Anyway, not much of a coincidence.

And yes we’ve been friends since high school, but we have also been friends since junior high school!

]]>For the chronograph there is no such effect, it stops when I push the pusher.

But of course, the watch doesn’t actually get wound at a random time, either. I wind the watch fully when I put it on (usually in the morning, but not always), and then sometimes during the day I’ll idly twist the crown once or twice or a few times.

I don’t know the duration of the ‘power reserve’ on the Luch, but there are several mechanical watch movements with a power reserve of about 40 hours, meaning the watch will run for about 40 hours after being wound completely. Suppose you put on such a watch at 8 a.m. What’s 40 hours after 8 a.m.? Midnight. If you have a watch with a 40-hour power reserve and you typically wind it and put it on around 8 a.m., having it stop within 40 seconds of midnight is really not surprising at all.

]]>The Luch was about $30 and I love it.

Another quirky watch is my Russian 24-hour watch, which has a rotating bezel to keep track of a second time zone. I bought this to go with the 24-hour clock in my office, which has a polar projection map that rotates with the hour hand so you can see the time anywhere in the world at a glance. Back before I had a cell phone and companion smart watch I used to travel with this 24-hour watch and use it as intended, not because I really needed to but just because that sort of thing is my idea of fun.

The reissue of the 1963 Chinese chronograph cost a lot more, maybe $300 or something. I got one for my brother for his birthday (he was born in 1963) and liked it so much I got one for myself too. Very distinctive look. And yes, the movement (visible through the display case back) is beautiful…and just such a fine bit of engineering, a column wheel chronograph. I love the fact that you can see how it all works.

Kindred, since you chose that moniker I’m guessing you won’t be too bored if I tell you that I also have two, count em two, Bulova men’s dress watches, bit in elegant gold-plated cases. They’re men’s watches but are tiny by today’’s standards, even for women’s watches. I got the first on eBay for $23, with the idea of wearing it to special hoity-toity occasions like the opera. It was made in 1946 from prewar parts. For my purpose I only need it to keep time within about a minute per hour. — put it on at 5 pm, take it off at 11 — but it was even worse than that so I bought a similar one (from 1955 or so) for about $50 that works fine. But I couldn’t bring myself to toss the old one, and ended up having it cleaned, which cost twice as much as buying the two watches in the first place. So now I two tiny, elegant dress watches.

I also have a quartz Seiko that is close to my platonic idea of watch design, and I’ve seriously considered (but rejected) spending thousands of dollars to buy a mechanical watch with similar looks and functionality. It just seems..I dunno, inelegant…to have to buy a battery every few years for a watch I only wear a few days per month.

To round out my ‘collection’ I also have a bronze blue-dial dive watch from Zelos. This one is my favorite daily wear watch.

]]>This nicely illustrates the difference between how we do stats when NHST is involved, vs when Bayes is involved. We can “reject the hypothesis” that the watch stopped randomly and uniformly according to your model. Note however, that we can reject that hypothesis no matter where it stopped because it only depends on the width of the interval you’re looking in ;-)

Of course, in reality, that’s not how watches work. First off, the one that ran out of spring tension and stopped will run from the last time it was wound for a number of seconds that depend on things like the amount of energy in the spring and the friction in the movement. For that watch, put a prior over when the watch was wound, and the number of seconds that it can run before stopping when wound. Collect some data on when Phil winds his watch, and how long it runs when wound (a gamma distribution is probably appropriate for a likelihood), then calculate a posterior probability to be within epsilon of the 12 position.

For the second watch, it was stopped by Phil after his travel, so we need a prior on the time it takes him to make the trip (perhaps again a gamma distribution), plus the amount of time it takes him to remember to stop the watch after his trip (another gamma distribution?). Then collect some data and calculate a posterior probability.

The relevance of these calculations is obvious because there’s a clear connection between the design of the generating process and what actually happens in the world.

One suspects that these probabilities are more concentrated around what happened than your uniform examples, so you could consider your uniform examples as lower bounds on the probability. My guess is the generative model calculations would be easily a factor of two larger.

]]>Those Seagull movements are pretty great. State of the art Swiss factory watchmaking, c. 1955. But still cool to look at, and fairly reliable all things considered.

]]>The first watch has a maximum of about 43,200 possible positions (12 hrs * 60 min * 60 s). If it stopped at 45s off, then at least 90 of those positions are relevant (stopping at 12 +/- 45s). Assuming it’s equally likely that it stops at any position (obviously it’s not, in reality, since it depends on when it was wound), then the likelihood of it stopping where it did, or equally close or closer, is 90/43,200 = 0.002083.

For the second watch, it sounds like there are 300 possible positions for the second hand (5 per second x 60 seconds), of which 3 are relevant (stopping at 12 +/- one tick). For the other two hands, it looks like there are 60 possible positions, of which only one is relevant (stopping at 12). So the probability of any one or more hands stopping at a relevant position is (3/300) + (1/60) + (1/60) = 0.043. So the total probability of at least one hand of each watch stopping where they did or closer, assuming they are equally likely to stop at any time, assuming each hand is equally likely to stop at any time, is 1/(0.002083 * 0.043333) = one in about 11,077.

Ok smart folks, please tell me all the ways that I’m wrong :-)

]]>Remember the research incumbency rule: The first thing that’s published, we assume is true. All critics are held to a higher standard. Indeed, I’m thinking we should criticize Yuling for bullying by daring to criticize a peer-reviewed blog post without first sending his confidential criticisms to Phil on the Q.T. I’m sensing a tone problem here. Who does Yuling thing he is, the replication police?

]]>No, you miscalculated the p-value! Don’t forget, Pr(woman)=0.52, so the correct p-value is 0.48^45 = 5e-15. Statistics is hard.

]]>I’m astonished. I wonder what the universe is trying to tell us. Probably something about sports or politics.

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