Eratosthenes's only tools were sticks, eyes, feet, and brains; plus a zest for experiment. With those tools he correctly deduced the circumference of the Earth, to high precision, with an error of only a few percent. That's pretty good figuring for 2200 years ago.
We cannot see outside what we are not inside. The universe is to us what the huge engine is to the miniature engine; and indication of any error in the tiny engine leads us to imagine trouble in the huge one.
Every limited mind demands a certain freedom of expression, and the man who cannot express himself satisfactorily without the stimulation derived from the spirited mode of two centuries ago should certainly be permitted to follow without undue restraint a practice so harmless, so free from essential error, and so sanctioned by precedent, as that of employing in his poetical compositions the smooth and inoffensive allowable rhyme.
A collection of errors does not make a truth: quality cannot stem from quantity – a value is not a weight. The reasons of the majority cannot be taken as good reasons.
Zarathustra was the first to consider the fight of good and evil the very wheel in the machinery of things: the transposition of morality into the metaphysical realm, as a force, cause, and end in itself, is his work. [...] Zarathustra created this most calamitous error, morality; consequently, he must also be the first to recognize it.
Even the good artisans fell into the same error as the poets; because they were good workmen they thought that they also knew all sorts of high matters, and this defect in them overshadowed their wisdom.
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.
Concepts which have proved useful for ordering things easily assume so great an authority over us, that we forget their terrestrial origin and accept them as unalterable facts. They then become labeled as 'conceptual necessities,' etc. The road of scientific progress is frequently blocked for long periods by such errors.
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.