Ok, so I tried this out on a small map with one AI. No surprise that it worked but it took me a a couple of cities to try and test with pops of 4,6,8,10 and 12. So if my city has more food than it needs, I just make them all science geeks. Got it.
Not exactly. In your core cities, you will probably want all citizens working the tiles. A taxman produces gold, only gold, & eats food. A scientist produces beakers, only beakers & eats food. A laborer produces (potentially) food, gold, and shields, and eats food. In your core, where corruption and waste are low, a laborer in a fully improved city can outproduce a specialist. Once you get out to the hinterlands, where corruption eats up most of the gold and shields, that's where you really want to focus on specialists. Neither food nor specialist output is affected by corruption or waste.
So do you recommend irrigating or mining all the city blocks? Irrigating seems to provide the most "spare" people, but what besides markets, banks, library and universities should I be building in my core, outer cities, and far flung villages.
A good rule of thumb, especially while you're in despotism, is: Mine green, irrigate brown. That rule goes out the window when it comes to food bonuses, but is otherwise pretty handy. Because of the despotism penalty, that rule saves lots of what would otherwise be wasted worker turns.
Ah, what to build . . . There's an article in my signature called "Multiplier Buildings: A Practical Primer." That might help you sort out what needs to be built and where. What you need, though, depends on how you want to win. For a conquest/domination victory, markets, libraries and raxes in the core. In the semi-core, add a few courthouses. In the farmlands, nothing. The question is not what a city needs. A city can survive with nothing. The question is: What is it that the empire needs for the city to have.
Sorry if these seem like dumb questions, but my preferred method of science usually involves pointy sticks!
Thanks
Pointy Stick Research has a long and hallowed tradition around here, and these are no dumber than the questions I asked when I first got here.