Thus Quotes - page 75
Matter is actually distributed very unevenly... conglomerated into stars and galactic systems. The average density is the density that we should get if all... could be evaporated into atoms of hydrogen, or protons, and... distributed evenly over the whole of space. ...three or four protons in every cubic foot. ...a million million times less than that of the most perfect vacuum that we can produce... The universe thus consists mostly of emptiness... consider a universe without any matter at all, an empty universe, as a good approximation. But we may also take as our first approximation a universe containing... three or four protons per cubic foot. The local deviations from the average, caused by the conglomeration of matter into stars and stellar systems, are then disregarded in the grand scale model, and are only taken into account when we come to study details.
Willem de Sitter
In both the solutions A and B the curvature is positive, in both three-dimensional space is finite: the universe has a definite size, we can speak of its radius, and, in the case A, of its total mass. In the case A... the density is proportional to the curvature... Thus, if we wish to have a finite density in a static universe, we must have a finite positive curvature.
Willem de Sitter
We... come to the conclusion... that the actual universe is neither the static nor the empty one. It differs so much from both of these that neither can be used as an appropriate grand scale model. We must thus look for other solutions of the general field-equations. On account of the expansion our solution must necessarily be a non-static one, and it must have a finite density. There is only one possible static solution possessing a finite density, viz. our old friend A, but of non-static solutions with finite density there exists a great variety.
Willem de Sitter
A question which has long troubled astronomers and physicists is what becomes of the energy that is continually being poured out into space by the sun and the stars. To this question a complete answer is given by the new theory. It is used up, diluted, or degraded, by the expansion of the universe. ...the light travelling through the expanding universe and, so to say, trying to reach a particular star, or stellar system, which is continually receding with great velocity, is losing energy in trying to catch up with it. It is this degradation of the light, technically known as the redshift of the spectral lines, by which we become aware of the receding velocities of the extra-galactic nebulae. It can be shown that the decrease of the total amount of radiant energy in the universe by this degradation exceeds the increase by the radiation of the stars. It would not be correct, however, to conclude that the expansion is caused by the energy thus lost by the radiation...
Willem de Sitter
The sequence of different positions of the same particle at different times forms a one-dimensional continuum in the four-dimensional space-time, which is called the world-line of the particle. All that physical experiments or observations can teach us refers to intersections of world-lines of different material particles, light-pulsations, etc., and how the course of the world-line is between these points of intersection is entirely irrelevant and outside the domain of physics. The system of intersecting world-lines can thus be twisted about at will, so long as no points of intersection are destroyed or created, and their order is not changed. It follows that the equations expressing the physical laws must be invariant for arbitrary transformations.
Willem de Sitter
In February 1917, it was found that a static solution with a positive curvature-the solution A-was not possible without the λ. In fact the curvature is proportional to λ (in solution A, λ is equal to the curvature; in B... it is three times the curvature). Thus, at the time when we had only the two static solutions A and B, and thought that these were the only possible ones, here was a plausible physical interpretation of the meaning of λ: it was the curvature of the world, and the square root of its reciprocal, the radius of curvature, could be conceived as providing a natural unit of length.
Willem de Sitter
Let no one think that I am dying of grief over my own dismal and ruined state. The sorrow that I feel, I can not at all express; but I can give a hint of it. From among those of the English community who were murdered at the hands of those disgraced ["black-faced"] black ones, one was my patron, and one was my well-wisher, and one my friend, and one my supporter, and one my pupil. Among the Hindustanis, some dear ones, some friends, some pupils, some beloveds. Thus every one of them was mingled with the dust. How harsh is the mourning for one dear one! He who would be a mourner for so many dear ones- how could his life not be difficult? Alas! So my friends died that now when I die, there would not even be anyone left to mourn for me.
Ghalib
In the early geological ages, when the Alps were low and the Himalayas not yet upheaved... from geological evidence of fossil and fauna, we find that an equitable climate and uniform climate prevailed over the whole surface of the globe. It is now conclusively proved that before the advent of glacial and inter-glacial periods a luxurious forest vegetation... flourished in the high latitude of the polar regions where the Sun goes below the horizon from November till March, thus showing that a warm climate prevailed in the Arctic regions in those days.
Bal Gangadhar Tilak
Supergravity theories generically contain non-compact global symmetry groups. The general rule is that the scalar fields of the theory in question parametrize a symmetric space. Thus, if the non-compact symmetry group is G, and its maximal compact subgroup is H, the scalar fields map the space-time into the symmetric space G/H, and the number of scalar fields is dim G – dim H. The first supergravity example of this type to be found, N = 4 supergravity is one of the most interesting. In this case there are two scalar fields and the symmetric space is SL(2,R)/SO(2).
John Henry Schwarz
The Sultan advanced to the fortifications of Kanauj, which consisted of seven distinct forts, washed by the Ganges which flowed under them like the ocean. In Kanauj there were nearly ten thousand temples, which the idolaters falsely and absurdly represented to have been founded by their ancestors two or three hundred thousand years ago. They worshipped and offered their vows and supplications to them in consequence of their great antiquity. Many of the inhabitants of the place fled and were scattered abroad like so many wretched widows and orphans, from the fear which oppressed them, in consequence of witnessing the fate of their deaf and dumb idols. Many of them thus effected their escape, and those who did not fly were put to death. The Sultan took all seven forts in one day, and gave his soldiers leave to plunder them and take prisoners.
Mahmud of Ghazni
Not only does it deny the corporate claim to liberty of men and women organized in national societies, but it refuses the much more fundamental claim of men and women to the free expression of human personality, which rests upon the eternal value of every human soul. True pride of race may be tested by the behaviour of its possessors towards their own fellow citizens and towards others. It will forbid conduct to individuals of which they should be ashamed in their private lives. It is thus evidently something far removed from the ideal of a race which by the German philosophy of to-day is called to stamp out the civilization of another. Between these two conceptions there is a great gulf fixed. ... Until these false creeds are abjured, and replaced by a wider toleration, they must continue to excite resistance. The future of humanity must not be left in the hands of those who would imprison and enslave it.
Edward Wood, 1st Earl of Halifax
In practice, quantum mechanics merely gives predictions with probabilities attached. This should be considered as a normal and quite acceptable feature of predictions made by science: different possible outcomes with different probabilities. In the world that is familiar to us, we always have such a situation when we make predictions. Thus the question remains: What is the reality described by quantum theories? I claim that we can attribute the fact that our predictions come with probability distributions to the fact that not all relevant data for the predictions are known to us, in particular important features of the initial state.
Gerardus 't Hooft
Flowers fade and fly, and flying fill the sky;
Their bloom departs, their perfume gone, yet who stands pitying by? ...
Oh, let me sadly bury them beside these steps to-night! ...
Farewell, dear flowers, for ever now, thus buried as 'twas best,
I have not yet divined when I with you shall sink to rest.
I who can bury flowers like this a laughing-stock shall be;
I cannot say in days to come what hands shall bury me.
See how when spring begins to fail each opening floweret fades;
So too there is a time of age and death for beauteous maids;
And when the fleeting spring is gone, and days of beauty o'er,
Flowers fall, and lovely maidens die, and both are known no more.
Herbert Giles
Love of God implies love of religion. And religion exemplifies that creative spirit of God which is at work in history as well as in the mind of man. Thus, one ought to love any religion, that is, religion as such, and in any form-as a manifestation of the moral spirit, the divine spirit of mankind.
Hermann Cohen
But that the state in general sees as right the sole means of accepting interest-bearing loans - thus debts, when it needs money and applies its other sovereign rights today only in an underhand manner to collect the incurred debts from the people, these are conditions for which one seeks in vain for a reasonable explanation. There is indeed no reasonable explanation for it, but only the fact that our entire thought even in national financial political matters is directed or corrupted in a private capitalistic manner.
Gottfried Feder
The concept of rotation led to geometrical exponential magnitudes, to the analysis of angles and of trigonometric functions, etc. I was delighted how thorough the analysis thus formed and extended, not only the often very complex and unsymmetric formulae which are fundamental in tidal theory, but also the technique of development parallels the concept.
Hermann Grassmann
As therefore, when we consult, not our own pleasures, but that of our friends, our behaviour will be pleasing and agreeable; our first enquiry must be, what those particulars are, with which the greatest part of mankind are universally delighted; and what those are which, in general, they detest, as troublesome and offensive: For thus we shall easily discover, what kind of conduct, in our intercourse with others, is to be avoided, and what to be adopted and pursued.
Giovanni della Casa
When looking at the two streams of research these men produced, it is tempting to characterize Buchanan as a somewhat romantic optimist holding the belief that the pursuits of selfish individuals can be channeled for the common good, if the right set of constitutional constraints are adopted, and believing that individuals are capable of designing constitutions that achieve this goal. Thus, some 35 years after the publication of The Calculus, we find Buchanan, in joint work with Roger Congleton (1998), accepting the fact that legislatures always will adopt the simple majority rule, and trying to design constitutional constraints that will lead to outcomes benefiting all members of the community under that rule.
Dennis Mueller
While I was pursuing the concept of geometrical product, as this idea was established by my father... I concluded that not only rectangles, but also parallelograms, may be viewed as products of two adjacent sides, provided that the sides are viewed not merely as lengths, but rather as directed magnitudes. When I joined this concept of geometrical product with the previously established idea of geometrical sum the most striking harmony resulted. Thus when I multiplied the sum of two vectors by a third coplaner vector, the result coincided (and must always coincide) with the result obtained by multiplying separately each of the two original vectors by the third... and adding together (with due attention to positive and negative values) the two products. [Thus A(B + C) = AB + AC. ]
From this harmony I came to see a whole new area of analysis was opening up which could lead to important results.
Hermann Grassmann
In Hindustan, especially in the province of Sylhet, which is a dependency of Bengal, it was the custom for the people of those parts to make eunuchs of some of their sons and give them to the governor in place of revenue (mal-wajibi)... This custom by degrees has been adopted in other provinces and every year some children are thus ruined and cut off from procreation. This practice has become common.
Jahangir
