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TWO:CHAPTER XVIReturning to our more immediate subject, we must observe that the Pythagoreans did not maintain, in anticipation of modern quantitative science, that all things are determined by number, but that all things are numbers, or are made out of numbers, two propositions not easily distinguished by unpractised thinkers. Numbers, in a word, were to them precisely what water had been to Thales, what air was to Anaximenes, the absolute principle of existence; only with them the idea of a limit, the leading inspiration of Greek thought, had reached a higher degree of abstraction. Number was, as it were, the exterior limit of the finite, and the interior limit of the infinite. Add to this that mathematical studies, cultivated in Egypt and Phoenicia for their practical utility alone, were being pursued in Hellas with ever-increasing ardour for the sake of their own delightfulness, for the intellectual discipline that they supplied��a discipline even12 more valuable then than now, and for the insight which they bestowed, or were believed to bestow, into the secret constitution of Nature; and that the more complicated arithmetical operations were habitually conducted with the aid of geometrical diagrams, thus suggesting the possibility of applying a similar treatment to every order of relations. Consider the lively emotions excited among an intelligent people at a time when multiplication and division, squaring and cubing, the rule of three, the construction and equivalence of figures, with all their manifold applications to industry, commerce, fine art, and tactics, were just as strange and wonderful as electrical phenomena are to us; consider also the magical influence still commonly attributed to particular numbers, and the intense eagerness to obtain exact numerical statements, even when they are of no practical value, exhibited by all who are thrown back on primitive ways of living, as, for example, in Alpine travelling, or on board an Atlantic steamer, and we shall cease to wonder that a mere form of thought, a lifeless abstraction, should once have been regarded as the solution of every problem, the cause of all existence; or that these speculations were more than once revived in after ages, and perished only with Greek philosophy itself.

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TWO:It was a little before eleven that Balmayne came in. He was very quiet and subdued; he sat and unfolded an evening paper. He shot a sign across to the Countess from a pair of eyes that gleamed like flames.Were this intellectual despondency to issue in a permanent suspense of judgment, it would be bad enough; but practically its consequences are of a much more mischievous character. The human mind is so constituted that it must either go forward or fall back; in no case can it stand still. Accordingly, the lazy sceptic almost always ends by conforming to the established creeds and customs of his age or of the society in which he lives; thus strengthening the hands of authority in its conflict with the more energetic or courageous enquirers, whose object is to discover, by the unaided efforts of reason, some new and positive principle either of action or of belief. And the guardians of orthodoxy are so well aware of the profit to be reaped from this alliance that, when debarred from putting down their opponents by law or by public opinion, they anxiously foster false scepticism where it is already rampant, and endeavour to create it where it does not exist. Sometimes disinterested morality is the object of their attack, and at other times the foundations of inductive science. Their favourite formula is that whatever objections may be urged against their own doctrines, others equally strong may be urged against the results of free thought; whereas the truth is that such objections, being applicable to all systems alike, exactly balance one another, leaving the special arguments against irrationalism to tell with as much force as before. And they also lay great stress on the internal dissensions of their assailants��dissensions which only bring out into more vivid relief the one point on which all are agreed, that, whatever else may be true, the traditional opinions are demonstrably false.

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TWO:When I left I got a lot of addresses of relations in The Netherlands, and undertook to send a postcard to each of these. They also gave me an introduction to the proprietor of an hotel whom they knew, in which they asked him to give me a bed; and thus armed I succeeded at last. It was high time too, for at nine o'clock everyone had to be at home. In the hotel everything was dark, for there was no gas in the town. At last I could lie down on my bed, and had a good rest, although I could not sleep a wink. I was too tired and had seen and experienced too much that day.

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