"It doesn't take more 2s to point at smaller pieces of reality, it takes more 2s to point at smaller pieces of the probability distribution.  If you assign probability 1/64 to something, it only takes you 6 'bits' to point there.  If you're already assigning 98/100 to some particular measurement coming in at exactly 0.891 seconds, you're only going to lose 0.03 'bits' each time, which is to say, once you can exactly predict the times, they're not helping you narrow down things much further.  It would only automatically take more bits to specify narrower pieces of reality if there was - some kind of - fixed probability distribution, or - this actually feels like it's pointing somewhere important but I don't know where yet."

"Theories only have so much probability to spread over all the possible precise measurements, so when there's more possible measurements, the probabilities on the vast majority of possible measurements have to be thinner.  Measuring things to three decimal places is one way to get lots of possible outcomes you're measuring, but it could also be something like - measuring three different things about it down to one-tenth apiece, say."

"If one theory puts lots of its probability with 0.002 seconds of 0.891 seconds, and another theory says 0.887 plus or minus 0.003 seconds, they've got some overlap, but measuring down to the nearest thousandth is pretty likely to do a good job of prying them apart.  Measuring down to the nearest hundredth instead, would be like adding up all the thousandths closest to that hundredth, to get the theory's predictions about what the measure would say as opposed to what was exactly real.  And then the two theories would give around the same probability to 0.89, down to the hundredth, and measuring at that precision wouldn't pry them apart."

"It doesn't take more 2s to point at smaller pieces of reality, it takes more 2s to point at smaller pieces of the probability distribution.  If you assign probability 1/64 to something, it takes you 6 'bits' to point there.  If you're already assigning 98/100 to some particular measurement coming in at exactly 0.891 seconds, you're only going to lose 0.03 'bits' each time.  Once you can exactly predict the measurements very certainly, they're not helping you narrow down things much further.  It would only automatically take more bits to specify narrower pieces of reality if there was - some kind of - fixed probability distribution, or - this actually feels like it's pointing somewhere important but I don't know where yet."

"Theories only have so much probability to spread over all the possible precise measurements, so when there's more possible measurements, the probabilities on the vast majority of possible measurements have to be thinner.  Measuring things to three decimal places is one way to get lots of possible outcomes you're measuring over.  But it could also be something like - measuring three different things about it down to one-tenth apiece, say."

"If one theory puts lots of its probability with 0.002 seconds of 0.891 seconds, and another theory says 0.887 plus or minus 0.003 seconds, they've got some overlap, but measuring down to the nearest thousandth is pretty likely to do a good job of prying them apart.  Measuring down to the nearest hundredth instead, would be like adding up all the thousandths closest to that hundredth, to get the theory's predictions about what the measure would say as opposed to what was exactly real.  And then the two theories would give around the same probability to measuring 0.89, if you were only measuring down to the hundredth, and measuring at that precision wouldn't pry them apart much."

"It doesn't take more 2s to point at smaller pieces of reality, it takes more 2s to point at smaller pieces of the probability distribution.  If you assign probability 1/64 to something, it takes you 6 'bits' to point there.  If you're already assigning 98/100 to some particular measurement coming in at exactly 0.891 seconds, you're only going to lose 0.03 2s each time.  Once you can exactly predict the measurements very certainly, they're not helping you narrow down things much further.  It would only automatically take more 'bits' to specify narrower pieces of reality if there was - some kind of - fixed probability distribution, or - this actually feels like it's pointing somewhere important but I don't know where yet."

"Theories only have so much probability to spread over all the possible precise measurements, so when there's more possible measurements, the probabilities on the vast majority of possible measurements have to be thinner.  Measuring things to three decimal places is one way to get lots of possible outcomes you're measuring over.  But it could also be something like - measuring three different things about it down to one-tenth apiece, say."

"If one theory puts lots of its probability with 0.002 seconds of 0.891 seconds, and another theory says 0.887 plus or minus 0.003 seconds, they've got some overlap, but measuring down to the nearest thousandth is pretty likely to do a good job of prying them apart.  Measuring down to the nearest hundredth instead, would be like adding up all the thousandths closest to that hundredth, to get the theory's predictions about what the measure would say as opposed to what was exactly real.  And then the two theories would give around the same probability to measuring 0.89, if you were only measuring down to the hundredth, and measuring at that precision wouldn't pry them apart much."

"It doesn't take more 2s to point at smaller pieces of reality, it takes more 2s to point at smaller pieces of the probability distribution.  If you assign probability 1/64 to something, it takes you 6 'bits' to point there.  If you're already assigning 98/100 to some particular measurement coming in at exactly 0.891 seconds, you're only going to lose 0.03 2s each time.  Once you can exactly predict the measurements very certainly, they're not helping you narrow down things much further.  It would only automatically take more 'bits' to specify narrower pieces of reality if there was - some kind of - fixed probability distribution, or - this actually feels like it's pointing somewhere important but I don't know where yet."

"Theories only have so much probability to spread over all the possible precise measurements, so when there's more possible measurements, the probabilities on the vast majority of possible measurements have to be thinner.  Measuring things to three decimal places is one way to get lots of possible outcomes you're measuring over.  But it could also be something like - measuring three different things about it down to one-tenth apiece, say."

"If one theory puts lots of its probability within 0.002 seconds of 0.891 seconds, and another theory says 0.887 plus or minus 0.003 seconds, they've got some overlap, but measuring down to the nearest thousandth is pretty likely to do a good job of prying them apart.  Measuring down to the nearest hundredth instead, would be like adding up all the thousandths closest to that hundredth, to get the theory's predictions about what the measure would say as opposed to what was exactly real.  And then the two theories would give around the same probability to measuring 0.89, if you were only measuring down to the hundredth, and measuring at that precision wouldn't pry them apart much."

"It doesn't take more 2s to point at smaller pieces of reality, it takes more 2s to point at smaller pieces of the probability distribution.  If you assign probability 1/64 to something, it takes you 6 'bits' to point there.  If you're already assigning 98/100 to some particular measurement coming in at exactly 0.891 seconds, you're only going to lose 0.03 2s each time.  Once you can exactly predict the measurements very certainly, they're not helping you narrow down things much further.  It would only automatically take more 'bits' to specify narrower pieces of reality if there was - some kind of - fixed probability distribution, or - this actually feels like it's pointing somewhere important but I don't know where yet."

"Precise claims don't have to talk about a smaller set of worlds, there can still be probability everywhere, it's that most of the probability will be concentrated in a narrower set of worlds."

"But theories only have so much probability to spread over all the possible precise measurements, so when there's more possible measurements, the probabilities on the vast majority of possible measurements have to be thinner.  Measuring things to three decimal places is one way to get lots of possible outcomes you're measuring over.  But it could also be something like - measuring three different things about it down to one-tenth apiece."

"If one theory puts lots of its probability within 0.002 seconds of 0.891 seconds, and another theory says 0.887 plus or minus 0.003 seconds, they've got some overlap, but measuring down to the nearest thousandth is pretty likely to do a good job of prying them apart.  Measuring down to the nearest hundredth instead, would be like adding up all the thousandths closest to that hundredth, to get the theory's predictions about what the measure would say as opposed to what was exactly real.  And then the two theories would give around the same probability to measuring 0.89, if you were only measuring down to the hundredth, and measuring at that precision wouldn't pry them apart much."