My experiments with random selection without replacement as an information processes reveal that what I call Paradoxical behavior is achieved with internal information loss, because internal and external losses may compound. Seemingly simpler Truncating behavior seems to require injection of random numbers (as with dither in digital audio processing).
Starting with the hypothesis that Paradoxical processes are behind the strangeness of quantum physics, this suggests that contrary to the laws of quantum physics, in some cases there IS data loss, and that drives the strangeness.
And I see how this could happen. What we know of as bosons (protons and neutrons) and leptons (electrons) could be complex structures built around and sustaining tiny black holes. These black holes provide the "gravity" that matter has. Meanwhile, the structure around the black holes keeps the black holes alive by capturing the Hawking Radiation and forcing it back into the holes. That overall process is information losing. Nothing but black holes can have an information losing character (like my Dumb process, information goes in but doesn't come out). The information lost is the precise time, giving it a granularity, so they don't exist in continous time but leaps ahead, meaning some information states don't exist. There is less information in the world than we think. The effects of this are profoundly paradoxical.
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