Newsgroups: alt.paranet.ufo
From: kymhorsell@gmail.com
Subject: a model of UFO navigation -- where are Triangles coming from? (1/n)

[uploaded 54 times; last 31/10/2024]

EXECUTIVE SUMMARY:
- In a similar way to modeling UFO interplanetary movements to
  "explain" the rise and fall of sightings over time, we can use the
  distance from putative bases on earth to predict the sighting
  density of objects across e.g. the USA.
- Assuming the sighting density per state population is related to
  some power of the distance from given points on earth, we can locate
  a small number of points where these models are both statistically
  relevant at high confidence and also explain a large part of the
  state-to-state differences in sightings.
- For Triangle UFO's (as an example) the pre 2006 and post 2006 data
  from the NUFORC database allows us to double check the relevant
  "best models". They are found to both include regions along the
  Antarctic coast as well as small areas along the Arctic coast.  No
  other points on earth explain all the data.
- We find the power law in the "best case" relating straight-line
  ("great circle") distance from the Antarctic to each US state is a
  power of around 4. I.e. the states *further* from the particular
  site in the Antarctic see more sightings per cap than those closer.
- This not only implies the objects are not appearing randomly over
  the US like a bunch of tourists, but there appears to be a
  considerable amount of loitering over the relevant destination
  areas.
- The data is consistent with Triangles flying direct to certain
  areas they find interesting and loitering longer on average in
  regions further from their "home base" than those closer.


In an earlier post we looked at trying to match up UFO sightings of
different types against planetary movements.  Given certain sightings
seemed to rise and fall depending on the distance from Earth of
various planets, we tried to create an "interplanetary flight model"
that predicted UFO sightings (across the US) as a function of starting
from different planets during or prior to a (sometimes annual) close
approach, flying at a constant speed along the relevant distance,
arriving and probabilistically being spotted by a N American.

We found there were certain sets of parameters that seemed to match up
against UFO sightings quite well, even allowing us to predict the trip
time for the chief suspects.

We can perform the same kind of calculations for suspected "bases"
here on planet dirt.

We have looked before at using "local conditions" at each point on
earth to see whether UFO sightings retain an imprint of weather or
other events occurring at points distant from the location where
various objects are sighted. And, again, that was found.

But this time we will use another property of distant places -- its
distance from the location where the relevant object is sighted.

We might posit that the further an object has flown from its suspected
start point (aka "base") the less likely it will be observed given the
possible number of locations it can appear rises sharply as the
distance increases. (And there are also strange consequences from
large distances where tracks across the sphere of the Earth
criss-cross more direct routes creating even more possibilities).

So we can perform this kind of calculation:
   for each spot on the earth presume UFO's start from there and fly
   to the centre of each US state. Does the density of UFO sightings
   in each state fit some kind of power-law function of the distance
   from the given start point?

Well of course I wouldn't be asking the question unless I knew most of
the answer already. :)

Let's look at the results for a particular type of object -- the
"Triangle". As usual I'm using the NUFORC database up to the end of
2021. This presents some idiosyncratic problems that might now
present as opportunities.

In Mar 2006 the NUFORC moved from telephone and letter reports of UFO
sightings to a web-based system. (I haven't done any guessing as to why
this happened at that time -- but go ahead yourself :).  This not only
increased the number of reports 10-fold in a matter of months it also changed
the type of reports and the types of people that submit them.  This makes
using the full period of the dataset ~1900-2021 for any given task
problematic.

But what we can do here is split the data into pre 2006 and post 2006
and essentially run our modeling twice. Now the differences in the 2
sections of the data are a benefit. If the same kinds of models are
found in each part it makes the results more robust -- the same type
of assumptions seem to predict the appearance of the objects in quite
different eras of UFO watching.

The distribution of Triangle UFO sightings looks like:

		Sightings per mn capita
State		<2006	>=2006

Alabama		3.49868	16.0528
Alaska		4.06266	43.3351
Arizona		4.10072	26.5082
Arkansas	2.35041	23.5041
California	2.12033	19.2363
Colorado	3.29877	35.5534
Connecticut	4.17724	29.5192
Delaware	2.11431	35.9433
Florida		1.52926	20.4723
Georgia		1.86004	15.6635
Hawaii		1.39704	17.4629
Idaho		2.41702	45.9234
Illinois	2.09953	20.14
Indiana		2.87023	21.9044
Iowa		4.80169	29.1303
Kansas		3.09104	24.7283
Kentucky	2.71181	26.4401
Louisiana	1.7128	16.0575
Maine		3.7613	54.1627
Maryland	1.33191	19.4792
Massachusetts	2.20769	24.1374
Michigan	3.02341	23.7841
Minnesota	2.36812	22.2239
Mississippi	2.33931	17.3777
Missouri	3.45186	31.8886
Montana		5.80861	53.2456
Nebraska	2.10949	16.8759
Nevada		2.07552	21.447
New.Hampshire	2.25461	66.8867
New.Jersey	2.00937	17.9727
New.Mexico	6.23469	30.2142
New.York	1.97012	12.7805
North.Carolina	2.58892	21.0101
North.Dakota	2.64226	33.0283
Ohio		2.66932	23.0767
Oklahoma	2.04534	22.7544
Oregon		3.72303	40.7051
Pennsylvania	2.57762	23.8235
Rhode.Island	3.78681	23.6676
South.Carolina	3.47212	30.0236
South.Dakota	2.32973	25.627
Tennessee	1.96961	23.9383
Texas		1.56539	12.7052
Utah		2.00272	25.0341
Vermont		3.19467	54.3095
Virginia	1.31218	19.5634
Washington	3.62604	40.4443
West.Virginia	2.71131	30.9089
Wisconsin	2.59905	25.644
Wyoming		3.41235	35.8296

When we take the straight line ("great circle") distance between the
center of each state and every 10x10 degree region across Earth we find
the following "top 10" best matches between some power of the distance
and the relevant state sighting density per capita:

2006 data:
Lat	Lng	R2
-85	85	0.29533058
-85	95	0.29302384
-85	105	0.28977774
-85	-105	0.28635705
-85	-115	0.28605394
-85	115	0.28602370
-85	-125	0.28497686
-75	85	0.28371493
-85	-135	0.28324145
-85	65	0.28298575

2020 data:
-75	55	0.44798858
65	-125	0.44221503
75	-115	0.44117760
65	-115	0.44076530
-75	-55	0.43486416
-75	-45	0.43042487
-75	65	0.42431659
15	-95	0.42115346
-75	45	0.42062016
-75	35	0.42054592


We immediately see a big chunk of the Antarctic coast seems to be
roughly in common between the 2 different (sub-)datasets.  The 2020
data has a better R2 -- meaning the model of using distance between
the region and each state "better explains" the (post 2006) density of
sightings in that state. Between grid (-75,55) and each US state about
45% of the state-to-state difference in sighting density is matched by
the simple power law using the great circle distance.

The best the 2006 data can do is an R2 of about 30% between a sightly
different location in the Antarctic (-85,85) and each state.

The 2006 shows one significant point in the ocean off N Greenland
while the corresp area in the 2020 data is off N Canada.

The 2020 data also shows an area across the ocean nr central America
that doesn't appear in the 2006 dataset.

Overall, the 2 sets of data suggest an area along the coast of around
the Antarctic Peninsula "best explains" the observed Triangle sightings
since ~1900.

When we examine what kind of model is involved there may be a surprise.

We have previously looked at UFO sighting density versus density of
(US) military bases and found some types of object fell off with the
inverse of the distance from states with large conc of USAF bases,
while others fell off at inverse square laws. These formulas suggest
some types of objects appear to view USAF bases as threats related to
aircraft intercept (1/r) or random area patrols (1/r2), resp.

But the models relating distance from Antarctic (in the case of
Triangle UFOs) are not inverse or inverse square. They are +ve powers.

For the 2020 dataset the best model relates to (-75,55) which is found to be:
    y = 1.12765e-17 * x^4.37322

I.e. the sighting density of Triangles increases from that location as
around the 4th power of the distance from Antarctica.

What does this mean?

In means the movement of Triangle UFO's is not random.
This kind of model is consistent with "missions" that include
a flight from a "base" area to a "destination" plus a lot of
loitering at the destination. The further the flight the longer the
loitering involved i.e. cost considerations. If an object loiters at the
destination longer then it's more likely to be seen, and considering social
media the number of people seeing a given object or (e.g.) a series of
objects over a month may not be simply proportional to how long those
objects are flying over the target area.

What we can say for certain, if Triangle UFO's are some kind of
aircraft flying from Antarctica to the US on a daily basis, they are
not appearing across the US in a purely random fashion.  They are
"interested" in something.

--
"Nothing in life is to be feared, it is only to be understood.
Now is the time to understand more, so that we may fear less."
- Marie Curie

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