3 ms·

I'm assuming the error of every clock has the same probability distribution. I think this is a reasonable assumption, because the phrase only mentions the numbe

by mrob 3y ago

I'm assuming the error of every clock has the same probability distribution. I think this is a reasonable assumption, because the phrase only mentions the number of clocks. In this case, the more clocks you average the lower your expected error.

ndsipa_pomu 3y ago
But with just two clocks, the distribution isn't evident. They could both be running fast and thus the average would be worse than the clock showing the earlier time. You'd have no way of knowing without consulting more clocks. Also, with clocks you should be measuring the rate at which they measure time. Typically clocks can run fast or slow which means that the time shown is a function of how long they've been running since they were last correct.
- mrob 3y ago
  It's possible for the person with the single clock to get lucky and have a more accurate time than the average, but the original quote says "knows the time". Using the traditional definition of knowledge as "justified true belief", somebody with a lucky clock does not truly know the time. Their belief is true, but not justified. It's really the person with multiple clocks who has more accurate knowledge of the time. The more clocks they average the more justification they have for their belief.
  - ndsipa_pomu 3y ago
    The single clock owner doesn't have to be especially lucky. Imagine if they had a clock that was two minutes fast and the dual clock owner had one that was merely a minute fast and the other was ten minutes slow. The average would be less accurate, despite owning the most accurate clock. Two clocks just don't work for statistical analysis (three clocks are unlikely to help either). Also, the single clock owner is justified in believing that they have the correct time as there's nothing to suggest that they could be wrong. Two clocks introduces doubt where there was none before. Rather than using "justified" true belief, humans tend to go for the easier option and would be more likely to go to the person with just one clock, until they find someone with enough clocks and clout to point out the likely correct time.

by mrob 3y ago

ndsipa_pomu 3y ago

But with just two clocks, the distribution isn't evident. They could both be running fast and thus the average would be worse than the clock showing the earlier time. You'd have no way of knowing without consulting more clocks. Also, with clocks you should be measuring the rate at which they measure time. Typically clocks can run fast or slow which means that the time shown is a function of how long they've been running since they were last correct.

mrob 3y ago
It's possible for the person with the single clock to get lucky and have a more accurate time than the average, but the original quote says "knows the time". Using the traditional definition of knowledge as "justified true belief", somebody with a lucky clock does not truly know the time. Their belief is true, but not justified. It's really the person with multiple clocks who has more accurate knowledge of the time. The more clocks they average the more justification they have for their belief.
- ndsipa_pomu 3y ago
  The single clock owner doesn't have to be especially lucky. Imagine if they had a clock that was two minutes fast and the dual clock owner had one that was merely a minute fast and the other was ten minutes slow. The average would be less accurate, despite owning the most accurate clock. Two clocks just don't work for statistical analysis (three clocks are unlikely to help either). Also, the single clock owner is justified in believing that they have the correct time as there's nothing to suggest that they could be wrong. Two clocks introduces doubt where there was none before. Rather than using "justified" true belief, humans tend to go for the easier option and would be more likely to go to the person with just one clock, until they find someone with enough clocks and clout to point out the likely correct time.