How often is the watch dead accurate?

A colleague and I were discussing the accuracy of watches last week. His watch has been gaining time for a number of years. Anyway I happened to mention that it would be more accurate if he just let it stop (reason being at least it would be accurate twice a day). Anyway, it bought up an interesting thought that if it was gaining say 5 mins a week, how many times a year would it show the accurate time?

Part of me thinks "who cares" however putting aside that it will be hours out of accuracy for a large chunk, I was just wondering :) I guess there is a formula for this sort of thing?

It would at least be accurate when it was changed from GMT to DST and vice versa :-)

Quote:

---

Originally Posted by SIB

It would at least be accurate when it was changed from GMT to DST and vice versa :-)

---

This, and at least twice a day if it's stopped......

The short answer is never.

The longer answer has to do with infinity.

43200secs (12 hours) divided by the number of seconds per day the watch gains is the number of days it would take to read right.

A simplistic answer, assuming a 12 hour dial, would be:

Code:

---

12 hours = 12 x 60 x 60 secs
        = 43200 secs


5 mins per week = (5 x 60) / 7 secs per day
                = 42.86 secs per day


Dividing the first figure by the second then gives us the number of days it will take for the 'fast' watch to gain 12 hours thus:


(12 x 60 x 60 x 7) / (5 x 60) = 1008 days
                              = 1008 / 365 years

---

In other words approximately once every two and three quarter years.

Quote:

---

Originally Posted by petethegeek

A simplistic answer, assuming a 12 hour dial, would be:

Code:

---

12 hours = 12 x 60 x 60 secs
        = 43200 secs


5 mins per week = (5 x 60) / 7 secs per day
                = 42.86 secs per day


Dividing the first figure by the second then gives us the number of days it will take for the 'fast' watch to gain 12 hours thus:


(12 x 60 x 60 x 7) / (5 x 60) = 1008 days
                              = 1008 / 365 years

---

In other words approximately once every two and three quarter years.

---

I have to admit to being a bit tipsy before writing this:

You're making the assumption that the seconds hands are in synch and that all you have to do is work out the minutes. If both watches were in perfect synch and the difference in time was exactly 5 minutes, your example would work. But that's not real. If the second hands weren't aligned and the watch always gained 5 minutes, they'd never meet.

The watch will have a time in hours minutes and seconds. You're looking for the probability that they are all aligned at the same time.

Given the seconds can be broken down infinitesimally there is an infinitesimally small chance they will align. It might happen every 10000000000000 days (or 1 day).

So that would lead you to believe that the stopped watch would be more accurate. That's true only when looking at time in large units, but like the previous example, the real time will match for an infinitesimally small period of time.

So the answer is 2*infinity or 1/10000000000000*infinity. Both are infinite. Both watches are as measurably accurate as each other, but the stopped one will be accurate more often.

It sounds as if guinea's answer is linked to Zeno's Paradox of Motion.

Which is something else I don't fully understand.

If it is stopped it is dead accurate
twice a day

If it has a date indicator then it will never be correct...

Quote:

---

Originally Posted by guinea

I have to admit to being a bit tipsy before writing this:

You're making the assumption that the seconds hands are in synch and that all you have to do is work out the minutes. If both watches were in perfect synch and the difference in time was exactly 5 minutes, your example would work. But that's not real. If the second hands weren't aligned and the watch always gained 5 minutes, they'd never meet.

The watch will have a time in hours minutes and seconds. You're looking for the probability that they are all aligned at the same time.

Given the seconds can be broken down infinitesimally there is an infinitesimally small chance they will align. It might happen every 10000000000000 days (or 1 day).

So that would lead you to believe that the stopped watch would be more accurate. That's true only when looking at time in large units, but like the previous example, the real time will match for an infinitesimally small period of time.

So the answer is 2*infinity or 1/10000000000000*infinity. Both are infinite. Both watches are as measurably accurate as each other, but the stopped one will be accurate more often.

---

The second hand is geared to the minute hand. If you never mess with the crown, the two hands will always stay in sync, therefore all you need to worry about is the minutes....

Quote:

---

Originally Posted by WingTsun

Get a Spring Drive and you'll no longer have to worry about it. :playful:

---

Spring drives are reported by owners to be +/- 1 to 2 seconds a month.

Same as any good quartz, but not a thermo-compensated one.

Quote:

---

Originally Posted by neilma

How often is the watch dead accurate?

---

All the time

http://i299.photobucket.com/albums/m...s/PB210028.jpg

Quote:

---

Originally Posted by WatchScout

All the time

http://i299.photobucket.com/albums/m...s/PB210028.jpg

---

Pff - it's not even displaying the right month!

;)

Quote:

---

Originally Posted by Cirrus

Pff - it's not even displaying the right month!

;)

---

:chuncky::chuncky:

It really depends which brane universe your friend exists in, and if they recently travelled on an aircraft.

Without going into detail it could be that he lives his life slightly fast, and so will die young, or that his watch is from the wrong dimension. In which case lizards will want it back and he will die young.

Either way, I wouldn't waste money on a service.

Quote:

---

Originally Posted by stooo

It really depends which brane universe your friend exists in, and if they recently travelled on an aircraft.

Without going into detail it could be that he lives his life slightly fast, and so will die young, or that his watch is from the wrong dimension. In which case lizards will want it back and he will die young.

Either way, I wouldn't waste money on a service.

---

That is true. Well, some of it.

Time runs faster at orbital height so presumably it runs marginally faster if you're taller.

Where I'm not clear is that while time itself may run faster, whether that causes the watch of a taller person (if worn at a slightly higher altitude) to speed up in relation or whether the watch stays constant (and therefore runs more slowly - relatively speaking at least).

The insinuation that some of that might be made up is preposterous. The basis of fact is anchored in Wikipedia and everyone knows factualness commutes and permeates through a chain of lies rendering them the truth.

http://en.m.wikipedia.org/wiki/Gravi..._time_dilation

Maybe if he is tall AND fat (or has a fat wife) it cancels itself out?

I might have elaborated a little about the dying young part, but the rest of is definitely isn't true.