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.
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
signs are an extremely personal language that we develop throughout our lives, by trial and error, until we begin to understand that God is guiding us.
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.
They (i. e., the Pythagoreans) did not advocate the free confrontation of conflicting points of view. Instead, like all orthodox religions, they practised a rigidity that prevented them from correcting their errors.