# Node Formation

Node formation is one of the cornerstones of our method. When we want to examine this on a large scale it becomes extremely complex. The word “cardinal” is derived from the Latin word cardo which means shortly pivot or lengthier around which something is turning.

What happens with the orientation extensions of buildings that are cardinally oriented? In our work, the term “orientation extensions” is used when a building is located on the Northern hemisphere and we extend the North Cardinal far enough so that it runs over the North pole spin axis. This only happens when that building is exactly cardinally oriented. In any other case, this extension line will run just somewhere around the globe without “hitting” anything of importance. The same applies to a building that is located on the Southern hemisphere but the extension would now run Southward.

When we combine the orientation extensions of a group of cardinally-oriented “contemporary” buildings, spread around the world, they will form a node on the spin axis of the Earth and become one big mathematical geodetic pattern. By using this method, we can find the exact location of the geographic North pole or spin axis.

It is relatively easy to understand that cardinal orientation of buildings and the spin axis of the Earth, the geographic North pole, go hand in hand. Nevertheless, we will explain in detail why and how it is important to fully understand our concept to get a glimpse of a vast and deeply-hidden ancient world.

## What Happens with the Orientation Extension

When we do some steps backward and look where this Northward running line is heading, we can see at a certain moment that it crosses the spin axis, also called the geographic North pole of the Earth. The geographic pole or spin axis is marked as a red dot in Fig. 2. Because we are only using one orientation extension line of a structure, we cannot pinpoint the exact location of the geographic pole. For that, we need at least two extension lines that originate from two different locations.

This extension line, running over the spin axis, does not seem to be very important and is also simple and logical. Nevertheless, it is the basis of our method that solves the big riddles of ancient history and some of the big questions in geology, like the waxing and waning of glaciation cycles. Before we go deeper into this matter, let us continue to do the same with another cardinally oriented structure, somewhere else on the globe.

## How This Extension Line Continues

The St. Peter’s Basilica, simply called The Vatican, is also cardinally oriented. The Basilica is not perfectly oriented and that was caused by the fact that the builders used the magnetic pole as their reference.

Around the time the Basilica was built (±1500AD), the position of the magnetic pole was almost at the spin axis of the Earth, as observed from Italy. According to the well-done research of McElhinny and McFadden in 2000, we can be reasonably certain that the magnetic pole was at 86.5°N, 145.0°E, at the time of the Basilica’s construction, ±1500AD.

If the Vatican had been built at another location like, for example in Washington, and the same compass was used, the deviation of the basilica’s orientation would have been much larger. That is something that is relatively easy to understand when you look at Fig. 4 and imagine the Vatican to be somewhere at the location of Washington. The angle between the red dot (the geo pole) and the green dot (the magnetic pole), seen from the location of Washington, is significantly larger, at around 4.2°.

Why did we choose the Vatican of all buildings? Who does not know the Vatican? Although the builders were aware of the importance of cardinal orientation were they unable to establish it perfectly. But that does not hinder our research regarding the phenomenon of nodal formation, using the White House and the Vatican, because the deviation of the Vatican is within our range of error which is ±1.5°.

## The First Node is Formed

Now we have the exact locations of two iconic buildings that are (almost) cardinally oriented we can calculate the first node with this intersection point.

Because we have now two buildings and two different locations, we can establish our first nodal position. The mathematics to find the actual intersection point is much quite difficult and is not part of this article – but we explain the details in the book we are working on.

The node “White House – Vatican” is located at 89.256°N, 77.035°W, and is not exactly located on the spin axis because, as we explained before, the Vatican is slightly counterclockwise oriented. But the node is close to the spin axis, 90.000°N, our current geographical North pole.

## How the Quantity of Nodes Grows Exponentially

We can continue to do this clustering with many more buildings around the world and you will see that the red dots will be growing rapidly.

The number of intersection points that can be made between a collection of buildings and their orientation extensions can be defined as ½(n2-n) or as ½n(n-1). Both are the same notation but in a different form, where n is the number of buildings. Some mathematicians prefer the former notation while others prefer the latter one.

It is relatively easy to understand that with more buildings, the node formation grows explosively because of the quadratic expression of n. For example, when we have 10 buildings (n=10) at 10 different locations we get a nodal network of 0.5×(102-10) = 45 nodes.

That is probably one of the main reasons why no one before found any correlations between building orientations and the formation of their nodes – because the computations are simply too complicated and too much effort.

In Fig. 6 we give an example how the number of nodes is formed from 4 separately located cardinally oriented buildings, buildings A to D. It is not possible to form a node between A-A, B-B, etc. Nodes are formed between A-B, A-C, and A-D. C-A, for example, is a node in another “direction” but it will form the same node that was already formed by A-C. There is either a cluster of “green” nodes or a cluster of “red” nodes. That is why it is necessary with very large numbers of structures to have a formula with which to calculate the number of nodes.

Bear in mind that not all orientations between structures lead to a successful intersection point, so the numbers below are the maximums.

## How the Number of Nodes Grows Exponentially

 Number of Orientation Extensions n Number of Nodes 0.5×(n2–n) * 2 1 3 3 4 6 5 10 6 15 7 21 8 28 9 36 10 45 20 190 100 4,950 200 19,900 300 44,850 500 124,750 552 152,076

*An interesting side note: Vedic counting is a method of adding up the separate digits in numbers. When we add up the digits that stand for the number of nodes they will always be 1, 3, 6, or 9. Strangely enough, the numbers 2, 4, 5, 7, and 8 will never occur in the final sum. For example, 45 is 4+5=9, 100 is 4+9+5+0=18⇒1+8=9. There is an intriguing rhythm in this pattern and there is a deep hidden knowledge in Vedic counting. It is based on the 3, 6 and 9 counting system – going far back into antiquity.

## From Observational Methods to Abstract Mathematics

The example given above in Fig. 5 is partially made in Google Earth and partially made in a drawing program. The exact location of the intersection point where the node is formed is calculated with a special proprietary program that is unique for our own research.

It is much more complicated to calculate this nodal position than it seems at first sight. There are basically two ways to do this; by using spherical mathematics or by using vectors. Both methods are difficult, even for most graduate Beta students.

With the more than 552 structures in the database, our computer takes several days, 24/7, to calculate the 152,076 nodes, to filter out all the noise, and to finally present the point cloud as shown in Fig. 9 below. Fig. 7 shows the full point cloud that combines the orientations of all the worldwide spread structures into one pattern, but it is in fact unusable without a deeper analysis.

It is the only way to establish such a nodal conglomeration and to prove that complicated dense nodes are formed by ancient, non-cardinally oriented structures that are spread all over the world. Until now, only large institutions with powerful facilities and intelligentsia were able to do this sort of complicated work.

## Things to Consider in This Point Cloud

The point cloud of Fig. 7 seems to be unreadable. The facts are that it is. It is like the burst of signals in the movie “Contact“. We have found contact between Earth’s history and Human civilizations over a period of time that might even be longer than we have suspected ourselves.

First of all, we need this pattern to find the weighed average. This weighed average is the equilibrium between left and right – which is located at 47.1°W. Because we are the designers of the method we are designated ones to understand it. Like for example the massive vertical lines around 71°W and 30°E. What do they exactly mean and what causes them?

They are caused by structures that are more Southerly located, they are cardinally oriented, and at the same time closer to the 47.1°W line than the majority, hence they cross all other orientations and form massive vertical lines. They have no significant meaning other than being cardinally oriented in combination with their typical position in the grid. The biggest clouds between non-cardinally oriented structures are formed between 30°W and 60°W with a climax around 47.1°W. These massive cloud formations are of real importance because they cannot be explained other than significant changes of the Earth’s skin in between the periods these structures were built.

## What Happens When We Examine the Intersections Along the 47.1°W Line?

Now that we have found a way to measure orientation clusters reliably we can examine their meaning in a bigger picture, that of the probability for their typical arrangement and that of their striking correlation with large climatic changes.

© 2015 – 2019 by Mario Buildreps

https://mariobuildreps.com

## 6 Responses

• John

Is there any way to get the data on the 552 structures? I’d love to study the intersections using custom techniques.

• Mario Buildreps

In the meantime we have over 590 structures and the list is still growing. We have spent so much time gathering the data that is why we do not give it away for free. Our data can be purchased here: https://mariobuildreps.com/purchase-database/

• John

Fair enough. Why is the number of structures only 590? How many more ancient structures offering good data would you estimate there to be? i’m having fun making and visualising my own data, any regions/structures that’d be good to investigate? My angle measurements are very similar to yours, i’ve also reproduced the general claims about orientations weighted to Greenland. Pretty excited to see where all this theory leads.

• Mario Buildreps

Only 590? There are lots of sites lost in time like the recent LIDAR scans in Guatemala recently proved. In our list are sites not many people have ever heard of and not much sites have slipped our attention. Consider looking through the eyes of a pragmatic mathematician; you need only 392 (let’s say 400) randomly taken samples to describe reality with eerie precision.
If a site is uniformly oriented, like Teotihuacan or Giza, there is only one direction. These sites are only 1 line in the database, no matter how intriguing these sites are. But if a site is (seemingly) chaotic oriented, like Chichen Itza, we have gathered all orientations. You must have a good quality (survey) map of Chichen Itza to perform a good job. GE is not good enough for that, although it might give you a rough indication. The same counts for the temples of Bagan; they are clustered in groups of orientation. Although there are thousands of these temples, there are just little over 20 groups in Bagan.

At the beginning of 2019 we have started a new project that we have named “1000”. Our database will contain at least 1000 separately oriented structures. I am happy to see you are surveying the same work, the more people who are on this train the better. 🙂

• John

Oh cheers! I never thought to use LIDAR, the data is way cleaner. I reproduced your results for El Caracol with a Pole IV intersection (https://ibb.co/KGsj35X). I’ve been hunting for ancient structures and found some really cool stuff! Had no idea so many pyramids existed around the world (https://ibb.co/BzBnQ8j). Not sure if you need a hand reaching 1000, I’ve got an accurate & fast semi automated technique for GE measurements or GE + non-orientated LIDAR data. I could measure the orientations of 590 structures in 3 days with full details on multiple orientations per structure like El Caracol either for improving accuracy or for independent verification of measurements.

• Mario Buildreps

You have done great work, John! El Caracol is an interesting structure because it is an astronomical observatory and the monuments seems to be reoriented a few times. On top of that appears Caracol to correlate with the changes of the solstices.
You really need hundreds of independent monuments at randomly spread locations to be close to 100% sure in your conclusions. And if you want to do this without hard mathematics the job gets increasingly difficult until you reach a point where it becomes impossible.