Complete knowledge of the nature of an analytic function must also include insight into its behavior for imaginary values of the arguments. Often the latter is indispensable even for a proper appreciation of the behavior of the function for real arguments. It is therefore essential that the original determination of the function concept be broadened to a domain of magnitudes which includes both the real and the imaginary quantities, on an equal footing, under the single designation complex numbers.
Carl Friedrich GaussRelated topics
appreciation behavior complete complex concept designation determination domain equal essential footing function imaginary include indispensable insight knowledge latter nature numbers original proper real single underRelated quotes
The Indian religious traditions... accepted the concept of non-being on an equal footing with that of being. Like many other Eastern religions, the Indian culture regarded Nothing as a state from which one might have come and to which one might return.. Where Western religious traditions sought to flee from nothingness... a state of non-being was something to be actively sought by Buddhist and Hindus in order to achieve Nirvana: oneness with the Cosmos.
John D. Barrow
I used to feel that women were here for one reason. Sex was simply another kind of exercise, another body function. I was convinced a girl and I couldn't communicate on equal footing because she wouldn't understand what I was doing. I didn't have time to take one girl out regularly and go through a normal high-school romance with all its phone calls and notes and squabbles. That took too much time. I needed to be in the gym. For me it was a simple matter of picking them up at the lake, and then never seeing them again.
Arnold Schwarzenegger
Man's quest for knowledge is an expanding series whose limit is infinity, but philosophy seeks to attain that limit at one blow, by a short circuit providing the certainty of complete and inalterable truth. Science meanwhile advances at its gradual pace, often slowing to a crawl, and for periods it even walks in place, but eventually it reaches the various ultimate trenches dug by philosophical thought, and, quite heedless of the fact that it is not supposed to be able to cross those final barriers to the intellect, goes right on.
Stanisław Lem
When scientists need to explain difficult points of theory, illustration by hypothetical example - rather than by total abstraction - works well (perhaps indispensably) as a rhetorical device. Such cases do not function as speculations in the pejorative sense - as silly stories that provide insight into complex mechanisms - but rather as idealized illustrations to exemplify a difficult point of theory. (Other fields, like philosophy and the law, use such conjectural cases as a standard device.)
Stephen Jay Gould
Rebellion against technology and civilization is real rebellion, a real attack on the values of the existing system. But the green anarchists, anarcho-primitivists, and so forth (The "GA Movement") have fallen under such heavy influence from the left that their rebellion against civilization has to great extent been neutralized. Instead of rebelling against the values of civilization, they have adopted many civilized values themselves and have constructed an imaginary picture of primitive societies that embodies these civilized values.
Theodore Kaczynski
