## Clocks

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saus
Posts: 176
Joined: Fri Nov 02, 2007 12:19 am UTC

### Clocks

(Just thought of this problem as I looked at 2 clocks with 2 different times)

You see 2 clocks with 2 different times.

You don't know which clock is right, or if either is right at all.

You could assign a probability to each time of the chance of it being the real time. But you do not have that information. You could say it's a 50% chance for each, but they are both ultimately independent of each other. They could both be wrong.

Given the information that you have, that is, the times of the two clocks, with no
probabilities associated with them, is there a most likely time of day and what is it?

Anpheus
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### Re: Clocks

Spoiler:
Without any more information, no. You said 'what time of day,' so if you're suggesting it is daytime, there are a few hours that are consistently twilight hours, typically between 7AM/PM and 9AM/PM each day. If it's pitch black or mid-day and one reads 7-9 and the other reads 10-6, you can pretty well guarantee that the latter is the more accurate clock.

Short of that bit of information, you cannot assign probabilities. If each clock is off by one second from the other, then I can see no real way for you to determine which is valid.
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saus
Posts: 176
Joined: Fri Nov 02, 2007 12:19 am UTC

### Re: Clocks

I have no answer to this, I just thought of the problem.

I thought maybe there could be an answer other than "no" because you have 2 pieces of information, so maybe in some way they can shed light on what time it truly is. I didn't intend time of day to mean just daytime.

JamesCFraser
Posts: 32
Joined: Wed Nov 14, 2007 9:47 pm UTC

### Re: Clocks

Spoiler:
With only the information you have provided, in such a simple form, I would have said all times of the day are equally likely.

However, if you knew some kind of distribution describing how far it is likely for the clocks to be out by, then you could calculate an answer

Macbi
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### Re: Clocks

An average?

That would make the most sense given no other info.
Indigo is a lie.
Which idiot decided that websites can't go within 4cm of the edge of the screen?
There should be a null word, for the question "Is anybody there?" and to see if microphones are on.

Buttons
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### Re: Clocks

We have no reason to suspect that either clock is telling us anything. Basically the question reduces to, "Some guy hands you a piece of paper with two numbers from 1 to 86,400 written on it. What time of day is it?" Naturally, there is no good answer.

Macbi
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### Re: Clocks

If we asume that the clocks are somewhat accurate than an average will help.
Indigo is a lie.
Which idiot decided that websites can't go within 4cm of the edge of the screen?
There should be a null word, for the question "Is anybody there?" and to see if microphones are on.

Buttons
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Location: Somerville

### Re: Clocks

Macbi wrote:If we asume that the clocks are somewhat accurate than an average will help.

Certainly. But from the information given, we have no reason to assume that.

Macbi
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Location: UKvia

### Re: Clocks

Is there some time of day that is more likely than the rest, independant of the clocks, like because of timezones etc.
Indigo is a lie.
Which idiot decided that websites can't go within 4cm of the edge of the screen?
There should be a null word, for the question "Is anybody there?" and to see if microphones are on.

Anpheus
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### Re: Clocks

You can only determine which clock is more accurate if one is in a twilight time period and the other is not, and you can see outside. During twilight there are a few specific times you can expect, and all others are day or night.
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freddyfish
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Joined: Sat Oct 20, 2007 3:08 am UTC

### Re: Clocks

well the most likely time of day is prolly day/night/twilight/whatever it actually is outside. as for the clocks, u cant determine anything without more info.

Anpheus
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### Re: Clocks

If the clock shows 12:00 and it's day out, do you know whether it is correct or not?

The only good evidence you have is twilight versus the rest of the day.

If all you had was a measure of outdoor brightness, and couldn't determine location and the suns position, you could measure the sunrise/sunset every day for a period of time and determine a correction for either clock, but the time zone would be unknowable. You could, for example, assume the sun rises at 6AM, and then wait for sunrise.
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quintopia
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### Re: Clocks

If they are both digital clocks, and one of them is blinking, then there is an increased probability that the non-blinking one is right.

xman
Posts: 2
Joined: Mon Nov 26, 2007 3:36 am UTC

### Re: Clocks

quintopia wrote:If they are both digital clocks, and one of them is blinking, then there is an increased probability that the non-blinking one is right.

A stopped clock is guaranteed right at least once a day (depending on if there is an AM/PM indicator). A clock that is slightly off is probably not going to be right as often.

quintopia
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### Re: Clocks

I was assuming neither clock was stopped, but if one is stopped, I would still trust the other one (which, on average, will be off by a few minutes (in the real world), whereas the other is off by an average of 12 hours.

hermaj
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### Re: Clocks

If one of the digital clocks was blinking you could probably use that information with the other clock to determine what time it might be. When it flashes, it's because it has been reset, and because digital clocks have an indication for AM/PM you can determine exactly how long ago the clock was reset (I mean, you wouldn't know how many days had passed but that doesn't matter for this).

...I've kind of lost where I'm going with this. Damn. I guess if you had some way of determining when the clock was reset, then you could add the hours on to that time and you'd have the correct time? I don't know.

Macbi
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### Re: Clocks

I've used that to track down the time of a power cut, but unless you know, say, that there was a lightning storm at 3:00, it doesn't help much.
Indigo is a lie.
Which idiot decided that websites can't go within 4cm of the edge of the screen?
There should be a null word, for the question "Is anybody there?" and to see if microphones are on.

Anpheus
I can't get any worse, can I?
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Location: A privileged frame of reference.

### Re: Clocks

In order to determine that time though, you need an accurate clock, watch, etc.
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DrStalker
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### Re: Clocks

If you know you longitude you can look at the stars to figure out the time. Of course, that involves completely ignoring the clocks.

(For practical solution to this situation I use a Google search for "World Time Clock" whenever I'm not sure which clock in my house is correct, which happens every daylight saving shift since I can't remember which devices change automatically correctly, which change automatically incorrectly, and which don't change. Then I sleep in, show up to work late and blame my alarm clock. )
There are two types of people in the world: 1) those that can extrapolate from incomplete data.

Reid
Posts: 31
Joined: Thu Nov 01, 2007 3:02 pm UTC

### Re: Clocks

DrStalker wrote:Then I sleep in, show up to work late and blame my alarm clock. )

An elegant solution.

If we could assume that both clocks were properly set and that the difference is just a matter of one or both clocks running consistently slower or faster is there a better strategy than guessing wildly?

quintopia
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### Re: Clocks

Assuming they are analog clocks in a sealed, locked, windowless room, and there are no other clocks accessible by any means, then no, guessing wildly is all you got, because all a clock is a means to measure accurately how many standard intervals have passed, and the time of day is an agreed-upon convention, like which way is "left." (See the left/right thread for more problems like this.)

EricH
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Location: Maryland

### Re: Clocks

Reid wrote:If we could assume that both clocks were properly set and that the difference is just a matter of one or both clocks running consistently slower or faster is there a better strategy than guessing wildly?

Your assumption allows us to find what time it was, when the clocks were set--or, more precisely, the last time they agreed. (Note the difference at a specific time, let an interval pass (say, an hour by the slower clock), and note the difference again. That tells you how fast they're diverging, and then some simple math will tell you what time it was when they agreed.) If it's possible that they've already diverged by more than 12 hours (for simple analog clocks), then we'd need a third clock, with a different bias, to be sure what time they were all set.
A second assumption I would add is that clock inaccuracy is likely to be a bell curve--most clocks are slightly off, one way or the other, but few are likely to be wildly inaccurate. ("Broken" is an exception, but I presume we can tell if a clock isn't changing at all....)
Since they could both be fast, or both be slow, or one of each, we still have to guess, but it doesn't have to be completely wild--we can minimize the error by guessing that the current clock time is the average of the two clocks.
With three clocks, not only can we be relatively sure about when they were set, but we can also make a better guess--find the median clock, such that the other two are diverging from it in opposite directions; if one is diverging from the median much faster than the other, then it's probably not accurate; discard it, and average the other two clocks. If they're diverging at similar rates, then the median clock is your best bet.
(Yes, I'm avoiding math with words like "similar" and "much faster"; if you were truly looking for an algorithm, you'd need to pick some numbers...)
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deja
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### Re: Clocks

someone mentioned a stopped clock is on average off by 12 hours. to me that doesn't seem true at all. Assuming is analog, and there is no am/pm indicator, then there are only 12 hours to work with. So if its stopped at 6, then the farthest time will ever be is at 12, meaning 6 hours off. and the closest it will be is at 6. so, its actually on average, only 3 hours off
Vu?

Robo-Jesus
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### Re: Clocks

Ahhh, I see what you did thar.
Nice work crafting such a scenario.
Now you're thinking with Portals.

quintopia
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### Re: Clocks

deja: that was me, and I was wrong. I was thinking of a clock with am/pm on it, and I should have said six hours.

skeptical scientist
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### Re: Clocks

deja wrote:someone mentioned a stopped clock is on average off by 12 hours. to me that doesn't seem true at all. Assuming is analog, and there is no am/pm indicator, then there are only 12 hours to work with. So if its stopped at 6, then the farthest time will ever be is at 12, meaning 6 hours off. and the closest it will be is at 6. so, its actually on average, only 3 hours off

Actually, if it says 6:00, then on average it's 0 hours off, since it's ahead as often as it is behind.

I know, I know, it depends whether you consider the signed or unsigned error.
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