On Numbers (1990-1999)

"I believe [...] that hypothesis testing has been greatly overemphasized in psychology and in the other disciplines that use it. It has diverted our attention from crucial issues. Mesmerized by a single all-purpose, mechanized, ‘objective’ ritual in which we convert numbers into other numbers and get a yes-no answer, we have come to neglect close scrutiny of where the numbers come from." (Jacob Cohen, "Things I have learned (so far)", American Psychologist 45, 1990)

"This stricture - that a bad model can only suggest - is stronger than it may appear. Bad models produce numbers, and thus present an unbearable temptation to use those numbers as if they do more than suggest. They cannot. If a model is bad as defined here, and the specific numbers it produces cannot be buttressed by some other arguments, then the numbers have no meaning except as illustration of the consequences that flow from the model's assumptions." (James S Hodges, "Six (or So) Things You Can Do with a Bad Model", 1991)

"If we imagine mathematics as a grand orchestra, the system of whole numbers could be likened to a bass drum: simple, direct, repetitive, providing the underlying rhythm for all the other instruments. There surely are more sophisticated concepts - the oboes and French horns and cellos of mathematics - and we examine some of these in later chapters. But whole numbers are always at the foundation." (William Dunham, "The Mathematical Universe", 1994)

"Mathematics is not a way of hanging numbers on things so that quantitative answers to ordinary questions can be obtained. It is a language that allows one to think about extraordinary questions." (James O Bullock, "Literacy in the Language of Mathematics", The American Mathematical Monthly, Vol. 101, No. 8, October, 1994)

"Number is therefore the most primitive instrument of bringing an unconscious awareness of order into consciousness." (Marie-Louise von Frany, "Creation Myths", 1995)

"You can be moved to tears by numbers - provided they are encoded and decoded fast enough." (Richard Dawkins, "River Out of Eden: A Darwinian View of Life", 1995)

"Numbers, in fact, are the atoms of the universe, combining with everything else." (Calvin C Clawson, Mathematical Mysteries: The Beauty and Magic of Numbers", 1996)

"Data are not just numbers, they are numbers with a context. [...] In data analysis, context provides meaning." (George W Cobb & David S Moore, "Mathematics, Statistics, and Teaching", American Mathematical Monthly, 1997)

"One of the best definitions of mathematics is 'the science of patterns'. Mathematics is how we detect, analyse, and classify regular patterns - be they numerical, geometric, or of some other kind. But what is a pattern? A pattern is a landmark in the magical maze. It's one of those things that you recognise when you see it, but it's not so easy to pin down the concept of a pattern once and for all with a neat, tidy, compact characterisation. In fact, the entire development of mathematics can be seen as a slow and erratic broadening of what we accept under the term 'pattern'." (Ian Stewart, "The Magical Maze: Seeing the World Through Mathematical Eyes", 1997)

"Our job is to see why the numbers turn out as they do. Along the way we shall come to understand why our 'intuition' about these numbers is badly off the mark. In fact, our intuition about probabilities often leads us astray - in many ways probability seems to be one of the areas in which human intuition is the least reliable. One consequence of this is that we tend to be unnecessarily impressed by 'coincidences' that are actually fairly likely. Another is that we adopt nonsensical strategies when betting on such things as horse races or lotteries. Our geometric intuition, based on our visual sense, is much better matched to reality. Perhaps the reason for the difference is that our evolutionary history has seldom placed us in situations where an intuitive grasp of probabilities adds much survival value. Usually a crude division into 'impossible', 'very unlikely', 'might happen', 'probably will happen', or 'certain' is enough." (Ian Stewart, "The Magical Maze: Seeing the World Through Mathematical Eyes", 1997)

"The purpose of plotting is to convey phenomena to the viewer’s cortex, not to provide a place to lookup observed numbers." (Kaye Basford & John W Tukey, "Graphical Analysis of Multi-Response Data", 1998)

"It is the same with the numbers generated by roulette: the smoothness of probability in the long term allows any amount of local lumpiness on which to exercise our obsession with pattern. As the sequence of data lengthens, the relative proportions of odd or even, red or black, do indeed approach closer and closer to the 50-50 ratio predicted by probability, but the absolute discrepancy between one and the other will increase." (John Haigh," Taking Chances: Winning With Probability", 1999)