Number itself is not an absolute, but a relative determination: it does not touch the nature of the thing itself. Nature has no difference of number, as we have, of odd and even, tens and hundreds; nor do the gods, spirits, or other rational beings define the numbers and measures of objects by the same series of terms. Both numbers and the methods of numbering are as diverse as are the fingers, heads, and mental equipment of the numberers. That which fits in with the numbers of nature will therefore never fit in with our numbers. Thus ten horses and ten men, although determined arithmetically by one and the same number, are in nature, or physically, wholly unequal to one another.[412] [Sidenote: The atoms.] [Sidenote: Time and space.] In order that men's minds may be better disposed for the reception of truth, it is necessary first to demolish the foundations of error;[413] Bruno accordingly sets himself to disprove the infinite divisibility of the continuum.[414] It was the common belief that there were no limits set to the dividing power of either nature or art, so that, however small a part might be arrived at, it was possible to divide it into yet smaller parts, on the analogy of the division of a fraction into tens of thousands of parts. Bruno denied this analogy to be justifiable, as in the latter case we are concerned not with division but with multiplication or addition, not with a continuum, but with discrete quantities, and it was part of his general theory that the addition of discretes might be carried on _ad infinitum_; the inverse process he denied. He thus held opinions directly contrary to those of Aristotle, with whom the mass of the universe was finite, limited by its enclosing sphere, the parts of the universe unlimited. Aristotle had an upper but not a lower limit; Bruno a lower but not an upper. So time and space, which Aristotle had treated as _finite_ in duration or extent, but as _infinitely divisible_, like the universe itself, are regarded by Bruno as unlimited in their dimensions, but as consisting of discrete minimal parts. "In every point of duration is beginning without end, and end without beginning"; it is the centre of two infinities. Therefore the whole of duration is one infinite instant, both beginning and end, as immeasurable space is an infinite _minimum_ or centre. "The beginning and source of all errors, both in physics and in mathematics, is the resolution of the continuous _in infinitum_. To us it is clear that the resolution both of nature and of true art, which does not advance beyond nature, descends from a finite magnitude and number to the atom, but that there is no limit to the extension of things either in nature or in thought, except in regard to the form of particular species. Everywhere and always we find the _minimum_, the _maximum_ nowhere and never. The _maximum_ and _minimum_, however, may in one sense coincide, so that we know the maximum to be everywhere, since