Objections... inspired Kronecker and others to attack Weierstrass' "sequential" definition of irrationals. Nevertheless, right or wrong, Weierstrass and his school made the theory work. The most useful results they obtained have not yet been questioned, at least on the ground of their great utility in mathematical analysis and its implications, by any competent judge in his right mind. This does not mean that objections cannot be well taken: it merely calls attention to the fact that in mathematics, as in everything else, this earth is not yet to be confused with the Kingdom of Heaven, that perfection is a chimaera, and that, in the words of Crelle, we can only hope for closer and closer approximations to mathematical truth-whatever that may be, if anything-precisely as in the Weierstrassian theory of convergent sequences of rationals defining irrationals.
Eric Temple BellRelated topics
analysis attack attention chimaera closer convergent defining definition earth everything fact great ground heaven hope judge kingdom least mathematics mean mind perfection right school take theory utility well work wrong yet others words kronecker weierstrassianRelated quotes
I see those pretended politicians who place all their subtlety, and who think they serve their country best, in circumventing those with whom they treat, interpreting the conditions of a treaty in such a manner, that all the advantage results to their own country. Far from blushing at conduct so contrary to equity, to right, and to national honesty, they boast of their dexterity, and pretend that they deserve the name of great negociators. How long shall public men boast of conduct which would disgrace a private individual? ...Shall powerful states abandon openly that which is honest, for that which may appear useful? It often happens for the happiness of the human race, that this pretended utility is fatal to the powers who follow it, and that, even among sovereigns, candour and right are found to be the safest policy.
Henry Temple, 3rd Viscount Palmerston
Our children grow up in a culture permeated with the idea that there are "smart people" and "dumb people". The social construction of the individual is as a bundle of aptitudes. There are people who are "good at math" and people who "can't do math." Everything is set up for children to attribute their first unsuccessful or unpleasant learning experiences to their own disabilities. As a result, children perceive failure as relegating them either to the group of "dumb people" or, more often, to a group of people "dumb at x" (where, as we have pointed out, x often equals mathematics). Within this framework children will define themselves in terms of their limitations, and this definition will be consolidated and reinforced throughout their lives. Only rarely does some exceptional event lead people to reorganize their intellectual self-image in such a way as to open up new perspectives on what is learnable.
Seymour Papert
I have a message for the judge, and I say this with all my heart: If this judge believes that somebody must be put in jail because a person is willing to stand on the biblical definition of marriage, and is willing to stand because they believe that the constitution does not allow the courts to make up law according to their own whims- if the judge believes that, then I would ask this of him: Let Kim go, but if you have to put someone in jail, I volunteer to go. Let me go. Lock me up if you think that's how freedom is best served. Because folks, I am willing to spend the next eight years in the White House leading this country, but I want you to know, I'm willing to spend the next eight years in jail, but I'm not willing to spend one day under the tyranny of people who believe they can take our freedom and conscience away!
Mike Huckabee
Ancient scriptures tell us that man is more than the physical body. In fact, we have two bodies: the physical and the astral, or subtle. But we are the soul! According to the ancient Vedic scriptures of India, the size of the soul is 1/10,000 the tip of a strand of hair. It is located in the heart region and is the actual life force. The physical, as well as the astral or subtle body, acts as a covering or costume that the soul wears in its journey throughout the material sphere. As we pass from costume to costume or from body to body through the process known as reincarnation, the impressions of previous lives imprint themselves on the subtle body and are carried with us during each lifetime. In the dream state, activity in the subtle body becomes more dominant than activity in the physical body. Our dream experiences are often impressions accumulated from many lifetimes.
Bhakti Tirtha Swami
I gave up on this stuff. I gave up on my species and ... I gave up on my countrymen. Because I think we squandered great gifts. I think humans were given great great gifts: walking upright, binocular vision, opposable thumb, large brain ... We grew. We had great gifts, and we gave it all up for both money and God ... We gave it all up to superstition, primitive superstition, primitive shit ... Invisible man in the sky, looking down, keeping track of what we do, make sure we don't do the wrong thing, if we do, he puts us in hell, where we burn forever. That kind of shit is very limiting for this brain we have. So we keep ourselves limited. And then we want a toy and a gizmo and gold and we want shiny things, and we want something to plug in that will make big big big things for us... And all that shit is nothing! It's nothing.
George Carlin
