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After 400 Years, Scientists Have Discovered A New Class of Shape

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By Akshat Rathi, The Conversation

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The work of the Greek polymath Plato has kept millions of people busy for millennia. A few among them have been mathematicians who have obsessed about Platonic solids, a class of geometric forms that are highly regular and are commonly found in nature.

Since Plato’s work, two other classes of regular convex polyhedra, as the collective of these shapes are called, have been found: Archimedian solids and Kepler solids. Nearly 400 years after the last class was described, researchers claim that they may have now invented a new, fourth class, which they call Goldberg polyhedra. Also, they believe that their rules show that an infinite number of such classes could exist.

Platonic love for geometry

Regular convex polyhedra need to have certain characteristics. First, each of the sides of the polyhedra needs to be of the same length. Second, the shape must be completely solid: that is, it must have a well-defined inside and outside that is separated by the shape itself. Third, any point on a line that connects two points in a shape must never fall outside the shape.

Platonic solids, the first class of such shapes, are well known. They consist of five different shapes: tetrahedron, cube, octahedron, dodecahedron and icosahedron. They have four, six, eight, twelve and twenty faces, respectively.

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These highly regular structures are commonly found in nature. For instance, the carbon atoms in a diamond are arranged in a tetrahedral shape. Common salt and fool’s gold (iron sulfide) form cubic crystals, and calcium fluoride forms octahedral crystals.

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The new discovery comes from researchers who were inspired by finding such interesting polyhedra in their own work that involved the human eye. Stan Schein at the University of California in Los Angeles was studying the retina of the eye when he became interested in the structure of protein called clathrin. Clathrin is involved in moving resources inside and outside cells, and in that process it forms only a handful number of shapes. These shapes intrigued Schein, who ended up coming up with a mathematical explanation for the phenomenon.

second lastDuring this work, Schein came across the work of 20th century mathematician Michael Goldberg who described a set of new shapes, which have been named after him, as Goldberg polyhedra. The easiest Goldberg polyhedron to imagine looks like a blown-up football, as the shape is made of many pentagons and hexagons connected to each other in a symmetrical manner (see image to the left).

However, Schein believes that Goldberg’s shapes – or cages, as geometers call them – are not polyhedra. “It may be confusing because Goldberg called them polyhedra, a perfectly sensible name to a graph theorist, but to a geometer, polyhedra require planar faces,” Schein said.

Instead, in a new paper in the Proceedings of the National Academy of Sciences, Schein and his colleague James Gayed have described that a fourth class of convex polyhedra, which given Goldberg’s influence they want to call Goldberg polyhedra, even at the cost of confusing others.

A crude way to describe Schein and Gayed’s work, according to David Craven at the University of Birmingham, “is to take a cube and blow it up like a balloon” – which would make its faces bulge (see image to the right). The point at which the new shapes breaks the third rule – which is, any point on a line that connects two points in that shape falls outside the shape – is what Schein and Gayed care about most.

fourth lastCraven said, “There are two problems: the bulging of the faces, whether it creates a shape like a saddle, and how you turn those bulging faces into multi-faceted shapes. The first is relatively easy to solve. The second is the main problem. Here one can draw hexagons on the side of the bulge, but these hexagons won’t be flat. The question is whether you can push and pull all these hexagons around to make each and everyone of them flat.”

During the imagined bulging process, even one that involves replacing the bulge with multiple hexagons, as Craven points out, there will be formation of internal angles. These angles formed between lines of the same faces – referred to as dihedral angle discrepancies – means that, according to Schein and Gayed, the shape is no longer a polyhedron. Instead they claimed to have found a way of making those angles zero, which makes all the faces flat, and what is left is a true convex polyhedron (see image below).

Their rules, they claim, can be applied to develop other classes of convex polyhedra. These shapes will be with more and more faces, and in that sense there should be an infinite variety of them.

Playing with shapes

Such mathematical discoveries don’t have immediate applications, but often many are found. For example, dome-shaped buildings are never circular in shape. Instead they are built like half-cut Goldberg polyhedra, consisting of many regular shapes that give more strength to the structure than using round-shaped construction material.

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However, there may be some immediate applications. The new rules create polyhedra that have structures similar to viruses or fullerenes, a carbon isotope. The fact that there has been no “cure” against influenza, or common flu, shows that stopping viruses is hard. But if we are able to describe the structure of a virus accurately, we get a step closer to finding a way of fighting them.

If nothing else, Schein’s work will invoke mathematicians to find other interesting geometric shapes, now that regular convex polyhedra may have been done with.

This article was origianlly posted on The Conversation and can be read here.

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Research Reveals Plants Can Think, Choose & Remember

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In Brief

  • The Facts:

    This article was written by Sayer Ji, founder of Greenmedinfo.com where it was originally published. Posted here with permission.

  • Reflect On:

    Does all form of life poses some type of 'consciousness' regardless of its biological structure? If so, what does this mean?

Modern science is only beginning to catch up to the wisdom of the ancients: plants possess sentience and a rudimentary form of intelligence. 

Plants are far more intelligent and capable than we given them credit. In fact, provocative research from 2010 published in Plant Signaling & Behavior proposes that since they cannot escape environmental stresses in the manner of animals, they have developed a “sophisticated, highly responsive and dynamic physiology,” which includes information processes such as “biological quantum computing” and “cellular light memory” which could be described as forms of plant intelligence. Titled, “Secret life of plants: from memory to intelligence,” the study highlights one particular “super power” of plants indicative of their success as intelligent beings:

“There are living trees that germinated long before Jesus Christ was born. What sort of life wisdom evolved in plants to make it possible to survive and propagate for so long a time in the same place they germinated?”

According to the researchers, “plants actually work as a biological quantum computing device that is capable to process quantum information encrypted in light intensity and in its energy.” This information processing includes a mechanism for processing memorized information. For example:

“plants can store and use information from the spectral composition of light for several days or more to anticipate changes that might appear in the near future in the environment, for example, for anticipation of pathogen attack.”

According to the study, “plants can actually think and remember.”

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Moreover, plant not only possess a mechanism for information gathering and processing, but appear to exercise agency or “choice” vis-à-vis different scenarios:

“different group of chloroplasts and cells in the same leaf under identical constant and stable light, temperature and relative humidity condition have different opinion “what to do” in such conditions and tests different scenarios of possible future development.”

The study also offers an explanation for why plants absorb more light energy than is needed for photosynthesis alone:

“Another possible answer to the above question is a light training of young naïve leaves. Let’s imagine when young leaf or flower is emerging out of a plant, it would be nice for that leaf or flower to know about the conditions in which it is going to emerge. Older, more experienced leaves that actually are acclimated to outside conditions can train naïve emerging young leaves with the PEPS [photoelectrophysiological signaling ]and cellular light memory mechanisms. This explains why plants possess a natural capacity to absorb more light energy than that required for photosynthetic CO2 assimilation. They need this absorbed energy in excess for optimization and training of light acclimatory and immune defenses.”

The authors leave us with the provocative conclusion:

“Our results suggest that plants are intelligent organisms capable of performing a sort of thinking process (understood as at the same time and non-stress conditions capable of performing several different scenarios of possible future definitive responses), and capable of memorizing this training.17 Indeed leaves in the dark are able to not only “see” the light,8,34 but also are able to differently remember its spectral composition and use this memorized information to increase their Darwinian fitness.”

Why is this discovery important?

There are many reasons why recognizing the sentience and intelligence of plants may have positive implications for the future of humanity. For one, it helps us all to transcend the dominant worldview that non-human life forms are best defined in strictly mechanistic terms, and that attributing a “life essence” or consciousness to them is a form of magical thinking. French philosopher Maurice Merleau-Pointy called this world view the “Great Object,” namely, that everything in the universe is compromised of material objects externally related to one another, and with consciousness merely an ephemeral subjectivity found only in humans.

To the contrary, if we open ourselves to the possibility that we are all participants in an interconnected web of life, as many indigenous peoples believed and actually experienced things to be, destroying the natural world simply to serve the essentially suicidal infinite economic growth model will be identified for the insanity that it is. If we recognize, as biologist James Lovelock proposed, the Earth as a whole should be looked upon more like a self-regulating organism (Gaia hypothesis), or as mycologist Paul Stamet envisions, that there is a fungi-based internet within the ground connecting all living things on the planet in an information-sharing network, we will be less likely to both perceive and to treat the natural world as “other” to be dominated. We’ve also been reporting on the role of exosomes as cross-kingdom messengers, which provides a plausible mechanism for how all of the Earth’s inhabitants — plant, fungal, bacteria, animal, etc. — are linked together in an open access, information sharing network.

Recognizing that plants, for instance, have consciousness, or that their simple presence in our environment has healing effects, reintroduces an element of wonder and mystery back into the experience of the natural world. A perfect example of this can be found in the singing plants of the sacred forest of Damanhur. Damanhurian researchers in the mid-70’s reported using custom equipment to capture electromagnetic changes on the surface of leaves and roots and transforming them into audible signals. The researchers also observed that the plants learned to control their electrical responses, indicating they had some rudimentary awareness of the music they were creating. To learn more visit the Damanhur project website, and watch the video below.


Sayer Ji is founder of Greenmedinfo.com, a reviewer at the International Journal of Human Nutrition and Functional Medicine, Co-founder and CEO of Systome Biomed, Vice Chairman of the Board of the National Health Federation, Steering Committee Member of the Global Non-GMO Foundation.


Original Article


If you’d like more information from Greenmedinfo, you can sign up for their newsletter here

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Meet The Kenyan Engineer Who Created Gloves That Turn Sign Language Into Audible Speech

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In Brief

  • The Facts:

    Innovator Roy Allela has invented gloves that read the unique hand movements involved in sign language and turn them into audible speech through an Android app. He calls his gloves Sign-IO.

  • Reflect On:

    We are creating a world where we can all truly communicate, but imagine what our world could be like if inventions like these, and many others, were not limited by costs and start-up processes. Think of what we'd solve if we all worked together.

Imagine a world where communication between everyone is THAT much easier. Well, we’re getting closer and closer to that as every year passes by.

25-year-old Kenyan engineer and innovator, Roy Allela, recently helped humanity take another step in this direction. Allela designed new gloves that will improve communication between those who are deaf and those who cannot understand sign language. His new invention is called the ‘Sign-IO’ gloves, which can translate sign language movements into audible speech.

Allela’s gloves contain sensors located on each finger that are able to detect the positioning of each finger, including how much each finger bends into a given position. This is important, as sign language contains many unique movements that require small details to be detected accurately. The gloves connect via Bluetooth to an Android phone, which then uses text-to-speech technology to allow the person witnessing the sign language to understand what is being said through audio.

Roy was inspired to create the gloves because he has a young niece who is deaf. No one in his family including Roy knows sign language, and thus they often struggled to communicate with her.

“My niece wears the gloves, pairs them with her phone or mine, then starts signing. I’m able to understand what she’s saying,” Allela said.

“People speak at different speeds and it’s the same with people who sign: some are really fast, others are slow, so we integrated that into the mobile application so that it’s comfortable for anyone to use it,” he continued, referring to the creative engineering involved in his project.

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The Sign-IO app, which vocalises words signed by the person wearing the gloves. Photograph: Brett Eloff/Royal Academy of Engineering.

Early on, Allela sees his gloves in schools for special needs children throughout his home country of Kenya. From there, he hopes to expand his business and invention to impact as many deaf people and children around the world as possible. As mentioned, the Sign-IO gloves are just one of many innovations furthering the connection of humanity, no matter what unique aspects of life we are experiencing.

Allela’s gloves are currently in the prototype phase of development and are not yet available to the public. Regardless, they are creating quite the buzz around the world given what they propose to do. Sign-IO was the 2018 grand winner of the “Hardware Trailblazer Award” at the American Society of Mechanical Engineers (ASME) global finals in New York, and also took home a second runner-up acknowledgement at the Royal Academy of Engineering Leaders in Innovation Fellowship in London.

The Takeaway

Imagine the world we could create if we did not have the limitations imposed by businesses, start-up costs, and so forth. There are incredible people out there who are able to do incredible things for the world, and they’re finding ways to do so even within a society that limits humanity’s potential. If we could bring these amazing minds together and blow off these limitations, then we could truly create a world where communication is not only possible for all, but that would just be the beginning!

As we discussed in our Hidden Energy technologies interview with Susan Manewich on CETV, it’s important to note that the suppression of new, life-changing technologies is not just as a result of the elite, it’s due to our level of consciousness as well. You can check out the interview to learn more on CETV. 

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CIA Document Claims Cosmonauts Used Telepathy “To Back Up Their Electronic Equipment” In Space

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In Brief

  • The Facts:

    A document found inside the CIA's electronic reading room goes into detail regarding several telepathic experiments performed successful, decades ago by both US and Soviet astronauts.

  • Reflect On:

    With decades of statistically strong results in the lab and so many real world examples, why is this topic still shunned by mainstream academia? And why is it studied by at the highest levels of government in multiple countries if it's fake?

“The Soviet Union is well aware of the benefits and applications of parapsychology research. In 1963, a Kremilin edict apparently gave top priority to biological research, which in Russia includes parapsychology. The major impetus behind the Soviet drive to harness the possible capabilities of telepathic communication, telekinetics, and bionics is said to come from the Soviet military and the KGB. Today it is reported that the USSR has twenty or more centres for the study of parapsychological phenomena, with an annual budget estimated in 1967 at over 13 million dollars and reported to be as high as 21 million dollars.

Soviet parapsychology research was actually stimulated by the 1960 French story concerning the US atomic submarine Nautilus. The French journalists splashed the now rather infamous Nautilus story in headlines “US Navy Uses ESP on Atomic Sub!” Ship to shore telepathy, according to the French, blipped along nicely even when the Nautilus was far under water. “Is telepathy a new secret weapon? Will ESP be a deciding factor in future warfare?” The speculating French sensationalized, “Has the American military learned the secret of mind power?” In Leningrad the Nautilus reports went off like a depth charge in the mind of L.L Vasilev.”

The above information comes from this declassified CIA document.

It goes on to mention that in  April of 1960, Dr. Leonid Leonidovich Vasiliev addressed a group of high-ranking soviet scientists stating:

We carried out extensive and until now completely unreported investigations under the Stalin regime. Today the American Navy is testing telepathy on their atomic submarines. Soviet scientists conducted a great many successful telepathy tests over a quarter of a century ago. It’s urgent that we throw off our prejudices. We must again plunge into the exploration of this vital field.

As you can see, telepathy and parapsychology, which include remote viewing, ESP and psychokinesis, have all been studied in-depth within black budget special access programs in multiple countries. These programs are often highly classified, and so whatever has been revealed in official documentation is only the tip of the iceberg. Sometimes, the declassification of documents is used to halt more questioning into the phenomenon. The STARGATE program is a great example of that in the United States. Although the documents that were declassified show some startling findings, like the fact that remote viewing is real and that it was used for intelligence collecting purposes, it’s safe to assume that many details of this program remain highly classified.

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Russel Targ was the co-founder of that program. Here’s a video of him sharing everything he knows about ESP.

The crazy thing about parapsychology is the fact that studies have yielded statistically significant results. I’m talking about hundreds if not thousands of studies that have been conducted worldwide have seen positive results.

There seems to be a deep concern that the whole field will be tarnished by studying a phenomenon that is tainted by its association with superstition, spiritualism and magic. Protecting against this possibility sometimes seems more important than encouraging scientific exploration or protecting academic freedom. But this may be changing. Cassandra Vieten, PhD and President/CEO at the Institute of Noetic Sciences (source)

Many of these results are just as strong, if not stronger, than a lot of the results that come from hard sciences like physics and mechanical engineering. The Department of Defence has openly stated that the phenomena within this realm is real, despite the fact that they are still somewhat inexplicable. As far back as 1999, the head of the statistics department at UC Irvine, Jessica Utts, published a paper showing the results dealing with parapsychology and mind-body connection are a lot stronger than the results used to approve some of our medications!

Again, most of what’s known is still protected and locked up by the black budget world.

The documents referenced above are also decades old, so just imagine what’s happened or what’s been discovered since then!

The documents also outline how these experiments were not limited to earth.

Soviet research into biocommunications phenomena does not appear to be earth-bound and limited to inner space, but apparently extends to outer space as well. The so-called Father of Soviet Rocketry, K.E Tsiolkovsky, stated that:

“In the coming era of space flights, telepathic abilities are necessary. While the space rocket must bring men toward knowledge of the grand secrets in the universe, the study of psychic phenomena can lead us toward knowledge of the mysteries of the human mind. It is precisely the solution of this secret which promises the greatest achievements.” (source)

There are reports that the Soviets are training their cosmonauts in telepathy to back-up their electronic equipment while in outer space. One of these back-up schemes is known to involve coded telepathic messages. This method was previously demonstrated in March 1967, when a coded telepathic message was flashed from Moscow to Leningrad. The involvement of astronauts or cosmonauts in telepathy experiments is not necessarily unprecedented. In February 1971, during the Apollo 14 flight to the moon, astronaut Edgar Mitchell made 150 separate attempts to project his thoughts from inside the space capsule back to an individual on earth. The results of the Apollo 14 experiments have been well-documented in detail and are published in the Journal of Parapsychology. source()

Mitchell used 25 numbered cards in the experiment, in which he attempted to send a thought message to four people regarding the symbols on each card. He said two of the four got 51 of the 200 correct, and the other two were less successful. (source)

Dr. Elizabeth Rauscher, a world-renowned physicist, researcher, and presenter who has done a lot of work for NASA, among several other organizations, has admitted that quantum entanglement experiments have also successfully been carried out from Earth to space.

Much Stronger Examples

Some materialistically inclined scientists and philosophers refuse to acknowledge these phenomena because they are not consistent with their exclusive conception of the world. Rejection of post-materialist investigation of nature or refusal to publish strong science findings supporting a post-materialist framework are antithetical to the true spirit of scientific inquiry, which is that empirical data must always be adequately dealt with. Data which do not fit favored theories and beliefs cannot be dismissed a priori. Such dismissal is the realm of ideology, not science. – Dr. Gary Schwartz, Professor of Psychology, Medicine, Neurology, Psychiatry, and Surgery at the University of Arizona (source)

Although the above mentioned phenomena is very intriguing, especially the Soviet part, we have to remember that there is still a lot of information that has not been disclosed yet. This is not really studied openly in mainstream academia yet, it’s only really studied at the highest levels of government.

I published a well-sourced article providing multiple examples from a CIA document that confirm the existence of humans with ‘special abilities’ who are able to do ‘impossible’ things. You can access that here. It’s very interesting and goes to show just how strong results in the field of parapsychology are, and what information may still be kept hidden from us.

Today, hundreds of scientists are coming together to emphasize that physical matter is not our only reality. They’ve created a manifesto, and you can find links and access more information about this initiative, which started a few years ago, in an article we published here.

There is an entire non-physical world out there for us to study.

“The day science begins to study non-physical phenomena, it will make more progress in one decade than in all the previous centuries of its existence.” – Nikola Tesla

The point is that this stuff is very real, and has been studied for a long time.

Here’s an interesting quote from the literature regarding remote viewing, one subject within the realm of parapsychology that allows a person to view other people or objects in different locations, regardless of the distance:

Here’s a telling quote from some of the declassified literature:

“To summarize, over the years, the back-and-forth criticism of protocols, refinement of methods, and successful replication of this type of remote viewing in independent laboratories has yielded considerable scientific evidence for the reality of the [remote viewing] phenomenon. Adding to the strength of these results was the discovery that a growing number of individuals could be found to demonstrate high-quality remote viewing, often to their own surprise. . . . The development of this capability at SRI has evolved to the point where visiting CIA personnel with no previous exposure to such concepts have performed well under controlled laboratory conditions.” (source)

One participant of the program, remote viewer Ingo Swann, was tasked with the job of taking a look at what could be going on off the planet.

Dr. Puthoff explains:

“To determine whether it was necessary to have a ‘beacon’ individual at the target site, Swann suggested carrying out an experiment to remote view the planet Jupiter before the upcoming NASA Pioneer 10 flyby. In that case, much to his chagrin (and ours) he found a ring around Jupiter, and wondered if perhaps he had remote viewed Saturn by mistake. Our colleagues in astronomy were quite unimpressed as well, until the flyby revealed that an unanticipated ring did in fact exist.”

The Takeaway

Why do we still ridicule parapsychology? It’s correlated with quantum physics, and it seems to be the next logical step for science. The fact that this type of study is not included within mainstream media is truly a shame, and it’s not fair that government agencies are the only ones who seem to be actively and heavily engaged in this type of study.

At the end of they day, no skeptic can deny the reality of parapsychological phenomena.

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