Crop circle symbols

A

Archaea

Guest
Here are some ideas and things I've discovered in my quest to decipher crop circles.

Some Things the C’s say

Snippets from sessions in this post are all taken from this article, written by Laura:

http://cassiopaea.org/2010/09/14/the-chilbolton-crop-circle-and-the-cassiopaeans-on-crop-circles/

In this session the C’s mention using a computer program to decipher crop circles.

05-07-95
A: Study mathematics for all possible unanswered pieces of the puzzle!!! Interpolate and use appropriate computer program, learning now increases your power tenfold, when you use some initiative, rather than asking us for all the answers directly!!!

And in this session the idea is expanded upon.

11-30-96
Q: (L) Okay, crop circles are a language, so to speak. Are they in some way related to mathematics?
A: Mathematics is the one and only true universal language.
Q: (L) Well, I just don’t see how they can be decoded.
A: In this room is all the mental power needed, with addition of another “room” in Wroclaw, (Ark was in Poland at the time of this session.) of course, that is needed to “crack” the code of our circles.
Q: (L) How do we start?
A: All one needs is a foundational point to build a computer program. And we have given you this already.
Q: (L) But nobody wants to hear what we have been saying!
A: Well, the circles are undeniable in their existence, our communication with you is deniable.
Q: (L) Well, if they don’t want to hear it as it is channeled, what makes the crop circles different?
A: Not point. If you can crack the code, this becomes an undeniable language that is ongoing, consistent, and demonstrable.

[...]

Q: (L) Ark asks: to crack the code, is it sufficient to have a collection of pictures? I’m sure he means crop circle pictures
A: Yes, to start with.
Q: (L) Ark says, to crack the code, we need an example. Can you point some out? (T) Example, as in crop circle pictures? (L) Well, no, how to crack it, or whatever.
A: Please review transcripts.
Q: (L) Can you tell us, I’m curious, too. What is it, is it about the using mathematics, or is it about something else?
A: You asked for interpretation of specific crop circles pictures before. Remember?!?

[...]

Q: (A) Can decoding of information from crop circles be automatized completely? Can this be done by a computer program, without human intervention, with out work of mind?
A: Not likely, and what would be the benefit? Learning is necessary for progress of soul. Remember, we are not here to lead by the hand. We will help, but some answers are for you to decipher, and you have been extraordinarily good at this, my Arkadiusz, since very early childhood. This is how you are building your power center. All there is is lessons and learning is fun. More fun even than teaching.

The crop circles and their meanings mentioned in the transcripts can be found at the article from where I got the sessions.

The Computer Program

I think that the problem of solving the meanings of crop circles might be a linear programming problem. The way I’ve been thinking about setting up this problem is by creating a matrix, where the rows of the matrix are different crop circles which utilize the same set of symbols.

Then, given that we know some of the meanings of crop circles from what the C’s have said, we can try to use a form of Gaussian elimination to find the meanings of the various symbols used in crop circles.

I haven’t tried any of this but here’s a quick example:

In the article the C’s said that this crop circle means “Planetary window.”

cropa06.gif


The article also say’s that the C’s said that this crop circle means “Planet.”

cropa02.gif


So if we put these two crop circles into our matrix...

[ Crop Circle 1] = [“Planetary window”]
[ Crop Circle 2] [“Planet” ]

Then “subtracting” the bottom row from the top row gives a pictograph for window, which looks like the 4 arcs in-between the disk and the ring for the “Planetary window” crop circle. I think that once a basic, rudimentary meaning for the symbols in the crop circles has been identified, it might be possible to find deeper meanings amongst the ratios and lengths in the crop circles.

For example, I think the arcs in the window pictograph may represent waves, and the ratios between their lengths might represent a difference in frequency.

Since these sessions are from a long time ago, I’m curious if the “network” has made any progress with the program? I hope no one minds me asking.

The Symbols

I think that in order to decode the meanings in crop circles, the various symbols used need to be isolated. Most crop circles are made up of more than one symbol, and I’ve tried to identify the various symbols that are common throughout the phenomenon. And since the thing I seem to do on this forum is make lists... I made a list.

Here’s what I have so far, with examples:

Images are from:
(http://www.temporarytemples.co.uk/imagelibrary)
(www.cropcirclecenter.com)
Or the article above:

1) The full disk, this is very common.
KE19601333_A_G.jpg
ME19771333_A_G.jpg

2) The ring, sometimes seen around a full disk, but not always.
CA19621333_A_G.jpg
AU19821333_A_G.jpg
UK19911333_Z1_G.jpg

3) The ring with dots, also usually found around a full disk.
NL19971333_F_G.jpg
UK19991333_B_G.jpg

4) A connecting line, usually connecting two of the other symbols.
NL19941333_B_G.jpg
UK19961333_A_G.jpg
US19981333_A_G.jpg

5) An arc, usually occurs around disks.
NL19991333_A_G.jpg
cropa06.gif

6) Two straight lines, sometimes occur in pairs around a connecting line, and sometimes they occur alone inside a ring.
cropa16.gif

7) A key, sometimes with two or three spokes, usually protrude from a disk or ring.
cropa17.gif
cropa12.gif

8) A semi circle or a D, sometimes alone, sometimes they form a ring with a line through it.
cropa18.gif
15-west-meon-hampshire-july.gif

9) A breaking line, can vary in length, usually between disks.

I couldn't find any pictures of a breaking line. It's a line which is between two disks, rings or objects usually and is perpendicular parallel to what a connecting line would be.

10) An L shape or a right angel, may be related to the key symbol.
cropa15.gif

11) An isosceles triangle, is rare.
UK19711333_A_G.jpg

12) A crescent, sometimes in rings, sometimes by themselves.
1-west-overton-hill-wilts-o.gif
31-east-meon-hampshire-july.gif

13) An eye shape.
22-east-field-alton-barnes-.gif

14) The square, similar to disks but rarer.
37-winterbourne-bassett-wil.gif
205_Cheesefoot_Head_nr_Winchester_Hampshire_09_08_2012_Wheat_OH2.jpg

15) The double connecting lines, usually connecting two rings or disks.

I couldn't find any pictures of double connecting lines either. A double connecting line is just two parallel connecting lines which connect the same two disks, rings or objects .

16) T, Y, and X shapes, Can be intersections between lines, can be like key shapes.
UK19911333_M_G.jpg

17) An equilateral triangle, found quite a lot well into the phenomenon.
cropa04.gif
IN19871333_A_G.jpg

18) The 5-sided star or pentagram, usually in rings or disks, makes for some fantastic crop circles.
cropa22.gif
ZA19961333_A_G.jpg

I'm sorry about not having a picture for all the symbols, I didn't want to use too many different sites.
 
9) A breaking line, can vary in length, usually between disks.

I couldn't find any pictures of a breaking line. It's a line which is between two disks, rings or objects usually and is parallel to what a connecting line would be.

My apologies, I made a mistake here. Instead of parallel, it should be perpendicular. I think this is a nice example of saying the exact opposite of what I mean. ;)

I tried to modify my post, but I couldn't find the modify button. :huh: I think it may have gone on holidays.
 
Here's another snippet from Laura's article that I think is relevant:

03-18-00
Q: Well, Barry W. has written a paper about the formation of solar systems and the necessity for a twin star system in such developments. According to his calculations and his theory, the mass of the companion star must be far less than what you indicated the mass of the proposed companion star for our solar system might be. He theorizes that the relationship should be the same as between a proton and an electron, mass wise. Is he correct?
A: Best to not quite fall into the mirror image atomic principles trap, lest one suppose to have completely conquered the atomic properties puzzle.
Q: Okay, can you give us an interpretation of this crop circle here that Barry has interpreted in his way?
A: Maybe a solar type system. Maybe not the one commanded by Sol.
Q: If it is not the one commanded by Sol, which one would it be? It must be one of such importance that such a message is being conveyed in a crop circle formation, I would think.
A: Maybe.
Q: What solar system would it be? What is the name of the star? Would we even know the star?
A: In or of Epsilon.
Q: Which Epsilon?
A: Major.

Q: There are a lot of stars called “epsilon.” Which constellation?
A: Adjoining constellation.
Q: What constellation?
A: No more information to be revealed at this time.
Q: Is this a solar system from which some of the aliens visiting our planet originate?
A: Something like that… From which someone originates.
Q: Someone who?
A: Take a wild guess!
Q: Are they STS or STO?
A: STS.
Q: Well, you have said that the crop circles are expressions of 6th density thoughts. Does this mean that we are being warned about this?
A: On wrong track. More like an historic pictogram.
Q: Is the orbit depicted without a planet depicting a planet that was destroyed?
A: No.
Q: What does the orbit without a planet depict?
A: Transference.
Q: Transference of that planet to another realm? Transference of what?
A: Those who were relocated after the prototypical population was completed.
Q: Are you saying that this is a pictogram of the mother planet of the human race?
A: Close. That which led to the human race as it now exists.

Q: As we measure time, what period of time does this pictograph represent, counting backward in years?
A: Millions.
Q: Getting back to the earth and companion star business, BW* is predicting that comets will begin hitting about the year 2003, based on the planet positions of this crop circle. Now, even if it is not a representation of planetary positions in our solar system, he COULD be picking up information psychically and using this information as a ‘bridge’ to present, or rationalize it. So, he has this prediction, what is the likelihood of this idea or prediction coming true?
A: Probably will not be.
Q: He said that the orbit of the companion star, based on his calculations, was about 5000 years long…
A: Our “companion star” data was meant as a clue for guidance purposes, not as the be all and end all.

I think this is interesting, in that we wouldn't know which solar system this crop circle is from at the moment, but we might learn which one it is in the future at some time. This makes me think that maybe crop circles are signs for 4D humans to use when they are exploring the galaxy. Of course, it could just be that the crop circles are telling a story of sorts, and the crop circle referenced above is like a picture in a picture book.

At any rate, I've been thinking about what the different symbols could mean, from these ones:

cropa10.gif


cropa19.gif


I think that maybe the disk represents the concept of concept, memory, thought or knowledge. And the connecting line is like a conduit through which the "experience" or information in the concept, thought, etc. can pass or travel. All the meanings of these CC’s are related in some way to concepts, knowledge, thoughts and memories.

cropa13.gif


cropa15.gif


cropa16.gif


cropa17.gif


From this, I think maybe the meaning of this crop circle:

cropa12.gif


Could be interpreted as a teacher longing to share their knowledge with a student or something. Or a well developed concept or piece of knowledge longing for another concept or piece of information with which it can continue to develop.

I'm also confused about what the difference between these two crop circles is:

cropa02.gif


cropa11.gif


Does anyone have any ideas?

Also, I think some of the symbols in my previous post may have been derivatives of other symbols, i.e. some symbols could be made up of other symbols, or be overlaps of other symbols. And I've also come to the conclusion that the ring represents a cycle, and an arc, of which several can be used to make a ring, might mean "part of a cycle."
 
Archaea said:
cropa02.gif



Does anyone have any ideas?

This one reminds me of supposedly recorded some kind of beam on videos showing explosion in tha fertilizer plant in USA and of Čeljabinsk's meteorite too :huh:
 
This one reminds me of supposedly recorded some kind of beam on videos showing explosion in tha fertilizer plant in USA and of Čeljabinsk's meteorite too :huh:

Yeah, it does look like a laser or meteorite. :lol:

I've been planning to make this next post for a while now, but have been exercising my powers of procrastination.

Ok, so, if a disk represents a concept and a ring represents a cycle of some sort (which I think I need to explain why I think that better) then maybe a ring with dots on it (symbol 3) represents a concept cycle. So a ring with four dots on it might mean concept A leads to concept B leads to concept C leads to concept D leads to concept A.

Another thing I was thinking is that if a disk represents a concept or a thought, and a ring represents a cycle then this CC:

cropa11.gif


Might represent a concept which has been through a cycle, making it more like a refined thought or concept. So the meaning "Train" given by the C's might mean train as in "train your mind" rather than train as in "choo choo train."

Here's another CC from Laura's article which uses the symbols of disks and rings:

observ1.jpeg


I think this CC might mean something like "from the refinement of knowledge comes many new concepts."

Also this CC:

cropa03.gif


The C's say means "Intierdimensionality," which I think is interesting because the edge of the Mandelbrot set is likened to the edge of a disk if I remember my fractal books correctly. So this crop circle might be representative a concept or a thought which is interdimensional. :)

The Mandelbrot set and the Julia set fractals are related, so these Julia set CC's:

19-stonehenge-wiltshire-07-07-96-wheat-oh-35mm-neg.jpg
28-windmill-hill-wiltshire-29-07-96-wheat-oh-35mm-neg.jpg

Which are mainly made up of disks, might mean something like "An interdimensional concept is made up of many ordinary concepts."

And finally I've attached a picture I drew using paint of what I think a CC with the meaning of "double meaning" :P would look like.
 

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Hi Archaea,

This is very interesting. Great job by gathering informations in one place. Eventually, in the future I can help setup a dedicated web page to the subject to try to have all crops circles and relevant informations associated with them in a way several can work on.

For the moment my question is how a computer program can be useful? I mean, is there an hidden complexity in those drawings need to be discovered that a computer program is need to extract it? Perhaps to extract geometric figures used to build the crops and interpret them? Do you have an idea?

Perhaps a way is to look about program used to decipher hieroglyphs, ancients writing.

I've another question: do you have investigate about the "state of the art" of CC deciphering on the web?
 
Hi Archaea,

Hello Ellipse, :)

This is very interesting. Great job by gathering informations in one place. Eventually, in the future I can help setup a dedicated web page to the subject to try to have all crops circles and relevant informations associated with them in a way several can work on.

That sounds pretty cool, I'd be interested in being a part of that project, it sure would be nice to have all the available data.

For the moment my question is how a computer program can be useful? I mean, is there an hidden complexity in those drawings need to be discovered that a computer program is need to extract it? Perhaps to extract geometric figures used to build the crops and interpret them? Do you have an idea?

Now there's something I hadn't considered. My thinking so far has been that there are several layers or levels to the CC messages:

1) The actual message from the meanings of the symbols and their relationships. (which is where I'm at now)

2) The formulas and other mathematical meanings from the ratios between the different symbols. I think the discussion with the C's about the CC with 19 disks and how 1, 7, 13 and 19 are all prime numbers falls into this category. To me that CC means something like "There's a concept with six directions on which lies three more concepts," which is a bit dry IMO, but I think the prime numbers stuff is gold. This is because 1 + 6n where n = {0, 1, 2, ...} is either a prime or a square of a prime for as far as I care to count, I think it would be neat if that was proved to be true.

3) The relative locations of the CC's. I think this might form another geometrical object.

I'm not sure if relative size or chronology of the CC's means anything, but then I'm not sure if anything means anything...

The computer program idea I presented above was something I thought might work because I had been studying linear programming and linear optimization (which is really cool in IMO, not like stats) and it seemed to me that it might provide a way to isolate the meanings of the different symbols using the information the C's had given. So far though, that thinking hasn't been very useful, so I'm not convinced that's what the C's meant by computer program.

Perhaps a way is to look about program used to decipher hieroglyphs, ancients writing.

I'm unaware of any program which does that, I did a quick Google search but nothing came up. Do you know of any program used for that purpose? If so, I'd be interested in learning how it works, It'd be really cool if it put the "sentences" into a matrix and then used linear optimization to reduce the matrix to find the key symbols and phrases, so all the user needed to do was put in a "key" and see if the meanings made sense, effectively unlocking the language. FWIW, I think the universal translators in STAR TREK use a similar method to this. ;)

I've another question: do you have investigate about the "state of the art" of CC deciphering on the web?

I've tried looking for what people think the CC's mean on the web. I think Laura's article is the best I've found so far that actually proposes some information regarding what I called "Layer 1" meanings. However, there has been some good stuff regarding "layer 2" meanings that I've come across, which if your interested, might be worth gathering up.

Having said that, a lot of stuff on the internet claim to have deciphered CC's, but they don't say anything 'juicy.' And from what I can tell, figuring this stuff out ourselves is supposed to be fun, so I think we can listen to all the ideas, but then use our critical thinking hats. Also I've been doing this for a couple of months now and it's not easy, sometimes I think I've got something, but when I check it I find I was way off... just thought I'd add that. :halo:
 
regarding mathematics, check out this representation of pi;

_http://www.telegraph.co.uk/news/newstopics/howaboutthat/2144652/Most-complex-crop-circle-ever-discovered-in-British-fields.html
 
Inquorate said:
regarding mathematics, check out this representation of pi;

_http://www.telegraph.co.uk/news/newstopics/howaboutthat/2144652/Most-complex-crop-circle-ever-discovered-in-British-fields.html

Amazing!

But I don't really see it (pi) yet. I gotta go to school.

Not 2013 but still, nice catch! ;)
 
easy-as-pi.jpg


Starting from the middle, and going around with each pi/5 section corresponding to an additional number and each step out radially to a new digit place.

I've been thinking about the idea of making some sort of computer assisted analysis of crop circles for a while now, there are just so many variables it is hard to know where to start. You can consider the counting of different elements in the circles, the ratios of sizes, the idea of 3-dimensionalizing them, the locations, other geometric properties within them, numerological aspects, the prime numbers, the list goes on... I just don't know where to start, but maybe just starting anywhere will be enough to lead to interesting results.
 
I did some tinkering with the idea of 3-dimensionalizing some of the crop circles. I decided to start with one that seemed easy to deal with and already had the 3D look to it.

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I started with this idea to match what the circle appeared like:
index.php

Then I added some rotation:
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I was thinking about a particular session where the C's mentioned hexagons and related it to rotating tetrahedrons. I didn't go with the tetrahedrons yet but embedded the object in a cube at a perspective that makes it appear to be in a hexagon, then made the two rotate in opposite directions. There are plenty of other ways to rotate them and I might mess with that or trying to do the tetrahedron thing.

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Edit: Had to go back to insert the pictures in the body of the post because they have to be uploaded first as attachments.
 

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Inquorate said:
regarding mathematics, check out this representation of pi;

_http://www.telegraph.co.uk/news/newstopics/howaboutthat/2144652/Most-complex-crop-circle-ever-discovered-in-British-fields.html

Ask_a_debtor said:
easy-as-pi.jpg


Starting from the middle, and going around with each pi/5 section corresponding to an additional number and each step out radially to a new digit place.

That's a pretty cool CC IMO, I figured I'd have a go at trying to figure out what it means... There is a disk with a ring around it, so I think that bit means "train," there are 3 smaller rings in the larger ring which might mean something like "triple cycle" or "three cycles" maybe. I don't know what the arc's with the breaks in the middle of the CC mean though, but I think they'd be representative of "semi-cycles."

So maybe this CC is representative of the lessons of 3D, although I think that that's a bit of a leap on my part. If I was going to put my interpretation of it's meaning into words I might go for something like "The pathway through the 3rd dimension." But I'm really not so sure if that's correct...

Ask_a_debtor said:
I did some tinkering with the idea of 3-dimensionalizing some of the crop circles. I decided to start with one that seemed easy to deal with and already had the 3D look to it.

index.php


I started with this idea to match what the circle appeared like:
index.php

Then I added some rotation:
index.php


I was thinking about a particular session where the C's mentioned hexagons and related it to rotating tetrahedrons. I didn't go with the tetrahedrons yet but embedded the object in a cube at a perspective that makes it appear to be in a hexagon, then made the two rotate in opposite directions. There are plenty of other ways to rotate them and I might mess with that or trying to do the tetrahedron thing.

Hi Ask_a_debtor,

I think you're right about the hexagon being a cube which is intersecting a 2D plane. I was thinking about whether or not I should've put hexagons and pentagons in the list of symbols, but I don't think it matters. If we do treat the hexagon as a symbol, however, I think this CC would be the one which defines it's meaning. This is because the "object" in the centre looks like a 3D object, but the shapes that it's made out of include a hexagon and some triangles and some other stuff, while the large hexagon around the outside looks just like a CC symbol... OSIT.

the large hexagon symbol is made up of a hexagonal block with a hexagonal ring around it, so maybe this CC is representative of the perspective of a higher dimension "train" from a lower dimensional awareness. However, if the cube idea is right, the hexagon would be related to the square symbol rather than the disk symbol. I have an idea of what the square symbol means though which I'll get to in a bit hopefully. Overall, I think this CC means "The perspective of a higher dimensional reality" or something.

Anyway, I have some more ideas which I'll quickly jot down here.

*I think it should be possible to find the meaning of the two straight lines (symbol 6) from these crop circles:

cropa16.gif
cropa18.gif
cropa21.gif

I think they might mean "movement," so when they are around a connecting line, then the overall meaning of that part of the CC might mean "movement through the conduit."

*The crescent (symbol 12) is like a disk missing a smaller disk, so it might mean something like “incomplete concept.”

*The “Alternating current” CC:

cropa08.gif


Is a bit strange IMO. It has a “Train” CC within it, but then it has what looks like directional fields in each quadrant. I think maybe it’s not necessarily about electricity exclusively, but could be about the flow of thought through perception or something... Perhaps it might be an idea to add “Directional field” to the list CC symbols?

*I think the eye shape (symbol 13) is the intersection of cycles or concepts. So the CC for symbol 13 in my first post might mean “the cycle formed from the intersection of cycles” or “Binary system.”

*This CC:

cropa24.gif


Which the C’s say means “Physical life pictorial” looks to me like two concepts are intersecting and the intersection is connected to another smaller concept. For some reason this combined with the C’s meaning reminds me of what I think about the short wave cycle.

*I've been learning about Fourier series lately, and to make a straight line using Fourier series you need an infinite series of cycles. This makes me think that maybe a square block might be representative of an infinite series of concepts, and a square "ring" might mean "the sum of infinite cycles." A Fourier series also uses both the sine and cosine trig functions, so maybe the square shape relates to the sum of concepts or cycles which are 90 degrees out of phase.

My thinking has been that if a disk relates to how a concept is perceived, then a square block relates to the reality of the concept as it is objectively. While a square "ring" would be the sum of infinite cycles, so would be the universe as it is.

*I think the equilateral triangle symbol means balance, or a least balance of three things. It's so obvious IMO but it seems to fit so far.

*There is also the astronomical interpretations of the CC's, like the "planet" CC and the "astronomical twin phenomenon" CC. So what is the connection between what I think the CC's mean and the astronomical interpretation of CC's, if any?

*I've also been feeling that some of my interpretations of CC's and meanings of symbols have been getting a bit "thin." I really feel like I'm missing something.
 
Archaea said:
I think you're right about the hexagon being a cube which is intersecting a 2D plane. I was thinking about whether or not I should've put hexagons and pentagons in the list of symbols, but I don't think it matters. If we do treat the hexagon as a symbol, however, I think this CC would be the one which defines it's meaning. This is because the "object" in the centre looks like a 3D object, but the shapes that it's made out of include a hexagon and some triangles and some other stuff, while the large hexagon around the outside looks just like a CC symbol... OSIT.

the large hexagon symbol is made up of a hexagonal block with a hexagonal ring around it, so maybe this CC is representative of the perspective of a higher dimension "train" from a lower dimensional awareness. However, if the cube idea is right, the hexagon would be related to the square symbol rather than the disk symbol. I have an idea of what the square symbol means though which I'll get to in a bit hopefully. Overall, I think this CC means "The perspective of a higher dimensional reality" or something.

Interesting interpretation, and your "overall" thought is along the same line of thought as my own. I seem to get the feeling that the ones that appear most "3D" (or are easiest to picture as three dimensional) are an attempt to portray higher dimensional symmetries. Like trying to explain a 3D object to a 2D inhabitant of "Flatland" using the available 2D framework.

*I've been learning about Fourier series lately, and to make a straight line using Fourier series you need an infinite series of cycles. This makes me think that maybe a square block might be representative of an infinite series of concepts, and a square "ring" might mean "the sum of infinite cycles." A Fourier series also uses both the sine and cosine trig functions, so maybe the square shape relates to the sum of concepts or cycles which are 90 degrees out of phase.

Funny coincidence - I've been studying a bit more on Fourier series lately as well. If you have some solid basic calculus background, this course from Stanford University is available in its entirety online!

http://see.stanford.edu/see/courseInfo.aspx?coll=84d174c2-d74f-493d-92ae-c3f45c0ee091

All of the lectures (30 one hour classes) were filmed and are available to download and watch. Also all of the lecture notes and homework assignments are available. Basically free college education!
 
Funny coincidence - I've been studying a bit more on Fourier series lately as well. If you have some solid basic calculus background, this course from Stanford University is available in its entirety online!

http://see.stanford.edu/see/courseInfo.aspx?coll=84d174c2-d74f-493d-92ae-c3f45c0ee091

All of the lectures (30 one hour classes) were filmed and are available to download and watch. Also all of the lecture notes and homework assignments are available. Basically free college education!

This might be a bit of a late reply :)

I like the idea of university courses being online for anyone to have a go on. I sometimes have a bit of difficulty learning from books if the subject matter is ahead of my level and having someone explain can help a lot, so I think that's pretty cool.

The reason I was interested in Fourier series was because I was looking for a "universal" function which could be used to solve any integral or differential equation. The idea being that if you input the universal function into the integral of differential equation you could then solve it using the function and then find a more concise or better function from the solution.

So the process would be something like:

1) Find the Fourier series of the function you want to integrate.
2) Integrate the Fourier series, which is easy because it's all trig functions.
3) Find a better function from the result of the integral.

I thought the theory was sound but it turns out you need to know how to integrate the function to find the Fourier series. :-[

Another possibility I came across while studying Fourier series was a Taylor series: (http://en.wikipedia.org/wiki/Taylor_series) which I think would work for a continuous one-to-one function. A Taylor series arises from the infinite integral of the infinite derivative which makes me think that any function can be put into the form of a polynomial, although the polynomial might have infinite degree.

So I tried it on some basic functions and it worked, although it seemed a bit lose and contrived on my part, so I thought I would have a go on some unknown integrals. Unfortunately when I Googled for unknown integrals I couldn't find any, :-[ seems to me that they may have already solved them all.

Anyway, I thought I'd have a go at trying to interpret a selection of crop circles and review what I think some of the crop circle symbols mean.

Interpretations

52_Hackpen_Hill_Wiltshire_15_07_2013_Wheat_OH.jpg


This one has an outer thick ring and an inner thick ring with a thin ring with dots and seven semi rings connecting the thick inner and outer rings which also intersect the four dots. The centre is also filled in, which makes this CC look similar to the CC which the C's said means "train." The inner object looks like an eight pointed star, so it could be a square with four triangles on it or two squares overlapping.

I think this CC might mean something like "the perception of objective reality" or "the perception formed from objective reality" or maybe "the objectivity of perception" or even "objective reality is formed from perception."

12-Winterbourne-Monkton-Wilts-23-05-2007-Barley-L2-.jpg


This CC has a disk in the centre with a ring around it, which is similar to the "train" CC, it also has three interlocking crescent shapes with a large outer ring. I think the crescent shapes mean something like incomplete concept. So maybe this CC means something like "the understanding that comes from training" or "understanding from training" or perhaps it's indicative of the process of learning a skill or something...

51-All-Cannings-Wilts-17-07-2007-Wheat-OH.jpg


This CC has a big disk with a ring around it connected to a smaller disk with a ring around it. then there's a smaller version next to it with a disk without a ring, then next to that is another version just with disks, then another version with just rings and no connecting line. I think this CC might be a series of pictographs representing the process of understanding how two different things are ultimately become connected. I also think that it could represent the development of a relationship as two people become connected and get to know each other better till the knowledge of each other is big and thick. I think another meaning could be the passage of knowledge from person to person and how that knowledge replicates itself but developes independently for each person.

18-Steyning-Bowl-(Cissbury)-Sussex-Wheat-11-07-04-OH.jpg


This CC has a large disk in the centre connected to four crescents each connected to a smaller disk. I think this CC might mean something like "one concept with a little knowledge of the other concepts leads to new concepts." I think this could be like when someone understands one aspect of a subject and they're learning about other aspects of the subject they think about new concepts.

7-East-Field-Alton-Barnes-Wiltshire-Wheat-20-06-04-FE.jpg


This is a nice and complex CC. I think this one means something like "understanding that one is developing" or even "self-actualization." I think this because this CC has a spiral which is connected to two disks and leads out to larger disks, which I think represents a process of development. It also has a weird intersection of connecting lines and funny pathways which lead to more disks, I think this might represent an understanding of the process of development. So my thinking is that when someone understands that they're developing then they're comfortable and happy and that's why I thought it could mean "self-actualization."

95-White-Sheet-Hill-near-Mere-Wiltshire-25th-June-2010-Wheat-OH.jpg


I think this is a nice looking CC, the only symbols in this one are disks and rings apart from the connecting concave triangles. I think this CC might just mean "mind" or "self." I think this because there are lots of disk and lots little rings around the place and it's also similar to the next CC.

W8_DebuggingTheUniversepic1_resized-232x300.jpg


This is the prime combos CC which Laura talked to the C's about, and is also in chapter 69 of the wave: http://cassiopaea.org/2012/03/25/the-wave-chapter-69-the-whirlpool-of-charybdis-the-sirens-and-the-navigator/. I think this CC might mean "growth."

Symbols

1) The disk. I think this means concept or memory.

2) The ring. I think this might mean cycle. While reviewing this thread I noticed that I never really explained why I think that the ring means cycle. It's because of the astronomical interpretation of crop circles and this transcript:

03-18-00
Q: Well, Barry W. has written a paper about the formation of solar systems and the necessity for a twin star system in such developments. According to his calculations and his theory, the mass of the companion star must be far less than what you indicated the mass of the proposed companion star for our solar system might be. He theorizes that the relationship should be the same as between a proton and an electron, mass wise. Is he correct?
A: Best to not quite fall into the mirror image atomic principles trap, lest one suppose to have completely conquered the atomic properties puzzle.
Q: Okay, can you give us an interpretation of this crop circle here that Barry has interpreted in his way?
A: Maybe a solar type system. Maybe not the one commanded by Sol.
Q: If it is not the one commanded by Sol, which one would it be? It must be one of such importance that such a message is being conveyed in a crop circle formation, I would think.
A: Maybe.
Q: What solar system would it be? What is the name of the star? Would we even know the star?
A: In or of Epsilon.
Q: Which Epsilon?
A: Major.
Q: There are a lot of stars called “epsilon.” Which constellation?
A: Adjoining constellation.
Q: What constellation?
A: No more information to be revealed at this time.
Q: Is this a solar system from which some of the aliens visiting our planet originate?
A: Something like that… From which someone originates.
Q: Someone who?
A: Take a wild guess!
Q: Are they STS or STO?
A: STS.
Q: Well, you have said that the crop circles are expressions of 6th density thoughts. Does this mean that we are being warned about this?
A: On wrong track. More like an historic pictogram.
Q: Is the orbit depicted without a planet depicting a planet that was destroyed?
A: No.
Q: What does the orbit without a planet depict?
A: Transference.
Q: Transference of that planet to another realm? Transference of what?
A: Those who were relocated after the prototypical population was completed.
Q: Are you saying that this is a pictogram of the mother planet of the human race?
A: Close. That which led to the human race as it now exists.
Q: As we measure time, what period of time does this pictograph represent, counting backward in years?
A: Millions.
Q: Getting back to the earth and companion star business, BW* is predicting that comets will begin hitting about the year 2003, based on the planet positions of this crop circle. Now, even if it is not a representation of planetary positions in our solar system, he COULD be picking up information psychically and using this information as a ‘bridge’ to present, or rationalize it. So, he has this prediction, what is the likelihood of this idea or prediction coming true?
A: Probably will not be.
Q: He said that the orbit of the companion star, based on his calculations, was about 5000 years long…
A: Our “companion star” data was meant as a clue for guidance purposes, not as the be all and end all.

3) The ring with dots. this symbol is just the above two symbols put together so I think it shouldn't be an actual symbol itself. I think it represents a concept cycle.

4) A connecting line. I think this one represents a connection or a conduit between two things.

5) An arc. This is just part of a ring, so I think it just means part of a cycle. I also think this one isn't really another symbol.

6) Two straight lines. I think these mean movement, so if they occur around a connecting line then they may represent movement through the connection.

7) A key. I don't know what these mean.

8) A semi circle or a D. These are just arcs I think, I think they would mean half cycle.

9) A breaking line. I have no ideas on this one either.

10) An L shape or a right angel. Ditto.

11) An isosceles triangle. Ditto ditto.

12) A crescent. I think this also isn't a symbol in itself but is just a disk minus another smaller disk. I think it means "incomplete concept" or "forming concept."

13) An eye shape. I think an eye shape is yet another symbol made up of disks or rings. I think they're just the intersection of two disks or rings and therefore mean something like "the intersection between concepts" or "the intersection between cycles."

14) The square. I think if the square is filled in then it's related to the disk and if it's just an outline of a square then it's related to the ring. I think the square block is the sum of an infinite amount of smaller and smaller disks, so if a disk is how a concept is perceived then a square block is what the concept is or represents objectively. I also think the square outline is an infinite sum of cycles and so might represent the reality of a cycle and how it fits into the universe of cycles.

15) The double connecting lines. I think this symbol is a derivative of the connecting line and indicates that there are two ways to get to something or two ways of perceiving something or just two connections.

16) T, Y, and X shapes. Dunno.

17) An equilateral triangle. I think this one means balance.

18) The 5-sided star or pentagram. I don't know what this one means either.

Discussion
The C's have said that CC's are messages and that they are a kind of almanac. Google defines an almanac to be "an annual calendar containing important dates and statistical information such as astronomical data and tide tables." But I don't understand just what that means given my interpretation of he CC's.

Most of the CC's as I understand them mean things like "growth" and "train," which don't seem to be extremely bewildering or even significant (in terms of being beyond the scope of everyday life.) So perhaps to fully understand the depth of the messages in the CC's it's necessary to understand that the mystery of the universe is in the moment.

By that I mean that while the messages in the CC's might seem somewhat "down to earth" (assuming my interpretations are correct) what they actually are doing is pointing out elements of our existence which we should be looking for and contemplating. Things like how we grow and how we develop skills.

From this I think the CC's would be able to show us things about ourselves and the nature of our existence which may have gone beyond our recognition until now, individually and maybe even for the whole of humanity.
 
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