On Ignorance (1600-1699)

"Every man is not a proper champion for truth, nor fit to take up the gauntlet in the cause of verity: many from the ignorance of these maxims, and an inconsiderate zeal for truth, have too rashly charged the troops of error, and remain as trophies unto the enemies of truth. A man may be in as just possession of truth as of a city, and yet be forced to surrender: ’tis therefore far better to enjoy her with peace than to hazard her on a battle: if therefore there rise any doubts in my way, I do forget them, or at least defer them, till my better settled judgment and more manly reason be able to resolve them." (Sir Thomas Browne, "Religio Medici", 1643)

"[…] the knowledge we have of the Mathematicks, hath no reason to elate us; since by them we know but numbers, and figures, creatures of our own, and are yet ignorant of our Maker’s." (Joseph Glanvill, "The Vanity of Dogmatizing", 1661)

"Physical science will not console me for the ignorance of morality in the times of affliction. But the science of ethics will always console me for the ignorance of the physical sciences." (Blaise Pascal, "Pensées", 1670)

"We know that there is an infinite, and we are ignorant of its nature." (Blaise Pascal, "Pensées", 1670) 

"[...] that all men are born ignorant of the causes of things, and that all have a desire of acquiring what is useful; [...]" (Baruch Spinoza, "Ethics", 1677)

"And thus many are ignorant of mathematical truths, not out of any imperfection of their faculties, or uncertainty in the things themselves, but for want of application in acquiring, examining, and by due ways comparing those ideas." (John Locke, "An Essay Concerning Human Understanding", 1689)

"They that are ignorant of Algebra cannot imagine the wonders in this kind are to be done by it: and what further improvements and helps advantageous to other parts of knowledge the sagacious mind of man may yet find out, it is not easy to determine. This at least I believe, that the ideas of quantity are not those alone that are capable of demonstration and knowledge; and that other, and perhaps more useful, parts of contemplation, would afford us certainty, if vices, passions, and domineering interest did not oppose and menace such endeavors." (John Locke, "An Essay Concerning Human Understanding", 1689)

"I believe the calculation of the quantity of probability might be improved to a very useful and pleasant speculation, and applied to a great many events which are accidental, besides those of games; only these cases would be infinitely more confused, as depending on chances which the most part of men are ignorant of." (John Arbuthnot, "Of the Laws of Chance", 1692)

On Ignorance (Unsourced)

"A judicious man uses statistics, not to get knowledge, but to save himself from having ignorance foisted upon him." (Thomas Carlyle)

"[...] chance has not reality in itself; it is only a term fi t to designate our ignorance concerning the manner in which the different parts of a phenomenon are arranged among themselves and in relation to the rest of Nature." (Pierre Simon Laplace)

"Education is a progressive discovery of our own ignorance." (Will Durant)

"Ignorance is the most delightful science in the world because it is acquired without labor or pains and keeps the mind from melancholy." (Giordano Bruno)

"Men are enclosed in their own ignorance as in a prison with slowly receding walls. Unable to see beyond, they marvel at the vastness of their mansion without ever suspecting the existence of an infinite world outside."  (Alfred Franklin)

"Nothing in education is so astonishing as the amount of ignorance it accumulates in the form of inert facts." (Henry B Adams)

"One great source of perplexity to me is an utter ignorance whether I note the right facts, and whether they are of sufficient importance to interest others." (Charles R Darwin)

"Statistics: The mathematical theory of ignorance." (Morris Kline)

"The Art of Chymistry, (Honoured Sir) although in its speculations most Noble and Delectable to a Philosophic Mind, and in its Practice highly Inservient, and Beneficial to Mankind; yet hath it not escaped Obloquies, the false Imputations of Detractors, and Calumniators, who either through Ignorance, Idleness, or Envoy (or all of the cojoined) have made a false Representation of this most Noble Art to the World, and endeavored to set Mankind at the greatest distance from that which is its highest interest to court." (Christopher Packe)

"The disclosure of a new fact, the leap forward, the conquest over yesterday’s ignorance, is an act not of reason but of imagination, of intuition." (Charles Nicolle)

"The truth of science has ever had not merely the task of evolving herself from the dull and uniform mist of ignorance, but also that of the repressing and dissolving the phantoms of the imagination." (Michael Faraday)

"The perpetual enemies of the human race, apart from man’s own nature, are ignorance and disease." (Alan Gregg)

"We receive the truths of science by compulsion. Nothing but ignorance is able to resist them." (Chauncey Wright)

On Ignorance (1925-1949)

"The most merciful thing in the world, I think, is the inability of the human mind to correlate all its contents. We live on a placid island of ignorance in the midst of black seas of infinity, and it was not meant that we should voyage far. The sciences, each straining in its own direction, have hitherto harmed us little; but some day the piecing together of dissociated knowledge will open up such terrifying vistas of reality, and of our frightful position therein, that we shall either go mad from the revelation or flee from the light into the peace and safety of a new dark age." (Howard P Lovecraft, "The Call of Cthulhu", 1926)

"If you are young, then I say: Learn something about statistics as soon as you can. Don’t dismiss it through ignorance or because it calls for thought. [...] If you are older and already crowned with the laurels of success, see to it that those under your wing who look to you for advice are encouraged to look into this subject. In this way you will show that your arteries are not yet hardened, and you will be able to reap the benefits without doing overmuch work yourself. Whoever you are, if your work calls for the interpretation of data, you may be able to do without statistics, but you won’t do as well." (Michael J Moroney, "Facts from Figures", 1927)

"[...] the valuable attributes of research men are conscious ignorance and active curiosity." (Willis R Whitney, "The Stimulation of Research in Pure Science Which Has Resulted from the Needs of Engineers and of Industry" Science Vol. 65 (1862), 1927)

"An addition to knowledge is won at the expense of an addition to ignorance. It is hard to empty the well of Truth with a leaky bucket." (Sir Arthur S Eddington, "The Nature of the Physical World", 1928)

"In scientific subjects, the natural remedy for dogmatism has been found in research. By temperament and training, the research worker is the antithesis of the pundit. What he is actively and constantly aware of is his ignorance, not his knowledge; the insufficiency of his concepts, of the terms and phrases in which he tries to excogitate his problems: not their final and exhaustive sufficiency. He is, therefore, usually only a good teacher for the few who wish to use their mind as a workshop, rather than to store it as a warehouse." (Sir Ronald A Fisher, "Eugenics, Academic and Practical Eugenics" Review Vol. 27, 1935)

"The fundamental gospel of statistics is to push back the domain of ignorance, prejudice, rule-of-thumb, arbitrary or premature decisions, tradition, and dogmatism and to increase the domain in which decisions are made and principles are formulated on the basis of analyzed quantitative facts." (Robert W Burgess, "The Whole Duty of the Statistical Forecaster", Journal of the American Statistical Association, Vol. 32, No. 200, 1937) 

"In the great struggle between ignorance, distrust and brutality on one side, knowledge, understanding and peace on the other the scientist must stand fearlessly on the side of the latter, strengthening link between man and man and preaching that the only effective weapon of self-defense is good-will to others." (Albert Szent-Györgyi, [Nobel lecture] 1937)

"It happens at times that a person believes that he has a world-view, but that there is yet one particular phenomenon that is of such a nature that it baffles the understanding, and that he explains differently and attempts to ignore in order not to harbor the thought that this phenomenon might overthrow the whole view, or that his reflection does not possess enough courage and resolution to penetrate the phenomenon with his world-view." (Søren Kierkegaard, 1938)

"The ignorant suppose that infinite number of drawings require an infinite amount of time; in reality it is quite enough that time to be infinitely subdivisible, as is the case in the famous parable of the Tortoise and the Hare. This infinitude harmonizes in an admirable manner with the sinuous numbers of Chance and of the Celestial Archetype of the Lottery, adored by the Platonists." (Jorge L Borges, The Babylon Lottery, 1941)

"[...] we know, and what we really know, practical assent and simulated ignorance [...] allows us to live with ideas which, if we truly put them to the test, ought to upset our whole life." (Albert Camus, "The Myth of Sisyphus", 1942)

"And how small is the sum of our actual knowledge. With regards to all the more important things, to the questions which concern us more nearly, it amounts to little beyond a consciousness of our own ignorance." (Kenneth Walker, "Meaning and Purpose", 1944)

"And nobody can get far without at least an acquaintance with the mathematics of probability, not to the extent of making its calculations and filling examination papers with typical equations, but enough to know when they can be trusted, and when they are cooked. For when their imaginary numbers correspond to exact quantities of hard coins unalterably stamped with heads and tails, they are safe within certain limits; for here we have solid certainty [...] but when the calculation is one of no constant and several very capricious variables, guesswork, personal bias, and pecuniary interests, come in so strong that those who began by ignorantly imagining that statistics cannot lie end by imagining, equally ignorantly, that they never do anything else." (George B Shaw, "The Vice of Gambling and the Virtue of Insurance", 1944)

"There are many things whose existence we allow, but whose character we are still in ignorance of.… Why should we be surprised, then, that comets, so rare a sight in the universe, are not embraced under definite laws, or that their return is at long intervals? [...] The day will yet come when the progress of research through long ages will reveal to sight the mysteries of nature that are now concealed.… The day will yet come when posterity will be amazed that we remained ignorant of things that will to them seem so plain." (C Doris Hellman, "The Comet of 1577: Its Place in the History of Astronomy", 1944)

On Ignorance (1950-1974)

"[...] the most interesting feature of this science astronomy (and of all science) is our eager ignorance." (Shapley Harlow, "Astronomy", Scientific American Vol. 183 (3), 1950)

"The greater the scientist, the more he is impressed with his ignorance of reality, and the more he realizes that his laws and labels, descriptions and definitions, are the products of his own thought." (Alan W Watts, "The Wisdom of Insecurity", 1951)

"We are not today tempted to search for these keys that unlock the whole of human knowledge and man’s experience. We know that we are ignorant; we are well taught it, and the more surely and deeply we know our own job the better able we are to appreciate the full measure of our pervasive ignorance." (J. Robert Oppenheimer, "Science and the Common Understanding", 1954)

"What the world needs is a fusion of the sciences and the humanities. The humanities express the symbolic, poetic, and prophetic qualities of the human spirit. Without them we would not be conscious of our history; we would lose our aspirations and the grace of expression that move men’s hearts. The sciences express the creative urge in man to construct a universe which is comprehensible in terms of the human intellect. Without them, mankind would find itself bewildered in a world of natural forces beyond comprehension, victims of ignorance, superstition and fear." (Isidor I Rabi, [address] 1954)

"Ignorance of the significance of facts renders us as blind to the solution of a problem as if we were matching colors in the dark." (Edward Hodnett, "The Art of Problem Solving" Part I, 1955)

"Chaos is but unperceived order; it is a word indicating the limitations of the human mind and the paucity of observational facts. The words ‘chaos’, ‘accidental’, ‘chance’, ‘unpredictable’ are conveniences behind which we hide our ignorance." (Harlow Shapley, "Of Stars and Men: Human Response to an Expanding Universe", 1958)

"The precise specification of our knowledge is, however, the same as the precise specification of our ignorance." (Sir Ronald A Fisher, Statistical Methods and Scientific Inference, 1959)

"First, I should be clear about what the act of discovery entails. It is rarely, on the frontier of knowledge or elsewhere, that new facts are 'discovered' in the sense of being encountered, as Newton suggested, in the form of islands of truth in an uncharted sea of ignorance. Or if they appear to be discovered in this way, it is almost always thanks to some happy hypothesis about where to navigate. Discovery, like surprise, favors the well-prepared mind." (Jerome S Bruner, "On Knowing: Essays for the Left Hand", 1962)

"An observer of our biological sciences today sees dark figures moving over a bridge of glass. We are faced with an ever expanding universe of light and darkness. The greater the circle of understanding becomes, the greater is the circumference of surrounding ignorance." (Erwin Chargaff, "Essays on Nucleic Acids", 1963)

"The problem of error has preoccupied philosophers since the earliest antiquity. According to the subtle remark made by a famous Greek philosopher, the man who makes a mistake is twice ignorant, for he does not know the correct answer, and he does not know that he does not know it." (Félix Borel, "Probability and Certainty", 1963)

"[…] in the statistical world you can multiply ignorance by a constant and get truth." (Raymond F Jones, "The Non-Statistical Man", 1964)

"Scientists seem able to go about their business in a state of indifference to, if not ignorance of, anything but the going, currently acceptable doctrine of their several disciplines." (Eric Larrabee, "Commentary Science and the Common Reader", 1966)

"Primary scientific papers are not meant to be final statement of indisputable truths; each is merely a tiny tentative step forward, through the jungle of ignorance." (Erwin Schrödinger, "Information, Communication, Knowledge", Nature Vol. 224 (5217), 1969)

On Ignorance (1800-1849)

"The appearance of chance will always bear a proportion to the ignorance of the observer." (William Paley, "Natural Theology or Evidences of the Existence and Attributes of the Deity", 1802)

"Man is formed for pure enjoyment; his duties are high, his destination is lofty; and he must, then, be most accused of ignorance and folly when he grovels in the dust, having wings which can carry him to the skies." (Sir Humphry Davy, [lectures] 1805)

"One of the strongest passions in a man of genius, is the love of truth. Full of the enthusiasm which a great discovery inspires, he burns with ardor to disseminate it, and the obstacles which ignorance and superstition, armed with power, oppose to it, only stimulate and increase his energy [...]" (Pierre Simon Laplace, "System of the World" Vol. 2, 1809)

"Probability has reference partly to our ignorance, partly to our knowledge [..] The theory of chance consists in reducing all the events of the same kind to a certain number of cases equally possible, that is to say, to such as we may be equally undecided about in regard to their existence, and in determining the number of cases favorable to the event whose probability is sought. The ratio of this number to that of all cases possible is the measure of this probability, which is thus simply a fraction whose number is the number of favorable cases and whose denominator is the number of all cases possible." (Pierre-Simon Laplace, "Philosophical Essay on Probabilities", 1814)

"It is almost as difficult to make a man unlearn his errors as his knowledge. Mal-information is more hopeless than non-information; for error is always more busy than ignorance. Ignorance is a blank sheet, on which we may write; but error is a scribbled one, on which we must first erase. Ignorance is contented to stand still with her back to the truth; but error is more presumptuous, and proceeds in the same direction. Ignorance has no light, but error follows a false one. The consequence is, that error, when she retraces her footsteps, has further to go, before she can arrive at the truth, than ignorance." (Charles C Colton, "Lacon", 1820)

"To invent without scruple a new principle to every new phenomenon, instead of adapting it to the old; to overload our hypothesis with a variety of this kind, are certain proofs that none of these principles is the just one, and that we only desire, by a number of falsehoods, to cover our ignorance of the truth." (David Hume, "Of the passions", 1826)

"When we are unable to explain the monuments of past changes, it is always more probable that the difference arises from our ignorance of all the existing agents, or all their possible effects in an indefinite lapse of time, than that some cause was formerly in operation which has ceased to act [...]"  (Sir Charles Lyell, "Principles of Geology" Vol. 1, 1830)

"The function of theory is to put all this in systematic order, clearly and comprehensively, and to trace each action to an adequate, compelling cause. […] Theory should cast a steady light on all phenomena so that we can more easily recognize and eliminate the weeds that always spring from ignorance; it should show how one thing is related to another, and keep the important and the unimportant separate. If concepts combine of their own accord to form that nucleus of truth we call a principle, if they spontaneously compose a pattern that becomes a rule, it is the task of the theorist to make this clear." (Carl von Clausewitz, "On War", 1832)

"So it happens at times that a person believes that he has a world-view, but that there is yet one particular phenomenon that is of such a nature that it baffles the understanding, and that he explains differently and attempts to ignore in order not to harbor the thought that this phenomenon might overthrow the whole view, or that his reflection does not possess enough courage and resolution to penetrate the phenomenon with his world-view." (Søren Kierkegaard, 1844)

"One has, however, no business to feel so much surprise of one’s ignorance, when one knows how impossible it is without statistics to conjecture the duration of life and percentage of deaths to births in mankind." (Charles R Darwin, 1845)

On Ignorance (-1599)

"This, therefore, is mathematics: she reminds you of the invisible form of the soul; she gives to her own discoveries; she awakens the mind and purifies the intellect; she brings light to our intrinsic ideas; she abolishes oblivion and ignorance which are ours by birth." (Proclus Lycaeus, cca 5th century)

"I know that the common herd of physicians, like the vulgar, if there happen to have been any innovation made about that day, such as the bath being used, a walk taken, or any unusual food eaten, all which were better done than otherwise, attribute notwithstanding the cause of these disorders, to some of these things, being ignorant of the true cause, but proscribing what may have been very proper." (Hippocrates, "On the Sacred Disease", cca 400 BC)

"The disease called Sacred [...] appears to me to be nowise more divine nor more sacred than other diseases, but has the natural cause from which it originates like other affections. Men regard its nature and cause as divine from ignorance and wonder, because it is not at all like to other disease." (Hippocrates, "On the Sacred Disease", cca 400 BC)

"If I am given a formula, and I am ignorant of its meaning, it cannot teach me anything, but if I already know it what does the formula teach me?" (Saint Augustine of Hippo , "De Magistro", 389)

"The truth of voice perishes with the sound; truth latent in the mind is hidden wisdom and invisible treasure; but the truth which illuminates books desires to manifest itself to every disciplinable sense. Let us consider how great a commodity of doctrine exists in books, - how easily, how secretly, how safely, they expose the nakedness of human ignorance without putting it to shame. These are the masters that instruct us without rods and ferules, without hard words and anger, without clothes or money. If you approach them, they are not asleep; if, investigating, you interrogate them, they conceal nothing; if you mistake them, they never grumble; if you are ignorant, they cannot laugh at you." (Richard de Burry, "Philobiblon", 1344)

"[...] the greatest point of all ignorance, not to know the goossenes of ignorance, and not to understand the benefite of knowledge [...]" (Robert Recorde, "The Castle of Knowledge", 1556)

On Ignorance (1700-1799)

"It may be observed of mathematicians that they only meddle with such things as are certain, passing by those that are doubtful and unknown. They profess not to know all things, neither do they affect to speak of all things. What they know to be true, and can make good by invincible arguments, that they publish and insert among their theorems. Of other things they are silent and pass no judgment at all, choosing rather to acknowledge their ignorance, than affirm anything rashly." (Isaac Barrow, "Mathematical Lecture", 1734)

"Though there be no such thing as Chance in the world, our ignorance of the real cause of any event has the same influence on the understanding, and begets a like species of belief or opinion."  (David Hume, "An Enquiry Concerning Human Understanding", 1748)

"[…] chance, that is, an infinite number of events, with respect to which our ignorance will not permit us to perceive their causes, and the chain that connects them together. Now, this chance has a greater share in our education than is imagined. It is this that places certain objects before us and, in consequence of this, occasions more happy ideas, and sometimes leads us to the greatest discoveries […]" (Claude A Helvetius, "On Mind", 1751)

"I find a frank acknowledgment of one’s ignorance is not only the easiest way to get rid of a difficulty, but the likeliest way to obtain information, and therefore I practice it: I think it an honest policy. Those who affect to be thought to know everything, and so undertake to explain everything, often remain long ignorant of many things that others could and would instruct them in, if they appeared less conceited." (Benjamin Franklin, [letter to John Lining", 1755)

"By the word simplicity, is not always meant folly or ignorance; but often, pure and upright Nature, free from artifice, craft or deceitful ornament." (Benjamin Franklin, Poor Richard's Almanack, 1733-1758)

"But ignorance of the different causes involved in the production of events, as well as their complexity, taken together with the imperfection of analysis, prevents our reaching the same certainty about the vast majority of phenomena. Thus there are things that are uncertain for us, things more or less probable, and we seek to compensate for the impossibility of knowing them by determining their different degrees of likelihood. So it was that we owe to the weakness of the human mind one of the most delicate and ingenious of mathematical theories, the science of chance or probability." (Pierre-Simon Laplace, "Recherches, 1º, sur l'Intégration des Équations Différentielles aux Différences Finies, et sur leur Usage dans la Théorie des Hasards", 1773)

"Ignorance is preferable to error; and he is less remote from the truth who believes nothing, than he who believes what is wrong." (Thomas Jefferson, "Notes on the State of Virginia", 1781)

"The word ‘chance’ then expresses only our ignorance of the causes of the phenomena that we observe to occur and to succeed one another in no apparent order. Probability is relative in part to this ignorance, and in part to our knowledge." (Pierre-Simon Laplace, "Mémoire sur les Approximations des Formules qui sont Fonctions de Très Grands Nombres", 1783)

"It is of the utmost importance to your real advancement in science, to avoid every source of error, or whatever may lead you to form an erroneous judgment. Now a true judgment can only be obtained by a profound view of nature, and a strict examination into the mutual connections and dependencies of things; you will hence see the necessity of strict and accurate examination, of time to acquire the requisite knowledge, and of attention to comprehend it: for among the various sources of error, we may reckon the precipitation of our judgment and a presumptuous ignorance as the principal." (George Adams, "Lectures on Natural and Experimental Philosophy" Vol. 1, 1794)

"The natural propensity of the human mind to know the cause of every effect often leads men into errors, and makes them satisfied with a word which does not remove their ignorance." (George Adams, "Lectures on Natural and Experimental Philosophy" Vol. 1, 1794)

On Ignorance (1850-1899)

"Metaphysics. The science to which ignorance goes to learn its knowledge, and knowledge to learn its ignorance. On which all men agree that it is the key, but no two upon how it is to be put into the lock." (Augustus De Morgan, [letter to Dr. Whewell] 1850)

"Nothing can be more puerile than the complaints sometimes made by certain cultivators of a science, that it is very difficult to make discoveries now that the soil has been exhausted, whereas they were so easily made when the ground was first broken. It is an error begotten by ignorance out of indolence. The first discovery did not drop upon the expectant idler who, with placid equanimity waited for the goods the gods might send, but was heavily obtained by patient, systematic, and intelligent labour; and, beyond all question, the same labour of the same mind which made the first discoveries in the new science, would now succeed in making many more, trampled though the field may be by the restless feet of those unmethodical inquirers who, running to and fro, anxiously exclaim, 'Who will show us any good thing?'" (George Gore, "Psychological Inquiries", Journal of Mental Science, 1862)

"It has often been said that, to make discoveries, one must be ignorant. This opinion, mistaken in itself, nevertheless conceals a truth. It means that it is better to know nothing than to keep in mind fixed ideas based on theories whose confirmation we constantly seek, neglecting meanwhile everything that fails to agree with them." (Claude Bernard, "An Introduction to the Study of Experimental Medicine", 1865)

"Nevertheless so profound is our ignorance, and so high our presumption, that we marvel when we hear of the extinction of an organic being; and as we do not see the cause, we invoke cataclysms to desolate the world, or invent laws on the duration of the forms of life!" (Charles Darwin, "On the Origin of Species by Means of Natural Selection", 1866)

"[T]he notion of a negative magnitude has become quite a familiar one […] But it is far otherwise with the notion which is really the fundamental one (and I cannot too strongly emphasize the assertion) underlying and pervading the whole of modern analysis and geometry, that of imaginary magnitude in analysis and of imaginary space (or space as a locus in quo of imaginary points and figures) in geometry: I use in each case the word imaginary as including real. This has not been, so far as I am aware, a subject of philosophical discussion or inquiry. […] considering the prominent position which the notion occupies-say even that the conclusion were that the notion belongs to mere technical mathematics, or has reference to nonentities in regard to which no science is possible, still it seems to me that (as a subject of philosophical discussion) the notion ought not to be thus ignored; it should at least be shown that there is a right to ignore it." (Arthur Cayley, [address before the meeting of the British Association at Southport] 1870)

"You cannot and need not expect to disturb the public in the possession of its medical superstitions. A man’s ignorance is as much his private property, and as precious in his own eyes, as his family Bible." (Oliver W Holmes, "The Young Practitioner", [speech] 1871)

"A wise man only remembers his ignorance in order to destroy it." (Clifford W Kingdon, "Aims and Instruments of Scientific Thought", The Popular Science Monthly Vol. 2, 1872)

"There are no limits in mathematics, and those that assert there are, are infinite ruffians, ignorant, lying blackguards. There is no differential calculus, no Taylor's theorem, no calculus of variations, [...] in mathematics. There is no quackery whatever in mathematics." (Augustus De Morgan, "A Budget of Paradoxes", 1872)

"You may read any quantity of books, and you may be almost as ignorant as you were at starting, if you don’t have, at the back of your minds, the change for words in definite images which can only be acquired through the operation of your observing faculties on the phenomena of nature." (Thomas H Huxley, "Science and Education", 1877)

"Dazzling source of light and heat, of motion, life, and beauty, the inimitable sun has in all ages received the earnest and grateful homage of mortals. The ignorant admire it because they feel the effects of its power and its value; the savant appreciates it because he has learned its unique importance in the system of the world; the artist salutes it because he sees in its splendor the virtual cause of all harmonies." (Camille Flammarion, Popular Astronomy: A General Description of the Heavens, 1880)

"You must not know too much, or be too precise or scientific about birds and trees and flowers and watercraft; a certain free margin, and even vagueness - perhaps ignorance, credulity - helps your enjoyment of these things." (Walt Whitman, "Specimen Days", 1882)

"Our task is only that of sending out a few pickets under the starry flag of science to the edge of that dark domain where the ensigns of the obstinate rebel, Ignorance, are flying undisputed." (Oliver W Holmes, "Medical Essays 1842–1882", 1883)

"I am convinced that it is impossible to expound the methods of induction in a sound manner, without resting them on the theory of probability. Perfect knowledge alone can give certainty, and in nature perfect knowledge would be infinite knowledge, which is clearly beyond our capacities. We have, therefore, to content ourselves with partial knowledge, - knowledge mingled with ignorance, producing doubt." (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1887)

"Our science is a drop, our ignorance a sea. Whatever else be certain, this at least is certain - that the world of our present natural knowledge is enveloped in a larger world of some sort whose residual properties [about which] we at present can frame no positive idea." (William James, "Is Life Worth Living?", 1895)

"Round about the accredited and orderly facts of every science there ever fl oats a sort of dust-cloud of exceptional observations, of occurrences minute and irregular and seldom met with, which it always proves more easy to ignore than to attend to […]" (William James, "The Will to Believe", 1896)

"Theory helps us to bear our ignorance of facts." (George Santayana, "The Sense of Beauty", 1896)

"The history of civilization proves beyond doubt just how sterile the repeated attempts of metaphysics to guess at nature’s laws have been. Instead, there is every reason to believe that when the human intellect ignores reality and concentrates within, it can no longer explain the simplest inner workings of life’s machinery or of the world around us." (Santiago Ramón y Cajal, "Reglas y Consejos sobre Investigacíon Cientifica: Los tónicos de la voluntad", 1897)

On Ignorance (2000-)

"We all would like to know more and, at the same time, to receive less information. In fact, the problem of a worker in today's knowledge industry is not the scarcity of information but its excess. The same holds for professionals: just think of a physician or an executive, constantly bombarded by information that is at best irrelevant. In order to learn anything we need time. And to make time we must use information filters allowing us to ignore most of the information aimed at us. We must ignore much to learn a little." (Mario Bunge, "Philosophy in Crisis: The Need for Reconstruction", 2001)

"Metaphorizing is a manner of thinking, not a property of thinking. It is a capacity of thought, not its quality. It represents a mental operation by which a previously existing entity is described in the characteristics of another one on the basis of some similarity or by reasoning. When we say that something is (like) something else, we have already performed a mental operation. This operation includes elements such as comparison, paralleling and shaping of the new image by ignoring its less satisfactory traits in order that this image obtains an aesthetic value. By this process, for an instant we invent a device, which serves as the pole vault for the comparison’s jump. Once the jump is made the pole vault is removed. This device could be a lightning-speed logical syllogism, or a momentary created term, which successfully merges the traits of the compared objects." (Ivan Mladenov, "Conceptualizing Metaphors: On Charles Peirce’s marginalia", 2006)

"But ignorance exists in the map, not in the territory. If I am ignorant about a phenomenon, that is a fact about my own state of mind, not a fact about the phenomenon itself. A phenomenon can seem mysterious to some particular person. There are no phenomena which are mysterious of themselves. To worship a phenomenon because it seems so wonderfully mysterious, is to worship your own ignorance." (Eliezer Yudkowsky, "Mysterious Answers To Mysterious Questions" 2007)

"Out of twinkling stardust all came, into dark matter all will fall. Death mocks us as we laugh defiance at entropy, yet ignorance birthed mortals sail forth upon time’s cruel sea." (Peter F Hamilton, "The Temporal Void", 2008)

"The instinctual shortcut that we take when we have 'too much information' is to engage with it selectively, picking out the parts we like and ignoring the remainder, making allies with those who have made the same choices and enemies of the rest." (Nate Silver, "The Signal and the Noise", 2012)

"Thus, when we speak of a mathematical concept, we speak not of a single isolated mental image, but rather of a family of mutually correcting mental images. They are privately owned, but publicly checked, examined, corrected, and accepted or rejected. This is the role of the mathematical research community, how it indoctrinates and certifies new members, how it reviews, accepts or rejects proposed publication, how it chooses directions of research to follow and develop, or to ignore and allow to die. All these social activities are based on a necessary condition: that the individual members have mental models that fit together, that yield the same answers to test questions. A new branch of mathematics is established when consensus is reached about the possible test questions and their answers. That collection of possible questions and answers (not necessarily explicit) becomes the means of accepting or rejecting proposed new members." (Reuben Hersh, "Mathematical Intuition: Poincaré, Pólya, Dewey" [in "The Courant–Friedrichs–Lewy (CFL) Condition", 2013])

"Our greatest enemies are ultimately not our political adversaries but entropy, evolution (in the form of pestilence and the flaws in human nature), and most of all ignorance - a shortfall of knowledge of how best to solve our problems." (Steven Pinker, "Enlightenment Now: The Case for Reason, Science, Humanism, and Progress", 2018)

"Images are generally resistant to change and ignore messages that do not conform to their internal settings. Sometimes, however, they do react and can alter in an incremental or even revolutionary manner. Humans can talk about and share their images and, in the symbolic universe they create, reflect upon what is and what might be." (Michael C Jackson, "Critical Systems Thinking and the Management of Complexity", 2019)

On Ignorance (1900-1924)

"If we say there is a limit - the ultimate atom - then, as all size is comparative, we can imagine a being to whom this atom seems as large as an apple or even a house does to us; and we then find it quite unthinkable that this mass of matter should be in its nature absolutely indivisible even by an infinite force. It follows that all explanations of phenomena can only be partial explanations. They can inform us of the last change or the last series of changes which brought about the actual conditions now existing, and they can often enable us to predict future changes to a limited extent; but both the infinite past and the remote future are alike beyond our powers. Yet the explanations that the theory of evolution gives us are none the less real and none the less important, especially when we compare its teachings with the wild guesses or the total ignorance of the thinkers of earlier ages." (Alfred R Wallace, "Evolution", The Sun, 1900)

"The state of a system at a given moment depends on two things - its initial state, and the law according to which that state varies. If we know both this law and this initial state, we have a simple mathematical problem to solve, and we fall back upon our first degree of ignorance. Then it often happens that we know the law and do not know the initial state. It may be asked, for instance, what is the present distribution of the minor planets? We know that from all time they have obeyed the laws of Kepler, but we do not know what was their initial distribution. In the kinetic theory of gases we assume that the gaseous molecules follow rectilinear paths and obey the laws of impact and elastic bodies; yet as we know nothing of their initial velocities, we know nothing of their present velocities. The calculus of probabilities alone enables us to predict the mean phenomena which will result from a combination of these velocities. This is the second degree of ignorance. Finally it is possible, that not only the initial conditions but the laws themselves are unknown. We then reach the third degree of ignorance, and in general we can no longer affirm anything at all as to the probability of a phenomenon. It often happens that instead of trying to discover an event by means of a more or less imperfect knowledge of the law, the events may be known, and we want to find the law; or that, instead of deducing effects from causes, we wish to deduce the causes."  (Henri Poincaré, "Science and Hypothesis", 1902)

"Ignorance is visited as sharply as willful disobedience - incapacity meets with the same punishment as crime. Nature’s discipline is not even a word and a blow, and the blow first; but the blow without the word. It is left to you to find out why your ears are boxed." (Thomas H Huxley, "Science and Education: A Liberal Education; and Where to Find It", 1904)

"Without this language [mathematics] most of the intimate analogies of things would have remained forever unknown to us; and we should forever have been ignorant of the internal harmony of the world, which is the only true objective reality." (Henri Poincaré, "The Value of Science", Popular Science Monthly, 1906)

"The method of solving problems by honest confession of one’s ignorance is called Algebra." (Mary E Boole, "Philosophy and Fun of Algebra", 1909)

"Chance is only the measure of our ignorance." (Henri Poincaré, "The Foundations of Science", 1913)

"Whatever the progress of human knowledge, there will always be room for ignorance, hence for chance and probability." (Emile Borel, Le hasard [Chance], 1914)

"[…] science deals with but a partial aspect of reality, and there is no faintest reason for supposing that everything science ignores is less real than what it accepts. [...] Why is it that science forms a closed system? Why is it that the elements of reality it ignores never come in to disturb it? The reason is that all the terms of physics are defined in terms of one another. The abstractions with which physics begins are all it ever has to do with." (John W N Sullivan, "The Limitations of Science", 1915)

"Ignorance may find a truth on its doorstep that erudition vainly seeks in the stars." (George Iles, "Canadian Stories", 1918)

"In regions where our ignorance is great, occasional guesses are permissible." (Sir Oliver Lodge, "On the Supposed Weight and Ultimate Fate of Radiation", Philosophical Magazine Vol. 41, 1921)

"There are no rival hypotheses except the outworn and completely refuted idea of special creation, now retained only by the ignorant, the dogmatic, and the prejudiced." (Horatio H Newman, "Evolution, Genetics, and Eugenics", 1921)

On Ignorance (1975-1999)

"As knowledge proceeds with spiraling movement to penetrate the vast universe of black mystery, one is continually astonished to discover that at the outer limit of awareness where science interfaces with the unknown, there is nothing but a growing edge, where knowledge and ignorance meet. The more one learns, the more one discovers the increasing magnitude of the unknown, as anyone who has tried to do “exhaustive” research knows very well!" (June Singer, "Androgyny: Toward a New Theory of Sexuality", 1976)

"Neither you nor I nor anybody else knows what makes a mathematician tick. It is not a question of cleverness. I know many mathematicians who are far abler than I am, but they have not been so lucky. An illustration may be given by considering two miners. One may be an expert geologist, but he does not find the golden nuggets that the ignorant miner does." (Louis J Mordell [quoted by Howard Eves, "Mathematical Circles Adieu", 1977])

"The catalogue of our ignorance has two, not one, gates: there is the obvious exit gate, through which questions answered and settled by experimental and theoretical developments march out and disappear into the textbooks and the applications; but there is also a more important, albeit less perspicuous, entrance gate, through which new riddles come to life in the scientifi c world." (Bruno Bertotti, "The Encyclopaedia of Ignorance: Everything You Ever Wanted to Know About the Unknown", 1977)

"The larger the sphere of our knowledge, the greater its contact with the infi nity of our ignorance." (Arthur Berry, "A Short History of Astronomy", Vol. 83 (1), 1978)

"The only solid piece of scientific truth about which I feel totally confident is that we are profoundly ignorant about nature." (Lewis Thomas, "The Medusa and the Snail: More Notes of a Biology Watcher", 1979)

"One can only conclude that some creationists, recoiling from the fearsome prospect of time’s abyss, have toppled backward into the abyss of ignorance." (Albritton Claude Jr., "The Abyss of Time: Changing Conceptions of the Earth’s Antiquity after the Sixteenth Century ", 1980)

"The difference between myth and science is the difference between divine inspiration of “unaided reason” (as Bertrand Russell put it) on the one hand and theories developed in observational contact with the real world on the other. It is the difference between the belief in prophets and critical thinking, between Credo quia absurdum (I believe because it is absurd–Tertullian) and De omnibus est dubitandum (Everything should be questioned–Descartes). To try to write a grand cosmical drama leads necessarily to myth. To try to let knowledge substitute ignorance in increasingly large regions of space and time is science." (Hannes Alfvén, "Cosmology: Myth or Science?", Journal of Astrophysics and Astronomy, 1984)

"Consider the unlearned, unaware of their ignorance, who think they know everything! As knowledge increases, ignorance decreases, but this kind of ignorance - unlearned ignorance - is no more than the lack of knowledge. With knowledge comes awareness of ignorance - learned ignorance - and the more we know, the more aware we become of what we do not know." (Edward R Harrison, "Masks of the Universe", 1985)

"The attitudes of mathematicians can be found not only in what they wrote, but in what they did not write. It is possible to divide mathematicians into those who gave complex numbers some kind of coverage, and those who sometimes or always ignored them." (Diana Willment, "Complex Numbers from 1600 to 1840" [Masters thesis], 1985)

"Where chaos begins, classical science stops. For as long as the world has had physicists inquiring into the laws of nature, it has suffered a special ignorance about disorder in the atmosphere, in the fluctuations of the wildlife populations, in the oscillations of the heart and the brain. The irregular side of nature, the discontinuous and erratic side these have been puzzles to science, or worse, monstrosities." (James Gleick, "Chaos", 1987)

"It is our responsibility as scientists, knowing the great progress which comes from a satisfactory philosophy of ignorance, the great progress which is the fruit of freedom of thought, to proclaim the value of this freedom; to teach how doubt is not to be feared but welcomed and discussed; and to demand this freedom as our duty to all coming generations." (Richard P (Feynman, "What Do You Care What Other People Think?", 1988)

"Illiteracy and innumeracy are social ills created in part by increased demand for words and numbers. As printing brought words to the masses and made literacy a prerequisite for productive life, so now computing has made numeracy an essential feature of today's society. But it is innumeracy, not numeracy, that dominates the headlines: ignorance of basic quantitative tools is endemic […] and is approaching epidemic levels […]." (Lynn A Steen, "Numeracy", Daedalus Vol. 119 No. 2, 1990)

"Ignorance of science and technology is becoming the ultimate self-indulgent luxury." (Jeremy Bernstein, "Cranks, Quarks, and the Cosmos: Writings on Science", 1993)

"The art of science is knowing which observations to ignore and which are the key to the puzzle." (Edward W Kolb, "Blind Watchers of the Sky", 1996)

"Whether our cosmological view of the universe is right or wrong, or just incomplete, we were brave enough to confront our ignorance and look. We looked with all our might, and with boldness and imagination managed to see a little bit farther than our predecessors. We were not proud of our blindness, but neither were we ashamed of it or intimidated by it, for we chose to look for the light of truth fully cognizant of our blindness. " (Edward W Kolb, "Blind Watchers of the Sky", 1996)

"Is a random outcome completely determined, and random only by virtue of our ignorance of the most minute contributing factors? Or are the contributing factors unknowable, and therefore render as random an outcome that can never be determined? Are seemingly random events merely the result of fluctuations superimposed on a determinate system, masking its predictability, or is there some disorderliness built into the system itself?" (Deborah J Bennett, "Randomness", 1998)

"There is no over-arching theory of complexity that allows us to ignore the contingent aspects of complex systems. If something really is complex, it cannot by adequately described by means of a simple theory. Engaging with complexity entails engaging with specific complex systems. Despite this we can, at a very basic level, make general remarks concerning the conditions for complex behaviour and the dynamics of complex systems. Furthermore, I suggest that complex systems can be modelled." (Paul Cilliers, "Complexity and Postmodernism", 1998)

"When the scientist tells you he does not know the answer, he is an ignorant man. When he tells you he has a hunch about how it is going to work, he is uncertain about it. When he is pretty sure of how it is going to work, and he tells you, 'This is the way it is going to work, I’ll bet', he still is in some doubt. And it is of paramount importance, in order to make progress, that we recognize this ignorance and this doubt. Because we have the doubt, we then propose looking in new directions for new ideas. The rate of development in science is not the rate at which you make observations alone but, much more important, the rate at which you create new things to test." (Richard P Feynman, "The Meaning of It All: Thoughts of a Citizen Scientist", 1998)

"Events may appear to us to be random, but this could be attributed to human ignorance about the details of the processes involved." (Brain S Everitt, "Chance Rules", 1999)