There's a book called How to Invent Everything: A Survival Guide for the Stranded Time Traveler that covers this stuff. Don't think it's comprehensive enough to actually invent everything from scratch, but still a fun read.

Skip electricity. That doesn't matter until you can make reliable turbines with copper and magnets. Go to steam power first. It can move things. Which will speed up delivery of copper and magnets. But also teach them to plant trees. Every tree removed to smelt and power a steam engine needs to have three more planted. You could start greening the Sahara before umit even starts collapsing. "he sure had this steam thing figured out. I guess we will forgive him for all these useless trees".

Electricity is easy to make though... a couple magnets and some copper wire.

Pretty much everyone in this thread needs to go read Ryan North's book "How to Invent Everything: A Survival Guide for the Stranded Time Traveler".

https://www.amazon.com/How-Invent-Everything-Survival-Stranded/dp/0735220158/

Or, if you don't have time, just print this out and keep it with you at all times:

I read a sci-fi short story about that once. A scientist brings back a guy from the future, but the guy either can't explain how things work or does so using a vocabulary the scientist doesn't understand.

It was like:

"How do you make a teleporter?"

"Well you take a zargnix and put it on top of a floon."

Me: The opposite of B, the opposite of B, plus or minus a square root...

Them: What does that mean?

Me: I have no idea.

I feel like you could still give science a head start by giving them rough ideas of how things work, like penicillin and steam power and whatnot

Even if you don't know all the ins and puts you can give them something to go off of to develop the technology faster

This reminds me of Dara O'Briain's bit about going back in time and thinking you'll impress the greatest minds in history with your future knowledge but it falls apart quickly.

https://www.youtube.com/watch?v=BVxOb8-d7Ic

I think it would actually be easier to wow people than people think. You'd just have to focus on older technology rather than completely modern stuff. If you know that steam engines are a thing, and even vaguely how they work, you can build the king a pump to get running water without having to run massive aqueducts, or a crane to build his massive projects, or any number of directly useful things. An understanding of basic germ theory could set you up to be the best doctor in the world. Or even just a bicycle would probably be quite useful to get around without a horse, and I'm sure anyone could make a rough mockup of a bike.

Go back in time with a 4th grade science book from 1997 and be a fucking wizard.

You could probably make explosives from manure. Use that to conquer a small community and make yourself the leader. And start a rebellion against the local lord and become the king. Then you have the resources and slaves to find copper and magnets and shit. Problem is the massive language barrier. Their language is just gibberish to us and vice versa.

If you paid attention in high school you could bring mathematics up to about the 17th century, if you really paid attention you could even grab some stuff from the 20th (wtf vectors why did you take so long to figure out?) and the 19th.

Plus there is just so much basic stuff you know. Used boiled and sealed water to clean a wound. Bleeding a person only makes them feel good for a bit and does nothing else. Steel in cement makes cement better. Or in the case of this picture zinc and copper and lemon.

You know, a fun project would be compiling an instruction book for elevating/fast forwarding technology just in case someone does get sent back in time.

I'm impressed at the strength of the guy's upper arm that he's sitting on.

Just spin a magnet in a copper coil.

BOOM! Electricity.

I'd actually be able to teach them how to make it if they have copper and magnets, since I know how to make a simple generator. They'd be SOL on how to use it though, because I don't know how to make something entirely from raw materials that would require electricity. Which means they also wouldn't know I am creating it with the generator... 🤔 Uh... Shit.

This is actually kinda wild to think about and I hadn't considered it before. Making electricity is easy! Using it is actually more complicated.

Forget mathematics, logic and philosophy. Teach them about Jeebus and establish a solid patriarchy. After that make a shitload of McDonald's and Facebook.

You'd still probably manage to get by offering services as an accountant. Illiteracy was the norm the world over for most of history, good math understanding was even rarer.