Thursday, 24 April 2014

Astrophysics Corner, Part 8 - The Shape of Space, with a Particular Emphasis on the Dodecahedron

In Book 1 of the Witches Stones series, a form of space travel takes advantage of a previously unknown peculiarity of the shape and dimensionality of space, called Omega-space:

“No human being understood exactly what happened when a spaceship slipped through "omega-space", instantaneously passing from one portion of the galaxy to another.”

The subject of the shape of space has long fascinated people.  The more primitive ancients tended to see the universe as a flat surface (the Earth), surrounded by water (the ocean), and with a dome-like structure above (the heavens) which were the domain of the bodies of the sky - the sun, moon, planets and stars.  Some theories said all of this was held up by a giant (Atlas), who was standing on the back of an equally enormous turtle.  What the turtle was standing on wasn’t considered a fair question - the famously facetious phrase “it’s turtles all the way down” was invented as a humorous evasion of the issue and has now become a standard joking response to skirt around any question involving an inconvenient  infinite regression.  I don’t think what was outside the dome was considered a fair question either.  Perhaps “it’s domes all the way up” might have been a good response.
Plato, in the Timaeus, looked at the universe both in its physical form and in an idealized form.  The former is subject to change and decay, the latter is eternal.  The former is also apprehended by the senses while the latter could be apprehended by pure reason.  In overall form, the universe was thought of as a sphere, the most perfect form, which the divine would naturally choose.
 It was also conceived to be related to one of the Platonic solids, the dodecahedron.  There are five platonic solids - the other four were thought to be what the matter of the physical universe was made of.  These are tetrahedron (fire), the octahedron (air), icosahedron (water) and cube (earth).   The shapes were matched with the four elements as then conceived, on the basis of such physical characteristics as spikiness, resistance to rolling and so forth.   The fifth, the dodecahedron was thought to represent the shape of the universe itself, perhaps partly because it is the platonic solid that looks most like a sphere.  You might think of a football (in North American terms, a soccer ball) to help you visualize the dodecahedron.   A dodecahedron is composed of 12 equal sized pentagons, however, while a soccer ball is technically a spherical truncated icosahedron, which is a combination of dodecahedron and icosahedron.
 Eventually other views of the universe came to be dominant.  Perhaps the one that we are all most familiar with is what might be described as the Newtonian view - that there are three dimensions that all go on forever, along with an absolute time that clicks along uniformly and relentlessly.  That’s what the average person probably thinks of when he or she hears the phrase “the shape of space”.
It might surprise you to know that mathematicians and astrophysicists (cosmologists) don’t see things that simply.  Mathematicians have devised a whole branch of mathematics (topology) that concerns itself with what spaces are logically possible and what characteristics those various spaces would have - dimensionality, distance metrics, axiomatic foundations and so forth.   Astrophysicists are actively seeking ways to measure the actual observable universe on the large scale to attempt to determine the shape of the space that we live in.  While doing so, they incorporate the complexities of Einstein’s theories of general and special relativity, which involve a much more elastic notion of space-time than Newton’s absolute space and time.
What is meant by measuring the large scale properties of the universe in order to infer its shape?  A useful analogy is that of intelligent creatures that live on a sphere, in only two dimensions.  How would they conceive of the space that they inhabit?  Well, since they can’t jump out into the third dimension, they have to do experiments to infer the large scale properties of their space.  If you find this example to be too contrived, you might think of people living on a planet with a very flat surface and a very opaque, cloudy atmosphere, tidally locked to its sun, such that all they saw when they looked up was a flat white sky and all that they saw when they looked around was a horizon stretching away.
One experiment these spherical surface bound creatures might try, is to simply walk in a straight line for a long time.  As we know, if you walked straight forward on an infinite plane, you would never come back to the same point, regardless of how long you walked.  But if you were walking in a straight line on the surface of a sphere, you would eventually come back to your starting point.  For example, if one of these creatures started at his equivalent of our north pole, he would eventually pass the equator, then the south pole, then the equator again, then back to the north pole.   Assuming that he could recognize some sort of unique landmark (or created one himself), he would know that he was back where he started.  From that, he could tell his space was unbounded (he didn’t come to a barrier he couldn’t cross) but still closed (he didn’t go on forever without coming back to his starting point).
Another experiment that these creatures could do involves measuring triangles.  On a flat Euclidian plane, we know that a triangle’s angles sum to 180 degrees (or pi radians).  But on a sphere, a triangle sums to more than 180 degrees, while on a saddle shaped surface it  sums to less than 180 degrees.  To see this for a sphere, just think of starting at the north pole, travelling straight down 0 longitude, turning right at the equator (i.e. a 90 degree turn), following the equator one fourth of the way, turning right again at the 90th longitude (another 90 degree turn), then ending up at the north pole. You would have done two right turns (180 degrees) and still had a 90 degree angle between the path you started on from the north pole, and the path you returned on.  That’s 270 degrees in all, more than the 180 degrees in a triangle on a plane.  So, once again, these creatures would know that the space that they inhabit is very different from a flat, infinite plane.
Similarly, human astrophysicists would like to measure certain large scale features of our observable universe to see what sort of space we live in.  One experiment would be to head out in a rocket for a long, long time and see if eventually you seemed to be passing the same bunch of galaxies that you started from.  Obviously that’s not exactly an achievable experiment for a number of reasons - for one thing, we lack such a rocket and for another the galaxies are constantly changing so you might not recognize them when you passed them again.  Plus, by the time you got back to let people know your result, they would probably have evolved into something else and you wouldn’t know how to communicate with them anyway.
But there are ways to attempt to measure the universe.  One is to examine large scale maps of the observable universe (usually based on satellite observations in various wavelengths, but especially microwave) to see whether the universe looks to be homogeneous and isotropic on all scales (i.e. it appears to be the same wherever you look in the sky, and on every scale).
This is generally done using a technique called spectral analysis, which is a mathematical algorithm for finding patterns or regularities in data of all sorts, based on math first developed by Fourier in the 19th century and elaborated by many others since then.   In simple cases, these patterns can be detected by humans without sophisticated mathematics or computer analysis, but in more complex cases, spectral analysis is used to discover where spikes of the “power” in a signal are located, which indicate some kind of regularity in the data, which could be in the time or the spatial domains.
For instance, in music we know there are various harmonics along with the fundamental note.  These can be uncovered using spectral analysis.  Extra-solar planets are often discovered via this technique - regularities in the dips in a stars light curve can reveal the presence of a planet or multiple planets.   Geophysical exploration makes wide use of these methods, to find interesting and possibly profitable anomalies in magnetic or gravitational data.  Electrical engineering makes wide use of it to examine the frequency responses of circuits - that’s where the expression “power spectra” comes from.  Many other examples of the use of spectral analysis could be listed.
In 2003, Luminet, Weeks et al produced a paper that examined the WMAP data (Wilkinson Microwave Anisotropy Probe), to examine the spherical harmonics in that dataset.  Basically, it is a temperature map of the sky, produced by a satellite telescope.  Much of the data maps quite well to infinite flat space, especially the higher harmonics.  But there are problems at some levels of the spherical harmonics that can’t be well explained by such a model.    Essentially some of the lower harmonics imply a finite universe, where the size of space itself cuts off some of the expected wavelengths in the spectrum.  In their paper they use the analogy of a bell, where some overtones are impossible because the wavelengths would be bigger than the bell itself.
They argue that something called a Poincare dodecahedral space fits the power spectra of the data very nicely.  Essentially, in this space any object “leaving the universe” (including light) goes out one face of the dodecahedron and returns from the opposite face, with a twist.  In this case, space would be unbounded but closed, rather like the sphere is for two dimensional creatures.  In this case it would be akin to a hyper-sphere and the Poincare dodecahedral space would bear a similar relationship to it that the dodecahedron bears to the sphere in our “normal” space.
So, amusingly enough, Plato might have been (more or less) right all along.  At least I think that’s one way of looking at it.  Read the paper “Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background” and judge for yourself.  It was in Nature and is also on the physics arxiv site (there was another paper on the subject in 2008 as well, using more data).
And here are a few visualizations just for fund (not strictly mathematically the same as what is described above, which is pretty hard to visualize J).


Tuesday, 22 April 2014

A picture of Mars, from the Dodecahedron Books Observatory

A picture of Mars, from the Dodecahedron Books Observatory

It's also known as the back yard.  There was a little post-processing done as well, in GIMP.

Telescope is a  6 inch Maksutov-Cassegrain reflector.  I think I had a 25 mm eyepiece in.  It was taken Sunday April 20, 2014, about 10:30 p.m.

Mars is fascinating.  No wonder so much SF has been written about it.

P.S. I know this isn't the most amazing amateur photo of Mars out there, ok.  :)  But I still like it, and I think it doesn't hurt to show non-specialists that they can enjoy the activity, too.  It's like breaking 100 in golf - no big deal to good players, but pretty cool for us duffers.

 Mars is great, but why not read about a trip to see a total solar eclipse in the U.S., during the summer of 2017?  

The Great American Solar Eclipse of 2017

Total solar eclipses are spectacular events, so much so that some people get hooked on them. They become eclipse addicts, who pursue these celestial events around the planet, from country to country as the predicted eclipses come and go. Of course, for most people, eclipse viewing is conditioned by the constraints of available vacation time and spare money. So, an eclipse through the heart of United States, during the height of the 2017 summer, brought the experience home for a lot more people than is usually the case.

This is an account of one such set of eclipse observers, journeying from Calgary, Canada to Idaho Falls, USA to take in the 2017 solar eclipse on a beautiful cloudless August day. It includes a description of the trip itself, through the coulees and mountain ranges of Alberta, Montana and Idaho, culminating in an unforgettable eclipse day in Idaho Falls. It also contains a reasonable amount of scientific and literary background on the eclipse phenomenon, and how it has been experienced by people through the years.

The story is about 12000 words, about 60 to 90 minutes at typical reading speeds and costs 99 cents.

Saturday, 19 April 2014

Where the Apple Falls - An Easter Story (now on Amazon, free for Easter)

The short story by Helena Puumala "Where the Apple Falls - An Easter Story" is now on Amazon.  It is free Easter Suday, Monday, and Tuesday, 99 cents after that.

This short story (approx. 6500 words) focuses on the complex and somewhat troubled relations between children, parents, and grandparents.  It also revolves around the mysterious forces of the universe, including the various notions of the divine held by the people in the story, which sometimes conflict, much as they do in the world in general.  An Easter service and a freshly planted apple tree draw the parties together, over one fateful Easter weekend.

The story is set in a Northern Ontario lake community, and continues to explore the setting and characters introduced in “Love at the Lake” and “The Boathouse Christ”, also by Helena Puumala.

Thursday, 17 April 2014

An Easy Promotional Device – One Page, Many Covers

Here’s a fairly quick way to put a lot of covers on one page, so that you can post them together online,  do a large format paper poster, or just have something to put on a table or in a binder.  It uses Microsoft Office products, but  your could use something else.  For the final stage I used Gimp, the open source image program (something like photoshop).

1.       Open up Powerpoint .  You could use various other programs, such as excel word or non-Office programs too.  Powerpoint is kind of nice, as it provides help aligning your images and text boxes on the fly.

2.       Open up a new blank page.

3.       Insert a cover jpg (use insert picture).   It makes sense to use the cover image you put on Amazon, Kobo, whatever but you can uses something else if you want to.

4.       You will want to resize that cover image, and place it somewhere appropriate on the page,  say the top left hand corner.

5.       Now, do a text box (use insert text box).  Add some descriptive text, choose font style and size, and position that text box next to the picture.  Your text might relate to where the books are on sale, prices and so forth.  Or they may be super-short blurbs about the content of the books.

6.        Repeat with more covers.  Probably six covers are about as many as you want to go, as more than that my crowd things a bit too much.  But, you never know.   Experiment.

7.       You could try different themes for different purposes.

o   Your six (or whatever number you choose) most recent books.

o   Your six most popular books.

o   Your six top books in a particular genre, if you write in multiple genres.

o   Six books in the same series (or two trilogies).

o    Six “books of the heart”.

8.       Depending on space considerations, you may have room for a text box with upcoming releases, a short bio, or whatever.

9.       Save that as a pdf (some large format printers want pdf, so this can be handy later).

10.   Open up the pdf in Gimp.

11.   Use the export command in Gimp to create a jpg or gif that you can load into your blog, Facebook site, website or whatever.

Now you have a document in various formats that you can use for promotion – Powerpoint, PDF, GIF and JPG.  You could even do a large format poster and hang it on your writing room wall for inspiration J.  Note that your actual jpgs, once printed, can be larger than what is shown in this blog.  Following are a couple of examples that I put together.

The first batch of covers shows six novels or stories that Helena Puumala has published with Dodecahedron Books.  The text boxes show the prices on Amazon/Kobo for the various novels and stories, including the paper book product for Kati 1.

·         Kati of Terra Book 1: Escape from the Drowned Planet.

·         Kati of Terra Book 2: On Assignment to the Planet of the Exalted.

·         The Witches’ Stones Book 1: Igniting the Blaze.

·         Northern Gothic Stories: An Anthology.

·         Love at the Lake: A Romantic Short Story.

·         The Boathouse Christ: A Paranormal Short Story.

·         Note that there is room for a text box showing upcoming works.
The second batch is similar to above, but has short blurbs related to the books, instead of pricing information.  As you can tell, it’s not easy to come up with short blurbs J.

The third batch of covers shows six alternative covers for Kati of Terra Book 3: Showdown on the Planet of the Slavers.  You might use this to solicit opinions on your facebook page or website to see what people prefer.  In this case, we were looking at what Kati ought to hold in her hand in the cover and we used this format to solicit opinions at an office party (the cover with flag/flowers and the cover with the lace crystal knife got the most votes):
·         A flag and flowers, representing Kati’s work with the Star Federation to bring peace and stability to planets that had been disrupted by the slaver Gorsh and his allies.
·         Kati with a stunner, a weapon she or Mikal has had to use on a few occasions against adversaries.  Used in all books.
·         Kati with a  cookie sheet.  Kati can improvise when necessary, and there is nothing quite like a hot cookie sheet to show an evil alien that you really mean business (note: don’t try this at home, but if you do get surprised by an evil alien while baking, wear your oven mitts while wielding the cookie sheet).  Used in the third book.
·         Kati with rifle.  She’s a country girl, so she knows a bit about rifles and her Granda node knows even more.  Used in the first book of the trilogy.
·         Kati with a lace crystal knife, the sharpest known weapon in the galaxy, for Kati of Terra, one of the sharpest knives in the drawer, when it comes to solving problems.  Needed in the second and third books.
·         Kati, with the bowl of wild raspberries that she used against the alien abductors, which allowed her young son to escape their clutches, back in the forest on Earth, at the beginning of the trilogy.


Saturday, 12 April 2014

The Boathouse Christ is free this weekend on Amazon

The short story ebook, by Helena Puumala, is free this weekend on Amazon.  It is part of a set of short stories set at a mythical Northern Ontario lakeside community, along with "Love at the Lake"  (99 cents) and "Where the Apple Falls" (on the blog this week).

Thursday, 10 April 2014

A Conversation with Helena Puumala, author of the Kati of Terra Series - The Ocean in Science Fiction (2)

March 24, 2014 The Bent Mast Pub and Restaurant, Victoria B.C.

Part Fifteen – The Ocean in Science Fiction (2)
Question: So here we in beautiful Victoria, British Columbia, on the southern end of Vancouver Island, at the Bent Mast pub, a nautically themed establishment with good food and a nice selection of craft beers.  Once more, we have Helena Puumala, author of the Kati of Terra series, and yours truly, the Dodecahedron Books blogger and data analyst.  Unfortunately, our geophysicist friend couldn’t make this outing.
Does being at the Bent Mast make you want to sing a Tarangayan sea shanty, Helena?

Answer: Maybe a bit, but I will leave the singing to others, as I don’t have quite the singing voice that Kati of Terra does. Perhaps we can ask the entertainers to do a version of “The Fiddler’s Green” later.
Question: That would be highly appropriate, as that song plays a central role in your upcoming novel “Kati of Terra Book Three: Showdown on the Planet of the Slavers”.  Nice plug setup, by the way.

Anyway, this is a great place to discuss “the Ocean in Science Fiction”.  As we noted in the first part of this blog, you have featured the ocean and ocean imagery fairly prominently in your writing, particularly in the Kati of Terra series, but also in your other SF series “The Witches’ Stones”, which you are currently working on.  Sometimes the ocean presents a barrier or an obstacle to your characters, at other times it is more of a facilitator, or even plays an active participant role.
Answer:  Well, water is both an obstacle and a facilitator of travel on Earth, so it’s natural that it would be similar on other habitable planets.

It’s true that in Kati 1 the ocean is an obstacle for Kati and Mikal, in their quest to escape from the slavers and get off the drowned planet, Macros 3.  But since they travel on a cargo/passenger sailing ship, the ocean is also a conduit for travel, and generally easier on the body than runnerbeast travel.  So, in that sense it is more of a facilitator, as is the river, during their other watery journey in that book.
Question: Yes, the ocean is pretty benign overall, though Kati’s healing skills are called upon due to one of the characters getting a near-lethal form of sea-sickness.  So, even in its more benign form it can still pose a danger.

In “Kati of Terra Book Two: On Assignment to the Planet of the Exalted”, you up the ante as far as the ocean’s helper role is concerned.
Answer: You mean the planetary spirit on Vultaire known as the Ocean Sister.  Yes, the Ocean went from being a neutral and passive conduit in Kati 1 to an active participant of the story, and a great help to Kati in Kati 2.  I posit the planet as having evolved its own intelligence, which manifests in various forms.  The Ocean Sister is one of those.  Though normally the planetary intelligence prefers to not interfere in human affairs, the sickness that has arisen in human society there has infected part of the planetary intelligence itself, so it has to step in to set things right.  Kati and Mikal are invaluable allies in this work, or perhaps the Ocean Sister and her sibs are invaluable allies in their work.

Question:  I really liked the Ocean Sister.  Of all the ways that the planetary intelligence could manifest, I liked her the best.  You really captured the wild exuberance of the living ocean in her manner, her speech and her way of thinking.   What made you think of using the ocean in this way?
Answer: It just came to me as I wrote the book, but I wouldn’t be surprised if others had used the notion of planetary spirits or evolutionary planetary consciousnesses helping humans in other stories.  I won’t claim it is entirely original.  I mean, what is, really?

Question:  Indeed, this is in many ways in the tradition of the mythology of the Greeks, stories told by Native Americans and the myths of many other nations and cultures. 
Answer: The Finnish epic, The Kavala also springs to mind.

Question:  Yeah, that’s a story that you would know well, given your background. It definitely seems that SF owes quite a debt to the ancient legends of our species, not the least of which are the ancient legends of the ocean.  The Ocean Sister is a sort of spin on Poseidon, though a much nicer and more approachable entity than that Greek god.  The Ocean Sister helps Kati, while Poseidon wasn’t all that helpful to Odysseus.
Answer: Yes, Poseidon/Neptune was kind of a tough guy, while the Ocean Sister is a bit of a softy, and seems a bit dizzy at times.  But she is capable of toughness when that’s needed.  I would characterize my Ocean Sister as more of a helpful guardian than a god or goddess, in the manner of the ancient Greeks.

Question:  One is reminded how freely and often SF borrows from ancient, and especially pre-Christian mythology. Consider how Spock is a Vulcan, or how the Romulans hail from Romulus. I suppose the associations between SF and ancient mythology are literally written in the stars, given the naming of constellations and the stories behind them.
Answer:  Yes, several constellations are water signs, so the ocean and space have a definite connections in the zodiac.  There’s Pisces, Aquarius, Eridanus - many water associated constellations, really.

Question:  And among the constellations are one that represents a whale (Cetus) and one that represents a dolphin.
Answer: The ancients also had a fascination with the intelligent creatures of the sea, such as the dolphin and the whale.  Dolphins were often helpers of humans in Greek myths, much as the Ocean Sister is a helper of Kati.  And the Bible has that whale story.  In SF, Andre Norton wrote several SF books that involved dolphins and Anne MacCaffery had dolphins on the planet of Pern.  They were also sentient beings who assisted human beings.  As we noted earlier, Star Trek has used cetaceans on several occasions, being central to the stories.

Question:  Getting a little more abstract, another aspect of the ocean that seems to have a resonance with SF is its similarity to space.  As our geophysicist friend Marvin Klafner said at Sombrio Beach, like space the ocean is a sort of plenum or monad within which other things exist. When one sits by the ocean, one often thinks about its apparent vastness, how it reminds one of notions of infinity or eternity.  These are very much the same emotions of wonder that one gets looking through a telescope or reading a Science Fiction novel.
Answer: Yes, to sit by the ocean side, especially in a very natural setting, and listen to the waves roll in and watch the surf is perhaps our most humanly graspable parallel to the realities of infinity and eternity.  Most of us will never have the opportunity to visit space, but the vastness of the ocean can act as a stand-in for that, as can reading good SF or watching a well done SF movie.

Question:  And in SF, space voyaging is more often compared to sea voyages than anything else.  Naval metaphors are very common.  Perhaps that’s why you made an ocean voyage on an old fashioned sailing ship such a central image in Kati 1.
Answer:   I suppose that could be.  I imagine Magellan, Vasco de Gama and Drake felt a lot of the same emotions as Kirk, Spock and McCoy are imagined to feel, or indeed as the Apollo astronauts must have felt on their way to the moon.  And, and in their own way, Kati and Mikal have now joined those adventurers in the ocean of space.