Moon Hotspot

[Haflinger]

-69, 71: 98%

So it's south of -69, 70, looks like. Maybe try -69, 69

[Shardoon]

Owner: Shardoon

Base Effectiveness: 99%

Last Moved: 10/2/2009

Date Purchased: 9/25/2009

Expires: 593 Days

Location: -70.00000, 69.00000

[Provost Zakharov]

Owner: Shardoon

Base Effectiveness: 99%

Last Moved: 10/2/2009

Date Purchased: 9/25/2009

Expires: 593 Days

Location: -70.00000, 69.00000

I just posted that datapoint, why would you move there?

edit: somebody try -71, 69

that looks like the next best candidate at this point.

Edited October 2, 2009 by Provost Zakharov

[sammykhalifa]

Location: -71.00000, 69.00000

99%

[Shardoon]

I just posted that datapoint, why would you move there?

edit: somebody try -71, 69

that looks like the next best candidate at this point.

serves me right.

[jonnygozy]

maybe -71, 70?

Edited October 2, 2009 by jonnygozy

[Golan 1st]

-71.00000, 66.00000: 99%

-71.00000, 67.00000: 99%

-71.00000, 68.00000: 99%

maybe -71, 70?

Very unlikely

It's closer to the (-69.39965, 71.90552) 98% location than it is to the (-71, 66) 99%.

Edited October 2, 2009 by Golan 1st

[jonnygozy]

-71.00000, 66.00000: 99%

-71.00000, 67.00000: 99%

-71.00000, 68.00000: 99%

Very unlikely

It's closer to the (-69.39965, 71.90552) 98% location than it is to the (-71, 66) 99%.

Hmmm, yeah with your new data points it doesn't look so good.

[Golan 1st]

If both coordinates are integers again, then

1. the latitude must be -71. Because If it's -70 or bigger, then it will be closer to the (-66, 66) 96%, than to (-75, 65) 97% and if it's -72 or smaller, it will be closer to (-72, 72) 98% than to (-70, 69) 99%.

2. The longitude must be smaller than 70. Otherwise it will be closer to (-72, 72) 98% than to (-71, 66) 99%. We already know that longitudes 66, 67, 68 and 69 with latitude -71 give 99%. So we know that the latitude must be equal or smaller than 65.

My guess for the hotspot is (-71, 65).

[jonnygozy]

Maybe admin didn't make it integers again just to screw with us.

Edited October 3, 2009 by jonnygozy

[Provost Zakharov]

I agree with (-71,65) being the most likely.

I developed a new method based on assuming integer coordinates, and I think it is better than what I had before. The new method calculates (-71,65) as the hotspot.

This is what the "efficiency regions" look like under my current model, assuming (-71,65) is the hotspot. Each band going out from the center represents 1% efficiency drop. The innermost region is 99%. 100% is not visible because it is not a region, just a single point. The only datapoint that doesn't match is the 94% point. My model predicts that spot should be 95%. I'm not sure what the problem is, I need more far-away datapoints to figure that out.

and for fun, a view of the whole moon:

(EDIT: this won't look the same as the in-game map, because google maps uses a different image map and a different projection method)

Edited October 3, 2009 by Provost Zakharov

[Ron Paul]

-71, 65 yields 99%.

I can try another set of coordinates to help find the sweet spot if you guys have another idea.

[Provost Zakharov]

If both coordinates are integers again, then

1. the latitude must be -71. Because If it's -70 or bigger, then it will be closer to the (-66, 66) 96%, than to (-75, 65) 97% and if it's -72 or smaller, it will be closer to (-72, 72) 98% than to (-70, 69) 99%.

2. The longitude must be smaller than 70. Otherwise it will be closer to (-72, 72) 98% than to (-71, 66) 99%. We already know that longitudes 66, 67, 68 and 69 with latitude -71 give 99%. So we know that the latitude must be equal or smaller than 65.

Wait, you seem to have a bunch of new datapoints there, where are you getting these? Can you post a full listing of all the datapoints you have, including all the old ones?

-71, 65 yields 99%.

I can try another set of coordinates to help find the sweet spot if you guys have another idea.

Thanks for trying it. Since that didn't work, I'm at a bit of a loss. I can't seem to make the numbers work. I wonder if my formula for calculating the efficiency is correct.

Right now I'm using

eff(pt, hs) = 100-100*d(pt,hs)/pi

where pt is any point, hs is the hotspot and d is the great circle distance function with radius = 1.

The algorithm is like this:

for every point p with integer coordinates on the map

-assume p is the hotspot

-calculate the efficiency of all known datapoints and count how many match

the points that match every datapoint are hotspot candidates.

Except I can't get all the points to match. If the efficiency formula was correct, there should be several points (or at least one, the hotspot) which matches every other point.

I've tried about a dozen other variations on the formula, including different rounding modes, having a constant multiple or exponent, etc. I also tried some other distance formulas but those weren't even close.

Of course, the efficiency formula itself could be derived by curve fitting or something, but we don't have enough datapoints for that. We'd need a bunch of much further out points, in the 60s, 70s 80s etc.

[Golan 1st]

Of course, we have no guarantee that the coordinates of the hotspot are integers at all

[Golan 1st]

Wait, you seem to have a bunch of new datapoints there, where are you getting these? Can you post a full listing of all the datapoints you have, including all the old ones?

(-70.37785, 173.67188) efficiency: 78%

(-79, 100) efficiency: 92%

(-79, 75) efficiency: 94%

(-66, 66) efficiency: 96%

(-69.5, 79) efficiency: 97%

(-68.18, 76.49) efficiency: 97%

(-75, 65) efficiency: 97%

(-68, 72) efficiency: 97%

(-73.6, 69.17) efficiency: 98%

(-69, 71) efficiency: 98%

(-69.39965, 71.90552) efficiency: 98%

(-72, 72) efficiency: 98%

(-70, 69) efficiency: 99%

(-71, 69) efficiency: 99%

(-71, 68) efficiency: 99%

(-71, 67) efficiency: 99%

(-71, 66) efficiency: 99%

(-71, 65) efficiency: 99%

This is the data I am using.

I have just realized that you are right. I did not post the data of the locations I had before moving the points.

Edited October 3, 2009 by Golan 1st

[Provost Zakharov]

Awesome! That far-out point at 78 really helped. I was able to find a new efficiency function that is capable of matching the data perfectly:

eff(hs,p) = 100 - 125*d(hs,p)/pi

Unfortunately, if this is correct, I believe it implies that the hotspot does not have integer coordinates. My calculations say that -71,68 is the only integer point that can be at the center and still match everything. We already have it marked down as 99%

Here's the new plot. Notice all points are in the correct band now:

Edited October 3, 2009 by Provost Zakharov

[KingBilly1]

i dont have a moon base or colony but try -71,71

[Golan 1st]

i dont have a moon base or colony but try -71,71

This cannot be the hotspot.

It's closer to (-72, 72) 98% than to most of the 99% locations we have

I will be very surprised if both coordinates are still integers

Edited October 3, 2009 by Golan 1st

[KingBilly1]

(-72, 72) efficiency: 98%

(-70, 69) efficiency: 99%

yes but it's inbetween those 2,so maybe worth a try though

[Golan 1st]

The distance from (-71, 71) to (-72, 72) (98%) is ~31km. The distance from (-71, 71) to (-71, 65) (99%) is ~59km.

So I don't think it's worth a try just to find that (-71, 71) is not the hotspot, which is something we already know without wasting money and being unable to move the wonder for another week.

[Overlord Shinnra]

-71.500, 72 --> 98%

-71,64 --> 99%

-71, 71.5 --> 98%

These are my tries.

[Provost Zakharov]

-71.500, 72 --> 98%

-71,64 --> 99%

-71, 71.5 --> 98%

These are my tries.

With these coordinates added to my model, the hotspot location is extremely constrainted. It must be inside a small square centered around {-70.9225, 67.01}, with dimensions 0.16 x 0.21 (degrees, lat x lon). (the actual feasible region is not a square, it's some kind of discrete polygon.) There are no integer coordinates inside the feasible region.

I think it's time we simply ask admin to clarify that it does not have integer coordinates, so that we can end the wild goose chase. 99% is the best result that can be achieved unless we can magically guess the coordinates to the full number of decimal places.

[Golan 1st]

With these coordinates added to my model, the hotspot location is extremely constrainted. It must be inside a small square centered around {-70.9225, 67.01}, with dimensions 0.16 x 0.21 (degrees, lat x lon). (the actual feasible region is not a square, it's some kind of discrete polygon.) There are no integer coordinates inside the feasible region.

I am not saying that you are wrong. It settles well with my calculations, but I am curious how you got this region.

I see no reason to prefer it over, let's say, (-71, 65.5) (and infinitely many other points, assuming there is no limit on the number of digits which can be used).

Edited October 5, 2009 by Golan 1st

[Provost Zakharov]

I am not saying that you are wrong. It settles well with my calculations, but I am curious how you got this region.

I see no reason to prefer it over, let's say, (-71, 65.5) (and infinitely many other points, assuming there is no limit on the number of digits which can be used).

Assuming my efficiency formula is correct, we can test if any particular spot "could be" the hotspot by checking if all the currently known datapoints match what the formula predicts.

The feasible region is the set of all points that "could be" the hotspot, as defined above.

To actually compute the feasible region "exactly" is impossible, so I just sampled the feasibility function (on a regular grid with spacing of 1/200th of a degree in each direction).

[Golan 1st]

Are you sure that these are all the points that could fit???

Do you have no problem with that 92% point?