The 11 Dimensional Brain

Blue Brain Team Discovers a Multi-Dimensional Universe in Brain Networks

Using mathematics in a novel way in neuroscience, the Blue Brain Project shows that the brain operates on many dimensions, not just the three dimensions that we are accustomed to.

For most people, it is a stretch of the imagination to understand the world in four dimensions but a new study has discovered structures in the brain with up to eleven dimensions – ground-breaking work that is beginning to reveal the brain’s deepest architectural secrets.

Using algebraic topology in a way that it has never been used before in neuroscience, a team from the Blue Brain Project has uncovered a universe of multi-dimensional geometrical structures and spaces within the networks of the brain.

The research, published today in Frontiers in Computational Neuroscience, shows that these structures arise when a group of neurons forms a clique: each neuron connects to every other neuron in the group in a very specific way that generates a precise geometric object. The more neurons there are in a clique, the higher the dimension of the geometric object.

PR neuroscience news topology blue brain project markram

Topology in neuroscience: The image attempts to illustrate something that can not be imaged – a universe of multi-dimensional structures and spaces. On the left is a digital copy of a part of the neocortex, the most evolved part of the brain. On the right are shapes of different sizes and geometries in an attempt to represent structures ranging from 1D to 7D and beyond. The “black-hole” in the middle is used to symbolise a complex x of multi-dimensional spaces, or cavities. Courtesy of the Blue Brain Project

“We found a world that we had never imagined,” says neuroscientist Henry Markram, director of Blue Brain Project and professor at the EPFL in Lausanne, Switzerland, and co-founder and Editor-in-Chief of Frontiers, “there are tens of millions of these objects even in a small speck of the brain, up through seven dimensions. In some networks, we even found structures with up to eleven dimensions.”

Markram suggests this may explain why it has been so hard to understand the brain. “The mathematics usually applied to study networks cannot detect the high-dimensional structures and spaces that we now see clearly.”

If 4D worlds stretch our imagination, worlds with 5, 6 or more dimensions are too complex for most of us to comprehend. This is where algebraic topology comes in: a branch of mathematics that can describe systems with any number of dimensions. The mathematicians who brought algebraic topology to the study of brain networks in the Blue Brain Project were Kathryn Hess from EPFL and Ran Levi from Aberdeen University.

“Algebraic topology is like a telescope and microscope at the same time. It can zoom into networks to find hidden structures – the trees in the forest – and see the empty spaces – the clearings – all at the same time,” explains Hess.

In 2015, Blue Brain published the first digital copy of a piece of the neocortex — the most evolved part of the brain and the seat of our sensations, actions, and consciousness. In this latest research, using algebraic topology, multiple tests were performed on the virtual brain tissue to show that the multi-dimensional brain structures discovered could never be produced by chance. Experiments were then performed on real brain tissue in the Blue Brain’s wet lab in Lausanne confirming that the earlier discoveries in the virtual tissue are biologically relevant and also suggesting that the brain constantly rewires during development to build a network with as many high-dimensional structures as possible.

When the researchers presented the virtual brain tissue with a stimulus, cliques of progressively higher dimensions assembled momentarily to enclose high-dimensional holes, that the researchers refer to as cavities. “The appearance of high-dimensional cavities when the brain is processing information means that the neurons in the network react to stimuli in an extremely organized manner,” says Levi. “It is as if the brain reacts to a stimulus by building then razing a tower of multi-dimensional blocks, starting with rods (1D), then planks (2D), then cubes (3D), and then more complex geometries with 4D, 5D, etc. The progression of activity through the brain resembles a multi-dimensional sandcastle that materializes out of the sand and then disintegrates.”

The big question these researchers are asking now is whether the intricacy of tasks we can perform depends on the complexity of the multi-dimensional “sandcastles” the brain can build. Neuroscience has also been struggling to find where the brain stores its memories. “They may be ‘hiding’ in high-dimensional cavities,” Markram speculates.

Original research article: Cliques of Neurons Bound into Cavities Provide a Missing Link between Structure and Function

Citation: Reimann MW, Nolte M, Scolamiero M, Turner K, Perin R, Chindemi G, Dłotko P, Levi R, Hess K and Markram H (2017) Cliques of Neurons Bound into Cavities Provide a Missing Link between Structure and Function. Front. Comput. Neurosci. 11:48. doi: 10.3389/fncom.2017.00048

This research was funded by: ETH Domain for the Blue Brain Project (BBP) and the Laboratory of Neural Microcircuitry (LNMC); The Blue Brain Project’s IBM BlueGene/Q system, BlueBrain IV, funded by ETH Board and hosted at the Swiss National Supercomputing Center (CSCS); NCCR Synapsy grant of the Swiss National Science Foundation; GUDHI project, supported by an Advanced Investigator Grant of the European Research Council and hosted by INRIA.


Vortex Based Math

Marko Rodin has discovered the source of the non-decaying spin of the electron. Although scientists know that all electrons in the universe spin, they have never discovered the source of this spin. Rodin has. He has discovered the underpinning geometry of the universe, the fabric of time itself. He has done this by reducing all higher mathematics – calculus, geometry, scalar math – to discrete-number mathematics.

With the introduction of Vortex-Based Mathematics you will be able to see how energy is expressing itself mathematically. This math has no anomalies and shows the dimensional shape and function of the universe as being a toroid or donut-shaped black hole. This is the template for the universe and it is all within our base ten decimal system!

The potential scope and breadth of the Rodin Solution is staggering; it is universally applicable in mathematics, science, biology, medicine, genetics, astronomy, chemistry, physics and computer science. The Rodin Solution will revolutionize computer hardware by creating a crucial gap space, or equi-potential major groove, in processors. This gap space generates underpinning nested vortices resulting in far higher efficiency with no heat build-up. The Rodin Solution replaces the binary code with a new code called the binary triplet which will revolutionize computer operating systems. It will transform physics and astrophysics by finally answering how black holes and pulsars work. Space travel will be revolutionized by reactionless drives that are unaffected by the weight they pull, making the present day combustion engine obsolete. The revolution brought on by reactionless drives will far surpass the societal changes wrought by the shift from steam engines to the present day combustion engine. The Rodin Solution can even be applied to ending pollution and drought by creating an inexhaustible, nonpolluting energy source. Because Rodin´s Vortex-Based Mathematics enables him to condense a trillion-fold calculation to only a few integer steps and because he is able to solve all the mathematical enigmas, the Rodin Solution will revolutionize computer information compression.

Rudimentary versions of the Rodin Coil, or Rodin Torus, have been created and tested by leading scientists and are presently being used by the U.S. Government in antennas that protect the four corners of the continental U.S.. Life-saving medical devices based on crude approximations of the Rodin Coil Torus are being manufactured and used in the treatment of cancer patients. Microsoft´s former senior researcher is using the Rodin Coil to research, develop and patent new computer information-compression schemes.

Although many people are applying aspects of the Rodin Solution, on the basis of private consultations and a Rodin monograph published 20 years ago, Marko Rodin has never explained key concepts such as the phasing and energization of the Rodin Coil. Although there has been a virtual stampede to get at this work, Rodin has remained silent or uncooperative, preferring to continue his work and research in isolation. He is now ready to reveal publicly the true power and scope of the Rodin Solution.

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Dolphins And Math Skills


Dolphins May Be Math Geniuses

The brainy marine mammals could be far more skilled at math than was ever thought possible before.

By Jennifer Viegas
Tue Jul 17, 2012

  • Complex, nonlinear math appears to explain a primary dolphin hunting technique.
  • The math involves addition, subtraction, multiplication and ratio comparisons.
  • It is possible that dolphins possess remarkable inborn math skills.
bottlenose dolphins

Bottlenose dolphins swimming. Analysis of a dolphin hunting technique suggests the animals may be natural math geniuses.

Dolphins may use complex nonlinear mathematics when hunting, according to a new study that suggests these brainy marine mammals could be far more skilled at math than was ever thought possible before.

Inspiration for the new study, published in the latest Proceedings of the Royal Society A, came after lead author Tim Leighton watched an episode of the Discovery Channel’s “Blue Planet” series and saw dolphins blowing multiple tiny bubbles around prey as they hunted.

“I immediately got hooked, because I knew that no man-made sonar would be able to operate in such bubble water,” explained Leighton, a professor of ultrasonics and underwater acoustics at the University of Southampton, where he is also an associate dean.

“These dolphins were either ‘blinding’ their most spectacular sensory apparatus when hunting — which would be odd, though they still have sight to reply on — or they have a sonar that can do what human sonar cannot…Perhaps they have something amazing,” he added.

Leighton and colleagues Paul White and student Gim Hwa Chua set out to determine what the amazing ability might be. They started by modeling the types of echolocation pulses that dolphins emit. The researchers processed them using nonlinear mathematics instead of the standard way of processing sonar returns. The technique worked, and could explain how dolphins achieve hunting success with bubbles.

The math involved is complex. Essentially it relies upon sending out pulses that vary in amplitude. The first may have a value of 1 while the second is 1/3 that amplitude.

“So, provided the dolphin remembers what the ratios of the two pulses were, and can multiply the second echo by that and add the echoes together, it can make the fish ‘visible’ to its sonar,” Leighton told Discovery News. “This is detection enhancement.”

But that’s not all. There must be a second stage to the hunt.

NEWS: Dolphins, Humans Share ‘Brainy’ Genes

“Bubbles cause false alarms because they scatter strongly and a dolphin cannot afford to waste its energy chasing false alarms while the real fish escape,” Leighton explained.

The second stage then involves subtracting the echoes from one another, ensuring the echo of the second pulse is first multiplied by three. The process, in short, therefore first entails making the fish visible to sonar by addition. The fish is then made invisible by subtraction to confirm it is a true target.

In order to confirm that dolphins use such nonlinear mathematical processing, some questions must still be answered. For example, for this technique to work, dolphins would have to use a frequency when they enter bubbly water that is sufficiently low, permitting them to hear frequencies that are twice as high in pitch.

“Until measurements are taken of wild dolphin sonar as they hunt in bubbly water, these questions will remain unanswered,” Leighton said. “What we have shown is that it is not impossible to distinguish targets in bubbly water using the same sort of pulses that dolphins use.”

If replicated, the sonar model may prove to be a huge benefit to humans. It might be able to detect covert circuitry, such as bugging devices hidden in walls, stones or foliage. It could also dramatically improve detection of sea mines.

“Currently, the navy uses dolphins or divers feeling with their hands in such difficult conditions as near shore bubbly water, for example in the Gulf,” he said.

How Stuff Works: Dolphins

In terms of dolphin math skills, prior studies conducted by the Dolphin Research Cetner in Florida have already determined that dolphins grasp various numerical concepts, such as recognizing and representing numerical values on an ordinal scale. Marine biologist Laela Sayigh of the Woods Hole Oceanographic Institution said, “In the wild, it would be very useful (for dolphins) to keep track of which areas were richer food sources.”

While dolphins are among the animal kingdom’s most intelligent animals, they are not likely the only math champs.

Parrots, chimpanzees and even pigeons have been shown to have an advanced understanding of numerical concepts. The studies together indicate that math ability is inborn in many species, with number sense, mathematical skills and verbal ability perhaps being separate talents in humans that we later learn to combine.



3.14 — Happy Pi Day

Happy Pi Day! Why Geeks Celebrate 3.14…

LiveScience Staff
Date: 14 March 2012 Time: 02:22 PM ET
Pi, the mathmatical constant, is a never-ending irrational number.
Pi, the mathmatical constant, is a never-ending irrational number.
CREDIT: bbbar | Shutterstock

If you’re celebrating Pi Day today (March 14), then you’re a certified math geek or physics geek or maybe even a tech geek. If you’re just an outside observer, we thought you might like to know why all the hubbub over 3.1415926535 … well, that could go on forever, so …

On Pi Day, pi enthusiasts wear clothing adorned with the pi symbol, eat pie, and even throw pi-related parties.

March 14 is chosen as the day to celebrate pi, because the numerical date, 3/14, represents the first 3 digits of pi. Hardcore Pi Day celebrants are planning special events for 9:26:53 a.m. on March 14, 2015, as the numerical date 3/14/15 9:26:53 represents the first 7 digits of pi, 3.141592653.

The concept of pi is important to mathematics because of its relationship to the circle; it is a constant representing the ratio of a circle’s circumference to its diameter. Since pi is found in so many different equations in math, physics and other sciences, it is considered one of the most important mathematical constants.

Pi is an irrational transcendental number, meaning that its decimal places will continue to infinity. It cannot be represented using decimal notation or a rational fraction. As such, 3.14 is not pi, but simply an easy notation for the first 3 places. Even the common use of 22/7 for pi is not exact. To date, pi has been calculated out to more than 1 trillion decimal places, and mathematicians continue to calculate further digits.

Pi Day was started at the Exploratorium, a San Francisco-based science museum known for its interactive exhibits, by staff physicist Larry Shaw in 1988. Staff and visitors celebrated the day by holding a circular parade and then eating fruit pies. The Exploratorium continues to hold an annual Pi Day Celebration, which has gotten larger each year. In 2012, the celebration expanded to the Internet, with both a webcast and a Second Life-based event.

It was in 2009 that Pi Day became a national event, with official recognition from theHouse of Representatives through Resolution 224. The hope is that official recognition of Pi Day will help to increase interest in math and science among the American public. Schools are urged to use the day to teach their students about the importance of pi and other mathematical concepts.

Fun celebrations for Pi Day have the somewhat pie-in-the-sky goal of showing students that learning about math and science doesn’t have to be boring. Interestingly, however, some mathematicians want to say goodbye to pi.



Archaeogeodesy can be defined as that area of study encompassing prehistoric and ancient place determination, navigation (on land or water), point positioning, measure and representation of the earth, geodynamic phenomena, and the applied astronomy. Archaeogeodesy, by combining fundamental astronomy, geodetic knowledge, applied mathematics, accurate positional data and archaeology, presents a methodology for investigating the architecture, placements, spatial properties, relationships and arrangements of prehistoric sites and monuments. As a new area of inquiry, archaeogeodesy presents unique avenues of assessing ancient understandings of geography, of place, and of the earth and the cosmos as evidenced by archaeological remains.

Miamisburg Mound, Ohio

We generally regard temporally, spatially and culturally diverse ancient monuments as unrelated. The many pyramids of Egypt, whether stepped, bent, or true, have interrelationships, however understudied. What of the other pyramids and similar mounds dispersed the world over? Few would argue no relationship between neighboring earthworks in North America, for example, yet their similarities to Neolithic mounds and circular embankments of the British Isles go relatively unnoticed. Visitors to Stonehenge and other stone circles who notice surrounding earthworks are unlikely to postulate connections, spatial or functional, to similar earthen monuments in distant Ohio because of an intervening ocean.

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The Math of Basketball

The Mathematics of Basketball

by Ron Cowen on 2 August 2011, 1:04 PM |

To shoot, or not to shoot, that is the question. Whether ’tis nobler to try to score right away or wait for a better chance.

Professional basketball players face that quandary multiple times in every game. And in an article posted at on 29 July, Brian Skinner, a graduate student in theoretical physics at the University of Minnesota, Twin Cities, provides some mathematical guidance for the best time to take aim.

Skinner, an avid basketball fan, was inspired to analyze the game when he heard a talk at an American Physical Society meeting in 2007 on the flow of traffic. Every driver tries to minimize his or her commuting time rather than reduce the average travel time of all drivers, resulting in a paradoxical situation: Closing a road may actually reduce congestion by forcing drivers to take a route many had avoided, speeding up the average commute.

That paradox reminded Skinner of the Patrick Ewing theory in basketball, named after the high-scoring player for the New York Knicks. Analysts had noticed that in games from which Ewing or other big scorers on a team were absent, that team was more likely to win. In addition, the diagrams and flow of players in basketball also resembled the traffic models Skinner had seen.

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Origins of “X”

Why Is ‘X’ Used to Represent the Unknown?

By Life’s Little Mysteries Staff
08 July 2011 1:36 PM ET

In algebra, the letter ‘x’ is often used to represent an unknown quantity or variable. Similarly, in English, x represents the unknown, as in X-rays, which baffled their discoverer, and Malcolm X, who chose the symbol to represent the forgotten name of his African ancestors.

This meaning of the letter x traces back to the Arabic word for “thing,” or šay’. In ancient texts, such as Al-Jabr, a manuscript written in Baghdad in 820 A.D. that established the rules of algebra, mathematical variables were called things. (An equation might read “three things equal 15,” for example — the thing being five.)

When Al-Jabr was later translated into Old Spanish, the word šay’ was written as “xei.” This soon came to be abbreviated as x.

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