Markets and the Writer's guild are both on the path to education. Yes, the science from the specialists is raw science and is boosted by NC, universities, etc. Since the quickest way to the Renaissance is Acoustics, which has the Musician's guild, the only guild that's not on the fastest path is the Artist guild. However, the Artist guild (Guilds tech), workshop, bank and windmill are all on the fastest path to Scientific Theory, which is another 2-3 specialist slots on every city and all 6 of the guild slots in the capital.
As for food, that's what the internal trade routes are for. You grow the cities as much as possible while getting the markets and guild up. That's all part of the normal micro managing. You don't have to run all the specialists slots all the time. You do need all the scientist slots filled all the time to get as many GS's as possible. Run the other types of specialist as much as possible for the bpt boost and definitely run as many specialists as possible for the 8 turns before you finishing a science building/wonder in the capital to maximize the bulb effect. You do the same thing in the end game when you're getting ready to bulb with your saved GSs.
With Korea, I'd normally maybe get like 8 or 9 GS's, so we'll say I get 8 extra as Babylon, which is the equivalent of 64 specialists.
As for this. Don't forget that if Korea had built academies with all 8 or 9 GS's that's an extra 16-18 beakers or 8-9 less specialists and it gets those extra beakers per academy from the first one planted.
Are you certain about the difference in the number of GS's generated or were you just counting all the GS's and academies you had as Babylon? After all, not counting the 1 free one at writing, some of them probably came from either liberty finisher, leaning tower of pisa, porcelain tower, hubble or were faith bought. Those shouldn't be counted in the difference since both Korea and Babylon can get all of those. At most, with all things being equal, if Korea generated 8-9 then Babylon would have only generated 12-13 or a difference of only 4-4.5. As academies that's a max of 48 beakers or only 12 specialists. Since Korea's academies also give the 2 extra beakers that specialists do, that's only a difference of 30-32 beakers from academies or only 15-16 specialists. Since both civs will be running 4 scientists per city that's only 4 cities with all science buildings to make up that difference.
But wait, there's more. Every time Korea finished a science building in the capital it got the equivalent of bulbing with a GS. Even in the early game where you likely only have 10 bpt, that's 80 beakers or 10 turns worth of Babylon's early academy. This is exactly why you get the libraries and hopefully markets built in your other cities before building/buying the library in the capital. In fact, the capital doesn't even need its library done until you're close to being able to start the NC anyway.
To put it simply. Korea needs a lot more micromanaging between growth and specialist use than Babylon does. However, that micromanaging gets you a lot more science a lot faster once you start having the specialist slots available.
Korea is guaranteed to have 6 bulbs from the UA, library, NC, university, public school, research lab and Oxford. If the capital can build the observatory it gets a 7th. If you're using Oxford to unlock building Hubble, like most folks do, the bulb effect from finishing it will likely be enough to finish at least 1 other late game tech, so you essentially get 2 late game techs with Oxford.
