To give a simple example, gunpowder is quite easy to make. You don't think the industry of the times would support its production?
They just started having gunpowder in the era of the question, but for a few centuries the guns were very crude and ineffective, and you couldn't make any better guns without better metalworking. There is another question about how you could make a modern gun in medieval times, and the answer is, even if you had a complete schematic it would border on impossible.
such a basic thing as a stirrup took a surprisingly long time to get to Europe
They already had stirrups in the 13th century.
About the strategy. Make up a better strategy using only the tools they had access to, and I (or anyone well-read in that time period) will show you how they would beat you.
I was making a more general point: it is not true that the military technology (at any age and for every society) was the best their industry an economy would support.
I (or anyone well-read in that time period) will show you how they would beat you.
No, you will not. The simple reason is that you cannot show me anything -- an argument of the kind "My cavalry charge would destroy your left flank! No, my left flank will withstand the charge and scatter the cavalry!" cannot be settled.
Imagine that you were instantly transported into (roughly) the 13th century. I'm not great at history, but I'm picturing sometime around the crusades. You're sitting there, reading this post on your computer, and BAM! Some guy in chain mail is asking you if thou art the spawn of a demon.
Given this situation, I present to you a challenge:
You are stranded in the past. You have no modern technology except your everyday clothes. The only thing you do have is your knowledge from the future.
What do you do?
I'll make this a little more structured for the sake of clarity.
1) You appear in Great Britain (or the appropriate analogue for your native culture).
2) Assume the language barrier is surmountable - in other words, it may not be easy, but you can communicate effectively (by learning the language, or simply adapting to an older version of your native tongue).
3) Further assume that you manage to gain the ear of a ruling lord (how is not important, just say you're a wizard or something) and that he provides you with enough money, labor, and expertise (carpenters, smiths, etc.) to build something *so long as you can describe it in enough detail*.
4) You are only allowed to pull from general, scientifically literate knowledge - high school/bachelor's level only.
5) You can't use your knowledge of future events to your advantage, as it requires too expert a grasp of history. Only your knowledge of the way the world actually works is available.
The reason for 4) has to do with the point of the question. I'm trying to figure out the kind of maps that we have today that are considered "general knowledge" - the kinds of things that are so obvious to us we tend to not realize that people in the past didn't know them.
I'll go first.
The germ theory of disease didn't achieve widespread acceptance until the 19th century. In other words, I'm the only person in the past who is quite confident about how diseases are spread. This means that I can offer practical advice about sanitation when dealing with injuries and plagues. I can make sure that people wash their hands before cutting other people up, and after dealing with corpses. I can make sure that cutting instruments are sanitized (they did have alcohol) before use. And so on. This should reduce the number of deaths from disease in the kingdom, and prove my worth to the king.
I'm trying to build a list of things like this - maps of the way the world really is that we take for granted.
Have fun!