Combinatorial Quotes & Sayings

The very term 'combinatorial methods' has an oxymoronic character. — Joel Spencer

Back in 1962, when I had by accident become the supervisor of Roberto Celis in Argentina, it occurred to me that antibody diversity might arise from the joining by disulphide bridges of a variety of small polypeptides in combinatorial patterns. — Cesar Milstein

I have to admit that he was not bad at combinatorial analysis - a branch, however, that even then I considered to be dried up. — Stanislaw Lem

But many, many stories were told; from what could be gathered, all fifty of the mine's inhabitants had reacted on each other, two by two, as in combinatorial analysis, that is to say, everyone with all the others, and especially every man with all the women, old maids or married, and every woman with all the men. All I had to do was to select two names at random, better if different sex, and ask a third person, "What happened with those two?" and lo and behold, a splendid story was unfolded for me, since everyone knew the story of everyone else. — Primo Levi

Combinatorial analysis, in the trivial sense of manipulating binomial and multinomial coefficients, and formally expanding powers of infinite series by applications ad libitum and ad nauseamque of the multinomial theorem, represented the best that academic mathematics could do in the Germany of the late 18th century. — Richard Askey

In reality, it is impossible to build such an agent because it is computationally intractable to perform the requisite calculations. Any attempt to do so succumbs to a combinatorial explosion just like the one described in our discussion of GOFAI. To see why this is so, consider one tiny subset of all possible worlds: those that consist of a single computer monitor floating in an endless vacuum. The monitor has 1, 000 x 1, 000 pixels, each of which is perpetually either on or off. Even this subset of possible worlds is enormously large: the 2(1,000 x 1,000) possible monitor states outnumber all the computations expected ever to take place in the observable universe. Thus, we could not even enumerate all the possible worlds in this tiny subset of all possible worlds, let alone perform more elaborate computations on each of them individually. — Nick Bostrom

I have never been a fan of science fiction. For me, fiction has to explore the combinatorial possibilities of people interacting under the constraints imposed by our biology and history. When an author is free to suspend the constraints, it's tennis without a net. — Steven Pinker

Our habits and our institutions, from language to cities, are constantly changing, and the mechanism of change turns out to be surprisingly Darwinian: it is gradual, undirected, mutational, inexorable, combinatorial, selective and in some vague sense progressive. — Matt Ridley

Reason is up to these demands because it is an open-ended combinatorial system, an engine for generating an unlimited number of new ideas. Once it is programmed with a basic self-interest and an ability to communicate with others, its own logic will impel it, in the fullness of time, to respect the interests of ever-increasing numbers of others. It is reason too that can always take note of the shortcomings of previous exercises of reasoning, and update and improve itself in response. And if you detect a flaw in this argument, it is reason that allows you to point it out and defend an alternative. — Steven Pinker

Every field has its taboos. In algebraic geometry the taboos are (1) writing a draft that can be followed by anyone but two or three of one's closest friends, (2) claiming that a result has applications, (3) mentioning the word 'combinatorial,' and (4) claiming that algebraic geometry existed before Grothendieck (only some handwaving references to 'the Italians' are allowed provided they are not supported by specific references). — Gian-Carlo Rota