Those who assert that the mathematical sciences say nothing of the beautiful or the good are in error. For these sciences say and prove a great deal about them; if they do not expressly mention them, but prove attributes which are their results or definitions, it is not true that they tell us nothing about them. The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree.
The near side of a galaxy is tens of thousands of light-years closer to us than the far side; thus we see the front as it was tens of thousands of years before the back. But typical events in galactic dynamics occupy tens of millions of years, so the error in thinking of an image of a galaxy as frozen in one moment of time is small.
Without scheming to do wrong, or to make others unhappy, there may be error and there may be misery. Thoughtlessness, want of attention to other people's feelings, and want of resolution, will do the business.
In [chess], where the pieces have different and "bizarre" motions, with various and variable values, what is only complex, is mistaken (a not unusual error) for what is profound
As the strata of the earth preserve in succession the living creatures of past epochs, so the shelves of libraries preserve in succession the errors of the past and their expositions, which like the former were very lively and made a great commotion in their own age but now stand petrified and stiff in a place where only the literary palaeontologist regards them.
All corporatism - even when practised in societies where hard work, enterprise and cooperation are as highly valued as in Korea - encourages inflexibility, discourages individual accountability, and risks magnifying errors by concealing them.
It is not to everyone's taste that truth should be pronounced pleasant. But at least let no one believe that error becomes truth when it is pronounced unpleasant.
And why are you so firmly, so triumphantly, convinced that only the normal and the positive--in other words, only what is conducive to welfare--is for the advantage of man? Is not reason in error as regards advantage? Does not man, perhaps, love something besides well-being? Perhaps he is just as fond of suffering? Perhaps suffering is just as great a benefit to him as well-being? Man is sometimes extraordinarily, passionately, in love with suffering, and that is a fact.
There is only one inborn erroneous notion ... that we exist in order to be happy ... So long as we persist in this inborn error ... the world seems to us full of contradictions. For at every step, in great things and small, we are bound to experience that the world and life are certainly not arranged for the purpose of maintaining a happy existence ... hence the countenances of almost all elderly persons wear the expression of ... disappointment.