South Table Mountain Rocks

 

The images and analysis are hereby released to the public domain.

A chap from Casper posted a drone video on YouTube flying over South Table Mountain in southern Wyoming just south of Rock Springs.  Another chap from Rock Springs made another similar drone video. The Google Earth image of that rock cross formation was imported into AutoCAD for this report and analyzed in depth from a geometry point of view. Google Earth, on my homestead property in Idaho, can be accurate to within inches if all its capabilities are mastered.

However, nothing can measure to thousandths of an inch even if on the ground with laser-based survey equipment. And further, the image derives from rough stones placed on the ground not even all that precisely. There is absolutely nothing in the original image that one would call precise.

A computer model, however, can be created by making “extremely precise assumptions” based on suggestions from the GE image. If nothing systematically develops that proves the assumption correct, then second, third or more assumptions can be tried. Once a good general drawing is created, it is easy to change it to something else. It only took one try.

For example, the Google Earth image for the northwest quadrant of the South Table Mountain cross, the angle is suggested around 87.8 to 88.5 degrees. It doesn’t take much of a computer program to let this angle vary from 87.8 to 88.5 in quite small steps and then check for the dimensionless ratios, the conjugate dimensionless ratio, and a host of other dimensionless constants to see if there was a “design intent”. Somebody with advanced knowledge would know dimensional units could vary within any given civilization over long periods of time, therefore basing any communication on dimensionless units solves that issue.

Given the nature of a “cross” using straight lines, this angle automatically determines both angles in the center of the cross.

With a second very basic assumption, the lengths of the lines can be assumed to be near equal.  GE provides that the length of the line is somewhere between 75 and 82 feet, depending on where you select the “starting and ending of the line”. A similarly simple program can allow this length to vary in small increments. In this case the length at 25 x pi = 78.53981635 was found to be interesting and developed secondary discoveries. The trick is in the design of the cross.  It has little circles at the end of each length and one can choose whether to use the center of the circle or the end of the line or maybe the tangent to the circle.

When the angle and line lengths are fixed, the entire diagram is complete temporarily, and then other dimensionless ratios can be checked. This type of step wise computer analysis allows the user to then find other relationships until a computer geometric model can be completed if one exists.

The use of Microsoft Excel can group multiple angle ratios and dozens of relationships come into focus where only highly imprecise measurements existed in the beginning. With due diligence, one can eventually find a very redundantly confirming model if one exists.

The final step in precisely fixing the diagram for the initial run of the computer is to move the east-west line center up and down and left and right relative to the center of the north-south line. The larger diameter stone circle center is near this precise location and again a simple computer program allows one to move it around in small steps.

Therefore, only three “Do Loops in C++” or “For Next” in Fortran or Basic allows one to make thousands of calculations in just seconds. The goal is to find enough mathematical relationships to determine all the variables that are being used. If you don’t have those skills, you won’t be doing it yourself. But…you could at least follow what somebody else did. One can think of this approach as a sort of “Greek mathematical vision”.

What should We Be Looking For

Most people would agree that the rock placement wasn’t just for the fun of making a cross, which cannot be seen all that well on the ground standing next to it. So why would anybody at any time go to the trouble of placing the stones so carefully? Some might think they were trying to make a sacred place where they could worship their gods. If that were the case, the builders would want to perform whatever they thought would please the gods.

One might wonder just how you “please your god” with an image? What geometric relationships might please your god? If you make the geometry fit some highly mathematical configuration, would that please your god? If you thought your god was up above, then making an image that can be seen far above might be the best alternative.

On the other hand, if one knows some serious geometry that would send a message forward into time when some dude measures it from above, that might also be worth doing. If you had a vision of major importance and you thought future mankind might not know it for a while, you might want to accelerate their growth in understanding. People with a heart set on helping others may have a special spiritua
l connection.

One thing seems certain. If there is no geometry there, then none was intended. If there is some geometry there, does multiple elements of it fit together in some type of organizational scheme which can be expanded into a model that tells us something we didn’t already know.

If we take the measurements using Google Earth and make a sketch, we can calculate side lengths and azimuths; eight small angles around the outside; and areas and perimeters as well as a host of dimensionless ratios using these basic numbers and combinations of the numbers.

In doing this manually, it would be nice to be able to calculate the perimeter (easy to do) and the area (not so easy manually). A simple way to find out if a quadrangle is “designed” or just happened is to look at the dimensionless ratio of perimeter squared divided by area (ft sqrd / ft sqrd). No matter if the measured dimensions are off a foot or so, the ratio will be similar and if designed, will indicate so.

A much easier scenario is to build our sketch in Autosketch where the area and perimeter are just a click away. If one finds something interesting, it is easy to move say the diagonal centers relative to each other and see how things change.

The image below is from Google Earth, used as part of their incidental use allowance. The initial computer guess is shown marked with the precision of Autosketch.

 

In the image above, the east wider portion of the north to south line has grass shaded from the afternoon sun in the west.  The northern part of the west to east line is likewise grass shaded from the southern sun. That is why the model was shifted to be more aligned with the actual rocks.

In the north, the line is terminated when it “gets to the circle” and likewise on the west. On the east the line terminates on the outside intersection with the circle and likewise on the bottom. The center of the large circle is quite close to the intersection of the lines. The systematic assumptions help confirm the design to the Google Earth Image.

This graphical solution was easily found to have an area of 3082.327294 and the perimeter 222.1675059 for this first example. Obviously, nobody could use Google or anything else and measure this precisely, but this is the “computer generated guess” for this selection.

Doing this it was easily found that the area was 3082.327294 and the perimeter 222.1675059 for this first example. Obviously, nobody could use Google or anything else and measure this precisely, but this is the “computer generated guess” for this selection.

In analysis of quadrangles (irregular squarish figure) we often divide the perimeter by pi to see what a circle with the same perimeter has for a radius. In this case, the number is 222.1675059/ pi = 70.71811351 and if one divides that number by 5, the result 14.1436227 is amazingly close to the square root of 200 at 14.14213562. If we then go backwards starting with the square root of 200, the perimeter becomes 222.1441469 which is only ¼ inch from the input selection. Nobody can measure anything like this cross with anything to this precision. Yet there it is in shining glory.

Measurements have taken us a “long way” but it may be time to reach a higher goal in numerical puzzles. Since humans are endeared to puzzles, had you given thought that maybe God likes puzzles too? Did God build the universe in a puzzle to attract our attention? Perhaps some mathematical geniuses will prove that thought wrong.  In a pig’s eye.

This event suggests that we maybe should check the area for something similar. In comparing circles to squares one should check out the Wikipedia article on “squaring the circle” which is an exercise dating back to Greek times. In this case, we want to go the other way “circling the square”. But now it seems obvious to some that a drunk Greek came over here and staggered up the cliff walls and put some rocks into a cross. Right!!! That’s how simple minded some folks are.

If we look at the ratio of area to perimeter in circles, we have pi x radius squared for area and pi x 2 x radius for the perimeter. The surviving ratio is radius/ 2, or in other words “something to do with radius”.

 Back to our selection, the area 3082.327294 divided by the perimeter 222.1675059 leaving 13.8738889. This is not too close to the square root of 200.  However, by reverse engineering, so to speak, if we take the natural log of 13.7838889 and subtract it from the square root of 200, we get 11.51212704 which then taken as the power of e (reverse logarithm) we get 99920.18937, suggesting that if we multiplied the ratio 13.8738889 by 100,000 and then take the natural logarithm of that we get 14.14293404 which is ridiculously close to the value we derived from the perimeter at 14.1436227. None of this information was used in the development of the computer guess which was primarily the average of several measurements. However, it does soundly increase the probability that the cross was designed.

If one wanted to put a name on this type of “mathematical wizardry” you might call it “Ancient Greek puzzles”. This is certainly not rocket- science or algebra or differential equations. The Wikipedia article on squaring the circle describes it best. Most readers of that article will not get very far until they are super-saturated with “Greek speak”, hence the source of the saying, “it was all Greek to me”.

Can we now construct a quadrangle that has the precise perimeter of the square root of 200 x 5 x pi and the area of that number times e^(sqrt 200)/100,000 times the perimeter or 3079.543466 instead of 3082.327294? On paper, this would be a daunting task. In Autosketch, if we have the perimeter and diagonals, we have the area.

If you don’t know how to use Autosketch, or something like it, in a word or three, “you screwed honey”!!! That is the end of your personal investigation. You now are less developed than perhaps some ancient Indians drunk on cacti-cake. Now you must rely on the work of others that have those skills.

How Do We Construct a Quadrangle of Known Perimeter?

Before we start, we need to consider “is there only one solution?” If there is more than one solution, or none, that might complicate things. So, before we jump off a cliff in search of a sky hook, perhaps we should invest a little more time into mathematical puzzles.

From our original computer guess, which we now think might be a little inaccurate, we do have the sides and angles already available for an initial search for continued clues. All we need is enough mathematical relationships in the form of equations to solve for the unknowns we are seeking, the lengths of the sides and the length of at least one diagonal even if they are not equal.

The image below is a small part of a much larger MS Excel spreadsheet showing the sides of the same selection used above.  The sides are marked clockwise from the NW quadrant S1 to S4 and the values equivalent to the Google Earth measurements are in army green in the center.

 

The values used in the Mathcad model derive from the Excel formula given directly above highlighted in a common color scheme. For example, in the top rows for S1 the ratio of S2 to S1 is taken to the square root and then multiplied by 16/10 shown in orange to get approximately the square root of natural log base 2.71828 at 1.648721. In light green we see the hyperfine frequency of hydrogen which is 1.42040575. In red we see a simple function of the speed of light at 299,792,458. Finally, in blue we see 1.3125 which is the ratio of the range of wavelengths (and frequencies) of the abundant Lyman Series for hydrogen. These are all relatively simple values used commonly throughout all the sciences. At this stage, although very close, they are just guesses. There is no reason to believe that there must be a solution, let alone a very precise one. If you are not familiar with these numbers, it is because you are not a technical person.

The initial Mathcad model is shown below and highlighted for the major elements in red. One should note at the bottom that the derived sides fit the assumptions to at least 11 digits. That is outrageously precise.oach to someone with a laptop computer playing Scrabble where he can enter his letters and let the laptop expert program suggest “key plays”, it will give him a major advantage.

Now the guesses have reached a new level. Any one of them could simply be an accident. But to be able to easily find four and then have them work together to make a “system of numbers” makes the accident theory fade a bit. But the “doubting dude” may still be on the fence.

One way to look at this model is to study the four equations where the defining constants are green boxed and underlined at the end. (square root of natural log e; speed of light; hyperfine frequency of hydrogen; and 1.3125 ratio of hydrogen wavelengths and frequencies in the most abundant hydrogen Lyman series) Ask yourself, “What kind of intelligence does it take to even know these fundamental constants can go backwards and start from type of simple pattern”? How would you write a computer program to find these relationships? I have to wonder if even advanced aliens could do it, or would even want to.

Look at the “systematic discovery” unnoticed in the beginning. There are four sides so there are 4 x 3 / (1 x 2) combinations of two in simple ratios like S2/S1. The input to equations 2 and 3 using the sum of S3+S2 and followed by the sum of S2+S1. These are the sum of the right side (east) and the sum of the top side (north). This is fairly systematic and other similar combinations were tried but nothing found. The final equation is the conjugate ratio of S4 & S1, the left (west) side. If I remember correctly, most of the other combinations were tried without finding anything.

The S2/S1 ratio of 1.061790001 looks intriguing to be 1+(1/(phi x 10)) but that is more complicated and I have found these “made-up numbers don’t work”. After taking the square root, I would know that multiplying by 1.6 is going to result in a 1.648xxx number.

The second equation sum gives 112.3598 and from previous work I know that fits repeated procedures at other locations around the world so I would immediately double it to get a 224.7xxxx type number near the orbital period of Venus and a relationship with the speed of light. This taken to the tenth root gives a number similar to the fifth root of half the speed of light shown in the values in data marked in red.

These are not just random mathematical operations, but systematic mathematical procedures used around the world, but in particular at Newgrange in Ireland. There appears to be some “systematic creational procedure” for the way mathematical and scientific constants fit together and ancient wisdom seems to be trying to tell us that.

 

There is an alien message delivered decades ago to a Canadian engineer not unlike the Star Trek opening message of “seek out new civilizations …..and destroy your ship before interfering with their development”. The explanation given to the Canadian was that all developing civilizations must have the free will to develop in their own way. Advanced civilizations can help them to learn for themselves, but they must do it their own way and not be shown the way of the advanced civilization. You may speculate all you want about why that would be, but I believe that is a basic fundamental of creation which is ongoing, and I have no idea what all is involved in it.

 

From other work on somewhat similar sites, these patterns seem to have a message to send forward to mankind when we become advanced enough to create these models and understand what was trying to be sent. It doesn’t seem likely that these stones, and others like them, were placed using laser measuring equipment or anything of that nature. It appears it might be more like a savant who has no idea why he is selecting the pattern elements or why he is putting them where he did.

People like to jump off into the alien intervention mode, but I think these “advanced civilizations” are better represented by modern day Tibetans than the Albert Einstein types. There appears to be similar communications at all the sites analyzed in this manner. It seems quite likely a lot of our “modern knowhow” came from ancient people. A case in point are numerous discoveries made in scientific experiments where the final important formula is revealed in the other measuring system of units than the one used in the experiment.

For example, nobody really knows the details of the development of the metric system and British system of measurements nor why they have the conversion basis that they do.  Take for instance the linear measure of meters to feet. In my high school 1959 Handbook of Chemistry and Physics, this conversion is 0.30479xx.  A few decades ago, it was legislated to be 0.3048 exactly.

Many folks have heard about the number 311,040,000,000,000 attributable to the Hindu age of Buddha and the related 7 cycles.  If we multiply seven times the Buddha number and then take the natural logarithm, we develop 35.3168279 using a ten key calculator. Now if we take the cube root of that number, we get 3.280907591 which would be the number of feet in a meter or the reciprocal 0.304793711 the number of meters in a foot. The story of Buddha may be just a cover for the revealing of important clues as to how the universe is put together.

So, what are we to think? Did Buddha tell the Hindu about this? Or did the folks who built the structure at Newgrange in Ireland move to Tibet? Perhaps they had a good reason to move to higher ground to maybe avoid some natural disasters at Newgrange like rising sea levels or tsunamis. Modern day Tibetans may not have any idea how they developed the way they did, but one thing is certain. If a major disaster happens on earth, they are the most likely to survive in natural caves and their way of life is so simple, they will simply pick up where they left off.  The rest of modern folks will be mentally destroyed because their infrastructure disappeared, and they will reverse- engineer on how to become a stone age civilization again. The first step would be to kill each other off until there are only a handful in various tribes around the world.

The image below is what should be called a “graphic solution”. After finding the Mathcad solution, it is amazing how close this solution really is.

This image reflects what a person with Autosketch skills could achieve, but a bit short of someone with Mathcad skills to solve multiple variables in an equal number of equations. While the diagonals are within a fraction of an inch, at precise values those differences make a big difference in the model. The other problem here is that Autosketch has only a 7-digit decimal limitation so obviously the scale needs to be changed to not require so many decimals.

The secondary Mathcad model image shown below shows how the diagonals were calculated from two basic equations with only two unknowns. The results show the diagonals only a fraction of an inch from the graphical solution. Don’t let the relationship of 2^^(128/12) fool you.  The reciprocal with decimal shifted is the ratio of the orbital period of Venus to Earth orbital period.  What does it take to know this???? Are you expert Scrabble Players at least looking at these “mathematical words?”

In the top portion, the Law of Cosines is used to find the key angles we need to “calculate the areas” instead of measuring. One can see the sum of the areas is 3080.6xxx which was quite close to the computer guess in Autosketch at 3082.

The reciprocal of 1.625498 is .61519583 and that times 365.25 (earth period) is the Venus period at 224.701 (see astronomical data from the 2000 epoch). But the value of 2^^(128/12) is much more precise and relates to our musical tuning system of steps in 2^^(1/12) or the frequency change on the piano from white key to black key. The number 128 is 2^⁽⁷⁾ . Maybe we now better understand why the Egyptians like “doubling and halving” other numbers. In music, doubling or halving are called octaves.

The value of 1.71850729 (97 x 1,771,657 both primes) will remain a puzzle for the scientific reader to resolve for himself. My hint is to examine the work of Jakob Steiner and think about his famous equation of X^^(1/x).  He also used the equation X^^(1/y). In that regard check out pi^^(1/e) and see how close that is to the ratio of the Mars to sun distance compared to the Earth to sun distance.

The old saying, “a picture is worth a thousand words” seems to be relevant in this analysis. Now you know things that even your favorite astronomer professor doesn’t know. Do you suppose what was done here is exactly what the creators of the rock cross were hoping would be done? Or is there still a lot to be found?

As a final check Microsoft Mathematics was used to see just how precise the Mathcad solution was.  In the image below the values the four equations entered into the “solve command” and the values resulting are within 11 digits of the Mathcad solution.

 

In the top portion, the Law of Cosines is used to find the key angles we need to “calculate the areas” instead of measuring. One can see the sum of the areas is 3080.6xxx which was quite close to the computer guess in Autosketch at 3082.

The reciprocal of 1.625498 is .61519583 and that times 365.25 (earth period) is the Venus period at 224.701 (see astronomical data from the 2000 epoch). But the value of 2^^(128/12) is much more precise and relates to our musical tuning system of steps in 2^^(1/12) or the frequency change on the piano from white key to black key. The number 128 is 2^⁽⁷⁾ . Maybe we now better understand why the Egyptians like “doubling and halving” other numbers. In music, doubling or halving are called octaves.

The value of 1.71850729 (97 x 1,771,657 both primes) will remain a puzzle for the scientific reader to resolve for himself. My hint is to examine the work of Jakob Steiner and think about his famous equation of X^^(1/x).  He also used the equation X^^(1/y). In that regard check out pi^^(1/e) and see how close that is to the ratio of the Mars to sun distance compared to the Earth to sun distance.

The old saying, “a picture is worth a thousand words” seems to be relevant in this analysis. Now you know things that even your favorite astronomer professor doesn’t know. Do you suppose what was done here is exactly what the creators of the rock cross were hoping would be done? Or is there still a lot to be found?

Does Rock Springs Really Rock?

If you have something like this pattern in your backyard, do you move forward like the Egyptians who peeled the super-fine casing blocks off the Great Pyramid to build outdoor latrines? How super-stupid do you need to be to deface such an enormous and beautiful pyramid? No telling where the pyramids would be today if the Brits had not stepped in.

If the local Wyoming Indians gain control of this South Table Mountain Site, it could be the end to field work by white folks. But perhaps there is already enough information herein to advance forward without a lot of further fieldwork. If the white folk Rock Springs can grow a pair, they will make certain the site remains available to anyone who wants to examine more of the detailed stonework. It could be that simply counting the stones in each row would contain valuable information. Let’s hope nobody steals the rocks for door stops!

The likely creators of this cross are covered in www.grand-canyon-dwellers.blogspot.com

 

Jim Branson

Retired Professional Engineering Manager

“bransonjim9 at Gmail dot com”