Mathematics taught at the high school level today is beyond what could be done in 1200. Several caveats:
A random adult from a 1st world country doesn’t necessarily recall their high school mathematics.
I’m sure 1200-era mathematicians had a lot of specialized knowledge not conveyed by modern high school. For a small example, they would probably be better at Euclid-style proofs than high school graduates. For a larger example, I believe mathematicians in the middle ages were expected to know a lot about astrology, as this was part of how they made money (not sure about 1200 exactly).
However, it seems possible that a smart person from today could make a rather good career as a mathematician in 1200, by reconstructing as much of modern mathematics as they could manage.
Of particular interest would be the theory of computation, because the construction of a mechanical computer might be accomplished much earlier—although, the construction of suitable clockwork would be required.
Other sciences would also be of interest, but advances would in general be more difficult to prove or convincingly establish. For example, you could accelerate science a little by writing a book about the cell theory, evolutionary theory, atomic theory, etc. But those theories may not be accepted within your lifetime.
One could write about probability theory along with the scientific method, but I don’t know to what extent that would fuel an early scientific revolution—to what extent was the scientific revolution bottlenecked by the ideas, vs the fertile ground of the time period?
Overall, I think the model you present in the post is most true of technology, less true of science, and least true of mathematics. Mathematics most fits the picture of:
Artifacts are not central at all; it’s mostly about actual knowledge in heads, and written in books.
The knowledge is not very context-sensitive; EG it does not depend on what tools are around.
Science fits this picture surprisingly less than mathematics; implements are very important, EG microscopes and telescopes.
Your discovery would be accepted much faster as you would build up street creed by inventing a handful of game changing thing like the printing press, ballistic, basic anatomy, scurvy remedies, or gunpowder
Of particular interest would be the theory of computation, because the construction of a mechanical computer might be accomplished much earlier—although, the construction of suitable clockwork would be required.
If you mean a universal mechanical computer (like Babbage’s analytical engine) then, as far as I know, none was ever built, because it’s actually really hard to have clockwork that good.
Mathematics taught at the high school level today is beyond what could be done in 1200. Several caveats:
A random adult from a 1st world country doesn’t necessarily recall their high school mathematics.
I’m sure 1200-era mathematicians had a lot of specialized knowledge not conveyed by modern high school. For a small example, they would probably be better at Euclid-style proofs than high school graduates. For a larger example, I believe mathematicians in the middle ages were expected to know a lot about astrology, as this was part of how they made money (not sure about 1200 exactly).
However, it seems possible that a smart person from today could make a rather good career as a mathematician in 1200, by reconstructing as much of modern mathematics as they could manage.
Of particular interest would be the theory of computation, because the construction of a mechanical computer might be accomplished much earlier—although, the construction of suitable clockwork would be required.
Other sciences would also be of interest, but advances would in general be more difficult to prove or convincingly establish. For example, you could accelerate science a little by writing a book about the cell theory, evolutionary theory, atomic theory, etc. But those theories may not be accepted within your lifetime.
One could write about probability theory along with the scientific method, but I don’t know to what extent that would fuel an early scientific revolution—to what extent was the scientific revolution bottlenecked by the ideas, vs the fertile ground of the time period?
Overall, I think the model you present in the post is most true of technology, less true of science, and least true of mathematics. Mathematics most fits the picture of:
Artifacts are not central at all; it’s mostly about actual knowledge in heads, and written in books.
The knowledge is not very context-sensitive; EG it does not depend on what tools are around.
Science fits this picture surprisingly less than mathematics; implements are very important, EG microscopes and telescopes.
Your discovery would be accepted much faster as you would build up street creed by inventing a handful of game changing thing like the printing press, ballistic, basic anatomy, scurvy remedies, or gunpowder
If you mean a universal mechanical computer (like Babbage’s analytical engine) then, as far as I know, none was ever built, because it’s actually really hard to have clockwork that good.