Statistical Tools V: Roulette

"As an instrument for selecting at random, I have found nothing superior to dice. It is most tedious to shuffle cards thoroughly be- tween each successive draw, and the method of mixing and stirring up marked balls in a bag is more tedious still. A teetotum or some form of roulette is preferable to these, but dice are better than all. When they are shaken and tossed in a basket, they hurtle so variously against one another and against the ribs of the basket-work that they tumble wildly about, and their positions at the outset afford no perceptible clue to what they will be after even a single good shake and toss." (Francis Galton, Nature vol. 42, 1890)

"In no subject is there a rule, compliance with which will lead to new knowledge or better understanding. Skillful observations, ingenious ideas, cunning tricks, daring suggestions, laborious calculations, all these may be required to advance a subject. Occasionally the conventional approach in a subject has to be studiously followed; on other occasions it has to be ruthlessly disregarded. Which of these methods, or in what order they should be employed is generally unpredictable. Analogies drawn from the history of science are frequently claimed to be a guide; but, as with forecasting the next game of roulette, the existence of the best analogy to the present is no guide whatever to the future. The most valuable lesson to be learnt from the history of scientific progress is how misleading and strangling such analogies have been, and how success has come to those who ignored them." (Thomas Gold, "Cosmology", 1956) 

“[In statistics] you have the fact that the concepts are not very clean. The idea of probability, of randomness, is not a clean mathematical idea. You cannot produce random numbers mathematically. They can only be produced by things like tossing dice or spinning a roulette wheel. With a formula, any formula, the number you get would be predictable and therefore not random. So as a statistician you have to rely on some conception of a world where things happen in some way at random, a conception which mathematicians don’t have.” (Lucien LeCam, [interview] 1988)

"Losing streaks and winning streaks occur frequently in games of chance, as they do in real life. Gamblers respond to these events in asymmetric fashion: they appeal to the law of averages to bring losing streaks to a speedy end. And they appeal to that same law of averages to suspend itself so that winning streaks will go on and on. The law of averages hears neither appeal. The last sequence of throws of the dice conveys absolutely no information about what the next throw will bring. Cards, coins, dice, and roulette wheels have no memory." (Peter L Bernstein, "Against the Gods: The Remarkable Story of Risk", 1996)

"The dice and the roulette wheel, along with the stock market and the bond market, are natural laboratories for the study of risk because they lend themselves so readily to quantification; their language is the language of numbers." (Peter L Bernstein, "Against the Gods: The Remarkable Story of Risk", 1996)

"The theory of probability can define the probabilities at the gaming casino or in a lottery - there is no need to spin the roulette wheel or count the lottery tickets to estimate the nature of the outcome - but in real life relevant information is essential. And the bother is that we never have all the information we would like. Nature has established patterns, but only for the most part. Theory, which abstracts from nature, is kinder: we either have the information we need or else we have no need for information." (Peter L Bernstein, "Against the Gods: The Remarkable Story of Risk", 1996)

“Sequences of random numbers also inevitably display certain regularities. […] The trouble is, just as no real die, coin, or roulette wheel is ever likely to be perfectly fair, no numerical recipe produces truly random numbers. The mere existence of a formula suggests some sort of predictability or pattern.” (Ivars Peterson, “The Jungles of Randomness: A Mathematical Safari”, 1998)

"The chance events due to deterministic chaos, on the other hand, occur even within a closed system determined by immutable laws. Our most cherished examples of chance - dice, roulette, coin-tossing – seem closer to chaos than to the whims of outside events. So, in this revised sense, dice are a good metaphor for chance after all. It's just that we've refined our concept of randomness. Indeed, the deterministic but possibly chaotic stripes of phase space may be the true source of probability." (Ian Stewart, "Does God Play Dice: The New Mathematics of Chaos", 2002)

"People sometimes appeal to the ‘law of averages’ to justify their faith in the gambler’s fallacy. They may reason that, since all outcomes are equally likely, in the long run they will come out roughly equal in frequency. However, the next throw is very much in the short run and the coin, die or roulette wheel has no memory of what went before." (Alan Graham, "Developing Thinking in Statistics", 2006)

"Another kind of error possibly related to the use of the representativeness heuristic is the gambler’s fallacy, otherwise known as the law of averages. If you are playing roulette and the last four spins of the wheel have led to the ball’s landing on black, you may think that the next ball is more likely than otherwise to land on red. This cannot be. The roulette wheel has no memory. The chance of black is just what it always is. The reason people tend to think otherwise may be that they expect the sequence of events to be representative of random sequences, and the typical random sequence at roulette does not have five blacks in a row." (Jonathan Baron, "Thinking and Deciding" 4th Ed, 2008)

"A very different - and very incorrect - argument is that successes must be balanced by failures (and failures by successes) so that things average out. Every coin flip that lands heads makes tails more likely. Every red at roulette makes black more likely. […] These beliefs are all incorrect. Good luck will certainly not continue indefinitely, but do not assume that good luck makes bad luck more likely, or vice versa." (Gary Smith, "Standard Deviations", 2014)

Stephen M Stigler - Collected Quotes

"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, "Testing Hypotheses or fitting Models? Another Look at Mass Extinctions" [in "Neutral Models in Biology"], 1987)

"[…] good statistics re- quires a conversation between scientists and mathematical statisticians." (Stephen M Stigler, Statistics on the Table: the history of statistical concepts and methods, 1999) 

"[…] if statisticians are to be able to understand the limits and generality of their methodology, its worth in different circumstances and the means of adapting it to others, then it will need more than just mathematical statistics, but it will surely not need less. But neither should mathematical statisticians be complacent; above all it is the conversation between theory and applications that is crucially important." (Stephen M Stigler, Statistics on the Table: the history of statistical concepts and methods, 1999)

"No scientific discovery is named after its original discoverer." (Stephen M. Stigler, Statistics on the Table: the history of statistical concepts and methods, 1999) 

"The theory of errors held that a normal population distribution would be produced through the accumulation of a large number of small accidental deviations, and there seemed to be no other way to account for the ubiquitous appearance of that normal outline." (Stephen M. Stigler, Statistics on the Table: the history of statistical concepts and methods, 1999) 

"The recurrence of regression fallacies is testimony to its subtlety, deceptive simplicity, and, I speculate, to the wide use of the word regression to describe least squares fitting of curves, lines, and surfaces." (Stephen M Stigler, Statistics on the Table: the history of statistical concepts and methods, 1999) 

"The whole of the nineteenth- century theory of errors was keyed to this point: observation = truth + error. Without an objective truth, this sort of a split would be impossible, for where would error end and truth begin?" (Stephen M Stigler, Statistics on the Table: the history of statistical concepts and methods, 1999) 

"There was a fundamental difference between the application of statistical methods in astronomy, in experimental psychology, and in the social sciences, and this difference had a profound effect upon the spread of the methods and the pace of their adoption. Astronomy could exploit a theory exterior to the observations, a theory that defined an object for their inference. Truth was-or so they thought-well differentiated from error. Experimental psychologists could, through experimental design, create a baseline for measurement, and control the factors important for their investigation. For them the object of their inference-usually the difference between a treatment and a control group, or between two treatments-was created in the design of the experiment." (Stephen M Stigler, Statistics on the Table: the history of statistical concepts and methods, 1999)

Francis Y Edgeworth - Collected Quotes

"[…] in the Law of Errors we are concerned only with the objective quantities about which mathematical reasoning is ordinarily exercised; whereas in the Method of Least Squares, as in the moral sciences, we are concerned with a psychical quantity - the greatest possible quantity of advantage." (Francis Y Edgeworth, "The method of least squares", 1883)

"It may be replied that the principles of greatest advantage and greatest proba￾bility do not coincide in .qeneral; that here, as in other depart￾ments of action~ when there is a discrepancy between the principle of utility and any other rul% the former should have precedence."  (Francis Y Edgeworth, "The method of least squares", 1883)

"The probable error, the mean error, the mean square of error, are forms divined to resemble in an essential feature the real object of which they are the imperfect symbols - the quantity of evil, the diminution of pleasure, incurred by error. The proper symbol, it is submitted, for the quantity of evil incurred by a simple error is not any power of the error, nor any definite function at all, but an almost arbitrary function, restricted only by the conditions that it should vanish when the independent variable, the error, vanishes, and continually increase with the increase of the error." (Francis Y Edgeworth, "The method of least squares", 1883)

"Our reasoning appears to become more accurate as our ignorance becomes more complete; that when we have embarked upon chaos we seem to drop down into a cosmos."  (Francis Y Edgeworth, "The Philosophy of Chance", Mind Vol. 9, 1884) 

"Probability may be described, agreeably to general usage, as importing partial incomplete belief." (Francis Y Edgeworth, "The Philosophy of Chance", Mind Vol. 9, 1884)

"Observations and statistics agree in being quantities grouped about a Mean; they differ, in that the Mean of observations is real, of statistics is fictitious. The mean of observations is a cause, as it were the source from which diverging errors emanate. The mean of statistics is a description, a representative quantity put for a whole group, the best representative of the group, that quantity which, if we must in practice put one quantity for many, minimizes the error unavoidably attending such practice. Thus measurements by the reduction of which we ascertain a real time, number, distance are observations. Returns of prices, exports and imports, legitimate and illegitimate marriages or births and so forth, the averages of which constitute the premises of practical reasoning, are statistics. In short, observations are different copies of one original; statistics are different originals affording one ‘generic portrait’. Different measurements of the same man are observations; but measurements of different men, grouped round l’homme moyen, are prima facie at least statistics." (Francis Y Edgeworth, 1885)

"What is required for the elimination of chance is not that the raw material of our observations should fulfill the law of error; but that they should be constant to any law." (Francis Y Edgeworth, 1885)

"The Calculus of Probabilities is an instrument which requires the living hand to direct it" (Francis Y Edgeworth, 1887)

"The swarm of probabilities flying hither and thither, does not settle down on any particular point" (Francis Y Edgeworth, 1887)

"However we define error, the idea of calculating its extent may appear paradoxical. A science of errors seems a contradiction in terms." (Francis Y Edgeworth, "The Element of Chance in Competitive Examinations", Journal of the Royal Statistical Society Vol. 53, 1890) 

"What real and permanent tendencies there are lie hid beneath the shifting superfices of chance, as it were a desert in which the inexperienced traveller mistakes the temporary agglomerations of drifting sand for the real configuration of the ground" (Francis Y Edgeworth, 1898)

"[...] the great objection to the geometric mean is its cumbrousness." (Francis Y Edgeworth, 1906)

On Least Squares Method

"From the foregoing we see that the two justifications each leave something to be desired. The first depends entirely on the hypothetical form of the probability of the error; as soon as that form is rejected, the values of the unknowns produced by the method of least squares are no more the most probable values than is the arithmetic mean in the simplest case mentioned above. The second justification leaves us entirely in the dark about what to do when the number of observations is not large. In this case the method of least squares no longer has the status of a law ordained by the probability calculus but has only the simplicity of the operations it entails to recommend it." (Carl Friedrich Gauss, "Anzeige: Theoria combinationis observationum erroribus minimis obnoxiae: Pars prior", Göttingische gelehrte Anzeigen, 1821)

"[…] in the Law of Errors we are concerned only with the objective quantities about which mathematical reasoning is ordinarily exercised; whereas in the Method of Least Squares, as in the moral sciences, we are concerned with a psychical quantity - the greatest possible quantity of advantage." (Francis Y Edgeworth, "The method of least squares", 1883) 

"The method of least squares is used in the analysis of data from planned experiments and also in the analysis of data from unplanned happenings. The word 'regression' is most often used to describe analysis of unplanned data. It is the tacit assumption that the requirements for the validity of least squares analysis are satisfied for unplanned data that produces a great deal of trouble." (George E P Box, "Use and Abuse of Regression", 1966)

"At the heart of probabilistic statistical analysis is the assumption that a set of data arises as a sample from a distribution in some class of probability distributions. The reasons for making distributional assumptions about data are several. First, if we can describe a set of data as a sample from a certain theoretical distribution, say a normal distribution (also called a Gaussian distribution), then we can achieve a valuable compactness of description for the data. For example, in the normal case, the data can be succinctly described by giving the mean and standard deviation and stating that the empirical (sample) distribution of the data is well approximated by the normal distribution. A second reason for distributional assumptions is that they can lead to useful statistical procedures. For example, the assumption that data are generated by normal probability distributions leads to the analysis of variance and least squares. Similarly, much of the theory and technology of reliability assumes samples from the exponential, Weibull, or gamma distribution. A third reason is that the assumptions allow us to characterize the sampling distribution of statistics computed during the analysis and thereby make inferences and probabilistic statements about unknown aspects of the underlying distribution. For example, assuming the data are a sample from a normal distribution allows us to use the t-distribution to form confidence intervals for the mean of the theoretical distribution. A fourth reason for distributional assumptions is that understanding the distribution of a set of data can sometimes shed light on the physical mechanisms involved in generating the data." (John M Chambers et al, "Graphical Methods for Data Analysis", 1983)

"Least squares' means just what it says: you minimise the (suitably weighted) squared difference between a set of measurements and their predicted values. This is done by varying the parameters you want to estimate: the predicted values are adjusted so as to be close to the measurements; squaring the differences means that greater importance is placed on removing the large deviations." (Roger J Barlow, "Statistics: A guide to the use of statistical methods in the physical sciences", 1989)

"Principal components and principal factor analysis lack a well-developed theoretical framework like that of least squares regression. They consequently provide no systematic way to test hypotheses about the number of factors to retain, the size of factor loadings, or the correlations between factors, for example. Such tests are possible using a different approach, based on maximum-likelihood estimation." (Lawrence C Hamilton, "Regression with Graphics: A second course in applied statistics", 1991)

"Fuzzy models should make good predictions even when they are asked to predict on regions that were not excited during the construction of the model. The generalization capabilities can be controlled by an appropriate initialization of the consequences (prior knowledge) and the use of the recursive least squares to improve the prior choices. The prior knowledge can be obtained from the data." (Jairo Espinosa et al, "Fuzzy Logic, Identification and Predictive Control", 2005)

"Often when people relate essentially the same variable in two different groups, or at two different times, they see this same phenomenon - the tendency of the response variable to be closer to the mean than the predicted value. Unfortunately, people try to interpret this by thinking that the performance of those far from the mean is deteriorating, but it’s just a mathematical fact about the correlation. So, today we try to be less judgmental about this phenomenon and we call it regression to the mean. We managed to get rid of the term 'mediocrity', but the name regression stuck as a name for the whole least squares fitting procedure - and that’s where we get the term regression line." (Richard D De Veaux et al, "Stats: Data and Models", 2016)

Richard Brodie - Collected Quotes

"A belief system, through its memes, can spread in a way that looks just like a conspiracy without any conscious intention on the part of the participants." (Richard Brodie, "Virus of the Mind", 2009)

"A meme is a replicator that uses the medium of our minds to replicate. Meme evolution happens because our minds are good at copying and innovating - ideas, behaviors, tunes, shapes, structures, and so on." (Richard Brodie, "Virus of the Mind", 2009)

"A mind is a terrible thing to waste." (Richard Brodie, "Virus of the Mind", 2009)

"A mutation is an error in copying. It produces a defective -  or possibly improved in some sense - copy instead of an exact duplicate of the original." (Richard Brodie, "Virus of the Mind", 2009)

"A virus is anything that takes external copying equipment and puts it to work making copies of itself." (Richard Brodie, "Virus of the Mind", 2009)

"A virus of the mind is something out in the world that infects people with memes. Those memes, in turn, influence the infected people’s behavior so that they help perpetuate and spread the virus." (Richard Brodie, "Virus of the Mind", 2009)

"All cultural institutions, regardless of their initial design or intention (if any), evolve to have but one goal: to perpetuate themselves." (Richard Brodie, "Virus of the Mind", 2009)

"Associations are connections between memes. When you are programmed with an association-meme, the presence of one thing triggers a thought or feeling about something else. This causes a change in your behavior, which can ultimately spread the meme to another mind." (Richard Brodie, "Virus of the Mind", 2009)

"Beliefs are like cow paths. The more often you walk down a path, the more it looks like the right way to go." (Richard Brodie, "Virus of the Mind", 2009)

"Complicated things arise naturally out of the forces of evolution. No conscious intention is necessary." (Richard Brodie, "Virus of the Mind", 2009)

"Evolution is a scientific model of how things become more complex; entropy describes how things become simpler. They are the creative and the destructive forces of the universe." (Richard Brodie, "Virus of the Mind", 2009)

"Evolution requires two things: replication, with a certain degree of fidelity; and innovation, or a certain degree of infidelity." (Richard Brodie, "Virus of the Mind", 2009)

"Gaining someone’s trust is an effective way to bypass their skepticism and make it possible to program them with new memes." (Richard Brodie, "Virus of the Mind", 2009)

"If we want to combat the mind viruses responsible for the decline of culture, we need to be conscious of our own programming, consciously adopting memes that take us in the direction we want to go." (Richard Brodie, "Virus of the Mind", 2009)

"If you currently believe in any concepts or subcultures or dogmas that meet these requirements, and you didn’t consciously choose to program yourself with these memes, you are infected with a mind virus." (Richard Brodie, "Virus of the Mind", 2009)

"Memes enter our minds without our permission. They become part of our mental programming and influence our lives without our even being aware of it." (Richard Brodie, "Virus of the Mind", 2009)

"Memetics is the study of the workings of memes: how they interact, replicate, and evolve." (Richard Brodie, "Virus of the Mind", 2009)

"One of the ways the memes you are programmed with greatly affect your future is through self-fulfilling prophecy." (Richard Brodie, "Virus of the Mind", 2009)

"Strategies are beliefs about cause and effect. When you are programmed with a strategy-meme, you unconsciously believe behaving a certain way is likely to produce a certain effect. That behavior may trigger a chain of events that results in spreading the strategy-meme to another mind." (Richard Brodie, "Virus of the Mind", 2009)

"Taking over bits of your mind and pulling you in different directions, mind viruses distract you from what’s most important to you in life and cause confusion, stress, and even despair." (Richard Brodie, "Virus of the Mind", 2009)

"The evolution of ideas, culture, and society revolves around the selfish meme just as the evolution of species revolves around the selfish gene." (Richard Brodie, "Virus of the Mind", 2009)

"The most interesting thing about memes is not whether they’re true or false; it’s that they are the building blocks of your mind." (Richard Brodie, "Virus of the Mind", 2009)

"The most popular and prevalent parts of our culture are the most effective at copying memes." (Richard Brodie, "Virus of the Mind", 2009)

"The universe contains many mechanisms for copying and dispersing information, and viruses are some of the things that are often copied and dispersed." (Richard Brodie, "Virus of the Mind", 2009)

"The very act of asking people a question can cause them to create or reinforce a meme in their minds. Asking enough of the right questions can actually change someone’s belief system, and therefore influence the person’s behavior." (Richard Brodie, "Virus of the Mind", 2009)

"The world is full of memes spread by mind viruses, all competing for a share of your mind, your perception, your attention. They care nothing for your well-being, but instead add to your confusion and subtract from your fulfillment." (Richard Brodie, "Virus of the Mind", 2009)

"Those new memes conflict with your old ones, and a mental tension is created. Your mind wants to resolve the conflict. It does so by creating a new meme." (Richard Brodie, "Virus of the Mind", 2009)

"Truth is not one of the strong selectors for memes." (Richard Brodie, "Virus of the Mind", 2009)

"Viewed through memetics, all values, morals, traditions, and ideas with respect to God and rights are the result of meme evolution. And meme evolution is guided by our genetic tendencies, which in turn evolved around sex." (Richard Brodie, "Virus of the Mind", 2009)

"We can either give up on the hope of having a fulfilling life and a better world or consciously choose which memes to program ourselves with and which we want to spread." (Richard Brodie, "Virus of the Mind", 2009)

"We have an enormous hunger to understand the world around us, which was extremely useful when the world was simple and mostly consisted of physical rewards and dangers. In the society of memes, however, we are constantly trying to make sense of things that simply have no sense." (Richard Brodie, "Virus of the Mind", 2009)

"You can be conditioned, through repetition, to acquire new distinction-memes that make reality look different to you and provide reinforcing evidence that keeps those distinction-memes in place." (Richard Brodie, "Virus of the Mind", 2009)

On Culture (Unsourced)

"[...] every culture in the world has had its own unique history and we can not therefore say that any culture observable in the present day world is an earlier form of any other." (Charles W Hart)

"He who cherishes the values of culture cannot fail to be a pacifist." (Albert Einstein)

"Human creative work is by excellence one of expression. The deep human desire is to be understood by other peoples. This expression which succeeds to be communicated is just what we call culture." (Grigore C Moisil)

"More and more, science has become not only increasingly necessary as a foundation for professional skill, but has come to be regarded as the most valuable instrument of culture." (Henry P Smith)

"Our models of communication [...] create what we disingenuously pretend they merely describe. As a result our science is [...] a reflexive one. We not only describe behavior; we create a particular corner of culture - culture that determines, in part, the kind of communicative world we inhabit." (James W Carey)

"Our will and testament has come about out of a vigorous conviction that a nation that does not highly esteem mathematical thought can never be capable of achieving the highest cultural goals and thereby enjoy the international respect which, in the long term, is an effective means of maintaining our position in the world, as well as asserting our right to live our own lives." (M Gustav Mittag-Leffler)

"Science with its strict analysis of the facts, its persevering search for new, more consummate truths, and its relentless struggle against discovered mistakes and prejudices - science must saturate all or technics, our culture, and everyday life." (Abram F Joffe)

"The acquiring of culture is the developing of an avid hunger for knowledge and beauty." (Jesse L Bennett [attributed])

"The highest culture is not obtained from the teacher when at school or college, so much as by our ever-diligent self-education when we become men." (Samuel Smiles)

"The mathematics of rhythm are universal. They don't belong to any particular culture." (John McLaughlin)

"The trademark of modern culture is science; if you can fake this, you’ve got it made." (Mario Bunge)

"We are caged by our cultural programming. Culture is a mass hallucination, and when you step outside the mass hallucination you see it for what it’s worth." (Terence McKenna)

On Culture (From Fiction to Science Fiction)

"The great law of culture is: Let each become all that he was created capable of being." (Thomas Carlyle, "Jean Paul Friedrich Richter" (1827)

"This history of culture will explain to us the motives, the conditions of life, and the thought of the writer or reformer." (Lev N Tolstoy, "War and Peace", 1867)

"Culture is then properly described not as having its origin in curiosity, but as having its origin in the love of perfection; it is a study of perfection." (Matthew Arnold, "Culture and Anarchy", 1869)

"Not a having and a resting, but a growing and a becoming is the character of perfection as culture conceives it." (Matthew Arnold, "Culture and Anarchy", 1869)

"The more elevated a culture, the richer its language. The number of words and their combinations depends directly on a sum of conceptions and ideas; without the latter there can be no understandings, no definitions, and, as a result, no reason to enrich a language." (Anton Chekhov, [letter to A.S. Suvorin] 1892)

"As the traveller who has been once from home is wiser than he who has never left his own door step, so a knowledge of one other culture should sharpen our ability to scrutinise more steadily, to appreciate more lovingly, our own." (Margaret Mead, "Coming of Age in Samoa", 1928)

"The worst difficulties from which we suffer do not come from without. They come from within [...] They come from a peculiar type of brainy people, always found in our country, who if they add something to our culture, take much from its strength. Our difficulties come from the mood of unwarrantable self-abasement into which we have been cast by a powerful section of our own intellectuals." (Winston Churchill, [speech] 1933)

"There are and have been worlds and cultures without end, each nursing the proud illusion that it is unique in space and time. There have been men without number suffering from the same megalomania; men who imagined themselves unique, irreplaceable, irreproducible. There will be more [...] more plus infinity. (Alfred Bester, "The Demolished Man", 1953)

"You don't have to burn books to destroy a culture. Just get people to stop reading them." (Ray Bradbury, "Fahrenheit 451", 1953)

"No one person can change a whole culture." (Poul Anderson, "Ghetto", 1954)

"When two alien cultures meet, the stronger must transform the weaker with love or hate." (Damon Knight, "Stranger Station", 1956)

"The meeting between ignorance and knowledge, between brutality and culture - it begins in the dignity with which we treat our dead." (Frank Herbert, "Dune", 1965)

"Homo can truly be called sapiens when he practices his specialty of being unspecialized. His repeated attempts to freeze himself into an all-answering pattern or culture or ideology, or whatever he has named it, have repeatedly brought ruin. Give him the pragmatic business of making his living, and he will usually do rather well. He adapts, within broad limits." (Poul Anderson, "The Queen of Air and Darkness", 1971)

"No culture as yet has actually forgotten history because no culture has really possessed more than fragments of it." (Edgar Pangborn, "Mount Charity", 1971)

"When one culture has the big guns and the other has none, there is a certain predictability about the outcome." (Joanna Russ, ‘"When It Changed", 1972)

"Man creates culture and through culture creates himself." (Pope John Paul II, "Osservatore Romano", 1980)

"A dying culture invariably exhibits personal rudeness. Bad manners. Lack of consideration for others in minor matters. A loss of politeness, of gentle manners, is more significant than is a riot." (Robert A. Heinlein, "Friday", 1982)

"Love was always a word that covered too much territory, from loving a spouse to loving a hobby or abstract justice, and the emotion-mongers of popular entertainment portrayed it as everlasting and exclusive. In a culture under stress the truth could not be concealed by sentimental fluff. The Greenhouse people learned to appreciate love without glorifying it." (George Turner, "Drowning Towers", 1987)

"Some cultures send their young people to the desert to seek visions and guidance, searching for true thinking spawned by the openness of the place, the loneliness, the beauty of emptiness." (Pat Murphy, "Rachel in Love", 1987)

"Most people don’t listen. They use the time when someone else is speaking to think of what they’re going to say next. True Listeners have always been revered among oral cultures, and prized for their rarity value." (Terry Pratchett, "Pyramids", 1989)

"As the soil, however rich it may be, cannot be productive without culture, so the mind without cultivation can never produce good fruit." (Seneca)

"Culture is acquainting ourselves with the best that has been known and said in the world, and thus with the history of the human spirit." (Matthew Arnold)

"Culture is the arts elevated to a set of beliefs." (Thomas Wolfe)

"Culture of the mind must be subservient to the heart." (Mohandas Gandhi)

"In rhetoric, this art of omission is a chief secret of power, and, in general, it is proof of high culture, to say the greatest matters in the simplest way. Veracity first of all, and forever." (Ralph W Emerson)

"It surprises me how our culture can destroy curiosity in the most curious of all animals - human beings." (Paul Maclean)

"Language is the road of a culture. It tells you where its people come from and where they are going." (Rita Mae Brown)

"No culture can live if it attempts to be exclusive." (Mohandas Gandhi)

"Noble life demands a noble architecture of noble uses of noble men. Lack of culture means what it has always meant: ignoble civilization and therefore imminent downfall." (Frank Lloyd Wright)

On Culture (1970-1979)

"If observation be the soil, reading is the manure of intellectual culture." (Daniel Drake, "Physician to the West: Selected Writings of Daniel Drake on Science and Society", 1970)

"Surely one of the most important characteristics of a scientific, introverted, specialized, hence infinitely intellectual culture is its drive toward, and faith in, total “awareness”. Awareness of almost every conceivable factor influencing almost every conceivable situation is our characteristic panacea or cure-all. In this sense, gnosis, the total consciousness, and self-consciousness are the major goals of our secular culture. We really believe that if we know or are aware of everything, if we can understand all relevant causes and factors, we can control everything." (Langdon Gilkey, "Religion and the Scientific Future: Reflections on Myth, Science, and Theology", 1970)

"What a lost person needs is a map of the territory, with his own position marked on it so he can see where he is in relation to everything else. Literature is not only a mirror; it is also a map, a geography of the mind. Our literature is one such map, if we can learn to read it as our literature, as the product of who and where we have been. We need such a map desperately, we need to know about here, because here is where we live. For the members of a country or a culture, shared knowledge of their place, their here, is not a luxury but a necessity. Without that knowledge we will not survive." (Margaret Atwood, "Survival: A Thematic Guide to Canadian Literature", 1972)

"[…] science is not sacrosanct. The restrictions it imposes (and there are many such restrictions though it is not easy to spell them out) are not necessary in order to have general coherent and successful views about the world. There are myths, there are the dogmas of theology, there is metaphysics, and there are many other ways of constructing a worldview. It is clear that a fruitful exchange between science and such ‘nonscientific’ world-views will be in even greater need of anarchism than is science itself. Thus, anarchism is not only possible, it is necessary both for the internal progress of science and for the development of our culture as a whole." (Paul Feyerabend, "Against Method", 1975)

"The ‘culture’ of a group or class, is the peculiar and distinctive ‘way of life’ of the group or class, the meanings, values and ideas embodied in institutions, in social relations, in systems of beliefs, in mores and customs, in the uses of objects and material life. Culture is the distinctive shapes in which this material and social organization of life expresses itself. A culture includes the ‘maps of meaning’ which make things intelligible to its members. These ‘maps of meaning’ are not simply carried around in the head: they are objectivated in the patterns of social organization and relationship through which the individual becomes a ‘social individual’. Culture is the way the social relations of a group are structured and shaped: but it is also the way those shapes are experienced, understood and interpreted." (John Clark et al "Subcultures, Cultures and Class", 1975)

"The influence of modern physics goes beyond technology. It extends to the realm of thought and culture where it has led to a deep revision in man's conception of the universe and his relation to it." (Fritjof Capra, "The Tao of Physics: An Exploration of the Parallels Between Modern Physics and Eastern Mysticism", 1975)

"I think the most significant creative activities of our or any other human culture - legal and ethical systems, art and music, science and technology - were made possible only through the collaborative work of the left and right cerebral hemispheres. [...] We might say that human culture is the function of corpus callosum." (Carl Sagan, "The Dragons of Eden: Speculations on the Evolution of Human", 1977)

"It is hard for us today to assimilate all the new ideas that are being suggested in response to the new information we have. We must remember that our picture of the universe is based not only on our scientific knowledge but also on our culture and our philosophy. What new discoveries lie ahead no one can say. There may well be civilizations in other parts of our galaxy or in other galaxies that have already accomplished much of what lies ahead for mankind. Others may just be beginning. The universe clearly presents an unending challenge." (Necia H Apfel & J Allen Hynek, "Architecture of the Universe", 1979)

On Culture (-1949)

"It is the destiny of our race to become united into one great body, thoroughly connected in all its parts, and possessed of similar culture. Nature, and even the passions and vices of Man, have from the beginning tended towards this end. A great part of the way towards it is already passed, and we may surely calculate that it will in time be reached." (Johann G Fichte, "The Vocation of Man", 1800)

"The highest possible stage in moral culture is when we recognize that we ought to control our thoughts." (Charles Darwin, "The Descent of Man", 1871)

"The man who is guided by concepts and abstractions only succeeds by such means in warding off misfortune, without ever gaining any happiness for himself from these abstractions. And while he aims for the greatest possible freedom from pain, the intuitive man, standing in the midst of a culture, already reaps from his intuition a harvest of continually inflowing illumination, cheer, and redemption - in addition to obtaining a defense against misfortune. To be sure, he suffers more intensely, when he suffers; he even suffers more frequently, since he does not understand how to learn from experience and keeps falling over and over again into the same ditch." (Friedrich Nietzsche," On Truth and Lie in an Extra-Moral Sense", 1873)

"The culture of the geometric imagination, tending to produce precision in remembrance and invention of visible forms will, therefore, tend directly to increase the appreciation of works of belles-letters." (Thomas Hill, "Uses of Mathesis", Bibliotheca Sacra Vol. 32, 1875)

"The more elevated a culture, the richer its language. The number of words and their combinations depends directly on a sum of conceptions and ideas; without the latter there can be no understandings, no definitions, and, as a result, no reason to enrich a language." (Anton Chekhov, [letter to A.S. Suvorin] 1892) 

"Our science, in contrast with others, is not founded on a single period of human history, but has accompanied the development of culture through all its stages. Mathematics is as much interwoven with Greek culture as with the most modern problems in Engineering. She not only lends a hand to the progressive natural sciences but participates at the same time in the abstract investigations of logicians and philosophers." (Felix Klein, "Klein und Riecke: Ueber angewandte Mathematik und Physik" 1900)

"It is true that mathematics, owing to the fact that its whole content is built up by means of purely logical deduction from a small number of universally comprehended principles, has not unfittingly been designated as the science of the self-evident. Experience however, shows that for the majority of the cultured, even of scientists, mathematics remains the science of the incomprehensible." (Alfred Pringsheim, "Jahresbericht der Deutschen Mathematiker Vereinigung Ueber Wert and angeblichen Unwert der Mathematik", 1904)

"The goal is nothing other than the coherence and completeness of the system not only in respect of all details, but also in respect of all physicists of all places, all times, all peoples, and all cultures." (Max Planck, "Acht Vorlesungen", 1910)

"Only in a free society is man able to create the inventions and cultural values which make life worthwhile to modern man." (Albert Einstein, "Science and Civilization", [speech] 1933)

"Science, unguided by a higher abstract principle, freely hands over its secrets to a vastly developed and commercially inspired technology, and the latter, even less restrained by a supreme culture saving principle, with the means of science creates all the instruments of power demanded from it by the organization of Might." (Johan Huizinga, "In the Shadow of Tomorrow", 1936)

"I see the tasks of social sciences to discover what kinds of order actually do exist in the whole range of the behavior of human beings; what kind of functional relationships between different parts of culture exist in space and over time, and what functionally more useful kinds of order can be created." (Robert S Lynd, "Knowledge of What?", 1939)

"[...] science, if given its head, is not just cold efficiency; its attitude is tolerant, friendly and humane. It has already become the dominant inspiration of human culture, so that modern poetry, painting and architecture derive their most constructive ideas from scientific thought." (Conrad H Waddington, "The Scientific Attitude", 1941)

"Science can give us only the tools in the box, these mechanical miracles that it has already given us. But of what use to us are miraculous tools until we have mastered the humane, cultural use of them? We do not want to live in a world where the machine has mastered the man; we want to live in a world where man has mastered the machine." (Frank L Wright, "Frank Lloyd Wright on Architecture: Selected Writings 1894-1940", 1941)

"A culture is an historically created system of explicit and implicit designs for living, which tends to be shared by all or specially designated members of a group at a specified point in time." (Clyde Kluckhohn & W H Kelley, "The Concept of Culture", 1945)

"[...] science is truly one of the highest expressions of human culture - dignified and intellectually honest, and withal a never-ending adventure. Personally, I feel much the same with regard to the more ecstatic moments in science as I do with regard to music. I see little difference between the thrill of scientific discovery and what one experiences when listening to the opening bars of the Ninth Symphony." (William T Astbury, "Science in Relation to the Community", School Science Review Nr. 109, 1948)

On Culture (1950-1959)

"A social system consists in a plurality of individual actors interacting with each other in a situation which has at least a physical or environmental aspect, actors who are motivated in terms of a tendency to the 'optimization of gratification' and whose relation to their situations, including each other, is defined and mediated in terms of a system of culturally structured and shared symbols." (Talcott Parsons, "The Social System", 1951)

"Culture consists of patterns, explicit and implicit, of and for behavior acquired and transmitted by symbols, constituting the distinctive achievement of human groups, including their embodiments in artifacts; the essential core of culture consists of traditional (i.e., historically derived and selected) ideas and especially their attached values; culture systems may, on the one hand, be considered as products of action, on the other as conditioning elements of further action." (Alfred L Kroeber & Clyde Kluckhohn, "Culture", 1952)

"[...] mathematics is what we make it; not by each of us acting without due regard for what constitutes mathematics in our culture, but by seeking to build up new theories in the light of the old, and to solve outstanding problems generally recognized as valuable for the progress of mathematics as we know it. Until we make it, it fails to 'exist'. And, having been made, it may at some future time even fail to be 'mathematics' any longer." (Raymond L Wilder, "Introduction to the Foundations of Mathematics", 1952)

"Rich in its past, dynamic in the present, prodigious for the future, replete with simple and yet profound ideas and methods, surely mathematics can give something to anyone’s culture." (Rudolph E Langer, "The Things I Should Have Done, I Did Not Do", The American Mathematical Monthly, Vol. 59 (7), 1952)

"The principal mathematical element in the culture, embodying the living and growing mass of modern mathematics, will be chiefly possessed by the professional mathematicians. True, certain professions, such as engineering, physics, and chemistry, which employ a great deal of mathematics, carry a sizable amount of the mathematical tradition, and in some of these, as in the case of physics and engineering research, some individuals contribute to the growth of the mathematical element in the culture. But, in the main, the mathematical element of our culture is dependent for its existence and growth on the class of those individuals known as ‘mathematicians’." (Raymond L Wilder, "Introduction to the Foundations of Mathematics", 1952)

"[...] there is a tendency to forget that all science is bound up with human culture in general, and that scientific findings, even those which at the moment appear the most advanced and esoteric and difficult to grasp, are meaningless outside their cultural context." (Erwin Schrödinger, "Are There Quantum Jumps?", The British Journal for the Philosophy of Science Vol. 3, 1952)

"'World view' differs from culture, ethos, mode of thought, and national character. It is the picture the members of a society have of the properties and characters upon their stage of action. While 'national character' refers to the way these people look to the outsider looking in on them, 'world view' refers to the way the world looks to that people looking out. Of all that is connoted by 'culture', 'world view' attends especially to the way a man, in a particular society, sees himself in relation to all else. It is the properties of existence as distinguished from and related to the self. It is, in short, a man's idea of the universe. It is that organization of ideas which answers to a man the questions: Where am I? Among what do I move? What are my relations to these things? (Robert Redfield, "The Primitive World View", 1952)

"The secret language of statistics, so appealing in a fact-minded culture, is employed to sensationalize, inflate, confuse, and oversimplify. Statistical methods and statistical terms are necessary in reporting the mass data of social and economic trends, business conditions, 'opinion' polls, the census. But without writers who use the words with honesty and understanding and readers who know what they mean, the result can only be semantic nonsense." (Darell Huff, "How to Lie with Statistics", 1954)

"Understanding mathematical logic, or the theory of relativity, is not an indispensable attribute of the cultured mind. But if one wishes to learn anything about these subjects, one must learn something. It is necessary to master the rudiments of the language, to practice a technique, to follow step by step a characteristic sequence of reasoning and to see a problem through from beginning to end." (James R Newman, "The World of Mathematics" Vol. I, 1956)

"The separation between the two cultures has been getting deeper under our eyes; there is now precious little communication between them. [...] The traditional culture [...] is, of course, mainly literary [...] the scientific culture is expansive, not restrictive." (Charles P Snow, New Statesman, 1956)

"A good many times I have been present at gatherings of people who, by the standards of traditional culture, are thought highly educated and who have with considerable gusto been expressing their incredulity at the illiteracy of scientists. Once or twice I have been provoked and have asked the company how many of them could describe the Second Law of Thermodynamics. The response was cold: it was also negative." (Charles P Snow, "The Two Cultures", [lecture] 1959)

"Mathematics is an aspect of culture as well as a collection of algorithms." (Carl B Boyer, "The History of the Calculus and Its Conceptual Development", 1959)