Quotes about analogy
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Gao Xingjian photo
Henry John Stephen Smith photo

“If we except the great name of Newton (and the exception is one that the great Gauss himself would have been delighted to make) it is probable that no mathematician of any age or country has ever surpassed Gauss in the combination of an abundant fertility of invention with an absolute vigorousness in demonstration, which the ancient Greeks themselves might have envied. It may be admitted, without any disparagement to the eminence of such great mathematicians as Euler and Cauchy that they were so overwhelmed with the exuberant wealth of their own creations, and so fascinated by the interest attaching to the results at which they arrived, that they did not greatly care to expend their time in arranging their ideas in a strictly logical order, or even in establishing by irrefragable proof propositions which they instinctively felt, and could almost see to be true. With Gauss the case was otherwise. It may seem paradoxical, but it is probably nevertheless true that it is precisely the effort after a logical perfection of form which has rendered the writings of Gauss open to the charge of obscurity and unnecessary difficulty. The fact is that there is neither obscurity nor difficulty in his writings, as long as we read them in the submissive spirit in which an intelligent schoolboy is made to read his Euclid. Every assertion that is made is fully proved, and the assertions succeed one another in a perfectly just analogical order… But when we have finished the perusal, we soon begin to feel that our work is but begun, that we are still standing on the threshold of the temple, and that there is a secret which lies behind the veil and is as yet concealed from us. No vestige appears of the process by which the result itself was obtained, perhaps not even a trace of the considerations which suggested the successive steps of the demonstration. Gauss says more than once that for brevity, he gives only the synthesis, and suppresses the analysis of his propositions. Pauca sed matura—few but well matured… If, on the other hand, we turn to a memoir of Euler's, there is a sort of free and luxuriant gracefulness about the whole performance, which tells of the quiet pleasure which Euler must have taken in each step of his work; but we are conscious nevertheless that we are at an immense distance from the severe grandeur of design which is characteristic of all Gauss's greater efforts.”

Henry John Stephen Smith (1826–1883) mathematician

As quoted by Alexander Macfarlane, Lectures on Ten British Physicists of the Nineteenth Century (1916) p. 95, https://books.google.com/books?id=43SBAAAAIAAJ&pg=PA95 "Henry John Stephen Smith (1826-1883) A Lecture delivered March 15, 1902"

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Marshall McLuhan photo
Alfred Korzybski photo
Miguel de Unamuno photo
Thomas Young (scientist) photo
Northrop Frye photo
Richard Whately photo
Charles Lyell photo
Bjarne Stroustrup photo

“Proof by analogy is fraud.”

[Stroustrup, Bjarne, The C++ Programming Language, 692]

Northrop Frye photo

“Education is a set of analogies to a genuinely human existence, of which the arts are the model. Merely human life is of course a demonic analogy or parody of genuinely human life.”

Northrop Frye (1912–1991) Canadian literary critic and literary theorist

Source: "Quotes", Notebooks and Lectures on the Bible and Other Religious Texts (2003), p. 149

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Samuel Vince photo

“What we mean by the laws of nature, are those laws which are deduced from that series of events, which, by divine appointment, follow each other in the moral and physical world; the former of which we shall here have occasion principally to consider, the present question altogether, respecting the moral government of God — a consideration which our author has entirely neglected, in his estimation of the credibility of miracles. Examining the question therefore upon this principle, it is manifest, that the extraordinary nature of the fact is no ground for disbelief, provided such a fact, in, a moral point of view, was, from the condition of man, become necessary; for in that case, the Deky, by dispensing his assistance in proportion to our wants, acted upon the same principle as in his more 'ordinary operations. For however ' opposite the physical effects may be, if their moral tendency be the same, they form a part of the jmoral law. Now in those actions which are called miracles, the Deity is directed by the same moral principle as in his usual dispensations; and therefore being influenced by the same motive to accomplish the same end, the laws of God's moral government are not violated, such laws being established by the motives and the ends produced, and not by the means employed. To prove therefore the moral laws to be the same in those actions called miraculous, as in common events, it is not the actions thetnselves which are to be considered, but the principles by which they were directed, and their consequences, for if these be the same, the Deity acts by the same laws. And here, moral analogy will be found to confirm the truth of the miracles recorded in scripture. But as the moral government of God is directed by motives which lie beyond the reach of human investigation, we have no principles by which we can judge concerning the probability of the happening of any new event which respects the moral world; we cannot therefore pronounce any extraordinary event of that nature to be a violation of the moral law of God's dispensations; but we can nevertheless judge of its agreement with that law, so far as it has fallen under our observation. But our author leaves out the consideration of God's moral government, and reasons simply -on the facts which arc said to have nappened, without any reference to an end; we will therefore examine how far his conclusions are just upon this principle.
He defines miracles to be "a violation of the laws of nature;" he undoubtedly means the physical laws, as no part of his reasoning has any reference to them in a moral point of view. Now these laws must be deduced, either from his own view of events only, or from that, and testimony jojntly; and if testimony beallowed on one part, it ought also to be admitted on the other, granting that there is no impossibility in the fact attested. But the laws by which the Deity governs the universe can, at best, only be inferred from the whole series of his dispensations from the beginning of the world; testimony must therefore necessarily be admitted in establishing these laws. Now our author, in deducing the laws of nature, rejects all well authenticated miraculous events, granted to be possible, and therefore not altogether incredible and to be rejected without examination, and thence establishes a law to prove against their credibility; but the proof of a position ought to proceed upon principles which are totally independent of any supposition of its being either true or falser. His conclusion therefore is not deduced by just reasoning from acknowledged principles, but it is a necessary consequence of his own arbitrary supposition. "Tis a miracle," says he, "that a dead man should come to life, because that has never been observed in any age or country." Now, testimony, confirmed by every proof which can tend to establish a true matter of fact, asserts that such an event; has happened. But our author argues against the credibility of this, because it is contrary to the laws of nature; and in establishing these laws, he rejects all such extraordinary facts, although they are authenticated by all the evidence which such facts can possibly admit of; taking thereby into consideration, events of that kind only which have fallen within the sphere of his own observations, as if the whole series of God's dispensations were necessarily included in the course of a few years. But who shall thus circumscribe the operations of divine power and infinite wisdom, and say, "Hitherto shall thou go, and no further."”

Samuel Vince (1749–1821) British mathematician, astronomer and physicist

Before he rejected circumstances of this kind in establishing the laws of nature, he should, at least, have shewn, that we have not all that evidence for them which we might "have had" upon supposition that they were true ; he should also have shewn, in a moral point of view, that the events were inconsistent with the ordinary operations of Providence ; and that there was no end to justify the means. Whereas, on the contrary, there is all the evidence for them which a real matter of fact can possibly have ; they are perfectly consistent with all the moral dispensations of Providence and at the same time that the resurrection of Jesus Christ is most unexceptionably attested, we discover a moral intention in the miracle, which very satisfactorily accounts for that exertion of divine power?
Source: The Credibility of Christianity Vindicated, p. 48; As quoted in " Book review http://books.google.nl/books?id=52tAAQAAMAAJ&pg=PA259," in The British Critic, Volume 12 (1798). F. and C. Rivington. p. 259-261

Jean Metzinger photo

“Instead of copying Nature, we [ Cubists ] create a 'milieu', of our own, wherein our sentiment can work itself out through a juxtaposition of colors. It is hard to explain it, but it may perhaps be illustrated by analogy of literature and music. Your [ Gelett Burgess is American] Edgar Poe did not attempt to reproduce Nature realistically. Some phase of life suggested an emotion, as that of horror in 'The Fall of the House of Ushur.”

Jean Metzinger (1883–1956) French painter

That subjective idea he translated into art. He made a composition of it.
Quote of Metzinger in 'The Wild Men of Paris', by Gelett Burgess https://monoskop.org/images/f/f3/Burgess_Gelett_1910_The_Wild_Men_of_Paris.pdf, in 'The Architectural Record, Vol XXVII, May 1910, p. 413

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Michele Bachmann photo

“I tell you this story because I think in our day and time, there is no analogy to that horrific action [the Holocaust]. But only to say, we are seeing eclipsed in front of our eyes a similar death and a similar taking away. It is this disenfranchisement that I think we have to answer to.”

Michele Bachmann (1956) American politician

Bachmann uses Holocaust to illustrate tax issue
MSNBC
2011-04-30
http://www.msnbc.msn.com/id/42836858/ns/politics-capitol_hill/
2001-05-01
comparing the next generation paying high taxes to the Holocaust
2010s

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Julia Serano photo
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Rudolf E. Kálmán photo

“I have been aware from the outset (end of January 1959, the birthdate of the second paper in the citation) that the deep analysis of something which is now called Kalman filtering were of major importance. But even with this immodesty I did not quite anticipate all the reactions to this work. Up to now there have been some 1000 related publications, at least two Citation Classics, etc. There is something to be explained.
To look for an explanation, let me suggest a historical analogy, at the risk of further immodesty. I am thinking of Newton, and specifically his most spectacular achievement, the law of Gravitation. Newton received very ample "recognition" (as it is called today) for this work. it astounded - really floored - all his contemporaries. But I am quite sure, having studied the matter and having added something to it, that nobody then (1700) really understood what Newton's contribution was. Indeed, it seemed an absolute miracle to his contemporaries that someone, an Englishman, actually a human being, in some magic and un-understandable way, could harness mathematics, an impractical and eternal something, and so use mathematics as to discover with it something fundamental about the universe.”

Rudolf E. Kálmán (1930–2016) Hungarian-born American electrical engineer

Kalman (1986) " Steele Prizes Awarded at the Annual Meeting in San Antonio http://www-history.mcs.st-and.ac.uk/Extras/Kalman_response.html", Notices Amer. Math. Soc. 34 (2) (1987), 228-229.

Ervin László photo
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Ken Livingstone photo

“No longer was light analogous to the discharge of a blunderbuss, but rather to the pulsating flight of birds.”

Banesh Hoffmann (1906–1986) American mathematician and physicist

[Banesh Hoffmann, The strange story of the quantum: an account for the general reader of the growth of the ideas underlying our present atomic knowledge, Courier Dover Publications, 1959, 0486205185, 7]

Robert M. Pirsig photo

“All this is just an analogy.”

Source: Zen and the Art of Motorcycle Maintenance (1974), Ch. 30

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Alfred North Whitehead photo

“Identification of rhythm as the causal counterpart of life; wherever there is some life, only perceptible to us when the analogies are sufficiently close.”

Alfred North Whitehead (1861–1947) English mathematician and philosopher

1910s, The Principles of Natural Knowledge (1919)

Mark Hopkins (educator) photo

“The movement has indeed been slow, and not such as man would have expected; but it has been analogous to the great movements of God in His providence and in His works. So, if we may credit the geologists, has this earth reached its present state. So have moved on the great empires. So retribution follows crime. So rise the tides. So grows the tree with long intervals of repose and apparent death. So comes on the spring, with battling elements and frequent reverses, with snowbanks and violets, and, if we had no experience, we might be doubtful what the end would be. But we know that back of all this, beyond these fluctuations, away in the serene heavens, the sun is moving steadily on; that these very agitations of the elements and seeming reverses, are not only the sign, but the result of his approach, and that the full warmth and radiance of the summer noontide are sure to come. So, O Divine Redeemer, Sun of Righteousness, come Thou! So will He come. It may be through clouds and darkness and tempest; but the heaven where He is, is serene; He is "traveling in the greatness of His strength; "and as surely as the throne of God abides, we know He shall yet reach the height and splendor of the highest noon, and that the light of millennial glory shall yet flood the earth.”

Mark Hopkins (educator) (1802–1887) American educationalist and theologian

Source: Dictionary of Burning Words of Brilliant Writers (1895), P. 418.

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James Braid photo

“…during a period in history psychology was still a branch of academic philosophy. The psychological concepts developed by philosophers of mind, such as “dominant ideas” (akin to the automatic thoughts of Beck’s cognitive therapy) “habit and association” (a subjective precursor of Pavlovian conditioning), and “imitation and sympathy” (which we now call “role-modelling” and “empathy”), are repeatedly mentioned by Braid as the theoretical framework upon which his science of hypnotism, “neuro-hypnology”, was built. Braid’s friend and collaborator, Prof. William B. Carpenter, discusses the theoretical principles of this in his Principles of Mental Physiology (1889), especially in the chapter ‘Of Common Sense’ which concludes by quoting an approving letter from the philosopher John Stuart Mill sent to Carpenter in 1872. Mill agrees with Carpenter’s contention that “common sense”, by which he means a kind of intellectual intuition analogous to the ancient Greek concept of nous, is a combination of innate and acquired judgements, which have a “reflexive” or “automatic” quality and appear to consciousness as “self-evident” truths.”

James Braid (1795–1860) Scottish surgeon, hypnotist, and hypnotherapist

James Braid, in The Original Philosophy of Hypnotherapy (from The Discovery of Hypnosis) http://ukhypnosis.wordpress.com/category/james-braid-the-founder-of-hypnotherapy/page/2/.

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Henry Adams photo
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“Life is too complicated to use analogies to describe it.”

Donald Miller (1971) American writer

Prayer and the Art of Volkswagen Maintenance (2000, Harvest House Publishers)

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Fabian Picardo photo

“Mr Tusk, who has been given to using the analogies of the divorce and divorce petition, is behaving like a cuckolded husband who is taking it out on the children.”

Fabian Picardo (1972) Gibraltarian politician and barrister

[3 April 2017, Gibraltar leader says EU chief Donald Tusk 'behaving like a cuckolded husband', http://www.independent.co.uk/news/world/europe/gibraltar-leader-fabian-picardo-donald-tusk-eu-council-president-cuckolded-husband-british-territory-a7664001.html, The Independent, 3 April 2017]
2017

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John R. Commons photo

“These individual actions are really trans-actions instead of either individual behavior or the "exchange" of commodities. It is this shift from commodities and individuals to transactions and working rules of collective action that marks the transition from the classical and hedonic schools to the institutional schools of economic thinking. The shift is a change in the ultimate unit of economic investigation. The classic and hedonic economists, with their communistic and anarchistic offshoots, founded their theories on the relation of man to nature, but institutionalism is a relation of man to man. The smallest unit of the classic economists was a commodity produced by labor. The smallest unit of the hedonic economists was the same or similar commodity enjoyed by ultimate consumers. One was the objective side, the other the subjective side, of the same relation between the individual and the forces of nature. The outcome, in either case, was the materialistic metaphor of an automatic equilibrium, analogous to the waves of the ocean, but personified as "seeking their level." But the smallest unit of the institutional economists is a unit of activity -- a transaction, with its participants. Transactions intervene between the labor of the classic economists and the pleasures of the hedonic economists, simply because it is society that controls access to the forces of nature, and transactions are, not the "exchange of commodities," but the alienation and acquisition, between individuals, of the rights of property and liberty created by society, which must therefore be negotiated between the parties concerned before labor can produce, or consumers can consume, or commodities be physically exchanged.”

John R. Commons (1862–1945) United States institutional economist and labor historian

"Institutional Economics," 1931

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Norbert Wiener photo

“It is my thesis that the physical functioning of the living individual and the operation of some of the newer communication machines are precisely parallel in their analogous attempts to control entropy through feedback. Both of them have sensory receptors as one stage in their cycle of operation: that is, in both of them there exists a special apparatus for collecting information from the outer world at low energy levels, and for making it available in the operation of the individual or of the machine. In both cases these external messages are not taken neat, but through the internal transforming powers of the apparatus, whether it be alive or dead. The information is then turned into a new form available for the further stages of performance. In both the animal and the machine this performance is made to be effective on the outer world. In both of them, their performed action on the outer world, and not merely their intended action, is reported back to the central regulatory apparatus. This complex of behavior is ignored by the average man, and in particular does not play the role that it should in our habitual analysis of society; for just as individual physical responses may be seen from this point of view, so may the organic responses of society itself. I do not mean that the sociologist is unaware of the existence and complex nature of communications in society, but until recently he has tended to overlook the extent to which they are the cement which binds its fabric together.”

Source: The Human Use of Human Beings (1950), p. 26-27 as cited in: Felix Geyer, Johannes van der Zouwen, (1994) " Norbert Wiener and the Social Sciences http://www.critcrim.org/redfeather/chaos/024Weiner.htm", Kybernetes, Vol. 23 Iss: 6/7, pp.46 - 61

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Richard L. Daft photo

“The management science approach to organizational decision making is the analog to the rational approach by individual managers. Management science came into being during World War II. At that time, mathematical and statistical techniques were applied to urgent, large-scale military problems that were beyond the ability of individual decision makers. Mathematicians, physicists, and operations researchers used systems analysis to develop artillery trajectories, antisubmarine strategies, and bombing strategies such as salvoing (discharging multiple shells simultaneously). Consider the problem of a battleship trying to sink an enemy ship several miles away. The calculation for aiming the battleship's guns should consider distance, wind speed, shell size, speed and direction of both ships, pitch and roll of the firing ship, and curvature of the earth. Methods for performing such calculations using trial and error and intuition are not accurate, take far too long, and may never achieve success.
This is where management science came in. Analysts were able to identify the relevant variables involved in aiming a ship's guns and could model them with the use of mathematical equations. Distance, speed, pitch, roll, shell size, and so on could be calculated and entered into the equations. The answer was immediate, and the guns could begin firing. Factors such as pitch and roll were soon measured mechanically and fed directly into the targeting mechanism. Today, the human element is completely removed from the targeting process. Radar picks up the target, and the entire sequence is computed automatically.”

Richard L. Daft (1964) American sociologist

Source: Organization Theory and Design, 2007-2010, p. 500

Plutarch photo

“The correct analogy for the mind is not a vessel that needs filling, but wood that needs igniting — no more — and then it motivates one towards originality and instills the desire for truth. Suppose someone were to go and ask his neighbors for fire and find a substantial blaze there, and just stay there continually warming himself: that is no different from someone who goes to someone else to get to some of his rationality, and fails to realize that he ought to ignite his own flame, his own intellect, but is happy to sit entranced by the lecture, and the words trigger only associative thinking and bring, as it were, only a flush to his cheeks and a glow to his limbs; but he has not dispelled or dispersed, in the warm light of philosophy, the internal dank gloom of his mind.”

οὐ γὰρ ὡς ἀγγεῖον ὁ νοῦς ἀποπληρώσεως ἀλλ' ὑπεκκαύματος μόνον ὥσπερ ὕλη δεῖται ὁρμὴν ἐμποιοῦντος εὑρετικὴν καὶ ὄρεξιν ἐπὶ τὴν ἀλήθειαν. ὥσπερ οὖν εἴ τις ἐκ γειτόνων πυρὸς δεόμενος, εἶτα πολὺ καὶ λαμπρὸν εὑρὼν αὐτοῦ καταμένοι διὰ τέλους θαλπόμενος, οὕτως εἴ τις ἥκων λόγου μεταλαβεῖν πρὸς ἄλλον οὐχ οἴεται δεῖν φῶς οἰκεῖον ἐξάπτειν καὶ νοῦν ἴδιον, ἀλλὰ χαίρων τῇ ἀκροάσει κάθηται θελγόμενος, οἷον ἔρευθος ἕλκει καὶ γάνωμα τὴν δόξαν ἀπὸ τῶν λόγων, τὸν δ᾽ ἐντὸς: εὐρῶτα τῆς ψυχῆς καὶ ζόφον οὐκ ἐκτεθέρμαγκεν οὐδ᾽ ἐξέωκε διὰ φιλοσοφίας.
On Listening to Lectures, Plutarch, Moralia 48C (variously called De auditione Philosophorum or De Auditu or De Recta Audiendi Ratione)
Moralia, Others

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“Language, intelligence, and humor, along with art, generosity, and musical ability, are often described as human equivalents of the peacock’s tail. However, peacocks afford a poor analogy for the role of courtship displays in humans. Other animal models offer a better fit. In a number of nonhuman species — species as diverse as sea dragons and grebes — males and females engage in a mutual courtship “dance,” in which the two partners mirror one another’s movements. In Clark’s grebes and Western grebes, for instance, the pair bond ritual culminates in the famous courtship rush: The male and female swim side by side along the top of the water, with their wings back and their heads and necks in a stereotyped posture. If we want a nonhuman analogue for the role of creative intelligence or humor in human courtship, we should think not of ornamented peacocks displaying while drab females evaluate them. We should think instead of grebes engaged in their mating rush or sea dragons engaged in their synchronized mirror dance. Once we have one of these alternative images fixed in our minds, we can then add the proviso that there is a slight skew such that, in the early stages of courtship, men tend to display more vigorously and women tend to be choosier. However, this should be seen as a qualification to the primary message that intelligence, humor, and other forms of sexual display are part of the mutual courtship process in our species.”

Source: The Ape that Thought It Was a Peacock: Does Evolutionary Psychology Exaggerate Human Sex Differences? (2013), p. 160

“Methods by which engineers stabilise their mechanisms suggest analogous possibilities for stabilising economic systems.”

Arnold Tustin (1899–1994) British engineer

Arnold Tustin (1957) " The mechanism of economic instability http://books.google.com/books?id=Nou8mkjPMPUC&pg=PA8" in: New Scientist, Oct. 27, 1957. p. 8

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“Science is not distinguished from myth by science being literally true and myth only a type of poetic analogy. While their aims are different, both are composed of symbols we use to deal with a slippery world.”

John Gray (1948) British philosopher

Beyond the Last Thought: Freud's cigars and the long way round to Nirvana (p. 96)
The Silence of Animals: On Progress and Other Modern Myths (2013)

“Analogously to Arnulf Rainer′s ‘overpaintings’, and extending thse with my own actionistic resources, the artist′s head should be in the picture, should become one with the picture, and disappear in it.”

Günter Brus (1938) Austrian artist

Source: Nervous Stillness on the Horizon (2006), P. 12 (Gunter Brus inDie Schastrommel.Organ der österreichischen Exilregierung.Bolzano:ed. Gunter Brus,June 1972,no.8a, p. 57.)

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“The great body of population dynamics, like those of the motion of the celestial bodies, can be solved—and what is most remarkable, there is a surprising analogy between the formulas employed in these calculations. I believe that I have achieved to some extent what I have long said about the possibility of founding a social mechanics on the model established by celestial mechanics—to formulate the motions of the social body in accordance with those of celestial bodies, and to find there again the same properties and laws of conservation.”

Adolphe Quetelet (1796–1874) Belgian astronomer, mathematician, statistician and sociologist

Astronomie élémentaire? (1834) as quoted by Theodore M. Porter, "From Quetelet to Maxwell: Social Statistics and the Origin of Statistical Physics" in The Natural Sciences and the Social Sciences: Some Critical and Historical Perspectives (2013) ed., I. Bernard Cohen

Anthony Crosland photo

“Militant leftism in politics appears to have its roots in broadly analogous sentiments. Every labour politician has observed that the most indignant members of his local Party are not usually the poorest, or the slum-dwellers, or those with most to gain from further economic change, but the younger, more self-conscious element, earning good incomes and living comfortably in neat new council houses: skilled engineering workers, electrical workers, draughtsmen, technicians, and the lower clerical grades. (Similarly the most militant local parties are not in the old industrial areas, but either in the newer high-wage engineering areas or in middle-class towns; Coventry or Margate are the characteristic strongholds.) Now it is people such as these who naturally resent the fact that despite their high economic status, often so much higher than their parents’, and their undoubted skill at work, they have no right to participate in the decisions of their firm, no influence over policy, and far fewer non-pecuniary privileges than the managerial grades; and outside their work they are conscious of a conspicuous educational handicap, of a style of life which is still looked down on by middle-class people often earning little if any more, of differences in accent, and generally of an inferior class position.”

The Future of Socialism by Anthony Crosland
The Future of Socialism (1956)

Charles Sanders Peirce photo

“We have here a question of difficulty, analogous to the question of nominalism and realism.”

Charles Sanders Peirce (1839–1914) American philosopher, logician, mathematician, and scientist

The Law of Mind (1892)

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“Though analogy is often misleading, it is the least misleading thing we have.”

Samuel Butler (1835–1902) novelist

Thought and Word, ii
The Note-Books of Samuel Butler (1912), Part VII - On the Making of Music, Pictures, and Books

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Béla H. Bánáthy photo

“Science focuses on the study of the natural world. It seeks to describe what exists. Focusing on problem finding, it studies and describes problems in its various domains. The humanities focus on understanding and discussing the human experience. In design, we focus on finding solutions and creating things and systems of value that do not yet exist.
The methods of science include controlled experiments, classification, pattern recognition, analysis, and deduction. In the humanities we apply analogy, metaphor, criticism, and (e)valuation. In design we devise alternatives, form patterns, synthesize, use conjecture, and model solutions. \
Science values objectivity, rationality, and neutrality. It has concern for the truth. The humanities value subjectivity, imagination, and commitment. They have a concern for justice. Design values practicality, ingenuity, creativity, and empathy. It has concerns for goodness of fit and for the impact of design on future generations.”

Béla H. Bánáthy (1919–2003) Hungarian linguist and systems scientist

Source: Designing Social Systems in a Changing World (1996), p. 34-35, as cited in Alexander Laszlo and Stanley Krippner (1992) " Systems Theories: Their Origins, Foundations, and Development http://archive.syntonyquest.org/elcTree/resourcesPDFs/SystemsTheory.pdf" In: J.S. Jordan (Ed.), Systems Theories and A Priori Aspects of Perception. Amsterdam: Elsevier Science, 1998. Ch. 3, pp. 47-74.

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“…analogies […] are figures intended to serve as fatal weapons if they succeed, and as innocent toys if they fail.”

Henry Adams (1838–1918) journalist, historian, academic, novelist

Mont Saint Michel and Chartres (1904)

E. W. Hobson photo

“The actual evolution of mathematical theories proceeds by a process of induction strictly analogous to the method of induction employed in building up the physical sciences; observation, comparison, classification, trial, and generalisation are essential in both cases. Not only are special results, obtained independently of one another, frequently seen to be really included in some generalisation, but branches of the subject which have been developed quite independently of one another are sometimes found to have connections which enable them to be synthesised in one single body of doctrine. The essential nature of mathematical thought manifests itself in the discernment of fundamental identity in the mathematical aspects of what are superficially very different domains. A striking example of this species of immanent identity of mathematical form was exhibited by the discovery of that distinguished mathematician... Major MacMahon, that all possible Latin squares are capable of enumeration by the consideration of certain differential operators. Here we have a case in which an enumeration, which appears to be not amenable to direct treatment, can actually be carried out in a simple manner when the underlying identity of the operation is recognised with that involved in certain operations due to differential operators, the calculus of which belongs superficially to a wholly different region of thought from that relating to Latin squares.”

E. W. Hobson (1856–1933) British mathematician

Source: Presidential Address British Association for the Advancement of Science, Section A (1910), p. 290; Cited in: Moritz (1914, 27): The Nature of Mathematics.

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