olutely necessary, and may
be said to be a necessity of that nature against which God himself is
unable to contend. 'What are these divine necessities of knowledge?'
Necessities of a knowledge without which neither gods, nor demigods,
can govern mankind. And far is he from being a divine man who cannot
distinguish one, two, odd and even; who cannot number day and night, and
is ignorant of the revolutions of the sun and stars; for to every higher
knowledge a knowledge of number is necessary--a fool may see this; how
much, is a matter requiring more careful consideration. 'Very true.'
But the legislator cannot enter into such details, and therefore we
must defer the more careful consideration of these matters to another
occasion. 'You seem to fear our habitual want of training in these
subjects.' Still more do I fear the danger of bad training, which is
often worse than none at all. 'Very true.' I think that a gentleman
and a freeman may be expected to know as much as an Egyptian child.
In Egypt, arithmetic is taught to children in their sports by a
distribution of apples or garlands among a greater or less number of
people; or a calculation is made of the various combinations which are
possible among a set of boxers or wrestlers; or they distribute cups
among the children, sometimes of gold, brass, and silver intermingled,
sometimes of one metal only. The knowledge of arithmetic which is thus
acquired is a great help, either to the general or to the manager of
a household; wherever measure is employed, men are more wide-awake in
their dealings, and they get rid of their ridiculous ignorance. 'What do
you mean?' I have observed this ignorance among my countrymen--they are
like pigs--and I am heartily ashamed both on my own behalf and on that
of all the Hellenes. 'In what respect?' Let me ask you a question. You
know that there are such things as length, breadth, and depth?
'Yes.' And the Hellenes imagine that they are commensurable (1) with
themselves, and (2) with each other; whereas they are only commensurable
with themselves. But if this is true, then we are in an unfortunate
case, and may well say to our compatriots that not to possess necessary
knowledge is a disgrace, though to possess such knowledge is nothing
very grand. 'Certainly.' The discussion of arithmetical problems is a
much better amusement for old men than their favourite game of draughts.
'True.' Mathematics, then, will be one of the subjects in which you