EXECUTIVE SUMMARY:
- Many experts in the area say crop circles and UFO activity are
linked.
- We look at whether crop circle descriptions appear to foretell or
predict UFO activity.
- While we have no idea why or how or who is making such crop circles,
some descriptions seem to predict activity of certain types of UFO's
in the future. We pick a 7d time horizon for no particular reason
and do not claim this is somehow the optimum or even the upper
limit of what might be predicted.
- Some crop circles appear to foretell future interactions with
aircraft. Other, similar work, suggests some crop circles may be a
reaction to the interaction of UFO's and aircraft, in particular
military aircraft. Whether they are a letter of complaint or a
warning is not determined. We also can't say whether the
information content of a crop circle layout is intentional,
incidental or accidental or whether "informative" circles are
created by hillbillies, UFO worshipers, or the UFO's themselves.
Whatever. It's all very exciting!


Well we can't say no-one warned us. Like the quantum physics world,
people interested in paranormal phenomena find it's all linked up. No
sooner do you start looking at one thing you quickly find you need to
look at another if only to try and satisfy yourself it has "nothing to
do with" the thing you were looking at first.

Today we'll look at the linkage between UFO's and crop circles. The
data I have to hand comes from the useful UK website <http://www.ukcropcircles.co.uk/> that lists "most" crop circles in
the country since around 2005.

Looking through the list of reports and photos you wonder if they mean anything. Many ufologists say they are trying to say something, but
exactly what remains as unclear as who produces these things. It's
pretty clear from the number of constructions that a group of people
running around the country can't make them all and keep it secret and
have their movements undiscovered by e.g. the farmers whose crops tend
to be mangled by the circles.

I was intro to the study of crop circles way back when I first started
using USENET in the 90s. My mental model back then was shaped by an
early childhood experience with them. Back in the 50s around age 6 I
saw a real (what was called then) "saucer nest" that appeared in a
vacant lot along the route I used to walk to preschool. (Yes. In
prehistory we walked to kindergarten even if it was a couple of
miles. Somehow kids didn't die of exhaustion or get kidnapped on the
way and it wasn't considered child abandonment or abuse). There was a
nice write-up in the local rag. It looked just like an area of long
grass where some section nr the middle had been blown flat with no
obvious route in or out through the remaining tall grass for anyone to
have gone in there and done the flattening.

So back then my mental model was more along the idea of a natural
phenomena. I guess I was predicting microbursts or something.

Flash forward to the 90s and the increasingly intricate designs that
started turning up -- I remember a picture of the infamous Julia Set
-- just seemed so fake. Those things with geometric patterns just had
to be man-made; only the rough ones like I remember from that
childhood experience were likely anything really interesting.

But now flash forward to the 2010s and many of these things just keep
turning up with noone coming forward to claim them. The growing body
of angry UK farmers want to know who to sue. The old story about 2
guys that travel around the country with a board and a rope sure
explained some of them, but these days a lot seem to be marked "not
accessible from the ground".

So we naturally want to get some idea of who is making them and why.
Given UFO's seem to be linked with other strange things -- unusual
abductions, cattle mutilations, mass animal deaths, etc -- and many of
the ufologists say there is a link, we need to check what UFO's have
to do with crop circles, or vice versa.

Quite a few months back the s/w I'm developing flagged a link on some preliminary data that was to hand at the time. It seemed there was
some robust link between the appearance of crop circles and certain UFO incidents -- e.g. those where a UFO had tangled with an airplane --
and even more specifically where a UFO had been chased or otherwise
tangled with a military aircraft.

But we really need to now look at a full spectrum of data. So using
the crop circle data (above) incl the brief English language
description of what each circle looks like, and the NUFORC day-by-day
sightings data (mostly over N Am and Canada -- but we can also treat it
as a proxy of global UFO activity) we can try to decide if
combinations of descriptive elements correlate closely with UFO sightings.

While there is already quite a lot of stuff churned out by my s/w
today we'll look at a very simple link. Seeing if crop circles somehow
describe UFO sightings in the near future. Are at least some of them
telling us one way or another what UFO's will be doing next?

We have to put on our science hats right here and underline this
doesn't determine that crop circles are created in one way or another
or by one group of people or "other". *How* any such information gets
into crop circles is an (AFAIK) open question. It could be
intentional. It could be accidental. Some group of hillbillies might
be making them with a rope and board. Maybe some UFO worshipping cult
is making them. Or -- of course -- UFO's may be hovering over fields
at night and squashing corn with their warp fields because they want
to rub our faces in how stoopid we are.

Personally I'll assume something fairly neutral. Something or someone associated with UFO's is making some of these things, and somehow
those things/people also influence UFO behaviour. Don't know anything
about how or why.

We call up the same s/w as prev described. It gathers data off the
Internet and cross correlates everything with everything else using
its experience with (now) years of similar work to bypass or estimate
results where it speeds up the work.

In this simple explication we'll use a "description of each crop
circle" created on a given date matched up against UFO sightings 7
days in the future. There are several 100 of them to match up.

By "description" I mean here something very simple. We look through
all the English language descriptions written up at the relevant web
site. We extract all the words, throw away the "junk words", ignore
words that are very rare in the text as well as too common in the test
("low entropy" words), and use the presence or absence of 2 words in
each write-up as a "very short" summary of what that circle looks like.

E.g. the circle descriptions contain like "central", "inner",
"square", "circle", etc. The description of a particular circle might
contain the word "square" but not contain the word "central". So the
summary +square,-central is one way that circle could be describe.
Each circle will have many possible summary descriptions like this. We
match up "all" of them against the daily sightings data.

Going through all these "match ups" robustly involves ignoring cases
that statistically can't be decided. We can then use normal
statistical tests to decide whether the remainder support a +ve
correlation or a -ve correlation. We total them all up and eventually
can say which description matches best against each type of UFO
activity (also described by a similar set of keywords that may or may
not be present in the relevant UFO report).

And the results are:


UFO kw Circle kws R2
(time t+7d) (time t)

Sphere -single with 0.52192294
Triangle -circular -three 0.48023659
Fireball -crescent -spiral 0.44894320
white -crop -small 0.32099998
orange -fold -many 0.29824326
red -central -complex 0.14743328
-green -pattern -spiral 0.14200538
black -outer -star 0.13984849
-violet -arms -connected 0.12805369
-gold -pointed -series 0.12725803
-grey -pointed -series 0.12218976
blue -large -three 0.11721407
-gray -formation -large 0.11577626
yellow -formation -various 0.11299903
-indigo -area -hexagon 0.11226353
-silver -area -hexagon 0.10132612
-purple -from -many 0.09822280
aircraft -hexagon -ringed 0.09623588
-dark -central -flower 0.08911406
-Teardrop -pointed -series 0.08537718
-pink -flower -intricate 0.08466518
-Changing -central -shape 0.08354755
plane -large -smaller 0.08126034
-copper -central -pointed 0.07202441

In the table keywords that are not present in a report are written
"-x". Other keywords were found in a report. The R2 statistic shows
how well circle reports of the specified type match up against UFO
reports 7 days later of that specified type. An R2 of say .52 says
the day-to-day wax and wane of UFO reports 7d days later follow a
similar wax and wane pattern of the relevant circle
reports. I.e. circles created at a given date (maybe reputed) somehow
"predict" the appearance of specific UFO activity 7d later the
majority of the time.

Given the number of things that COULD happen 7d in the future getting
it right 1/2 the time is an unusual level of skill. ("Skill" is a
technical term in Data Science. Skills that are near 0 are no better
than guessing. +ve skills mean information is being used to inform a prediction. And -ve skill means somehow information is being used to
derive the wrong prediction -- if you do the opposite of what that
psychic says you'll be getting ahead!).

So nr the top of our table is seems "crop circles" are seeming mostly describing events in the future related to 3 types of UFO's --
triangles, spheres and fireballs. A crop circle whose description (as presently notated by the good folks at the crop circle website) does
not include the word "single" but does include "with" tends to
foretell in 7d there will be a UFO sighting in N Am that involves a
Sphere type object. The data then shows about 1/2 the time this does
happen. This is the best example the s/w finds at the present. But
it's still looking and thinking and will probably find more things
the more it looks.

Down at the bottom of the table are several other UFO "types" (shapes)
at low R2. It's likely these only turn out to be somewhat skillfully
predicted because those types are "similar" to the 3 major types that
are predicted well. Maybe they are "subsidiary" aircraft/phenomena.
E.g. Triangle UFO's may be the farmer's truck of the sky and Changing
UFO's are more like their attendant or protective drones.

We also see certain colors are predicted reasonably well by various
types of circles. And some are predicted to a lesser extent. (Many
more, of course, are not predicted at all).

And, finally, some crop circles predict there will be a future UFO
sighting involving aircraft/planes. But the crystal ball for that is
hazy in that the R2 is down to less than 10%.

These kinds of models are the "assembly language" of Data Science
models. It's usual in a real application 100s or 1000s of them are
strung together in committees or networks and are used to make an
aggregate decision about something. If you look at the table (and
squint a bit :) you might estimate joining up several of the lines
for the same type of UFO event might get a better accuracy than the
top-line 50%.

Preliminary results from the S/W were saying combined models could
predict future UFO events better than 95% of the time. But there is a "decreasing returns" problem. These kinda of Ia's or statistical
models can be very accurate and out-perform humans by an order of
magnitude, but they are almost impossible for a human to understand.
They might "get the right answer" much of the time, but they can not
explain to a mere mortal how they are doing it. This is of course
another area of active research -- creating AI's that may be a bit
dumb but at least can convincingly explain their answers to mere people.


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