One of the many importants ideas introduced by Minkowski into the study of convex bodies was that of gauge function. Roughly, the gauge function is the equation of a convex body. Minkowski showed that the gauge function could be defined in a purely geometric way and that it must have certain properties analogous to those possessed by the distance of a point from the origin. He also showed that conversely given any function possessing these properties, there exists a convex body with the given function as its gauge function.
Carl Ludwig SiegelRelated topics
body certain convex distance equation function gauge given origin point study way minkowskiRelated quotes
Because finally, "the equal right of every citizen to the free exercise of his religion according to the dictates of conscience” is held by the same tenure with all his other rights. If we recur to its origin, it is equally the gift of nature; if we weigh its importance, it cannot be less dear to us; if we consider "the declaration of those rights which pertain to the good people of Virginia as the basis and foundation of government,” it is enumerated with equal solemnity, or rather studied emphasis.
James Madison
The nude gains its enduring value from the fact that it reconciles several contrary states. It takes the most sensual and immediately interesting object, the human body, and puts it out of reach of time and desire; it takes the most purely rational concept of which mankind is capable, mathematical order, and makes it a delight to the senses; and it takes the vague fears of the unknown and sweetens them by showing that the gods are like men and may be worshiped for their life-giving beauty rather than their death-dealing powers.
Kenneth Clark
Of the various executive abilities, no one excited more anxious concern than that of placing the interests of our fellow-citizens in the hands of honest men, with understanding sufficient for their stations. No duty is at the same time more difficult to fulfil. The knowledge of character possessed by a single individual is of necessity limited. To seek out the best through the whole Union, we must resort to the information which from the best of men, acting disinterestedly and with the purest motives, is sometimes incorrect.
Thomas Jefferson
Do not do anything without signing yourself with the sign of the Cross! When you depart on a journey, when you begin your work, when you go to study, when you are alone, and when you are with other people, seal yourself with the Holy Cross on your forehead, your body, your chest, your heart, your lips, your eyes, your ears. All of you should be sealed with the sign of Christ's victory over hell. Then you will no longer be afraid of charms, evil spirits, or sorcery, because these are dissolved by the power of the Cross like wax before fire and like dust before the wind.
Cleopa Ilie
There's one uneasy borderline between what is external and what is internal, and this borderline is defined exactly by the sense organs and the skin and the introduction of external things within my own body. Consciousness is altered by physical events and physical objects, which impinge upon my sense organs, or which I introduce into my body.
Now the name traditionally given to external objects or processes which change you internally is sacrament. Sacraments are the visible and tangible techniques for bringing you close to your own divinity.
Timothy Leary
