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.
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.
Were half the power that fills the world with terror, Were half the wealth bestowed on camps and courts, Given to redeem the human mind from error, There were no need of arsenals or forts.
The mind moves by instincts, associations and premonitions and not by fixed dates or completed processes. Action and reaction will occur simultaneously: or the cause actually be found after the effect. Errors will be resisted before they have been properly promulgated: notions will be first defined long after they are dead.
Another error is an impatience of doubt and haste to assertion without due and mature suspension of judgment. For the two ways of contemplation are not unlike the two ways of action commonly spoken of by the ancients; the one plain and smooth in the beginning, and in the end impassable; the other rough and troublesome in the entrance, but after a while fair and even. So it is in contemplation; if a man will begin with certainties, he shall end in doubts; but if he will be content to begin with doubts, he shall end in certainties.
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.
For knowing is spoken of in three ways: it may be either universal knowledge or knowledge proper to the matter in hand or actualising such knowledge; consequently three kinds of error also are possible.
To let them share in the highest offices is to take a risk; inevitably, their unjust standards will cause them to commit injustice, and their lack of judgement will lead them into error. On the other hand there is a risk in not giving them a share, and in their non participation, for when there are many who have no property and no honours they inevitably constitute a huge hostile element in the state. But it can still remain open to them to participate in deliberating and judging.
To free a man from error is to give, not to take away. Knowledge that a thing is false is a truth. Error always does harm; sooner or later it will bring mischief to the man who harbors it.