The Great Lake Huron Rock Puzzle

 

As a boy, I found this chunk of limestone on the shoreline of southern Lake Huron, Canada near the town of Goderich:

The rock is 23 cm (9 in) long, 13 cm (5 in) high and weighs 6 kg (14 lbs).  Rounded and smoothed then split into eight pieces by the forces of nature:

I had been looking for fossils, but was intrigued by this piece of limestone that natural forces had split into eight pieces, making it into a challenging 3D puzzle.  The trick is to find the flat base and build up from there, otherwise the rock will not hold together!

 Here is the step by step assembly of the rock puzzle:

 

 

 

Length:  9 inches (23 cm)  Height:  5 inches (13 cm)

Weight: 14 lbs (6 kg)

A video of the assembly:

DIGI-COMP 1 Computer

The DIGI-COMP 1 was the first computer I owned -- a working mechanical computer to assemble and experiment with.  It came with an excellent manual that was a computer education in itself.

There is an excellent video on the DIGI-COMP 1:

The wonderful RETROCMP site for restoration of classic computers has an excellent and comprehensive page on the DIGI-COMP 1:

DIGI-COMP 1 - introduction

Here is a link to the excellent instructional manual that came with the computer (and is useful if you want to use the emulation shown below):

DIGI-COMP 1 INSTRUCTION MANUAL

Here is a link to the parts list and assembly instructions:

DIGI-COMP 1 PARTS LIST AND ASSEMBLY INSTRUCTIONS

Two DIGI-COMP enthusiasts Larry Groebe and Kevin Williams created an excellent working emulation in javascript:

DIGI-COMP 1 - EMULATOR

A fun unboxing video of a vintage Sixties DIGI-COMP 1

The Three Body Problem

From: Movies of the Periodic Planar Collisionless Three-Body Orbits

Predicting eclipses was important to many ancient peoples and involved trying to understand the combined motions of three celestial bodies:  the sun, the earth and the moon.  This was the beginning of the the famous Three Body Problem that received its modern scientific formulation in Newton's Principia (Book 1 - Proposition 66):

 Let three bodies—whose forces decrease as the squares of the distances—attract one another, and let the accelerative attractions of any two toward the third be to each other inversely as the squares of the distances...

You can study this proposition in the Motte translation of Newton's Principia at the Internet Archives:

Principia:  Book 1, Propostion 66 

  

Newton wrote to Edmond Halley that the theory of the motions of the moon made his head ache and kept him awake so often that he would think of it no more, but this problem was now out there to tantalize mathematicians and astronomical physicists.  Others soon wanted to solve the more general three body problem and also came up against intractable difficulties and complications that finally led the great mathematician Henri Poincare to conclude that even varying the initial conditions of the three bodies in the very smallest ways would lead to vastly different results.  This led to the development of Chaos Theory, the popular example of which is the idea of flapping butterfly's wings in one place leading to a tornado in another place.

Solving the Three Body Problem - hosted and written by Matt O'Dowd (PBS Space Time Series)

Though many great mathematicians could not solve the three body problem, they did make progress by finding more and more examples of  stable, periodic orbit configurations.



Leonard Euler the great 18th century mathematician began this trend by finding periodic solutions where the three bodies are collinear, or in a row or straight line:

 

Lagrange continued this trend by finding stable configurations when the three bodies are configured at the vertices of an equilateral triangle.

In 1993, a solution with three equal masses moving around a figure-eight shape was discovered by physicist Cris Moore at the Santa Fe Institute:
 

Today, physicists and mathematicians continue to search for and find further special case solutions:

 

Physicists Discover a Whopping 13 New Solutions to Three-Body Problem 

The Institute of Physics Belgrade has a great website for exploring these solutions: 

THREE-BODY GALLERY 

 Institute of Physics Belgrade

A good example from this gallery shows how the figure-eight configuration of Cris Moore is mapped onto the shape sphere:

Figure-Eight Configuration and Shape Sphere Version

 

The shape sphere provides a kind of condensed version of the orbits.  

For example, try to image if we had to represent numbers just as a bunch of dots.  Works well for low numbers, but is totally unwieldy and confusing for large numbers.  So the decimal system was developed as a condensed representation for numbers, and it is a system that itself reveals a lot more about a number than a bunch of dots ever could!  

Likewise shape sphere representations of stable three body configurations give us some help in dividing these configurations into families. 

The three red dots on the equator of a shape sphere represent the three possible collision points:  body 1 with 2, body 2 with 3 and body 3 with 1.  Needless to say all stable three body configurations will studiously avoid these three points!

As a side light: the shape sphere was first mentioned in James Joyce's novel Finnegans Wake (p. 295) where we see:  "As Great Shapesphere Puns it."   You can view this page of the Wake at the Internet Archives:

Finnegans Wake Page 295

 In 2017 XiaoMing Li and ShiJun Liao (at Shanghai Jiaotong University, China) used a supercomputer to hit the three body jackpot:

Scientists discover more than 600 new periodic orbits of the famous three-body problem

Many of these periodic three body orbits are stunningly beautiful and mesmerizing to see in action, and you can now watch animated gifs of them in all their glory:

Movies of the Periodic Planar Collisionless Three-Body Orbits in Real Space or on Shape Sphere 

Here are a few examples from the above set:

The orbit lines for the example below (and many others) seem to present a 3-D diagram, but this is an illusion!  The orbit paths are all in fact on a flat plane.

Birds of Prey: White-Tailed Eagle

This picture comes from the websiteof the Governor of Volgograd Oblast

The White-tailed Eagle from Scotland and Northern Europe is considered to have one of the largest average wing spans among living eagles:  about 7 feet (218 cm). X Recorded wing spans go up to 8 feet (253 cm)

  

DinoAnimals Top Ten Eagles Page

 

The Ebird website has an excellent page on the white-tailed eagle with many other links and videos:

 

                         Ebird:  White-tailed Eagle

The White-tailed Eagle from Elite Falconry  has captured some stunning flight videos:

Flying over the west coast of the Orkney Islands in March 2018.

Elite Falconry's White Tailed Eagle flies with Ospreys over Loch Moy

 

White Tailed Eagle Captures amazing footage of Ayrshire

 

White Tailed Sea Eagle captures amazing footage of Mar Lodge Estate.

White Tailed Eagle Over Fife

Over the Dolomites in Italy
 

Or take an exciting flight with...

Victor Over the Alps!

The Vampire Squid from Hell

Yes, it is Vampyroteuthis Infernalis which translates to "Vampire Squid from Hell". When threatened, the Vampire Squid can literally turn itself inside out to reveal a defensive set of threatening spikes as seen in this gif made by Meme Guy from a Monterey Bay Aquarium Research Institute video:

Bruce Robison, the resident expert on Vampire Squids at the Monterey Bay Aquarium Research Institute (MBARI) gives us a good introduction to this fascinating creature in this video produced by the Science Friday YouTube Channel:

The Animals Network has put together a concise page of what is currently known about this mysterious denizen of the deepest depths - as far as 3,000 ft. below sea level and more!

Animals Network: Vampire Squid

For years marine biologists have puzzled over what the mysterious vampire squid eats. Recent research by Henk-Jan Hoving and Bruce Robison at the Monterey Bay Aquarium Research Institute (MBARI) finally reveals the answer. These deep-sea creatures use long, retractile filaments to passively harvest particles and aggregates of detritus, or marine snow, sinking from the waters above. This feeding strategy, unknown in any other cephalopod (this group of animals includes squid and octopods), allows vampire squid to thrive in the oxygen minimum zone where there are few predators but marine detritus is abundant:

 MBARI:  What the Vampire Squid Really Eats

On the Smithsonian Ocean Portal family tree of cephalopods you can see the Vampire Squid has its own unique branch:

Smithsonian Ocean: Cephalopods

One of the most fascinating and comprehensive web pages on the vampire squid is provided by the Tree of Life Web Project:

Tree of Life Web Project: The Vampire Squid

Nautilus Live had an exciting close encounter with a vampire squid:

 Almost a mile deep off Socorro Island, we had an extended visit with a Vampyroteuthis infernalis--literally meaning "vampire squid from hell." Neither squid nor octopus, this fierce-sounding cephalopod actually reels in specks of marine snow using two retractable filaments and mucus-covered suckers! 

This close encounter was captured with both our normal ROV Hercules HD camera and a low light camera for bioluminescence designed by Dr. Brennan Phillips at University of Rhode Island's Graduate School of Oceanography and David Gruber at the City College of New York/Baruch College.

Close Encounter With a Vampire Squid 

 

 

The Legendary Giant Squid

The giant squid emerges from the realm of myth and legend as the fearsome KRAKEN:

 
It is only recently that live giant squids were filmed:

Giant Squid Caught on Tape for First Time for Discovery Channel's  

Monster Squid: The Giant Is Real

Washington Post June 23, 2019: 
Scientists captured video of a giant squid

The giant squid is an invertebrate (spineless creature) and is the largest member of the Cephalopod family.  The amazing Smithsonian Ocean website provides a family tree as well lots of other fascinating information about cephalopods:

Smithsonian Ocean: Cephalopods

The cephalopods are a diverse class of mollusks. Today, scientists divide the living cephalopods into three groups, called superorders. Many details of cephalopod evolutionary classification continue to change as scientists find new clues from genetic testing and newly discovered fossils. (Created by Ashley Gallagher for the Ocean Portal)

The Smithsonian Ocean Portal also provides a fascinating and informative page on the giant squid:

 The Giant Squid

 

This female giant squid is the larger of two on display in the Smithsonian's Sant Ocean Hall. (Don Hurlbert/Smithsonian Institution

The Museum of New Zealand - Te Papa Tongarewa provides a great page on...

The difference between colossal squid, giant squid, and octopus 

Mental Floss provides...

20 Freaky Facts About the Giant Squid 

The Amazing and Mysterious Octopus

An octopus in an aquarium in Brest, France. The animals are highly intelligent, but researchers are uncertain how the trait evolved. CreditCreditFred Tanneau/Agence France-Presse — Getty Images

The octopus is an invertebrate (spineless creature) and belongs to the Cephalopod family.  The amazing Smithsonian Ocean Portal provides a family tree as well lots of other fascinating information about cephalopods:

Smithsonian Ocean: Cephalopods

The cephalopods are a diverse class of mollusks. Today, scientists divide the living cephalopods into three groups, called superorders. Many details of cephalopod evolutionary classification continue to change as scientists find new clues from genetic testing and newly discovered fossils. (Created by Ashley Gallagher for the Ocean Portal)

Cephalopods have been around for a VERY long time and have been among the dominant large predators in the ocean before they became every animals favorite dish.  The Earth Archives provides a good look at...

500 Million Years of Cephalopod Fossils

Animalogic provides a good introduction to the octopus as well as explaining what makes them...

The World’s Greatest Escape Artists

W

10 reasons why the octopus is one of the most incredible creatures in the sea:

The National Aquarium provides this helpful infographic:

  

The octopus makes a good mother as reported by Pang Quong:   In Port Phillip Bay during October, one of our small octopus(Octopus pallidus) lay their eggs in small caves ,bottle or old tyres. The female stays with her eggs until they all hatch. Over about 3 weeks I checked the progress of one female and her eggs:

It was long assumed that the octopus was a solitary, antisocial creature, until the recent discovery of two octopus "cities":  Octlantis and Octopolis:

 Octlantis is a just-discovered underwater city engineered by octopuses

The gloomy octopus, lonely no more in Octlantis.

Why octopuses are building small “cities” off the coast of Australia

A map of Octlantis, the second settlement of gloomy octopuses found off the coast of Australia. About 10 to 15 octopuses live here, in mounds of shells that have been constructed over generations.

'Octlantis': Bustling Octopus Community Discovered Off Australia

One of the most comprehensive web pages on the octopus can be found at ourmarinespecies.com:

Octopuses: Characteristics, habitats, reproduction and more

The Daily Catch: An Octopus has 3 Hearts, 9 Brains & Blue Blood


The nine brains of the octopus all add up to a considerable intelligence:

New York Times: Yes, the Octopus Is Smart as Heck. But Why?

 Coconut Carrying Octopus

Scientific American: The Mind of an Octopus 

Credit: HENRIK SORENSEN Getty Images

The New Yorker: Why Not Eat Octopus?


And one (or rather eight!) of the most fascinating things about the octopus:  their tentacles, each one of which has its own mini-brain!

Credit:  Kelly Murphy Illustration

Sputnick News: Octopus’ All-Mighty Tentacles May Shed Light on Extra-Terrestrial Life 

Researchers model how octopus arms make decisions 

Cosmos: How the octopus got its smarts

Visit our other two octopus posts:  The Legendary Giant Squid
The Vampire Squid From Hell