According to Plutarch, Numa did not allow for graven images because he subscribed to the Pythagorean belief in the omnipotence of deity. According to Pythagoras, such a deity can only be comprehended and worshiped through the intellect. Because of the supreme characteristic of this being, he reasoned that it would be impious to fashion God in the image of man or beasts.
...they made no statues in bodily form for them, convinced that it was impious to liken higher things to lower, and that it was impossible to apprehend Deity except by the intellect. Their sacrifices, too, were altogether appropriate to the Pythagorean worship; for most of them involved no bloodshed, but were made with flour, drink-offerings, and the least costly gifts.
Numa also instituted a Roman Sabbath or 'holiday' because he supported the Pythagorean practice of separating divine worship from the performance of temporal duties. Numa believed that, in order to fully appreciate the importance of religious ceremonies, the people had to carve out time apart from their daily activities.
At all public and solemn processions of the priests, heralds were sent on before through the city, bidding the people make holiday, and putting a stop to all labour. For, just as it is said that the Pythagoreans do not allow men to worship and pray to their gods cursorily and by the way, but would have them go from their homes directly to this office, with their minds prepared for it, so Numa thought that his citizens ought neither to hear nor see any divine service while they were occupied with other matters and therefore unable to pay attention.