The origins of the Pensieve are little known, however the nature of which they are used it familiar with most wizards. A Pensieve is a device used to view memories, which may not be your own, I evaluate on them better than just remembering them inside your head.
Because of how dangerous they can be if used incorrectly or by a person you do not wish to view your memories, most Pensieves are evidently buried with their owners once they die to withhold giving away any personal information not wanted to be seen by people who may abuse it. However some witches and wizards will pass on their Pensieves as either a family heirloom or for other traditions, for example the Hogwarts Pensieve that is used by the Head Teacher of Hogwarts.
We first get a glimpse of it in Goblet of Fire when Harry is sitting in a courtroom watching a Death Eater Trail. It is then used more frequently in Half-Blood Prince when harry had to repeatedly watch memories that linked with how Voldemort had came to be.
The Pensieve was also used to help develop the plot further, for example we see how Snape had had strong feelings towards Harry’s mother, Lily.
One of the most climatic ways in which it is used was when Severus Snape was on his deathbed and gives Harry his final memories of which is stored his life and how it felt towards Lily and Harry. Harry finds out that Snape was a good person the entire time and that the only reason he hadn’t been able to be affectionate is that he was the son of the man Snape had hated, James Potter.
However there is only inconsistency between how the user is experiencing the Pensieve in the story. In Goblet of Fire, Harry is actually sitting in the courtroom itself and his viewing it from a person who actually would be there. However it Half-Blood Prince (film adaption) Harry is just watching the memory unfold and isn’t actually in Slughorns office.
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