The “Butterfly Effect” is a valid concept whereby a small change to initial conditions in complex systems can lead to huge changes later on. The thought-experiment is that a butterfly flapping its wings in one location can, over time, lead to very different weather in a far distant location, as compared to if the butterfly had not flapped its wings. This term initially arose when an early experiment in weather simulation models showed a vastly different outcome when the simulation was restarted with values whose changes were below anything that could be measured at the time in reality — thus showing that effects too small to detect can magnify.
The “Mandela Effect”, on the other hand, is a fetid pile of dingo’s kidneys that is a fancy way of noting human memory is fallible and that false memories are reinforced through repetition. The human brain has a bad case of “sunk cost” fallacy, and rather than admit to itself it has been remembering something incorrectly for decades, would rather believe in parallel universe intruding into daily life on a regular basis. (The human brain is also lazy, or if you prefer, “efficient”, so it merges similar memories together, thus freeing up some storage space for other things and improving search time. For most of our actual needs, “close enough” works; it doesn’t matter that Kirk never actually said “Beam me up, Scotty” in the original series.)
