The Immortality Of Mathematical Unity

Many people think that religion and science are mutually exclusive. Not the gringa. She believes that they are inextricably linked. One cannot exist without the other. One explains the mysteries of the other. They are mirror images reflecting and confirming the existence of each other. Follow the gringa on a mathematically spiritual rabbit trail and see where we end up on the other side of the mirror.

The gringa read a little ditty about Roman dodecahedrons. They are a 12 sided object with each side shaped like a 5-sided pentagon. Each pentagon has a hole in it. The sides of the pentagons connect to create a hollow center. At each corner junction is a knob.  These strange little doo-dads have been found in all sorts of places: central Europe, France, southwest Germany, Austria, Switzerland, Hungary, Belgium, the UK, etc. They are very mysterious objects usually constructed of bronze or stone.

As archaeologists have continued to uncover these thingamajigs, they have scoured the annals of ancient literature, government records, science annals and religious texts to no avail. No one seems to have ever mentioned them. It is perplexing, indeed, for archaeologists to determine what the heck they are. Considering the time period in which they were constructed (200 AD), the materials from which they are made (stone or metal), the skilled craftsmanship required, it is highly unlikely such investment was made for the purpose of a flower vase, children’s toy or gaming device.

The gringa agrees with one speculation, especially since there is no written record accounting for them. I agree with the theory that they are some religious relic of kabbalistic intent. These dodecahedrons may have been been secretly used by elite Roman religionists, objects of great mystical power. Let’s explore the possibilities.

A mathematician will explain that there are 30 edges, 20 vertices (points of angle),  and twelve faces. In a nutshell, to a mathematician, a dodecahedron is the only 3-dimensional geometric shape that is a polyhedron comprised of pentagons. In other words, it is unique, one of kind.

A mathematician will explain further fascinating aspects:

  • It is a pentagon inside as well.
  • A perfect cube can be created within it.
  • A tetrahedron can be created within it.
  • A decagon can be created within it and is, in fact, created based upon the geometric shape of the pentagon. So, without a dodecahedron, a decagon could not exist.
  • An octahedron can be created within the tetrahedron.
  • The icosahedron is the dual-opposite of the dodecahedron. This means that none of the other geometric solids fit within the icosahedron without the dodecahedron existing in the first place. One cannot exist without the other and vice versa. The physical connection that bears evidence of this “duality” is created by connecting each pentagon’s vertex (the middle holes) with lines.
  • All 5 geometric shapes (cube, tetrahedron, decagon, octahedron & dodecahedron ) fit within one another within the icosahedron.
  • The geometric solid dodecahedron contains 12 pyramids.
  • The geometry of dodecahedron is a union of crystals, lattices and organic life.

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That’s some deep stuff from math. Seeing as how the Roman dodecahedrons all had holes in each pentagon’s center, it is easy to see that whoever was using it for whatever purpose was aware of the icosahedron duality aspect. The gringa’s pretty certain a detail like that is no coinky-dink.

So what, then, would be a relationship that would tie an advanced mathematical object to religious use? That would be the symbology of numerology. The most important and repetitive numbers in the geometry of the dodecahedron is 5 and 12, most importantly 12. It is the geometry of 5 and 12 which create the dodecahedron so that the dodecahedron can, in turn, create everything else. Let’s see what superstition, religions and mysticism have to say about these numbers:

The Number 5

  • Ancient Chinese superstitions attributed this number as having a duality: good luck and bad luck. Philosophically, the number 5 is indicative of the five elements so this number is also featured in much of ancient Chinese medicine that is still in practice today.
  • In Christian symbology, the number represents the creation of mankind who has 5 fingers, toes and senses.
  • Judeo-Christian mysticism attributes God’s grace to the number 5 based on a formula developed from the 10 Commandments: First 5 commandments are about man’s relationship with God, the other 5 about mankind’s relationships with one another, all of which require grace because of man’s inability to achieve perfection. This is further confirmed by the number of offerings required in order to receive grace: 1. Sin Offering; 2. Trespass Offering; 3. Burnt Offering; 4. Grain Offering; 5. Peace Offering.
  • There are 5 Pillars of Islam which define how to live a Muslim lifestyle.
  • Muslim mysticism attributes the number as symbolic of doubt and weakness, the spiritual and physical condition of mankind.
  • Hinduism teaches that the number represents the elements of nature, in essence, it represents the divine’s creation, mankind and the Earth. Lord Shiva’s 5 faces are turned toward different directions observing these elements, each face having a different name.
  • The condition of man after death is of joining the 5 elements, meaning he becomes Panchaka, a part of the group of 5. Panchakona is the Hindi word for pentagon.

The gringa’s conclusion, then, is that the pentagons which comprise the dodecahedron represent mankind and the Earth.

The number 12

  • To understand how ancient Chinese philosophers would view the number, you have to break it down into the components of 10 and 2. The number 10 is a yin number, meaning evenly balanced, as is the number 2, hence the number 12. As an evenly balanced number it would be regarded as good luck. 2 is considered especially lucky because of the superstitious belief that all good things come in pairs. That can be determined by a quick scan of human physiology: 2 eyes, 2 hands, 2 feet. Lose one and a person is significantly impaired, incomplete, imperfect. Thus, the number 2 is also symbolic of perfection, thus, the divine.
  • Judeo-Christian teaching is that this is the divine number, the number that represents the godhead: 12 tribes, 12 disciples, and 12 zodiac star systems in the heavens from whence the 12 Roman gods were derived.
  • Muslims teach that there were originally 12 ruling Imams mentored and appointed by Muhammad.
  • Buddhism features 12 life stations that are achieved on the path to enlightenment.

The twelve individual pentagons that symbolize man individually, once united, form the representation of the godhead, the creator of mankind. In other words, these Roman dodecahedrons teach us that:

  • All of mankind serves its own purpose in representing an aspect of the godhead.
  • Once each aspect accepts that it needs the existence and support of the other aspects, it can then unite.
  • Once all aspects unite, they form the image of the godhead.
  • All of Earth (the dodecahedron) and all of the dual Spiritual (the icosahedron) are contained within this union, thus…

Unity of all mankind will lead to immortality and the physical restoration of the Earth. That is the mystical message of the Roman dodecahedron. At least that’s the road the gringa has travelled. And the building block of the godhead is mankind. Man has always thought that without God, man could not exist. But the geometric model shows that without mankind, the godhead could not exist. The practical take-away from all of that for the gringa is: respect all religions, respect all cultures, respect all people. Get along and, like the Vulcans say, live long and prosper. Heck, we might, in fact, achieve some mystical end-game accomplishment and become immortal, enjoying world peace for ever and ever.

Sources: The Vintage News

Tutor Ming

Mystical Numbers

My Islamic Dream


Image Credits: Before It’s News Science & Tech



Space For Europe IS the ESA

With ESA Astronaut Tim Peake performing a spacewalk this week on the International Space Station, the gringa thinks it’s only fitting to turn the limelight toward Europe’s space agency and their long history of achievement. The European Space Agency (ESA) is to Europe what NASA is to the United States, JAXA is to Japan and Rocosmos is to Russia. ESA is comprised of 22 member states who collaborate with their financial resources and intellectual talents to provide a gateway to the stars for all of Europe. Members are: Austria, Belgium, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Ireland, Italy, Luxembourg, the Netherlands, Norway, Poland, Portugal, Romania, Spain, Sweden, Switzerland and the United Kingdom. Canada, Bulgaria, Cyprus, Malta, Latvia, Lithuania, Slovakia and Slovenia all make their own contributions as well through contractual agreements of cooperation.

The goals of the ESA are to discover more about Earth and its surrounding Solar System, as well as the entire Universe. These goals are met while at the same time promoting development of European technologies and sharing these with the world’s other space agencies.

Paris is the location of ESA headquarters. Germany is where ESA’s Astronaut Centre and Space Operations Centre are located. Astronomy Centres are found in Canada and Spain with the Earth Observation centre in Italy. The UK houses the centre for Space Applications and Telecommunications and launch bases are scattered throughout Belgium, the U.S.A., Russia and French Guiana. It can be rather dizzying with all of these operational centres spread all over the world. So, to keep things simple, because the gringa likes simple, for more information about ESA, simply go to their website,, or drop them a line or pick up the phone:

Communication Department
European Space Agency
8-10 rue Mario Nikis
75738 Paris
Cedex 15

Tel: + 33 1 5369 7155
Fax: + 33 1 5369 7690

ESA desires to explore space for peaceful purposes. While doing this it wants Europeans to benefit economic growth from the support services required to travel to the stars. Since its conception over thirty years ago, ESA has focused on long-term goals that are adaptable to a world that changes rapidly. The gringa wishes to highlight just a smattering of successful ESA missions:

  • ESRO-4, 1972: The ESRO-4 (European Space Research Organisation) satellite carried five experiments concentrating on Earth’s ionosphere, atmosphere, radiation belts and penetration of solar particle radiation into the magnetosphere. It was launched on 22 November 1972, on a NASA Scout rocket from the Western Test Range in California, and reentered Earth’s atmosphere after a successful mission on 15 April 1974.
  • 1977-2002 Mission Meteosat: launched multiple weather satellites
  • 1979 Mission Ariane: first launch of commercial launcher to secure Europe’s independent space access
  • 1983 Mission Spacelab: launched laboratory module for NASA’s Space Shuttle
  • 1985 Mission Giotto: intercept of Halley’s Comet and Comet Grigg-Skjellerup
  • 1990 Mission Hubble Space Telescope: ESA contribution of solar arrays and Faint Object Camera for Hubble Space Telescope
  • 1998 Mission ARD: launch of first European experimental re-entry vehicle
  • 2003 Mission Mars Express: launch of Europe’s first Red Planet orbiter
  • 2005 Mission Venus Express: launch of Europe’s first Venus orbiter
  • 2008-2012 Mission ATV: launch space truck for ISS re-supply
  • 2015 Mission Lisa Pathfinder: launch of technology to detect gravitational waves

Which brings the gringa to the current ESA Mission, “Principia”.  This six month mission is named after Isaac Newton’s book on physics, “Naturalis Principia Mathematica”. Peake’s mission objectives are to maintain the weightless research laboratory, conduct over thirty scientific experiments, and perform a spacewalk with fellow crewman Astronaut Tim Kopra, working together to replace a Solar Shunt Unit.

Preparing for the spacewalk involves breathing pure oxygen for two hours (to purge nitrogen) before embarking. Once spacesuits are donned, the astronauts enter an airlock where air pressure is gradually reduced until they can safely exit the ISS.

Upon successful completion of Mission Principia, ESA will then turn its attention and efforts to the next scheduled mission, Mission Exomars. Later on this year ESA will launch a Mars orbiter, rover and surface platform to the Red Planet. The gringa is so excited! To Mars! To Mars!


Source and Photo Credit:


The Girl Who Loved To Count

And who says girls are bad at math? Most definitely Katherine Johnson is not!

Born in West Virgina in 1918, she was a girl who grew up in a time when not only were women not expected to grow up and do great things, but a woman of color had the additional obstacle of racism. But that didn’t stop Katherine from counting and that is the fascination that led to her greatness that culminated in her service at NASA.

When describing her youthful obsession, she said, “I counted everything. I counted the steps to the road, the steps up to the church, the number of dishes and silverware I washed… anything that could be counted, I did.” And what did all that counting lead to? The 2015 National Medal of Freedom.

She was an amazing achiever. At the tender age of ten she was a freshman in high school. Imagine that in the time period and circumstances she was in! The gringa is in awe! And, apparently, her father was as well. He did what was necessary to see that his daughter fulfilled her potential.

Eventually he relocated the entire family to Institute, West Virginia so Katherine could complete her education and she graduated college at the age of eighteen.  Katherine then went on to teach, raise a family and eventually work for the National Advisory Committee for Aeronautics in 1953 which would later be replaced by NASA. In the time before there were computers to do the tedious job of counting and recording, people like Katherine did the job.

As a “human computer”, Katherine completed mission assignments like calculating the trajectory for the first American in space, Alan Shepard. Once computers did exist, Katherine was the back up that double checked the computer’s accuracy on calculations. Her work was so respected that before John Glenn made his spaceflight aboard Friendship 7, he specifically asked for Katherine to do the recheck on his mission calculations.

Katherine worked on the Apollo Moon landing mission as well as the early beginnings of the shuttle program. She continued to serve the people of the United States of America, as well as the entire world, through her extraordinary work at NASA until 1986.

The Presidential Medal of Freedom medal that she was awarded on Tuesday, November 24, 2015, was not the only merit to her name. In addition to honorary doctorates, in 1967 she received the NASA Lunar Orbiter Spacecraft and Operations team award for her work in navigation.

What does NASA have to say about Katherine? The following are quoted from NASA Administrator Charles Bolden’s public statement:

“She’s one of the greatest minds ever to grace our agency or our country…”

“Katherine’s legacy is a big part of the reason that my fellow astronauts and I were able to get to space…”

NASA Deputy Administrator Dava Newman said:  “We are fortunate that when faced with the adversity of racial and gender barriers, she found the courage to say ‘tell them I’m coming’.

And the gringa will close with those simple yet bold words from a great woman.



Source & Photo Credit:



How To Get A Job With NASA As A Research Assistant

If you have dreams of outer space like the gringa, just what opportunity is there at NASA? Who are they looking for? What qualifications should upcoming NASA employees plan to pad their resumes with? How much does such an interesting and dynamic job pay?

Over half of the jobs available with NASA are at the professional levels for engineers and scientists. If you plan to have a top notch job application for one of these positions, be sure to take as many classes as possible in mathematics, computer and aerospace engineering, meteorology, and even accounting.

About twenty-five percent of opportunities are for administrative staff. This kind of NASA role involves analytical skills, top notch researching abilities, specialization with information technology, and budgeting experience. These are college graduate level careers and critical for project management.

There is high level competition to get coveted aerospace industry jobs. One of the things to do to secure your best chance of getting hired at NASA is to find a mentor. Many universities have agreements with NASA for research assistants. Check this avenue out to help get a foot in the door for a shot at a job that has earning potential from $11,000 – $30,000 annually.

An example of a NASA research assistant job with a college is one that was recently advertised by the Department of Astronomy and Astrophysics at Penn State University. They announced an opening for a Research Assistant in the “Science Planner on the Science Operations Team of the Swift Gamma-Ray Burst” program. This is an ongoing NASA mission that has been operating since 2004.  Such a position requires a college degree in Physics or Astronomy.

Need scientists only apply? Well, not according to Angela Beaman who has a degree in Fine Arts. She got a research assistant position with NASA through the Horticulture Department at Iowa State University. The first thing she did was let a childhood curiosity about plants encourage an adult decision to pursue more knowledge. She showed up at the university’s horticultural center and simply started asking questions. That eventually led to a NASA fellowship studying the cultivation of basil through hydroponics. She explains that the most important trait to have in pursuing career dreams at NASA is determination which will see a person through a lifetime of continuing education.

As the gringa tends to her humble little patio garden, I consider how important these things are that we often take for granted. For space exploration to be possible at the “next level”, it’s not enough to know how to keep humans alive. We also have to know how to keep alive organisms that are life sustaining. Astronauts have to be able to provide some green stuff for long-term missions. This not only feeds their stomachs, but also their lungs as technology advances to create a self-contained biosphere that can sustain life through a long-duration mission. If you want to be a part, take some classes, ask questions, and get involved on any level.


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A Bit Of Sun & Hope For Humanity

Coming up in December is the one year anniversary of the test flight of the Orion spacecraft that launched from Kennedy Space Center December 5, 2014. The test flight was unmanned. Because of its success, the next time Orion punches through the Earth’s atmosphere, it will deliver astronauts to an asteroid in our Moon’s orbit to rehearse their Red Planet mission. That is the ultimate goal, after all, to have a full astronaut crew heading out to deep space with a final destination of Mars.

The amazing new technologies that will send astronauts farther than they have ever gone before is thanks, in part, to the students of science, technology, engineering and mathematics (STEM). NASA and Lockheed Martin offered students the opportunity to collaborate in this daring mission with a program called “Exploration Design Challenge”. What problem were these students asked to solve? The students were challenged to solve the most dangerous issue that faces humans in space – exposure to radiation. The gringa is very proud to say that these students rose to the challenge and their very own radiation experiment was on board for Orion’s test flight. If there was ever a reason for parents to encourage their children in STEM curriculum, parents, the time is NOW!

The emerging generation of scientists will inherit a planet that is rapidly changing. NASA needs this young talent more than ever. Researchers will manage the data collected from satellites and airborne missions. Engineers will keep these missions alive with their technological expertise. These are the critical thinkers the world needs to face the future challenges of rising sea levels and extreme weather events due to climate change. The next generation of astronaut explorers will be the ones to aid our planet in finding freshwater resources out in the cosmos to help replenish are own that are rapidly becoming depleted.

In 2014 NASA studies were published and revealed a rapidly melting western sheet of ice in Antarctica. This appears to be irreversible. Later in the same year, NASA, along with researchers at the University of California, Irvine, concluded that the potential threat of groundwater loss to America’s stable water supply may have previously been underestimated and things were worse than scientists thought. In August of 2014, NASA published research based on the discovery of a large amount of a compound creating ozone depletion. This was an unexpected surprise considering that for decades such a compound has been banned worldwide. Our world is in trouble and our best resource to solve these problems is in the minds of our youth.

The gringa is getting depressed with all this bad news so, let’s get back to the good news! The Orion! I simply must know all I can about this spaceship because the gringa is putting in that ship all her hopes that it is going to be the mother ship of a future fleet of ships that’s going to save humanity’s bacon.

The purpose of the test flight was to see if Orion was up to the task of the most dangerous parts of the mission. Those would be lift-off, entry, separations, the jettison of the Launch Abort System, descent and splashdown. However, most important of all was to test the heat shield that needed to be strong enough to protect astronauts, as well as all the technology on board, from 4,000 degree Fahrenheit temperatures and the related radiation. Is the dear reader dying to know Orion’s report card? The gringa is!

At 7:05am at Cape Canaveral Air Force Station in Florida, Orion was prepped to lift off with the help of a United Launch Alliance Delta IV Heavy rocket. Three RS-68 engines created almost two million pounds of thrust which then pushed a 1.63 million pound spacecraft into orbit. After about four minutes the side boosters disengaged and fell away to Earth. The center booster remained with Orion for another ninety seconds. When its fuel was spent, it disengaged and also fell back to Earth. The next thing to release its hold on Orion was the structural supports and the Launch Abort System. Orion was headed out of Earth’s atmosphere.

Seventeen minutes and thirty-nine seconds after lift-off, Orion began its orbit. Two hours into its flight, Orion traveled through the Van Allen radiation belts which are 3,609 miles away. Data recorders provided critical calculations on the doses of radiation within the cabin. This determined if the craft was of sound design and safe to man with a human crew. Three hours and twenty-three minutes into its flight, Orion headed for Earth’s atmosphere where the heat shield withstood the brutal re-entry friction.

What is re-entry like? Orion hit Earth’s atmosphere at a speed of 20,000 mph. The gringa can only say, “Incredible!” The spacecraft gets so amazingly hot at that speed, it is eventually enveloped in plasma. Plasma is considered the fourth state of matter after solids, liquids and gases. When plasma is created on Orion upon re-entry, what happens is that the heat and friction become so energized that electrons break free from their nucleus and travel along with them. That’s what the Sun does all the time. It’s just a big, ol’ ball of plasma. Orion creates a little bit of Sun on re-entry. The gringa’s mind is filled with the Beatles refrain, “Here comes the sun, little darlin’. Here comes the sun. And I say it’s alright.” After all, ultimately that IS the plan, RIGHT? Orion is going to help launch the scientific efforts that hopefully will make everything wrong with the environment alright? Or, at least give humanity some viable options and hope?

After picking up Orion as it bobbed amongst the waves of the Pacific of the coast of Baja, California, NASA used the data to make improvements for the upcoming manned mission. Astronauts will continue their own preparations for a mission that is sure to make history in so many ways. If everyone at NASA is excited about the future, then they truly believe in the mission. The gringa will take her cue from them and toss out the doom and gloom and grab hold of hope and positivity. I will hold fast to an exciting future that most certainly is full of change, but change is not necessarily always a bad thing.