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Old 06-10-2019, 05:48 AM
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Is my solution to this puzzle reasonable?


Note the deadline has passed so I'm not asking you to do my homework -- though I am asking you to check it.
https://fivethirtyeight.com/features...scape-at-dawn/

First I assume the sat phone doesn't have GPS nor is it a LEO system because that is too easy (since location can be determined by which satellites you hit/Doppler shift)

I say call when the sun is fully visible and say "Help I've been kidnapped and am on a small island surrounded by salt water and the sun just became fully visible. I will call again at sunset"

Timing dawn determines longitude, and the length of the day determines latitude. Even if these are off by a few minutes an isolated island should be findable. Scratching HELP/SOS in the sand is not a bad idea.

I may be overestimating how accurate this method of determining location is. Is the fact that it is salt water really all that important?

Thanks,
Brian
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Old 06-10-2019, 06:35 AM
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I say call when the sun is fully visible and say "Help I've been kidnapped and am on a small island surrounded by salt water and the sun just became fully visible. I will call again at sunset"

Timing dawn determines longitude, and the length of the day determines latitude. Even if these are off by a few minutes an isolated island should be findable.
If that's not the intended answer, you're probably on the right track. The only problem I can think of is that your method wouldn't work very well around the equinoxes, since the day & night length are equal pretty much everywhere on Earth on that day. Maybe the fact that you were kidnapped on a "snowy night" was supposed to preclude this, but I've seen plenty of snowy March 21sts in my part of the world.

It's also not clear to me whether it was intended that you could make more than one phone call, though that's more a question of "what is the intended answer" instead of "what is a valid answer".
  #3  
Old 06-10-2019, 07:15 AM
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If you watch the sun rise you can make your call when it is as just past half way risen. This will give you one minute before the sun is just touching the horizon. Tell them what you know about your location, (island, its size, climate) and get them to mark your time call of the moment the sun is free of the horizon. Then you will run out of phone call. You will have established your longitude to easily 1/60th of a degree (only needs to be to within 4 seconds with the timing). That is one nautical mile at the equator. There cannot be many small islands that match the description on such a fine longitude constraint. Indeed very unlikely to be more than one.

Last edited by Francis Vaughan; 06-10-2019 at 07:16 AM.
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Old 06-10-2019, 07:34 AM
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Well, I think the rules are that you have to call by daybreak and making a second call at sunset is not allowed.

but it should be easy to determine longitude by calling them at daybreak and letting them determine your local solar time.

Since it is cool, you can estimate lattitude as temperate; when the sun rises you can determine directions. But I don't know if this will be able to tell you if you are in the northern or southern hemisphere. Just a bit of astronomy knowledge should allow you to recognize Polaris in the sky or not ..... which puts you in a particular hemisphere....don't know if that is allowed. You know the day roughly since its wintertime where you were.
Also you can determine if the tide is coming in or receding at the time of your call, so that can help.

I think those clues with a small flat sandy island would be enough to locate

the food and 'pint' bottles could indicate some nearby country, but I don't think that is strong enough data to be confident

Last edited by Sigene; 06-10-2019 at 07:35 AM.
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Old 06-10-2019, 07:49 AM
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If two calls are not allowed (though it is IMHO within the contraints), my other idea is to call when your shadow is exactly X water bottles long (alternatively when it is exactly your height) -- though I'd be worried it never gets that short.

Brian
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Old 06-10-2019, 08:00 AM
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I would hope and pray that I am in the Northern hemisphere, because I could give a rough estimate of latitude based on the height of the north star. I think that qualifies under "Your knowledge of astronomy is too weak to try to estimate your location by the stars, but you’re not stupid." I do recall that my fist outstreched is roughly 10 degrees.

I thought that my rough estimate may not be good enough for rescue purposes, but if each degree of latitude is 69 miles (which I had to google), I think I could get within 500 miles of my latitude.

And then of course calling right at daybreak should give longitude more precisely.

ETA: but in this scenario I would expect not to be rescued. Getting all that info across in one minute and making someone believe it, plus the time to organize an actual rescue party from who-knows how many miles away, doesn't sound promising.

ETAA: I could also use the water bottles to more accurately estimate the latitude. But again, in the southern hemisphere I'm screwed.

Last edited by Ravenman; 06-10-2019 at 08:04 AM.
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Old 06-10-2019, 08:14 AM
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Calling at the moment of sunrise would narrow it down to an sort of north-south arc (not exactly a line of longitude, but kind if similar). Which, would I presume narrow it down to a dozen or so islands of the approximate size that are out of sight of other land. Few enough for a billionaire's people to check?

If you could call at exactly local noon, with an estimate of the sun height (e.g. how long your shadow is), that's going to get latitude and longitude which should do it (as an extra check you could also estimate the angle between the sunrise and noon locations).
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Old 06-10-2019, 08:52 AM
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You also know that the boat's wake stirred up something bioluminescent: That'll narrow down location, too.

What's hanging me up is the "you don't know enough about astronomy..." bit. Just how much astronomy knowledge are we assuming? Even perfect knowledge wouldn't be enough, without access to some sort of chronometer. And knowing that you can use time of sunrise to give one coordinate is itself astronomical knowledge.
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Old 06-10-2019, 09:50 AM
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If you could call at exactly local noon, with an estimate of the sun height (e.g. how long your shadow is), that's going to get latitude and longitude which should do it (as an extra check you could also estimate the angle between the sunrise and noon locations).
But you don't know the exact direction of north/south to begin with, so the only way to judge the timing of local noon is by looking at the length of the shadow. It won't be accurate at all - I think the best you can do is "it looks like it hasn't gotten any longer in the past 10 minutes".
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Old 06-10-2019, 10:10 AM
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But you don't know the exact direction of north/south to begin with, so the only way to judge the timing of local noon is by looking at the length of the shadow. It won't be accurate at all - I think the best you can do is "it looks like it hasn't gotten any longer in the past 10 minutes".
Well, you got "a few" days' worth of food and drink, no, so you could use day 1 to plot the shadow of some object, and on day 2, you should be able to know well enough where "noon" is. I don't know if that "few days" is an important detail, but it sounds like you don't have to call at daybreak of day 1, so perhaps that opens up some other possibilities.

Last edited by pulykamell; 06-10-2019 at 10:11 AM.
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Old 06-10-2019, 10:13 AM
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You also know that the boat's wake stirred up something bioluminescent: That'll narrow down location, too.
While there are some good locations for regular/predictable bioluminescence (the 3 bioluminescent bays of Puerto Rico come to mind), the actual phenomenon isn't that restricted and can occur worldwide.

I think the OP's onto a good idea.

All else I can say is - liverwurst + peanutbutter on rye? That's some sick torture there.
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Old 06-10-2019, 10:25 AM
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I suppose writing a message on a torn piece of shirt in blood and launching it in an empty water bottle would be too slow.

Last edited by bob++; 06-10-2019 at 10:28 AM.
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Old 06-10-2019, 10:46 AM
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All else I can say is - liverwurst + peanutbutter on rye? That's some sick torture there.
Weird thing is I read that and thought, that's clearly trying to be a bit disgusting, but that sounds like a darned fine lunch to me! Plus reasonably calorie dense, I would think, depending on how peanut buttery and liverwursty it is.
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Old 06-10-2019, 10:58 AM
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But you don't know the exact direction of north/south to begin with, so the only way to judge the timing of local noon is by looking at the length of the shadow. It won't be accurate at all - I think the best you can do is "it looks like it hasn't gotten any longer in the past 10 minutes".
Yeah, that's why I wrote 'if'. Getting sunrise fairly precisely is easier than getting noon precisely. Though you should be able to get a decent direction of the sun at noon, since it's not changing too quickly. Mark that, then wait until sunset and call, giving them the approximate angle of sunset (compared to noon) and exact time. Which doesn't meet the puzzle's implied 'Escape at Dawn' constraint.

If you can find north/south by the stars, you can call in the morning and give the angle between N and the sunrise as well as the exact moment of sunrise, to get a rough latitude and longitude. If you have zero knowledge of constellations or stars, you're not going to know whether you've found N or S, but narrowing it down to one of two spots on the globe is probably enough to get rescued.


I think the bioluminescence doesn't narrow things down any more than 'it's not cold here' does.
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Old 06-10-2019, 11:01 AM
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Assuming two phone calls are do-able, if you make the first call right at sunrise, this should give a rough longitude. If you made the second call exactly at sunset, couldn't your rescuers figure out a rough latitude based on the "length" of the day?
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Old 06-10-2019, 11:11 AM
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Assuming two phone calls are do-able, if you make the first call right at sunrise, this should give a rough longitude. If you made the second call exactly at sunset, couldn't your rescuers figure out a rough latitude based on the "length" of the day?
yes, that was my solution in the OP

You have one minute of battery. I made the leap that two 30 second calls was OK. Will find out Friday

Brian
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Old 06-10-2019, 11:20 AM
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"you don't know enough about astronomy..."
Yeah, but do I know how to find Polaris? If so, I can measure the distance above the horizon in "satphone units," and then call when the Sun has just risen, which give both Lat and Lon.

Last edited by beowulff; 06-10-2019 at 11:21 AM.
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Old 06-10-2019, 11:40 AM
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Yeah, but do I know how to find Polaris?
You're making an assumption about which hemisphere you're in, there. How good are you at finding Crux and the Centauris?
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Old 06-10-2019, 11:44 AM
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Yeah, but do I know how to find Polaris? If so, I can measure the distance above the horizon in "satphone units," and then call when the Sun has just risen, which give both Lat and Lon.
The more I think about it, I think that part is more about prohibiting someone from triangulating their position based on locating Venus, Betelgeuse, the Vogon Mothership, and Delta Airlines flight 954, and referring to one's photographic memory of almanacs and flight schedules; rather than an elementary "I see Polaris so I'm in the northern hemisphere." I'm still a little unclear as to whether "My fist is about 10 degrees of arc, so Polaris is 25 degrees above the horizon" falls afoul of the rule. I don't think it does.

Last edited by Ravenman; 06-10-2019 at 11:45 AM.
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Old 06-10-2019, 11:51 AM
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The puzzle writer confirmed on twitter that there is no limit to the number of calls, just the time limit.
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Old 06-10-2019, 12:04 PM
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Just to check things out, I went here to get a look at the current day/night map of the world. I saved that map, clicked on +12 to get a half day later map and saved that.

Flipping back and forth between them gave two congruences for the civil twilight curve. (No sunrise/sunset curve.)

One was in the central Pacific S. of Hawaii and the other was in the Congo. (The 12hr choice fixed things near the equator.)

So it would work today, sort of. Large margin of error. Possibly really large at high latitudes, which seems to ruled out. And really terrible, as noted, around the equinoxes which again might be ruled out.

I think part of the solution is to use the Sat phone's ability to get the current time. So, wait until the Sun starts to rise (just the top). Turn on phone, get time. Turn off phone. Wait until the Sun just about finishes setting. Turn on phone, get time, make call.

If you on an island in the SW pacific in one of more numerous archipelagos, you're still going to be stuck.
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Old 06-10-2019, 12:06 PM
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You're making an assumption about which hemisphere you're in, there. How good are you at finding Crux and the Centauris?
I could tell if I wasn't in the northern hemisphere, and then nothing else from the stars if that was the case. Even in the northern hemisphere at best I could tell whether or not I was in the tropic. The sun would be much more help to me than the stars, and not that much anyway.

Not phoning before daylight is either a red herring or very significant, but I don't know why the kidnappers would care. Maybe the position of the satellite or multiple satellites that pick up the call would reveal the location in the time before daybreak. The more calls you make the more the satellite positions should help.

If the phone can text, you could send a lot of info at different times of the day with one minute of battery.
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Old 06-10-2019, 12:51 PM
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I think if allowed two phone calls, you are great.

If limited to one call, I would first determine and set up W-E line and thus N-S line. This would tell you N or S hemisphere. Then I would wait for an international space station flyover and call during that and say exactly when it crosses the north-south line.

The ISS is bright as hell, and covers all temperate areas over the course of a few nights. I think this one call could get you a smaller search window than sunrise and sunset even.
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Old 06-10-2019, 01:43 PM
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The more I think about it, I think that part is more about prohibiting someone from triangulating their position based on locating Venus, Betelgeuse, the Vogon Mothership, and Delta Airlines flight 954, and referring to one's photographic memory of almanacs and flight schedules; rather than an elementary "I see Polaris so I'm in the northern hemisphere." I'm still a little unclear as to whether "My fist is about 10 degrees of arc, so Polaris is 25 degrees above the horizon" falls afoul of the rule. I don't think it does.
I take it to mean that any knowledge about individual stars (or constellations) is unusable, but general astronomical principles are OK.

So, using The Dipper to find Polaris is out. But it's OK to pick some stars, mark their directions, then re-check their locations every half hour or so during the night, determine what point they're rotating around, and call the direction of that point Axis (we don't know if it's North or South yet)

Now draw a circle with Axis marked and divide it as accurately as you can. When you can see first light, you can mark East (perpendicular to Axis towards the light). If it's winter in the northern hemisphere, the sun will rise south of east, and vice versa for winter, so assuming I remember the date I was kidnapped, as soon as the sun gets localized, I can mark North and South on the Axis line (and if I can't remember the date, if I can remember where I was kidnapped, there's a very good chance that the snowy night will let me make a guess about which hemisphere is currently winter).

Now (assuming the sun isn't due East*) make the call, telling them "I've been kidnapped and need to be rescued. I'm on a roughly tropical island about a mile across with no other land in sight. The sun is just rising and it's at an angle of X degrees south/north of East. Please hurry I hate liverwurst"


* If it's near the equinox, well, you may have to get latitude by waiting until noon and measuring the length of your shadow, since 'sun rising due east' won't help locate you. Then wait to sunset so they get the moment of sunset and your length of shadow latitude

Last edited by Quercus; 06-10-2019 at 01:45 PM.
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Old 06-10-2019, 02:07 PM
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Stick a water bottle in the sand, call when it has zero shadow, which establishes exact local noon. Remember whether or not you saw the big dipper last night -so you can communicate north or south hemisphere, too. Given that it is winter in your home-hemisphere ( it was snowing), whether or not your un-shod feet are cold will shorten the line of local noon which matches yours, if you are in your home hemisphere. Mention the color of the wake luminescence, it could help narrow it down further.
Curious that you are instructed to wait for daylight to make the call. I cannot think of a Satphone that only works at daylight.
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Old 06-10-2019, 02:11 PM
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At daybreak I'd examine the sat phone for any identifying numbers or marks. Then I'd dial 1 (703) 482-0623 or 1 (202)456-1414, identify myself and issue very direct threats against the President and Vice-President. I'd throw in any id on the phone I was using and tell them it was a sat phone and that I had more information about the threat. Then I'd sit back and see just how efficient the NSA is.
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Old 06-10-2019, 02:32 PM
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Stick a water bottle in the sand, call when it has zero shadow, which establishes exact local noon.
That will only work if you're in the tropics, and even then only on two days of the year.

The more I think about it, the more I think that the only valid solution is "The kidnappers have left me on some deserted beach somewhere. Track the location of this phone". I'm pretty sure that (given law enforcement authority) that's possible to do for any satellite phone, and it's the only solution that doesn't require any astronomical knowledge.
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Old 06-10-2019, 02:37 PM
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At daybreak I'd examine the sat phone for any identifying numbers or marks. Then I'd dial 1 (703) 482-0623 or 1 (202)456-1414, identify myself and issue very direct threats against the President and Vice-President. I'd throw in any id on the phone I was using and tell them it was a sat phone and that I had more information about the threat. Then I'd sit back and see just how efficient the NSA is.
Now that's good "out of the box" thinking.
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Old 06-10-2019, 02:42 PM
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That will only work if you're in the tropics, and even then only on two days of the year.

The more I think about it, the more I think that the only valid solution is "The kidnappers have left me on some deserted beach somewhere. Track the location of this phone". I'm pretty sure that (given law enforcement authority) that's possible to do for any satellite phone, and it's the only solution that doesn't require any astronomical knowledge.
The puzzle writer also said on twitter that the phone is not trackable.
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Old 06-10-2019, 03:39 PM
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The thing is, calling at sunrise/set isn't hard to determine, and doesn't require any calculations (or even knowing the time) on your part -- the people at the other end of the call are responsible for that.
Now knowing that the time of sunrise/set will determine your location does require some knowledge, but IMHO is allowed in the puzzle.
As mentioned in the OP 9and in the solution I sent in), I assumed the phone was't trackable or else the problem is too easy (I'm not sure how trackable GEO phones are -- certainly less so than LEO phones)

The main issue I have is the fact that it is salt water isn't important (though makes you more finable than if you were in the middle of a rain forest) You could be in Lake Superior and my solution works.
Unless that is a red herring (salt water -- herring)

Brian
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Old 06-10-2019, 03:55 PM
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The main issue I have is the fact that it is salt water isn't important (though makes you more finable than if you were in the middle of a rain forest) You could be in Lake Superior and my solution works.
Unless that is a red herring (salt water -- herring)

Brian
It's pretty easy to determine that it is salt water anyway.
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Old 06-10-2019, 04:05 PM
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I think the salt water just means "you won't be able to survive here on your own, long-term".
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Old 06-10-2019, 04:17 PM
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Even simpler you could do this with one call in the morning.

When the person calls at sunrise it is h hours before local noon so you'll need the equation of time also. This means they are h * pi / 12 radians away from the from the sun. There's your longitude BUT since we know sunrise is located on a cosine curve (counting the Sun as 0 radians) we simply need to calculate cos(-h * pi / 12) and multiply by the appropriate amplitude, take into account the Sun's declination and there you go.

To visualize this, look at a map of the curve of sunlight. It doesn't look like a cosine curve but that is because of the scaling on a Mercator map at extreme latitudes. For now just fool yourself that it is a cosine curve. The curve represents everywhere the sun is on the horizon. You claim that from that first phone call you know the longitude right? You also know the longitude of the sun-solar spot. On our graph it is an offset so if in reality the sub-solar point is at 140 deg W and the person is at 170 deg E on our graph that means we made the mark on your at -50 deg. Ok back to the curve of sunlight map. You know your friend is at 170 deg E right? So make a vertical line and where it intersects the curve, that's where your friend is at.
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Old 06-10-2019, 04:37 PM
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The puzzle writer also said on twitter that the phone is not trackable.
Then the puzzle writer should have made up a different situation, because that is counterfactual.
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Old 06-10-2019, 04:46 PM
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But Saint Cad, you don't know what h is, especially since you don't have any chronometer other than the phone itself. I suppose you could turn it on at sunrise just long enough to read the time and then turn it off, and then turn it back on at sunset, but that's not really a big improvement over calling at both times.

(and yes, you can use the time of noon in place of either of those times, but it's much easier to determine the precise moment of sunrise/set than of noon)
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Old 06-10-2019, 04:48 PM
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Even simpler you could do this with one call in the morning.

When the person calls at sunrise it is h hours before local noon so you'll need the equation of time also. This means they are h * pi / 12 radians away from the from the sun. There's your longitude BUT since we know sunrise is located on a cosine curve (counting the Sun as 0 radians) we simply need to calculate cos(-h * pi / 12) and multiply by the appropriate amplitude, take into account the Sun's declination and there you go.

To visualize this, look at a map of the curve of sunlight. It doesn't look like a cosine curve but that is because of the scaling on a Mercator map at extreme latitudes. For now just fool yourself that it is a cosine curve. The curve represents everywhere the sun is on the horizon. You claim that from that first phone call you know the longitude right? You also know the longitude of the sun-solar spot. On our graph it is an offset so if in reality the sub-solar point is at 140 deg W and the person is at 170 deg E on our graph that means we made the mark on your at -50 deg. Ok back to the curve of sunlight map. You know your friend is at 170 deg E right? So make a vertical line and where it intersects the curve, that's where your friend is at.
How would we be able to figure out what the local time is? Seems to me like at sunrise you could be anywhere along the edge of the sunlight curve, right? I don't think you actually know what the longitude is just from the call, unless I'm missing something.
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Old 06-10-2019, 05:40 PM
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The receiver will know THIER local time. Lets say it is exactly as pictured. Since it is dawn they know you are somewhere south of Sri Lanka (or in the Barents Sea)
But I don't see how that gets you latitude

Brian
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Old 06-10-2019, 05:46 PM
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Stick a water bottle in the sand, call when it has zero shadow, which establishes exact local noon.
That will only work if you're in the tropics, and even then only on two days of the year.
Stick a water bottle in the sand, and as it gets to noon, trace the top end of the shadow with your finger in the sand. Measure how tall the shadow is, compared to the bottle.

Then at dusk, make your call.

"Help! I've been stranded on a tiny island. The sun has just kissed the horizon this very second. At noon, shadows were (some fraction) of the object casting the shadow. As I measured the shadow, the line curved clockwise/anticlockwise. Come get me!"
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Old 06-10-2019, 05:52 PM
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How precisely can you time noon/measure fractions of a shadow (uh, between 2/3 and 5/8)
Granted I don't know how precise the length of day gets you (as mentioned, depends on location and time of year)

Brian
  #40  
Old 06-10-2019, 06:03 PM
K2500 is offline
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But someone already knows where you are, you just got to get them to give that information to your people.

Call you're people(who are also not stupid) at day break and have them record the time and roughly describe your location so they have something to work with if the kidnappers fall through. Since they're intelligent they could probably negotiate a deal with the kidnappers that involves your rescue.
  #41  
Old 06-10-2019, 06:09 PM
N9IWP is offline
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I guess "pay the ransom and get my location" is a valid solution.

Brian
  #42  
Old 06-10-2019, 06:44 PM
Saint Cad is online now
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Originally Posted by Delayed Reflex View Post
How would we be able to figure out what the local time is? Seems to me like at sunrise you could be anywhere along the edge of the sunlight curve, right? I don't think you actually know what the longitude is just from the call, unless I'm missing something.
One. I misread the exact scenario
Two. This line from the OP messed me up
Quote:
Timing dawn determines longitude
As pointed out easy IF you know you're local time.
  #43  
Old 06-10-2019, 06:51 PM
N9IWP is offline
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OK, not longitude, but a more or less N/S line
And I misread the map, if it is dawn, you are probably south of Mexico (or in Hudson Bay)

Brian

Last edited by N9IWP; 06-10-2019 at 06:54 PM.
  #44  
Old 06-10-2019, 08:06 PM
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I wish I could offer more help for a solution I think the solutions here are very cool to ponder. I did however want to add:
1) Very cool thought provoking riddle - thanks N9IWP

2) This scenario strikes me as remarkably similar to an episode of the old British TV show "The Prisoner". I recall Number 6 trying to use some similar method (of course without a cell phone) to determine the latitude and longitude of the The Village. Ring any bells?

Maybe the Riddler is a Prisoner fan?
  #45  
Old 06-10-2019, 08:15 PM
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Originally Posted by N9IWP View Post
I guess "pay the ransom and get my location" is a valid solution.

Brian
Yeah...
Quote:
“If your people pay our ransom,” he continues, “We’ll come get you. Otherwise, there won’t be any more paper bags. Remember, wait until daylight to make that call.”
Better hope you didn't sign a "No-ransom" agreement.
  #46  
Old 06-10-2019, 08:56 PM
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Quote:
As I measured the shadow, the line curved clockwise/anticlockwise.
Quote:
How precisely can you time noon/measure fractions of a shadow
Quote:
it's much easier to determine the precise moment of sunrise/set than of noon
Quote:
But you don't know the exact direction of north/south to begin with, so the only way to judge the timing of local noon is by looking at the length of the shadow. It won't be accurate at all - I think the best you can do is "it looks like it hasn't gotten any longer in the past 10 minutes".

I thought every Boy Scout, experienced puzzler, or astronomy buff already knew this trick, but I suppose not, so I'll post it:

You don't need to estimate the length of a shadow to find noon. You plant an object with an obvious tip in the sand, standing vertically. A water bottle will do. At some point in the day, at any time, you mark the shadow's tip with any object. Another water bottle will work, especially if laid on its side, but I'd prefer a seashell or pebble.

Then you wait at least 15 minutes, but preferably several hours. You then mark the tip again. Connect the two marks with a line. Wait a few hours more and verify with a third point.

This line is a direct east/west line. It's not an arc. The shadow changes length as the sun moves through the sky, such that the shadow traces a perfect line. Your first point is West. Your last point is East. That gives you North and South as well. Whatever point on the line forms a right angle with a line to the original "gnomon" water bottle is noon. If the line is to the North of the bottle, you're in the Northern hemisphere. If South, then Southern.

No need to measure shadows. No need to know the length unless you want a better estimate of longitude. But this technique is simple, quick, and gives you both time, direction, and hemisphere. You can get all this information, plus map the entire island, in under an hour.
  #47  
Old 06-10-2019, 09:06 PM
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Doesn't help a lot for determining your location (other than hemisphere) and by the time you have determined noon it is probably past it...

Brian
  #48  
Old 06-10-2019, 09:16 PM
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A novel idea


I was just hit with some inspiration. How about manufacturing an astrolabe out of the water bottle?

1. Drink the bottle of water so you stay hydrated.
2. Refill it halfway with salt water. You coulda used the fresh water, but why?
3. Tilt the bottle on its side, such that the water level is touching both the plastic notch in the center of the bottom and the center of the cap. This means you're holding the bottle perfectly level, and therefore can "shoot" the horizon.
4. Mark the water level on both the near side and far side with scratches or other permanent marker substitute. This gives a diameter.

Take a nap. You've earned it. Wait for noon.

5. At noon, rotate the bottle (i.e., a barrel roll) such that the scratches point to the sun.
6. While holding the scratches steadily in line w/ the sun, mark the new water level. You can mark both side,s but only one is necessary, and probably easier to read later.

7. You now have two marks on a circle. The angle between the two yields the sun's maximum angle of elevation. 90 degrees minus this angle is your approximate latitude, if you can adjust for the season.

Coupled with your stick-compass, rough sketch of the island, longitude from timing sunrise, and latitude from the astrolabe, you're all set. Enjoy your beach vacation and await your friends' arrival.
  #49  
Old 06-10-2019, 09:19 PM
Chessic Sense is offline
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Originally Posted by N9IWP View Post
Doesn't help a lot for determining your location (other than hemisphere) and by the time you have determined noon it is probably past it...

Brian
Not at all. You can determine noon any time 30 minutes after sunrise. You mark the shadow in the morning, then again 15 or so minutes later, and technically, you have a line.

You can project that line as far as you want. Whatever point on that line is at a right angle to the water bottle is noon, even if the current time is still 7:15 am.

Hell, you can project (heh) when sunset is by just mirroring your sunrise point (which is in the West) to the East side of your line. You have a whole clock in 15 or 30 minutes, and every extra shadow marking increases your accuracy.

After 4 markings (which takes one hour), you're as accurate as you'll need to be.
  #50  
Old 06-10-2019, 09:33 PM
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Slight correction to the astrolabe idea. Instead of trying to calculate my latitude from my measurement, I can just stop once I've measured the sun's angle of elevation. My billionaire friends back home can punch that into a NOAA.gov calculator or whatever to do the seasonal adjustment. Hell, I don't even need to know the current date because they already do.

For what it's worth, and as my username might suggest, I'd give them a rough map of my island's shape by naming squares on a chess board. If I say the square, it's sand. If I don't, it's water. There's even enough time to describe my system to them. An 8x8 grid ought to give them a good idea of what mile-by-half-mile island I'm on.

"If my island were on a chess board, it'd be shaped as...a8, b8, c8, d8...break...a7 b7...break...a6 b6 c6 d6..." and so on.
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