"I share the view of Pythagoras that the world is number. The ultimate substrate of the universe is math. There's no way to test that - it's pure metaphysical speculation."
- Bart Kosko

This excerpt describes one of the machines which comprised the City Fathers:

The Librarian was that one of the 134 machines comprising the City Fathers which had prime charge of the memory banks, and was additionally charged with teaching; it did not collect information, but only catalogued and dispensed it. Interpretation was not one of its functions.

“CARD A CCEPTED. PROCEED...”

[After getting the answer,] Chris sat back, scratching his head in exasperation. He had hoped for a clear-cut, yes-or-no answer, but what he had gotten stood squarely in the middle.

Then he noticed that the booth had not returned his card to him. This was quite usual; it meant only that the Librarian, which spent its whole mechanical life substituting free association for thinking, had a related subject it would talk about if he liked. Usually it wasn’t worth while exploring these, for the Librarian could go on forever if so encouraged; all he needed to do now was to say “Return,” and he could take his card and go. But the take-cover alert wasn’t over yet; so, instead, he said, “Proceed.”

Ultimately, the City Fathers were charged with the survival of the city:

"Chris, the City Fathers are not interested in your welfare; I suppose you know that. They're interested in only one thing: the survival of the city. That's their prime directive. Otherwise they have no interest in people at all; after all, they're only machines.

The City Fathers had authority over many areas in the city:

lately they had been bearing down heavily on his interest in history-but what good was that aboard an Okie city? The City Fathers themselves were the city's historians, just as they were its library, its accounting department, its schools and much of its government. No live person was needed to teach the subject or to write about it, and at best, as far as Chris could see, it could never be more than a hobby for an Okie citizen.

How do you create new City Fathers?

"The arrangement with the machinery is cumbersome, but not difficult in principle. We can lend you our Brood assembly until she replicates herself; then you reset the daughter machine, feed her scrap, and out come City Fathers to the number that you'll need-probably about a third as many as we carry, and it'll take maybe ten years. You can use the time feeding them data, because in the beginning they'll be idiots except for the computation function.

Compare this system to another which seems to consist of a single entity; check out the Big Computer, from Millennium, by John Varley.