There are several views on personal identity over time: 1. The biological view sees identity as related to the organism - as long as the body is alive, identity persists. 2. The psychological view defines identity through psychology and continuity of memory. 3. The brain view claims the brain is central to identity - if the brain was transferred, identity would too. 4. Nihilism denies the existence of personal identity altogether. The lump of clay/statue puzzle presents a coincidence problem that various theories address - whether the objects fully overlap, are temporal parts, or are mistakenly seen as distinct. Defining personal identity remains challenging with open questions.