I've been turning over this question with friends recently: if you travel back in time, and can bring only your own body and memories--no raw materials, no machines, no books, etc., what ideas do you bring?

For instance, I could probably draw and explain how to fabricate every part of a fixed gear bicycle, or at least a velocipede. But that only works in a time which has (at a minimum!) access to reasonably efficient axle bearings, and ideally rubberized tires, gears, etc. The window is small!

Other ideas we've turned over (and laughed at the implications of trying to advance them in inappropriate times)

- Hand washing
- Germ theory
- Calculus
- Post-structuralism
- Lagrangians, diffeq
- Cryptographic ciphers (executable via analogue techniques)
- Boiling/alcohol for sterilization
- Queer theory
- Biodiversity (e.g. prevent the German forestry disaster)
- Crop rotation
- Randomized controlled trials
- Silent reading
- Eyeglasses
- Marxism
- Suspension bridges
- Japanese joinery

@aphyr the best answer I read to this (specifically about travel to medieval Europe) is to sneak mentions of the health benefits of certain kinds of mould into some galenic texts so the monks all copy it, and bingo you've given them penicillin
@anandamide @aphyr And a few decades later you've given them penicillin-resistant bacteria. That one needs either incredible discipline in how it's deplyed or 20th century level biochemistry to play arms race with the bacteria (and we still might lose).
@aphyr Incubators! "Put this baby that was born too early in a low temperature oven" was one of those 'crazy but it works' ideas at the time. Though I'm not sure I'm comfy with accelerating overpopulation...

@aphyr there is a very specific time window where knowing how to solve 3rd and 4th degree polinomials can make you rich, or at least famous in very specific circles

practical? not very :D

(also, it involves things of very questionable morality such as negative numbers and their square roots)

@aphyr A decent number system with zero and negative numbers. Maybe some elementary algebra and i^2 = -1.

Optical quality glass.

A list of vitamin C rich foods and a half-assed world map.

If there's metallurgy good enough to form wires, bootstrap a chemical battery to induced magnetism to manufacture permanent magnets to make motors and generators.

Steam engine.

Iodine good.