A Quote by Carl Friedrich Gauss
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.
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What is the real function, the essential function, the supreme function, of language? Isn't it merely to convey ideas and emotions? Certainly. Then if we can do it with words of fonetic brevity and compactness, why keep the present cumbersome forms?
Gratitude: An imaginary emotion that rewards an imaginary behavior, altruism. Both imaginaries are false faces for selfishness, which is a real and honest emotion.
The often cruel behavior of Christians toward unbelievers and even toward dissenters among themselves is shocking evidence of the function of that image in relation to values and behavior.
It is certain that the real function of art is to increase our self-consciousness; to make us more aware of what we are, and therefore of what the universe in which we live really is. And since mathematics, in its own way, also performs this function, it is not only aesthetically charming but profoundly significant. It is an art, and a great art.
One might think this means that imaginary numbers are just a mathematical game having nothing to do with the real world. From the viewpoint of positivist philosophy, however, one cannot determine what is real. All one can do is find which mathematical models describe the universe we live in. It turns out that a mathematical model involving imaginary time predicts not only effects we have already observed but also effects we have not been able to measure yet nevertheless believe in for other reasons. So what is real and what is imaginary? Is the distinction just in our minds?
From the original watchtower through the anchored balloon to the reconnaissance aircraft and remote sensing-satellites, one and the same function has been indefinitely repeated, the eye's function being the function of a weapon.
It is fortunate that molecular synthesis also serves the utilitarian function of producing quantities of rare or novel substances which satisfy human needs, especially with regard to health, and the scientific function of stimulating research and education throughout the whole discipline of chemistry.
A function of a variable quantity is an analytic expression composed in any way whatsoever of the variable quantity and numbers or constant quantities.
Perverted pride is a great misfortune in men; but pride in its original function, for which God created it, is indispensable to a proper manhood.
Good design is not about form following function. It is function with cultural content. By adding "cultural content" to the concept of "form follows function," objects cease to be finite or predictable. Maybe the right way to interpret the dictum is to first acknowledge that the function needs to be clearly understood before the form is considered.
One can say that the author is an ideological product, since we represent him as the opposite of his historically real function. (When a historically given function is represented in a figure that inverts it, one has an ideological production.) The author is therefore the ideological figure by which one marks the manner in which we fear the proliferation of meaning.
Rhetoric is rooted in an essential function of language itself, a function that is wholly realistic and continually born anew: the use of language as a symbolic means of inducing cooperation in beings that by nature respond to symbols.
Be a function of your values rather than a function of the impulse or desire of any given moment.
When real nobleness accompanies that imaginary one of birth, the imaginary seems to mix with real, and becomes real too.
For just as for a flute-player, a sculptor, or an artist, and, in general, for all things that have a function or activity, the good and the well is thought to reside in the function, so would it seem to be for man, if he has a function.
In the 1920s the young English physicist Paul Dirac began trying to understand and describe the space-time evolution of the electron, the first elementary particle discovered by J.J. Thomson in 1897. Dirac was puzzled by an unprecedented property of space-time, discovered by Lorentz in his studies of electromagnetic forces, whereby if space was real, time had to be imaginary, and vice versa. In other words, space and time had to be a ‘complex’ mixture of two quantities, one real and the other imaginary.
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