Pure Quotes - page 15
One of my conjectures was solved in six months, a second in five years, a third in ten. But the basic conjecture, despite heroic efforts rewarded by two Fields Medals, remains a conjecture, now called MLC: the Mandelbrot Set is locally connected. The notion that these conjectures might have been reached by pure thought - with no picture - is simply inconceivable.
Benoît Mandelbrot
I always saw a close kinship between the needs of "pure" mathematics and a certain hero of Greek mythology, Antaeus. The son of Earth, he had to touch the ground every so often in order to reestablish contact with his Mother; otherwise his strength waned. To strangle him, Hercules simply held him off the ground. Back to mathematics. Separation from any down-to-earth input could safely be complete for long periods - but not forever. In particular, the mathematical study of Brownian motion deserved a fresh contact with reality.
Benoît Mandelbrot
From the beginning I could not believe that the "efficient market” hypothesis was dependent on a pure Brownian motion white noise or any truly random random walk. Place a minuscule colloidal molecule on a horizontal table that covers unlimited acres. Bombard it from every direction with thousands of minute atoms; and then if you wait long enough that original molecule can have traveled a billion miles in one direction. That's truly a random Bachelier-Einstein walk, but not my notion of economic fluctuations.
Paul Samuelson
The will is the living principle of the rational soul, is indeed itself reason, when purely and simply apprehended. That reason is itself active, means, that the pure will, as such, rules and is effectual. The infinite reason alone lies immediately and entirely in the purely spiritual order. The finite being lives necessarily at the same time in a sensuous order; that is to say, in one which presents to him other objects than those of pure reason; a material object, to be advanced by instruments and powers, standing indeed under the immediate command of the will, but whose efficacy is conditional also on its own natural laws.
Johann Gottlieb Fichte
The administrators of the executive power may be either elective or not; and in the former case all or only some of them may be elective. They are elective in a proper democracy, that is to say, in a democracy which recognizes representation. If all the public officials are directly elected by the whole people, the democracy is a pure democracy; if only some, it is a mixed democracy. The public officials may also fill vacancies themselves; this is the case in a pure aristocracy. But if only some of the magistrates are thus replaced by the public officers, and if the others are again directly elected by the people, then the form of government is that of a democratic aristocracy. A permanent president (monarch) may also be elected to exercise the executive power during his lifetime. In all these cases, either all citizens of the commonwealth, or only some of them, are eligible to office. Eligibility may, therefore, be limited or unlimited.
Johann Gottlieb Fichte
It is doubtful whether the artist [unknown] altogether knew what he depicted here in this panel, and even more doubtful whether he could have expressed it in words. That which we praise here as well thought-out and cleverly arranged may, in fact, have been achieved by him unconsciously; for the artist was transformed by pure harmoniousness while executing this picture, and his feeling become his law. Only his disposition, his spiritual exaltation, could have brought forth such a fruit as this picture. Just as the pious man prays without speaking a word and the Almighty hearkens unto him, so the artist with true feeling paints and the sensitive man understands and recognizes it; while even the less sensitive gain some inkling of it.
Caspar David Friedrich
Gently rising hills block the view into the distance; line the wishes and desires of the children, who enjoy the blissful moments of the present without wanting to know what lies beyond. Bushes in bloom, nourishing herbs, and sweet-smelling flowers surround the quiet clear stream in which the pure blue of the cloudless sky is reflected like the glorious image of God in the souls of the children... There is no stone to be seen here, no withered branch, no fallen leaves. The whole of nature breathes, peace, joy, innocence and life.
Caspar David Friedrich
It is my tamanna (deep desire) to do something for our society; I am inspired by the desire to live and die for my country; ...I want the glory of Gujarat to reach the whole world. ...I've used the mantra of lokprem (love for people) through Lok Kalyan Melas organised by the government to make the administrative machinery an instrument of lokseva (service of the people). ... To the baseless propaganda of the Congress, I have only this to say: Oh lord! Please give wisdom to those indulging in evil propaganda and give strength to those who live by good and good pure thoughts.
Narendra Modi
When the Sachar Committee members met and asked me, "Mr. Modi what have you done for Muslims in Gujarat?” I told them: Nothing, I have done nothing for Muslims. But please go on to note that I have done nothing for Hindus or Jains or Sikhs either. I am responsible for 5.5 crore Gujaratis and whatever I do, is aimed at serving the interests of all these 5.5 crore people of my state. When the pure waters of Narmada flow into Sabarmati on account of our river linking project, do you expect me to measure how many litres are consumed by Hindus and how much water goes to Muslim households? My job is to ensure that every person, every household gets adequate supplies of clean drinking water. Please don't expect me to adopt your divisive terminology and vision.
Narendra Modi
If you pass the light from a sodium flash through a prism, you get a pattern very different from the familiar continuous rainbow that Newton elicited from natural sunlight. Instead of a continuous pattern, in which all gradations of pure color are apparently represented, the sodium flash generates a series of lines of light. ...in the musical analogy, sodium produces a chord where sunlight produced all possible tones-"white noise."
Frank Wilczek
The bases of music are rhythm and harmony. Rhythm is ordered recurrence in time... As the planets move around the sun, they repeat their orbits periodically; thus there is already a primitive kind of rhythm in their motion.... Harmony... can be considered a special kind of rhythm.... pure musical tones are produced when the vibrations are... periodic or... repeat themselves regularly in time. Two tones harmonize if their intervals of repetition are in rhythm-or, in mathematical language, if their periods are in proportion. Kepler... in the third book of Harmonice mundi... attempted to make other... related, connections between musical harmony and mathematical proportion.
Frank Wilczek
God, the pure limit and pure beginning of all that we are, have, and do, standing over in infinite qualitative difference to man and all that is human, nowhere and never identical with that which we call God, experience, surmise, and pray to as God, the unconditioned Halt as opposed to all human rest, the Yes in our No and the No in our Yes, the first and last and as such unknown, but nowhere and never a magnitude amongst others in the medium known to us, God the Lord, the Creator and Redeemer... that is the living God.
Karl Barth
