Let's consider a multi-polar world where exchanges between the differerent poles are nearly in-existant (the other sides are considered decadant, too far away and previous interactions often escalated in military tensions, ...).
Close examples in our world would include China/Europe in the XVIth century, Russia/USA in the XXth century though the links where never closed as much as in this imaginary world.
As a result each side is at best ignorant and at worst ridiculing the little known from the other civilisation-poles.
Assuming that :
- the split happened after the scientific revolution on that world (Newton,...)
- science development was very similar to ours with government grants 'guiding' research ( which has the side effect that at first if one pole makes claim of some sort, other poles will consider this as propaganda and stop or reduce research in those topics)
Keeping in mind a few examples of serendipity at work in the field of science:
- 1928 Flemming discovered penicilia
- 1917 phage therapy was considered the most likely cure for bacterial infections and still actively researched in Russia.
Similarly electronics could have happened in one pole while another one would be more on the
steam punk side of things...
So how long would it take for a fully trained scientist to not be able to understand the science from another pole (assuming that he/she has family roots in a small area of the world where they speak a vernacular language which remained understandable across borders?
Let's make it more specific: How long before it takes more than 10 years scientific study of the other poles science to reach the level where being able to understand a PhD thesis ? If any which parameters could make this process faster or slower?