But what do we even mean by changing the laws of physics so as to “make time reusable”? The first answer that suggests itself is simply to define a “time-traveling Turing machine,” which can move not only left and right on its work tape, but also backwards and forwards in time. If we do this, then we’ve made time into another space dimension by definition, so it’s not at all surprising if we end up being able to solve exactly the PSPACE problems.
But wait: if time is reusable, then “when” does it get reused? Should we think of some “secondary” time parameter that inexorably marches forward, even as the Turing machine scuttles back and forth in the “original” time? But if so, then why can’t the Turing machine also go backwards in the secondary time? Then we could introduce a tertiary time parameter to count out the Turing machine’s movements in the secondary time, and so on forever.
But this is stupid. What the endless proliferation of times is telling us is that we haven’t really made time reusable. Instead, we’ve simply redefined the time dimension to be yet another space dimension, and then snuck in a new time dimension that behaves in the same boring, conventional way as the old time dimension. We then perform the sleight-of-hand of letting an exponential amount of the secondary time elapse, even as we restrict the “original” time to be polynomially bounded. The trivial, uninformative result is then that we can solve PSPACE problems in “polynomial time.”
Q. Can you command buildings (e.g., resource processors and collectors) to travel back in time using a chronoporter?I'd rather have a timebomb.
A. No, but this is not a limitation of the engine. This was an explicit choice for gameplay reasons. However, buildings can be sent to the future with a chronobomb.
Q. OK, what is a chronobomb?
A. A bomb that sends everything in an area to the future. This is useful to bottleneck your opponents, and is a weapon that one of the alien races has.
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posted by doobiedoo at 3:19 PM on March 28