Measure-relations can only be studied in abstract notions of quantity, and their dependence on one another can only be represented by formulæ. On certain assumptions, however, they are decomposable into relations which, taken separately, are capable of geometric representation; and thus it becomes possible to express geometrically the calculated results. In this way, to come to solid ground, we cannot, it is true, avoid abstract considerations in our formulæ, but at least the results of calculation may subsequently be presented in a geometric form. The foundations of these two parts of the question are established in the celebrated memoir of Gauss, Disqusitiones generales circa superficies curvas.
Bernhard RiemannRelated topics
abstract certain form ground memoir possible question representation study take thus way relations gauss partsRelated quotes
The professional administrators - especially those at higher levels - serve key roles at the boundary of the organization, between the professionals inside and interested parties - governments, client associations, and so on - on the outside. On the one hand, the administrators are expected to protect the professionals' autonomy, to "buffer" them from external pressures. On the other hand, the administrators are expected to woo these outsiders to support the organization, both morally and financially. Thus, the external roles of the manager-maintaining liaison contacts, acting as figurehead and spokesman in a public relations capacity, negotiating with outside agencies-emerge as primary ones in professional administration.
Henry Mintzberg
God has permitted and does permit us to be shaken by adversity. Difficult times lie ahead. We will be greatly tested. We have to take this warning seriously and live spiritually... Many saints would have loved to have lived in our times and have had our chance to struggle for Christ... Our struggle matters because it is not a struggle against an Ali Pasha, or a Hitler and a Mussolini, but a struggle against the devil himself. For this reason, our wages will be heavenly... The saints will become more holy and the vile will become more vile. Yet I feel great consolation inside. This is only a storm; like past storms, it will pass. May the Good God take evil and turn it into good. Amen.
Paisios of Mount Athos
By the help of God and with His precious assistance, I say that Algebra is a scientific art. The objects with which it deals are absolute numbers and measurable quantities which, though themselves unknown, are related to "things" which are known, whereby the determination of the unknown quantities is possible. Such a thing is either a quantity or a unique relation, which is only determined by careful examination. What one searches for in the algebraic art are the relations which lead from the known to the unknown, to discover which is the object of Algebra as stated above. The perfection of this art consists in knowledge of the scientific method by which one determines numerical and geometric unknowns.
Omar Khayyám
The seventeenth century witnessed the birth of modern science as we know it today. The science was something new, based on a direct confrontation of nature by experiment and observation. But there was another feature of the new science-a dependence on numbers, on real numbers of actual experience.
...The ancients knew a few numerical laws... But prior to the Scientific Revolution, the goal of science (or the study of nature) was not to seek laws of nature expressed in terms of numbers or number relations. ...the new science ...not only found laws based on numbers but they were also willing to express these laws in terms of higher powers of numbers-squares and cubes.
I. Bernard Cohen
Whether by the House or by the People, if an Abolitionist be chosen President of the United States, you will have presented to you the question of whether you will permit the government to pass into the hands of your avowed and implacable enemies... such a result would be a species of revolution by which the purposes of the Government would be destroyed and the observance of its mere forms entitled to no respect. In that event, in such manner as should be most expedient, I should deem it your duty to provide for your safely outside the Union of those who have shown the will, and would have acquired the power, to deprive you of your birthright and reduce you to worse than the Colonial dependence of your fathers.
Jefferson Davis