It is essential to realize at this point that the formalism to be developed, although we cast it initially primarily in the framework of natural systems, is in fact applicable to any situation in which a class of objects is associated with real numbers, or in fact classified or indexed by any set whatever. It is thus applicable to any situation in which classification, or recognition, or discrimination is involved; indeed, one of the aims of our formalism is to point up the essential equivalence of the measurement problem in physics with all types of recognition or classification mechanisms based on observable properties of the objects being recognized or classified.
Robert RosenRelated topics
cast classification classified discrimination equivalence formalism measurement natural observable point problem real set situation thus whateverRelated quotes
Our situations are arranged by higher agents to allow us to become tired of trying to manipulate the material energy. Due to not being properly appreciative of the beauty of relationship with the Lord, humankind is given a temporary arena in which to act out our desires. This environment is designed to frustrate, disgust, and disappoint us, to make us contemplative and introspective. Ultimately it is meant to drive us away from the temporary world in favor of that which is eternal. This is arranged for us to finally realize that our happiness lies not in dabbling with the material energy but in serving the Lord unconditionally, thus becoming whole again.
Bhakti Tirtha Swami
Quantum theory may be formulated using Hilbert spaces over any of the three associative normed division algebras: the real numbers, the complex numbers and the quaternions. Indeed, these three choices appear naturally in a number of axiomatic approaches. However, there are internal problems with real or quaternionic quantum theory. Here we argue that these problems can be resolved if we treat real, complex and quaternionic quantum theory as part of a unified structure. Dyson called this structure the "three-fold way".... This three-fold classification sheds light on the physics of time reversal symmetry, and it already plays an important role in particle physics.
John C. Baez
The bank mania is one of the most threatening of these imitations. It is raising up a moneyed aristocracy in our country which has already set the government at defiance, and although forced at length to yield a little on this first essay of their strength, their principles are unyielded and unyielding. These have taken deep root in the hearts of that class from which our legislators are drawn, and the sop to Cerberus from fable has become history. Their principles lay hold of the good, their pelf of the bad, and thus those whom the Constitution had placed as guards to its portals, are sophisticated or suborned from their duties.
Thomas Jefferson
The success of mathematical physics led the social scientist to be jealous of its power without quite understanding the intellectual attitudes that had contributed to this power. The use of mathematical formulae had accompanied the development of the natural sciences and become the mode in the social sciences. Just as primitive peoples adopt the Western modes of denationalized clothing and of parliamentatism out of a vague feeling that these magic rites and vestments will at once put them abreast of modern culture and technique, so the economists have developed the habit of dressing up their rather imprecise ideas in the language of the infinitesimal calculus.
Norbert Wiener
It's like going out and saying, "That tree is a car." Well, the tree's not a car. A tree's a tree. Marriage is marriage. You can say that tree is something other than it is. It can redefine it. But it doesn't change the essential nature of what marriage is. Marriage is a union between a man and a woman for the purposes of the benefit of both the man and the woman, a natural unitive according to nature, unitive, that is for the purposes of having and rearing children and for the benefit of both the man and the woman involved in that relationship. And for the benefit of society because we need to have stable families of men and woman bonded together to raise children. That's what marriage is.
Rick Santorum