Surely the extrapolation is wrong?
at 4 heads, just randomly select a jury of 3. and you're back on track.
at a million heads, just sum up all their guesses, divide by one million, and then check the over/under of 0.50
Are two heads better than one?
31–40 of 78 posts
Re: Are two heads better than one?
#32Sailors in the past had a similar adage: “Never go to sea with two chronometers; take one or three.” They relied on precise clocks to calculate longitude.
I think it is different in the continuous case though, because you can average two (reasonably accurate) chronometers and get a better measurement. But we can't average true and false, at least not in the context of this problem definition. But the chronometers are will sync with each other if you don't store them apart, which would result correlated noise that an average won't fix.
You can definitely average two relatively accurate chronometers but you if you only have two it’s difficult to tell if one is way fast or way slow.
In a perfect world they drift less than a minute per day and you’re relatively close to the time with an average or just by picking one and knowing that you don’t have massive time skew.
I believe this saying was first made about compasses which also had mechanical failures. Having three lets you know which one failed. The same goes for mechanical watches, which can fail in inconsistent ways, slow one day and fast the next is problematic the same goes for a compass that is wildly off, how do you know which one of the two is off?
Re: Are two heads better than one?
#33Re: Are two heads better than one?
#34Surely the extrapolation is wrong? at 4 heads, just randomly select a jury of 3. and you're back on track. at a million heads, just sum up all their guesses, divide by one million, and then check the over/under of 0.50
For 4 vs 3, you’re saying the same thing.
He wrote:
If our number N of friends is odd, our chances of guessing correctly don’t improve when we move to N+1 friends.
Re: Are two heads better than one?
#35Surely the extrapolation is wrong? at 4 heads, just randomly select a jury of 3. and you're back on track. at a million heads, just sum up all their guesses, divide by one million, and then check the over/under of 0.50
I misread the article too, but it states that with 3 or 4 on the jury the probability has increased to 0.9, instead of 0.8 with 1 or 2. It's just that an incremental extra jury member from odd to even never increases the information, even when it's 9999 to 10000.
Re: Are two heads better than one?
#36Earlier quoted context omitted.
I think it is different in the continuous case though, because you can average two (reasonably accurate) chronometers and get a better measurement. But we can't average true and false, at least not in the context of this problem definition. But the chronometers are will sync with each other if you don't store them apart, which would result correlated noise that an average won't fix.
You can definitely average two relatively accurate chronometers but you if you only have two it’s difficult to tell if one is way fast or way slow. In a perfect world they drift less than a minute per day and you’re relatively close to the time with an average or just by picking one and knowing that you don’t have massive time skew. I believe this saying was first made about compasses which also had mechanical failur…
> In a perfect world they drift less than a minute per day...
A minute per day would be far too much drift for navigation, wouldn't it?
From Wikipedia [1]:
> For every four seconds that the time source is in error, the east–west position may be off by up to just over one nautical mile as the angular speed of Earth is latitude dependent.
That makes me think a minute might be your budget for an entire voyage? But I don't know much about navigation. And it is beside the point, your argument isn't changed if we put in a different constant, so I only mention out of interest.
> Having three lets you know which one failed.
I guess I hadn't considered when it stops for a minute and then continues ticking steadily, and you would want to discard the measurement from the faulty watch.
But if I just bring one watch as the expression councils, isn't that even worse? I don't even know it malfunctioned and if it failed entirely I don't have any reference for the time at the port.
My interpretation had been that you look back and forth between the watches unable to make a decision, which doesn't matter if you always split the difference, but I see your point.
Re: Are two heads better than one?
#37Earlier quoted context omitted.
You can definitely average two relatively accurate chronometers but you if you only have two it’s difficult to tell if one is way fast or way slow. In a perfect world they drift less than a minute per day and you’re relatively close to the time with an average or just by picking one and knowing that you don’t have massive time skew. I believe this saying was first made about compasses which also had mechanical failur…
> In a perfect world they drift less than a minute per day... A minute per day would be far too much drift for navigation, wouldn't it? From Wikipedia [1]: > For every four seconds that the time source is in error, the east–west position may be off by up to just over one nautical mile as the angular speed of Earth is latitude dependent. That makes me think a minute might be your budget for an entire voyage? But I don…
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.
Re: Are two heads better than one?
#38Earlier quoted context omitted.
> In a perfect world they drift less than a minute per day... A minute per day would be far too much drift for navigation, wouldn't it? From Wikipedia [1]: > For every four seconds that the time source is in error, the east–west position may be off by up to just over one nautical mile as the angular speed of Earth is latitude dependent. That makes me think a minute might be your budget for an entire voyage? But I don…
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…
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.
Re: Are two heads better than one?
#39Earlier quoted context omitted.
> In a perfect world they drift less than a minute per day... A minute per day would be far too much drift for navigation, wouldn't it? From Wikipedia [1]: > For every four seconds that the time source is in error, the east–west position may be off by up to just over one nautical mile as the angular speed of Earth is latitude dependent. That makes me think a minute might be your budget for an entire voyage? But I don…
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…
> A well serviced rolex in 2026 with laser cut gears drifts +/- 15sec per day.
Modern Rolex (and Omega et al) are more like +/-2s.