I recited Pi to 22,514 decimal points in five hours and nine minutes. I was able to do this because of weeks of study, aided by the unusual synaesthesic way my mind perceives numbers as complex multidimensional coloured and textured shapes.
The only protection as a historian is to institute a process of research and writing that minimizes the possibility of error. And that I have tried to do, aided by modern technology, which enables me, having long since moved beyond longhand, to use a computer for both organizing and taking notes.
Of the properties of mathematics, as a language, the most peculiar one is that by playing formal games with an input mathematical text, one can get an output text which seemingly carries new knowledge. The basic examples are furnished by scientific or technological calculations: general laws plus initial conditions produce predictions, often only after time-consuming and computer-aided work. One can say that the input contains an implicit knowledge which is thereby made explicit.
Coming back is the thing that enables you to see how all the dots in your life are connected, how one decision leads you another, how one twist of fate, good or bad, brings you to a door that later takes you to another door, which aided by several detours--long hallways and unforeseen stairwells--eventually puts you in the place you are now.
The oldest problem in economic education is how to exclude the incompetent. A certain glib mastery of verbiage-the ability to speak portentously and sententiously about the relation of money supply to the price level-is easy for the unlearned and may even be aided by a mildly enfeebled intellect. The requirement that there be ability to master difficult models, including ones for which mathematical competence is required, is a highly useful screening device.
Darwinism undermined traditional morality and the value of human life. Then, evolutionary progress became the new moral imperative. This aided the advance of eugenics, which was overtly founded on Darwinian principles. Some eugenicists began advocating euthanasia and infanticide for the disabled. On a parallel track, some prominent Darwinists argued that human racial competition and war is part of the Darwinian struggle for existence. Hitler imbibed these social Darwinist ideas, blended in virulent anti-Semitism, and--there you have it: Holocaust
No compact among men . . . can be pronounced everlasting and inviolable, and if I may so express myself, that no Wall of words, that no mound of parchment can be so formed as to stand against the sweeping torrent of boundless ambition on the one side, aided by the sapping current of corrupted morals on the other.
It has taken me nearly twenty years of studied self-restraint, aided by the natural decay of my faculties, to make myself dull enough to be accepted as a serious person by the British public; and I am not sure that I am not still regarded as a suspicious character in some quarters.