If reincarnation is real, would you know if you got reincarnated?

Some people who believe in reincarnation use such memories as proof - the kids who understand foreign languages they've never been exposed to, people who recall specific details about a place that has to be confirmed by historians, etc. It doesn't account for the majority that don't have any knowledge that could be attributed to a previous life, but it's still fairly interesting as a theory. I'd take reincarnation over Heaven but there isn't enough evidence in any case.