Time Travel

I think medical knowledge and technology would be largely useless for anything but saving yourself and, perhaps, a few close friends. Maybe once established it could prove useful.

The reason is that the churches control the information and most of medicine. You unique approach will not win favor with the church. Practicing medicine, outside of a small area I will cover, in modern ways could get you burned at the stake.

As for other fields you can't go wrong with military technology. The real mavericks of the day were military men who didn't give a fig for dogma if it brought victory. Think early firearms, flintlocks and conceptual ideas like simple armored wagons and tactics. As I understand it they had access to small amounts of black powder and metalworking ability to produce firearms.

You first foot-in-the-door to get you out of the rank poverty 90% enjoyed might be had the details of history. Knowing ahead of time what people are going to do could grant you an edge as long as you avoid any hint of being a soothsayer or witch. A note to a royal about an upcoming historical battle could be turned in your favor if it can produce a victory.

Give up starting as a healer. Get the big guy's better ear by granting him victory. Then wealth and a tolerance for your odd ideas will be provisionally granted. You will stat as royal underling. A few investments and favors and some luck you should be able to gain some small amount of independent power. Once you have a bit of money and land, pretty much standard rewards for services to the elite, you can get to work providing your holdings with advancements like crop rotation.

Also a pocket full of Viagra might help. The one area the church could never control was marital aids, aphrodisiacs and sound midwifery practices that allowed the rulers to produce healthy heirs. This might be better done as something of a reclusive polymath than as a central figure in the public eye.

Once you get your foot in the door the biggest bang for the buck isn't actual medicine so much as sanitation. On your estate you could set up clean water, sanitation and work on the rude basics of hygiene. But you will have to be subtle about it. And make sure surrounding land owners benefit. Otherwise jealousy will have them killing you outright or sending in the church.

Be doubly sure to cultivate the church, to attend services and to gain favor with the PTB in the church hierarchy. Generous contributions, building churches and cultivating a pious image will be essential. There will be no room for atheists.

You could also set yourself up as a the guy who protects the royal houses from smallpox. You could find a local milkmaid with cowpox and use her suppurations as primitive vaccine. Hopefully the anti-vax folks won't send back one of theirs or we may all be doomed. This would likely have to be done on the QT and only for the elites. Your not going to get far if you have to explain to the church what your doing and how it works. It will smack of witchcraft.

Good luck. In those days people dropped by the thousands from malnutrition, overwork, lousy sanitation, conscription as fodder for elites during the constant religious wars and as object lessons by the church to keep the rest in line. Helping anyone will automatically make you the enemy of the other side. Unless your a peasant. In which case you despised by everyone.

You will have to lay low, learn the language and religion and players before you make your move. Generally peripheral small settlements well away from the eyes of the church and power centers. Near a coast and perhaps a river for more abundant food cleaner water ans sanitation would be a the best place to start. Once your on your feet and have become adept at avoiding attention and the churches eye try one of the culture centers and try to gain the favor of an up and coming nobleman.

Your odds might be better if you land, or can get to the middle east. The Byzantines of the day were relatively open to new ideas. the area mentioned is still pretty much filthy, face down in puke, and sleeping with cattle in the bedroom. In fact they were better off in that area 500 years earlier. Slaughtering peasants and religious wars seem to be the major pastimes of the time concerned. Pretty grim.

Vaccination for Smallpox MIGHT actually be something you could introduce without getting yourself burned at the stake. Even in Jenner's time just a century later, there was stil tremendous opposition though. Being a pioneer is always tricky.

Modern neuroscience idea in the 17th century... good question. I can't think of one which would be directly useful.

Teaching a few influential luminaries about learning systems and basic theory of computation could produce some interesting long term effects. Laying out the fundamentals of the philosophy of science a century early would be cool too. Oh, and the theory of chemistry; kill that damn alchemy a bit sooner. All of this could be done via letters to familiar names.

For the 9th century... oh, just staying alive it tough enough. For big effects, agriculture and breeding innovations are relatively safe and easy. You may even be able to get a patron (more food = more fodder for the pews and the wars).