Hackpen Hill Koch fractal, Wiltshire
18th August 1997
Geometrics Outliers ('grapeshot')
Flattened Grain in Crop Fields
Exalting the checksum and exterminating the message? A call for better record-keeping of crop circle features
Crop circles manifest in the dark night with sheer size, complexity, precision and speed. If this does not blow you away just buy a crop circle calendar and enjoy pretty pictures. The rest of us should become systematic in researching them, however.
Is flattened crop a low-bandwidth and noisy communications medium? Certainly. But the message might not be complex, should not violate our free will, and is best targeted to those ready to accept it, not those in authority. Until we ourselves extract the full bandwidth that IS there, we are not worthy of asking the question, and until we prove that, the bandwidth won't likely increase.
Croppies agree that to decode a message any authentic formations must be well differentiated from cargo cult artifacts. However, there's little agreement on authenticity, nor message.
We are slow learners. Eventually, an astrophysicist realized the Barbury Castle formation encoded pi to ten digits. Aliens are teaching us pi? Doubtful. But we can be sure that what Lucy Pringle hails as "a seminal event", Suzanne Taylor is "almost certain" is an artifact. But Suzanne, the skeptic, elegantly says this:
"... speculation about whether they are real or not is the wrong conversation -- just what our gossipy society likes to dwell on, instead of on the majesty of life. Let's just hang out in majesty to see what that's all about and what we should do."I agree. Let's just open ourselves up to these and see if they don't sort themselves into two separate camps, the genuine and the artifactual. How do we do this?
Some try to authenticate circles by finding features difficult to lay out on the ground with string and poles:
More esoterically, one might douse or sense strange energy fields emanating from them.
All these determinations, however, are subjective.
You may find the two circles defining the inner and outer bounds of a crop ring can be perfectly filled with an unseen inscribed contruction-line regular polygon. Finding this is a delightful exercise, but what it really conveys is the ratio of the circles. The coarse manifestation of laid grain reveals, with analysis, an infinitely precise design intent.
Zef Damen's beautiful renderings of these into rules that can be reconstructed with straightedge-and-compass are a vital resource.
With computers, we can numerically reproduce these geometric features to far greater precision than is found in the crop. Consider the Chilbolton 2000 formation, interesting for its location in both time and space.
How long would it take to flatten this much crop on the ground, given cookbook instructions such as Zef Damon's? I have no idea, but I do know that it took me over two hours to make a model that you can download and view with E-Drawings of only the geometric parts, using a fast computer and a sophisticated drafting program. I actually constructed only one quarter of this dually symmetric formation. Simply mirroring the rest saved even more time compared to flattening crop.
Further evidence for this conviction is lent by Bert Janssen's work on squaring the circle. His formation measured on the ground formed a squared circle, but if you construct the same figure with the implied tangencies (that is, the square intersects the point of tangency of the small guide circle and the derived circle), you arrive at only a 98.97% accuracy, pretty good but not infinitely perfect: further evidence that at least part of the formation was created on the ground numerically rather than geometrically.
Crop formations seem to have these general characteristics:
From this I infer that whatever technology is used, the technique is to
In radio communications, it is the stable reference of the carrier wave that enables us to decode (or de-modulate) the modulation on that wave that contains the message.
Did we send our Aceribo SETI message out into the far reaches of outer space with error detection and correction elements? No mention of that in the Wikipedia article -- without adding error control bits, each pixel failing to make it to it's destination makes the message exponentially more unrecoverable. Given the distance/power product of this signal, the correction bits should probably have outnumbered data bits! No matter; the Aceribo message was just a photo-op anyway: it was only sent once, over a period of three minutes, to a star system that will have moved out of the beam by the time the message gets to it!
In contrast to the message we sent, the much more elegant Circlemakers
The Noise Figure of a crop formation is simply a single number that expresses the degree to which the flattened crop deviates from the design intent, and each formation will contain its own characteristic number.
Non-geometric formation elements are not incorporated in the determination.
The Noise Figure lets us determine the granularity of the formation, that is, the level of confidence that a measurement we derive from a feature therein is information, rather than noise.
afco = area of flattened crop outside the design intent, in pixels
adi = area of the design intent, in pixels
I am not aware that anyone has yet done this kind of analysis, let alone even the data acquisition that would make it possible.
They must be measured to the precision dictated by the noise figure, or we have no hope to decode them.
Image analysis software is readily available.
Here is a crude normalized derivation of the 2000 Chilbolton formation,
of which Zef Damen has done a phenomenal deconstruction of the geometric parts.
Chilbolton, August 13, 2000
Zef rightly omitted the small detached circles from his deconstruction, because they are obviously asymmetric,
especially evident top-to-bottom. Because they are not checksum, they are likely message.
To determine whether the left-right features are asymmetric too, I copied, rotated 180°
and overlaid on the other half, in blue. While these are apparently asymmetrical along both axes, without
a noise figure, we can't tell if the asymmetry is intentional or accidental.
Referring to the Koch fractal at the top of this page, note the phenomenal number of outliers that could serve as message.
The number of different outlier parameters may represent a modulation mode. Since outliers are part of a rough geometric pattern with a definable center, defining the deviation from a mean (rather than the absolute macro measurement) would drop out the geometric contribution to these parameters. This is analogous to subtracting the carrier wave from a radio signal.
Referring to our Chilbolton formation above, we find 2 sets of 13 3-outlier strings, or 78 circles. Multiplying by the 9 parameters above yields 702 information entities, each of which may possibly have the resolution of an ASCII character.
The Big Question
Indeed, the formation that appeared at Lockeridge, Wiltshire on August 6, 1998, "The Queen" so resembled a contented chicken that at least one croppie denounced it as a hoax, despite its flawless execution and beautifully lain crop.
In conclusion, the human race has been mainly just gawking at these formations, and this has to change. The tourist photos pilots have been taking of these structures so far are inadequate to decode them, and therefore the information content of much of these formations may be already lost.
What we immediately must do is insist that pilots who provide the crop formation research community with photos give us (sell us) images taken from directly overhead, with as high an altitude (to minimize existing geographic features and optical distortion) and resolution as humanly possible, not the artful isometric calendar shots, or the grainy internet jpgs.
Anything by Freddy Silva. While his book Secrets in the Fields is not recommended for anyone made queasy by every possible numerological or mathematical significance slung about like so much grapeshot, it is an eloquent, information-packed labor of love.