Scientists have discovered an entirely new shape and it is all over you!

It turns out that your skin cells employ a shape previously unknown to both biologists and mathematicians...

Science Alert: Scientists Have Discovered an Entirely New Shape, And It Was Hiding in Your Cells

Gizmodo: The 'Scutoid' Is Geometry's Newest Shape, and It Could Be All Over Your Body


The original research article: 

Scutoids are a geometrical solution to three-dimensional packing of epithelia

The 'scutoid' shape (d) was named in homage to the scutellum 

 – a posterior portion of the thorax in some insects, which resembles the same mini-triangle shape (e)...  
Some fun and educational videos about scutoids...

The STEMulus Network: NEW SHAPE DISCOVERED...

 Brand new 'scutoid' shape discovered by scientists in skin cells...

How Living Cells Work Solved by Mathematics?

Queensland University of Technology (QUT) researcher Dr. Robyn Araujo has developed new mathematics to solve a longstanding mystery of how the incredibly complex biological networks within cells can adapt and reset themselves after exposure to a new stimulus.

 Physics.Org Article:  Math sheds light on how living cells 'think'

Cosmos Magazine:  Maths researchers find the rules that govern how cells work

Dr. Robyn Araujo's Research Paper in Nature Communications (2018)

Abstract :  Robustness, and the ability to function and thrive amid changing and unfavorable environments, is a fundamental requirement for living systems. Until now it has been an open question how large and complex biological networks can exhibit robust behaviors, such as perfect adaptation to a variable stimulus, since complexity is generally associated with fragility. Here we report that all networks that exhibit robust perfect adaptation (RPA) to a persistent change in stimulus are decomposable into well-defined modules, of which there exist two distinct classes. These two modular classes represent a topological basis for all RPA-capable networks, and generate the full set of topological realizations of the internal model principle for RPA in complex, self-organizing, evolvable bionetworks. This unexpected result supports the notion that evolutionary processes are empowered by simple and scalable modular design principles that promote robust performance no matter how large or complex the underlying networks become.  

M-theory, Strings and the Theory of Everything Including Edward Witten

Einstein and Maxwell were fortunate to find the mathematics they needed already available.  When Newton developed his Theory of Gravitation, the mathematics he needed had not been developed, so he invented Calculus.  Likewise when Edward Witten began his work on String Theory and M-Theory he had to do pioneering work on many of the mathematical tools required and is the only physicist to win the top award in Mathematics:  the Fields Medal.  Here is the official Fields citation of his mathematical achievments:

Stephen Hawking in his book The Grand Design co-authored with Leonard Mlodinow notes that:

M-theory is the most general supersymmetric theory of gravity. For these reasons M-theory is the only candidate for a complete theory of the universe.

Read Natalie Wolchover's articles from Quanta Magazine:

Why Is M-Theory the Leading Candidate 

for Theory of Everything?

Edward Witten - A Physicist’s Physicist Ponders 

the Nature of Reality 

Ed Witten - Mystery Theory ('Big Ideas' Interview)

Edward Witten: String Theory and the Universe

Futurism Magazine's Mind Blowing Theories About the Universe

Scientific American: The Elusive Theory of Everything

Ancient DNA shaking up our knowledge of the past

The use of DNA analysis is overturning a lot of cherished ideas dug up by archeologists...

Ancient DNA Tells Tales of Humans’ Migratory History 

Excellent summary of ancient DNA research:

Ancient DNA: the first three decades

Genes of ‘extinct’ Caribbean islanders found in living people

Jorge Estevez and other members of the Higuayagua Taino community dance at a festival in New York City. Taino groups have fought against the idea that indigenous Caribbean islanders died out after European contact.

Ancient DNA analysis reveals Minoan and Mycenaean origins

On islands in the Gulf of Alaska, ground squirrels are not a recent, human-mediated introduction (as previously thought) and may have colonized via a natural dispersal event or an ancient human translocation:

 Integrating archaeology and ancient DNA analysis to address invasive species colonization in the Gulf of Alaska

Evidence of human use of ground squirrels on Chirikof Island, Alaska: (a) parka created by Susan Malutin, Grace Harrod, and community volunteers for the Alutiiq Museum in 1999, with support from the Alaska State Museum grant-in-aid program (catalog number AM405; photo by Marnie Leist); (b) skeletal elements showing cut marks across the occipital condyle of the cranium; and (c) burning and calcification seen on a proximal femur, distal humerus, and proximal ulna.

Quon: New Mathematical Picture Language

From the time of Euclid, pictures have been an important part of mathematics.  We get a better understanding of complex numbers and their mind-bending equations by picturing them in terms of vectors and graphs:

Non-Euclidean Geometry is best explained in terms of Euclidean models:

"A picture is worth 1,000 symbols,” quips Professor Arthur Jaffe. Jaffe and postdoctoral fellow Zhengwei Liu have developed a pictorial mathematical language that can convey pages of algebraic equations in a single 3-D drawing:

Harvard Gazette: Picture-perfect approach to science 

Pictorial laws appear to unify ideas from disparate, interdisciplinary fields of knowledge, linking them beautifully like elements of a da Vinci painting. The group is working to expand the pictorial mathematical language first outlined last year by Arthur Jaffe, the Landon T. Clay Professor of Mathematics and Theoretical Science, and postdoctoral fellow Zhengwei Liu:

Here is the ground breaking paper by Arthur Jaffe, the Landon T. Clay Professor of Mathematics and Theoretical Science, and postdoctoral fellow Zhengwei Liu:

 Mathematical picture language program

Further helpful information:

Harvard Gazette:  Making Math More Lego-like 

New Scientist: The New Language of Mathematics

Math Now Has a 3D Language

Index of Past Posts Arranged by Subject Area

Here is an expanded index of past posts. We are always revisiting and revising these posts, seeking to add more information on each subject:

Posts Sorted by Subject

Great Horned Frogs! Beelzebufo was One Tough Amphibian	Amphibians
Apes: We Know Less Than We Think about Them	Apes
Wild Gorillas Compose Happy Songs - New Scientist	Apes, Music
Ancient DNA shaking up our knowledge of the past	Archaeology and DNA
Laser Light Imaging, Detection, And Ranging Technology or "LIDAR" Revolutionizing Archaeology	Archaeology and Lasers
The Amazing Antikythera Mechanism	Archaeology and Astronomy
The Three Body Problem	Astronomy
Just Passing Through	Astronomy
Gravitational waves from a binary black hole merger observed by three detectors in a landmark collaboration	Astronomy
Are we are all from a galaxy far, far away?	Astronomy
TRAPPIST-1 Planetary System	Astronomy
Hubble 25: A Quarter-Century of Discovery with the Hubble Space Telescope	Astronomy
Wheels Within Wheels	Astronomy
Origin of Elements in the Solar System	Astronomy
Observable Universe in a Single Image	Astronomy
Scientists have discovered an entirely new shape and it is all over you!	Biology, Mathematics
How Living Cells Work Solved by Mathematics?	Biology, Mathematics
Birds of Prey: Introduction to Raptors	Birds
Birds of Prey: The Osprey	Birds
Birds of Prey: Owls	Birds
Birds of Prey: Haast's Eagle	Birds
Birds of Prey: Great Nicobar Serpent Eagle	Birds
Birds of Prey: Steller's Sea Eagle	Birds
Birds of Prey: Eagle on Stilts	Birds
Birds of Prey: Gyrfalcon	Birds
Birds of Prey: White-Tailed Eagle	Birds
Brain Gym	Brain
Reduce Dementia Risk by Nearly 30%?	Brain
Restoring Consciousness Even After Many Years in a Vegetative State	Brain
Unexpected Source for the Brain's Development	Brain
Reasons for Left or Right-Handedness	Brain
DIGI-COMP I COMPUTER	Computers
Lost Continent of Zealandia	Earth Science
Timeline of the Far Future	Ecology
Open Courses offered by Universities	Education
Pioneering Physics Show The Mechanical Universe Now on YouTube	Education
Potential Source of Clean, Limitless Energy?	Energy
Producing Energy From Evaporating Water	Energy
Interactive Human Evolution Timeline	Evolution
The Great Lake Huron Rock Puzzle	Geology
Meanwhile back in Labrador, four billion years ago...	Geology
Top Ten Websites for Science	Internet
The Cambridge University Effect and its Scrambled History	Language and Spelling
Rocks Rolling Downhill	Life Sciences
Secret Life of Dolphins	Marine Life
Ruby Seadragons Found in the Wild	Marine Life
The Amazing and Mysterious Octopus	Marine Life
The Legendary Giant Squid	Marine Life
The Vampire Squid From Hell	Marine Life
2017 American Samoa Expedition	Marine Science
Quon: New Mathematical Picture Language	Mathematics
In Addition to Monstrous Moonshine, There are 23 Other Moonshines!	Mathematics
Mathematicians Tame Rogue Waves	Mathematics
Babylonians beat Greeks to the Invention of Trigonometry	Mathematics
Mathematics of Islamic Tiling Patterns	Mathematics
IMAGINARY NUMBERS SAVE LIVES AT SEA!	Mathematics
Hexaflexagons, Dodecaflexagons and Beyond!	Mathematics
Zika's Cancer Fighting Potential	Medical Research
Ben Franklin's Amazing Musical Instrument	Music and Inventions
Ouch! U of T paleontologists identify 508-million-year-old sea creature with can opener-like pincers	Paleontology
Great great great great grandpa?	Paleontology
Are You Living In a Computer Simulation?	Philosophy
Is the Human Mind Bound to the Physical World?	Philosophy, Brain
Light Invisible: Exploring the Electromagnetic Spectrum	Physics
Fascinating Science of the Trebuchet	Physics
Einstein's Relativity better than Quantum Mechanics at Explaining Berkelium Behavior	Physics
Holographic Principle and Stereograms	Physics
Map of Physics by Dominic Walliman	Physics
Topology and Physics	Physics, Mathematics
M-theory, Strings and the Theory of Everything Including Edward Witten	Physics, Mathematics
Algebraic Topology finds an application in neuroscience	Physics, Mathematics
Ten Equations that Changed the World	Physics, Mathematics
Game Show or Monty Hall Problem	Probability and Statistics
Titanoboa the Super Serpent	Reptiles
Engineers Build Robot Drone That Mimics Bat Flight	Robotics
Best Websites for Learning Science	Science in General
Cassini’s First Grand Finale Dive	Space
NASA Image and Video Library	Space
Journey to Jupiter	Space
Nasa's Eyes: An Immersive Space Exploration	Space
Best Full Disk view of Earth	Space

Laser Light Imaging, Detection, And Ranging Technology or "LIDAR" Revolutionizing Archaeology

"Lidar is revolutionising archaeology the way the Hubble Space Telescope revolutionised astronomy," Francisco Estrada-Belli, a Tulane University archaeologist, told National Geographic.

LASER SCANS REVEAL MAYA “MEGALOPOLIS” 

BELOW GUATEMALAN JUNGLE 

 "Using a revolutionary technology known as LiDAR (short for 'Light Detection And Ranging'), scholars digitally removed the tree canopy from aerial images of the now-unpopulated landscape, revealing the ruins of a sprawling pre-Columbian civilization that was far more complex and interconnected than most Maya specialists had supposed."

BBC News Report: Sprawling Maya network discovered 

under Guatemala jungle 

How Does Lidar Work?  This NEON Science video overviews what lidar or light detection and ranging is, how it works and what types of information it can provide. The video was produced by the National Ecological Observatory Network - a non profit project devoted to open science and open data:

 Meanwhile in Cambodia...

Beyond Angkor: How lasers revealed a lost city 

And in the UK:  Archaeologists have discovered more than 3,000 historical sites and monuments in the New Forest thanks to Lidar (Light Detecting and Ranging). The technique beams harmless lasers into the ground to build a 3D map, revealing the hidden history of the New Forest including a Roman road: 

 This short film shows the landscape around Stonehenge as recorded by LIDAR survey (airborne 3D scanning). Millions of measurements were taken across the landscape, and here they have been turned into a 'solid' computer model to show how well the archaeology is recorded by this method:

A website set up by the US Geological Survey and  intended to "facilitate data access, user coordination and education of lidar remote sensing for scientific needs":

 USGS Center for LIDAR Information Coordination and Knowledge 

Lidar Industry News and Education 

Game Show or Monty Hall Problem

Many consider probability to be just calculations based on common sense, but the Monty Hall problem is a clear example of how even a simple problem can have a counter-intuitive solution:

Game Show or Monty Hall Problem

  
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

 In 1990 Marilyn Vos Savant had this problem sent in to her "Ask Marilyn" column for Parade magazine.  The problem is easy to state but the answer Marilyn provided was counter-intuitive and unleashed a storm of controversy...

Marilyn Vos Savant and the Game Show Problem

The Numberphile Channel 

provides a good video summary of the problem and its solution:

The  University of California Math Website provides a detailed explanation of the problem as well as information on its history:

The Monty Hall Problem