If, for the sake of discussion, creation of the time machine takes an hour, and travel in the machine is instantaneous, then when I am first given the slide rule it is an hour old. But if it is an hour old and I have it for another hour before giving it to my past self, it is 2 hours old. But if it is 2 hours old and I have it for another hour before giving it to myself, it is 3 hours old. Ad infinitum.
Am I missing something?
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Only if you keep giving yourself the same slide rule, or watch, or artifact, or piece of paper. there is a simple way out of this:
I am sitting here now at my desk. Suddenly, NtCrawler from 2005 appears to me and gives me a watch. So far, in this thread people assumed that I would keep that watch around, wait until 2005, in order to go back in time and give it to myself. But that would make it a djinn. So a simple way to prevent that:
I keep that watch. But before my scheduled depature back in time in 2005, I go out shopping, buy the exact same watch that I already have, and THAT’s the watch I use to give to myself. So it’s still one watch, with a definite beginning, and a traceable timeline. It’s simply a year older when time passes past my departure in 2005. Am I right?
And what would happen if I gave myself the WRONG watch? Well, using Douglas Adams and his Hithhiker writings as a guide, I suppose the universe would implode and recreate itself into something even stranger than before