As a bit of a fun project, I would like to put together a collection of slogans, and am asking for contributions. Such a collection may or may not turn out to be "useful", but at least it will be amusing. I'm thinking of a slogan (apart from being a Scottish Highland war-cry) as a pithy little phrase or saying or motto or truism ..., just short of being poetry, that can tweak the neural pathways to follow a previously traveled path of understanding. Slogans tend to be little gems, often found in the folklore, but sometimes published, such as the 5 slogans in Jim Lambek & P. Scott's "Intro to higher order categorical logic" - these are: I: many objects of interest in mathematics congregate in concrete categories. II: many objects of interest to mathematicians are themselves small categories. III: many objects of interest to mathematicians may be viewed as functors from small categories to Sets. IV: many important concepts in mathematics arise as adjoints, right or left, to previously known functors. V: many equivalence and duality theorems in mathematics arise as an equivalence of fixed subcategories induced by a pair of adjoint functors. I think there are many more such gems; I like (and use) the one that says: the arrows always go through the limit. - I attribute this one to Armin Frei circa 1971 at UBC. Another really good one is: adjoints are the unity and identity of opposites. - I attribute this one to Bill Lawvwere Here are a couple more, from the physics of information: * there is no information without representation. * there is no processing without a process. - attributed to Benjamin Schumacher of Kenyon College. Each slogan can explode into rich and meaningful ideas, sort of the "url's of the mind" (if you like that kind of cyber-geek talk). Anyway, I hope the intention is clear, and that everyone will contribute their favourites as well. Please either post a response or send to me directly (no flames please), along with appropriate credit if known; I will assemble, and depending on how it goes, make the collection available. Could be fun and interesting - I look forward to your responses. Best regards to all .... Al /\ / Al R. Vilcius, Canada / \ / mailto:al.r@vilcius.com /--->\ / Tel./FAX (905) 854-3342 /3371 / \/ web site: http://www.VILCIUS.com