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 Forum index » Archive » Archive: The Haunted Apiary (Let Op!) » The Haunted Apiary (Let Op!): Puzzles
[LOCKED] [PUZZLE] GPS Coordinate Anomalies
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WhatTheDilly-O
Boot

Joined: 29 Jul 2004
Posts: 18

 		Even though there are so many points, It's still very unlikely that, given the pecision of 4 decimal places, any three would make a perfect geometric right angle unless they were meant to. If anyone has the brains and, more importantly, the inestimable patience to figure out if any three make exact right angles, I think that would probably put an end to the debate of whether or not these locations draw out shapes.

PostPosted: Fri Aug 13, 2004 3:19 am
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danteGA
Boot

Joined: 12 Aug 2004
Posts: 65
WhatTheDilly-O wrote:
Even though there are so many points, It's still very unlikely that, given the pecision of 4 decimal places, any three would make a perfect geometric right angle unless they were meant to. If anyone has the brains and, more importantly, the inestimable patience to figure out if any three make exact right angles, I think that would probably put an end to the debate of whether or not these locations draw out shapes.


Well this is a good question... how seriously *should* we take the 4 decimal places? Given the close clustering of coordinates around certain locations, it might be possible to assume that there is some degree of 'noise' present. So, if we ignore for a moment the columnwise pairings of the coordinates, and *if* we are willing to accept a little noise in the coordinates (yes, I know these are both big IFs), there are a number of locations that seem suspiciously aligned, even all the way across country.

For example:

Same latitude:

32.7852 -117.1289 SAN DIEGO CA
32.8163 -83.7079 MACON GA


42.2792 -83.7485 ANN ARBOR MI
42.3247 -71.065 42.3 -71.1 BOSTON MA


Same longitude:

32.767 -117.0569 SAN DIEGO CA
46.4128 -117.0266 LEWISTON ID

42.2792 -83.7485 ANN ARBOR MI
32.8163 -83.7079 MACON GA


AND if you notice how I sneakily constructed my examples, there would appear to be something very close to a right angle at Macon, GA and at Ann Arbor, MI and at San Diego, CA (too bad Lewiston and Ann Arbor aren't at the same latitude and I would have a square!).

Now I agree that the fact that there are four decimal places leaves this open to question, but this is an in principle demonstration that horizontals and verticals do seem present.

(Note in passing: if you keep the pairs together, there are only a few points that seem reasonably aligned, and you are still faced with the 4-decimal problem. For example:
35.3519 -94.3487 FORT SMITH AR
42.5052 -94.1579 FORT DODGE IA)

Even so, it is reasonable to wonder about the odds of randomly-selected U.S. cities or locations lining up more or less evenly. I am willing to accept that this could all be coincidence...

dante

PostPosted: Fri Aug 13, 2004 10:15 am
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Mukaikubo
Boot

Joined: 28 Jul 2004
Posts: 56

 		It'll take a lot of computer power, but I'll try to bunge something together to test all possible sets of 3 points for right-angles.

PostPosted: Fri Aug 13, 2004 10:17 am
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jegger
Decorated

Joined: 05 Aug 2004
Posts: 222
Location: Atlanta, GA

 		[SPEC] Distribution
I am struck by the fact that the lengths between pairs seems to follow a power law distribution. (This was stated earlier, but I can not find the post.) The PM's could have chosen any distribution that they wanted, which says to me that this distribution arises from the process that they used for choosing these values. What sort of phenomena result in this distribution? Networks. Weblogs. Word distribution. A sort of a "rich get richer" scenario. A network node is more valuable when more connections are made to it. A weblog is more valuable when more people read it. Words are more valuable when more people use them. In this situation, there are many more short pairs than long pairs. Extending the previous statements, I might say:
Pairs are more valuable when they are shorter. Why? I have no idea.

Another premise can be found here:
http://interconnected.org/notes/2002/12/Origin_of_power_laws.txt
This person's theory is that the power law can arise when random chunks are removed from a scarce resource. It includes a Perl script to test the hypothesis.

"This means something"
/me starts building a model of the US from mashed potatoes Smile [/url]

PostPosted: Fri Aug 13, 2004 11:13 am
Last edited by jegger on Fri Aug 13, 2004 11:22 am; edited 1 time in total
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Mukaikubo
Boot

Joined: 28 Jul 2004
Posts: 56

 		That'd be my observation that the distances follow a power-law distribution- hope it sparks some good thinking.

Okay, there are no A-B-C triple coordinates that form a right angle (i.e. line A-B perpendicular to line B-C). Currently I'm testing whether there are any lines A-B and C-D that form a perfect right angle.

PostPosted: Fri Aug 13, 2004 11:20 am
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jegger
Decorated

Joined: 05 Aug 2004
Posts: 222
Location: Atlanta, GA

 		Re: [SPEC] Distribution
jegger wrote:
I am struck by the fact that the lengths between pairs seems to follow a power law distribution. (This was stated earlier, but I can not find the post.) The PM's could have chosen any distribution that they wanted, which says to me that this distribution arises from the process that they used for choosing these values. What sort of phenomena result in this distribution? Networks. Weblogs. Word distribution. A sort of a "rich get richer" scenario. A network node is more valuable when more connections are made to it. A weblog is more valuable when more people read it. Words are more valuable when more people use them. In this situation, there are many more short pairs than long pairs. Extending the previous statements, I might say:
Pairs are more valuable when they are shorter. Why? I have no idea.

Another premise can be found here:
http://interconnected.org/notes/2002/12/Origin_of_power_laws.txt
This person's theory is that the power law can arise when random chunks are removed from a scarce resource. It includes a Perl script to test the hypothesis.

"This means something"
* jegger starts building a model of the US from mashed potatoes Smile [/url]


I just thought of something disheartening. Let's say that you had a sampling of random locations (a scarce resource) and chose pairs at random. You might end up with a power law distribution by default. Perhaps shuffling the points and graphing the distances would determine if this is the case.

PostPosted: Fri Aug 13, 2004 12:27 pm
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vpisteve
Asshatministrator


Joined: 30 Sep 2002
Posts: 2441
Location: 1987

 		Locked as per mass player request. Please use one of the [PUZZLE] Axons: xxxx threads for further discussion.

Your helpful admin.

Locky!
_________________
Making the world a better place, one less mime at a time.

PostPosted: Fri Aug 13, 2004 9:12 pm
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