. It will not be the product of special talent.
In Essays of a Catholic Layman in England (1931).
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Apart from its healthful mental training as a branch of ordinary education, geology as an open-air pursuit affords an admirable training in habits of observation, furnishes a delightful relief from the cares and routine of everyday life, takes us into the open fields and the free fresh face of nature, leads us into all manner of sequestered nooks, whither hardly any other occupation or interest would be likely to send us, sets before us problems of the highest interest regarding the history of the ground beneath our feet, and thus gives a new charm to scenery which may be already replete with attractions.
Outlines of Field-Geology (1900), 251-2.
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As a single footstep will not make a path on the earth, so a single thought will not make a pathway in the mind. To make a deep physical path, we walk again and again. To make a deep mental path, we must think over and over the kind of thoughts we wish to dominate our lives.
From The Art of Living, Day by Day 91972), 77. Frequently misattributed to Henry David Thoreau.
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As an exercise of the reasoning faculty, pure mathematics is an admirable exercise, because it consists of reasoning alone, and does not encumber the student with an exercise of judgment: and it is well to begin with learning one thing at a time, and to defer a combination of mental exercises to a later period.
In Annotations to Bacon’s Essays (1873), Essay 1, 493.
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As natural selection works solely by and for the good of each being, all corporeal and mental endowments will tend to progress towards perfection.
On the Origin of Species by Means of Natural Selection (1866), 577.
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As to Science, she has never sought to ally herself to civil power. She has never attempted to throw odium or inflict social ruin on any human being. She has never subjected anyone to mental torment, physical torture, least of all to death, for the purpose of upholding or promoting her ideas. She presents herself unstained by cruelties and crimes. But in the Vatican—we have only to recall the Inquisition—the hands that are now raised in appeals to the Most Merciful are crimsoned. They have been steeped in blood!
History of the Conflict between Religion and Science (1875), xi.
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As, no matter what cunning system of checks we devise, we must in the end trust some one whom we do not check, but to whom we give unreserved confidence, so there is a point at which the understanding and mental processes must be taken as understood without further question or definition in words. And I should say that this point should be fixed pretty early in the discussion.
Samuel Butler, Henry Festing Jones (ed.), The Note-Books of Samuel Butler (1917), 220-221.
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But, as we consider the totality of similarly broad and fundamental aspects of life, we cannot defend division by two as a natural principle of objective order. Indeed, the ‘stuff’ of the universe often strikes our senses as complex and shaded continua, admittedly with faster and slower moments, and bigger and smaller steps, along the way. Nature does not dictate dualities, trinities, quarterings, or any ‘objective’ basis for human taxonomies; most of our chosen schemes, and our designated numbers of categories, record human choices from a cornucopia of possibilities offered by natural variation from place to place, and permitted by the flexibility of our mental capacities. How many seasons (if we wish to divide by seasons at all) does a year contain? How many stages shall we recognize in a human life?
…...
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By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and in effect increases the mental power of the race.
In An Introduction to Mathematics (1911), 59.
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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.
From 'Radium and Its Products', Harper’s Magazine (Dec 1904), 52.
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Consciousness is not sharply defined, but fades into sub-consciousness; and beyond that we must postulate something indefinite but yet continuous with our mental nature. This I take it be the world-stuff.
From Gifford Lecture, Edinburgh, (1927), 'Reality', collected in The Nature of the Physical World (1928), 280.
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Doubtless it is true that while consciousness is occupied in the scientific interpretation of a thing, which is now and again “a thing of beauty,” it is not occupied in the aesthetic appreciation of it. But it is no less true that the same consciousness may at another time be so wholly possessed by the aesthetic appreciation as to exclude all thought of the scientific interpretation. The inability of a man of science to take the poetic view simply shows his mental limitation; as the mental limitation of a poet is shown by his inability to take the scientific view. The broader mind can take both.
In An Autobiography (1904), Vol. 1, 485.
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Electricity is often called wonderful, beautiful; but it is so only in common with the other forces of nature. The beauty of electricity or of any other force is not that the power is mysterious, and unexpected, touching every sense at unawares in turn, but that it is under law, and that the taught intellect can even govern it largely. The human mind is placed above, and not beneath it, and it is in such a point of view that the mental education afforded by science is rendered super-eminent in dignity, in practical application and utility; for by enabling the mind to apply the natural power through law, it conveys the gifts of God to man.
Notes for a Friday Discourse at the Royal Institution (1858).
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Engineering training deals with the exact sciences. That sort of exactness makes for truth and conscience. It might be good for the world if more men had that sort of mental start in life even if they did not pursue the profession.
Reprint of his 1916 statement in 'Engineering as a Profession', Engineer’s Week (1954).
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Every one should keep a mental waste-paper basket and the older he grows the more things he will consign to it—torn up to irrecoverable tatters.
Samuel Butler, Henry Festing Jones (ed.), The Note-Books of Samuel Butler (1917), 216.
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Experience is the great teacher; unfortunately, experience leaves mental scars, and scar tissue contracts.
From speech 'In the Time of Henry Jacob Bigelow', given to the Boston Surgical Society, Medalist Meeting (6 Jun 1921). Printed in Journal of the Medical Association (1921), 77, 599.
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For twenty pages perhaps, he read slowly, carefully, dutifully, with pauses for self-examination and working out examples. Then, just as it was working up and the pauses should have been more scrupulous than ever, a kind of swoon and ecstasy would fall on him, and he read ravening on, sitting up till dawn to finish the book, as though it were a novel. After that his passion was stayed; the book went back to the Library and he was done with mathematics till the next bout. Not much remained with him after these orgies, but something remained: a sensation in the mind, a worshiping acknowledgment of something isolated and unassailable, or a remembered mental joy at the rightness of thoughts coming together to a conclusion, accurate thoughts, thoughts in just intonation, coming together like unaccompanied voices coming to a close.
In Mr. Fortune’s Maggot (1927), 161.
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Frege has the merit of ... finding a third assertion by recognising the world of logic which is neither mental nor physical.
Our Knowledge of the External World (1914), 201.
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From the standpoint of observation, then, we must regard it as a highly probable hypothesis that the beginnings of the mental life date from as far back as the beginnings of life at large.
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Genetics has enticed a great many explorers during the past two decades. They have labored with fruit-flies and guinea-pigs, with sweet peas and corn, with thousands of animals and plants in fact, and they have made heredity no longer a mystery but an exact science to be ranked close behind physics and chemistry in definiteness of conception. One is inclined to believe, however, that the unique magnetic attraction of genetics lies in the vision of potential good which it holds for mankind rather than a circumscribed interest in the hereditary mechanisms of the lowly species used as laboratory material. If man had been found to be sharply demarcated from the rest of the occupants of the world, so that his heritage of physical form, of physiological function, and of mental attributes came about in a superior manner setting him apart as lord of creation, interest in the genetics of the humbler organisms—if one admits the truth—would have flagged severely. Biologists would have turned their attention largely to the ways of human heredity, in spite of the fact that the difficulties encountered would have rendered progress slow and uncertain. Since this was not the case, since the laws ruling the inheritance of the denizens of the garden and the inmates of the stable were found to be applicable to prince and potentate as well, one could shut himself up in his laboratory and labor to his heart's content, feeling certain that any truth which it fell to his lot to discover had a real human interest, after all.
Mankind at the Crossroads (1923), v-vi.
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Grouches are nearly always pinheads, small men who have never made any effort to improve their mental capacity.
As quoted from an interview by B.C. Forbes in The American Magazine (Jan 1921), 10.
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He who would know what geometry is, must venture boldly into its depths and learn to think and feel as a geometer. I believe that it is impossible to do this, and to study geometry as it admits of being studied and am conscious it can be taught, without finding the reason invigorated, the invention quickened, the sentiment of the orderly and beautiful awakened and enhanced, and reverence for truth, the foundation of all integrity of character, converted into a fixed principle of the mental and moral constitution, according to the old and expressive adage “abeunt studia in mores”.
In 'A Probationary Lecture on Geometry, in Collected Mathematical Papers (1908), Vol. 2, 9. [The Latin phrase, “abeunt studia in mores” translates as “studies pass on into character”. —Webmaster]
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Hypothesis is the most important mental technique of the investigator, and its main function is to suggest new experiments or new observations. Indeed, most experiments and many observations are carried out with the deliberate object of testing an hypothesis. Another function is to help one see the significance of an object or event that otherwise would mean nothing. For instance, a mind prepared by the hypothesis of evolution would make many more significant observations on a field excursion than one not so prepared. Hypotheses should be used as tools to uncover new facts rather than as ends in themselves.
The Art of Scientific Investigation (1953), 46.
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I [do not know] when the end of science will come. ... What I do know is that our species is dumber than we normally admit to ourselves. This limit of our mental faculties, and not necessarily of science itself, ensures to me that we have only just begun to figure out the universe.
In Death by Black Hole: And Other Cosmic Quandaries (2007), 17.
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I am willing to believe that my unobtainable sixty seconds within a sponge or a flatworm might not reveal any mental acuity that I would care to ca ll consciousness. But I am also confident ... that vultures and sloths, as close evolutionary relatives with the same basic set of organs, lie on our side of any meaningful (and necessarily fuzzy) border–and that we are therefore not mistaken when we look them in the eye and see a glimmer of emotional and conceptual affinity.
…...
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I believe that the present laws of physics are at least incomplete without a translation into terms of mental phenomena.
In 'Physics and the Explanation of Life', Foundations of Physics 1970, I, 35-45.
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I grew up in Japan and Hong Kong and then came to the States. Japan was a huge influence on me because, as a child, I would hear the oxcarts come and collect our sewage at night out of our house from the latrine and then take it off to the farms as fertilizer. And then the food would come back in oxcarts during the day. I always had this sort of “our poop became food” mental model. The idea of “waste equals food” was pretty inculcated, that everything was precious and the systems were coherent and cyclical.
In interview with Kerry A. Dolan, 'William McDonough On Cradle-to-Cradle Design', Forbes (4 Aug 2010)
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I know no study which is so unutterably saddening as that of the evolution of humanity, as it is set forth in the annals of history. Out of the darkness of prehistoric ages man emerges with the marks of his lowly origin strong upon him. He is a brute, only more intelligent than the other brutes, a blind prey to impulses, which as often as not led him to destruction; a victim to endless illusions, which make his mental existence a terror and a burden, and fill his physical life with barren toil and battle.
'Agnosticism' (1889). In Collected Essays (1894), Vol. 5, 256.
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I maintain that in every special natural doctrine only so much science proper is to be met with as mathematics; for… science proper, especially [science] of nature, requires a pure portion, lying at the foundation of the empirical, and based upon a priori knowledge of natural things. … To the possibility of a determinate natural thing, and therefore to cognise it à priori, is further requisite that the intuition corresponding à priori to the conception should be given; in other words, that the conception should be constructed. But the cognition of the reason through construction of conceptions is mathematical. A pure philosophy of nature in general, namely, one that only investigates what constitutes a nature in general, may thus be possible without mathematics; but a pure doctrine of nature respecting determinate natural things (corporeal doctrine and mental doctrine), is only possible by means of mathematics; and as in every natural doctrine only so much science proper is to be met with therein as there is cognition à priori, a doctrine of nature can only contain so much science proper as there is in it of applied mathematics.
From Preface to The Metaphysical Foundations of Natural Science (1786), as translated by Ernest Belford Boax, in Kant’s Prolegomena: And The Metaphysical Foundations of Natural Science (1883), 140.
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I myself, a professional mathematician, on re-reading my own work find it strains my mental powers to recall to mind from the figures the meanings of the demonstrations, meanings which I myself originally put into the figures and the text from my mind. But when I attempt to remedy the obscurity of the material by putting in extra words, I see myself falling into the opposite fault of becoming chatty in something mathematical.
Astronomia Nova, New Astronomy, (1609), Introduction, second paragraph.
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I think that in order to achieve progress in the study of language and human cognitive faculties in general it is necessary first to establish 'psychic distance' from the 'mental facts' to which Köhler referred, and then to explore the possibilities for developing explanatory theories... We must recognize that even the most familiar phenomena require explanation and that we have no privileged access to the underlying mechanisms, no more so than in physiology or physics.
Language and Mind (1972, enlarged edition), 26.
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I was sitting writing at my textbook but the work did not progress; my thoughts were elsewhere. I turned my chair to the fire and dozed. Again the atoms were gambolling before my eyes. This time the smaller groups kept modestly in the background. My mental eye, rendered more acute by the repeated visions of the kind, could now distinguish larger structures of manifold confirmation: long rows, sometimes more closely fitted together all twining and twisting in snake like motion. But look! What was that? One of the snakes had seized hold of its own tail, and the form whirled mockingly before my eyes. As if by a flash of lightning I awoke; and this time also I spent the rest of the night in working out the rest of the hypothesis. Let us learn to dream, gentlemen, then perhaps we shall find the truth... But let us beware of publishing our dreams till they have been tested by waking understanding.
Kekule at Benzolfest in Berichte (1890), 23, 1302.
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I would... establish the conviction that Chemistry, as an independent science, offers one of the most powerful means towards the attainment of a higher mental cultivation; that the study of Chemistry is profitable, not only inasmuch as it promotes the material interests of mankind, but also because it furnishes us with insight into those wonders of creation which immediately surround us, and with which our existence, life, and development, are most closely connected.
Familiar Letters on Chemistry (1859), 4th edn., 1.
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Iconography becomes even more revealing when processes or concepts, rather than objects, must be depicted–for the constraint of a definite ‘thing’ cedes directly to the imagination. How can we draw ‘evolution’ or ‘social organization,’ not to mention the more mundane ‘digestion’ or ‘self-interest,’ without portraying more of a mental structure than a physical reality? If we wish to trace the history of ideas, iconography becomes a candid camera trained upon the scholar’s mind.
…...
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If Freud is not the Pasteur of mental illness, he is at least its Hippocrates.
In The Intelligent Man's Guide to Science: The Biological Sciences (1960), 723. Also in Isaac Asimov’s Book of Science and Nature Quotations (1988), 220.
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If I have put the case of science at all correctly, the reader will have recognised that modern science does much more than demand that it shall be left in undisturbed possession of what the theologian and metaphysician please to term its “legitimate field.” It claims that the whole range of phenomena, mental as well as physical—the entire universe—is its field. It asserts that the scientific method is the sole gateway to the whole region of knowledge.
From The Grammar of Science (1892), 29-30.
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If one looks with a cold eye at the mess man has made of history, it is difficult to avoid the conclusion that he has been afflicted by some built-in mental disorder which drives him towards self-destruction.
In The Ghost in the Machine (1967).
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If the man of science chose to follow the example of historians and pulpit-orators, and to obscure strange and peculiar phenomena by employing a hollow pomp of big and sounding words, this would be his opportunity; for we have approached one of the greatest mysteries which surround the problem of animated nature and distinguish it above all other problems of science. To discover the relations of man and woman to the egg-cell would be almost equivalent of the egg-cell in the body of the mother, the transfer to it by means of the seed, of the physical and mental characteristics of the father, affect all the questions which the human mind has ever raised in regard to existence.
Quoted in Ernst Heinrich Philipp August Haeckel, The Evolution of Man (1897), vol 1, 148.
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If you ask ... the man in the street ... the human significance of mathematics, the answer of the world will be, that mathematics has given mankind a metrical and computatory art essential to the effective conduct of daily life, that mathematics admits of countless applications in engineering and the natural sciences, and finally that mathematics is a most excellent instrumentality for giving mental discipline... [A mathematician will add] that mathematics is the exact science, the science of exact thought or of rigorous thinking.
Address (28 Mar 1912), Michigan School Masters' Club, Ann Arbor, 'The Humanization of the Teaching of Mathematics. Printed in Science (26 Apr 1912). Collected in The Human Worth of Rigorous Thinking: Essays and Addresses (1916), 65-66.
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In attempting to understand the elements out of which mental phenomena are compounded, it is of the greatest importance to remember that from the protozoa to man there is nowhere a very wide gap either in structure or in behaviour. From this fact it is a highly probable inference that there is also nowhere a very wide mental gap.
Lecture II, 'Instinct and Habit', The Analysis of Mind
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In fact, whenever energy is transmitted from one body to another in time, there must be a medium or substance in which the energy exists after it leaves one body and before it reaches the other ... and if we admit this medium as an hypothesis, I think it ought to occupy a prominent place in our investigations, and that we ought to endeavour to construct a mental representation of all the details of its action, and this has been my constant aim in this treatise.
A Treatise on Electricity and Magnetism (1873), Vol. 2, 438.
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In Institutions of a lower grade [secondary schools], it [geology] receives far less attention than its merits deserve. Why should not a science, whose facts possess a thrilling interest; whose reasonings are admirably adapted for mental discipline, and often severely tax the strongest powers; and whose results are, many of them, as grand and ennobling as those of Astronomy itself; … why should not such a science be thought as essential in education as the kindred branches of Chemistry and Astronomy?
In 'Preface', Elementary Geology (1840, 1841), vi.
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In Man the brain presents an ascensive step in development, higher and more strongly marked than that by which the preceding subclass was distinguished from the one below it. Not only do the cerebral hemispheres overlap the olfactory lobes and cerebellum, but they extend in advance of the one, and further back than the other. Their posterior development is so marked, that anatomists have assigned to that part the character of a third lobe; it is peculiar to the genus Homo, and equally peculiar is the 'posterior horn of the lateral ventricle,' and the 'hippocampus minor,' which characterize the hind lobe of each hemisphere. The superficial grey matter of the cerebrum, through the number and depth of the convolutions, attains its maximum of extent in Man. Peculiar mental powers are associated with this highest form of brain, and their consequences wonderfully illustrate the value of the cerebral character; according to my estimate of which, I am led to regard the genus Homo, as not merely a representative of a distinct order, but of a distinct subclass of the Mammalia, for which I propose a name of 'ARCHENCEPHALA.'
'On the Characters, Principles of Division, and Primary Groups of the Class MAMMALIA' (1857), Journal of the Proceedings of the Linnean Society of London (1858), 2, 19-20.
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In nature there is no law of refraction, only different cases of refraction. The law of refraction is a concise compendious rule, devised by us for the mental reconstruction of a fact.
In The Science of Mechanics (1893), 485-486.
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In scientific study, or, as I prefer to phrase it, in creative scholarship, the truth is the single end sought; all yields to that. The truth is supreme, not only in the vague mystical sense in which that expression has come to be a platitude, but in a special, definite, concrete sense. Facts and the immediate and necessary inductions from facts displace all pre-conceptions, all deductions from general principles, all favourite theories. Previous mental constructions are bowled over as childish play-structures by facts as they come rolling into the mind. The dearest doctrines, the most fascinating hypotheses, the most cherished creations of the reason and of the imagination perish from a mind thoroughly inspired with the scientific spirit in the presence of incompatible facts. Previous intellectual affections are crushed without hesitation and without remorse. Facts are placed before reasonings and before ideals, even though the reasonings and the ideals be more beautiful, be seemingly more lofty, be seemingly better, be seemingly truer. The seemingly absurd and the seemingly impossible are sometimes true. The scientific disposition is to accept facts upon evidence, however absurd they may appear to our pre-conceptions.
The Ethical Functions of Scientific Study: An Address Delivered at the Annual Commencement of the University of Michigan, 28 June 1888, 7-8.
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In the discovery of lemmas the best aid is a mental aptitude for it. For we may see many who are quick at solutions and yet do not work by method ; thus Cratistus in our time was able to obtain the required result from first principles, and those the fewest possible, but it was his natural gift which helped him to the discovery.
Proclus
As given in Euclid, The Thirteen Books of Euclid's Elements, translated from the text of Johan Ludvig Heiberg by Sir Thomas Little Heath, Vol. 1, Introduction and Books 1,2 (1908), 133. The passage also states that Proclus gives the definition of the term lemma as a proposition not proved beforehand. Glenn Raymond Morrow in A Commentary on the First Book of Euclid's Elements (1992), 165, states nothing more seems to be known of Cratistus.
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In the distant future I see open fields for far more important researches. Psychology will be based on a new foundation, that of the necessary acquirement of each mental power and capacity by gradation. Light will be thrown on the origin of man and his history.
On The Origin of Species by Means of Natural Selection (1859, 1882), 428 .
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In the future I see open fields for more important researches. Psychology will be securely based on the foundation already laid by Mr. Herbert Spencer, that of the necessary acquirement of each mental power and capacity by graduation.
Origin of Species
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In the training and in the exercise of medicine a remoteness abides between the field of neurology and that of mental health, psychiatry. It is sometimes blamed to prejudice on the part of the one side or the other. It is both more grave and less grave than that. It has a reasonable basis. It is rooted in the energy-mind problem. Physiology has not enough to offer about the brain in relation to the mind to lend the psychiatrist much help.
In 'The Brain Collaborates With Psyche', Man On His Nature: The Gifford Lectures, Edinburgh 1937-8 (1940), 283.
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Induction. The mental operation by which from a number of individual instances, we arrive at a general law. The process, according to Hamilton, is only logically valid when all the instances included in the law are enumerated. This being seldom, if ever, possible, the conclusion of an Induction is usually liable to more or less uncertainty, and Induction is therefore incapable of giving us necessary (general) truths.
Stated as narrative, not a direct quote, by his biographer W.H.S. Monck in 'Glossary of Philosophical Terms', appended in Sir William Hamilton (1881), 181.
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Infidels are intellectual discoverers. They sail the unknown seas and find new isles and continents in the infinite realms of thought. An Infidel is one who has found a new fact, who has an idea of his own, and who in the mental sky has seen another star. He is an intellectual capitalist, and for that reason excites the envy and hatred of the theological pauper.
In 'The Great Infidels', The Works of Robert G. Ingersoll (1902), Vol. 3, 309.
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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.
From Reglas y Consejos sobre Investigacíon Cientifica: Los tónicos de la voluntad. (1897), as translated by Neely and Larry W. Swanson, in Advice for a Young Investigator (1999), 34.
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Inventive genius requires pleasurable mental activity as a condition for its vigorous exercise. “Necessity is the mother of invention” is a silly proverb. “Necessity is the mother of futile dodges” is much closer to the truth. The basis of growth of modern invention is science, and science is almost wholly the outgrowth of pleasurable intellectual curiosity.
In 'Technical Education and Its Relation to Science and Literature', The Aims of Education and Other Essays (1917), 69.
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It has been asserted … that the power of observation is not developed by mathematical studies; while the truth is, that; from the most elementary mathematical notion that arises in the mind of a child to the farthest verge to which mathematical investigation has been pushed and applied, this power is in constant exercise. By observation, as here used, can only be meant the fixing of the attention upon objects (physical or mental) so as to note distinctive peculiarities—to recognize resemblances, differences, and other relations. Now the first mental act of the child recognizing the distinction between one and more than one, between one and two, two and three, etc., is exactly this. So, again, the first geometrical notions are as pure an exercise of this power as can be given. To know a straight line, to distinguish it from a curve; to recognize a triangle and distinguish the several forms—what are these, and all perception of form, but a series of observations? Nor is it alone in securing these fundamental conceptions of number and form that observation plays so important a part. The very genius of the common geometry as a method of reasoning—a system of investigation—is, that it is but a series of observations. The figure being before the eye in actual representation, or before the mind in conception, is so closely scrutinized, that all its distinctive features are perceived; auxiliary lines are drawn (the imagination leading in this), and a new series of inspections is made; and thus, by means of direct, simple observations, the investigation proceeds. So characteristic of common geometry is this method of investigation, that Comte, perhaps the ablest of all writers upon the philosophy of mathematics, is disposed to class geometry, as to its method, with the natural sciences, being based upon observation. Moreover, when we consider applied mathematics, we need only to notice that the exercise of this faculty is so essential, that the basis of all such reasoning, the very material with which we build, have received the name observations. Thus we might proceed to consider the whole range of the human faculties, and find for the most of them ample scope for exercise in mathematical studies. Certainly, the memory will not be found to be neglected. The very first steps in number—counting, the multiplication table, etc., make heavy demands on this power; while the higher branches require the memorizing of formulas which are simply appalling to the uninitiated. So the imagination, the creative faculty of the mind, has constant exercise in all original mathematical investigations, from the solution of the simplest problems to the discovery of the most recondite principle; for it is not by sure, consecutive steps, as many suppose, that we advance from the known to the unknown. The imagination, not the logical faculty, leads in this advance. In fact, practical observation is often in advance of logical exposition. Thus, in the discovery of truth, the imagination habitually presents hypotheses, and observation supplies facts, which it may require ages for the tardy reason to connect logically with the known. Of this truth, mathematics, as well as all other sciences, affords abundant illustrations. So remarkably true is this, that today it is seriously questioned by the majority of thinkers, whether the sublimest branch of mathematics,—the infinitesimal calculus—has anything more than an empirical foundation, mathematicians themselves not being agreed as to its logical basis. That the imagination, and not the logical faculty, leads in all original investigation, no one who has ever succeeded in producing an original demonstration of one of the simpler propositions of geometry, can have any doubt. Nor are induction, analogy, the scrutinization of premises or the search for them, or the balancing of probabilities, spheres of mental operations foreign to mathematics. No one, indeed, can claim preeminence for mathematical studies in all these departments of intellectual culture, but it may, perhaps, be claimed that scarcely any department of science affords discipline to so great a number of faculties, and that none presents so complete a gradation in the exercise of these faculties, from the first principles of the science to the farthest extent of its applications, as mathematics.
In 'Mathematics', in Henry Kiddle and Alexander J. Schem, The Cyclopedia of Education, (1877.) As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 27-29.
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It is difficult for the matter-of-fact physicist to accept the view that the substratum of everything is of mental character. But no one can deny that mind is the first and most direct thing in our experience, and all else is remote inference—inference either intuitive or deliberate.
From Gifford Lecture, Edinburgh, (1927), 'Reality', collected in The Nature of the Physical World (1928), 281.
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It is evident, therefore, that one of the most fundamental problems of psychology is that of investigating the laws of mental growth. When these laws are known, the door of the future will in a measure be opened; determination of the child's present status will enable us to forecast what manner of adult he will become.
In The Intelligence of School Children: How Children Differ in Ability, the Use of Mental Tests in School Grading and the Proper Education of Exceptional Children (1919), 136
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It is impossible for us adequately to conceive the boldness of the measure which aimed at universal education through the establishment of free schools. ... it had no precedent in the world's history ... But time has ratified its soundness. Two centuries proclaim it to be as wise as it was courageous, as beneficient as it was disinterested. ... The establishment of free schools was one of those grand mental and moral experiments whose effects could not be developed and made manifest in a single generation. ... The sincerity of our gratitude must be tested by our efforts to perpetuate and improve what they established. The gratitude of the lips only is an unholy offering.
Tenth Report of the Secretary of the Massachusetts Board of Education (1946). Life and Works of Horace Mann (1891), Vol. 4, 111-112.
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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 consists 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 visualization, however, we must content ourselves with two incomplete analogies—the wave picture and the corpuscular picture.
The Physical Principles of the Quantum Theory, trans. Carl Eckart and Frank C. Hoyt (1949), 11.
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It is said of Jacobi, that he attracted the particular attention and friendship of Böckh, the director of the philological seminary at Berlin, by the great talent he displayed for philology, and only at the end of two years’ study at the University, and after a severe mental struggle, was able to make his final choice in favor of mathematics.
In Collected Mathematical Papers, Vol. 2 (1908), 661.
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It may well be doubted whether, in all the range of science, there is any field so fascinating to the explorer—so rich in hidden treasures—so fruitful in delightful surprises—as that of Pure Mathematics. The charm lies chiefly, I think, in the absolute certainty of its results; for that is what, beyond all mental treasures, the human intellect craves for. Let us only be sure of something! More light, more light!
Written without pseudonym as Charles L. Dodgson. Opening remarks in Introduction to A New Theory of Parallels (1888, 1890), xv.
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It may well be doubted whether, in all the range of Science, there is any field so fascinating to the explorer—so rich in hidden treasures—so fruitful in delightful surprises—as that of Pure Mathematics. The charm lies chiefly, I think, in the absolute certainty of its results: for that is what, beyond all mental treasures, the human intellect craves for. Let us only be sure of something! More light, more light … “And if our fate be death, give light and let us die” This is the cry that, through all the ages, is going up from perplexed Humanity, and Science has little else to offer, that will really meet the demands of its votaries, than the conclusions of Pure Mathematics.
Opening of 'Introduction', A New Theory of Parallels (1890), xv. As a non-fiction work, the author’s name on the title page of this book was Charles Lutwidge Dodgson. Being better known for his works of fiction as Lewis Carroll, all quotes relating to this one person, published under either name, are gathered on this single web page under his pen name.
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It took Freud 38 years to understand it. You have one night. The psych exam is in 12 hours. And your id wants to party. Your ego wants to conk out. But your superego knows you need to stay awake tonight to cram. Fortunately, you've got Vivarin [caffeine tablets]. It helps keep you awake and mentally alert… So all your brainpower can focus on understanding the brain. If Freud had used Vivarin, maybe he could have understood the brain faster, too.
Advertisement by SmithKline Beecham for Vivarin, student newspaper, Columbia Daily Spectator (16 Apr 1990), Vol. 114, No. 113, (16 April 1990), 4.
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It was his [Leibnitz’s] love of method and order, and the conviction that such order and harmony existed in the real world, and that our success in understanding it depended upon the degree and order which we could attain in our own thoughts, that originally was probably nothing more than a habit which by degrees grew into a formal rule. This habit was acquired by early occupation with legal and mathematical questions. We have seen how the theory of combinations and arrangements of elements had a special interest for him. We also saw how mathematical calculations served him as a type and model of clear and orderly reasoning, and how he tried to introduce method and system into logical discussions, by reducing to a small number of terms the multitude of compound notions he had to deal with. This tendency increased in strength, and even in those early years he elaborated the idea of a general arithmetic, with a universal language of symbols, or a characteristic which would be applicable to all reasoning processes, and reduce philosophical investigations to that simplicity and certainty which the use of algebraic symbols had introduced into mathematics.
A mental attitude such as this is always highly favorable for mathematical as well as for philosophical investigations. Wherever progress depends upon precision and clearness of thought, and wherever such can be gained by reducing a variety of investigations to a general method, by bringing a multitude of notions under a common term or symbol, it proves inestimable. It necessarily imports the special qualities of number—viz., their continuity, infinity and infinite divisibility—like mathematical quantities—and destroys the notion that irreconcilable contrasts exist in nature, or gaps which cannot be bridged over. Thus, in his letter to Arnaud, Leibnitz expresses it as his opinion that geometry, or the philosophy of space, forms a step to the philosophy of motion—i.e., of corporeal things—and the philosophy of motion a step to the philosophy of mind.
In Leibnitz (1884), 44-45. [The first sentence is reworded to better introduce the quotation. —Webmaster]
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Kant, discussing the various modes of perception by which the human mind apprehends nature, concluded that it is specially prone to see nature through mathematical spectacles. Just as a man wearing blue spectacles would see only a blue world, so Kant thought that, with our mental bias, we tend to see only a mathematical world.
In The Mysterious Universe (1930), 115.
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Let him [the author] be permitted also in all humility to add … that in consequence of the large arrears of algebraical and arithmetical speculations waiting in his mind their turn to be called into outward existence, he is driven to the alternative of leaving the fruits of his meditations to perish (as has been the fate of too many foregone theories, the still-born progeny of his brain, now forever resolved back again into the primordial matter of thought), or venturing to produce from time to time such imperfect sketches as the present, calculated to evoke the mental co-operation of his readers, in whom the algebraical instinct has been to some extent developed, rather than to satisfy the strict demands of rigorously systematic exposition.
In Philosophic Magazine (1863), 460.
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Like almost every subject of human interest, this one [mathematics] is just as easy or as difficult as we choose to make it. A lifetime may be spent by a philosopher in discussing the truth of the simplest axiom. The simplest fact as to our existence may fill us with such wonder that our minds will remain overwhelmed with wonder all the time. A Scotch ploughman makes a working religion out of a system which appalls a mental philosopher. Some boys of ten years of age study the methods of the differential calculus; other much cleverer boys working at mathematics to the age of nineteen have a difficulty in comprehending the fundamental ideas of the calculus.
In Teaching of Mathematics (1902), 19-20.
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Mathematicians boast of their exacting achievements, but in reality they are absorbed in mental acrobatics and contribute nothing to society.
From Complete Works on Japan’s Philosophical Thought (1956). As quoted and cited in Alan L. Mackay, A Dictionary of Scientific Quotations (1991), 185.
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Mathematics … above all other subjects, makes the student lust after knowledge, fills him, as it were, with a longing to fathom the cause of things and to employ his own powers independently; it collects his mental forces and concentrates them on a single point and thus awakens the spirit of individual inquiry, self-confidence and the joy of doing; it fascinates because of the view-points which it offers and creates certainty and assurance, owing to the universal validity of its methods. Thus, both what he receives and what he himself contributes toward the proper conception and solution of a problem, combine to mature the student and to make him skillful, to lead him away from the surface of things and to exercise him in the perception of their essence. A student thus prepared thirsts after knowledge and is ready for the university and its sciences. Thus it appears, that higher mathematics is the best guide to philosophy and to the philosophic conception of the world (considered as a self-contained whole) and of one’s own being.
In Die Mathematik die Fackelträgerin einer neuen Zeit (1889), 40. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 49.
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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. For example, a mathematician represents the motion of planets of the solar system by a flow line of an incompressible fluid in a 54-dimensional phase space, whose volume is given by the Liouville measure
Mathematics and Physics (1981), Foreward. Reprinted in Mathematics as Metaphor: Selected Essays of Yuri I. Manin (2007), 90.
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Mathematics gives the young man a clear idea of demonstration and habituates him to form long trains of thought and reasoning methodically connected and sustained by the final certainty of the result; and it has the further advantage, from a purely moral point of view, of inspiring an absolute and fanatical respect for truth. In addition to all this, mathematics, and chiefly algebra and infinitesimal calculus, excite to a high degree the conception of the signs and symbols—necessary instruments to extend the power and reach of the human mind by summarizing an aggregate of relations in a condensed form and in a kind of mechanical way. These auxiliaries are of special value in mathematics because they are there adequate to their definitions, a characteristic which they do not possess to the same degree in the physical and mathematical [natural?] sciences.
There are, in fact, a mass of mental and moral faculties that can be put in full play only by instruction in mathematics; and they would be made still more available if the teaching was directed so as to leave free play to the personal work of the student.
In 'Science as an Instrument of Education', Popular Science Monthly (1897), 253.
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Mathematics has beauties of its own—a symmetry and proportion in its results, a lack of superfluity, an exact adaptation of means to ends, which is exceedingly remarkable and to be found only in the works of the greatest beauty. … When this subject is properly and concretely presented, the mental emotion should be that of enjoyment of beauty, not that of repulsion from the ugly and the unpleasant.
In The Teaching of Mathematics in the Elementary and the Secondary School (1906), 44-45.
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Mental events proceeding beneath the threshold of consciousness are the substrate upon which all conscious experience depends. To argue that all we need of our mental equipment is that part of which we are conscious is about as helpful as equating the United States with the Senate or England with the Houses of Parliament.
Quoted in 'Anthony (George) Stevens' in Gale, Contemporary Authors Online (2005).
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Modern war, even from the consideration of physical welfare, is not creative. Soldiers and civilians alike are supposed to put on mental khaki. … War means the death of that fertile war which consists of the free, restless conflict of ideas. The war which matters is that of the scientist with nature; of the farmer with the tawny desert; of … philosopher against … mob stupidity. Such war is creative. … Inventions that further life and joy; freedom; new knowledge, whether Luther Burbank’s about the breeding of fruits or Einstein's about relativity; great cathedrals and Beethoven's music: these modern mechanical war can destroy but never produce. At its most inventive height, war creates the Maxim gun, the submarine, disseminable germs of disease, life-blasting gases. Spiritually and intellectually, modern war is not creative.
From ‘The Stagnation of War’, in Allen D. Hole (ed.) The Messenger of Peace (Nov 1924), 49, No. 11, 162-163.
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Nature is objective, and nature is knowable, but we can only view her through a glass darkly–and many clouds upon our vision are of our own making: social and cultural biases, psychological preferences, and mental limitations (in universal modes of thought, not just individualized stupidity).
In Chap. 1, 'Huxley’s Chessboard', Full House: The Spread of Excellence From Plato to Darwin (1996, 2011), 8.
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Neither the absolute nor the relative size of the brain can be used to measure the degree of mental ability in animal or in man. So far as man is concerned, the weights of the brains or the volumes of the cranial cavities of a hundred celebrities of all branches of knowledge all over the world have been listed. … At the bottom of those lists are Gall, the famous phrenologist, Anatole France, the French novelist, and Gambetta, the French statesman, each with about 1,100 cc brain mass. The lists are topped by Dean Jonathan Swift, the English writer, Lord Byron, the English poet, and Turgenev, the Russian novelist, all with about 2,000 cc … Now our mental test! Had Turgenev really twice the mental ability of Anatole France?
In 'The Human Brain in the Light of Its Phylogenetic Development', Scientific Monthly (Aug 1948), 67, No. 2, 104-105. Collected in Sherwood Larned Washburn and ‎Davida Wolffson (eds.), The Shorter Anthropological Papers of Franz Weidenreich Published in the Period 1939-1948: A Memorial Volume (1949), 18.
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No physiologist who calmly considers the question in connection with the general truths of his science, can long resist the conviction that different parts of the cerebrum subserve different kinds of mental action. Localization of function is the law of all organization whatever: separateness of duty is universally accompanied with separateness of structure: and it would be marvellous were an exception to exist in the cerebral hemispheres.
The Principles of Psychology (1855), 607.
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Nothing has afforded me so convincing a proof of the unity of the Deity as these purely mental conceptions of numerical and mathematical science which have been by slow degrees vouchsafed to man, and are still granted in these latter times by the Differential Calculus, now superseded by the Higher Algebra, all of which must have existed in that sublimely omniscient Mind from eternity.
Martha Somerville (ed.) Personal Recollections, from Early Life to Old Age, of Mary Somerville (1874), 140-141.
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On the other hand, ethnic psychology must always come to the assistance of individual psychology, when the developmental forms of the complex mental processes are in question.
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One rarely hears of the mathematical recitation as a preparation for public speaking. Yet mathematics shares with these studies [foreign languages, drawing and natural science] their advantages, and has another in a higher degree than either of them.
Most readers will agree that a prime requisite for healthful experience in public speaking is that the attention of the speaker and hearers alike be drawn wholly away from the speaker and concentrated upon the thought. In perhaps no other classroom is this so easy as in the mathematical, where the close reasoning, the rigorous demonstration, the tracing of necessary conclusions from given hypotheses, commands and secures the entire mental power of the student who is explaining, and of his classmates. In what other circumstances do students feel so instinctively that manner counts for so little and mind for so much? In what other circumstances, therefore, is a simple, unaffected, easy, graceful manner so naturally and so healthfully cultivated? Mannerisms that are mere affectation or the result of bad literary habit recede to the background and finally disappear, while those peculiarities that are the expression of personality and are inseparable from its activity continually develop, where the student frequently presents, to an audience of his intellectual peers, a connected train of reasoning. …
One would almost wish that our institutions of the science and art of public speaking would put over their doors the motto that Plato had over the entrance to his school of philosophy: “Let no one who is unacquainted with geometry enter here.”
In A Scrap-book of Elementary Mathematics: Notes, Recreations, Essays (1908), 210-211.
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One-story intellects, two-story intellects, three-story intellects with skylights. All fact-collectors, who have no aim beyond their facts, are one-story men. Two-story men compare, reason, generalize, using the labors of the fact-collectors as well as their own. Three-story men idealize, imagine, predict; their best illumination comes from above, through the skylight. There are minds with large ground-floors, that can store an infinite amount of knowledge; some librarians, for instance, who know enough of books to help other people, without being able to make much other use of their knowledge, have intellects of this class. Your great working lawyer has two spacious stories; his mind is clear, because his mental floors are large, and he has room to arrange his thoughts so that lie can get at them,—facts below, principles above, and all in ordered series; poets are often narrow below, incapable of clear statement, and with small power of consecutive reasoning, but full of light, if sometimes rather bare of furniture, in the attics.
The Poet at the Breakfast Table (1883), 50.
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Our great mistake in education is ... the worship of book-learning—the confusion of instruction and education. We strain the memory instead of cultivating the mind. … We ought to follow exactly the opposite course with children—to give them a wholesome variety of mental food, and endeavour to cultivate their tastes, rather than to fill their minds with dry facts.
The Pleasures of Life (Appleton, 1887), 183-184, or (2007), 71.
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Our natural way of thinking about these coarser emotions is that the mental perception of some fact excites the mental affection called the emotion, and that this latter state of mind gives rise to the bodily expression. My theory, on the contrary, is that the bodily changes follow directly the perception of the exciting fact, and that our feeling of the same changes as they occur IS the emotion. Common-sense says, we lose our fortune, are sorry and weep; we meet a bear, are frightened and run; we are insulted by a rival, are angry and strike. The hypothesis here to be defended says that this order of sequence is incorrect, that the one mental state is not immediately induced by the other, that the bodily manifestations must first be interposed between, and that the more rational statement is that we feel sorry because we cry, angry because we strike, afraid because we tremble, and not that we cry, strike, or tremble, because we are sorry, angry, or fearful, as the case may be. Without the bodily states following on the perception, the latter would be purely cognitive in form, pale, colorless, destitute of emotional warmth. We might then see the bear, and judge it best to run, receive the insult and deem it right to strike, but we should not actually feel afraid or angry.
The Principles or Psychology (1890), Vol. 2, 449-50.
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Our purpose is to be able to measure the intellectual capacity of a child who is brought to us in order to know whether he is normal or retarded. ... We do not attempt to establish or prepare a prognosis and we leave unanswered the question of whether this retardation is curable, or even improveable. We shall limit ourselves to ascertaining the truth in regard to his present mental state.
Alfred Binet and Theodore Simon (1873-1961, French psychologist) 'New Methods for the Diagnosis of the Intellectual Level of Subnormals' (1905), in The Development of Intelligence in Children, trans. Elizabeth Kite (1916), 37.
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Our school education ignores, in a thousand ways, the rules of healthy development; and the results … are gained very generally at the cost of physical and mental health.
Lecture (2 Dec 1959) delivered in Clinton Hall, New York City. Published in 'Medicine as a Profession for Women', The English Woman’s Journal (1 May 1860), 5, No. 27, 148. (Prepared together with Emily Blackwell.) The Blackwells recognized the connection between health and learning. They also wanted that teachers (of whom 90% were women) should “diffuse among women the physiological and sanitary knowledge which they will need.”
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People who are unused to learning, learn little, and that slowly, while those more accustomed do much more and do it more easily. The same thing also happens in connection with research. Those who are altogether unfamiliar with this become blinded and bewildered as soon as their minds begin to work: they readily withdraw from the inquiry, in a state of mental fatigue and exhaustion, much like people who attempt to race without having been trained. He, on the other hand, who is accustomed to research, seeks and penetrates everywhere mentally, passing constantly from one topic to another; nor does he ever give up his investigation; he pursues it not merely for a matter of days, but throughout his whole life. Also by transferring his mind to other ideas which are yet not foreign to the questions at issue, he persists till he reaches the solution.
'On Paralysis'. Quoted in A. J. Brock, Greek Medicine: Being Extracts Illustrative of Medical Writers from Hippocrates to Galen (1929), 185.
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Persons possessing great intellect and a capacity for excelling in the creative arts and also in the sciences are generally likely to have heavier brains than the ordinary individual. Arguing from this we might expect to find a corresponding lightness in the brain of the criminal, but this is not always the case ... Many criminals show not a single anomaly in their physical or mental make-up, while many persons with marked evidences of morphological aberration have never exhibited the criminal tendency.
Every attempt to prove crime to be due to a constitution peculiar only to criminals has failed signally. It is because most criminals are drawn from the ranks of the low, the degraded, the outcast, that investigators were ever deceived into attempting to set up a 'type' of criminal. The social conditions which foster the great majority of crimes are more needful of study and improvement.
From study of known normal brains we have learned that there is a certain range of variation. No two brains are exactly alike, and the greatest source of error in the assertions of Benedict and Lombroso has been the finding of this or that variation in a criminal’s brains, and maintaining such to be characteristic of the 'criminal constitution,' unmindful of the fact that like variations of structure may and do exist in the brains of normal, moral persons.
Address to the American Association for the Advancement of Science in Philadelphia (28 Dec 1904), as quoted in 'Americans of Future Will Have Best Brains', New York Times (29 Dec 1904), 6.
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Physiological psychology, on the other hand, is competent to investigate the relations that hold between the processes of the physical and those of the mental life.
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Psychiatrist David Shainberg argued that mental illness, which appears chaotic, is actually the reverse. Mental illness occurs when images of the self become rigid and closed, restricting an open creative response to the world.[Co-author with David Peat]
In John F. Briggs and David Peat, Seven Life Lessons of Chaos: Spiritual Wisdom from the Science of Change (1999, 2000), 29. A footnote gives the source of this idea as from David Shainberg, The Transforming Self: New Dimensions in Psychoanalytic Process (1973).
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Psychoanalysis is that mental illness for which it regards itself a therapy.
…...
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Psychological introspection goes hand in hand with the methods of experimental physiology. If one wants to put the main emphasis on the characteristic of the method, our science, experimental psychology, is to be distinguished from the ordinary mental philosophy [Seelenlehre], based purely on introspection.
In Grundzüge der physiologischen Psychologie [Principles of Physiological Psychology] (1874), 2-3. Trans. K. Damiger, Constructing the Subject: Historical Origins of Psychological Research (1990), 206.
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Psychology … tells us that we rarely work through reasons and evidence in a systematic way; weighing information carefully and suspending the impulse to draw conclusions. Instead, much of the time we use mental shortcuts or rules of thumb that save us mental effort. These habits often work reasonably well, but they also can lead us to conclusions we might dismiss if we applied more thought.
As co-author with Kathleen Hall Jamieson, in unSpun: Finding Facts in a World of Disinformation (2007), 70.
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Psychology must not only strive to become a useful basis for the other mental sciences, but it must also turn again and again to the historical sciences, in order to obtain an understanding for the more highly developed metal processes.
An Introduction to Psychology (1912)
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Quantum provides us with a striking illustration of the fact that though we can fully understand a connection … we can only speak of it in images and parables. We must be clear that when it comes to atoms, language can be used only as in poetry. The poet, too, is not nearly so concerned with describing facts as with creating images and establishing mental connections.
In conversation during first meeting with Werner Heisenberg (summer 1920), as quoted in Werner Heisenberg and Arnold J. Pomerans (trans.), Physics and Beyond: Encounters and Conversations (1971), 41. As cited in Philip Kuberski, The Forgèd Feature: Toward a Poetics of Uncertainty: New and Selected Essays (1995), 177-178.
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Recurrences of like cases in which A is always connected with B, that is, like results under like circumstances, that is again, the essence of the connection of cause and effect, exist but in the abstraction which we perform for the purpose of mentally reproducing the facts. Let a fact become familiar, and we no longer require this putting into relief of its connecting marks, our attention is no longer attracted to the new and surprising, and we cease to speak of cause and effect.
In The Science of Mechanics (1893), 483.
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Science has its being in a perpetual mental restlessness.
From 'Poetry and Science', in W.H. Harlow, Essays and Studies by Members of the English Association (1932), Vol. 17, 12.
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Science is a game—but a game with reality, a game with sharpened knives … If a man cuts a picture carefully into 1000 pieces, you solve the puzzle when you reassemble the pieces into a picture; in the success or failure, both your intelligences compete. In the presentation of a scientific problem, the other player is the good Lord. He has not only set the problem but also has devised the rules of the game—but they are not completely known, half of them are left for you to discover or to deduce. The experiment is the tempered blade which you wield with success against the spirits of darkness—or which defeats you shamefully. The uncertainty is how many of the rules God himself has permanently ordained, and how many apparently are caused by your own mental inertia, while the solution generally becomes possible only through freedom from its limitations.
Quoted in Walter Moore, Schrödinger: Life and Thought (1989), 348.
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Science quickens and cultivates directly the faculty of observation, which in very many persons lies almost dormant through life, the power of accurate and rapid generalizations, and the mental habit of method and arrangement; it accustoms young persons to trace the sequence of cause and effect; it familiarizes then with a kind of reasoning which interests them, and which they can promptly comprehend; and it is perhaps the best corrective for that indolence which is the vice of half-awakened minds, and which shrinks from any exertion that is not, like an effort of memory, merely mechanical.
Anonymous
Report of the Royal Commission on Education (1861), Parliamentary Papers (1864), Vol 20, 32-33, as cited in Paul White, Thomas Huxley: Making the "Man of Science" (2003), 77, footnote. Also quoted in John Lubbock, The Pleasures of Life (1887, 2007), 63.
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Science, illuminating ray!
Fair mental beam, extend thy sway, And shine from pole to pole!
From thy accumulated store,
O'er every mind thy riches pour, Excite from low desires to soar, And dignify the soul.
'Botany', I. From Poems on Conchology and Botany (1831), 176.
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SCIENCE! thou fair effusive ray
From the great source of mental Day,
Free, generous, and refin'd!
Descend with all thy treasures fraught,
Illumine each bewilder'd thought,
And bless my labour'g mind.
'Hymn to Science' (1739). In Robin Dix (ed.), The Poetical Works of Mark Akenside (1996), 406.
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Scientific education is a training in mental integrity. All along the history of culture from savagery to modern civilization men have imagined what ought to be, and then have tried to prove it true. This is the very spirit of metaphysic philosophy. When the imagination is not disciplined by unrelenting facts, it invents falsehood, and, when error has thus been invented, the heavens and the earth are ransacked for its proof.
From address (1 Oct 1884), at inauguration of the Corcoran School of Science and Arts, Columbian University, Washington, D.C. Published in 'The Larger Import of Scientific Education', Popular Science Monthly (Feb 1885), 26, 455.
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So in regard to mental qualities, their transmission is manifest in our dogs, horses and other domestic animals. Besides special tastes and habits, general intelligence, courage, bad and good tempers. etc., are certainly transmitted.
The Descent of Man
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Some of my cousins who had the great advantage of University education used to tease me with arguments to prove that nothing has any existence except what we think of it. … These amusing mental acrobatics are all right to play with. They are perfectly harmless and perfectly useless. ... I always rested on the following argument. … We look up to the sky and see the sun. Our eyes are dazzled and our senses record the fact. So here is this great sun standing apparently on no better foundation than our physical senses. But happily there is a method, apart altogether from our physical senses, of testing the reality of the sun. It is by mathematics. By means of prolonged processes of mathematics, entirely separate from the senses, astronomers are able to calculate when an eclipse will occur. They predict by pure reason that a black spot will pass across the sun on a certain day. You go and look, and your sense of sight immediately tells you that their calculations are vindicated. So here you have the evidence of the senses reinforced by the entirely separate evidence of a vast independent process of mathematical reasoning. We have taken what is called in military map-making “a cross bearing.” When my metaphysical friends tell me that the data on which the astronomers made their calculations, were necessarily obtained originally through the evidence of the senses, I say, “no.” They might, in theory at any rate, be obtained by automatic calculating-machines set in motion by the light falling upon them without admixture of the human senses at any stage. When it is persisted that we should have to be told about the calculations and use our ears for that purpose, I reply that the mathematical process has a reality and virtue in itself, and that onie discovered it constitutes a new and independent factor. I am also at this point accustomed to reaffirm with emphasis my conviction that the sun is real, and also that it is hot— in fact hot as Hell, and that if the metaphysicians doubt it they should go there and see.
In My Early Life (1930).
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Sooner or later for good or ill, a united mankind, equipped with science and power, will probably turn its attention to the other planets, not only for economic exploitation, but also as possible homes for man... The goal for the solar system would seem to be that it should become an interplanetary community of very diverse worlds... each contributing to the common experience its characteristic view of the universe. Through the pooling of this wealth of experience, through this “commonwealth of worlds,” new levels of mental and spiritual development should become possible, levels at present quite inconceivable to man.
…...
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Spoken words are the symbols of mental experience, and written words are the symbols of spoken words.
Aristotle
In De Interpretatione, translated by E.M. Edghill in On Interpretation, Chap. 1, second sentence.
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Strange as it may sound, the power of mathematics rests on its evasion of all unnecessary thought and on its wonderful saving of mental operations.
As quoted, without source, in E.T. Bell, Men of Mathematics (1937), Vol. 1, l (Roman numeral 'l').
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That mathematics “do not cultivate the power of generalization,”; … will be admitted by no person of competent knowledge, except in a very qualified sense. The generalizations of mathematics, are, no doubt, a different thing from the generalizations of physical science; but in the difficulty of seizing them, and the mental tension they require, they are no contemptible preparation for the most arduous efforts of the scientific mind. Even the fundamental notions of the higher mathematics, from those of the differential calculus upwards are products of a very high abstraction. … To perceive the mathematical laws common to the results of many mathematical operations, even in so simple a case as that of the binomial theorem, involves a vigorous exercise of the same faculty which gave us Kepler’s laws, and rose through those laws to the theory of universal gravitation. Every process of what has been called Universal Geometry—the great creation of Descartes and his successors, in which a single train of reasoning solves whole classes of problems at once, and others common to large groups of them—is a practical lesson in the management of wide generalizations, and abstraction of the points of agreement from those of difference among objects of great and confusing diversity, to which the purely inductive sciences cannot furnish many superior. Even so elementary an operation as that of abstracting from the particular configuration of the triangles or other figures, and the relative situation of the particular lines or points, in the diagram which aids the apprehension of a common geometrical demonstration, is a very useful, and far from being always an easy, exercise of the faculty of generalization so strangely imagined to have no place or part in the processes of mathematics.
In An Examination of Sir William Hamilton’s Philosophy (1878), 612-13.
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The ability to play is one of the principal criteria of mental health.
In 'Childhood’s Promises', Television & Children (1980), 3, No. 3, 17.
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The animal kingdom exhibits a series of mental developments which may be regarded as antecedents to the mental development of man, for the mental life of animals shows itself to be throughout, in its elements and in the general laws governing the combination of the elements, the same as the mental life of man.
Outline of Psychology (1902)
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The arguments for the two substances [mind and body] have, we believe, entirely lost their validity; they are no longer compatible with ascertained science and clear thinking. The one substance with two sets of properties, two sides, the physical and the mental—a double-faced unity—would appear to comply with all the exigencies of the case. … The mind is destined to be a double study—to conjoin the mental philosopher with the physical philosopher.
From concluding paragraph in Mind and Body: The Theories of their Relation (1872), 195.
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The attitude which the man in the street unconsciously adopts towards science is capricious and varied. At one moment he scorns the scientist for a highbrow, at another anathematizes him for blasphemously undermining his religion; but at the mention of a name like Edison he falls into a coma of veneration. When he stops to think, he does recognize, however, that the whole atmosphere of the world in which he lives is tinged by science, as is shown most immediately and strikingly by our modern conveniences and material resources. A little deeper thinking shows him that the influence of science goes much farther and colors the entire mental outlook of modern civilised man on the world about him.
Reflections of a Physicist (1950), 81.
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The concepts of ‘soul’ or ‘life’ do not occur in atomic physics, and they could not, even indirectly, be derived as complicated consequences of some natural law. Their existence certainly does not indicate the presence of any fundamental substance other than energy, but it shows only the action of other kinds of forms which we cannot match with the mathematical forms of modern atomic physics ... If we want to describe living or mental processes, we shall have to broaden these structures. It may be that we shall have to introduce yet other concepts.
…...
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The desire to economize time and mental effort in arithmetical computations, and to eliminate human liability to error is probably as old as the science of arithmetic itself.
Opening of proposal submitted to I.B.M., 'Proposed Automatic Calculating Machine' (1937). As quoted by I. Bernard Cohen, in Howard Aiken: Portrait of a Computer Pioneer (2000), 63.
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The discoverer and the poet are inventors; and they are so because their mental vision detects the unapparent, unsuspected facts, almost as vividly as ocular vision rests on the apparent and familiar.
From 'The Principles of Success in Literature', The Fortnightly (1865), 1, 574.
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The dogma of the Ghost in the Machine ... maintains that there exist both bodies and minds; that there occur physical processes and mental processes; that there are mechanical causes of corporeal movements and mental causes of corporeal movements.
The Concept of Mind (1949), 22.
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The endeavour to observe oneself must inevitably introduce changes into the course of mental events,—changes which could not have occurred without it, and whose usual consequence is that the very process which was to have been observed disappears from consciousness.
In Principles of Physiological Psychology (1873, 1904), Vol. 1, 5.
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The fact that man produces a concept ‘I’ besides the totality of his mental and emotional experiences or perceptions does not prove that there must be any specific existence behind such a concept. We are succumbing to illusions produced by our self-created language, without reaching a better understanding of anything. Most of so-called philosophy is due to this kind of fallacy.
…...
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The family unit is the institution for the systematic production of mental illness.
From interview on TV program, The Tonight Show With Johnny Carson. As quoted and cited in David Berg, Run, Brother, Run: A Memoir of a Murder in My Family (2013), 242.
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The function of ignoring, of inattention, is as vital a factor in mental progress as the function of attention itself.
In The Principles of Psychology (1918), Vol. 2, 371.
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The general mental qualification necessary for scientific advancement is that which is usually denominated “common sense,” though added to this, imagination, induction, and trained logic, either of common language or of mathematics, are important adjuncts.
From presidential address (24 Nov 1877) to the Philosophical Society of Washington. As cited by L.A. Bauer in his retiring president address (5 Dec 1908), 'The Instruments and Methods of Research', published in Philosophical Society of Washington Bulletin, 15, 103. Reprinted in William Crookes (ed.) The Chemical News and Journal of Industrial Science (30 Jul 1909), 59.
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The general statement that the mental faculties are class concepts, belonging to descriptive psychology, relieves us of the necessity of discussing them and their significance at the present stage of our inquiry.
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The greatest enemy, however, to true arithmetic work is found in so-called practical or illustrative problems, which are freely given to our pupils, of a degree of difficulty and complexity altogether unsuited to their age and mental development. … I am, myself, no bad mathematician, and all the reasoning powers with which nature endowed me have long been as fully developed as they are ever likely to be; but I have, not infrequently, been puzzled, and at times foiled, by the subtle logical difficulty running through one of these problems, given to my own children. The head-master of one of our Boston high schools confessed to me that he had sometimes been unable to unravel one of these tangled skeins, in trying to help his own daughter through her evening’s work. During this summer, Dr. Fairbairn, the distinguished head of one of the colleges of Oxford, England, told me that not only had he himself encountered a similar difficulty, in the case of his own children, but that, on one occasion, having as his guest one of the first mathematicians of England, the two together had been completely puzzled by one of these arithmetical conundrums.
Address before the Grammar-School Section of the Massachusetts Teachers’ Association (25 Nov 1887), 'The Teaching of Arithmetic in the Boston Schools', printed The Academy (Jan 1888). Collected in Francis Amasa Walker, Discussions in Education (1899), 253.
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The history of philosophy is to a great extent that of a certain clash of human temperaments… I will write these traits down in two columns. I think you will practically recognize the two types of mental make-up that I mean if I head the columns by the titles “tender-minded” and “tough-minded” respectively.
THE TENDER-MINDED. Rationalistic (going by “principles”), Intellectualistic, Idealistic, Optimistic, Religious, Free-willist, Monistic, Dogmatical.
THE TOUGH-MINDED. Empiricist (going by “facts”), Sensationalistic, Materialistic, Pessimistic, Irreligious, Fatalistic, Pluralistic, Sceptical.
'The Present Dilemma in Philosophy', in Pragmatism: A New Way for Some Old Ways of Thinking, Popular Lectures on Philosophy (1907), 6, 12.
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The idea that the bumps or depressions on a man's head indicate the presence or absence of certain moral characteristics in his mental equipment is one of the absurdities developed from studies in this field that has long since been discarded by science. The ideas of the phrenologist Gall, however ridiculous they may now seem in the light of a century's progress, were nevertheless destined to become metamorphosed into the modern principles of cerebral localization.
From 'Looking for "The Face Within the Face" in Man', in the New York Times, 4 Mar 1906, SM page 3.
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The instinct to command others, in its primitive essence, is a carnivorous, altogether bestial and savage instinct. Under the influence of the mental development of man, it takes on a somewhat more ideal form and becomes somewhat ennobled, presenting itself as the instrument of reason and the devoted servant of that abstraction, or political fiction, which is called the public good. But in its essence it remains just as baneful, and it becomes even more so when, with the application of science, it extends its scope and intensifies the power of its action. If there is a devil in history, it is this power principle.
In Mikhail Aleksandrovich Bakunin, Grigorii Petrovich Maksimov, Max Nettlau, The political philosophy of Bakunin (1953), 248.
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The logical feebleness of science is not sufficiently borne in mind. It keeps down the weed of superstition, not by logic but by slowly rendering the mental soil unfit for its cultivation.
In 'Science and Spirits', Fragments of Science for Unscientific People (1871), 409.
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The mathematician starts with a few propositions, the proof of which is so obvious that they are called self-evident, and the rest of his work consists of subtle deductions from them. The teaching of languages, at any rate as ordinarily practised, is of the same general nature authority and tradition furnish the data, and the mental operations are deductive.
In 'Scientific Education: Notes of an After-Dinner Speech' (Delivered to Liverpool Philomathic Society, Apr 1869), published in Macmillan’s Magazine (Jun 1869), 20, No. 116, 177. Collected in Lay Sermons, Addresses, and Reviews (1871), Chap 4, 66.
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The meaning of geography is as much a sealed book to the person of ordinary intelligence and education as the meaning of a great cathedral would be to a backwoodsman, and yet no cathedral can be more suggestive of past history in its many architectural forms than is the land about us, with its innumerable and marvellously significant geographic forms. It makes one grieve to think of opportunity for mental enjoyment that is last because of the failure of education in this respect.
'Geographic Methods in Geologic Investigation', The National Geographic Magazine, 1889, 1, 23.
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The mental process by which hypotheses are suggested is obscure. Ordinarily they flash into consciousness without premonition, and it would he easy to ascribe them to a mysterious intuition or creative faculty; but this would contravene one of the broadest generalizations of modern psychology. Just as in the domain of matter nothing is created from nothing, just as in the domain of life there is no spontaneous generation, so in the domain of mind there are no ideas which do not owe their existence to antecedent ideas which stand in the relation of parent to child.
In Address (11 Dec 1895) as President of the Geological Society, 'The Origin of Hypotheses, illustrated by the Discussion of a Topographical Problem', printed as Presidential Address of Grove Karl Gilbert (1896), 4. Also collected in Science (1896), 3, 2.
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The moon landing will, no doubt, be an epoch-making event—a phenomena of awe, unrestrained excitement and sensation. But, the most wondrous event would be if man could relinquish all the stains and defilements of the untamed mind and progress toward achieving the real mental peace and satisfaction when he reaches the moon.
In 'Reactions to Man’s Landing on the Moon Show Broad Variations in Opinions', The New York Times (21 Jul 1969), 6.
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The name chronic alcoholism applies to the collective symptoms of a disordered condition of the mental, motor, and sensory functions of the nervous system, these symptoms assuming a chronic form, and without their being immediately connected with any of those (organic) modifications of the central or peripheric portions of the nervous system which may be detected during life, or discovered after death by ocular inspection; such symptoms, moreover, affecting individuals who have persisted for a considerable length of time in the abuse of alcoholic liquors.
Published in Swedish in 1849. Translation quoted in William Marcet On Chronic Alcoholic Intoxication (1868), 21.
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The one who stays in my mind as the ideal man of science is, not Huxley or Tyndall, Hooker or Lubbock, still less my friend, philosopher and guide Herbert Spencer, but Francis Galton, whom I used to observe and listen to—I regret to add, without the least reciprocity—with rapt attention. Even to-day. I can conjure up, from memory’s misty deep, that tall figure with its attitude of perfect physical and mental poise; the clean-shaven face, the thin, compressed mouth with its enigmatical smile; the long upper lip and firm chin, and, as if presiding over the whole personality of the man, the prominent dark eyebrows from beneath which gleamed, with penetrating humour, contemplative grey eyes. Fascinating to me was Francis Galton’s all-embracing but apparently impersonal beneficence. But, to a recent and enthusiastic convert to the scientific method, the most relevant of Galton’s many gifts was the unique contribution of three separate and distinct processes of the intellect; a continuous curiosity about, and rapid apprehension of individual facts, whether common or uncommon; the faculty for ingenious trains of reasoning; and, more admirable than either of these, because the talent was wholly beyond my reach, the capacity for correcting and verifying his own hypotheses, by the statistical handling of masses of data, whether collected by himself or supplied by other students of the problem.
In My Apprenticeship (1926), 134-135.
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The participation in the general development of the mental powers without special reference to his future vocation must be recognized as the essential aim of mathematical instruction.
In Anleitung zum Mathematischen Unterricht an höheren Schulen (1906), 12.
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The popularisation of scientific doctrines is producing as great an alteration in the mental state of society as the material applications of science are effecting in its outward life. Such indeed is the respect paid to science, that the most absurd opinions may become current, provided they are expressed in language, the sound of which recals [sic] some well-known scientific phrase.
'Introductory Lecture on Experimental Physics' (1871). In W. D. Niven (ed.), The Scientific Papers of James Clerk Maxwell (1890), Vol. 2, 242.
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The product of mental labor—science—always stands far below its value, because the labor-time necessary to reproduce it has no relation at all to the labor-time required for its original production.
Karl Marx
…...
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The publication in 1859 of the Origin of Species by Charles Darwin made a marked epoch in my own mental development, as it did in that of human thought generally. Its effect was to demolish a multitude of dogmatic barriers by a single stroke, and to arouse a spirit of rebellion against all ancient authorities whose positive and unauthenticated statements were contradicted by modern science.
Memories of My Life (1908), 287.
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The pursuit of natural knowledge, the investigation of the world – mental and material – in which we live, is not a dull and spiritless affair: rather is it a voyage of adventure of the human mind, a holiday for reckless and imaginative souls.
A.V. Hill
In speech at Nobel Banquet, Stockholm (10 Dec 1923). Collected in Carl Gustaf Santesson (ed.), Les Prix Nobel en 1921-1922 (1923).
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The results of ethnic psychology constitute, at the same time, our chief source of information regarding the general psychology of the complex mental processes.
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The right that must become paramount is not the right to procreate, but rather the right of every child to be born with a sound physical and mental constitution, based on a sound genotype. No parents will in that future time have the right to burden society with a malformed or mentally incompetent child. Just as every child must have the right to full educational opportunity and a sound nutrition, so every child has the inalienable right to a sound heritage.
Expressing concern that in a coming overpopulated world, “sacred rights of man must alter.” Presidential Address (28 Dec 1970) to the American Association for the Advancement of Science. 'Science: Endless Horizons or Golden Age?', Science (8 Jan 1971), 171, No. 3866, 24. As quoted in obituary by Douglas Martin, New York Times (20 Jan 2005).
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The saying often quoted from Lord Kelvin… that “where you cannot measure your knowledge is meagre and unsatisfactory,” as applied in mental and social science, is misleading and pernicious. This is another way of saying that these sciences are not science in the sense of physical science and cannot attempt to be such without forfeiting their proper nature and function. Insistence on a concretely quantitative economics means the use of statistics of physical magnitudes, whose economic meaning and significance is uncertain and dubious. (Even wheat is approximately homogeneous only if measured in economic terms.) And a similar statement would even apply more to other social sciences. In this field, the Kelvin dictum very largely means in practice, “if you cannot measure, measure anyhow!”
'What is Truth' in Economics? (1956), 166.
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The sense for style … is an aesthetic sense, based on admiration for the direct attainment of a foreseen end, simply and without waste. Style in art, style in literature, style in science, style in logic, style in practical execution have fundamentally the same aesthetic qualities, namely, attainment and restraint. The love of a subject in itself and for itself, where it is not the sleepy pleasure of pacing a mental quarter-deck, is the love of style as manifested in that study. Here we are brought back to the position from which we started, the utility of education. Style, in its finest sense, is the last acquirement of the educated mind; it is also the most useful. It pervades the whole being. The administrator with a sense for style hates waste; the engineer with a sense for style economises his material; the artisan with a sense for style prefers good work. Style is the ultimate morality of the mind.
In 'The Aims of Education', The Aims of Education and Other Essays (1929), 23.
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The study of mathematics is apt to commence in disappointment. … We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet's father, this greatest science eludes the efforts of our mental weapons to grasp it.
Opening of Chap 1, in An Introduction to Mathematics (1911), 7.
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The study of mathematics is apt to commence in disappointment. The important applications of the science, the theoretical interest of its ideas, and the logical rigour of its methods all generate the expectation of a speedy introduction to processes of interest. We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet's father, this great science eludes the efforts of our mental weapons to grasp it.
Opening to An Introduction to Mathematics (1911), 7.
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The universe is of the nature of a thought or sensation in a universal Mind… To put the conclusion crudely—the stuff of the world is mind-stuff. As is often the way with crude statements, I shall have to explain that by “mind” I do not exactly mean mind and by “stuff” I do not at all mean stuff. Still that is about as near as we can get to the idea in a simple phrase. The mind-stuff of the world is something more general than our individual conscious minds; but we may think of its nature as not altogether foreign to feelings in our consciousness… Having granted this, the mental activity of the part of world constituting ourselves occasions no great surprise; it is known to us by direct self-knowledge, and we do not explain it away as something other than we know it to be—or rather, it knows itself to be.
From Gifford Lecture, Edinburgh, (1927), 'Reality', collected in The Nature of the Physical World (1928), 276.
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The vacuum-apparatus requires that its manipulators constantly handle considerable amounts of mercury. Mercury is a strong poison, particularly dangerous because of its liquid form and noticeable volatility even at room temperature. Its poisonous character has been rather lost sight of during the present generation. My co-workers and myself found from personal experience-confirmed on many sides when published—that protracted stay in an atmosphere charged with only 1/100 of the amount of mercury required for its saturation, sufficed to induce chronic mercury poisoning. This first reveals itself as an affection of the nerves, causing headaches, numbness, mental lassitude, depression, and loss of memory; such are very disturbing to one engaged in intellectual occupations.
Hydrides of Boron and Silicon (1933), 203.
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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) . But the prods often in clude dreams, quirks, and errors–just as we may obtain crucial bursts of energy from foodstuffs or pharmaceuticals of no objective or enduring value. Great truth can emerge from small error. Evolution is thrilling, liberating, and correct. And Macrauchenia is a litoptern.
…...
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There cannot be mental atrophy in any person who continues to observe, to remember what he observes, and to seek answers for his unceasing hows and whys about things.
From interview with Mary R. Mullett, 'How to Keep Young Mentally', The American Magazine (Dec 1921), 92, 68.
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There is as much difference between a collection of mentally free citizens and a community molded by modern methods of propaganda as there is between a heap of raw materials and a battleship.
From An Outline of Intellectual Rubbish (1937, 1943), 9. Collected in The Basic Writings of Bertrand Russell (2009), 61.
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There is no fundamental difference between man and the higher animals in their mental faculties ... The lower animals, like man, manifestly feel pleasure and pain, happiness, and misery.
…...
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There is no more wild, free, vigorous growth of the forest, but everything is in pots or rows like a rococo garden... The pupil is in the age of spontaneous variation which at no period of life is so great. He does not want a standardized, overpeptonized mental diet. It palls on his appetite.
Hall, GS (1904b). Adolescence: Its psychology and its relations to physiology, anthropology, sociology, sex, crime, religion and education (1904), Vol. 2, 509.
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There isn’t one, not one, instance where it’s known what pattern of neural connectivity realizes a certain cognitive content, inate or learned, in either the infant’s nervous system or the adult’s. To be sure, our brains must somehow register the contents of our mental states. The trouble is: Nobody knows how—by what neurological means—they do so. Nobody can look at the patterns of connectivity (or of anything else) in a brain and figure out whether it belongs to somebody who knows algebra, or who speaks English, or who believes that Washington was the Father of his country.
In Critical Condition: Polemic Essays on Cognitive science and the Philosophy of the Mind (1988), 269-71. In Vinoth Ramachandra, Subverting Global Myths: Theology and the Public Issues Shaping our World (2008), 180.
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This notion that “science” is something that belongs in a separate compartment of its own, apart from everyday life, is one that I should like to challenge. We live in a scientific age; yet we assume that knowledge of science is the prerogative of only a small number of human beings, isolated and priest-like in their laboratories. This is not true. It cannot be true. The materials of science are the materials of life itself. Science is part of the reality of living; it is the what, the how, and the why of everything in our experience. It is impossible to understand man without understanding his environment and the forces that have molded him physically and mentally.
Address upon receiving National Book Award at reception, Hotel Commodore, New York (27 Jan 1952). As cited in Linda Lear, Rachel Carson: Witness for Nature (1997), 218-219.
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This whole theory of electrostatics constitutes a group of abstract ideas and general propositions, formulated in the clear and precise language of geometry and algebra, and connected with one another by the rules of strict logic. This whole fully satisfies the reason of a French physicist and his taste for clarity, simplicity and order. The same does not hold for the Englishman. These abstract notions of material points, force, line of force, and equipotential surface do not satisfy his need to imagine concrete, material, visible, and tangible things. 'So long as we cling to this mode of representation,' says an English physicist, 'we cannot form a mental representation of the phenomena which are really happening.' It is to satisfy the need that he goes and creates a model.
The French or German physicist conceives, in the space separating two conductors, abstract lines of force having no thickness or real existence; the English physicist materializes these lines and thickens them to the dimensions of a tube which he will fill with vulcanised rubber. In place of a family of lines of ideal forces, conceivable only by reason, he will have a bundle of elastic strings, visible and tangible, firmly glued at both ends to the surfaces of the two conductors, and, when stretched, trying both to contact and to expand. When the two conductors approach each other, he sees the elastic strings drawing closer together; then he sees each of them bunch up and grow large. Such is the famous model of electrostatic action imagined by Faraday and admired as a work of genius by Maxwell and the whole English school.
The employment of similar mechanical models, recalling by certain more or less rough analogies the particular features of the theory being expounded, is a regular feature of the English treatises on physics. Here is a book* [by Oliver Lodge] intended to expound the modern theories of electricity and to expound a new theory. In it are nothing but strings which move around pulleys, which roll around drums, which go through pearl beads, which carry weights; and tubes which pump water while others swell and contract; toothed wheels which are geared to one another and engage hooks. We thought we were entering the tranquil and neatly ordered abode of reason, but we find ourselves in a factory.
*Footnote: O. Lodge, Les Théories Modernes (Modern Views on Electricity) (1889), 16.
The Aim and Structure of Physical Theory (1906), 2nd edition (1914), trans. Philip P. Wiener (1954), 70-1.
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Those who have taken upon them to lay down the law of nature as a thing already searched out and understood, whether they have spoken in simple assurance or professional affectation, have therein done philosophy and the sciences great injury. For as they have been successful in inducing belief, so they have been effective in quenching and stopping inquiry; and have done more harm by spoiling and putting an end to other men's efforts than good by their own. Those on the other hand who have taken a contrary course, and asserted that absolutely nothing can be known — whether it were from hatred of the ancient sophists, or from uncertainty and fluctuation of mind, or even from a kind of fullness of learning, that they fell upon this opinion — have certainly advanced reasons for it that are not to be despised; but yet they have neither started from true principles nor rested in the just conclusion, zeal and affectation having carried them much too far...
Now my method, though hard to practice, is easy to explain; and it is this. I propose to establish progressive stages of certainty. The evidence of the sense, helped and guarded by a certain process of correction, I retain. But the mental operation which follows the act of sense I for the most part reject; and instead of it I open and lay out a new and certain path for the mind to proceed in, starting directly from the simple sensuous perception.
Novum Organum (1620)
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To regard such a positive mental science [psychology] as rising above the sphere of history, and establishing the permanent and unchanging laws of human nature, is therefore possible only to a person who mistakes the transient conditions of a certain historical age for the permanent conditions of human life.
The Idea of History (1946), 224.
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Under certain given circumstances, and only under those circumstances, an agglomeration of men presents new characteristics very different from those of the individuals composing it. The sentiments and ideas of all the persons in the gathering take one and the same direction, and their conscious personality vanishes. A collective mind is formed, doubtless transitory, but presenting very clearly defined characteristics. The gathering has thus become what, in the absence of a better expression, I will call an organized crowd, or, if the term is considered preferable, a psychological crowd. It forms a single being and is subject to the law of the mental unity of crowds.
From Psychologie des Foules (1895), 12. English text in The Crowd: A Study of the Popular Mind (1897), Book 1, Chap. 1, 1-2. The original French text is, “Dans certaines circonstances données, et seulement dans ces circonstances, une agglomération d’hommes possède des caractères nouveaux fort différents de ceux des individus composant cette agglomération. La personnalité consciente s’évanouit, les sentiments et les idées de toutes les unités sont orientés dans une même direction. Il se forme une âme collective, transitoire sans doute, mais présentant des caractères très nets. La collectivité est alors devenue ce que, faute d’une expression meilleure, j’appellerai une foule organisée, ou, si l’on préfère, une foule psychologique. Elle forme un seul être et se trouve soumise à la loi de l'unité mentale des foules.”
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Unhappily for the physiologist, the subjects of the principal department of his science, that of animal physiology, are sentient beings; and every experiment, every new or unusual situation of such a being, is necessarily attended by pain or suffering of a bodily or mental kind.
A Critical and Experimental Essay on the Circulation of the Blood (1831), 1.
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Very few of us can now place ourselves in the mental condition in which even such philosophers as the great Descartes were involved in the days before Newton had announced the true laws of the motion of bodies.
'Introductory Lecture on Experimental Physics', 1871. In W. D. Niven (ed.), The Scientific Papers of James Clerk Maxwell (1890), Vol. 2, 241.
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We are having wool pulled over our eyes if we let ourselves be convinced that scientists, taken as a group, are anything special in the way of brains. They are very ordinary professional men, and all they know is their own trade, just like all other professional men. There are some geniuses among them, just as there are mental giants in any other field of endeavor.
In Science is a Sacred Cow (1950), 23-24.
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We may, I think, draw a yet higher and deeper teaching from the phenomena of degeneration. We seem to learn from it the absolute necessity of labour and effort, of struggle and difficulty, of discomfort and pain, as the condition of all progress, whether physical or mental, and that the lower the organism the more need there is of these ever-present stimuli, not only to effect progress, but to avoid retrogression. And if so, does not this afford us the nearest attainable solution of the great problem of the origin of evil? What we call evil is the essential condition of progress in the lower stages of the development of conscious organisms, and will only cease when the mind has become so thoroughly healthy, so well balanced, and so highly organised, that the happiness derived from mental activity, moral harmony, and the social affections, will itself be a sufficient stimulus to higher progress and to the attainment of a more perfect life.
In 'Two Darwinian Essays', Nature (1880), 22, 142.
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We wanted to fly. We also had such big egos that we felt that we could fly the crates they shipped these things in. We honestly felt that, with things that were wrong, we always had a mental workaround on them.
Rejecting concern about Apollo spacecraft safety. From interview with Ron Stone (24 May 1999) for NASA Johnson Space Center Oral History Project.
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Whatever be the detail with which you cram your student, the chance of his meeting in after life exactly that detail is almost infinitesimal; and if he does meet it, he will probably have forgotten what you taught him about it. The really useful training yields a comprehension of a few general principles with a thorough grounding in the way they apply to a variety of concrete details. In subsequent practice the men will have forgotten your particular details; but they will remember by an unconscious common sense how to apply principles to immediate circumstances. Your learning is useless to you till you have lost your textbooks, burnt your lecture notes, and forgotten the minutiae which you learned by heart for the examination. What, in the way of detail, you continually require will stick in your memory as obvious facts like the sun and the moon; and what you casually require can be looked up in any work of reference. The function of a University is to enable you to shed details in favor of principles. When I speak of principles I am hardly even thinking of verbal formulations. A principle which has thoroughly soaked into you is rather a mental habit than a formal statement. It becomes the way the mind reacts to the appropriate stimulus in the form of illustrative circumstances. Nobody goes about with his knowledge clearly and consciously before him. Mental cultivation is nothing else than the satisfactory way in which the mind will function when it is poked up into activity.
In 'The Rhythm of Education', The Aims of Education: & Other Essays (1917), 41.
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When a man lacks mental balance in pneumonia he is said to be delirious. When he lacks mental balance without the pneumonia, he is pronounced insane by all smart doctors.
Martin H. Fischer, Howard Fabing (ed.) and Ray Marr (ed.), Fischerisms (1944).
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When living with the Indians in their homes and pursuing my ethnological studies: One day I suddenly realized with a rude shock that, unlike my Indian friends, I was an alien, a stranger in my native land; its fauna and flora had no fond, familiar place amid my mental imagery, nor did any thoughts of human aspiration or love give to its hills and valleys the charm of personal companionship. I was alone, even in my loneliness.
Opening of Preface, Indian Games and Dances with Native Songs (1915), v.
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When two minds of a high order, interested in kindred subjects, come together, their conversation is chiefly remarkable for the summariness of its allusions and the rapidity of its transitions. Before one of them is half through a sentence the other knows his meaning and replies. ... His mental lungs breathe more deeply, in an atmosphere more broad and vast...
In The Principles of Psychology (1918), Vol. 2, 370.
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When we survey our lives and endeavours we soon observe that almost the whole of our actions and desires are bound up with the existence of other human beings. We see that our whole nature resembles that of the social animals. We eat food that others have grown, wear clothes that others have made, live in houses that others have built. The greater part of our knowledge and beliefs has been communicated to us by other people through the medium of a language which others have created. Without language our mental capacities would be poor indeed, comparable to those of the higher animals; we have, therefore, to admit that we owe our principal advantage over the beasts to the fact of living in human society. The individual, if left alone from birth would remain primitive and beast-like in his thoughts and feelings to a degree that we can hardly conceive. The individual is what he is and has the significance that he has not so much in virtue of his individuality, but rather as a member of a great human society, which directs his material and spiritual existence from the cradle to the grave.
…...
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While we maintain the unity of the human species, we at the same time repel the depressing assumption of superior and inferior races of men. There are nations more susceptible of cultivation, more highly civilized, more ennobled by mental cultivation than others—but none in themselves nobler than others. All are in like degree designed for freedom.
Cosmos: A Sketch of a Physical Description of the Universe (1845-62), trans. E. C. Otte (1849), Vol 1, 368.
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While we maintain the unity of the human species, we at the same time repel the depressing assumption of superior and inferior races of men. There are nations more susceptible of cultivation, more highly civilized, more enobled by mental cultivation than others, but none in themselves nobler than others. All are in like degree designed for freedom; a freedom which, in the ruder conditions of society, belongs only to the individual, but which, in social states enjoying political institutions, appertains as a right to the whole body of the community.
In Cosmos: A Sketch of a Physical Description of the Universe (1850), Vol. 1, 358, as translated by E.C. Otté.
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Whoever would not remain in complete ignorance of the resources which cause him to act; whoever would seize, at a single philosophical glance, the nature of man and animals, and their relations to external objects; whoever would establish, on the intellectual and moral functions, a solid doctrine of mental diseases, of the general and governing influence of the brain in the states of health and disease, should know, that it is indispensable, that the study of the organization of the brain should march side by side with that of its functions.
On the Organ of the Moral Qualities and Intellectual Faculties, and the Plurality of the Cerebral Organs (1835), 45-6.
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You may take it as an instance of male injustice if I assert that envy and jealousy play an even greater part in the mental life of women than of men. It is not that I think these characteristics are absent in men or that I think they have no other roots in women than envy for the penis; but I am inclined to attribute their greater amount in women to this latter influence.
New Introductory Lectures on Psycho-Analysis (1933), in James Strachey (ed.), The Standard Edition of the Complete Psychological Works of Sigmund Freud (1964), Vol. 22, 125.
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You must learn to talk clearly. The jargon of scientific terminology which rolls off your tongues is mental garbage
Martin H. Fischer, Howard Fabing (ed.) and Ray Marr (ed.), Fischerisms (1944).
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You will be astonished to find how the whole mental disposition of your children changes with advancing years. A young child and the same when nearly grown, sometimes differ almost as much as do a caterpillar and butterfly.
Letter to E. Haeckel (19 Nov 1868). In Charles Darwin and Francis Darwin, The Life and Letters of Charles Darwin (1887), 104.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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