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Aptitude Review of Bad Science
#1
I had a thought.  Cry

Overturn the tables 

No disguised voice in a phone-in radio show... no.  Naughty 
 http://1.bp.blogspot.com/-ZCxnQ9M9vDg/UD...cience.jpg

Quote:https://pseudoastro.wordpress.com/tag/19...-latitude/

THM  review  Bad Science 



June 28, 2011

The Magical Hyperbolic Tetrahedral Geometry of 19.5° Latitude
Filed under: earth,jupiter,magical thinking,mars,misconceptions,moon,neptune,pluto,sun,uranus,venus — bad psi @ 9:54 am 
Tags: 19.5 degrees19.5 degrees latitude19.5°19.5° latitudecherry pickinghypberbolic geometryRCHrichard c hoaglandrichard hoaglandtetrahedral geometry

 


Introduction

[Image: hyperbolic_geometry.jpg?w=396&h=432]
"Hyperbolic Tetrahedral Geometry"
Take a tetrahedron (4-sided solid made of four equilateral triangles) and put it in a sphere such that each point of the pyramid touches the inside surface of the sphere. Draw a straight line through the center of the sphere such that one end of the line intersects a point of the pyramid; think of this line as the polar axis, and now orient it in your mind so that the line that goes through the pyramid point is down. Now draw a line around the circle’s equator. Now, if you take the angle between the equator, the center of the sphere, and one of the three non-pole points of the pyramid, you get 19.5°.

That’s the magic of Richard C. Hoagland’s hyperbolic geometry and all the claims of importance for the 19.5° latitude that I’m going to explore in this post.
Richard C. Hoagland’s Magical Thinking
Richard C. Hoagland says a lot of stuff. Almost everything he says sounds crazy. Over the decades, he has built up a vast conspiracy-laden mythology about the universe, how it supposedly works, and why things are the way they are.
To go into every single one of his claims, as I’ve said before in other posts about Hoagland (like herehere, or here), would be next to impossible. As in previous posts, the point in this is to go over a very specific claim.
The “19.5° is an important number” stems from his whole “hyperdimensional physics” mythos. Again, something I’m not going to go into. Partly because it’s incomprehensible, nonsensical, and made up. Suffice to say, “A tenet of these views holds that vast amounts of energy originating from dimensions we cannot perceive are available at latitudes 19.5° both south and north on the Sun and every planet in the solar system” (quote source).
In other words, Hoagland and fellow believers claim that it is at 19.5° latitude on every body in the solar system that we have the biggest/bestest/scarriest/craziest/powerfulest/whateverest feature. 

Let’s take a look, shall we?
What’s at 19.5° Latitude?  Arrow  June 28, 2011


Taken from Hoagland’s own website, we have a short list proving that everything of importance in the solar system is at 19.5° latitude.  Note that everything in this table is directly copied from his website except for the comments, which I have simplified/shortened/clarified.
Object
Feature
Latitude
Importance
Venus
Alta Regio
19.5° N
A Volcanic Region

Beta Regio
25.0° S
A Volcanic Region
Earth
Hawaiian Caldera
19.6° N
Largest Shield Volcano (on Earth)
Moon
Tsiolkovskii
19.6° S
Unique Farside “mare-like” Lava
Mars
Olympus Mons
19.3° N
Largest Shield Volcano (on Mars)
Jupiter
Great Red Spot
22.0° S
Vast Atmospheric “Vorticular Upwelling”
Saturn
North/South Equatorial Belts
±20.0° N/S
Region of “Storms” Observed from Earth
Uranus
Northern/Southern IR 1-2 K “Dip”
±20.0° N/S
“Upwelling” Created by High-Altitude Clouds
Neptune
Great Dark Spot
20.0° S
Presumably Same as Jovian Counterpart*
*Hoagland calls this “Neptune Great Red Spot” but it has, since it was observed by Voyager 2 in 1989, disappeared.
Since Hoagland posted this (his page is ©1989), many other people have found other things on other planets that they claim enhances this idea. One such site, for example, indicates that the Pyramid of the Sun is at 19.6° N (on Earth). Other people claim, such as Will Hart, that all solar storms and susnspots originate from 19.5° latitude on the sun; another twist from this site about the sun is “sunspot activity and the region of peak temperatures is limited to 19.5 degreees north and south.” Others remark simply, “It is interesting how most planets in our solar system display phenomena at this latitude.” The list of claims goes on.
Dissecting the List, and Are These Features Important?
One of the first things you should notice from Hoagland’s list is that only one of the 9 things I pulled (the ones I didn’t are on Jupiter’s moon Io) is at 19.5°. Two more are within 0.1° of it. For a precise geometric phenomenon where huge amounts of energy are released, this isn’t very precise.
On Earth, Mauna Loa, Hawai’i, with a summit at 19.48° is a correct claim of the largest shield volcano presently on the planet. However, it’s really not that spectacular a volcano in terms of energetic potential. The Yellowstone caldera is about 34×45 miles (55×72 km) across. That’s just the caldera. It is at a latitude 44.4° N. The most recent known supervolcano eruption on Earth was in Lake Taupo, about 26,500 years ago, and its latitude is 38.82° S.
Additionally, the largest earthquakes – more releases of energy – since 1900 haven’t been anywhere near 19.5°. None of them.
As for structures on the Earth to harness this energy, one might consider the Pyramid of the Sun and say, “wow, that’s pretty neat that it’s at 19.5°.” But what about Egypt’s pyramids? Or South America’s? What about other architecture, say, Stonehenge? None of these are near 19.5°. This is what we call “cherry picking” to an extreme.
[Image: moon_full_big.jpg]If we want to expand the notion of cherry picking, let’s go to the moon. Hoagland has found some random feature at 19.5° … err, 19.6° … latitude on the far side that has something to do with a volcanic feature. Except that the moon is covered in volcanic features. When you look at the moon, all those dark splotches on the near side are vast volcanic areas where ancient impacts allowed magma from deep below the crust to breach the surface and fill them. And these seas of volcanic material — maria (plural) — are not in any way centered around 19.5°. Nor are the smaller volcanic features that we observe today still strewn throughout them.
Or there’s Mars. Hoagland and his ilk claim that the vast Olympus Mons volcano – the tallest volcano in the solar system – is centered at 19.3° on Mars and is perfect evidence for this hyperbolic geometry. Except that it’s not. The caldera complex of Olympus Mons (there are at least 6 distinct calderas at the summit) range between latitudes 17.8° and 18.8° North. In addition to that, Olympus Mons is so vast with a diameter of around 650 km that the northern scarps start at around 23.5° N while the southern margin is around 13.5° N latitude. So with it spanning over 10°, it’s not that hard to hit it. Besides, Mars has 23 othermajor volcanoes, and Alba Patera, which is actually the most voluminous volcano in the solar system (as Mauna Loa is the most voluminous volcano on Earth), has a caldera centered at 40.3° N.
The claim of the sun having sunspots centered at 19.5° is also wrong, as can be seen on any given day.
We can also look at other features of interest. I’ll name only one for brevity since I think I’ve made my point by now. Saturn’s moon Enceladus was, in the last few years, shown to have active geysers spewing material from the interior of the moon. What’s their latitude? About 90° S — that’s right, the south pole. Not anywhere near 19.5° North nor South latitude.
Final Thoughts
This particular magical belief is only supported by very very careful cherry-picking. As clearly shown above, even in the features that these people claim shows 19.5° is special, more than half the time they’re just wrong, off the mark, or are being very generous with reporting their numbers. And still the features that are “correct” are not especially unique.
I don’t really think much else needs to be said on this topic. It’s just made up and features are found to fit it while ignoring everything else.

Comments (26)





THM shall disect this err... umm... 'article of faith' published June 28, 2011


We have the benefit of foresight that this present gives, as a reference horizon opposed to hindsight like expat/Linke bad psi guy.



Read the Article
https://pseudoastro.wordpress.com/tag/19...-latitude/
begin shredding.



Study challenges widely accepted theory of Yellowstone formation

Date:

February 10, 2016

Source:
University of Illinois at Urbana-Champaign

[Image: 160210135338_1_540x360.jpg]
Geology professor Lijun Liu used computer simulations to study the origins of the Yellowstone supervolcano.
[i]Credit: Photo by L. Brian Stauffer[/i]




Understanding the complex geological processes that form supervolcanoes could ultimately help geologists determine what triggers their eruptions. A new study using an advanced computer model casts doubt on previously held theories about the Yellowstone supervolcano's origins, adding to the mystery of Yellowstone's formation.


"Our model covered the entire history of Yellowstone volcanic activities," said Lijun Liu, a geology professor at the University of Illinois. Liu's computer model accounted for the last 40 million years, prior to even the earliest signs of Yellowstone's volcanism.
Yellowstone is one of the largest remaining active supervolcanoes. True to its name, a supervolcano is capable of erupting on a much larger scale than an ordinary volcano. The origins of Yellowstone are still under much debate. One of the most prevalent views is that Yellowstone's supervolcano was formed by a vertical column of hot rocks rising from the top of the earth's core, known as a mantle plume.
"The majority of previous studies have relied on conceptual, idealized models, which are not physically and geologically accurate," Liu said. Some recent studies reproduced key geophysical factors in a laboratory setting, including a rising plume and a sinking oceanic plate. However, these studies failed to account for the comprehensive set of geological variables that change over time, influencing the volcanic history.
"Our physical model is more sophisticated and realistic than previous studies, because we simultaneously consider many more relevant dynamic processes," Liu said.
Using the Blue Waters supercomputer at the National Center for Supercomputing Applications at the U. of I., one of the fastest supercomputers in the world, Liu's team created a computer model that replicated both the plate tectonic history of the surface and the geophysical image of the Earth's interior. This study is the first to use a high-performance supercomputer to interpret the layers of complicated geophysical data underlying Yellowstone, Liu said.
The main goal of the study was to examine whether the initiation and subsequent development of the Yellowstone volcanic system was driven by a mantle plume. The simulated data showed that the plume was blocked from traveling upward toward the surface by ancient tectonic plates, meaning that the plume could not have played a significant role in forming Yellowstone, Liu said.
The researchers published their findings in the journal Geophysical Research Letters.
The researchers also examined many other factors that could have played a role in forming Yellowstone. These simulations discounted most of the other theories of Yellowstone's origins, Liu said. As a result, formation of the Yellowstone volcanic system remains mysterious.
Supervolcanoes are hazardous natural phenomena that evoke public concern, partly because their formation is not well understood. While this area of research is still far from predicting eruptions, Liu said, improving the fundamental understanding of the underlying dynamics of supervolcano formation is key to many future applications of relevant geophysical knowledge.
"This research indicates that we need a multidisciplinary approach to understand complicated natural processes like Yellowstone," Liu said. "I know people like simple models, but the Earth is not simple."






Journal Reference:


  1. Tiffany Leonard, Lijun Liu. The Role of a Mantle Plume on the Formation of Yellowstone VolcanismGeophysical Research Letters, 2016; DOI: 10.1002/2015GL067131

University of Illinois at Urbana-Champaign. "Study challenges widely accepted theory of Yellowstone formation." ScienceDaily. ScienceDaily, 10 February 2016. <www.sciencedaily.com/releases/2016/02/160210135338.htm>
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Reply
#2
...
you know ... I just labored an elaborate response,
and it was completely blocked from posting.
The page would not accept the post, and then it was lost.
That really sucks.
I could not even try again to reword the post.

the 19.5 angle has it's counterpart in the 70.5 angle. {19.5 + 70.5 = 90}
That angle is the maxiumum "electron spin" angle ... coupling of electrons etc
It has to do with the microscopic origins of macroscopic magnetism.
Cones and angular momentum, magnetochemistry.
see page 19
http://spsr.utsi.edu/articles/jbis2007.pdf

Look at an octahedron replicated into a packed 3D lattice of octahedrons.
the 19.5 and 70.5 angles are replicated throughout that geometry ,
pretty much like in Hoagland's 2D planar model.
... the tetrahedron being a building block of the universe.  

The octahedron can be viewed as two pyramids glued base to base.
The fundamental pyramid here would be 2 units high with a 2 by 2 base.

the full cap angles ... the full peak angles ... of each pyramid,
evolve from; 
the corner angles
and the:
side face angles
so
there are two sets of full cap or peak angles.

the Corner Angles cross sect each other with two full cap or peak angles of 70.5 each.

the Side Face angles cross sect with two full cap or peak angles with angle tangents of {4 / 3}.

that cap angle from the Side Face cross section of the pyramids in the octahedron,
{or better put the isosceles of the cross section},
is also  
the Side Face angle of the Khafre pyramid which is modeled after the 3-4-5 triangle.

thus the Khafre Pyramid fundamental geometry can be developed, 
by expanding 2D tetrahedral grids.

that is all I can do to ressurrect my original post

[Image: a37zaMZ.jpg]


Stu wants to play Hoagy's flute into submission ... it is his infatuation.
However the geometry in Hoagy's design evolves from the important building block of the universe.
... the tetrahedron.
...
Reply
#3
Everything electronic I try to put my thoughts on does that to me Vic. It's almost like there's an intelligence inside these modern computing and communications devices that doesn't want certain things we think to be told.
an AI which reads and says "Nope, too close to the truth, can't have that" and wipes certain things. it is infuriating, because I think of that as squelching me..
I tend to go in afterwards out of frustration and write another even more scathing replacement, because ...well ... fuck that!

It's a pain in the ass to remember to do all the time, but the best way I know around it is to always select and copy your posting before hitting the post button.

especially long well thought out ones. Little else is more frustrating that having a masterpost go poof! into the void
On a satellite I ride. Nothing down below can hide.
Reply
#4
Keith.
Either that or Lincoln might have wrote some code, he's wiley.

Vianova!!!

We'll have a blast shredding bad science's credibility.


Geometry will result as we delve...

The opening article demonstrates clearly that both Bad Science and Hoagland equally have just been updated with the latest research they were equally unaware of at the time of their writings.

Knowing what we know know we can say full well that this is pretty much 45degree angle from equator to the axis

One claimed skillset of SwRI's inside anti-hoagland guy in disguise is crater counting.

I will use his own words to demonstrate what I think of his 'skill' and discount them.

 
Quote:I don’t really think much else needs to be said on this topic. It’s just made up and features are found to fit it while ignoring everything else.

Counting craters requires knowing what kind of crater.




Quote:Tuesday, August 25th, 2015, 04:39 am (This post was last modified: Tuesday, August 25th, 2015, 04:54 am by EA.)
Before the Rebuild I noted that Occator was a Divet in what is argueably Highlands.

Note: In yellow the Enigmatic Bright Spots encircle  the perimeter of all the "Other Craters"

While @ Occator   the brighspots surround and outnumber all albedo.

That may be a 'tell'


[Image: PIA19606_fig1--geomorph-v1.jpg]

What if that highland was subtle like Yellowstone. NOT Hawaii? Laney Mons



There may be a reason it may be flat as in: Salt flat

it may seem counter-intuitive.

Central Crater Peak  

Quote:Others remark simply, “It is interesting how most planets in our solar system display phenomena at this latitude.” The list of claims goes on.

Dissecting the List, and Are These Features Important?
One of the first things you should notice...  Hear that knock @ the door   Enter Occator

[Image: PIA19630brights.jpg]
Awesome Keith!!!

A good investigator excludes nothing.
A good improvisor includes everything.


What if occator was a super cryovolcanic-caldera?

Dormant for now?
Quote:On Earth, Mauna Loa, Hawai’i, with a summit at 19.48° is a correct claim of the largest shield volcano presently on the planet. However, it’s really not that spectacular a volcano in terms of energetic potential. The Yellowstone caldera is about 34×45 miles (55×72 km) across. That’s just the caldera. It is at a latitude 44.4° N. The most recent known supervolcano eruption on Earth was in Lake Taupo, about 26,500 years ago, and its latitude is 38.82° S.

Scientists Believe Mars Crater is the Remains of an Ancient Supervolcano
October 3, 2013
Space
[Image: Eden-Patera-Basin-on-Mars-Could-Have-Bee...uption.jpg]New research suggests the Eden Patera basin on Mars could have been formed by an explosive volcanic eruption, not the impact of a large object. Seen above, for the basin and surrounding area, higher elevations (reds and yellows) and lower elevations (blues and grays) are indicated. Credit: NASA/JPL/GSFC

Based on images and topographic data, new research shows that the Eden Patera basin on Mars is a volcanic caldera, not an impact crater.

Tucson, Arizona — A research project led by Joseph R. Michalski, Senior Scientist at the Planetary Science Institute, has identified what could be a supervolcano on Mars – the first discovery of its kind.
In a paper published October 3 in the journal Nature, Michalski and co-author Jacob E. Bleacher of NASA Goddard Space Flight Center describe a new type of volcanic construction on Mars that until now has gone unrecognized.
The volcano in question, a vast circular basin on the face of the Red Planet, previously had been classified as an impact crater. Researchers now suggest the basin is actually the remains of an ancient supervolcano eruption. Their assessment is based on images and topographic data from NASA’s Mars Odyssey, Mars Global Surveyor and Mars Reconnaissance Orbiter spacecraft, as well as the European Space Agency’s Mars Express orbiter.
In the Nature paper Michalski and Bleacher lay out their case that the basin, recently named Eden Patera, is a volcanic caldera. Because a caldera is a depression, it can look like a crater formed by an impact, rather than a volcano.
“On Mars, young volcanoes have a very distinctive appearance that allows us to identify them,” Michalski said. “The long-standing question has been what ancient volcanoes on Mars look like. Perhaps they look like this one.”
The researchers also suggest a large body of magma loaded with dissolved gas (similar to the carbonation in soda) rose through thin crust to the surface quickly. Like a bottle of soda that has been shaken, this supervolcano would have blown its contents far and wide if the top came off suddenly.
“This highly explosive type of eruption is a game-changer, spewing many times more ash and other material than typical, younger Martian volcanoes,” Bleacher said. “During these types of eruptions on Earth, the debris may spread so far through the atmosphere and remain so long that it alters the global temperature for years.”
[Image: Mars-Crater-May-Be-Ancient-Supervolcano.jpg]The dark color indicates younger material draped across the Eden Patera depression. Credit: ESA
After the material is expelled from the eruption, the depression that is left can collapse even further, causing the ground around it to sink. Eruptions like these happened in ages past at what is now Yellowstone National Park in the western United States, Lake Toba in Indonesia and Lake Taupo in New Zealand.
Volcanoes previously had not been identified in the Arabia Terra region of Mars, where Eden Patera is located. The battered, heavily eroded terrain is known for its impact craters. But as Michalski examined this particular basin more closely, he noticed it lacked the typical raised rim of an impact crater. He also could not find a nearby blanket of ejecta, the melted rock that splashes outside the crater when an object hits.
The absence of such key features caused Michalski to suspect volcanic activity. He contacted Bleacher, a volcano specialist, who identified features at Eden Patera that usually indicate volcanism, such as a series of rock ledges that looked like the “bathtub rings” left after a lava lake slowly drains. In addition, the outside of the basin is ringed by the kinds of faults and valleys that occur when the ground collapses because of activity below the surface. The existence of these and other volcanic features in one place convinced the scientists Eden Patera should be reclassified.

The team found a few more basins that are candidate volcanoes nearby, suggesting conditions in Arabia Terra might have been favorable for supervolcanoes. It is also possible massive eruptions here could have been responsible for volcanic deposits elsewhere on Mars that have never been linked to a known volcano.
“If just a handful of volcanoes like these were once active, they could have had a major impact on the evolution of Mars,” Bleacher said.
Project funding was provided by the NASA Mars Data Analysis program.
Publication: Joseph R. Michalski & Jacob E. Bleacher, “Supervolcanoes within an ancient volcanic province in Arabia Terra, Mars,” Nature 502, 47–52 (03 October 2013); doi:10.1038/nature12482
Source: Planetary Science Institute
Images: NASA/JPL/GSFC; ESA




Impact crater or supervolcano caldera?
May 21, 2015 

 
[Image: impactcrater.jpg]
Siloe Patera. Credit: ESA/DLR/FU Berlin, CC BY-SA 3.0 IGO

At first glance, the region covered by this latest Mars Express image release appears to be pockmarked with impact craters. But the largest structure among them may hold a rather explosive secret: it could be remains of an ancient supervolcano.

The images presented here were taken by the high-resolution stereo camera on ESA's Mars Express on 26 November 2014, and focus on the Siloe Patera feature in the Arabia Terra region of Mars.
Siloe Patera comprises two large nested craters, close to the centre of the main colour image. The outer rim measures about 40 x 30 km and, at its deepest point, the crater dips as low as 1750 m below the surrounding plains.
Some scientists believe that Siloe Patera and a number of similar features in Arabia Terra are calderas, the collapsed centres of volcanoes. But not just any volcanoes: these are thought to be martian supervolcanoes.
On Earth, a supervolcano is defined as a volcano that can produce at least 1000 cubic kilometres of volcanic materials in an eruption – thousands of times larger than 'normal' volcanic eruptions and powerful enough to alter global climate. An example is the Yellowstone caldera in the United States.


Supervolcanoes occur when magma is trapped below the surface, leading to a huge built up in pressure. They erupt suddenly in violent explosions and thus do not 'grow' sloping mountains like Olympus Mons.
[Image: mountain5.gif]
 That makes them hard to identify, especially millions or billions of years later. 

[Image: 1-impactcrater.jpg]
Siloe Patera in context. Credit: NASA MGS MOLA Science Team
But a number of irregularly shaped craters have been detected in the Arabia Terra region that could represent a family of ancient supervolcano calderas.
Siloe Patera is one such example. It is characterised by two depressions with steep-sided walls, collapse features and low topographic relief. The two depressions could even represent two different eruptive episodes due to collapse as the underlying magma pressure was released, or as the magma chamber migrated below the surface.
By comparison, impact craters include features such as a central peak, uplifted crater rims and ejecta blankets surrounding them. Indeed, impact craters are widespread in this scene: textbook examples can be found in the two side-by-side craters just above Siloe Patera, and in the large crater at the far right of the scene. These craters each exhibit a central peak, terraced crater walls and a surrounding ejecta blanket.


An impact crater with depth to diameter ratio comparable to Siloe Patera would be expected to show these features – unless perhaps the crater had undergone extensive erosion or modification – but it does not. 
Looking in more detail at Siloe Patera, as shown in the perspective view, numerous small channels and gullies are seen, cut into the walls and partly flowing into the depression. A prominent valley-like feature is present in the foreground, which cuts into the depression on one side.


[Image: 2-impactcrater.jpg]
 Perspective view of Siloe Patera. Credit: ESA/DLR/FU Berlin, CC BY-SA 3.0 IGO
The valley, along with numerous other small channels in the immediate vicinity, appears to cut through material to the lower left of the craters that could be either ejecta from an impact or volcanic flow.
If it is impact ejecta, then its asymmetric distribution could be explained either by an oblique meteoroid impact or by selective erosion of the blanket. Alternatively, it could be the product of lava flow from this part of the caldera.


[Image: 3-impactcrater.jpg]
Siloe Patera in 3D. Credit: ESA/DLR/FU Berlin, CC BY-SA 3.0 IGO
Arabia Terra is already known to comprise plains of fine-grained, layered sulphate- and clay-bearing materials. The source of the material has been much debated, but lava and dust from eruptions could be the explanation.
Without any doubt, more data and high-resolution coverage – and even in situ sampling – would be necessary to resolve this mystery. And since the gases released in supervolcano eruptions could have had significant effects on the martian climate, this is a topic of great interest.
[Image: 1x1.gif] Explore further: Mars's mysterious elongated crater 
Provided by: European Space Agency


Read more at: http://phys.org/news/2015-05-impact-crat...a.html#jCp



Wait till Jupiter and Saturn start hurling planetismals at earth and mars and watch how entirely skewed crater counting will prove to be over the next few replies.
There could be revision in certain dates or epochs,stay tuned.
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Reply
#5
QRW arrives @ solution.
https://pseudoastro.wordpress.com/tag/19...-latitude/
50 / 50 is equilibrium = all ma'at @ that.


"From Duels to Battlefields: Computing Equilibria of Blotto and Other Games,"


I don't mean to be Velodromatic Keith   but doink-headstarted out the same way.   

http://thehiddenmission.com/forum/showth...hp?tid=430

Vic is the spotter and I am the sniper and you are the Bullitt as seen through the reticule as we reverse the ridicule with a direct hit.

Kill Two youareaduck with one stoned electric ashalar.


"Our doink-headonly works for..." 

You identified the need for the forum to reclaim dignity.

We ain't Phone-y

[Image: oddcouple2.jpg]
http://thehiddenmission.com/forum/showth...?tid=13997


"Our doink-headonly works for two competitors, so we will need to wait for the general election to try this," said Saeed Seddighin, a graduate student in computer science at UMD who will present the group's findings at the AAAI meeting.

Captain Of TheEnterprisemission.com---solving the Colonel Blotto scenario---Captain and Taniel,SwRI,RCH fanblogger


One might expect that the imbalance
that can be obtained between the two modes be highest
when the detection probabilities are around 1/2, "Our doink-headonly works for two competitors" 


Quote:[Image: 271F05AA00000578-3017232-image-a-20_1427670839417.jpg]
Richard Hoagland--- 1/2 ---Bad Sci
[Image: 265E408F00000578-2982450-image-m-6_1425638770771.jpg]

  
which corresponds to the highest entropy (information content) of
the measurement register.



PUBLIC RELEASE: 11-FEB-2016
UMD-led team first to solve well-known game theory scenario

New doink-headcould help political strategists, business leaders make better decisions

UNIVERSITY OF MARYLAND

A team of computer scientists from the University of Maryland, Stanford University and Microsoft Research is the first to solve a game theory scenario that has vexed researchers for nearly a century. The game, known as "Colonel Blotto," has been used to analyze the potential outcomes of elections and other similar two-party conflicts since its invention in 1921. Until now, however, the game has been of limited use because it lacked a definitive solution.

A new doink-headdeveloped by the UMD-led team is capable of solving the Colonel Blotto scenario. A notable achievement in its own right, the doink-headcould also provide political strategists, business leaders and other decision-makers with a powerful new tool for making informed choices. The team will report its findings at the Association for the Advancement of Artificial Intelligence (AAAI) Conference in Phoenix on February 15, 2016.

"Our doink-headcan potentially be used to compute the best resource investment strategy for any competitor up against a single opponent," said Mohammad Hajiaghayi, the Jack and Rita G. Minker Associate Professor of Computer Science at UMD and lead on the project. "As long as we have sufficient data on a given scenario, we can use our doink-headto find the best strategy for a wide variety of leaders, such as political candidates, sports teams, companies and military leaders."

Colonel Blotto pits two competitors against one another and requires each to make difficult decisions on how to deploy limited resources. In its simplest form, each player assigns a limited number of resources, or troops, to a number of battlefields. Players must do this without any knowledge of their opponent's strategy. Players win a given battlefield if they allocate more troops than their opponent; the player who wins the most battlefields also wins the game.

The game can be extended to real-world scenarios, such as a U.S. presidential general election. In this example, each candidate is a player; resources such as campaign staff, stump time and funding are the troops; and each state is a battlefield. The game can also apply to high-profile consumer product competition, such as the ongoing battle between Apple's iPhone and Google's Android mobile phone products.

"From presidential elections to marketing decisions, competition for attention and loyalty is a part of daily life. However, the behavior of individuals in response to such competitions is not yet well understood," said Hajiaghayi, who also holds a joint appointment at the University of Maryland Institute for Advanced Computer Studies (UMIACS). "We show that such strategic behavior is computationally tractable. Given a description of the competition, we can determine which strategies will maximize the outcomes for a given player."

Although the rules of Colonel Blotto are relatively simple, the potential strategies a player can employ are nearly limitless, depending on the number of battlefields and the total resources available to each player. The solution achieved by Hajiaghayi and his colleagues does not necessarily favor one player over another, but rather represents an equilibrium in which both players have deployed the best strategy they possibly can in relation to their opponent's strategy.

The large variety of possible strategies has been the key obstacle to finding a computational solution to the game. Hajiaghayi and his team overcame this issue by limiting the total number of possible strategies to a relative handful of representative choices.

"We found that the strategies of the players can be accurately represented by a reasonably small number of possibilities," Hajiaghayi said. "This is a more general approach, but it works well as a proof-of-concept. Many others have tried to solve Colonel Blotto for specific scenarios, but we are the first to take a more general approach and solve the theory."

This solution enabled the team to develop a generalized algorithm, which can now be applied to specific scenarios, such as the 2016 presidential election.

"Our doink-headonly works for two competitors, so we will need to wait for the general election to try this," said Saeed Seddighin, a graduate student in computer science at UMD who will present the group's findings at the AAAI meeting. "If we know how a given state voted in previous elections relative to the resources each candidate invested in that state, then we can use the same investment data from this year's election cycle to predict whether each candidate has deployed his or her best possible strategy nationwide."

###

The study, "From Duels to Battlefields: Computing Equilibria of Blotto and Other Games," AmirMahdi Ahmadinejad, Sina Dehghani, MohammadTaghi Hajiaghayi, Brendan Lucier, Hamid Mahini and Saeed Seddighin, will be presented on February 15, 2016, at the Association for the Advancement of Artificial Intelligence (AAAI) Conference in Phoenix, Arizona.

This work was supported by the National Science Foundation (Award Nos. 1053605 and CCF-1161626), the Office of Naval Research (Award No. N000141110662), the Defense Advanced Research Projects Agency (Award No. FA9550-12-1-0423) and Google. The content of this article does not necessarily reflect the views of these organizations.

Media Relations Contact: Matthew Wright, 301-405-9267, mewright@umd.edu

University of Maryland 
College of Computer, Mathematical, and Natural Sciences 






Quote:One might expect that the imbalance
that can be obtained between the two modes be highest
when the detection probabilities are around 1/2, which
corresponds to the highest entropy (information content) of
the measurement register. 

---

50/50 chance.


---

However, we show in Appendix A 
that the probabilities that maximise the average unbalance
are actually 1/3 and 2/3 for the two arms respectively.

are actually ~.333 and ~.666 for the two arms respectively.








Physicists create first photonic Maxwell's demon


February 12, 2016 by Lisa Zyga

[Image: photonicmaxw.jpg]
Experimental setup of the photonic Maxwell’s demon: The demon’s measurement is implemented by high transmittance beam splitters (BS) and highly sensitive avalanche photodiodes (APDs). The two photodiodes are the work extraction mechanism that use the imbalance in the pulse energies created by the demon to charge a capacitor. Credit: Vidrighin, et al. ©2016 American Physical Society

(Phys.org)—Maxwell's demon, a hypothetical being that appears to violate the second law of thermodynamics, has been widely studied since it was first proposed in 1867 by James Clerk Maxwell. But most of these studies have been theoretical, with only a handful of experiments having actually realized Maxwell's demon.
Now in a new paper, physicists have reported what they believe is the first photonic implementation of Maxwell's demon, by showing that measurements made on two light beams can be used to create an energy imbalance between the beams, from which work can be extracted. One of the interesting things about this experiment is that the extracted work can then be used to charge a battery, providing direct evidence of the "demon's" activity.
The physicists, Mihai D. Vidrighin, et al., carried out the experiment at the University of Oxford and published a paper on their results in a recent issue of Physical Review Letters.
"Our work shows how photonics can be used as a platform to investigate the relation between energy and information," coauthor Oscar Dahlsten, at the University of Oxford and the London Institute for Mathematical Sciences, told Phys.org.

In the original thought experiment, a demon stands between two boxes of gas particles. At first, the average energy (or speed) of gas molecules in each box is the same. But the demon can open a tiny door in the wall between the boxes, measure the energy of each gas particle that floats toward the door, and only allow high-energy particles to pass through one way and low-energy particles to pass through the other way. Over time, one box gains a higher average energy than the other, which creates a pressure difference. The resulting pushing force can then be used to do work. It appears as if the demon has extracted work from the system, even though the system was initially in equilibrium at a single temperature, in violation of the second law of thermodynamics.
Over the years, physicists have resolved this apparent paradox by explaining that, even though the demon may not do work directly on the system, the demon does gain information from its measurements. Erasing this information from the demon's memory requires work, so that overall there can be no net gain in work.
In the photonic version, the physicists replaced the boxes of gas particles with two pulses of light. They implemented the demon using a combination of a photodetector, which can measure the number of photons from each pulse, and a feed-forward operation, which like the open door can escort the brighter beam (with more photons) in one direction and the dimmer beam (with fewer photons) in the other. The different beams fall on different photodiodes, which generate an electric current that goes to a capacitor, but from opposite directions. If the pulse energies were equal, they would cancel out. But the imbalance in the pulse energies—and in the resulting photoelectric charge—is what charges the capacitor.

Even though the researchers did not aim to realize optimal work extraction, it's possible that some type of Maxwell's demon could one day have practical applications.
"Often we have more information available than thermodynamics supposes," Dahlsten said, explaining that things are normally not fully random and have a degree of predictability. "We can then use demon set-ups such as this one to extract work, making use of that information. Similarly, we can use extra information to reduce work costs of, for example, cooling systems. Personally I think that sort of technology will have a real impact on meeting the energy challenge facing the world."
Due to differences between the photonic implementation and previous implementations of Maxwell's demon, traditional theoretical models do not provide a clear path for connecting work extraction to the information acquired by measurement in a fundamental way. So the researchers derived a new model that accounts for the subtleties of the new set-up, in which they relate work extraction to the information acquired by measurement.
The researchers hope that the new model will lead to a better understanding of the link between information and thermodynamics, which is necessary for understanding thermodynamics at the microscale and below. As the scientists explain, recent developments of technologies consisting of just a single or few particles require a better understanding of microscale thermodynamics, similar to how the steam engine drove scientists to better understand macroscopic thermodynamics in the 19th century.
A theory of of microscale thermodynamics could have a variety of applications, including making energy-harvesting technology more efficient. It could also allow researchers to investigate the role of quantum coherence in thermodynamics, with applications in quantum information technologies.
"We are already thinking of ways in which features such as entanglement can be introduced in future experiments based on this one, as our interests gravitate around quantum information," Dahlsten said.
 Explore further: Could Maxwell's Demon Exist in Nanoscale Systems?
More information: Mihai D. Vidrighin, et al. "Photonic Maxwell's Demon." Physical Review Letters. DOI: 10.1103/PhysRevLett.116.050401 , Also at arXiv:1510.02164 [quant-ph] 
Journal reference: Physical Review Letters


Read more at: http://phys.org/news/2016-02-physicists-...n.html#jCp

--------------------------------------------------------










In our experiment, we record oscilloscope traces of the voltage
across capacitor C, at the same time recording outcomes
of the APD detection, as depicted in Figure 1. In Figure 2
we illustrate how the voltage depends on the APD signals and
how, while the average voltage is close to zero when we ignore
the demon’s measurement, it becomes significantly different
from zero (relative to fluctuations) when we apply a sign flip
conditioned on the APD measurement outcomes. This conditional
operation emulates unitary feedback on the two thermal
optical modes.

The demon’s measurement can be tuned by varying the
amount of light sent towards the single-photon detectors. This
allows us to change the photon detection rates from zero to
one (detections per pulse), and as we show in Appendix A,
the imbalance that can be created in the two optical modes
depends only on these rates. One might expect that the imbalance
that can be obtained between the two modes be highest
when the detection probabilities are around 1/2, which
corresponds to the highest entropy (information content) of
the measurement register. However, we show in Appendix
A that the probabilities that maximise the average unbalance
are actually 1/3 and 2/3 for the two arms respectively. For
our experiment, we set one of the arms to a detection rate of
0.311 ± 0.008 and scan the rate p1 corresponding to the other
arm. There are two different ways in which feed-forward
could be applied, corresponding to a change of the sign of the
voltage across the capacitor corresponding to either one of the
two asymmetric outputs of the demon’s measurement. Which
of these two strategies is optimal depends on the choice of p1.
In Figure 3 we show the average voltage that can be
obtained with different measurement and feedback settings
and compare this to the thermodynamic bound introduced in
Equation 2. If no information were acquired by the demon’s
measurement, the bound would demand that no work should
be extracted. We thus find that the work extraction is caused
by the acquisition of information in our setup and that the
strategy that we apply for using the information yields results
that are close to a thermodynamic limit.
DISCUSSION
The experiment presented in this work links very different
regimes: the single photon regime, a measurement yielding
single bit outcomes, intense light fields with thermal occupation
number corresponding to very high temperatures and the
room temperature system composed of detectors, electronics
and the environment. We are able to show that the setup is like
Maxwell’s demon, in the sense that work extraction is limited
by information acquired through measurement. However, the
quantity bounded by information is not the average work extracted
per cycle, as is usually the case [2, 3, 5, 16] but the ratio
between the average work extraction and the standard deviation
of the single cycle work distribution. Rather than defining
the energy efficiency of the demon’s control, this quantity describes
the purity of the work produced, being related to the
concept of strength of work introduced in [13]. This quantity
is of relevance in scenarios in which low fluctuations are
important, such as cooling experiments.
Our work demonstrates how photonics can provide a valid
experimental platform for thermodynamic scenarios. This offers
the perspective of moving into the quantum domain, to
further explore the interface between quantum information
and thermodynamics thanks to the capability to engineer the
wave-function of multi-photon states. In addition, the techniques
presented can be extended to opto-mechanical oscillators
[38] and spin-ensembles [39], where single-particle operations
can be used to study the link between information and
thermodynamics in stationary matter systems.



====================


The author always leave behind the real answer as usual. I suspect the author ever built a real dome by himself all due respect. Because the book contains not a single dome photo or full dome data. It is considered a bible for Geodesic Dome mathematics but lack of practical example and obscure explanation of major formulas make the reader how to follow.
What I need to know is value of theta for getting floor radius. But the author again doesn’t explain how to find theta here.
Below is how I calculated the theta to get the floor radius on frequency three 5/8 icosahedron dome.
The image is generated by Geodome. It divides radius 9 even segment and uses 6 of them to construct dome.
[Image: 3v_59_icosa.jpg?w=640]

The middle point of vertical line, diameter of the dome, is center of the circle and radius is half of the diameter. I assumed the length of diameter as 9 units. Half of 9 is 4.5.
I could make a right angle triangle whose hypotenuse is radius of the circle. The base of triangle is floor radius of the dome. The height is 1.5 units.

Apply Pythagoras theorem to find the base,
4.5^2 = 1.5^2 + x^2
x^2 = (20.25 – 2.25)
x = 4.2426

Apply arcsin or arccos to find the angle Phi,
Phi = arcsin(1.5/4.5) gives 19.471 degrees.


[Image: floor_radius_formula1.jpg]

Quote:
Quote:are actually 1/3 and 2/3 for the two arms respectively.

are actually ~.333 and ~.666 for the two arms respectively.

Another method is to simple variable manipulation of r.
Let r represents hypotenuse of the right angle triangle and radius of the circle.
Then the height of the triangle becomes one third of r. The radius is evenly divided by 9 segments.
Apply sine angle formula on Phi,
sin(Phi) = (1/3) x r / r
= 1/3
Phi = arcsin(1/3)
= 19.471 degrees
[img=640x0]https://butterflyofdream.files.wordpress.com/2014/04/floor_radius_formula1.jpg?w=640&h=428[/img]

I can use the angle of Phi for any size of 3v 5/9 icosa dome generated by Geodome to find floor raidus.
And it makes me calculate the radius of dome with a floor radius. Because floor radius is dictates usable floor area of real size dome.

Floor area = Pi x (floor radius)^2
There are two examples.
When the floor radius, x is 20 cm, applying simple cosine angle law gives radius of dome.
20 = r x cos(Phi)
r = 20 / cos(phi)
= 20 / cos(19.471)
= 20 / 0.9428
= 21.21 (cm)

If the floor radius is 200 cm, the dome radius is 212.13 cm.
r = 200 / 0.9428
= 212.13 cm

I set radius of the real size dome as 213 cm, which I will start cutting lumbers soon.
[img=640x0]https://butterflyofdream.files.wordpress.com/2014/04/floor_radius_formula2.jpg?w=640&h=428[/img]
[Image: floor_radius_formula2.jpg]
Tektonic vs Techtonic

EquilibriumArrow Yellowstoned.


Work extracted best if you looking for the answer(data) @ 19.5 in the datasphere.

Eye work for you.

Graphics soon,stay tuned.
Reply
#6
...


Quote:Phi = arcsin(1.5/4.5) gives 19.471 degrees.  


actually his equation here is not correct,
so he must be taking a shortcut and not writing out all the steps.

The cosine of 19.47122063 is also the tangent of angle Y in my diagram posted earlier.

One great failing of modern geometry in universities is easily shown in that cosine.
I have seen graduate geometry students that do the computations for that cosine,
and get the appropriate decimal:
0.942809042
but
they really never have a clue in these decimals that they are a simple fraction in a square root.
0.942809042 = square root {8 / 9} .... or sqrt 8 / by 3.
 
This is one method of transposing from tetrahedral to phi.
Note the isosceles triangle at the bottom that is developed from angle c.

[Image: H55pnHf.jpg]
Reply
#7
Maxwell's Demon is able to work for you?  LilD

Is the example I posted a theoretical breakthrough.

Is there Tesla-like energy Doh

What of this Equilibrium that you can sneak energy from in the form of gnosis/information?

The example below was constructed to build a dome.

He has no Idea I am going to build a principle on itz simplicity.

I don't see a Dome.

I see a Planet.
As near an Equilibrium of E=MC2 and all of its rotating potential you can get no body @ rest for the wicked
[Image: floor_radius_formula1.jpg]


Below I begin to clarify that 19.5 may actually be capable of creating work from models trying to obtain equilibrium.

Can I replicate this experiment:

[Image: 25076374445_d677d03b19_o.jpg]

http://journals.aps.org/prl/abstract/10....116.050401



Note that everything in this table is directly copied from his website except for the comments, which I have simplified/shortened/clarified-bad psi RCH Radio telephoney guy


From bad psi's own words I am Author eyes'd/Authorized that exact same tactical arguement against him.

I attempt to clarify this 9 Circle idea that is not my idea.

Imagine:

Equilibrium is as   Sheep The Equator was

[Image: 24445442734_0f79a0667e_o.jpg]
Quote: “A tenet of these views holds that vast amounts of energy originating from dimensions we cannot perceive are available at latitudes 19.5° both south and north on the Sun and every planet in the solar system”

vast is a relative term Like Olympus Mons to entire Hawaii

Law of Thermodynamics
This dome building guy was onto sum-thing or Bong7bp   on something

Did he think Lava Dome or Lava-lamp? Reefer

Further revision and discussion after brewskie.


Further Reading.

Hypothetical Hypotenuse is High Pot In Use?
Quote:Another method is to simple variable manipulation of r.
Let r represents hypotenuse of the right angle triangle and radius of the circle.
Then the height of the triangle becomes one third of r. The radius is evenly divided by 9 segments.
Apply sine angle formula on Phi,
sin(Phi) = (1/3) x r / r
= 1/3 = ~.333
Phi = arcsin(1/3)
= 19.471 degrees

Recall:
Equibrium can be two containers of specic capacity.

What energy may be contained betwixt is not fixed.

[Image: 24781188220_e75ec0e538_o.jpg]

This Dome-head has me tinfoil-hatting? Naughty

To produce work we must extract from the equilibrium equals equator on our domicile world we revolve on.


Dome is eye'll / Domicile

Tangents?
Do tangents create the frame of reference?
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Reply
#8
Thanx Wook!

http://thehiddenmission.com/forum/showth...#pid229015
No Big Bang? Quantum equation predicts universe has no beginning

February 9, 2015
[Image: 65689925.57QAeyB2.IMG_09498.jpg]

Quote:Ali and coauthor Saurya Das at the University of Lethbridge in Alberta, Canada, have shown in a paper published in Physics Letters B that the Big Bang singularity can be resolved by their new model in which the universe has no beginning and no end.



https://butterflyofdream.wordpress.com/2...cosa-dome/

The physicists emphasize that their quantum correction terms are not applied ad hoc in an attempt to specifically eliminate the Big Bang singularity. Their work is based on ideas by the theoretical physicist David Bohm, who is also known for his contributions to the philosophy of physics. 



Quote:Starting in the 1950s, Bohm explored replacing classical geodesics 

[Image: 3v_59_icosa.jpg?w=640]
(the shortest path between two points on a curved surface) with Arrow quantum trajectories.(QRW)

 
In their paper, Ali and Das applied these Bohmian trajectories to an equation developed in the 1950s by physicist Amal Kumar Raychaudhuri at Presidency University in Kolkata, India. Raychaudhuri was also Das's teacher when he was an undergraduate student of that institution in the '90s. 
Using the quantum-corrected Raychaudhuri equation, Ali and Das derived quantum-corrected Friedmann equations, which describe the expansion and evolution of universe (including the Big Bang) within the context of general relativity.

That filled in a piece of the geodesics puzzle like I was trying to figure out how to make a quantum geodesic Domicile work.
[Image: floor_radius_formula_book1.jpg?w=640&h=428]


geodesics Red Flag quantum trajectories = tangent = frame of reference.

What a wicked Mobius Trip!  Dance004
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Reply
#9
...
Perhaps I missed it earlier, 
but the link to your images on the chicken scratch paper notebook geometry is here:
https://butterflyofdream.wordpress.com/2...cosa-dome/

Ok, I see that you finally just posted it, on a second quick review of your last post.
It was irritating to have to try and find it on the net,
to read it in full to see where his ... phi ... comes from

this link you posted here:
https://farm2.staticflickr.com/1594/2478...e538_o.jpg

is useless when using the values exhibited, and not even close.
Note their disclaimer pointing to the need to use precise values.

"edge b" is square root 18 ... to be exact.
Then it works.
edge a ... is square root 2.25 ... which yes, = 1.5. 

All that rounding off of values is highly inefficient.
Whoever is chicken scratching the geometry on the notebook paper,
has no idea of what phi is.
He also does not have a clue of what square root 18 is {edge b}.

I can however offer a geometry {or a few} that will display phi geometry, 
and tetrahedral geometry in one package.
I will consider doing that.
...

The "no big bang" universal creation aspect is valid enough to consider.
But there probably was a Big Bang somewhere of some fashion,
that contributed greatly to current conditions,
and this universe is an offshoot of infinite universes all connected.

As fas as modern physics may be concerned,
that Big Bang event is their starting point for their calculations to measure any theory criteria,
from quark gluon plasma to the speed of light.
A universe with no beginning and no end makes far more sense,
than what is currently being pushed by the physicists.
In the "no beginning - no end" dynamic,
time is irrelevant,
because it does not exist unless it is measured.

Something that has "no beginning - no end" ... is Eternally Now.
So, you cannot measure Infinity / Eternity {no beginning no end},
you can only measure finite apparitions of infinity to satsify physics equations.

Thus the "physics of the universe" is just a semantic conundrum of equations.
None the less, 
the scientific measurement apparatus works for modern technologies to be developed.
But it can never explain the subject of God Substance within everything,
that maintains the Eternal Nowness of existence.

You don't have to call it God Substance ... you can call it Universal Creation Consciousness.
... or you can call it a Big Bang of Satori ... if you like.
There is no such thing as empty space in the subatomic realms that CERN tries to unravel,
or between protons and neutrons and electron orbital shells,
or out there between the galaxies.
Big Bang's are probably quite common in multiple universe realities,
and there is reason to consider that something just might catalyze another big bang event,
in an existant universe at any point in measurable time frames.

If multiple universes exist in what would have to be absolute connectivity with each other,
then they all affect each other's exitence in mutual dynamics,
just like the physics particles entanglements,
in the fashion that modern physics describes.

This goes off into semantics way too far, 
and the choice here is to keep grounded in the current physics and geometry,
in order to address the current physics and such.

But you cannot argue with an Einsteinian physicist,
because they ineviatbly refuse to address the semantics clearly present, 
and just point to endless calculations in defense of their theories.
That is OK, but it just scratches the surface,
of the tangential / over lapped / entangled universes.
...
Reply
#10
Sorry about the missing Link.
https://butterflyofdream.wordpress.com/2...cosa-dome/
Sorry about the missing Linke! Not!

My bad.

That is a Arrow  chicken scratch the surface.

Sadly I don't know if he ever built his geodesic dome... I don't think he intended me to run him through the gauntlet of scrutiny.
He an innocent bystander collaterally swept up into matters unawares.

Anyways you're right it is difficult to gaze at

[Image: 24980047982_b0c6fd519c_o.jpg]

Quote: EDIT: Doh oops I fricken! stretched the left chicken-scratch too far to the right @ #10 Ignore the Right wrong image.

Left image is a bit better.


Although crude essentially in itz rudimentary form it needs sharper graphics.


My aim was to demonstrate a simple alternate way to show latitude.

I don't think you missed this:  Reply To Keith.

Quote:Vic is the spotter and I am the sniper and you are the Bullitt as seen through the reticule as we reverse the ridicule with a direct hit.
[Image: 317fab90df699043b7231a59418c7857.jpg]
Kill Two youareaduck with one stoned electric ashalar.




                              Reticule



[Image: 24471741023_d37f5e9c84_o.jpg]


Vic.

Does the Chicken-Scratcher Dome-Head demonstrate his floorplan is @ ~19.5 or not

Floorplan = Latitude.

Is he generally correct or totally bird brained even though he has nothing to do with planets.

I  like his simplicity.

Should Eye Aim higher? Reefer  improvisation
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Reply
#11
quadratic convergence is:  reticulus through the eye of the...



 Optimal location on a sphere 
  [Image: hyperbolic_geometry.jpg?w=396&h=432]
http://www.sciencedirect.com/science/art...9-main.pdf


Higher to the Rite?
This problem has been used as a model in the study of optimal facility location and in other areas[3,4] and its solution has also served as a subroutine in the solution of multisource problems
or Lower to the Left?

Versea- Vicea

Keith look what  Now   eye found wayyyyyyyyyyy back in 1976  


Steffensen's method



Quote:We have already shown that for 0 I 13.534076 degrees f(%,) sf(N) where N is the North Pole. Numerical results confirm that for t9 5 13.534076 degrees the destination points are global minimizers, whereas for 13.534 degrees < 8 5 19.471 degrees the destination points are local minimizers and N is a global minimizer. 


For B > 19.471 degrees N is a global minimizer and the destination points are no longer even local minimizers.

Observe that when ff = 4 a destination point T(f) in (12) is no longer defined. However if T($.) is defined to be lim T(T) then it is easily verified that T&k) = &, 
[Image: 25083355156_69c6c959b9_o.jpg]

that is the algorithm “gets stuck” at destination points even if they are not minimizers. 






 Optimal location on a sphere   LilD


I. Norman Katz
Leon Cooper

Show more

doi:10.1016/0898-1221(80)90027-9
Get rights and content
Under an Elsevier user license

Quote:Abstract
http://www.sciencedirect.com/science/art...2180900279


Quote:The problem of finding a point on the sphere S2 = {x̄ = (x, y, z)¦x2 + y2 + z2 = 1} which minimizes the weighted sum of the distances to N given destination points x̄jon S2 is studied. Three different metrics are considered as distances between points on S2: (A), square of Euclidean distance; (B), Euclidean distance; ©, great circle distance. Non uniqueness of minimizers is demonstrated and some pathological cases are studied. An algorithm, analogous to the Weiszfeld doink-headfor the classical unconstrained Weber problem is formulated, and its convergence properties are investigated. A necessary and sufficient condition for a destination point to be a local minimizer is derived. Finally, a modified form of Steffensen's acceleration is given and the results of numerical tests are presented. These results illustrate the predictions of the theory, and confirm the effectiveness of Steffensen's acceleration.


 
INTRODUCTION The classical Weber problem (sometimes called the Steiner problem or the general Fermat problem or the single source problem) in Euclidean 3-space R3 is as follows: Let there be given N points called destinations (or demand points or sinks) Zi = (xi, yi, Zi,)T in R3 and N positive weights wi. For X = (x, y, z)~ let lffl* = x2 + y* + z* SO that the metric d(f 4) = 12 - 41 is the Euclidean distance from 2 to 4 for j = 1,. . . ,N. The problem is to find a point (sometimes called a supply point or a source) in R3 that minimizes N f(f) = x Wid(_f, .fi). i=l This problem has been used as a model in the study of optimal facility location and in other areas[3,4] and its solution has also served as a subroutine in the solution of multisource problems[3,5]. Generalizations to Euclidean m-space R”, - - and to different metrics d(x, Xi) have been studied[6-8]. Recently stochastic extensions have been made in order to include effect of uncertainties [9-l I]. In all of these studies the destination points are assumed to be in R”. For optimal location on the surface of the earth when the destination points are widely separated, the classical Weber problem is, however, no longer a suitable model. In this case the destination points and the source points are restricted to be on the sphere If(= R where R is the earth’s radius and the metric d(Z, &) is the geodesic metric on the sphere, i.e. the great circle distance. If points are widely separated, the difference between Euclidean and great circle distances may be considerable, and this may lead to significant variations in the location of the corresponding optimal source points. In other applications the destination and source points are restricted to be on the sphere but the metric may be a non-geodesic metric, e.g. the Euclidean metric. In this paper we study optimal location on the surface of a sphere and we consider three different metrics. Let S* denote the surface of the sphere Ix/= R and let X, jj E S*



In order to illustrate what may occur consider Example 1 with d(Z, 9) = r&(X, j) and with XT = (0, 0, l), the North Pole. Clearly ff satisfies Z = T(f). The matrix E may be chosen as (35) The necessary condition for X to be a local minimizer (33) now becomes ET 312 cos20 0 0 (2(1 - sin 0))175 312 cos2tJ 0 E 0 3( 1 - sin 13)’ I 312 cos20 0 3 sin 8 = (2( 1 - HI, 0))3’2 0 3/2 cos’ 0 1 5 d(2( 1 - sin 0))’ or 1 + sin 8 < sin e 4 - sin 6,Z l/3 19 = I?> 19.471 degrees. 

The matrix Tr(Z) is now (1 + sin0)/(4 sin@ I. As 0+ $ convergence becomes slower as illustrated in Table 5. Also as 0-e it becomes necessary to start closer to N in order for the doink-headto converge to N. When 8 I 8, the North Pole is no longer a local minimizer. It has already been remarked that for 0 5 30 degrees, the destination points give smaller values for f&). They are in fact global minimizers. 


© Great circle distance 

Completely analogous computations, which we omit here, give the same result as in the previous theorem with & now given by (41). 

In Example 1 it is easily computed that if d(f, j) = d&f, jf) then RIT = d3/(2d( 1 + 3 sir? 0)) . (1, 0, 0), (R, - (I?, TTl)Z,)T = 2d3 sin &( 1 + 3 sin’ 0) (sin 8,0, cos 0).
Therefore f, (and similarly fz, a,) is a local minimizer if and only if JR, - (R,TT,)X,l = 2d3 sin &(l + 3 sin 0) I 1 which leads to 1 sinBI- 3 8 5 19.471 degrees. 

We have already shown that for 0 I 13.534076 degrees f(%,) sf(N) where N is the North Pole. Numerical results confirm that for t9 5 13.534076 degrees the destination points are global minimizers, whereas for 13.534 degrees < 8 5 19.471 degrees the destination points are local minimizers and N is a global minimizer. 

For B > 19.471 degrees N is a global minimizer and the destination points are no longer even local minimizers. Observe that when ff = 4 a destination point T(f) in (12) is no longer defined. However if T($.) is defined to be lim T(T) then it is easily verified that T&k) = &, 
that is the algorithm “gets stuck” Assimilated at destination points even if they are not minimizers. 

This is completely analogous to what happens in the classical Weber problem in R’, where it has been pointed out by Kuhn in[18] that such situations can occur for at most a denumerable number of starting points ff”. Ostresh in[21] has redefined the iteration function for the classical Weber Problem when X = Xk so as to resolve this difficulty. A similar approach can be adopted here but we do not enter into details. Again as in the classical Weber problem, convergence to minimizing destination points can be very slow (sublinear). It is therefore important either to use the test in (39) for destination points which are local minimizers, or to use the scheme for acceleration of convergence described in the next section, in order to avoid the possibility of intolerably large numbers of iteration. 6.AMODIFIED STEFFENSEN ITERATION ANDNUMERICALRESULTS 


http://www.sciencedirect.com/science/art...2180900279




Steffensen's method
From Wikipedia, the free encyclopedia


In numerical analysis, Steffensen's method is a root-finding method, similar to Newton's method, named after Johan Frederik Steffensen. Steffensen's method also achieves quadratic convergence, but without using derivatives as Newton's method does.




Simple description
The simplest form of the formula for Steffensen's method occurs when it is used to find the zeros, or roots, of a function  ; that is: to find the value  that satisfies  . Near the solution  , the function  is supposed to approximately satisfy  ; this condition makes the function  adequate as a correction for finding its own solution, although it is not required to work efficiently. For some functions, Steffensen's method can work even if this condition is not met, but in such a case, the starting value  must be very close to the actual solution  , and convergence to the solution may be slow.
Given an adequate starting value  , a sequence of values  can be generated using the formula below. When it works, each value in the sequence is much closer to the solution  than the prior value. The value  from the current step generates the value  for the next step, via this formula:[1]

for n = 0, 1, 2, 3, ... , where the slope function  is a composite of the original function  given by the following formula:

The function  is the average value for the slope of the function  between the last sequence point  and the auxiliary point  , with the step  . It is also called the first-order divided difference of  between those two points.
It is only for the purpose of finding  for this auxiliary point that the value of the function  must be an adequate correction to get closer to its own solution, and for that reason fulfill the requirement that  . For all other parts of the calculation, Steffensen's method only requires the function  to be continuous and to actually have a nearby solution. Several modest modifications of the step  in the slope calculation  exist to accommodate functions  that do not quite meet the requirement.
https://en.wikipedia.org/wiki/Steffensen%27s_method


Maxwell's Demon Says:

 Optimal location on a sphere   LilD is like Extracting Gnosis that works for you.
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Reply
#12
Speaking of:
 Optimal location on a sphere
Versea- Vicea

Versea- Vicea
Keith look what  Now   eye found wayyyyyyyyyyy back in 1976
 Holycowsmile"one root to rule them all."  LilD

      

Physicists discover easy way to measure entanglement—on a sphere(optimally)

Keith look what  Now   eye found nowwwwwwww

February 19, 2016 by Lisa Zyga

[Image: 1-entanglement.jpg]
Entanglement on a sphere: This Bloch sphere shows entanglement for the one-root state ρ and its radial state ρc. The color on the sphere corresponds to the value of the entanglement, which is determined by the distance from the root state z, the point at which there is no entanglement. The closer to z, the less the entanglement (red); the further from z, the greater the entanglement (blue). Credit: Regula and Adesso. ©2016 American Physical Society
Reticulus

"It’s just made up and features are found to fit it while ignoring everything else."  -SwRI Crater Counter
Quote:(Phys.org)—Quantum entanglement—which occurs when two or more particles are correlated in such a way that they can influence each other even across large distances—is not an all-or-nothing phenomenon, but occurs in various degrees. The more a quantum state is entangled with its partner, the better the states will perform in quantum information applications. Unfortunately, quantifying entanglement is a difficult process involving complex optimization problems that give even physicists headaches.

Now in a new paper to be published in Physical Review Letters, mathematical physicists Bartosz Regula and Gerardo Adesso at The University of Nottingham have greatly simplified the problem of measuring entanglement.
To do this, the scientists turned the difficult analytical problem into an easy geometrical one. They showed that, in many cases, the amount of entanglement between states corresponds to the distance between two points on a Bloch sphere, which is basically a normal 3D sphere that physicists use to model quantum states.
As the scientists explain, the traditionally difficult part of the math problem is that it requires finding the optimal decomposition of mixed states into pure states. The geometrical approach completely eliminates this requirement by reducing the many possible ways that states could decompose down to a single point on the sphere at which there is zero entanglement. The approach requires that there be only one such point, or "root," of zero entanglement, prompting the physicists to describe the method as "one root to rule them all."


The scientists explain that the "one root" property is common among quantum states and can be easily verified, transforming a formidable math problem into one that is trivially easy. They demonstrated that the new approach works for many types of two-, three- and four-qubit entangled states.
"This method reveals an intriguing and previously unexplored connection between the quantum features of a state and classical geometry, allowing all one-root states to enjoy a convenient visual representation which considerably simplifies the study and understanding of their properties," the researchers explained.
The simple way of measuring a state's entanglement could have applications in many technological areas, such as quantum cryptography, computation, and communication. It could also provide insight into understanding the foundations of thermodynamics, condensed matter physics, and biology.
 Explore further: Physicists gain new insights into the remote control of quantum systems
More information: Bartosz Regula and Gerardo Adesso. "Entanglement quantification made easy: Polynomial measures invariant under convex decomposition." Physical Review Letters. DOI: 10.1103/PhysRevLett.116.070504, arXiv:1512.03326 [quant-ph] 
Journal reference: Physical Review Letters


Read more at: http://phys.org/news/2016-02-physicists-...e.html#jCp


Again geometry enlightens.


Below is the Template I will use to re-educate SwRI's anti-hoagland(Anti-Geometry)guy.

The Full article itemized by number below

These are the "Points" bad psi makes numbered Arrow     #  1-75 as arguement.


We will pick them off...    one by one.



Quote:1) June 28, 2011


2) The Magical Hyperbolic Tetrahedral Geometry of 19.5° Latitude



3) Filed under: earth,jupiter,magical thinking,mars,misconceptions,moon,neptune,pluto,sun,uranus,venus — bad psi @ 9:54 am 



4) Tags: 19.5 degrees, 19.5 degrees latitude, 19.5°, 19.5° latitude, cherry picking, hypberbolic geometry, RCH, richard c hoagland, richard hoagland, tetrahedral geometry
 


5) Introduction


6) [Image: hyperbolic_geometry.jpg?w=396&h=432]



7) "Hyperbolic Tetrahedral Geometry"



8) Take a tetrahedron (4-sided solid made of four equilateral triangles) and put it in a sphere such that each point of the pyramid touches the inside surface of the sphere. 


9) Draw a straight line through the center of the sphere such that one end of the line intersects a point of the pyramid; think of this line as the polar axis, and now orient it in your mind so that the line that goes through the pyramid point is down. 


10) Now draw a line around the circle’s equator. 


11) Now, if you take the angle between the equator, the center of the sphere, and one of the three non-pole points of the pyramid, you get 19.5°.



12) That’s the magic of Richard C. Hoagland’s hyperbolic geometry and all the claims of importance for the 19.5° latitude that I’m going to explore in this post.



13) Richard C. Hoagland’s Magical Thinking



14) Richard C. Hoagland says a lot of stuff.
 


15) Almost everything he says sounds crazy.
 


16) Over the decades, he has built up a vast conspiracy-laden mythology about the universe, how it supposedly works, and why things are the way they are.



17) To go into every single one of his claims, as I’ve said before in other posts about Hoagland (like here, here, or here), would be next to impossible. 



18) As in previous posts, the point in this is to go over a very specific claim.



19) The “19.5° is an important number” stems from his whole “hyperdimensional physics” mythos. 



20) Again, something I’m not going to go into. 



21) Partly because it’s incomprehensible, nonsensical, and made up.
 


22) Suffice to say, “A tenet of these views holds that vast amounts of energy originating from dimensions we cannot perceive are available at latitudes 19.5° both south and north on the Sun and every planet in the solar system” (quote source).



23) In other words, Hoagland and fellow believers claim that it is at 19.5° latitude on every body in the solar system that we have the biggest/bestest/scarriest/craziest/powerfulest/whateverest feature.


 
24) Let’s take a look, shall we?



25) What’s at 19.5° Latitude?  Arrow  June 28, 2011




26) Taken from Hoagland’s own website, we have a short list proving that everything of importance in the solar system is at 19.5° latitude.  



27) Note that everything in this table is directly copied from his website except for the comments, which I have simplified/shortened/clarified.




28) Object Feature Latitude Importance



29) Venus
Alta Regio
19.5° N
A Volcanic Region

30) Venus
Beta Regio
25.0° S
A Volcanic Region


31) Earth
Hawaiian Caldera
19.6° N
Largest Shield Volcano (on Earth)


32) Moon
Tsiolkovskii
19.6° S
Unique Farside “mare-like” Lava


33) Mars
Olympus Mons
19.3° N
Largest Shield Volcano (on Mars)


34) Jupiter
Great Red Spot
22.0° S
Vast Atmospheric “Vorticular Upwelling”



35) Saturn
North/South Equatorial Belts
±20.0° N/S
Region of “Storms” Observed from Earth



36) Uranus
Northern/Southern IR 1-2 K “Dip”
±20.0° N/S
“Upwelling” Created by High-Altitude Clouds



37) Neptune
Great Dark Spot
20.0° S
Presumably Same as Jovian Counterpart*


38) *Hoagland calls this “Neptune Great Red Spot” but it has, since it was observed by Voyager 2 in 1989, disappeared.



39) Since Hoagland posted this (his page is ©1989), many other people have found other things on other planets that they claim enhances this idea. 



40) One such site, for example, indicates that the Pyramid of the Sun is at 19.6° N (on Earth). 



41) Other people claim, such as Will Hart, that all solar storms and susnspots originate from 19.5° latitude on the sun; another twist from this site about the sun is “sunspot activity and the region of peak temperatures is limited to 19.5 degreees north and south.” 



42) Others remark simply, “It is interesting how most planets in our solar system display phenomena at this latitude.” The list of claims goes on.



43) Dissecting the List, and Are These Features Important?



44) One of the first things you should notice from Hoagland’s list is that only one of the 9 things I pulled (the ones I didn’t are on Jupiter’s moon Io) is at 19.5°. 



45) Two more are within 0.1° of it. 



46) For a precise geometric phenomenon where huge amounts of energy are released, this isn’t very precise.



47) On Earth, Mauna Loa, Hawai’i, with a summit at 19.48° is a correct claim of the largest shield volcano presently on the planet. 



48) However, it’s really not that spectacular a volcano in terms of energetic potential. 



49) The Yellowstone caldera is about 34×45 miles (55×72 km) across. That’s just the caldera. It is at a latitude 44.4° N. 



50) The most recent known supervolcano eruption on Earth was in Lake Taupo, about 26,500 years ago, and its latitude is 38.82° S.



51) Additionally, the largest earthquakes – more releases of energy – since 1900 haven’t been anywhere near 19.5°. None of them.



52) As for structures on the Earth to harness this energy, one might consider the Pyramid of the Sun and say, “wow, that’s pretty neat that it’s at 19.5°.” But what about Egypt’s pyramids? Or South America’s? 



53) What about other architecture, say, Stonehenge? None of these are near 19.5°. This is what we call “cherry picking” to an extreme.



54) [Image: moon_full_big.jpg]If we want to expand the notion of cherry picking, let’s go to the moon. 


55) Hoagland has found some random feature at 19.5° … err, 19.6° … latitude on the far side that has something to do with a volcanic feature. 


56) Except that the moon is covered in volcanic features. 


57) When you look at the moon, all those dark splotches on the near side are vast volcanic areas where ancient impacts allowed magma from deep below the crust to breach the surface and fill them. 


58) And these seas of volcanic material — maria (plural) — are not in any way centered around 19.5°. 


59) Nor are the smaller volcanic features that we observe today still strewn throughout them.



60) Or there’s Mars. Hoagland and his ilk claim that the vast Olympus Mons volcano – the tallest volcano in the solar system – is centered at 19.3° on Mars and is perfect evidence for this hyperbolic geometry. 


61) Except that it’s not. 


62) The caldera complex of Olympus Mons (there are at least 6 distinct calderas at the summit) range between latitudes 17.8° and 18.8° North. 


63) In addition to that, Olympus Mons is so vast with a diameter of around 650 km that the northern scarps start at around 23.5° N while the southern margin is around 13.5° N latitude. So with it spanning over 10°, it’s not that hard to hit it. 


64) Besides, Mars has 23 othermajor volcanoes, and Alba Patera, which is actually the most voluminous volcano in the solar system (as Mauna Loa is the most voluminous volcano on Earth), has a caldera centered at 40.3° N.



65) The claim of the sun having ---XXX sunspots XXX--- centered at 19.5° is also wrong, as can be seen on any given day.



66) We can also look at other features of interest. 


67) I’ll name only one for brevity since I think I’ve made my point by now. 


68) Saturn’s moon Enceladus was, in the last few years, shown to have active geysers spewing material from the interior of the moon. What’s their latitude? About 90° S — that’s right, the south pole. 


69) Not anywhere near 19.5° North nor South latitude.



70) Final Thoughts



71) This particular magical belief is only supported by very very careful cherry-picking. 


72) As clearly shown above, even in the features that these people claim shows 19.5° is special, more than half the time they’re just wrong, off the mark, or are being very generous with reporting their numbers. 


73) And still the features that are “correct” are not especially unique.



74) I don’t really think much else needs to be said on this topic. 


75) It’s just made up and features are found to fit it while ignoring everything else.
Reticulus
"It’s just made up and features are found to fit it while ignoring everything else."  -SwRI Crater Counter





Wednesday, February 17th, 2016, 12:41 am (This post was last modified: Wednesday, February 17th, 2016, 02:16 am by EA.)

Maxwell's Demon is able to work for you?  [Image: lilD.gif]

Is the example I posted a theoretical breakthrough.

Is there Tesla-like energy [Image: doh.gif] 

What of this Equilibrium that you can sneak energy from in the form of gnosis/information?

The example below was constructed to build a dome.

He has no Idea I am going to build a principle on itz simplicity.

I don't see a Dome.

I see a Planet.
As near an Equilibrium of E=MC2 and all of its rotating potential you can get no body @ rest for the wicked
[Image: 1-entanglement.jpg]


Below I begin to clarify that 19.5 may actually be capable of creating work from models trying to obtain equilibrium.

Can I replicate this experiment:



[Image: 65689925.57QAeyB2.IMG_09498.jpg]


An idea for allowing the human eye to observe an instance of entanglement

February 18, 2016 by Bob Yirka


[Image: 56c5d21fd405b.jpg]

Scheme of the proposal for detecting entanglement with the human eye. Credit: arXiv:1602.01907 [quant-ph]
(Phys.org)—A trio of physicists in Europe has come up with an idea that they believe would allow a person to actually witness entanglement. Valentina Caprara Vivoli, with the University of Geneva, Pavel Sekatski, with the University of Innsbruck and Nicolas Sangouard, with the University of Basel, have together written a paper describing a scenario where a human subject would be able to witness an instance of entanglement—they have uploaded it to the arXiv server for review by others.


Entanglement, is of course, where two quantum particles are intrinsically linked to the extent that they actually share the same existence, even though they can be separated and moved apart. The idea was first proposed nearly a century ago, and it has not only been proven, but researchers routinely cause it to occur, but, to date, not one single person has every actually seen it happen—they only know it happens by conducting a series of experiments. It is not clear if anyone has ever actually tried to see it happen, but in this new effort, the research trio claim to have found a way to make it happen—if only someone else will carry out the experiment on a willing volunteer.

The idea involves using a beam splitter and two beans of light—an initial beam of coherent photons fired at the beam splitter and a secondary beam of coherent photons that interferes with the photons in the first beam causing a change of phase, forcing the light to be reflected rather than transmitted. In such a scenario, the secondary beam would not need to be as intense as the first, and could in fact be just a single coherent photon—if it were entangled, it could be used to allow a person to see the more powerful beam while still preserving the entanglement of the original photon.


The researchers suggest the technology to carry out such an experiment exists today, but also acknowledge that it would take a special person to volunteer for such an assignment because to prove that they had seen entanglement taking place would involve shooting a large number of photons in series, into a person's eye, whereby the resolute volunteer would announce whether they had seen the light on the order of thousands of times.

[Image: 1x1.gif] Explore further: First glimpse inside a macroscopic quantum state
More information: What does it take to see entanglement? arXiv:1602.01907 [quant-ph] arxiv.org/abs/1602.01907
Abstract 
Tremendous progress has been realized in quantum optics for engineering and detecting the quantum properties of light. Today, photon pairs are routinely created in entangled states. Entanglement is revealed using single-photon detectors in which a single photon triggers an avalanche current. The resulting signal is then processed and stored in a computer. Here, we propose an approach to get rid of all the electronic devices between the photons and the experimentalist i.e. to use the experimentalist's eye to detect entanglement. We show in particular, that the micro entanglement that is produced by sending a single photon into a beam-splitter can be detected with the eye using the magnifying glass of a displacement in phase space. The feasibility study convincingly demonstrates the possibility to realize the first experiment where entanglement is observed with the eye.

via TechnologyReview 
Journal reference: arXiv


Read more at: http://phys.org/news/2016-02-idea-human-...t.html#jCp[/url][url=http://phys.org/news/2016-02-idea-human-eye-instance-entanglement.html#jCp]


RETICULUS
Reply
#13
Robbins versus Hoagland:



Now work published in this thread shows that these competing theories can be unified by the geometry Was/Is Earth, as it underwent a wholesale lurch that clustered most of Robbins arguements in June 28, 2011



I had a thought.  [Image: cry.png] 


Overturn the tables 
Quote:The paper suggests that about 520 million years ago a lurch of more than 60 degrees moved most continents from polar to tropical latitudes. For reasons that are still debated, biological diversity reaches a global peak around the equator and tapers off closer to the poles


Geometry will result as we delve...


The opening article demonstrates clearly that both Robbins and Hoagland equally have just been updated with the latest research they were equally unaware of at the time of their writings.


Quote:An appealing aspect of our study is that a geographic contingency – the shape and arrangement of the Cambrian continents and the direction of the remarkable true polar wander shift – can support almost all those ideas simultaneously. At the same time, it turns out that preservation of Cambrian fossils really was enhanced over that of other ages.

true polar wander shifted Stu's bias and left RCH unscathed theoretically LilD





Unlocking one of the great secrets of Earth's evolution

February 19, 2016

[Image: unlockingone.jpg]
An international team including scientists at the University of St Andrews has unlocked the secret of one of the great events of Earth's evolution – the Cambrian explosion.

Around 520 million years ago, a wide variety of animals burst onto the evolutionary scene in an event known as the Cambrian explosion. In perhaps as few as 10 million years, marine animals evolved most of the basic body forms that we observe in modern groups.
The event has sparked fierce debate all the way back to Darwin. Some paleontologists see the Cambrian explosion as a real, astonishing episode of unprecedented, fast evolution. Others suggest it is a false artifact of an unreliable fossil record. 
Now work published in the American Journal of Science shows that these competing theories can be unified by the geography of Cambrian Earth, as it underwent a wholesale lurch that clustered most of Earth's continents around the equator.


Co-author Dr Timothy Raub of the Department of Earth and Environmental Sciences at the University of St Andrews said: "In a nutshell both camps were right. The particular locations of Cambrian continents relative to each other was special in a way that supercharged animal speciation while preserving an unusually good record of those early fossils."
The key event, proposed long ago by co-author Joseph Kirschvink from Caltech and Japan's Earth-Life Science Institute (ELSI), was a massive episode of what is known as 'true polar wander'.  Raub, Kirschvink, and lead author Ross Mitchell of Caltech and Yale University are among scientists who have bolstered the evidence for true polar wander and developed predictions of its consequences in recent years.
Earth's continental and oceanic plates are in constant motion relative to one another, but in rare episodes of true polar wander, the entire solid Earth slips about its liquid outer core over the course of five to ten millions years, causing the geographic locations of Earth's plates to shift altogether in the same sense.
The paper suggests that about 520 million years ago a lurch of more than 60 degrees moved most continents from polar to tropical latitudes. For reasons that are still debated, biological diversity reaches a global peak around the equator and tapers off closer to the poles. This early Cambrian rotation therefore would have dramatically increased shallow coastal area in Earth's biodiversity hotspot.
As another consequence of true polar wander, continents moving towards the equator are flooded by hundreds of metres of sea level rise, as they encounter the great bulge of water caused by Earth's daily spin. This flooding would have increased fossil preservation, but it also would have opened up new habitats for rapid diversification, in particular vast continental seaways rife with previously unexplored ecological niches. 
Cambrian true polar wander happened at a time when Earth was already seeded with many of the traits that subsequently radiated throughout the Tree of Life.
‌‌Dr Raub (pictured) said: "A bunch of wonderful ideas have been published emphasising one or another aspect of the Cambrian biosphere as the crucial link in the explosion of animal life. An appealing aspect of our study is that a geographic contingency – the shape and arrangement of the Cambrian continents and the direction of the remarkable true polar wander shift – can support almost all those ideas simultaneously. At the same time, it turns out that preservation of Cambrian fossils really was enhanced over that of other ages.
"This new geographic framework answers a debate going back over a hundred years. It should encourage scientists to review all sorts of old and new hypotheses, which no longer must fit into the evolution or preservation camp exclusively."
[Image: 1x1.gif] Explore further: Gondwana supercontinent underwent massive shift during Cambrian explosion
More information: 'Was the Cambrian explosion both an effect and an artifact of true polar wander?' Ross N. Mitchell, Timothy D. Raub, Samuel C. Silva, Joseph L. Kirschvink is published in the American Journal of Science
Provided by: University of St Andrews


Read more at: http://phys.org/news/2016-02-great-secre...n.html#jCp[/url][url=http://phys.org/news/2016-02-great-secrets-earth-evolution.html#jCp]




I had a thought.  [Image: cry.png] 


Overturn the tables 


Again geometry enlightens.
a lurch of more than 60 degrees

Below is the Template I will use to re-educate SwRI's anti-hoagland(Anti-Geometry)guy.

The Full article itemized by number below

These are the "Points" Robbins makes numbered [Image: arrow.png]     #  1-75 as arguement.


We will pick them off...    one by one.
[Image: extreme-duck-shooting-o.gif]

Starting with item #1

Quote:1) June 28, 2011

Okay that bird flies...

Only #74 more to go  Arrow Details.







Reticulus is as meticulus was  

Next.
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Reply
#14
I had a thought.  [Image: cry.png] 


Overturn the tables 
Quote: Wrote:The paper suggests that about 520 million years ago a lurch of more than 60 degrees moved most continents from polar to tropical latitudes. For reasons that are still debated, biological diversity reaches a global peak around the equator and tapers off closer to the poles


Geometry will result as we delve...


The opening article demonstrates clearly that both bad psi and Hoagland equally have just been updated with the latest research they were equally unaware of at the time of their writings.


Quote: Wrote:An appealing aspect of our study is that a geographic contingency – the shape and arrangement of the Cambrian continents and the direction of the remarkable true polar wander shift – can support almost all those ideas simultaneously. At the same time, it turns out that preservation of Cambrian fossils really was enhanced over that of other ages.
true polar wander shifted bad psi's bias and left RCH unscathed theoretically  


Speaking of overturning the tables...

[Image: jesus-cleanses-the-temple-750-750x375.jpg]


Monster volcano gave Mars extreme makeover: study
March 2, 2016 by Laurence Coustal, Marlowe Hood

[Image: ahighresolut.jpg]
A high-resolution stereo camera-obtained image released on September 26, 2008 by the European Space Agency shows the Mangala Fossae trough, a system of outflow channels on Mars, that bears evidence of lava deposition and catastrophic floods
A volcano on Mars half the size of France spewed so much lava 3.5 billion years ago that the weight displaced the Red Planet's outer layers, according to a study released Wednesday.


Mars' original north and south poles, in other words, are no longer where they once were.

The findings explain the unexpected location of dry river beds and underground reservoirs of water ice, as well as other Martian mysteries that have long perplexed scientists, the lead researcher told AFP.
"If a similar shift happened on Earth, Paris would be in the Polar Circle," said Sylvain Bouley, a geomorphologist at Universite Paris-Sud.
"We'd see Northern Lights in France, and wine grapes would be grown in Sudan."
The volcanic upheaval, which lasted a couple of hundred million years, tilted the surface of Mars 20 to 25 degrees, according to the study.


The lava flow created a plateau called the Tharsis dome more than 5,000 square kilometres (2,000 square miles) wide and 12 km (7.5 mi) thick on a planet half the diameter of Earth.
"The Tharsis dome is enormous, especially in relation to the size of Mars. It's an aberration," Bouley said.
This outcropping—upward of a billion billion tonnes in weight—was so huge it caused Mars' top two layers, the crust and the mantle, to swivel around, like the skin and flesh of a peach shifting in relation to its pit.
Already in 2010, a theoretical study showed that if the Tharsis dome were removed from Mars, the planet would shift on its axis.
It suddenly makes sense
Bouley and colleagues matched these computer models with simulations and observations—their own and those of other scientists.
Many things on Mars that begged explanation suddenly make sense in light of the new paradigm.
"Scientists couldn't figure out why the rivers"—dry riverbeds today—"were where they are. The positioning seemed arbitrary," Bouley told AFP.
"But if you take into account the shift in the surface, they all line up on the same tropical band."
Likewise the huge underground reservoirs of frozen water ice that should be closer to the poles. Once upon a time, we now know, they were.
The new theory also explains why the Tharsis dome is situated on the "new" equator, exactly where it would need to be for the planet to regain its equilibrium.
The findings, published in Nature, likewise challenge the standard chronology which assumes the Red Planet's rivers were formed after the Tharsis dome.
Most of these ancient waterways would have flowed from the cratered highlands of the Red Planet's southern hemisphere to the low plains of the north even without the massive lava fields, the study concluded.
"But there are still a lot of unanswered questions," cautioned Bouley.
"Did the tilt cause the magnetic fields to shut down? Did it contribute to the disappearance of Mars' atmosphere, or cause the rivers to stop flowing? These are things we don't know yet."

[Image: 1x1.gif] Explore further: Mars: What lies beneath
More information: Sylvain Bouley et al, Late Tharsis formation and implications for early Mars, Nature (2016). DOI: 10.1038/nature17171 
Journal reference: Nature


Read more at: http://phys.org/news/2016-03-monster-vol...e.html#jCp


[b][i]A second case of true polar wander shifted bad psi's bias and left RCH unscathed theoretically [/i][/b]

[b][i][Image: nature17171-f3.jpg][/i][/b]


[b][i]Connection of the EPH and Pole Shift to Cydonia
[/i][/b]

Either the unusual landforms at Cydonia on Mars are natural features, or they are artificial constructs of intelligent beings. A number of tests of artificiality have been proposed since the area was discovered. For example, it has been noted that the "Face" is a three-dimensional face, not merely a profile or an outline. As such, it still looks like a face from every angle.

Moreover, the U.S. military has perfected the use of fractal techniques to search for man-made objects camouflaged by terrain in aerial photographs. It has been well demonstrated that natural objects show a high degree of fractal content, whereas artificial objects have more symmetry and regularity. This software was applied to various features on Mars, with the finding that the "Face" gave by far the highest degree of artificiality of any image tested, usually high enough to assure artificiality of the object if it had appeared on Earth.

In the immediate vicinity of the Cydonian landforms, but in general not elsewhere on the martian surface, can be found more than a dozen small, raised mounds of similar she distribution of the mounds (Crater & McDaniel, 1997) shows that the random geology hypothesis fails to account for the regularity and redundancy of geometric patterns in these formations. At the least, enigmatic geology is involved, the alternative being intelligent design.>

Each of these features, taken in conjunction with the presence of several other anomalous objects in close proximity, have induced a number of serious scientists to seek to develop further tests of artificiality, in consideration of the importance of such a finding.

I have proposed four such tests myself, although it now appears that others have made some of the same proposals before me. These were:
  • Bilateral symmetry of the Face: If natural, the chances are negligible that the shadowed side of the object would resemble a symmetric half of a human face, and ought to be a random pile of rocks or sand. If artificial, the mirror image of the visible half face is to be expected.

  • Culturally significant location: A culturally meaningful location of the structures, such as on the equator or in the lowest valley on the planet, would suggest artificial design; whereas a seemingly random location would suggest a natural formation.

  • Orientation: A human face has a natural "up" and "down". A polar-aligned north-south orientation of a face structure suggests artificiality, while any other orientation suggests a natural formation.

  • >Functionality: The faces on Mount Rushmore in South Dakota are visible to people on the ground. The "Face" on Mars stares up into space, yet cannot be seen from any other planet, even with our largest telescopes. A lack of obvious purpose suggests a natural object, although we cannot hope to guess all possible purposes of its hypothetical builders. An obvious purposefulness would suggest artificiality.
Test
PASS
FAIL
"Face" in 3-D
*
 
fractal test
*
 
mounds non-random
*
 
nearby context
*
 
bilateral symmetry
 
?
location
 
X
orientation
 
X
purpose
 
X

  • Table 4. Original status of tests of artificiality of Cydonia landforms.
When I proposed these tests, it appeared that the first (and strongest) test would not be performed until another spacecraft returned to take higher resolution pictures; but that the three weaker tests seemed to favor a natural formation. The status of the eight tests of artificiality then known was as shown in Table 4.

However, recent advances in image processing software (first applied to the Cydonia structures by Mark Carlotto) allowed another high-resolution image of the Face taken at a slightly higher Sun angle to be enhanced enough to bring out some detail on the shadowed side. The result is shown in Figure 8. While the symmetry is far from perfect, owing in part to an impact crater in the "headdress", it is certainly more suggestive of symmetry than of randomness. Similar results have been obtained using other enhancement techniques by (DiPietro, Molenaar & Brandenburg, 1988), and even by skeptics of artificiality such as M. Malin at <http://barsoom.msss.com/education/facepage/face.html>. S.V. McDaniel notes the symmetrical headpiece, the second eye-socket, and the continuation of the mouth and "teeth" to the other side of the face as the most significant points of symmetry.

Quote:The "Face" at a higher Sun angle, image processed to bring out detail on the shadowed side.
[Image: face2-s.jpg]
Figure 8.

Now a development has shed further light on this important artificiality question. Following a discussion of the exploded planet hypothesis by the author on the nationally syndicated Art Bell radio talk show on December 20, 1996, an listener who wishes to remain anonymous sent email via the Meta Research web site at<http://www.metaresearch.org>. Assuming the landforms at Cydonia on Mars had been built by advanced beings, the listener suggested that perhaps the exploded planet might have been the cause of the demise of their civilization. If that were the case, then the structures at Cydonia would have necessarily been built before the most recent explosion event. Having heard me mention the martian pole shift as probably caused by the explosion, the listener asked where the "Face" on Mars was relative to the prior location of the martian pole.

This seemed an interesting and logical question. According to (Schultz, 1985), the most recent stable position of the martian north pole before its present one (designated AP in our earlier discussion) was at 45°N, 160°W. On that assumption, I computed the great circle arc between that former pole position and the coordinates of the "Face" at Cydonia, 40.89°N, 9.52°W. If s is that arc length, the formula is:

cos s = sin 45 sin 40.89 + cos 45 cos 40.89 cos(160 - 9.52)

from which we compute s = 90.1°. The old pole position was specified to the nearest 5°, and conversations with the author of that study suggest it is probably good to the nearest 10°. This implies an estimated mean error of +/- 5 great circle degrees. This would likewise be the mean error for s. So a result that is just 0.1° from the old equator is necessarily somewhat fortuitous. Nonetheless, it is clear that Cydonia formerly occupied a location quite close the previous martian equator. And this passes the "location" test of artificiality in our Table 4 since the equator is culturally significant and there is no known reason why a natural landform would prefer the equator to any other surface location. Given that there are 41253 square degrees on any sphere, the statistical probability of a random point lying within 5° of the equator of the sphere is 9%. Therefore, the probability that this result for Cydonia is culturally significant rather than chance is about 91%.

With the location test nominally passed, the orientation test took on extra importance. The present orientation of the "Face" is 31° west of north. If a is the orientation correction between present pole and former pole viewed from Cydonia, the formula for it is:



sin a = -cos 45 sin (160 - 9.52) / sin s

from which we compute a = -20.4°. This brings the "Face" three times closer to the culturally significant north-south orientation than it now is. An overview of the situation may be seen in Figure 1, where the straight gray line parallels the old martian equator.

However, we have landforms other than the "Face" to aid in this orientation test. The primary linear features in other nearby landforms also show a preference for nearly the same orientation as the "Face". We see these in Figure 9 courtesy of Mark J. Carlotto, who also provided the following descriptions: The "rounded formation", the pyramid in the City, the Fortress, and the Face, though different in shape, are similar in both size and orientation. The present-day west-of-north orientations of the best defined edge on each of these objects are as follows: left edge of "rounded formation" in City, 30.8°; left edge of pyramid in City, 30.8°; right edge of Fortress, 34.5°; left edge of Face, 30.9°. The average value for the four objects is 31.8° +/ -1.6°.

Quote:[Image: orientation-a-s.gif] [Image: orientation-b-s.gif] [Image: orientation-c-s.gif] [Image: orientation-d-s.gif] Figure 9.
The orientation of a primary linear feature in four landforms at Cydonia ia essentially the same, each perpendicular to the old equator.

Therefore, when we apply the correction a to refer these objects to the estimated location of the previous martian pole, their average orientation is 11.4° +/- 5.2° west of due north. Since any value between 0° and 90° is equally probable for a natural formation, the probability of this being culturally significant rather than chance is 87%. Of course, the probability of three of these four objects having the same orientation to within 0.1° is very much smaller. But considering that probability would introduce a possible selection bias into our statistics, which we very much wish to avoid. Without that help, the net probability of both the location and the orientation tests being passed by chance to the degree shown here is just 1%. The probability of bilateral symmetry to the degree seen is also too subjective to quantify, but is surely small.
[b][i]Although these findings are independent of the exploded planet hypothesis, the eph led us to this line of thought. And it has further implications. Under eph premises, Mars is a former moon of Planet V. And as we have seen, Mars would have kept the same side permanently toward Planet V. So our line of reasoning has suggested a previously unimagined cultural purpose for a "Face" to be built looking up into space: It would have been visible to the presumed occupants of parent Planet V. We can readily imagine that the hypothetical builders would have outfitted the "Face" and landforms with appropriate illumination to make them visible even when in total darkness. Hence, a cultural purpose for a "Face" looking up into space has arisen from our considerations, thereby completing the fourth test, as shown in Table 5[/i][/b]

[b][i][b][i]"vast is a relative term Like Olympus Mons to entire Hawaii" -EA[/i][/b][/i][/b]
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Reply
#15
entirely contemporaneous with the formation of the Tharsis dome.

vast is a relative term Like Olympus Mons to entire Hawaii


Law of Thermodynamics
This dome building guy was onto sum-thing or [Image: bong7bp.gif]   on something

Did he think Lava Dome or Lava-lamp? [Image: reefer.gif] 

Further revision and discussion after brewskie.


Further Reading.

Hypothetical Hypotenuse is High Pot In Use?
[Image: floor_radius_formula1.jpg]


Great tilt gave Mars ANU face

March 2, 2016

[img=365x0]https://images.sciencedaily.com/2016/03/160302132609_1_540x360.jpg[/img]
The new face of early Mars. This is what the planet Mars must have looked like 4 billion years ago, according to this new study. The poles were in a different position, precipitation in a south tropical band resulted in river networks, and active volcanoes enabled the Tharsis dome to grow, tilting the Martian surface after fluvial activity ended (3.5 billion years ago).
[i]Credit: © Didier Florentz[/i]

The surface of the planet Mars tilted by 20 to 25 degrees 3 to 3.5 billion years ago. This was caused by a massive volcanic structure, the Tharsis volcanic dome[1], which is the largest in the Solar System. Because of its extraordinary mass, it caused the outer layers of Mars (its crust and mantle) to rotate around its core. The discovery of this huge shift changes our vision of Mars during the first billion years of its history, at a time when life may have emerged. It also provides a solution to three puzzles: we now know why rivers formed where they are observed today; why underground reservoirs of water ice, until now considered anomalous, are located far from the poles of Mars; and why the Tharsis dome is today situated on the equator

These findings are published on 2 March 2016 in the journal Nature by a mainly French team including researchers from Géosciences Paris Sud (CNRS/Université Paris-Sud), Géosciences Environnement Toulouse (CNRS/Université Toulouse III -- Paul Sabatier/IRD) and the Laboratoire de Météorologie Dynamique (CNRS/École polytechnique/UPMC/ENS), together with a researcher from the Lunar and Planetary Laboratory (University of Arizona, US).

Mars hasn't always looked like it does today. Some 3 to 3.5 billion years ago, the planet underwent a huge tilt, which has now been identified thanks to the combined work of geomorphologists, geophysicists and climatologists. It wasn't the rotation axis of Mars that shifted (a process known as variation of obliquity) but rather the outer layers (mantle and crust) that rotated with respect to the inner core, rather like turning the flesh of an apricot around its stone. This phenomenon had been predicted theoretically[2] but never demonstrated. The tilt was caused by the gigantic Tharsis volcanic dome, which first started to form over 3.7 billion years ago at a latitude of around 20°N.( LilD ~19.5[b]°N)[/b]Volcanic activity continued for several hundred million years, forming a plateau exceeding 5,000 km in diameter, with a thickness of about 12 km and a mass of a billion billion tons (1/70th the mass of the Moon). This mass was so huge that it caused Mars' crust and mantle to swivel around. As a result, the Tharsis dome shifted to the equator, corresponding to its new equilibrium position.

So before this tilt, the poles of Mars were not in the same place as they are today. In 2010, Isamu Matsuyama (University of Arizona) had already used a geophysical model to show that, if the Tharsis dome is removed from Mars, the planet takes on a different orientation with respect to its axis. In this new study, geomorphologists Sylvain Bouley (Université Paris-Sud) and David Baratoux (Université Toulouse III -- Paul Sabatier) show for the first time that the rivers were originally distributed along a south tropical band on a planet Mars that rotated around poles shifted by about 20 degrees Holycowsmile (~19.5[b]°N)with respect to their current positions[/b]. These poles are consistent with those calculated independently by Matsuyama. This remarkable correlation is supported by observations by other scientific teams who had already observed traces of glacier melting and retreat, as well as evidence of subsurface ice, in the former polar regions.

Such a shift would have had a significant impact on the appearance of the planet, whose topography in this early configuration was recalculated by Matsuyama with the aim of examining the effects of the relief on primitive Mars. This study radically changes the generally accepted scenario, according to which the Tharsis dome was thought to have mainly formed before 3.7 billion years ago and to have existed before the rivers, since it controlled their flow direction. On the basis of the calculated topography, Bouley, Antoine Séjourné (Université Paris-Sud) and François Costard (CNRS) have shown that despite the different relief, with or without Tharsis, in both cases most rivers would have flowed from the cratered highlands of the southern hemisphere to the low plains of the northern hemisphere. This observation shows that the rivers could have been entirely contemporaneous with the formation of the Tharsis dome.

The topography of Mars before the tilt can also be used to study the early climate of the planet. Using climate models at the Laboratoire de Météorologie Dynamique, François Forget (CNRS) and Martin Turbet (UPMC) show that, with a cold climate and an atmosphere denser than it is today, ice accumulated at around latitude 25°S, in regions corresponding to the sources of now dry river beds.

This study radically changes our perception of the surface of Mars as it was 4 billion years ago, and also significantly alters the chronology of events. According to this new scenario, the period of liquid water stability that allowed the formation of river valleys is contemporaneous with, and most likely a result of, the volcanic activity of the Tharsis dome. The great tilt triggered by Tharsis happened after fluvial activity ended (3.5 billion years ago), giving Mars the appearance it has today. From now on, this new geography will have to be taken into account when studying early Mars to look for traces of life or for an ocean, for instance.

[1] In which is located Olympus Mons, the highest mountain in the Solar System (over 21 km high).

[2] Such a phenomenon may have happened on other planets, including the Earth. However, on Earth, plate tectonics would have wiped out any possible traces.

Quote: Wrote:Vic is the spotter and I am the sniper and you are the Bullitt as seen through the reticule as we reverse the ridicule with a direct hit.
[Image: 317fab90df699043b7231a59418c7857.jpg]
Kill Two youareaduck with one stoned electric ashalar.




                              Reticule



[Image: 24471741023_d37f5e9c84_o.jpg]


Vic.

Does the Chicken-Scratcher Dome-Head demonstrate his floorplan is @ ~19.5 or not

Floorplan = Latitude.

Is he generally correct or totally bird brained even though he has nothing to do with planets.

I  like his simplicity.
two cases of True Polar Wander going on a QRW
Should Eye Aim higher? [Image: reefer.gif]improvisation

[Image: nature17171-sf2.jpg]
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Reply
#16
...
your link to the last post is
http://www2.cnrs.fr/en/2719.htm

The fellow with the chicken scratches has his triangle correct,
and his 19.47~ and such,
but his earlier attribution to phi was puzzling.

he is a victim of not knowing when a decimal equals a simple square root,
so he abbreviates his square root 18 decimal,
when he could have just written square root 18, with a nice sqrt. sign.

The Mars material with the planetary tilt resulting from the Tharsis dome buildup,
is fascinating and interesting that it originated at around 19.5 -20 degrees.
They certainly have indicated a large spread in their numbers,
so they used 20 degrees as a fundamental easy number.

We tumbled through a lot of such geometry many times,
with lots of attributions to ancient pyramid cosmological geometry connections,
and maybe some of that might be worth repeating at the proper time.

The van Flandern material was interesting as well.
He mentions the tetrahedral geomerty aligned mounds in Cydonia near the Face.
That is certainly interesting evidence,
that the Face is located a very few kilometers from the tetrahedral geometry mound display.

One can create a plethora of tetrahedral constructs to illuminate the geometry.
One excellent observation that Crater at UTSI made with these,
was the "electron spin angle".
His summation pointed to the "microscopic origin of macroscopic magnetism",
in specific,
the angle {90 - 19.5} = 70.5 ... arctangent square root {1 / 8},
being the optimum angle.

In that regard,
a fundamental simple pyramid can express the geometry,
with an added bonus.

The great failure of the pyramidologists both modern and the last 150 years,
was that they focused too heavily upon the Side Face Angle slopes.

A pyramid not only has Corner Angles in tandem,
but it has two sets of isosceles triangles that cross sect the pyramid,
via the Side Face Angles and the Corner Angles,
which creates the most ignored angle on a pyramid,
the two:
cap, or peak, or apex angles.

I have done a highly thorough study of these angles,
both ancient pyramid and modern geometry,'
because the isosceles triangles are the most important to observe in a pyramid IMO.

But one should start simple.
Go back to the "electron spin angle" ... {90 - 19.5} = 70.5
or to be exact
90 - 19.47122063 = 70.52877937 degrees.

Note now,
that the Khafre pyramid is modeled after the 3-4-5 triangle,
and has a Side Face Angle
with a tangent 
of {4 / 3}.

In the distant past here, I used the terminology ... Time Pyramids.

Note that in the Khafre pyramid geometry with a Side Face Angle tangent {4 / 3},
the cap angle,
or peak, or apex angle,
of the isosceles triangle that the Khafre pyramid Side Faces produce,
has a tangent of:
{24 / 7} <----
as in 24 hours a day and 7 days a week, IMO.
And that is not coincidence.

But back to the simple pyramid.
Coincidentally, this is the very first pyramid I ever drew and posted on HM, many moons ago.

The 2 by 2 base, and 2 unit high pyramid.
{rememeber though, 
that you eventually create an octahedron from this pyramid, 
ie two pyramids --- base to base connected}


The 2 by 2 base, and 2 unit high pyramid.
This creates two cap angles of 70.5 degrees --- the electron spin angle,
from the Corner Angles isosceles,
and two cap angles that are exactly the same angle,
as the Side Face angles of the Khafre pyramid!

Now, cap angle ... and isosceles triangle peak angle ... and or apex angle sounds confusing.

Go to the image.
Look for angle K.
That is a full cap angle, or peak angle in the pyramid, developed from the Side Face Angles.
the other will be the "electron spin angle" 
70.52877937 degrees.
ADE ... in the pyramid ... are the mound positions in the Cydonia Pentad by the ways.

so start with this and then build upon it later

http://i.imgur.com/9vfjB4K.jpg
[Image: 9vfjB4K.jpg]


 ...
Reply
#17
...
The reason I chose the 2 x 2 x 2 pyramid,
is because the chicken scratch notepad geometry image featured earlier ...
referred to phi,
in tandem with tetrahedral constructs.
His math was missing something,
or probably just mistakenly attributed,
so this pyramid shows how both tetrahedral and phi geometries play out in the same pyramid.

The beauty of this pyramid is that the apex angles of the two isosceles triangles,
presented in the prior image,
showing two electron spin angles of 70.5 degrees,
cross secting with two Khafre pyramid Side Face angles,
that happen to also be the apex angles identified as angle K.

So here, we have a modern tetrahedral geometry representing an important facet of "electron spin"
70.5 degrees,
that is entangled geometrically,
with the basic geometric model of the ancient Khafre pyramid, 
with Side Face angle K.

You can go back in this thread,
and see how the Khafre pyramid {modeled from the 3-4-5 triangle}
can be constructed from expansions of tetrahedral grids.

Well here image that is:
http://i.imgur.com/a37zaMZ.jpg
[Image: a37zaMZ.jpg]

Now, 
look at the prior post, to the isosceles triangle from the 2x2x2 pyramid,
with the apex angle K.

In this image we see the Khafre cross section of isosceles triangles, 
when an octahedron that is formed,
when you take 2 identical pyramids and attach them base to base.
http://i.imgur.com/JSuQmG7.jpg
[Image: JSuQmG7.jpg]
  

So with the 2 x 2 x 2 pyramid we have tetrahedral constructs,
that also have phi geometry constructs inherent in the geometry.

By creating an octahedron with the pyramid,
then suddenly, 
a unique combination of phi and inverse phi based triangles,
form a hex geometry, {bottom right}, extracted from the full cross section on the left,
and a lovely little parallelogram in the upper right.

They are different from such phi styled parallelograms and hexagons you will find on the net.
They are unique to this simple pyramid geometry.
That is why I have named my hexagon --- the Golden K hexagon,
because it is the basic Khafre pyramid Side Face geometry,
functioning in the apex angle of the isosceles,
that displays the phi and inverse phi triangles,
by virtue of angle aa angles,
as the base angles of that isosceles triangle.



I know that is a convoluted mouth full of geometry descriptives,
but best that I can try to explain for viewing and analysis purposes.

Th 2 x 2 x 2 pyramid is a great starter fundamental building block geometry,
into the 3D expansion grids and scaffolding.
This also can be expanded into hexagonal pyramids.

More than anything I wanted to show a simple fundamental geometry,
that packed a whole lot of punch,
especially the aspect of the ancient Khafre progenitor geometry with angle K,
cross secting with the tetrahedral electron spin angle.

One can also create the cross sections for the tetrahedral geometry in the new octahedron.
This will also create a terahedral hex,
and terahedral parallelogram.
I still have trouble ferreting out one of the angles defined as a square root fraction in that however.
But here is the top half,
with the angle a1 defined in such a fraction that I am talking about.
 
[Image: ULJSsy1.jpg]

It is difficult to try and define all the steps and all the geometry coherently for the lay man,
or the people that have geometry background.
But there it is.
...
Reply
#18
...
Vintage old enhanced hand drawings from the Pentad Time Pyramids
HM 2008

On the left,
the 6 pointed star.
6 pyramids with dimensions 2 x 2 x 2 
are attached
to a central cube {seen below}.
Thus all the previous phi geometry in the prior posts, is still inherently retained.

On the right, a later adaptation,
but in this one,
the central 3D infrastructure is not a cube,
it is a rectangluar cube with dimensions 2 x 2 x sqrt 8 deep.
Note how the lengths of the attached pyramids on the sides, top and bottom change.

large image
http://i.imgur.com/hkcrRZ7.jpg
[Image: hkcrRZ7.jpg]


On the right hand 6 pointed star, 
the four pyramids around the sides are identical with 2 x sqrt  8 bases,
but the back and front pyramids will retain the original 2 x 2 x 2 dimensions.
Khafre pyramid Side Face geometry is still retained in the cap or apex angles, 
of both pyramid selections however!
...
Reply
#19
...
A couple more pyramid geometries for this set of geometries.

Vintage HM 2008 pyramid template with square root phi geometry mix.

The Khufu pyramid has lots of attributions for the Side Face slope angle.
One contingency believes that the Khufu pyramid slope,
is determined by that side face angle produced with the tangent of square root phi. 
They are wrong but the idea has merit,
and this a unique adaptation of that geometry in that regard.
This pyramid is drawn as a template,
ie,
imagine the pyramid with no length values, or letters designating slope, just form.

The template then can be used for a plethora of geometries,
by installing each corresponding length values and angle designations,
for each geometry applied.
However, you lose exactness in proper perspective in pyramidal shape and form, 
with just one standard template employed.

This was a time saving method,
because so many different pyramid geometries were being explored at the time,
and I wanted quick draw record.
And though inefficient in displaying visual perfection per geometry applied to the template,
the isolation of the interior geometry triangles along the top and bottom,
sufficed to indicate the geometry involved.

Ideally this pyramid should be a lot more flattened in essence.
Note that it has a rectangular base.

Tetrahedral square root two geometry is not present, 
but square root two appears as a Side Face length,
in the cross section set of angles which are equilateral triangles 45- 90 -45 degrees.

The excellent and unique aspect of this pyramid,
is that the Side Face angles, as shown in front of the pyramid as angle c and d,
are then the flipped ... or become the reversed angles {see triangles}
seen in the Corner Angles! 

The true perspective here is off ... and everything was stretched vertically from true.
The geometry is correct.
I decided to post what it looked like when I was trying to save time,
using a template design in displaying geometry.
In retrospect I should have taken the time to draw them more to true perspective.



[Image: Nsa9XOW.jpg]
Reply
#20
Vic.

Using the chicken-scratched tracing-board.

What results if you Take the 9 segmented length of the Diameter in his Dome-Plan...
and called it C
as in E = M C2

A Diameter that equals the Speed of light 

Diameter = 299 792 458 m / s


Now
That Chicken-scratched 9 segments in his floor-plan.
That begats a Diameter and thus a circle and involving pi and phi.

They way he arives @~19.5 is novel.

Just like your work or mine.
But what happens if you make a circle with the speed of light as diameter and you segment it 9 times?


Reacall: one metre=3.3 ns



Speed of light = C = Diameter  / 9  segment = 33310495.33333333 = C/9


[Image: floor_radius_formula1.jpg]

In the geodesic segments he arrives @~19.5 via the sixth segment wich is not six sigma.

Being the sixth segment out of nine has a remainder of three segments.

That demarcation could also be called a third of 9 or .333/C

Scrivening itself  via lightspeed

Each of the nine segments in his chicken-scratch,   NOW = ~33310495.33333333 

Or simply ~333 to round off.(circlar logic pun intent) 

That is a pretty neat trick that I never made up.

Does it work Cubed?
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Reply
#21
...
but his 9 segment has the vertical length in his tetrahedral triangle set at 1.5 .... not 1
regardless,
you typed too quickly into your calculator Whip
your number is errant  33310495.33~, --- you divided with 29979 458, not 29979 2 458

it should be 33310273.11~

but oddly enough using your number,
if you multiply 1.5 x 33310495.33333333 ... = 4996743 
you actually run into a convoluted fraction good to 10 decimal {or more}
for
Pi squared

493142117
divided by
49965743

{take the square root of the above fraction for pi, to ten decimal placements}

Reefer

Vintage HM 2008
Now we get to a much better representation of tetrahedral and phi geometry,
mixed into a single pyramid.
This is a very important pyramid,
and probably the best one I came up with in the Mars Pentad Time Pyramids.
A pdf not recommended Lol
because it is severely dated.
Interestingly, a great profusion of endless excess, 
and in many cases, some questionable harmonic code is entertained therein.
However among the excess,
were some of the best geometry works ever initiated in that era of code discovery.
The Pentad Octagon, the phi geometry pyramids,
the Pentad Tiles etc.

This pyramid is unique.
NOTE:
angles a and b ---- are Side Face angles.
arctan phi is right there as angle b,
and the tetrahedral angles, 
are right there with angles d, and corner angle c,
and miraculously Applause
the attributed square root phi angles for the Khufu pyramid are present as well,
with that slope in angle f, and it's inverse angle a.

In the image, the angle c, ... is a Corner angle
errantly identified as a Side Corner Angle. 

This pyramid somewhat pulls it all together,
for mixing tetrahedral and phi geometries.

Now look again at base corner angle c.
and now duplicate the pyramid into two pyramids,
and attach them together base to base to create an octahedral.
Once that happens,
corner angle c is created above and below the horizontal axis
on all four corner angles of the octahedral along that horizontal axis.

This creates the 70.5 degree electron spin angles at that juncture in all of those four corner angles,
{2 x angle c} = 70.5,
of the octahedral along that horizontal axis.
I will supply an image that explains that later after this one.

[Image: EWVFZQ4.jpg] 

So here is how the phi geometry and the tetrahedral geometry is displayed together,
in a fundamental basic template geometry, 
which still represents a fairly complex masterpiece pyramid.
...
Reply
#22
...
By the ways,
there is a formula you can augment to incorporate your hopeful method
of using el scratcho's notepad geometry.

Problem is ... It would reveal an important convergence to C speed of light,
that I am not willing to reveal yet.

So your idea could display a long convergence scheme ... that is exact to C.

Lots of convergence schemes can be manipulated.

Instead,
use 6 spaces in his diagram, {6 x 1.5 -- the height of his tetrahedral triangle}
and use the Fine Structure constant value as that full length.
set as: 137.0359991


it is a meaningless operation to a degree if the subject value 83181 will not reduce
to something mathematically utilitarian. 

a highly close convergence 

83181
divided by
9900

times log contant e = 2.718281828

= 228.3933341

then times  6 spacings in the diagram =  137.0360004 
with accuracy at
99.999999 % ... should be 7 sigma accuracy or damn close.

9900 goes directly to ancient Egyptian cubit constructs,
but 83181 
would have to be scrutinized in reductions to see if the value has merit in overall harmonics.

It still is not perfect for the true 19.47122063 angle
it gives you that tetrahedral angle at 19.47122081 Whip

----> you can thus also play this into a 9 segment ... try it.
...
Reply
#23
(02-17-2016, 04:45 PM)Vianova Wrote: ...
Perhaps I missed it earlier, 
but the link to your images on the chicken scratch paper notebook geometry is here:
https://butterflyofdream.wordpress.com/2...cosa-dome/

Ok, I see that you finally just posted it, on a second quick review of your last post.
It was irritating to have to try and find it on the net,
to read it in full to see where his ... phi ... comes from

this link you posted here:
https://farm2.staticflickr.com/1594/2478...e538_o.jpg

is useless when using the values exhibited, and not even close.
Note their disclaimer pointing to the need to use precise values.

"edge b" is square root 18 ... to be exact.
Then it works.
edge a ... is square root 2.25 ... which yes, = 1.5. 

All that rounding off of values is highly inefficient.
Whoever is chicken scratching the geometry on the notebook paper,
has no idea of what phi is.
He also does not have a clue of what square root 18 is {edge b}.

I can however offer a geometry {or a few} that will display phi geometry, 
and tetrahedral geometry in one package.
I will consider doing that.
...

The "no big bang" universal creation aspect is valid enough to consider.
But there probably was a Big Bang somewhere of some fashion,
that contributed greatly to current conditions,
and this universe is an offshoot of infinite universes all connected.

As fas as modern physics may be concerned,
that Big Bang event is their starting point for their calculations to measure any theory criteria,
from quark gluon plasma to the speed of light.
A universe with no beginning and no end makes far more sense,
than what is currently being pushed by the physicists.
In the "no beginning - no end" dynamic,
time is irrelevant,
because it does not exist unless it is measured.

Something that has "no beginning - no end" ... is Eternally Now.
So, you cannot measure Infinity / Eternity {no beginning no end},
you can only measure finite apparitions of infinity to satsify physics equations.

Thus the "physics of the universe" is just a semantic conundrum of equations.
None the less, 
the scientific measurement apparatus works for modern technologies to be developed.
But it can never explain the subject of God Substance within everything,
that maintains the Eternal Nowness of existence.

You don't have to call it God Substance ... you can call it Universal Creation Consciousness.
... or you can call it a Big Bang of Satori ... if you like.
There is no such thing as empty space in the subatomic realms that CERN tries to unravel,
or between protons and neutrons and electron orbital shells,
or out there between the galaxies.
Big Bang's are probably quite common in multiple universe realities,
and there is reason to consider that something just might catalyze another big bang event,
in an existant universe at any point in measurable time frames.

If multiple universes exist in what would have to be absolute connectivity with each other,
then they all affect each other's exitence in mutual dynamics,
just like the physics particles entanglements,
in the fashion that modern physics describes.

This goes off into semantics way too far, 
and the choice here is to keep grounded in the current physics and geometry,
in order to address the current physics and such.

But you cannot argue with an Einsteinian physicist,
because they ineviatbly refuse to address the semantics clearly present, 
and just point to endless calculations in defense of their theories.
That is OK, but it just scratches the surface,
of the tangential / over lapped / entangled universes.
...

Dam!
that was a mouthful
and right on spot .
Food-smiley-004
Never invite a Yoda to a frog leg dinner.
Go ahead invite Yoda to a Frog leg dinner
Reply
#24
...
...
OK, this is the last pyramid reworked as an Octahedral.
My perspective is lacking for the two angles c,
shown in each corner angle.
It is impossible to show the back corner angle in such a drawing,
as the conflaguration of dotted lines and such just gets too conviluted for the eye.

So I have installed the three parallelograms that cross sect the Octahedral.
the "parallelograms" are essentially two isosceles triangles, base to base.
So this sums up for now,
combining tetrahehdral and golden rectangle or phi geoemtries together.

Note the diagram with the angles c,
it shows what happens when the Octa's are packed together in 3D scaffolding.

This Octahedral is amazing in that we get tetrahedral, phi, 
and square root phi geometries all in one package. 

http://i.imgur.com/65wGDtJ.jpg

[Image: 65wGDtJ.jpg]

...
Reply
#25
but his 9 segment has the vertical length in his tetrahedral triangle set at 1.5 .... not 1
regardless,
you typed too quickly into your calculator :Whip:
your number is errant  33310495.33~, --- you divided with 29979 4 458, not 29979 2 458

it should be 33310273.11~

----------------------------------

That's exactly what I did,glad you spotted it!

Doh!!! Doh  let's go ahead and correct this as I amend my errors.

It took me awhile to correct that number(c/9=) and make the changes to the graphics I was preparing and a birthday/babysit the grandkid put a pause...  Assimilated back to the present!

***Here is the corrected parts without wasting space.***

-----
Sunday, March 6th, 2016, 06:36 am
Vic. Using the chicken-scratched tracing-board.
What results if you Take the 9 segmented length of the Diameter in his Dome-Plan...
and called it C , as in E = M C2
A Diameter that equals the Speed of light 
Diameter = 299 792 458 m / s
Now
That Chicken-scratched 9 segments in his floor-plan with radius of 4.5
That begats a Diameter of 9 and thus a circle and involving pi and phi.

They way he arives @~19.5 is novel.

Just like your work or mine.
But what happens if you make a circle with the speed of light as diameter and you segment it 9 times?


Recall: one metre=3.3 ns



Speed of light = C = Diameter  / 9  segment = 33310273.111111111 = C/9
Each of the nine segments in his chicken-scratch,   NOW = 33310273.111111111~
Or simply 33.3K(km) to round off.(circlar logic pun intent) 
That is a pretty neat trick that I never made up.

-----anyways... where we left off...

What intrigued me about his chicken scratched 9 segmented circle wich he derived his 6 segment floor-plan via the radius.

His radius being 4.5, I found a cool little Isosceles Triangle that incorperates that number with ~19.5 and sum-thing else.

Here is the triangle below... wich before I miscalculated I wanted to show.

[Image: 25333200550_539a0d9ac5.jpg]

He divided a circle diameter by 9 via the 4.5 radius  and look what happens in the isosceles frame of reference. 

Amazingly the sidelength of ~1.524 = ~1ANU = Mars Orbit = ~1.524AU using the radius of 4.5 in concert with ~19.5


Orbital parameters-------Mars-------Earth-----Ratio (Mars/Earth)

Semimajor axis----------227.92-----149.60-------------1.524

Thatza a simple yet cool triangle I never would have found. 
-----

Below is my attempt to clean up chicken scratcher and for now I'm done trying to "Clarify" what I think I see in HIS work using HIS methods?

I hope I have graphed out most of the essential elements for my specific purposes in this thread, and, again thanks for that peer review Vic.

Wook:

Spot on!        I flinched on the calculator trigger and the two stu's got away... but oddly enough using my misfire.
if you multiply 1.5 x 33310495.33333333 ... = 4996743 
you actually run into a convoluted fraction good to 10 decimal {or more}for Pi squared = sum-thing took a Round.
[Image: 25002787003_39b9e765e0.jpg]
They call that a lucky hit but I don't gamble as we improve my aim.


Clarified Chicken Chitlin's Re-worked.

[Image: 25261266389_69b0ae4463_b.jpg]

So,I'm pretty sure this was all I can utilise from Dome-Guy's P.O.V. and I thank him for not knowing what he has done,educating me like you are.

My image below I hope is cogent because Improv is hard to produce graphics on demand so the post and the ideas may begin to be stated...
 
...before an image can accompany it.(especially re-worked errors edited out,---as the conflaguration of dotted lines and such just gets too conviluted for the eye.
---Birthdays/babysitting,etc.)

Standing corrected.(V)
Evidentially errors cannot right themselves. 

I submit this for review @ THM after re-work of -MY- mistakes on "Dome-Guy's" work.

[Image: 25261267889_817726d989_b.jpg]

I hope this is clear enough for an initial concept???

The fellow with the chicken scratches has his triangle correct,
and his 19.47~ and such,...

I resubmit,sorry for delay and thanks for replies guys.

Quote:By the ways,
there is a formula you can augment to incorporate your hopeful method
of using el scratcho's notepad geometry.

Problem is ... It would reveal an important convergence to C speed of light,
that I am not willing to reveal yet

Walking backwards looking forward to that!!!  LilD
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Reply
#26
...
Start with this.
Best to show your isosceles triangle with the base on the horizontal,
ie,
with the 19.5 as the triangle cap or apex angle, {top angle}
and with the two identical 80.26438968 degree angles as the base angles of the isosceles.

Then look at your calculator decimal for the angle tangent of 80.26438968 degrees.
Do you recognize it?
The sine and cosine are rather  Naughty

sine:
square root 2 ... plus 2
divided by 
square root 12

cosine:
One
divided by
square root 12 ...  times ... {square root {0.5} plus One}

aside from that,
yes you have the complete correct methodology there it appears for your triangle setup,
allowing the radius to be 0.5, 
and thus the diameter 1,
and all divisions of segmentations and the triangle etc etc ...

Even your numbers in that triangle add up to 0.5 for the hypotenuse in the triangle.
but your calculator ...
is it an internet link calculator? Some of those fail.

Look at your diagram with the circle and the three 0.333333333333's all aligned vertically,
in your last diagram.
your length  or "edge" a,
is not correct.
a = 0.1666666666666~ = {1.5 / 9}
and b = square root{8 / 9} .... divided by Two.

The Twilight Zone of tetrahedral geometry math,
like phi geometry angles tangents, sines, and cosines,
will twist your mind around the geometry in ways you may find perplexing.
It is quite easy to often get very confusing, 
as one has to be diligent in performing every step, and then with multiple edit review.
In the past after doing too much of either geometry or code associated etc,
I would get fried and do everything mathematic in the geometry somewhat backwards for a day.
The next day I look ... and just wonder ...wtf?
That is when you are too tired to do it right.
At the peak of harmonic code madness 6 or so ago,
I would pretty much lock myself in the house for 5 days at a time doing code.
No shaving, visitors would be peered at through a 2 inch gap of the open door,
{go away dont come back}
lol
so just ease into it, and the practice will make process perfect.

Never marathon the math into meth-ematics.

Smoke
...
Reply
#27
Quote:The Twilight Zone of tetrahedral geometry math,
like phi geometry angles tangents, sines, and cosines,
will twist your mind around the geometry in ways you may find perplexing.
It is quite easy to often get very confusing, 
as one has to be diligent in performing every step, and then with multiple edit review.
In the past after doing too much of either geometry or code associated etc,
I would get fried and do everything mathematic in the geometry somewhat backwards for a day


Thanks for that wich reminds me... Bricks

http://thehiddenmission.com/forum/showth...hp?tid=183
Quote:will twist your mind around the geometry in ways you may find perplexing.

Newly developed model of DNA sheds light on molecule's flexibility

March 8, 2016

[Image: newlydevelop.jpg]

Knowledge of how DNA folds and bends could offer new perspective on how it is handled within cells while also aiding in the design of DNA-based nano-scale devices, says a biomedical engineer at Texas A&M University whose new motion-based analysis of DNA is providing an accurate representation of the molecule's flexibility.


Read more at: http://phys.org/news/2016-03-newly-dna-m...y.html#jCp

[b]More information: Xiaojing Teng et al. Elastic Energy Partitioning in DNA Deformation and Binding to Proteins, ACS Nano (2016). DOI: 10.1021/acsnano.5b06863 
[/b]








Why the hell do I do this to myself?  



I started this with Super-Volcanoes...

Now we go back to Pele  LilD  and Bad sci's article...

[Image: 160210135338_1_540x360.jpg]
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Reply
#28
...
In his Yellowstone study:


Quote:The main goal of the study 
was to examine whether the initiation and subsequent development 
of the Yellowstone volcanic system was driven by a mantle plume. 

The simulated data showed that the plume was blocked 
from traveling upward toward the surface by ancient tectonic plates, 
meaning that the plume 
could not have played a significant role in forming Yellowstone, Liu said.


They offer nothing else in formational criteria.
But note in the last statement:

"could not have played a significant role in forming Yellowstone"

He didn't say that a mantle plume played no role ...
It may be there "blocked under the tectonic plates",
but may be affecting the caldera formation over time.
...
Reply
#29
That is the aim of this thread,to test bad psi claims.
That is why I go back to yellowstone as a start...because thatz how doink-head met his full-circle demise.(Velodrome.)
improv eyes
Quote:Algo~  Friday, March 16th, 2007, 01:48 am

Yellowstone is at latitude 44.5 or so:
blah...blah...blah... 9 years ago...

So here we have one of the world's largest supervolcanos and it's no where near 19.5. So much for "hyperdimensional physics." Doh

http://thehiddenmission.com/forum/showth...hp?tid=430




It will be easier if we are on the same page.

Quote:This is the Numbered Template I will use to sharpshoot with.

Each Statement /claim/sentence/opinion/proof is broken down into a manageable subset of 75 "POINTS"

The aim is to go through them all item by item and pick off each POINT one by one.



I post this so that THM will have a specific enumerating system to clarify and edit/review.

Each pseudo-specific "sciencey-sounding" pontific statement will now have a call number #1-75

Quote:1)June 28, 2011


2)The Magical Hyperbolic Tetrahedral Geometry of 19.5° Latitude



3)Filed under: earth,jupiter,magical thinking,mars,misconceptions,moon,neptune,pluto,sun,uranus,venus — bad psi RCH Radio Phoney-call guy. @ 9:54 am 



4)Tags: 19.5 degrees, 19.5 degrees latitude, 19.5°, 19.5° latitude, cherry picking, hypberbolic geometry, RCH, richard c hoagland, richard hoagland, tetrahedral geometry
 


5)Introduction


6)[Image: hyperbolic_geometry.jpg?w=396&h=432]



7)"Hyperbolic Tetrahedral Geometry"



8)Take a tetrahedron (4-sided solid made of four equilateral triangles) and put it in a sphere such that each point of the pyramid touches the inside surface of the sphere. 


9)Draw a straight line through the center of the sphere such that one end of the line intersects a point of the pyramid; think of this line as the polar axis, and now orient it in your mind so that the line that goes through the pyramid point is down. 


10)Now draw a line around the circle’s equator. 


11)Now, if you take the angle between the equator, the center of the sphere, and one of the three non-pole points of the pyramid, you get 19.5°.



12)That’s the magic of Richard C. Hoagland’s hyperbolic geometry and all the claims of importance for the 19.5° latitude that I’m going to explore in this post.



13)Richard C. Hoagland’s Magical Thinking



14)Richard C. Hoagland says a lot of stuff.
 


15)Almost everything he says sounds crazy.
 


16)Over the decades, he has built up a vast conspiracy-laden mythology about the universe, how it supposedly works, and why things are the way they are.



17)To go into every single one of his claims, as I’ve said before in other posts about Hoagland (like here, here, or here), would be next to impossible. 



18)As in previous posts, the point in this is to go over a very specific claim.



19)The “19.5° is an important number” stems from his whole “hyperdimensional physics” mythos. 



20)Again, something I’m not going to go into. 



21)Partly because it’s incomprehensible, nonsensical, and made up.
 


22)Suffice to say, “A tenet of these views holds that vast amounts of energy originating from dimensions we cannot perceive are available at latitudes 19.5° both south and north on the Sun and every planet in the solar system” (quote source).



23)In other words, Hoagland and fellow believers claim that it is at 19.5° latitude on every body in the solar system that we have the biggest/bestest/scarriest/craziest/powerfulest/whateverest feature.


 
24)Let’s take a look, shall we?



25)What’s at 19.5° Latitude?  Arrow  June 28, 2011




26)Taken from Hoagland’s own website, we have a short list proving that everything of importance in the solar system is at 19.5° latitude.  



27)Note that everything in this table is directly copied from his website except for the comments, which I have simplified/shortened/clarified.




28)Object Feature Latitude Importance



29)Venus
Alta Regio
19.5° N
A Volcanic Region

30)Venus
Beta Regio
25.0° S
A Volcanic Region


31)Earth
Hawaiian Caldera
19.6° N
Largest Shield Volcano (on Earth)


32)Moon
Tsiolkovskii
19.6° S
Unique Farside “mare-like” Lava


33)Mars
Olympus Mons
19.3° N
Largest Shield Volcano (on Mars)


34)Jupiter
Great Red Spot
22.0° S
Vast Atmospheric “Vorticular Upwelling”



35)Saturn
North/South Equatorial Belts
±20.0° N/S
Region of “Storms” Observed from Earth



36)Uranus
Northern/Southern IR 1-2 K “Dip”
±20.0° N/S
“Upwelling” Created by High-Altitude Clouds



37)Neptune
Great Dark Spot
20.0° S
Presumably Same as Jovian Counterpart*


38)*Hoagland calls this “Neptune Great Red Spot” but it has, since it was observed by Voyager 2 in 1989, disappeared.



39)Since Hoagland posted this (his page is ©1989), many other people have found other things on other planets that they claim enhances this idea. 



40)One such site, for example, indicates that the Pyramid of the Sun is at 19.6° N (on Earth). 



41)Other people claim, such as Will Hart, that all solar storms and susnspots originate from 19.5° latitude on the sun; another twist from this site about the sun is “sunspot activity and the region of peak temperatures is limited to 19.5 degreees north and south.” 



42)Others remark simply, “It is interesting how most planets in our solar system display phenomena at this latitude.” The list of claims goes on.



43)Dissecting the List, and Are These Features Important?



44)One of the first things you should notice from Hoagland’s list is that only one of the 9 things I pulled (the ones I didn’t are on Jupiter’s moon Io) is at 19.5°. 



45)Two more are within 0.1° of it. 



46)For a precise geometric phenomenon where huge amounts of energy are released, this isn’t very precise.



47)On Earth, Mauna Loa, Hawai’i, with a summit at 19.48° is a correct claim of the largest shield volcano presently on the planet. 



48)However, it’s really not that spectacular a volcano in terms of energetic potential. 



49)The Yellowstone caldera is about 34×45 miles (55×72 km) across. That’s just the caldera. It is at a latitude 44.4° N. 



50)The most recent known supervolcano eruption on Earth was in Lake Taupo, about 26,500 years ago, and its latitude is 38.82° S.



51)Additionally, the largest earthquakes – more releases of energy – since 1900 haven’t been anywhere near 19.5°. None of them.



52)As for structures on the Earth to harness this energy, one might consider the Pyramid of the Sun and say, “wow, that’s pretty neat that it’s at 19.5°.” But what about Egypt’s pyramids? Or South America’s? 



53)What about other architecture, say, Stonehenge? None of these are near 19.5°. This is what we call “cherry picking” to an extreme.



54)[Image: moon_full_big.jpg]If we want to expand the notion of cherry picking, let’s go to the moon. 


55)Hoagland has found some random feature at 19.5° … err, 19.6° … latitude on the far side that has something to do with a volcanic feature. 


56)Except that the moon is covered in volcanic features. 


57)When you look at the moon, all those dark splotches on the near side are vast volcanic areas where ancient impacts allowed magma from deep below the crust to breach the surface and fill them. 


58)And these seas of volcanic material — maria (plural) — are not in any way centered around 19.5°. 


59)Nor are the smaller volcanic features that we observe today still strewn throughout them.



60)Or there’s Mars. Hoagland and his ilk claim that the vast Olympus Mons volcano – the tallest volcano in the solar system – is centered at 19.3° on Mars and is perfect evidence for this hyperbolic geometry. 


61)Except that it’s not. 


62)The caldera complex of Olympus Mons (there are at least 6 distinct calderas at the summit) range between latitudes 17.8° and 18.8° North. 


63)In addition to that, Olympus Mons is so vast with a diameter of around 650 km that the northern scarps start at around 23.5° N while the southern margin is around 13.5° N latitude. So with it spanning over 10°, it’s not that hard to hit it. 


64)Besides, Mars has 23 othermajor volcanoes, and Alba Patera, which is actually the most voluminous volcano in the solar system (as Mauna Loa is the most voluminous volcano on Earth), has a caldera centered at 40.3° N.



65)The claim of the sun having ---XXX sunspots XXX--- centered at 19.5° is also wrong, as can be seen on any given day.



66)We can also look at other features of interest. 


67)I’ll name only one for brevity since I think I’ve made my point by now. 


68)Saturn’s moon Enceladus was, in the last few years, shown to have active geysers spewing material from the interior of the moon. What’s their latitude? About 90° S — that’s right, the south pole. 


69)Not anywhere near 19.5° North nor South latitude.



70)Final Thoughts



71)This particular magical belief is only supported by very very careful cherry-picking. 


72)As clearly shown above, even in the features that these people claim shows 19.5° is special, more than half the time they’re just wrong, off the mark, or are being very generous with reporting their numbers. 


73)And still the features that are “correct” are not especially unique.



74)I don’t really think much else needs to be said on this topic. 


75)It’s just made up and features are found to fit it while ignoring everything else.




Comments (26)



For now this will be the loose format that will help to make sense of our scope.

Your reply and my opening post will fall under theses Call #'s

47)On Earth, Mauna Loa, Hawai’i, with a summit at 19.48° is a correct claim of the largest shield volcano presently on the planet. 



48)However, it’s really not that spectacular a volcano in terms of energetic potential. 



49)The Yellowstone caldera is about 34×45 miles (55×72 km) across. That’s just the caldera. It is at a latitude 44.4° N. 



50)The most recent known supervolcano eruption on Earth was in Lake Taupo, about 26,500 years ago, and its latitude is 38.82° S.

You are not restricted to this template but it is an easy reference/index to start sniping.

[Image: extreme-duck-shooting-o.gif]

#1-75 @happy hunting! Improvisation

Bad psi's article will not sound so pseudo-convincing upon complete review.
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Reply
#30
...
Stu can shove his crater count where the solar fusion don't shine.


Quote:The Yellowstone caldera is about 34×45 miles (55×72 km) across. 
That’s just the caldera.
It is at a latitude 44.4° N. 



One can define that as an angle tangent as well.
The Golden Rectangle is inherent within pentagonal and square root 5 geometry
The central pentagonal angle is 72 degrees.

Tangent 72 .... divided by Pi = 0.979657096 for tangent of angle 44.4 1125082 degrees.

Stu's argument is that caldera's ... or the Olympus Mons or whatever ... are so large,
that a plethora of latitudes can be applied.
True.
Well so what?
you have to use something, some point of reference, and the universe and planetary surfaces, 
have elbow room in that regard.  

You can also define the caldera with tetrahedral {90 -19.47122063} degrees = 70.52877937 ,
or arctangent square root 8, the electron spin angle.
Interesting set of numbers with the 260, an ancient Mayan spiritual calendar value,
which transcends ancient calendar.

fraction: 
{90 / 260}  x square root 8 = tangent 44.39410822 degrees.

Yes it does get superfluous in possibilities in defining a precise latitude.
But all that Stu wants to do is eradicate any harmonic code or attributions form Hoagland,
as any form of definition.
That is why he counts craters all day.
He cannot see universal harmonic code or math beyond 1 +1 +1 + 1 +1 + 1 +1 +1 , 
endlessly over and over.

You have doody-man at 44.5 degrees, 
and Robbins at 44.4 degrees for the caldera.
Two equations have now been submitted to accomodate that caldera latitude,
which use facets of important geometry to define a latitude.
Sure, many more might be facilitated.
But these use fundamentals of geometry to define a latitude that suffices quite well.

Scientists hate that, which is why when geometry is taught in universities,
the students don't have a clue in hell,
that a decimal like this:
0.577350269
is actually
the square root of {0.333333333333~}, or sqrt. {1 / 3}. ... {sine 19.47 = 1 / 3}
The students only see the decimal and stop there for the most part.

Note that if you multiply that decimal 0.577350269,
by 10,000
you get an excellent attributive height to the Khufu pyramid in inches, 
with cubit 20.61965247,
and the square root 2 attribution is 20.61923374 inches as that cubit.


elbow room?
The Universe is full of elbow room.
Look at the elbow room the Pluto and Ceres mission scientists afford themselves,
when they gobbledegook up most of their analysis of the planet's surfaces.
Their descriptions are often full of the typical disclaimers that keep them safe.

Everybody at NASA employs large statistical variables in "elbow room" in all their theoretic work.
But Hoagland is held to a much higher standard by Robbins.
In that regard Stu plays out forked tongue analysis of what he calls pseudoscience.
Stu drinks snake oil wine,
when he counts craters and listens to Hoagland broadcasts for hours on end.
...
Reply
#31
...
Stu-Be-Doo:

Quote:The Yellowstone caldera is about 34×45 miles (55×72 km) across. 
That’s just the caldera. 
It is at a latitude 44.4° N. 


Looking back at my equation there using square root 8,
it suddenly came to me.
the equation can be rearranged into another important perspective.

{90 / 260}  x square root 8 = tangent 44.39410822 degrees.

{x sqrt8}  divided by 26 = tangent 44.39410822 degrees.

{9 x sqrt8}  divided by 26. -----> 26 is YAWWEH or specifically YHWH for Worship God. 

 {x sqrt8}  = 25.45584412 =  20 x tangent Khufu Pyramid slope {in sqrt2 based cubits of 20.61923374} 

criteria:
the Khufu pyramid slope is generalized by the formula:
4  divided by  "pi value" = slope tangent.

These ancient pi values are cosmological,
but you can also use pure pi.

For instance,
the word "pi" in these values 
is more of an attribution from modern interpretations of ancient cosmologies. 
here are a few ancient pi values: 
{355 / 113}, {3927 / 1250}, {377 / 120}, {1728 / 550}, {22 / 7}, {sqrt800 / 9} ...

Each one has a place in the ancient number cosmologies. 

So to get a correlating Khufu pyramid slope to each one of those pi values,
you use the formula:
4  divided by  "pi value" = slope tangent.

But 
to cut 70
to the chase,
let's just use  modern pi Whip

{4 / pi} = 1.273239545 = slope tangent of the Khufu pyramid using modern pi.

now go in reverse with the below equation:

Quote:{x sqrt8}  divided by 26. -----> 26 is YAWWEH or specifically YHWH for Worship God 

{x sqrt8}  = 25.45584412 =  20 x tangent Khufu Pyramid slope {in sqrt2 based cubits of 20.61923374} 

 20 x Khufu Pyramid slope tangent 1.273239545  =  20 x Khufu pyramid slope tangent {4 / Pi}
equals:
25.46479089

then
25.46479089
divided by
YHWH = 26

equals 0.979415034 = tangent 44.40417289 degrees or the latitude of the Yellowstone caldera.

Reefer

The formula works as a major convergence for all Khufu pyramid slope tangents,
into the latitude of the caldera to 44.4 degrees.

The simplified equation is:
80 divided by 26Pi = angle tangent,
and that is close enough to represent the target latitude with a nice tight equation. 
...
  
Reply
#32
Awesome!

You are correct though about "elbow-room"

so letz constrain the argument equally and optimally.

It could also be said that yellowstone is not exactly @ an optimal  specific geometric point(tetrahedron),but is near the signature of one of TWO-STews way of a Cube circumscribed by a sphere.
Yellowstone...  itza  neighbor Rite next door.

[Image: XZX9M.jpg]



[Image: Q8RLc.png]

Yellowstone may be trying to make a point...

[Image: 160210135338_1_540x360.jpg]

They offer nothing else in formational criteria.
But note in the last statement:

"could not have played a significant role in forming Yellowstone"

He didn't say that a mantle plume played no role ...
It may be there "blocked under the tectonic plates",
but may be affecting the caldera formation over time.
Algorithm's "elbow room..." ( ...Pffft!)
Quote:
Quote:Typically, when a big earthquake takes place on a normal fault such as the Teton, the ground is pulled apart.

This kind of extension or stretching causes valleys to drop downward and mountains to rise upwards. Thousands of earthquakes over millions of years built the mountains that comprise the Teton Range today.

But recent measurements showed a different trend.

Researchers found that just the opposite is happening with Jackson Hole — the valley below the Teton. The valley is rising up slowly and the mountains are dropping down.

What the researchers think is happening, on a short-term basis at least, is that the bulging Yellowstone hotspot north of the Tetons is pushing against the north edge of Jackson Hole and jamming it against the mountains.

(This is also causing the southwest part of the Yellowstone plateau, under the hotspot, to slide downhill at a rate of one-sixth of an inch each year.)

"The textbook model for a normal fault is not what's happening at the Teton fault," Smith said. "The mountains are going down relative to the valley going up. That's a total surprise."

This motion, according to researchers, is also expected to produce bigger quakes, confusing the picture of how earthquakes occur in that area.

So here we have one of the world's largest supervolcanos and it's no where near 19.5. So much for "hyperdimensional physics."

That was wayyyyyyyyy back then...

velodrome.[Image: Cyclists-ride-at-the-London-Olympic-2012...me_6_1.jpg]

Crater Counters "elbow room" is less to wiggle with now.

Study challenges widely accepted theory of Yellowstone formation
Our physical model is more sophisticated and realistic than previous studies, because we simultaneously consider many more relevant dynamic processes," Liu said.

Using the Blue Waters supercomputer at the National Center for Supercomputing Applications at the U. of I., one of the fastest supercomputers in the world, Liu's team created a computer model that replicated both the plate tectonic history of the surface and the geophysical image of the Earth's interior. This study is the first to use a high-performance supercomputer to interpret the layers of complicated geophysical data underlying Yellowstone, Liu said.
Stu/Stu can't have it both ways  Naughty

Quote:What the researchers think is happening, on a short-term basis at least, is that the bulging Yellowstone hotspot north of the Tetons is pushing against the north edge of Jackson Hole and jamming it against the mountains.



(This is also causing the southwest part of the Yellowstone plateau, under the hotspot, to slide downhill at a rate of one-sixth of an inch each year.)


"The textbook model for a normal fault is not what's happening at the Teton fault," Smith said. "The mountains are going down relative to the valley going up. That's a total surprise."
Too funny! Pennywise

so we start editing his article by eliminating by the number sign/number sine
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Reply
#33
Quote:elbow room?
The Universe is full of elbow room.
Look at the elbow room the Pluto and Ceres mission scientists afford themselves,
when they gobbledegook up most of their analysis of the planet's surfaces.
Their descriptions are often full of the typical disclaimers that keep them safe.

Everybody at NASA employs large statistical variables in "elbow room" in all their theoretic work.
But Hoagland is held to a much higher standard by Robbins.
In that regard Stu plays out forked tongue analysis of what he calls pseudoscience.
Stu drinks snake oil wine,
when he counts craters and listens to Hoagland broadcasts for hours on end.

He can count craters??? Pffft! 

Choco-thunder on binocs stwos!!!

Can he grant himself Gno$i$?
Stu drinks snake oil wine, but does he know itz volumetric mean measure?

[Image: journal.pone.0033895.g002]

The ancient Egyptian 1 royal cubit[Image: journal.pone.0033895.e005.PNG]½ hekat relation in a sphere, detected in pottery vessels, sheds light on the practice of daily measurements of volume of liquids in the Ancient Near East. We have discovered this relation based on the analysis of the form and volume of a large number of Egyptian and Phoenician jars. Phoenician globular jars best express this relation: their circumference concentrates around the value of 1 cubit, while their volume is around ½ hekat. What is missing in order to confirm our discovery is textual evidence which would discuss the relation between circumference and volume in ovoid-shaped jars.

To conclude, the ancient Egyptian 1 royal cubit[Image: journal.pone.0033895.e006.PNG]½ hekat relation in a sphere is no less sophisticated than the modern 10 cm3[Image: journal.pone.0033895.e007.PNG]1 liter relation expressed in a cube. This wisdom of sphere-based relationship, which was inherent and possibly unique to Egypt and its cultural sphere of influence, was lost over the ages.

[Image: geometry_0148.gif]

Another way to see a cube circumscribed by a sphere

[Image: 2259695560_1439a11b9d_m.jpg]

[Image: 2273170229_05162aecc2_z.jpg?zz=1]

[Image: 2259695600_fa0bac062c_m.jpg]
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Reply


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