For some reason, every other comment on this page (as of 02/21/09) referred to the theatrical feature Arcadia of My Youth, AKA My Youth in Arcadia, and the English dub Vengeance of the Space Pirate (these comments have finally been removed or reposted to the correct film). Please read the title at the top of the page; this is The Mystery of the Arcadia, a completely separate film featuring the same main character. This feature is a 35 minute theatrical short that was produced during the run of the 1978 Space Pirate Captain Harlock television series, which drew the bulk of its narrative from that series' thirteenth episode (Witch Castle in the Sea of Death) and added around fifteen minutes of new animation. The feature focuses on the relationships between Captain Harlock, his young ward Mayu Oyama, and the ship's mysterious central computer, climaxing with an undersea battle with the witch Aman in a story paralleling that of the famous Japanese folk tale "Urashima Taro." It's a non-essential but fun film aimed at fans of the original series, though it breaks with that series' internal continuity via its re-writing of the source episode.
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