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Comment by ndsipa_pomu | Hacker News Reader

A simpler example may be that a person with one clock knows the time, but a person with two clocks is never quite sure.

It's a popular phrase, but it doesn't make sense if you think about it. The person with two clocks can average the time of both of them and get a result they can be more confident in than the person with only one.

That only works if both clocks are wrong in opposite directions and so confidence wouldn't be appropriate. Taking the average might work if you've got a whole bunch of clocks and they show a distribution such as a bell curve - that's what's required to become more confident than the single clock owner.

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.

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.

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.

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.

I have many clocks and typically I am sure about the time. I keep them in sync or know which one is off.

How do you keep them in sync? I bet you're using an established time source.

Walk around with a wristwatch. Even if the watch isn't synced to something authoritative, you can still use it to get all the clocks the same as each other (and the watch).

What if the watch runs fast - how do you synchronise the other clocks to an untrustworthy watch? For extra points, assume that the clocks are all in different rooms so you can only see one at a time and it takes an unknown number of seconds to go from one room to another.

The easy answer is that the watch doesn't run that fast. If it runs, say, 10 seconds fast a day (which is a lot), then if walking from one room to the other takes a minute, the watch is off by... 0.007 seconds. I'm not going to be setting the clock that accurately.

But if the clock just runs consistently fast (and if I know how fast it runs), then I can use the watch to measure how long it took to walk from one clock to the other, and from that I can compute the correct time to set the second clock to.

How could you know how fast it runs without comparing to an accurate time source? Maybe it's running slow and you don't even realise it.

Well, I can compare it to all the clocks.

But, you know, if I have no accurate source of time, why do I bother having a watch and N clocks?

You're a clock collector?

Sorry for the offtopicness but could you please email hn@ycombinator.com?

I don't mean to pester you but there's an important issue with your account that we need you to know about.

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