you’ve thoroughly convinced me that your formalisms do not break in the way I thought they did because of the limitation I’m referencing in this post.
That said, I still think point 1 is invalid: no, I don’t think any computational system until the end of time will know to 5 decimal places what temperature it was 500 feet in the air off the instantaneous shape of the surface of the ocean [edit: at gps 0,0] the exact moment that the apple made contact with newton’s scalp skin. it’s just too chaotic.
Maybe you can manage three, or something. Or maybe I’m wrong and you can actually get more than 5. but then I can go further and say you definitely can’t get ten decimal places, or fifteen. There’s just no way you can collect all of the thermal noise from that moment in time and run it backwards. I think. well, I guess I can imagine that this might not be true; there are ways the past might be unique and possible to exactly infer, and I definitely believe the past is quite unique at the level of humans who had any significant impact on history at all, so ancestor sims are in fact probably possible.
But as you say—gotta use simplifying abstraction for that to work.
“just too chaotic” is covered by “entire past lightcone”. no matter how chaotic, the past lightcone is one whole computation which you can just run naively, if you’ve got room. you get all decimal places, just like an agent in conway’s game of life can build a complete exact simulation of its past if it’s got room in the future.
you’ve thoroughly convinced me that your formalisms do not break in the way I thought they did because of the limitation I’m referencing in this post.
That said, I still think point 1 is invalid: no, I don’t think any computational system until the end of time will know to 5 decimal places what temperature it was 500 feet in the air off the instantaneous shape of the surface of the ocean [edit: at gps 0,0] the exact moment that the apple made contact with newton’s scalp skin. it’s just too chaotic.
Maybe you can manage three, or something. Or maybe I’m wrong and you can actually get more than 5. but then I can go further and say you definitely can’t get ten decimal places, or fifteen. There’s just no way you can collect all of the thermal noise from that moment in time and run it backwards. I think. well, I guess I can imagine that this might not be true; there are ways the past might be unique and possible to exactly infer, and I definitely believe the past is quite unique at the level of humans who had any significant impact on history at all, so ancestor sims are in fact probably possible.
But as you say—gotta use simplifying abstraction for that to work.
“just too chaotic” is covered by “entire past lightcone”. no matter how chaotic, the past lightcone is one whole computation which you can just run naively, if you’ve got room. you get all decimal places, just like an agent in conway’s game of life can build a complete exact simulation of its past if it’s got room in the future.
(yes, maybe quantum breaks this)
I guess core to my claim is I don’t think you ever have room in the universe. it would take astronomically huge amounts of waste.