"How did these invention ideas come simultaneous to completely different people?"
Science and invention, more often than not, respond to current demand. If there's a demand for an invention, or a new influential theory that poses some kind of testable question, then multiple inventors/scientists will research the same idea/question, which can result in multiple people coming up with the same result. It's not like ideas sprinkle themselves randomly amongst the population, and that the same idea is some huge coincidence.
For example, today, many hundreds of mathematicians are currently working on the Riemann Hypothesis, because there is a very clear need in the mathematics community (and beyond) for a proof either way (also because there's a million dollar prize involved as well). If multiple people discover the solution, I would not be in the least bit surprised.

