people have the belief that they live a continuous, linear stream of consciousness (whatever that means).
i've made arguments before as to why this is erroneous; but here is another interesting argument that undoes the seeming coherence of such a statement.
think of reality as a computational process, generating frames one after another, possibly splitting into timelines.
where is your consciousness? one might be tempted to answer that it's the set of bytes representing the state of the brain. if i split the world into two timelines, which one is the "fake copy" and which one is the "continuous original"? one might answer that the copy is whichever new data structure has new bytes copied to it, and that the original is whichever presence in memory hasn't been moved; the same bytes, supposedly stored on the same hardware transistors.
if i were to split timelines by creating two copies and destroying the original, one might answer that this is akin to killing the original and creating two "fakes copies".
however, there exist persistent data structures, which represent new sets of data as added constructions on top of an original one. this is a perfectly reasonable way to do computation, and one would probably agree that if someone is only ever running a single timeline, people have continuous consciousness.
however, i were to run a world simulation using persistent data structures and generate a timeline split, which one is the "continuous person"? just like with continuous single timeline computation, both new timelines are merely new data structures with their own set of whichever data is different, and pointers back to whichever sets of data are unchanged.
the least unreasonable choice someone who believes in linear streams of consciousness could make is that somehow persistent data structures are not a valid form of universe computation; that a computation ought to be run by reusing the same memory locations. surely the arbitraryness of such a claim despite its functional equivalence to persistent data structures for single-timeline computation demonstrates well enough how the notion of linear streams of consciousness doesn't make sense.