lol, I build NC sooo late. I always kinda chuckle when I see other players insist small/NC is the only way to be competitive and thus the game is boring. It's not, nor is it necessarily the optimum.
I personally think there are several good science approaches, the two most obvious are:
One, put out fast settlers. Build 3 cities, hurry libraries and build NC in capital, while developing on growth.
OR: continue to expand and put out new cities, ignore NC, and build it later after you've built all the early cities you can build. This puts you a little farther behind AI initially, but not for long as more cities=more pop, and eventually more available scientist specialists, jungle sites, mountain sites, what-have-you. With spies in the renaissance and 5-10 good, growing cities later, I actually seem to end up the same, if not better on science, so remember, you don't always have to do it the same way every game to win.
The main difference is late-game and is due to how growth slows down on large cities. It is totally true that you can have the same population and thus science rate for less happiness cost when you go small/tall in the beginning so it feels optimum, however, once you hit 25+ pop the rate of growth slows down significantly, whereas with many cities growing toward pop 25 I can quickly get far more population late-game due to the growth rate differences even without many food caravans which means more gold and other things as well. The only bad thing about wide is reduced policy rate, but honestly, even this works out with some work and you should have no trouble filling rationalism and the critical trees, I never have. If some of you are struggling to adjust to playing wide, try a religious game--many of the benefits scale with empire size, and can drastically ease the happiness, culture, and faith shortages.
Remember there is a time-lag between spies and constabularies, so being behind the AI in the beginning is fine. I've had plenty of games where I was caught up, 3 techs behind, or even five on a bad game. Caught up the same on all of them with some good spy placement choices and tech order . Where you want to start pulling ahead is the industrial where tech leads are easier to lock down and runaways in science begin. You want to be that runaway. I've found the time you reach the public school-->research lab path to be far more significant than when you take education, and often saving Oxford for later is just as useful for bulbing the porcelain tower tech or breaking into Plastics easily. There are a myriad of paths and I'm not convinced one of them is the best, though Civ V does feel more restrictive than the previous Civs. Mainly bc you can't trade science and there is a very distinct path for optimum science.
You can totally suck in the beginning, but if you succeed diplomatically putting the world to war while you develop you can also catch up on a tough game. Each game will be different and you'll learn how to adapt to each one the more you learn--this is what makes Civ V fun!
