Guncotton - Aqua Fortis + Cotton/Cellulose = smokeless powder = much better guns than blackpowder ones.
OR
Hot Air Observation Balloons
I don’t think the tangible benefits of improved hygiene would be obvious over the hypothetical 2 years. But the utility of (better/any) guns and aerial views should be instantly obvious to a despot.
And seriously, people, you think they didn’t know how to make soap?
It’s a tossup between the optical telegraph and the printing press.
Since but since we are a client of our patron, I think the telegraph would be better as it is harder to use to stir up discontent against the king. As a plus, if it spreads, it’ll prevent a lot of wars. For example, part of the reason for the first crusade was the slow communication speed, once they heard about the local Muslim ruler in Jeruselum molesting pilgrims, then mustered an army, the ruler had been long replaced by a moderate who let Christians get to the holy sites.
It’ll be especially useful in the Roman empire, as they had both the resorces, and a dire need for rapid communication. The continuation and enrichment of the Roman empire would have created more stability for other improvements.
China had an early printing press and it did not help much.
Birth Control
Arabic numbers to Roman times. There were some strange numbering systems back then and it made it difficult to understand mathematical concepts. Having our current base-10 number system would make that much easier. If you could also teach algebra and trig, that would be even better.
Four field crop rotation.
“A four-field rotation was pioneered by farmers, namely in the region Waasland in the early 16th century and popularised by the British agriculturist Charles Townshend in the 18th century. The system (wheat, turnips, barley and clover), opened up a fodder crop and grazing crop allowing livestock to be bred year-round. The four-field crop rotation was a key development in the British Agricultural Revolution.”
Don’t forget basic probability theory. That was a revolutionary concept that didn’t exist until the sixteenth century.
I’d definitely say movable type.
Can I convince the Native Americans in South and Central America to use the wheel as more than a toy? Really, I just want to see what would happen.
I suspect that I could bring “hindu-Arabic” numbers and modern math notation, Distillation (although I’ll probably take several tries to get it right, and might might end up with giving somebody too much methanol), and paper, for starters.
The math is straightforward, and it’d have to be by example.
Distillation can be done with ceramic pieces (make an alembic) or with metal containers. Finding and making them might require persuasion or getting money, though.
Paper will require trial and error, but I’ve made paper at home. The problem (as L. Sprague de Camp observed in Lest Darkness Fall) is in making sizing – the stuff you add so ink doesn’t spread, and so your paper acts more like writing paper and less like a paper towel. de Camp’s Martin Padway used clay, but I understand “classic” sizing used glue made from animal hides.
For that matter, I can maybe introduce “composition” as a rubber substitute – basically animal gelatine/glue mixed with sweetener (sugar, if you can get it, or honey) and tempering (gypsum or suchlike). They used to use this for printing inking rollers, but you can use it for anyplace that we would use rubber or plastic. The problem is that it can flow and melt.
Hey, how about Movable Type and Printing? Lotta work i n rediscovering techniques for metal casting and getting parts together.
Shamefully stolen from Ken Follet’‘s book: I’'d replace the practice of bloodletting with that of keeping the ill and their rooms clean and using wine, vinegar and soap for wahing hands and sanitizing stuff that goes from patient to patient. That should yield better results fast, and utilize the placebo effect and fit the mindset of the time (well not the ancient theory of the four body fluids, but some theory on how cleanliness is next to godliness, or something.
Also, spinning wheels as opposed to spindles.
The Romans were way ahead of you.
What’s next, going back to the Aztecs and teaching them about chocolate?
I’d take a small flintlock pistol. It’s just an example of a weapon, what I’m really bringing is the process for making black powder. Cannons would be the first thing to make, followed by flintlock weapons, bombs, and the use of gunpowder as an explosive for mining, excavation, etc.
Can’t take anything with you. Point is what do know how to do, working only from memory.
A Bic lighter.
For the Middle Ages, the formula for concrete. The Romans had it but it was lost by the Middle ages.
Well then, I just bring the process of making gunpowder. It won’t be that difficult to get a cannon made, especially after showing the explosive power of the black powder using simply a hole in the ground. Even in the Middle Ages there wasn’t much knowledge about how to make potassium nitrate or how to corn charcoal to form the final product.
I’d much rather explain the process for making steel using a reverbatory furnace, but it would require a large investment in construction and may be difficult to convince anyone it’s worth the effort.
Well since I’m not allowed to take anything with me, it’d require a fair bit of studying and practicing, but I’d take back the knowledge required to build a modern compound bow. They weren’t invented until the 1960’s but I don’t think there is any technology in them that is inherently modern. They would provide a vastly superior advantage to any ancient army.
Even in the days of early firearms and cannons, I think an army wielding compound bows would be fierce.
Also, I’d try to learn how to build a bicycle and take that knowledge back to the past as well. I’m not sure what technology is required but I think a basic bicycle could be built from ancient components, even though they weren’t invented until the 1800’s.
But this is assuming I have several months or years preparing for my time travel trip. If it were going to happen today or tomorrow, I wouldn’t be able to offer much I don’t think.
Why make gunpowder when you can make the way superior nitrocellulose even easier?
Where do I get nitric acid in ancient Rome?
Electricity; wires, batteries, generators and transformers can be easily built out of materials available back then, either period (for insulation, use cloth or paper saturated with resin or tar; permanent magnets can be made by passing current through coils wound around pieces of iron, preferably while heated and cooled; batteries can be made with two dissimilar metals, like copper and iron, in a jar filled with salt water or vinegar).
Also, while I don’t know Morse code, I can easily see a basic telegraph system being set up with an improvised signaling scheme (in lieu of an electronic oscillator, an AC generator can be used to create a tone).
Maybe even a crude light bulb of sorts (not tungsten), although it would have to be filled with some inert gas (how well would a fire work for removing oxygen from the air?).