Misquoted: Andrew Lang's Using Statistics for Support rather than Illumination

The quote is from Andrew Lang's speech from 1910 (see [3]) referenced in several other places (see [4], [5], [6]) without specifying the source:

"Politicians use statistics in the same way that a drunk uses lamp-posts - for support rather than illumination." (Andrew Lang, [speech] 1910)

I like this quote because it reflects by a metaphor one of misuses of Statistics, people looking for supporting their beliefs, faith, opinions, conviction and/or biases (by twisting the numbers), rather than for changing their mind (illumination). Here Statistics refer mainly to data obtained by statistical methods, no matter whether they were obtained by simple aggregations or more complex techniques (including data visualization). It applies to politics, business as well as to daily life situations. In extremis, it has to do with cherry-picking or filtering rooted in data.

The Quote Investigator [1] traces back the metaphor behind the quote to Alfred E Housman who in a translation of Marcus Manilius' Astronomicon edition from 1903, where referring to manuscripts (abbreviated MS for singular and MSS for plural) said:

"And critics who treat MS evidence as rational men treat all evidence, and test it by reason and by the knowledge which they have acquired, these are blamed for rashness and capriciousness by gentlemen who use MSS as drunkards use lamp-posts, - not to light them on their way but to dissimulate their instability." [2] (Alfred E Housman, 1903)

Here are the three references mentioned above via the Quote Investigator (though there seem to be other earlier sources whose text is not publicly available):

"I shall try not to use statistics as a drunken man uses lamp-posts, for support rather than for illumination;" [4] (Francis Yeats-Brown, 1937)

 "For blue books are particularly prone to use their statistics not as a living record of social progress but (to quote a deservedly immortal phrase of Andrew Lang) ‘as a drunken man uses lamp-posts - for support rather than for illumination’." [5] (G A N Lowndes, 1937)

"Their case, as has been amply proved by these recapitulations to-night, is a very lame case indeed. The few new facts which the Debate has elicited from that side of the House have been used by them, as was said in another connection, as a drunken man uses lampposts - more for support than for illumination." [6] (McEwene Hansard, [speech] 1937) 

Several similar formulations of the metaphor can be found in other later works:

"Many use statistics as a drunken man uses o lamp-post - for support rather than for illumination." (The Lancet, 1941)

"Many people use statistics as a drunkard uses a street lamp - for support rather than illumination. It is not enough to avoid outright falsehood; one must be on the alert to detect possible distortion of truth. One can hardly pick up a newspaper without seeing some sensational headline based on scanty or doubtful data." (Anna C Rogers, "Graphic Charts Handbook", 1961)

 "Of course, you all know the old story that some people use statistics the way an inebriate uses a lamppost - for support rather than for illumination. It is not really that bad at all times. Statistics are indeed used for illumination, the difficulty is that everybody is trying to illuminate a different point." (Hyman L Lewis, [in Gerhard Bry's "Business Cycle Indicators for States and Regions"] 1961)

"The use of statistical methods to analyze data does not make a study any more 'scientific', 'rigorous', or 'objective'. The purpose of quantitative analysis is not to sanctify a set of findings. Unfortunately, some studies, in the words of one critic, 'use statistics as a drunk uses a street lamp, for support rather than illumination'. Quantitative techniques will be more likely to illuminate if the data analyst is guided in methodological choices by a substantive understanding of the problem he or she is trying to learn about. Good procedures in data analysis involve techniques that help to (a) answer the substantive questions at hand, (b) squeeze all the relevant information out of the data, and (c) learn something new about the world." (Edward R Tufte, "Data Analysis for Politics and Policy", 1974)

"Beware of the man who, like the drunk with a lamppost, uses numbers for support rather than for illumination." (Lawrence Malkin, "The National Debt", 1987)

"It is worth mentioning the statement of a statistician which says 'Statistics should not be used as a blind man uses a lamp-post for support instead of illumination.'" (Padmalochan Hazarika, "A Textbook of Business Statistics", 2007)

"Statistics should not be used as a blind man uses a lamp post for support rather than for illumination." (C B Gupta & Vijay Gupta, "Introduction to Statistical Methods", 2009)

"An unsophisticated forecaster uses statistics as a drunken man uses lamp-posts - for support rather than for illumination." (Anthony Carpi & Anne Egger, "The Process of Science", 2010) [attributed in current form to Lang]

"Statistics, as such, do not prove anything. They are simply tools in the hands of the statisticians. If a statistician misuses the data, then the blame lies squarely on him and not on the subject matter. A competent doctor can cure a disease by making good use of the medicine but the same medicine in the hands of an incompetent doctor becomes a poison. The fault in this case is not o the medicine but of the unqualified doctor. In the same way, Statistics is never faulty but the fault lies with the users. In fact, Statistics should not be relied upon blindly nor distrusted outright. 'Statistics should not be used as a blind man uses a lamp post for support rather than for illumination, whereas its real purpose is to serve as illumination and not as a support.'" (TR Jain & VK Ohri, "Introductory Microeconomics for Class 11" 2023)

Other attributions of the quote are given to Mark Twain, David Ogilvy and others:

"People commonly use statistics like a drunk uses a lamppost: for support rather than for illumination." (R Preston McAfee, "Competitive Solutions: The Strategist's Toolkit", 2009) [attributed to Mark Twain]

 "I notice increasing reluctance on the part of marketing executives to use judgement; they are coming to rely too much on research and they use it as a drunkard uses a lamp post - for support rather than for illumination." (David Ogilvy, "Confessions of an Advertising Man", 1971) 

Variations of the metaphor entered other fields as well:

"No business can safely run with accounts that are being used principally for support rather than for illumination." (Mark Thomas et al, "The Complete CEO",  2006)

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References:
[1] Quote Investigator (2014) People Use Statistics as a Drunk Uses a Lamppost - For Support Rather Than Illumination (link)
[2] Marcus Manilius translated by Alfred E Housman (1903) Astronomicon
[3] Alan L. Mackay (1977) The Harvest of a Quiet Eye
[4] Francis Yeats-Brown (1937) Lancer at Large
[5] G A N Lowndes (1937) The Silent Social Revolution: An Account of the Expansion of Public Education in England and Wales 1895-1935
[6] McEwene Hansard (1937) speech

Misquoted: Gauss on the Queen of Mathematics

The following two quotes from Carl Friedrich Gauss are frequently met in books on Mathematics and Science (sometimes with slight differences in formulation as they were translated from German):

"Mathematics is the Queen of the Sciences, and Arithmetic the Queen of Mathematics." 
"Mathematics is the Queen of the Sciences, and Number Theory the Queen of Mathematics."

The earliest occurrence of the quotes I met first in Eric T Bell's "Mathematics: Queen & Servant of Science" (1951), which is probably one of the most quoted sources for the quotes:

"Mathematics is Queen of the Sciences and Arithmetic the Queen of Mathematics. She often condescends to render service to astronomy and other natural sciences, but under all  circumstances the first place is her due."

However, doing a little research I found an earlier reference in John T Merz' "European Thought in the Nineteenth Century" Vol II (1903), who cites Sartorius von Waltershausen's "Gauss zum Gedächtniss" (1856) as source:

"Mathematics is the Queen of the Sciences, and arithmetic the Queen of Mathematics. She frequently condescends to do service for astronomy and other natural sciences, but to her belongs, under all circumstances, the foremost place."

Arithmetic, at least the way introduced in schools, is the study of numbers and their properties in report with the basic operations (addition, subtraction, multiplication, division, exponentiation and extraction of roots). In exchange, Number Theory appeared while studying the intrinsic properties of integers and integer-valued functions, what is known also as Higher Arithmetic. Even if the earliest discoveries date from early antiquity, the basis were put by Fermat, Euler, Gauss and others mathematicians, incorporating over time domains like Complex Analysis, Group theory or Galois theory.

According to Merriam-Webster, "Number Theory" was used for the first time around 1864 and it took some time until it was incorporated in mathematical texts. Arithmetic and Number Theory become synonymous in the 20th century (which might be strange for some). Thus, in some occurrence of the quote "Arithmetic" was replaced by "Number Theory" to reflect nowadays’ interpretation of Gauss' words. The two quotes seem to mean the same thing, though they probably need to be interpreted upon case through the historical context.  

'Queen' is used here metaphorically as an analogy between the meanings associated with a queen (ruler, fertility, authority), respectively the roles taken by Mathematics and Arithmetic in science. Therefore, a science considered as a queen could be seen as having a high fecundity of ideas and authority in another field. As "Queen of Science" were considered also Metaphysics (Immanuel Kant), Philosophy and even Theology. Also Physics and Chemistry have a statute of royalty.

The importance of Higher Arithmetic in respect to Mathematics, is stressed by Gauss in a letter to Dirichlet from 1838: 

"I place this part of Mathematics above all others (and have always done so)."

The idea is reiterated by David Hilbert half of century later:

"We thus see how arithmetic, the queen of mathematical science, has conquered large domains and has assumed the leadership. That this was not done earlier and more completely, seems to me to depend on the fact that the theory of numbers has only in quite recent times arrived at maturity." (David Hilbert, "Theorie der Algebraischen Zahlkörper", Bericht der Mathematiker-Vereinigung,' vol. IV, 1897)

Paraphrasing Godfrey H Hardy, even if Number Theory began as an experimental science, its role in the further development of Mathematics is important, worthily of the status of a 'queen'.

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Misquoted: Cicero on Probability is the Very Guide of Life

The "probability is the very guide of life" adage is attributed to Joseph Butler (1692-1752) and surprisingly (see [6]) Marcus Tullius Cicero (106-43 BC). Surprisingly because at first glance it is hard to believe that a concept relatively new as the one of probability was known to the antics, even if philosophical texts on divinity, fate, divination, causality or similar topics approached notions like chance or plausibility. 

The concept of probability entered in common usage only starting with 14th century via the French vocabulary, the term being derived directly from the Latin probabilitatem/probabilitas which belong to the family of words derived from 'probabilis' and translated as 'probable' or 'plausible'. 

Cicero used indeed 'probable' (Latin: probabilis) close to its actual meaning and provides a definition for it in "De Inventione" (cca. 91 and 88 BC), one of his earliest works, considered by historians as one of the main works on rhetoric:

"That is probable which for the most part usually comes to pass, or which is a part of the ordinary beliefs of mankind, or which contains in itself some resemblance to these qualities, whether such resemblance be true or false." [1]

Cicero used 'probable' also in "De Natura Deorum" (cca. 45 BC) with the same meaning:

"For we are not people who believe that there is nothing whatever which is true; but we say that some falsehoods are so blended with all truths, and have so great a resemblance to them, that there is no certain rule for judging of, or assenting to propositions; from which this maxim also follows, that many things are probable, which, though they are not evident to the senses, have still so persuasive and beautiful an aspect, that a wise man chooses to direct his conduct by them." [2]

"But, as it is the peculiar property of the Academy to interpose no personal judgment of its own, but to admit those opinions which appear most probable, to compare arguments, and to set forth all that may be reasonably stated in favour of each proposition; and so, without putting forth any authority of its own, to leave the judgment of the hearers free and unprejudiced; we will retain this custom, which has been handed down from Socrates; and this method, dear brother Quintus, if you please, we will adopt as often as possible in all our dialogues together." [2]

However, from 'probable' to 'probability' (Latin: probabilitas) there's an important leap of meaning. The use of 'probability' can be explained by translator's choice of using it in the detriment of terms like 'chance', 'odds' or 'possible', though searches in the online texts of the book in the translations of Charles D Yonge (1878) and Francis Brooks (1896) provided no proximate occurrences of the adage. 

Even more surprising, a similar form of the adage appears in Sextus Empiricus' "Outlines of Pyrrhonism"  (cca. 3rd century):

"Furthermore, as regards the End (the aim of life) we differ from the New Academy; for whereas the men who profess to conform to its doctrine use probability as the guide of life; we live in an undogmatic way by following the laws, customs, and natural affections." [3]

Do we have here another situation in which the translator assumed a choice of words or maybe in the original text there were indeed references to probability? Unfortunately, the available translation used as source for the quote is from Greek. 

The adage in its quoted form can be found in Joseph Butler's "The Analogy of Religion" (1736):

"Probable evidence, in its very nature, affords but an imperfect kind of information, and is to be considered as relative only to beings of limited capacities. For nothing which is the possible object of knowledge, whether past, present, or future, can be probable to an infinite Intelligence; since it cannot but be discerned absolutely as it is in itself, certainly true, or certainly false. To us, probability is the very guide of life." [4]

According to Butler we use probability to guide us in life when we deal with incomplete (imperfect) information, when we can't discern whether things are false or true and/or nuances of grey exist in between. For Cicero the things more probable tend to happen even if the senses can't discern which of the things are more probable, the wisdom of a person relying in the ability in identifying and evaluating the things probable. One can recognize in Cicero’s definition an early glimpse of entropy – the movement toward more probable states.

Despite the deep role propabilities play in life, we can still question adage's generalization - the degree to which we use probabilities to guide us in life. We do occasionally think in terms of the probabilities for an event to happen; we do tend to believe that what is more probable to happen will happen. Probably, the more we are caught in scientific endeavors, the more likely we use probabilities in decision making. Though, there's a limit to it, limit associated to the degree we are able to understand and use probabilities. 

I'd like to believe that Cicero's thoughts were in the proximate range of meaning associated with the early concept of probability, though a deeper analysis of the original text is needed and even then we can only advance suppositions.

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References:
[1] Marcus Tullius Cicero (cca. 91 and 88 BC) "De inventione", ["On Invention"]
[2] Marcus Tullius Cicero (45 BC) "De Natura Deorum" ["On the Nature of the Gods"]
[3] Sextus Empiricus (cca. 3rd century) "Outlines of Pyrrhonism"
[4] Joseph Butler (1736) "The Analogy of Religion, Natural and Revealed, to the Constitution and Course of Nature"
[5] Stanford Encyclopedia of Philosophy (2014) Probability in Medieval and Renaissance Philosophy [source]
[6] Kate L Roberts (1922) Hoyt's New Cyclopedia Of Practical Quotations

Misquoted: Ronald H Coase on Torturing the Data in Statistics

Statistics, through its methods, techniques and models rooted in mathematical reasoning, allows exploring, analyzing and summarizing a given set of data, being used to support decision-making, experiments, theories and ultimately to gain and communicate insights. When used adequately, statistics can prove to be a useful toolset, however as soon its use deviates from the mathematical rigor and principles on which it was built, it can be easily misused. Moreover, the results obtained with the help of statistics, can be easily denatured in communication, even when the statistical results are valid. 

The easiness with which statistics can be misused is probably best reflected in sayings like 'if you torture the data long enough it will confess'.  The formulation is attributed by several sources to the economist Ronald H Coase, however according to Coase the reference made by him in the 1960’s was slightly different: 'if you torture the data enough, nature will always confess' (see [1]). The latter formulation is not necessarily negative if one considers the persistence needed by researchers in revealing nature’s secrets. In exchange, the former formulation seems to stress only the negative aspect. 

The word 'torture' seems to be used instead of 'abuse', though metaphorically it has more weight, it draws the attention and sticks with the reader or audience. As the Quotes Investigator remarks [1], ‘torturing the data’ was employed as metaphor much earlier. For example, a 1933 article contains the following passage: 

"The evidence submitted by the committee from its own questionnaire warrants no such conclusion. To torture the data given in Table I into evidence supporting a twelve-hour minimum of professional training is indeed a statistical feat, but one which the committee accomplishes to its own satisfaction." ("The Elementary School Journal" Vol. 33 (7), 1933)

More than a decade earlier, in a similar context with Coase's quote, John Dewey remarked:

"Active experimentation must force the apparent facts of nature into forms different to those in which they familiarly present themselves; and thus make them tell the truth about themselves, as torture may compel an unwilling witness to reveal what he has been concealing." (John Dewey, "Reconstruction in Philosophy", 1920)

Torture was used metaphorically from 1600s, if we consider the following quote from Sir Francis Bacon’s 'Advancement of Learning':

"Another diversity of Methods is according to the subject or matter which is handled; for there is a great difference in delivery of the Mathematics, which are the most abstracted of knowledges, and Policy, which is the most immersed […], yet we see how that opinion, besides the weakness of it, hath been of ill desert towards learning, as that which taketh the way to reduce learning to certain empty and barren generalities; being but the very husks and shells of sciences, all the kernel being forced out and expulsed with the torture and press of the method." (Sir Francis Bacon, Advancement of Learning, 1605)

However a similar metaphor with closer meaning can be found almost two centuries later:

"One very reprehensible mode of theory-making consists, after honest deductions from a few facts have been made, in torturing other facts to suit the end proposed, in omitting some, and in making use of any authority that may lend assistance to the object desired; while all those which militate against it are carefully put on one side or doubted." (Henry De la Beche, "Sections and Views, Illustrative of Geological Phaenomena", 1830)

Probably, also the following quote from Goethe deservers some attention:

"Someday someone will write a pathology of experimental physics and bring to light all those swindles which subvert our reason, beguile our judgement and, what is worse, stand in the way of any practical progress. The phenomena must be freed once and for all from their grim torture chamber of empiricism, mechanism, and dogmatism; they must be brought before the jury of man's common sense." (Johann Wolfgang von Goethe)

Alternatives to Coase’s formulation were used in several later sources, replacing 'data' with 'statistics' or 'numbers':

"Beware of the problem of testing too many hypotheses; the more you torture the data, the more likely they are to confess, but confessions obtained under duress may not be admissible in the court of scientific opinion." (Stephen M Stigler, "Neutral Models in Biology", 1987)

"Torture numbers, and they will confess to anything." (Gregg Easterbrook, New Republic, 1989)

"[…] an honest exploratory study should indicate how many comparisons were made […] most experts agree that large numbers of comparisons will produce apparently statistically significant findings that are actually due to chance. The data torturer will act as if every positive result confirmed a major hypothesis. The honest investigator will limit the study to focused questions, all of which make biologic sense. The cautious reader should look at the number of ‘significant’ results in the context of how many comparisons were made." (James L Mills, "Data torturing", New England Journal of Medicine, 1993)

"This is true only if you torture the statistics until they produce the confession you want." (Larry Schweikart, "Myths of the 1980s Distort Debate over Tax Cuts", 2001) [source] 

"Even properly done statistics can’t be trusted. The plethora of available statistical techniques and analyses grants researchers an enormous amount of freedom when analyzing their data, and it is trivially easy to ‘torture the data until it confesses’." (Alex Reinhart, "Statistics Done Wrong: The Woefully Complete Guide", 2015)

There is also a psychological component attached to data or facts' torturing to fit the reality, tendency derived from the way the human mind works, the limits and fallacies associated with mind's workings. 

"What are the models? Well, the first rule is that you’ve got to have multiple models - because if you just have one or two that you’re using, the nature of human psychology is such that you’ll torture reality so that it fits your models, or at least you’ll think it does." (Charles Munger, 1994)

Independently of the formulation and context used, the fact remains: statistics (aka data, numbers) can be easily abused, and the reader/audience should be aware of it!

More quotes on Statistics' misusage at sql-troubles.blogspot.com.

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References:
[1] Quote Investigator (2021) "If You Torture the Data Long Enough, It Will Confess" [source]
[2] Wikiquote (2021) Ronald Coase [source]

Misquoted: Jacque Hadamard on Complex Numbers

"The shortest path between two truths in the real domain passes through the complex domain." 

Probably this is one of the most known quotes on complex numbers as it easy to remember and reflects the fact that important problems in algebra, analysis, geometry, number theory and physics can be simplified by considering them into the complex plane. Even if the quote reflects pretty good the idea, the actual quote comes from Jacque Hadamard’s "An Essay on the Psychology of Invention in the Mathematical Field" published in 1945:

"It has been written that the shortest and best way between two truths of the real domain often passes through the imaginary one."

[French: "On a pu écrire depuis que la voie la plus courte et la meilleure entre deux vérités du domaine réel passe souvent par le domaine imaginaire." (Jacques Hadamard, "Essai sur la psychologie de l'invention dans le domaine mathématique", 1945)]

Here Hadamard refers to Paul Painlevé, who in his "Analyse des travaux scientifiques" published in 1900 wrote as follows:

"The natural development of this work soon led the geometers in their studies to embrace imaginary as well as real values of the variable. The theory of Taylor series, that of elliptic functions, the vast field of Cauchy analysis, caused a burst of productivity derived from this generalization. It came to appear that, between two truths of the real domain, the easiest and shortest path quite often passes through the complex domain."

Actually, "la voie" can be translated as "the way" as well as "the path", the latter being closer to Painlevé’s quote, to whom the metaphor can be attributed to. Painlevé is not the first who stressed this important advantage of the complex numbers over the real ones, however his metaphor captures this aspect the best. 

"At the beginning I would ask anyone who wants to introduce a new function in analysis to clarify whether he intends to confine it to real magnitudes (real values of the argument) and regard the imaginary values as just vestigial - or whether he subscribes to my fundamental proposition that in the realm of magnitudes the imaginary ones a+b√−1 = a+bi have to be regarded as enjoying equal rights with the real ones. We are not talking about practical utility here; rather analysis is, to my mind, a self-sufficient science. It would lose immeasurably in beauty and symmetry from the rejection of any fictive magnitudes. At each stage truths, which otherwise are quite generally valid, would have to be encumbered with all sorts of qualifications." (Carl F Gauss, [letter to Bessel] 1811)

"The origin and the immediate purpose for the introduction of complex number into mathematics is the theory of creating simpler dependency laws (slope laws) between complex magnitudes by expressing these laws through numerical operations. And, if we give these dependency laws an expanded range by assigning complex values to the variable magnitudes, on which the dependency laws are based, then what makes its appearance is a harmony and regularity which is especially indirect and lasting." (Bernhard Riemann, "Grundlagen für eine allgemeine Theorie der Funktionen einer veränderlichen complexen Grösse", 1851)

"The conception of the inconceivable [imaginary], this measurement of what not only does not, but cannot exist, is one of the finest achievements of the human intellect. No one can deny that such imaginings are indeed imaginary. But they lead to results grander than any which flow from the imagination of the poet. The imaginary calculus is one of the master keys to physical science. These realms of the inconceivable afford in many places our only mode of passage to the domains of positive knowledge. Light itself lay in darkness until this imaginary calculus threw light upon light. And in all modern researches into electricity, magnetism, and heat, and other subtile physical inquiries, these are the most powerful instruments." (Thomas Hill, “The Imagination in Mathematics”, North American Review Vol. 85, 1857)

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Misquoted: Herbert G Wells on Mathematical Literacy

"Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write."

The above quote on statistical literacy is often attributed to Herbert G Wells though it belongs to the statistician Samuel S Wilks, who in a 1951 presidential address was paraphrasing Wells:

"Perhaps H. G. Wells was right when he said ‘statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write’!" [4]

The original quote comes from “Mankind in the Making”, first published in 1903 (and not in 1911 as Wikipedia states):

"The great body of physical science, a great deal of the essential fact of financial science, and endless social and political problems are only accessible and only thinkable to those who have had a sound training in mathematical analysis, and the time may not be very remote when it will be understood that for complete initiation as an efficient citizen of one of the new great complex world-wide States that are now developing, it is as necessary to be able to compute, to think in averages and maxima and minima, as it is now to be able to read and write." [1]

Even if Wells mentions averages, maxima and minima, tools of statistics, the text refers to mathematical analysis and not statistics. Wilk’s paraphrasing makes sense in nowadays contexts, and seems somehow natural, even if statistical literacy is more about understanding and (critically) evaluating statements that involve rates and percentages.

Another paraphrasing of the same quote and probably closer to the essence of statistical literacy can be found in George A Lundberg paper published in 1940, however without giving credit to Wells:

"The time is perhaps at hand when it will be recognized that for intelligent living in modern society it is as necessary to be able to think in averages, percentages, and deviations as it is to be able to read and write." [2]

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References:
[1] “Mankind in the Making”, by Herbert G Wells, 1903 [Source]
[2] “Statistics in Modern Social Thought”, by George A Lundberg [in “Contemporary Social Theory”, Ed. by H. E. Barnes, H. Becker & F. Becker, 1940] [Source]
[3] “The H. G. Wells Quote on Statistics: A Question of Accuracy”, by James W Tankard Jr., Historia Mathematics 6, 1979 [Source]
[4] “Undergraduate Statistical Education”, by  Samuel S Wilks, Journal of the American Statistical Association, Vol. 46, 1951 [Source]