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RogerS comments on Removing Bias From the Definition of Reductionism - Less Wrong
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Ah, is that so.
Yes, I can see that that's one way of looking at it.
I don't think so, since the information I would be comparing in this case (the "file contents") would be just a reduction of the information in two regions of space-time.
And under determinsim, all the information in any spatial slice will be reproduced throughout time. Hence the false positives.
I'm not clear what you are meaning by "spatial slice". That sounds like all of space at a particular moment in time. In speaking of a space-time region I am speaking of a small amount of space (e.g. that occupied by one file on a hard drive) at a particular moment in time.
Your can prove conservation of information over small space times volumes without positing information as an ontological extra ingredient. You will also get false positives over larger space time volumes.