Merry Christmas from Dodecahedron Books

Merry Christmas, and here are a few free Christmas related stories to enjoy:

A Christmas Miracle at the Lake

Here's a heart warming Christmas tale, by Helena Puumala. It follows the characters in her "at the lake" stories, as they spend Christmas at the snowed in confines of their summer cottages, where something wonderful happens on Christmas Eve.

U.S.: https://www.amazon.com/dp/B00RAWMO32

U.K: https://www.amazon.co.uk/dp/B00RAWMO32

Canada: https://www.amazon.ca/dp/B00RAWMO32 

Three Holiday Stories, Plus One

In the Western World, three holidays dominate the imagination - Christmas, Easter and Halloween. They occur at critical times of the year, mid-Winter, Spring and late Autumn, and deal with the very deep issues of life, death and new life (or continuing life). These stories pick up on those themes, via several families who grapple with strange events and their spiritual and paranormal significance, though the ordering is a bit different than the conventional one.

The first story is set at Halloween and details a young girls awakening knowledge of her paranormal and spiritual energies. The next story is set at Easter and introduces religious and ethical tensions, and the promise of rebirth. The last story is set at Christmas, and deals with the theme of how life can overcome death, and forgiveness and acceptance can overcome bigotry. A bonus story also deals with the life and death issues. especially how different people deal with grief.

U.S.: https://www.amazon.com/dp/B06Y4T5CFW

U.K: https://www.amazon.co.uk/dp/B06Y4T5CFW 

Canada: https://www.amazon.ca/dp/B06Y4T5CFW

 

Miranda and the Christmas Elf 

The little pre-school girl, Miranda, is feeling unsafe because of bullies in the neighbourhood and family troubles between her mother and father. Can her friend, young elementary grade age Nathan, use his special powers to call on the North Pole for some Christmas Eve magic, to help her out?

The story is a heartwarming Christmas tale, suitable for children and adults, which will bring a little Christmas magic to us all. It is about 9000 words, or around an hour or so, at typical reading speeds.

U.S.: https://www.amazon.com/dp/B019MCY3RM

U.K.: https://www.amazon.co.uk/dp/B019MCY3RM

Canada: https://www.amazon.ca/dp/B019MCY3RM

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Strictly speaking, the next ones aren't Christmas themes, but they are great stories for kids, and therefore nice virtual stocking stuffers, for your little ones.  Reading a story to (or with) your child on Christmas Day is a great way to bond, and to create wonderful memories for the future.

Nathan’s Adventure In the Other-Other Land: A Children’s Story: Book 1 - To Rescue a Princess

Young Nathan discovers some new playmates in the Other-Other Land, a wonderful, magical world that exists behind the Magic Mirror. But disaster strikes, and Nathan must help Prince Roland rescue his sister, the Princess Pepper, from the clutches of the Black Flying Dragon of the Dark Mountain.

But the rescue will not be easy. There are said to be many fearsome obstacles along the way, including treacherous quicksand swamps, complete with monsters, poisonous mushrooms that can walk and jump and that hate people, and ferocious bands of roaming tigers. And then, there is the dragon and his minions to contend with.

Will Nathan and Roland (with the aid of their trusty ponies) outwit their enemies and overcome the many dangers of the journey to the Dark Mountain? Can they save the feisty Princess Pepper? Come along for the ride and find out for yourself.

The story is about 10,000 words, a suitable length for an elementary grade child to read in an hour or two. It can also be read to a younger child over a few bed-times. There are 15 short chapters with 15 original hand-drawn pictures to go along with them. Note that the writing includes some humorous passages that parents and older readers will enjoy.

The book is available from Amazon in both e-book and print versions.

https://www.amazon.com/dp/B00PHAEFLS

https://www.amazon.co.uk/dp/B00PHAEFLS

 https://www.amazon.ca/dp/B00PHAEFLS

Nathan's Adventure in the Other-Other Land, A Children's Story: Book 2 - To Defeat the Wizard's Curse

Young Nathan, a resident of our everyday world, is called back to the Other-Other Land, beyond the Magic Mirror, for another adventure. On this occasion he must aid the Princess Pepper in her efforts to overcome a drought that is slowly making the Other -Other Land barren, and leaving its people at risk of famine. She is sure that it is the result of a curse by an evil Wizard, who is in cahoots with the Kingdom’s enemy, The Terrible Bing. She, Nathan and his cousin Scott, must travel far to discover the source, and hopefully lift the curse, perhaps with the help of the Princess’s long-lost mother. Many dangers lurk along the way – evil Wizards don’t take kindly to children tampering with their nasty schemes.

https://www.amazon.com/dp/B01N5ERZMJ

https://www.amazon.co.uk/dp/B01N5ERZMJ

https://www.amazon.ca/dp/B01N5ERZMJ

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And if you enjoyed Helena Puumala's short fiction, try her longer Science Fiction and Romance series, Kati of Terra and The Witches' Stones.  Both are on Kindle Unlimited, and The Witches' Stones books are on special  Kindle Countdown from Dec 26 to 29. 

Kati of Terra Book One - Escape from the Drowned Planet

https://www.amazon.com/dp/B00811WVXO

https://www.amazon.co.uk/dp/B00811WVXO

https://www.amazon.ca/dp/B00811WVXO

 In saving her small son from alien abductors, a 24-year-old Earth woman, Katie, finds herself abducted instead. She awakens from a drug-induced coma on a spaceship, in a room full of children, both human and alien, and two other women, younger than she is. The young women adapt to the situation as best they can, keeping the youngsters calm and entertained. But, when a drugged alien man wearing a uniform is added to the captive cargo, it becomes clear that this is an intergalactic slave operation.

The slave traders implant their captives with “translation nodes” in order to allow communication among various groups. These are living entities, normally docile, merely enhancing certain brain functions, such as language acquisition. However, Katie discovers that she has accidentally received a very special “granda node”, a long-lived node with its own cantankerous personality, including a fondness for criminality and lethal weaponry. Fortunately for Katie, it also values its freedom. With its help, she escapes on a fringe planet, dragging the peace officer along—also at the granda’s suggestion.

She finds herself on a strange world, with a somewhat deranged personality, quite possibly a killer, in her head, and partnered with a man from an advanced civilization who abhors killing. He is a Federation Peace Officer, captured by the slavers while attempting to bring them to justice. His task is complicated by the fact that he has sworn to avoid the taking of sentient life during the performance of his duties. He can and does, however, make vigorous use of non-lethal weaponry. Since, before leaving the ship, Katie had promised to help her co-captives gain their liberty, she and the alien peace officer find that they have a common cause.

But first they must find their way off the primitive planet and get to the Federated Civilization, avoiding the slavers who have been left on the planet to re-capture them. Their flight is complicated by the fact that the planet has had a global warming catastrophe some centuries back – the locals refer to it as the Drowned World. This has forced the inhabitants to revert to a pre-industrial state of development; however, they are a wily and resourceful people, mostly helpful, but they can also be dangerous.

Kati (to mark her escape, she adopts a slight name change) and Mikal seek a Federation beacon, which had been hidden on this planet ages ago, to aid in situations such as this, (in accord with a longstanding Federation policy for fringe worlds). They must embark on an arduous trek across two continents and an ocean, seeking the temple that holds the beacon. They travel on foot, by cart, by riverboat, by tall sailing ship, and on pack animals, always pursued by the dangerous slavers.

They must rely on their wits, guile, charm and acting abilities to avoid recapture, while their chasers have advanced technology and ruthlessness on their side. Fortunately, they are able to make many friends who help them along the way, and their quest becomes a series of adventures, both frightening and funny, and involving a cast of engaging characters.

To complicate matters, Kati finds herself falling in love with Mikal, the strange, handsome and amusing alien. He seems to be reciprocating, though they both struggle against an untimely romantic entanglement.
Will Kati and Mikal escape from the Drowned Planet? Can they ultimately bring the slavers to justice, as Mikal has sworn to do? Can they free the remaining captives of the slavers, as Kati has promised to do? Read this book and the rest of the series to find out all.

At about 200,000 words (equivalent to a paperback of about 400 pages), the book is an excellent value.

The Witches' Stones Book One - Rescue from the Planet of the Amartos

 Sarah Mackenzie had trained as a space ship mechanic at the Space Port of her home city on Earth. She left Earth to explore the galaxy, and, some months later, landed a dream assignment, to become the ship mechanic of an Explorer ship, the Beth 117.

The Beth was on its way to a planet at the edge of the galaxy, where its crewmembers were to search for the Witches’ Stones, or amartos, the mysterious crystals, which the Witches of the world, Kordea, use to channel and augment their psychic energies.

Sarah has no idea that she, herself, happens to be Stone-sensitive, just like the Witches are.
Under perilous circumstances, she comes across the cache of the Stones which the Explorers are looking for, and, unwittingly, “keys” them, igniting a psychic blaze that attracts the attention of The Organization, the implacable foe of the Terra Confederation, the centuries-old star-spanning government of most of the human race, and its non-human allies. To make use of amarto-energy, The Organization needs, not just the Stones, but also amarto-sensitive individuals whom they enslave to the devices which they have developed in their pursuit of galactic domination. Thus, they want not just the cache of Stones; they also want Sarah.

To forestall galactic war, rescuers, from a counter-intelligence group, known as The Agency, are sent to the Planet of the Amartos. A fast scoutship, manned by an Agent and a Pilot, must try to fetch Sarah and the amartos, bringing them to a safe haven among the Kordean Witches.

Sarah, herself, has to deal with serious conflicts. In the psychic realm she must choose between The Organization and the Kordean Witches, while retaining mastery over her own mind. In the physical reality, she has become the centre of an armed battle between the Terran scoutship and a military task force sent by The Organization to capture her and the Stones. Her determination to keep control of her own self sends her into unexplored mental realities, while exciting but dangerous physical events swirl around her and the crew of the scoutship, Camin.

To further complicate things, she senses within herself, the beginnings of an attraction to the handsome Agent sent to rescue her. However, she’s merely a naive young woman from Earth; surely, her hopes are beyond realization....

The novel is about 100,000 words, or 250 pages. It is the first book in the Witches' Stones series, which will explore the struggle for power among the Terra Confederation, the Kordean Witches and The Organization, as well as the personal and romantic entanglements of the characters. Book 2 will follow in May, 2015.

https://www.amazon.com/dp/B008PNIRP4

https://www.amazon.co.uk/dp/B008PNIRP4

https://www.amazon.ca/dp/B008PNIRP4

Oumuamua – As Improbably Skinny as the Most Slender Human Skyscrapers

Oumuamua – As Improbably Skinny as the Most Slender Human Skyscrapers

Alien Technology?

A story on the BBC website reports that the interstellar visitor object, Oumuamua is being examined for signs of alien technology.  Billionaire Yuri Milner will be funding a project, making use of the Green Bank Radio Telescope in West Virginia, to listen for any signals (intentional or not) that would indicate a non-natural source. That might include actual attempts at communication, or radio signals that leak from the object unintentionally, say from some type of electrical machinery.  Even an unexplained heat signature would be of interest.

It seems like a real long shot, but then the term “long” is very apt for this object, as it is very unusual for its long shape, about a 10 to 1 ratio of long axis to short axis.

Estimating Oumuamua’s Size and Shape

Contrary to what one might expect based on pictures in the media, we haven’t actually been able to photograph it in the glorious detail generally shown, as above.  Those are artist renderings.  In fact we haven’t really been able to photograph it at all, as far as its shape is concerned.  From the distance at which we have observed it, it is just a speck of light, albeit a speck that varies in brightness.

Why don’t we have nice photos?  Basically, it is too small.  It is thought to be about 800 meters long, by 80 meters wide, by 80 meters deep.  A little trigonometry shows that an 0.8 km object would subtend an angle of about 0.016 arc seconds, even at the relatively close distance of 10,000,000 km. 

The telescopes and cameras that were used to photograph Oumuamua had a resolution, at best, of only about 0.1 arc seconds per pixel, so it can’t really be seen as an extended object, at the distances at which it has been observed (it was at roughly Mars-like distances when first observed, as indicated in the picture taken from the Nature paper).

The reason that the object is thought to have this shape is due to its light curve. Oumuamua varies in how bright it is by about 2.5 magnitudes over about 8 hours, which is equivalent to a brightness change of about 10 times, as explained below:

• The magnitude scale is constructed so that a difference of 5 magnitudes equals a difference of 100 time in intrinsic magnitude.  Another way of looking at that, is that each magnitude change represents about 2.5 times change in brightness.
• So, 5 magnitudes is about 2.5 raised to the fifth power, which is about 98.  A difference of 2.5 magnitudes is about 2.5 railed to the power 2.5, which is 9.88, or nearly 10.

• Note that I am making some approximations here, but they are close enough for the purpose, given the uncertainties in observational data, anyway.  

The most likely reason for this change in brightness is that it is that Oumuamua is rotating every 8 hours, with its short profile facing Earth when it is dimmest and its long profile facing Earth when it is brightest (like a North American football tumbling end over end after a kick-off, as observed from the kicker’s point of view). So, the difference of a factor of 10 in brightness would be due to the change in the amount of surface area facing the Earth, and thus the amount of reflecting surface that is reflecting sunlight back to us.

An Underestimate of the Elongation?

On interesting aspect of this explanation, is that the 10 to 1 elongation estimate might well be a significant underestimate, depending on the angle of Oumuamua’s rotation plane, as seen from the Earth.

I mocked up a model of the interstellar asteroid, with approximately the same ratio of dimensions as Oumuamua.  This was a piece of scrap wood with dimensions of about 15 inches by 1.50 inches by 1.75 inches.  That’s pretty close to the 10 to 1 elongation of Oumuamua.

I then mounted this on a tripod, using some good old duct tape.  The tripod could be rotated in all three dimensions.  That was then placed next to a wall with a light source across the room.  This was meant to very roughly model the situation of the asteroid, relative to the Earth, with the size of the shadow on the wall corresponding to the amount of area that the asteroid would present to the sun, and thereby the amount of light being reflected back to an observer on Earth.

This exercise is also a straightforward example of projecting a 3-D object onto a 2-D surface (more trigonometry), but a picture is worth a thousand words, so I thought this would be interesting an persuasive in illustrating the mathematical situation.

I have named this the “propeller” in the images below.  One can think of how a spinning propeller would look to an observer, at various angles.  Remember, though, that the propeller is rotating very slowly, about once every 8 hours, so the apparent size of it can be easily measured at various stages in the rotation.  Note also, that the pictures had to be taken at a bit of an angle, otherwise there would be no shadow to measure, since the photographer would block the light (“shades” of the observer affecting the observation).  So, the photos are a bit distorted, relative to the shadow measurements actually taken with a tape measure.  

Case 1 is the situation that is yields the maximum ratio of length to width/depth.  When the asteroid model is pointing straight up and down, relative to the observer, its shadow  measures about 17 inches long by 1.75 inches wide (the shadow is a bit longer than the model, because the light source is a non-spherical light bulb about 10 feet away, so there are some complicated penumbra effects).  When it is pointing sideways, relative to the observer, it measures about 1.75 inches long by 1.75 inches wide.  So, that yields an elongation of about 10, which is the elongation estimated for Oumuamua in the reports. 

Case 2 is the situation that is yields the minimum ratio of length to width/depth, which is to say no elongation at all.  When the asteroid model is pointing straight up and down, relative to the observer, its shadow  measures about 16 inches long by 1.75 inches wide.  When it is pointing sideways, relative to the observer, it measures about the same.  So, that yields an elongation of about 1, or no elongation at all.  So, if a long object (but relatively small) was to fly away from us, spinning like a propeller face on, we wouldn’t really know anything about its shape, as it would seem equally bright throughout its rotation.  

Case 3 is an intermediate situation, with the plane of the propeller at about 45 degrees to the observers line of sight.  When the asteroid model is pointing straight up and down, relative to the observer, its shadow measures about 16.5 inches long by 2.25 inches wide.  When it is pointing sideways, relative to the observer, it measures about 13.5 inches long by 1.75 inches wide.  So, that yields an elongation of well under 2, or not much at all, event thought we know that the dimensions of the object are actually 10 to 1.  So, for such an object oriented at an oblique angle, we would be seriously misled about its real size.  The same is true for other oblique angles – even an object inclined only 30 degrees from straight-on yields a fairly small apparent elongation, on the order of 2. 

Of course, if one followed the object for quite a long time through its orbit, its orientation relative to the Earth would constantly shift, so that would provide extra information.  But, in practice, it would become difficult to see at all, as it continued in its orbit.  Here’s a quote in the Nature discovery paper:

“The inset shows the inner solar system, with the solid line segment along ‘Oumuamua’s trajectory indicating the short window of two weeks during which it was bright enough (median magnitude of light curve V~20-24) to be studied by large telescopes on Earth.”

So, Oumuamua is a weird shaped object, at least 10 to 1 ratio of length to width, according to the light curve.  But, from this little modelling experiment, it seems likely that it is actually considerably more elongated than that, given that it is probably not at the most favorable angle to estimate elongation via the light curve.  So, that means that it probably goes from being a weird object to a very weird object, at least as far as this simple modelling experiment is concerned.

I should note that an early version of  the Astrophysical Journal paper alludes to this issue noting that the “axis ratio is a lower limit because of the effects of projection, and is extreme relative to most asteroids”.

Even a 10 to 1 ratio is surprisingly elongated.  In fact, skyscrapers with that elongation are considered to be very slender structures, as is described in the skyscraper.org website:

WHAT IS SLENDERNESS?   

"Slenderness" is an engineering definition. Structural engineers generally consider skyscrapers with a minimum 1:10 or 1:12 ratio (of the width of the building's base to its height) to be "slender." Slenderness is a proportion based on the width of the base to the height of the building.

The World Trade Center North Tower was the tallest building in the world on its completion in 1971. But at a height of 1,368 feet and with a big square floor plate, 209 feet on each side, the ratio of its base to height was less than 1:7. This image compares at the same scale the former 1 WTC and the residential tower 432 Park Avenue, now under construction. The base of the apartment building is 93 feet square, and the shaft will rise to 1,396 feet, making its slenderness ratio 1:15. To visualize a 1:12 ratio, we show a ruler 1-inch wide and set on end. The eighteen towers on our chart range from a ratio of 1:10 to an extraordinary 1:23 at 111 W. 57 Street.

 

Here’s a photo of the Empire State Building, in New York (which is not considered a slender building).  It has an elongation of perhaps 7 or 8 to 1, based on floor space, number of stories, and overall height.

It is hard to find a natural rock formation on Earth that comes anywhere near a 10 to 1 elongation.  Here’s the well-known Chimney Rock, in the U.S.A. (Nebraska).  It only looks to be about 4 to 1 elongation, on average, considering just the top spire.

So, if you observed Oumuamua from a spaceship, very close up (like the recent ESA mission to the comet), its shape might remind you of a skyscraper, and possibly an extremely skinny one (though if it looked too much like the Empire State Building, you might be running short of oxygen).  As far as we know, there is nothing like it in our solar system. 

The question is, what process made such an unusual object (see my earlier Oumuamua blog for more on that).  I guess that’s the question on Russian billionaire Yuri Milner’s mind as well.

Sources:

Nature letter

doi:10.1038/nature25020

A brief visit from a red and extremely elongated interstellar asteroid

Karen J. Meech, Robert Weryk, Marco Micheli, Jan T. Kleyna, Olivier R. Hainaut, Robert Jedicke, Richard J. Wainscoat,Kenneth C. Chambers, Jacqueline V. Keane, Andreea Petric, Larry Denneau, Eugene Magnier, Travis Berger, Mark E. Huber, Heather Flewelling, Chris Waters, Eva Schunova-Lilly & Serge Chastel

http://www.bbc.com/news/science-environment-42329244

http://skyscraper.org/EXHIBITIONS/TEN_TOPS/slender.php

http://dodecahedronbooks.blogspot.ca/2017/11/an-interstellar-oddity-oumuamua-1i2017.html

Google Images

Astrophysical Journal Letters (submitted): Interstellar Interloper 1I/2017 U1: Observations from the NOT and WIYN Telescopes, David Jewitt,Jane Luu, Jayadev Rajagopal, Ralf Kotulla, Susan Ridgway, Wilson Liu and Thomas Augusteijn

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Now that you have read about a real interstellar interloper (natural or not), you should consider reading some Science Fiction.  How about a short story, also about interstellar interlopers.  It also features one possible scenario to explain why we haven’t met ET yet (as far as we know, anyway).  Only 99 cents on Amazon.

Oh, and it has dogs.  Everyone loves dogs, don’t they?

The Zoo Hypothesis or The News of the World: A Science Fiction Story

In the field known as Astrobiology, there is a research program called SETI, The Search for Extraterrestrial Intelligence.  At the heart of SETI, there is a mystery known as The Great Silence, or The Fermi Paradox, named after the famous physicist Enrico Fermi.  Essentially, he asked “If they exist, where are they?”.

Some quite cogent arguments maintain that if there was extraterrestrial intelligence, they should have visited the Earth by now. This story, a bit tongue in cheek, gives a fictional account of one explanation for The Great Silence, known as The Zoo Hypothesis.  Are we a protected species, in a Cosmic Zoo?  If so, how did this come about?  Read on, for one possible solution to The Fermi Paradox.

The short story is about 6300 words, or about half an hour at typical reading speeds.  It will set you back 99 cents, unless it is free, which it occasionally is.

 https://www.amazon.com/dp/B076RR1PGD

https://www.amazon.co.uk/dp/B076RR1PGD

https://www.amazon.ca/dp/B076RR1PGD