Visualize Quotes (8 quotes)
I mean, if 10 years from now, when you are doing something quick and dirty, you suddenly visualize that I am looking over your shoulders and say to yourself “Dijkstra would not have liked this”, well, that would be enough immortality for me.
In concluding paragraph of 'Introducing a Course on Calculi' (30 Aug 1995) in the E. W. Dijkstra Archive manuscript EWD1213.
I’d like the [Cosmos] series to be so visually stimulating that somebody who isn’t even interested in the concepts will just watch for the effects. And I’d like people who are prepared to do some thinking to be really stimulated.
Quoted by Dennis Meredith, in 'Carl Sagan’s Cosmic Connection and Extraterrestrial Life-Wish', Science Digest (Jun 1979), 85, 38. Reproduced in Carl Sagan and Tom Head, Conversations With Sagan (2006), 55.
It is usually not recognized that for every injurious or parasitic microbe there are dozens of beneficial ones. Without the latter, there would be no bread to eat nor wine to drink, no fertile soils and no potable waters, no clothing and no sanitation. One can visualize no form of higher life without the existence of the microbes. They are the universal scavengers. They keep in constant circulation the chemical elements which are so essential to the continuation of plant and animal life.
In My Life With the Microbes (1954), 4.
Many times every day I think of taking off in that missile. I’ve tried a thousand times to visualize that moment, to anticipate how I’ll feel if I’m first, which I very much want to be. But whether I go first or go later. I approach it now with some awe, and I’m sure I’ll approach it with even more awe on my day. In spite of the fact that I will he very busy getting set and keeping tabs on all the instruments, there’s no question that I’ll need—and will have—all my confidence.
As he wrote in an article for Life (14 Sep 1959), 38.
The rockets that have made spaceflight possible are an advance that, more than any other technological victory of the twentieth century, was grounded in science fiction… . One thing that no science fiction writer visualized, however, as far as I know, was that the landings on the Moon would be watched by people on Earth by way of television.
In Asimov on Physics (1976), 35. Also in Isaac Asimov’s Book of Science and Nature Quotations (1988), 307.
To be a scholar of mathematics you must be born with talent, insight, concentration, taste, luck, drive and the ability to visualize and guess.
In I Want to be a Mathematician: An Automathography (1985), 400.
Today it is no longer questioned that the principles of the analysts are the more far-reaching. Indeed, the synthesists lack two things in order to engage in a general theory of algebraic configurations: these are on the one hand a definition of imaginary elements, on the other an interpretation of general algebraic concepts. Both of these have subsequently been developed in synthetic form, but to do this the essential principle of synthetic geometry had to be set aside. This principle which manifests itself so brilliantly in the theory of linear forms and the forms of the second degree, is the possibility of immediate proof by means of visualized constructions.
In Riemannsche Flächen (1906), Bd. 1, 234.
Where should I start? Start from the statement of the problem. ... What can I do? Visualize the problem as a whole as clearly and as vividly as you can. ... What can I gain by doing so? You should understand the problem, familiarize yourself with it, impress its purpose on your mind.
How to Solve It: a New Aspect of Mathematical Method (1957), 33.