I wonder if that sort of transform is in general useful? Changing your logical uncertainty into an equivalent uncertainty about measure. For the calculator problem you’d say you knew exactly the answer to all multiplication problems, you just didn’t know what the calculators had been programmed to calculate. So when you saw the answer 56,088 on your Mars calculator, you’d immediately know that your Venus calculator was flashing 56,088 as well (barring asteroids, etc). This information does not travel faster than light—if someone typed 123x456 on your Mars calculator while someone else typed 123x456 on your Venus calculator, you would not know that they were both flashing 56,088 - you’d have to wait until you learned that they both typed the same input. Or if you told someone to think of an input, then tell someone else who would go to Venus and type it in there, you’d still have to wait for them to get to Venus (which they can do a light speed, whynot).
How about whether P=NP, then? No matter what, once you saw 56,088 on Mars you’d know the correct answer to “what’s on the Venus calculator?” But before you saw it, your estimate of the probability “56,088 is on the Venus calculator” would depend on how you transformed the problem. Maybe you knew they’d type 123x45?, so your probability was 1⁄10. Maybe you knew they’d type 123x???, so your probability was 1/1000. Maybe you had no idea so you had a sort of a complete ignorance prior.
I think this transform comes down to choosing appropriate reference classes for your logical uncertainty.
I wonder if that sort of transform is in general useful? Changing your logical uncertainty into an equivalent uncertainty about measure. For the calculator problem you’d say you knew exactly the answer to all multiplication problems, you just didn’t know what the calculators had been programmed to calculate. So when you saw the answer 56,088 on your Mars calculator, you’d immediately know that your Venus calculator was flashing 56,088 as well (barring asteroids, etc). This information does not travel faster than light—if someone typed 123x456 on your Mars calculator while someone else typed 123x456 on your Venus calculator, you would not know that they were both flashing 56,088 - you’d have to wait until you learned that they both typed the same input. Or if you told someone to think of an input, then tell someone else who would go to Venus and type it in there, you’d still have to wait for them to get to Venus (which they can do a light speed, whynot).
How about whether P=NP, then? No matter what, once you saw 56,088 on Mars you’d know the correct answer to “what’s on the Venus calculator?” But before you saw it, your estimate of the probability “56,088 is on the Venus calculator” would depend on how you transformed the problem. Maybe you knew they’d type 123x45?, so your probability was 1⁄10. Maybe you knew they’d type 123x???, so your probability was 1/1000. Maybe you had no idea so you had a sort of a complete ignorance prior.
I think this transform comes down to choosing appropriate reference classes for your logical uncertainty.