i. “The party that negotiates in haste is often at a disadvantage.” (Howard Raiffa)

ii. “Advice: don’t embarrass your bargaining partner by forcing him or her to make all the concessions.” (-ll-)

iii. “Disputants often fare poorly when they each act greedily and deceptively.” (-ll-)

iv. “Each man does seek his own interest, but, unfortunately, not according to the dictates of reason.” (Kenneth Waltz)

v. “Whatever is said after I’m gone is irrelevant.” (Jimmy Savile)

vi. “Trust is an important lubricant of a social system. It is extremely efficient; it saves a lot of trouble to have a fair degree of reliance on other people’s word. Unfortunately this is not a commodity which can be bought very easily. If you have to buy it, you already have some doubts about what you have bought.” (Kenneth Arrow)

vii. “… an author never does more damage to his readers than when he hides a difficulty.” (Évariste Galois)

viii. “A technical argument by a trusted author, which is hard to check and looks similar to arguments known to be correct, is hardly ever checked in detail” (Vladimir Voevodsky)

ix. “Suppose you want to teach the “cat” concept to a very young child. Do you explain that a cat is a relatively small, primarily carnivorous mammal with retractible claws, a distinctive sonic output, etc.? I’ll bet not. You probably show the kid a lot of different cats, saying “kitty” each time, until it gets the idea. To put it more generally, generalizations are best made by abstraction from experience. They should come one at a time; too many at once overload the circuits.” (Ralph P. Boas Jr.)

x. “Every author has several motivations for writing, and authors of technical books always have, as one motivation, the personal need to understand; that is, they write because they want to learn, or to understand a phenomenon, or to think through a set of ideas.” (Albert Wymore)

xi. “Great mathematics is achieved by solving difficult problems not by fabricating elaborate theories in search of a problem.” (Harold Davenport)

xii. “Is science really gaining in its assault on the totality of the unsolved? As science learns one answer, it is characteristically true that it also learns several new questions. It is as though science were working in a great forest of ignorance, making an ever larger circular clearing within which, not to insist on the pun, things are clear… But as that circle becomes larger and larger, the circumference of contact with ignorance also gets longer and longer. Science learns more and more. But there is an ultimate sense in which it does not gain; for the volume of the appreciated but not understood keeps getting larger. We keep, in science, getting a more and more sophisticated view of our essential ignorance.” (Warren Weaver)

xiii. “When things get too complicated, it sometimes makes sense to stop and wonder: Have I asked the right question?” (Enrico Bombieri)

xiv. “The mean and variance are unambiguously determined by the distribution, but a distribution is, of course, not determined by its mean and variance: A number of different distributions have the same mean and the same variance.” (Richard von Mises)

xv. “Algorithms existed for at least five thousand years, but people did not know that they were algorithmizing. Then came Turing (and Post and Church and Markov and others) and formalized the notion.” (Doron Zeilberger)

xvi. “When a problem seems intractable, it is often a good idea to try to study “toy” versions of it in the hope that as the toys become increasingly larger and more sophisticated, they would metamorphose, in the limit, to the real thing.” (-ll-)

xvii. “The kind of mathematics foisted on children in schools is not meaningful, fun, or even very useful. This does not mean that an individual child cannot turn it into a valuable and enjoyable personal game. For some the game is scoring grades; for others it is outwitting the teacher and the system. For many, school math is enjoyable in its repetitiveness, precisely because it is so mindless and dissociated that it provides a shelter from having to think about what is going on in the classroom. But all this proves is the ingenuity of children. It is not a justifications for school math to say that despite its intrinsic dullness, inventive children can find excitement and meaning in it.” (Seymour Papert)

xviii. “The optimist believes that this is the best of all possible worlds, and the pessimist fears that this might be the case.” (Ivar Ekeland)

xix. “An equilibrium is not always an optimum; it might not even be good. This may be the most important discovery of game theory.” (-ll-)

xxi. “It’s not all that rare for people to suffer from a self-hating monologue. Any good theories about what’s going on there?”

“If there’s things you don’t like about your life, you can blame yourself, or you can blame others. If you blame others and you’re of low status, you’ll be told to cut that out and start blaming yourself. If you blame yourself and you can’t solve the problems, self-hate is the result.” (Nancy Lebovitz & ‘The Nybbler’)


December 1, 2017 - Posted by | Mathematics, Quotes/aphorisms, Science, Statistics


  1. Why do people so often assume that the geometry of our knowledge is a circle?

    Assuming that some ignorance is harder to clear and that the people doing the clearing aren’t coordinating the geometry of their clearing and some of them have better tools and are more motivated than others, the shape of our knowledge is likely to be very odd.

    Comment by Stefan | December 5, 2017 | Reply

    • If you’d written that comment somewhere else, I’d probably have added that as another quote in this post. 🙂 There’s also the issue that some areas are more amenable to analysis than others, for various reasons, so the number of- and type of available tools also varies across fields.

      (A simple guess at an answer, made after having spent roughly a total of 10 seconds on that question: ‘Circles are simple. All models are wrong, but some are useful.’) (…after another minute: ‘a complaint that ‘a circle model’ may not be useful will probably, in some contexts in particular, be very valid’).

      Comment by US | December 5, 2017 | Reply

      • The main point of such analogies is presumably that potential knowledge is not some ‘box’ of a fixed size, so that every time someone learns something new there’ll be less ‘new stuff’ for others to find (in the box) out. Every time biologists find ‘a missing link’, the number of ‘missing links’ doubles. Some people may find this counter-intuitive, and such quotes then aim at trying to make such dynamics of the discovery process easier to understand. Of course such quotes/models are also very simplistic and wrong. Any kind of ‘true model’ is much too confusing to deal with.

        Comment by US | December 5, 2017

      • The question was a bit of a joke. I’ve used the knowledge-as-a-circle-analogy myself many times, but visualizing a bunch of different scientist clearing forest made it seem wrong. So I’m switching to the clearing-analogy from now on.

        The forest of ignorance can grow back, scientist can get stuck or be lured into the forest by butterflies of confusion or power-squirrels. Some of them will try to clear trees with a sponge while others use CTL harvesters.

        Of course it’s hard to imagine what starting a forest fire (Newton?) or deforestation caused soil erosion would be analogous to.

        Comment by Stefan | December 5, 2017

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