Well, the same argument can be made for textile mills. Clothing is a necessity, just as much as food (particularly in a cold climate), and absorbs an enormous amount labor.
The argument can only be made if you insist that the amount of labor invested into textile weaving is the same as the amount of labor invested into grain-threshing, which I'd be rather doubtful about, since it contradicts pretty much everything I've heard or read about pre-industrial labor distribution.
And again, as pointed out before, textile mills allow the creation of an import export economy, which feeds into the ports, roads, and other transportation systems, and increases our links to other parts of the world. There is a reason that watermills for grinding grain did not kick off the industrial revoultion. It was the textile mill that did that.
This frankly sounds like a rather fallacious argument, because it implies that we wouldn't see similar effects anyway if we revolutionized other areas of our economy. Yes, if we develop and build textile mills we'll likely see an increase in import-export trade as merchants come and go to sell fibers and buy cloth. And if we develop and build a foundry that can mass-produce steel, we'll see an increase in import-export trade as merchants come and go to sell ore and buy ingots. If we introduce gunpowder and begin blast-mining, merchants will come to buy ore and sell other things. If we introduce new techniques that allow for the mass-production of boats and ships, merchants will come to sell us timber and buy other things. And so on, and so forth.
In short; if we introduce something that results in a major change to supply and demand, we'll see an uptick in trade as merchants react accordingly; that's how the market economy works.
It's pretty much the same with regards to roads and other forms of transportations. Yes, textile mills will increase a demand for better transportation infrastructure due to the increased amount of materials that need to be moved from a to be, but again it's the same for many other areas as well. If we increase the amount of ore that our mines can produce by introducing technologies such as blast-mining, mine carts, and the like, we'll see a similar increase as more ore (and, correspondingly, more fuel) needs to be transported to smelters, more ingots need to be transported to metalworkers, and the resulting goods need to be transported to customers. Same spiel in regards to other goods and resources again as well.
On the flipside, this also means that improved transportation infrastructure and technology benefits pretty much every aspect of the economy. We've already made a fairly good start with the introduction of concrete roads, with the only thing left to do actually building them, but it might also be a good idea to look into things like the
King road drag, for the creation of improved dirt road in areas where building concrete roads might not be economical (or at least urgent), and the
wagonway as a predecessor of railway for routes that see a particularly high amount of traffic.
As for your claim that the textile mill started the industrial revolution; that omits and simplifies so many preceding technological, and in some cases social or administrative, developments...
The textile mill is one of the earliest symptoms of the industrial revolution, and quite possibly helped speed it up, yes. But would it have been possible to design, build, and - most importantly - mass-produce a machine as complex as
this without preceding developments in mining, smelting and metalworking reducing the cost of so many complex parts? Without the preceding agricultural revolution - itself a result of various technological and social developments - resulting in a large influx of both unskilled workers (in the form of previous farm workers), and raw materials such as flax, hemp, wool, cotton, and the like? Without preceding developments in printing, education, and engineering allowing for inventors capable of designing such complex machines? Without the many other factors I'm undoubtedly forgetting right now?
If those many developments and prerequisites are missing, then there will be no industrial revolution, and right now we simply don't meet those requirements yet.
Err... discovering blood groups and other things like the periodic table of elements would require centuries of work by those institutions. Why shouldn't we just provide it in a book since we already have that information? Knowledge is not benefited by ignorance. The more people know, the better those institutions will be able to function. Not to mention the easier it will be to attract people to found and run those institutions.
The mere fact that we already know so much about mathematics, chemistry, and biology that is unknown to Westeros, just based on our generalist knowledge is a sign of how important that information is. It's what we consider foundational generalist knowledge that any educated person should know. Just take blood types for example, the mere fact that we know that is enough to leapfrog medical reaserch. Instead of trying to figure out why blood can usually not be shared, but that sometimes it can, instead healers would know that there are certain types of blood (just as there are different hair colors) and that the body attacks those that are registered as foreign. That's a huge help in increasing basic knowledge of how the human body works.
It's a question of priorities and applicability/immediate usefulness. If we're writing a book on blood groups or the periodic table, then we're not working on setting up the institutions that could perform such research on their own, or writing books introducing technologies for agriculture, mining, metalworking, mechanical engineering, and the like.
As such, we need to consider and compare what we would stand to gain. Let's say we go and write that book on blood types, for example; how does this help us/our kingdom within the next 5-10 in-game years or so? The answer would likely be "fairly little", because even if the average village healer knew about blood types, it's likely he wouldn't be able to put this knowledge to any practical use, since the necessary equipment to perform blood transfusions would be either outright technologically unfeasible, or likely far beyond the means of the average village healer.
By contrast, using that time to set up R&D organizations and facilities would improve our action economy, since they could either potentially develop innovations on their own, meaning we do not have to spend actions to do so, or because we can create a brief outline of an idea/technology and leave it to them to figure out the details, instead of having to work out everything ourselves. This in turn would allow us to introduce more technologies overall within the same span of time.
This doesn't mean we shouldn't write books containing our theoretical knowledge at all, but it does mean that - at least as far as I'm concerned - such books are a lot lower on our list of priorities compared to topics with more immediate practical applications.
This basic instruction should also probably include the scientific method.
IIRC the Maesters already use the scientific method - or at least something close to it. But either way; no. If the scientific method needs to be introduced, it would be as part of our efforts to establish research and development organizations and facilities as outlined under point four, alongside statistical data gathering and analysis, and possibly as part of the higher educational facilities under point three.
We might want to go ahead and distribute our printing press and thereby gain the benefits of others being able to print like we can. I had been holding off in the hope that we could convince the Citadel to send us copies of their books in exchange for sending them the printing press. Maybe we could accelerate that effort?
It's worth keeping in mind that while the Citadel's probably the most prominent center of learning in ASOIAF/GOT, it can't really be the only one. The Free Cities/Essos seems every bit as technologically advanced as Westeros, and in some cases potentially even more so. Myr is known for its advanced glassworking, for example, and IIRC Joffrey's crossbow was also some advanced model from one of the Free Cities. So, they'll have to have their own guilds, colleges, universities, and whatnot.
As such, while we shouldn't make enemies of the Citadel/Maesters unnecessarily, we also shouldn't think of them as the only source of knowledge available to us; there's nothing stopping us from sending out trading expeditions to visit the cities of Essos and seek out books to purchase.
As for the printing press; IIRC we just recently sent one (or the plans for one) to the queen of the Stormlands, and secrets/technological developments in general have a sort of "expiration date", in the sense that they'll eventually become known and more widespread. So I'm perfectly fine with trading or selling printing presses in order to get as much out of our current advantage as possible, while we're currently still the only one with the full knowledge of how to make and operate them.
A postal service is a good idea. Either we could charter a postal service, or we could attach it to the Road Wardens. I think I'd prefer to charter it though. Of course, continuing to expand the road network would be necessary.
Expanding/improving the road/transportation network is a good idea in general, since as I said above it would benefit pretty much every aspect of our economy and the kingdom.
The main problem I see with this is the feudal nature of our realm; we can build roads within our own domain all we want, but if we want to, for example, build a road connecting the White Knife with the Weeping Water or the Broken Branch, we'll have to convince or order the various lords through whose domains the road would pass, which would cost time, effort, and influence.
It's part of the reason why I think another one of our mid- to long-term goals should be governmental reforms for the North; to make it much easier to implement improvement such as concrete roads, schools, and the like throughout the entire realm.
Rewards for certain achievements could be useful. I think particularly in chemistry, in which we could create a book (purporting to be the knowledge of an older civilization) containing as much knowledge on chemistry as we have, and then basically provide a reward to whoever can succeed in recreating something in the book. It wouldn't be that strange for a king to do something like that. That would be a way for us to try and push forward the fertilizer industry without having to spend so many actions on it ourself.
Patents are the gold standard here though it will be difficult to establish it. Perhaps we can sell it to the guilds as a way to ensure masters continue to get a benefit from techniques they discover? Basically the master teaches the method or knowledge to the guild which then collects rents from other members of the guild who use the knowledge and then provides the majority of that rent to the master (or his heirs) that discovered the method? That would leverage the fact that the guilds already exist and that a major part of their effort is to prevent the unauthorized practice of their craft.
Subverting (sorta) the guilds for that was more or less what I had in mind. The main problem I can see with that is the potential of monopolies forming, as we get kingdom and potentially continent-spanning guilds of carpenters, blacksmiths, and whatnot.
I'd be more inclined towards something like inviting the masters of various crafts guilds, laying out the issue - ie, we want to spread knowledge around since it benefits the realm as a whole, they want to hoard knowledge since it benefits their members - and then trying to work out some sort of compromise that hopefully achieves our overall aim while preventing such monopolies.
As for the rewards, I was thinking less in terms of offering ready-made solutions and asking people to make it work, since that frankly doesn't save us much time, and more in terms of offering rewards and recognition for solving problems we want solved.
In your example, for example, we would have to write that book on chemistry, first, before we can ask people to try and develop fertilizer with it, in which case we could probably just add the extra work to develop the fertilizer ourselves since that'd probably easier/faster than writing the rest of the book.
Instead, we'd announce a task/issue we want solved and let people come up with their own solutions. This would not only let us save time, it would potentially also net us several different solutions that we can make use of, possibly including ones we might not have thought of ourselves.
For example, if we announce that we offer a reward for those who develop new tools or techniques to reduce the cost of building and maintaining roads of all kinds, there might be one person who's somewhat technically inclined and develops a device similar to the fresno scraper, a second might lack the engineering skills and be more inclined towards simpler solutions and come up with something akin to the King road drag in order to cheaply make and maintain simple dirt roads, and a third might be a stonemason or miner who notices how easily small stones seem to interlock when you put weight on them, and propose something similar to macadam roads.
It only requires us to draft and publish the announcement, and after rewarding all three we'd have three more road-construction methods we can make use of.
Going back to your example, rather than writing a book on chemistry and requesting someone try to use it to develop fertilizer, we could just announce that we are offering a reward for anyone who develops a method to better fertilize fields for the growing of crops. Some alchemists might then come up with fertilizers like blood/bone/fish meal, but we might also see something like a primitive liquid manure spreader design from it.
True, this is why I tend to see creating the books as the first step on the path to eventually founding these kinds of organizations.
And in my opinion it continues to be a case of trying to put the cart in front of the horse.