I’ve never heard the bring one or three, I’ve always just heard three. I think that exact saying implies that if you have two and one isn’t working out you’ll go crazy but if you have one you’ll be oblivious until it’s too late.

A well serviced rolex in 2026 with laser cut gears drifts +/- 15sec per day.

One with hand filed gears is going to be +/- a minute on a good day, and that’s what early navigation was using. I have watches with hand filed gears and they can be a bit rough.

Prior to that, it was dead reckoning, dragging a string every now and again to calculate speed and heading and the current and then guesstimating your location on a twice daily basis.

Those two wildly inaccurate systems mapped most of the world for us.

Reading the comment thread here made me realize the idea seems to be that having 2 just means double the probability of one of them failing in some undetectable way. The resulting error magnitude is reduced by half, but the probability of that error is doubled. So it gains you nothing to expected value to have 2. Unlike with 3, where the probability of undetectable failure and the error rate from partial failure are both reduced by the ability to make comparative measurements (eg pick the middle number not the average)

> A well serviced rolex in 2026 with laser cut gears drifts +/- 15sec per day.

Modern Rolex (and Omega et al) are more like +/-2s.

Interesting, thanks for sharing.

Though not without significant errors, the most amusing to me being that islands had a tendency to multiply because different maps would be combined and the cartographer would mistake the same island on two maps as being separate islands due to errors. A weird case of aliasing I suppose.