Jowett: calculating

Ath. To consecrate every sort of dance or melody. First we should ordain festivals — calculating for the year what they ought to be, and at what time, and in honour of what Gods, sons of Gods, and heroes they ought to be celebrated ; and, in the next place, what hymns ought to be sung at the several sacrifices, and with what dances the particular festival is to be honoured. This has to be arranged at first by certain persons, and, when arranged, the whole assembly of the citizens are to offer sacrifices and libations to the Fates and all the other Gods, and to consecrate the several odes to gods and heroes : and if any one offers any other hymns or dances to any one of the Gods, the priests and priestesses, acting in concert with the guardians of the law, shall, with the sanction of religion and the law, exclude him, and he who is excluded, if he do not submit, shall be liable all his life long to have a suit of impiety brought against him by any one who likes. LAWS BOOK VII

I mean, as I was saying, that arithmetic has a very great and elevating effect, compelling the soul to reason about abstract number, and rebelling against the introduction of visible or tangible objects into the argument. You know how steadily the masters of the art repel and ridicule anyone who attempts to divide absolute unity when he is calculating, and if you divide, they multiply, taking care that one shall continue one and not become lost in fractions. THE REPUBLIC   BOOK VII

And this, surely, must be the work of the calculating and rational principle in the soul ? THE REPUBLIC BOOK X