The Boathouse Chist, free on Amazon Wednesday to Sunday

As part of the kickoff to Amazon Unlimited, Helena Puumala's short fiction piece The Boathouse Christ will be free on Amazon this week, as a Kindle ebook.

A teenage girl inadvertently materializes the image of a Christ on the Cross on the outside wall of her parents’ boathouse, at their cottage on a Northern Ontario lake. She spends hours praying to the figure while her parents and their neighbours express their distress. Then it is discovered that the girl, Terese, also has marks on her body, recreating the wounds of the Christ.

What is to be done?

A neighbouring girl offers her help, along with that of Terese’s psychic grandmother, demonstrating to her parents that she, indeed, as she gently claims, has some interesting talents, although Terese is the one who has truly rare abilities, but ones that she is afraid of. The families of both girls learn something about themselves, and about each other during the uncanny events of one (or perhaps two) October weekends, including Hallowe’en.

http://www.amazon.com/The-Boathouse-Christ-Helena-Puumala-ebook/dp/B00JBRD90Q 

Thoughts on the new Amazon Kindle Unlimited Subscription Service and The Long Tail

Amazon has just come out (July 18, 2014) with a program known as “Kindle Unlimited”.  As of now, it only applies to the U.S. site (Amazon.com), but if successful it will no doubt be rolled out to other Amazon sites around the world.  It is not clear to me if the program applies to non-Americans who have accounts on Amazon.com.  The basic idea is that for $9.99 per month, the subscriber gets unlimited access to all of the books in the KDP Select pool, about 600,000 titles at this time.   They can download up to ten titles at a time, but have to read or delete one or more of these titles before they can download another one.

Note that any Amazon book can still be purchased outside the Kindle Unlimited program, in the “regular” Kindle ebook store.  This could be the case for people who want to “own” a copy of the book rather than rent it or who simply don’t want to sign up for a monthly subscription fee.  Amazon Kindle Unlimited subscribers can still purchase books at full price, if they prefer.

The writer or publisher gets paid a fee every time one of his or her books is downloaded and read up to the 10% mark.  That’s the point at which a customer is assumed to have committed to the book, similar to the 10% sample available on the regular Amazon kindle website.  This ensures that readers don’t load up their kindles with books that they never get around to reading, and thus don’t drive down the unit price per download unnecessarily. 

The writer’s cut is based on dividing his or her downloads into overall  pool of money  e.g. if the pool of money was $2 million, and there were 1 million downloads, each download would be worth $2.  If an author had 10 downloads that month, he or she would receive $20.  Presumably, the pool will be based on the number of subscribers to the program.  The details of that are still unclear, but for this July the pool is set at $2 million.

To be eligible for the program, books must be enrolled in a program called KDP Select – that program requires the writer/publisher to be exclusive to Amazon.  Any book that is in that program is also automatically enrolled in Kindle Unlimited.  So, for example, if one wants to enrol a book in Kindle Unlimited that is currently published on Kobo or iBooks, that book would first have to be “unpublished” on the competing site.  By the letter of the contract, you shouldn’t even have the story available for free on your own blog or website.  It’s up to the writer/publisher, whether or not to enrol a book in the program.  On the one hand, it is another revenue stream from within Amazon; on the other hand, it means you can’t make any money on other ebook retail sites and can’t make your book available to people who use those sites.  In our case, for example, it would mean taking books off Kobo, where we know we have some loyal readers.

One interesting wrinkle of the program is that any book downloaded and “read” would be worth the same amount of money to the author/publisher, regardless of length.  So, a 25 page (10,000 word) $0.99 short story ebook would pay the writer as much as a 500 page (200,000 word) $3.99 epic length novel.  In the non-subscription part of the Amazon store, the 99 cent short story would pay the writer/publisher about 35 cents, while the $3.99 novel would pay about $2.80.  So, depending on what the fee per download of the subscription service ends up calculating out to, it would probably be more profitable for the writer/publisher to have short books downloaded by subscribers, but have longer books purchased by non-subscribers.  But, that’s clearly something outside of the writer/publisher’s control.  Readers will do what is best for them, depending on whether they think they will save money in the long run by going subscription, or whether they think they would be better off buying books on a one-off basis (including downloading free promotion copies, when available). 

One wonders how long Amazon will maintain the 5 days out of each 90 days that a writer/publisher can offer books for free, if enrolled in KDP Select.  The free days obviously represent no value to Kindle Unlimited subscribers – they can get as many books as they like for “free” anyway, as long as they pony up $9.99 per month.  Free still has value for non-subscribers, though.  It seems to me that it would be to Amazon’s advantage to drop “free” in the near future, as that would encourage cost-sensitive voracious readers to sign up for Kindle Unlimited.  As long as “free” is a possibility, voracious readers may want to stay out of the new program, and just read free books as they come up.  Note that if Amazon does abandon “free”, it will probably be done incrementally, in stages over a year or two.

Putting on my strategic thinking cap, it seems to me that Kindle Unlimited is an effort to further monetize the “long tail” in the ebook market.  The long tail constitutes that vast majority of books that are not hits or best-sellers (i.e. that don’t sell in the hundreds of thousands to tens of millions).  That’s anything from the solid mid-list books, purchased in the tens of thousands to the niche books that are only purchased by a few dozen people.  Amazon has already been quite successful at making money from the long tail – they basically created that market via the development of the kindle and their independent publishing outlet KDP and they have made a lot of money doing that.  But I suspect that they think that there is a lot of value left in that long tail market, that is currently being siphoned off by free books.  I think they want to turn that into cash.

The other strategic consideration for Amazon is to get writers to commit to being solely available on their store.  That would put the other retailers at a competitive disadvantage, being unable to offer a selection as large as Amazon’s.  And in a long tail world, large selection and an effective user-generated referral system (like Amazon reviews and Also-Boughts) are the keys to success.  That’s why the big box print bookstores (like Chapters or Barnes and Noble) beat the small scale shopping mall book stores during the 90’s and 2000’s, and that’s why the ebook retailers are prevailing over the big box print stores in the 2010’s, in their turn.

Another interesting aspect of Kindle Unlimited is that, as of the date of the writing of this blog (July 21, 2014), none of the “big five” publishers have signed on to the program (Penguin/Random House, Harper-Collins, Hachette, MacMillan, and Simon and Schuster).  That primarily leaves books produced by the mid-size publishers to independent/self-published writers.  Will that stifle the program?  My guess is that Amazon thinks not.  The kind of “long tail” consumers that they are after are often voracious, experimental readers who are content with Indies – indeed they may even prefer them to the safety of the big publishing houses.  Plus, not all of the biggest best-sellers are published by the big five.  For example, Hunger Games is published by Scholastic and it will be in the program, as will the Harry Potter books.  So, the new program will have some big name draws, even without the Big Five.

Some Indie writers have worried that Amazon and other retailers may eventually push them into an Indie and self-published ghetto, where they will languish, since they assume that most readers will automatically go to the part of the store dominated by the big name publishers and writers.  Other Indies have expressed what amounts to a “bring it on” attitude.  They think consumers don’t care about the publisher, and only want good books at a good price.  Since Indies have far lower overhead costs than big publishers, they think a lower priced Indie section would attract plenty of readers, especially their coveted loyal, voracious readers.

Indeed some of the big publishers have lobbied for just such a development. They may be getting their wish.  At this moment, it looks like Kindle Unlimited may be a de facto Indie section.  How that plays out is yet to be seen, however.  It may be that it is the big publishers who will be forced to cry uncle and sign up with Kindle Unlimited, if a significant part of the Amazon book buying public chooses to sign up with the subscription service.

So, there are a lot of interesting possibilities for readers, writers, publishers and retailers coming up.  Everyone will be trying to figure out what this new Amazon program portends for them.  Readers will be trying to calculate whether it will save them money, or cost them money to enroll.  Writer/publishers will be trying to estimate whether they will gain more from downloads than they lose in sales, on Amazon and other sites such as Kobo and Nook.  Other big ebook retailers, such as Kobo, will be trying to determine how they can best respond, in a strategic business sense.  And Amazon, as always, will be watching their data carefully, refining their algorithms and adjusting their business strategies in the manner that they feel best advantages them.

As for our little venture, Dodecahedron Books will enrol some of our shorter fiction in Kindle Unlimited, hoping it gets some downloads and drives some business to the longer books, like the Kati of Terra series and the Witches’ Stones series.  Other than that, it is a matter of observe, write, publish and try to enjoy the ride, which is all that anyone can do in the long run or the long tail J.

Love at the Lake, free on Amazon Wed August 23 to Sunday Aug 28

Amazon has come up with a new subscripton program, called Amazon Unlimited.  I will blog about the details of that later, and my thoughts about it.  But, as a result of this new development, we have recently re-enrolled three of Helena Pummala's short fiction works in KDP Select.  So, Love at the Lake, a romance, will be free to download from Amazon later this week (Wednesday to Sunday).  So, enjoy it free, or via the subscription program, if you have signed up for that.

http://www.amazon.com/Love-at-Lake-Helena-Puumala-ebook/dp/B00IPSZKLS

Astrophysics Corner Part 10 - The Face on Mars, a Dolphin on Jupiter and George Washington on a House For Sale Sign

Pareidolia - The Face on Mars, a Dolphin on Jupiter and George Washington on a House For Sale Sign

Update, May 2019
Here's another nice bit of pareidolia, taken by the Juno orbiter at Jupiter:

“There’s a Christ on the Stanniks’ boathouse,” Miles said at lunch, one fine mid-October Saturday.

“Come again?” Hannah said to her son who was spooning up soup with the hearty appetite of a growing twelve year old.  “There’s a what on the Stanniks’ boathouse?”
“Christ,” Miles responded, between mouthfuls.  “A picture of the Christ.  On the Cross.  On the outside, back wall of their boathouse.”
http://www.amazon.com/Boathouse-Christ-Helena-Puumala-ebook/dp/B00JBRD90Q

 Helena Puumala’s short story “The Boathouse Christ” centers around the appearance of an eerie likeness of a crucified Christ, on the side of a boathouse located in a lakeside community.  In the story it becomes clear that something truly mysterious is going on, but as we know, that’s not usually the case.  Most of have come across the phenomenon of eerie facial likeness in our daily lives.  In fact, it is a common enough that it has a name - pareidolia (I am indebted to astrophysics PhD student, soon to be PhD, Scott Olausen, for pointing this out).

The term apophenia refers to the process whereby a fairly random stimulus is perceived as being significant, and facial pareidolia is a specific variant of that.  The human mind is wonderful at recognizing patterns in data, even when they aren’t really there.  It is especially good at recognizing faces or things that might be construed as faces, which is very useful trait for a highly social animal like a human being.  Apparently, this happens very quickly, at a subconscious level, before it rises to the level of conscious thought.  Neurological studies indicate that we seem to have a lot of neurons that are devoted to this task – we are hard wired for it.  It is theorized that this trait should have a great deal of survival value, so evolution has selected for it.  Not only do we quickly recognize faces, but we also quickly attach an emotional value to the face - whether it is happy or sad, angry of indifferent, potential mate or helper or potential rival or foe.

It turns out that computer programs designed to recognize faces also make false positive identifications, seeing “faces” in collections of shapes that only superficially resemble faces.  For example there might be two circles over another circle and a line, which the computer program “sees” as eyes, nose and mouth, so it calls it a face.   I suppose that’s to be expected, as computer programs are ultimately creations of human minds, so it is not surprising  that they might share our biases.

Below is an image of George Washington that I came across the other day, on my walk to work.  It was on the back of a “house for sale” sign and it immediately caught my eye.  Perhaps I was primed a bit, by the famous image of George Washington sculpted into Mount Rushmore, which I have included for comparison.  I should note that the Mount Rushmore picture is actually one I took myself a few years ago, during a visit to South Dakota, U.S.A..  I would encourage any reader to take a trip there someday - it is quite an achievement (tastefully done) and the surrounding area of the Black Hills and Badlands National Park are pretty amazing too.

 

In the case of the miraculous appearance of George Washington on the back of a House For Sale sign, it was a matter of the morning sun casting shadows of nearby leaves on bushes in just the right way to be reminiscent of George Washington, especially for someone who is very familiar with the Mount Rushmore icon, as I am.  In this case it was easy for me to establish that the image was merely a trick of the light, by interposing my body between the sun (low on the eastern horizon) and the sign.  The image went away immediately.

You can also read George’s state of mind quite easily – I think I can, anyway.  The House For Sale sign George Washington appears to be rather sad, in my opinion.  Even Mount Rushmore George seems a bit sad.  I guess being the father of a country is no laughing matter.

There have, of course, been many reports of religious iconography being produced in similar matters.  There was the famous case of the Virgin Mary on a grilled cheese sandwich, for example, shown below.  Eventually, that fetched 28 grand on eBay for the owner, when it was purchased by an internet casino.  God really does work in mysterious ways.  I can’t say I get it - the picture looks more like a silent film star to me.

Another famous case, and one that has a connection to space science and science fiction is the so-called face on Mars.  That’s a formation in the Cydonia region of Mars that has a remarkable resemblance to a face, at least when the light hits it from certain angles, as in the Viking probe picture below.  The effect is far less convincing in the Mars Global Surveyor picture, also shown below, though some still see enough evidence of geometrical symmetry to insist that it must be the work of intelligent agents.  Proponents of the theory that it is not a natural tend to link it with ancient Egyptian wonders such as the Sphinx, which is undeniably not a natural phenomenon. 

The case is also made that there are a lot of mathematical relationships within the face and environs, and that these cannot merely be coincidences.  Arguments like that tend to run up against problems related to statistical theory, mainly how to interpret results when one makes many post-hoc a-theoretical multiple comparisons.  Essentially, when you are analyzing data after the fact, and have a lot of data to sift through, you can find many spurious correlations, even in a randomly generated dataset.  So, one has to be very careful when judging these claims.

Ultimately, everyone will have to make up their own minds about the Mars feature, at least until NASA or some other space agency sends a probe to the area.  The more I look at the Mars Global Surveyor picture, the more it starts looking like a face.  But since I can’t stand in front of it, like I could with George Washington on a House for Sale sign, it may just be pareidolia after all.

Happy Bastille Day and happy birthday to Helena Puumala

France is one of the originators of democracy, and Helena is the originator of Kati of Terra, a tireless protagonist on behalf of democracy.  And, the blogger's wife.  :)

Astrophysics Corner, Part 9 - The Lace Crystal Knife, or a Nice Sharp Blade

Davo pulled out a smallish wooden box, and opened it to display the pieces of something which had been savagely destroyed, probably by bashing it against a hard object.  Xoraya clucked sadly to see them, and then rooted among the broken components until she came up with a transparent crystalline object attached to metal casings at both ends.

“Lace crystal,” she said, directing her words to Kati.  “So hard that it’s almost impossible to break, and capable of resonating at speeds which are completely undetectable by human, or lizard, senses.  That’s partly what makes the knives made of it so deadly; the vibration adds to the sharpness.”

http://www.amazon.com/Kati-Terra-Book-Three-Showdown-ebook/dp/B00KHBN8FG

From Kati of Terra Book Three: Showdown on the Planet of the Slavers.

In Kati of Terra Books 2 and 3, a particularly deadly type of weapon is described, “the lace crystal knife”.  As the above selection states, it is incredibly sharp, as well as having certain other characteristics, relating to its resonator properties. That makes one wonder, in our world, what is the sharpest blade that has been made?

First, let’s think about what we mean by sharpness, in this context.  I would say we are talking about penetrating power, and specifically penetrating power focussed on a small surface area, that doesn’t cause much damage outside of the intended area of penetration. That would produce what we would call a clean cut.

After all, a missile, artillery shell or bullet has a lot of penetrating power, but they tend to do a lot more damage than required - we generally don’t want to destroy the object that we are cutting, particularly if we are engaged in activities like surgery or preparing thin samples for microscopes.  Even with weaponry, the idea behind an edged weapon is to overpower the opponent without doing a lot of collateral damage.  That’s certainly the idea behind the assassin‘s weapon, the lace crystal knife, in the Kati of Terra books.

So, cutting power or penetrating power, is a matter of applying a lot of force over a small area – in other words, pressure or force per unit area.  We can work out a few examples, using Kati as a model (she’s always willing to help) – these will all just be ballpark figures, to get some feel for the physics involved.

First, let’s assume that Kati of Terra weighs about 115 pounds, and is wearing her regular hiking boots, that have dimensions of roughly 3 inches by 10 inches.  That gives 115 pounds divided by 30 square inches, or about 4 pounds per square inch pressure.

Now, let’s have her put on some high heels, with a heel dimension of about 1 inch square.  If we assume half of her weight is on the heel, then the resulting pressure is  about 60 pounds per square inch under that spiked heel.  So, the pressure that can be exerted by that spiked heel is now about 15 times as much as with the hiking boots.

Now, let’s try some ice skates.  We will assume the blades are about one eighth inch thick, which then yields a pressure of about 92 pounds per square inch, on average over the blade.  But when stopping, accelerating or turning, the surface area might go down considerably, perhaps to only one-tenth of that value, thus yielding a pressure of 920 pounds per square inch, for very short time intervals.  No wonder the ice chips fly, and hockey players can be badly cut by an opponent’s skates.  Naturally, that is compounded by the fact that the hockey player’s skate might be traveling quite fast when it collides with the other player.  That would multiply the effective force by many times (the blade decelerates in a small distance/time interval, so it and anything it collided with would probably be experiencing a significant g-force).

Obviously,  blades can get a lot sharper than a skate blade – a lot shaper.  In fact, it turns out that human beings have been making very sharp blades for a long time, since some of the sharpest edges attainable are via amorphous materials like glass, in particular volcanic glass or obsidian.  Apparently, obsidian can be fractured down to points that are only molecules wide, tapering to a very fine point, due to their amorphous structure and consequent conchoidal fracture.  That’s harder to do with more rigid crystalline structures such as diamond – at the molecular level they want to maintain their structure, so there is a limit to how sharp a point they can come to (though diamond blades can be made very sharp, as well).

And people have had access to natural obsidian for as long as we have been making tools, so our primitive ancestors had surprisingly sharp knives.  Mesoamericans had quite fearsome weapons, swords that incorporated obsidian blades along with wooden serrated edges, which could result in terrible wounds.  Apparently, obsidian is still used for some of the sharpest surgical tools, to cut rather than tear at the cellular level.  This also gives one a new appreciation of the implications of the term “The Obsidian Order” in Star Trek Deep Space Nine”.

Here's a scanning electron microscope photo of an obsidian blade and a steel blade.

The down side to obsidian or glass cutting instruments is that they can get dull after a limited number of uses.  Once the cutting edges are down to molecules thick, even small lateral forces can cause them to chip or break, so they can wear down fairly quickly.  For this reason, metal blades are much more useful, generally speaking.  With hardened steel, for example, sharpness and toughness or durability can be combined.  Even here, the techniques are old – something called Damascus Steel was used for swords for many centuries before the techniques for creating it were forgotten, within the recent past.  It has been difficult to exceed these blades, in practice. In fact, they have been found to include carbon nanotubes, a modern materials science mainstay.

As for lasers, apparently the best medical lasers can be very finely focussed, down to the 25 micron level or so (a micron is a millionth of a meter or thousandth of a millimeter).  But the finest obsidian blades actually go down to the nanometers level (a billionth of a meter or a millionth of a millimeter), so lasers are still rather crude in this regard.

As for the lace crystal knife of the Kati of Terra universe, its many amazing properties may be the result of its ability to focus energy from the quantum level, the so-called zero-point or vacuum energy.  That can be seen by the scintillation of the lace crystal knife that Kati has in her hands on the cover of Kati 3.

Perhaps the cutting edge can be deformed from its usual crystalline structure at the micro level, via zero-point energy, the way water molecules can be elongated in an extremely strong magnetic field, such as those near the astrophysical bodies known as magnetars.

This would also help explain the apparent psychic or mental connection that some species, notably the Chrystallorians seem to have with the material.  After all, we all know that there appears to be some kind of connection between consciousness and matter, when you get down to the quantum realm, based on ideas like the collapse of the wave function.  Lace crystal just happens to have properties that accentuate that phenomenon.

At any rate, that’s Science Fiction – it’s anything from a lot of Science and a little Fiction to a little Science and a lot of Fiction.  And what seems like fiction in the present, may become the science of the future.

Sources: Phys.org, Wiki

Kati of Terra Book 2 now available in trade paperback on Amazon

http://www.amazon.com/Kati-TerraBook-Two-Assignment-Exalted/dp/149968326X/ref=sr_1_2?s=books&ie=UTF8&qid=1404784284&sr=1-2&keywords=kati+of+terra+book+2

Kati of Terra Book Two: On Assignment to the Planet of the Exalted is now available in an attractive trade paper version, on Amazon.  Kati Two will look beautiful on your bookshelf, especially if you also have Kati One to accompany her. :)

Book Statistics Corner, Part 5 – Amazon Reviewer Trends of Ten of the Most Popular Book Series

In a couple of previous  blogs, we looked at some statistics on sales for popular book series of the recent past.   As a memory refresher, those book series are repeated below:

Author and Series	Total
J.K. Rowling - Harry Potter	447,000,000
Dan Brown - Robert Langdon	200,000,000
Stephanie Myers – Twilight	120,000,000
Suzanne Collins - Hunger Games	50,000,000
Robert Jordan - Wheel of Time	44,000,000
Stephen King - The Dark Tower	30,000,000
G.R.R. Martin - Game of Thrones	24,000,000
Veronica Roth – Divergent	20,000,000
Douglas Adams - Hitchhikers Guide	16,000,000
Patrick O'Brian - Aubrey/Maturin	4,000,000

As noted previously, these 10 series represent nearly 1 billion copies sold.

In the last blog, we focused primarily on how the number of Goodreads raters varied by the position of book within the series.  In other words, we tracked the number of people who rated book 1, book 2, book 3, etc. (normalized to book 1 = 100) to see if there was a pattern to the data.  And in fact we did discover a very prominent trend, which was true for most of the series that we looked at; for the most part,  the number of books rated by the Goodreads community declined from book to book, with the drop-off best modelled as our old friend, the power law.

 

Naturally we didn’t do this merely to analyse the behaviour of Goodreads raters, as interesting and worthy as that exercise might be.  We were, in fact, assuming that the number of Goodreads raters were a reasonably constant fraction of the number of people who had actually purchased and read the books in question.  So, we assumed that the pattern of Goodreads raters was likely to be quite similar to the pattern of purchasers, a sort of attenuated mirror image.  We examined the Harry Potter series in detail (a series for which reasonably accurate book by book sales are known) to verify that the number of Goodreads raters does, in fact, reflect the sales of the individual books.

The people on Goodreads are an interesting sample of avid readers, but their willingness to rate a book is a reflection of the popularity of a book over a long period.  You don’t have to have bought a book very recently to be able to add it to your Goodreads “have read” list and to rate that book.  That’s interesting data, but what about the more recent developments in the book trade?  A lot has happened in the past 5 to 10 years, particularly the rise on-line book sales, both physical books and ebooks.  This includes the vast new supply of books that have been added to the world’s “book population” by small publishers and self-publishers (generally speaking we can use the term Indie for these)  as well as the increased production of the big publishers, front-list and back-list.

In this blog we will look at Amazon data, to try to get a handle on the newer publishing world.  For the most part, Amazon reviewers have purchased their books fairly recently, and usually from Amazon.  As time goes on, those books are being purchased more and more in the kindle/ebook format, which is a very different experience from buying physical books.  Ebooks are instantaneous, always available, and relatively cheap (see Dodecahedron blog “Imagine that you had a magic wineglass” for some further exploration of those ideas).  So, how have these new facts changed the pattern of book buying within these popular series listed earlier in the blog?

Let’s look at the book series in detail, focusing on the number of Amazon raters vs the position of the book within the series, and compare that with our previous results using Goodreads raters.  Again, we will go by series book sales, from largest to smallest.  In the graphs that follow, Amazon data will be in blue (lines and diamond markers), while Goodreads data will be in red (lines and square markers).  The best fit equations of these graphs are also shown, highlighted in the appropriate colors.  Also included is the R-square, which is a way of measuring how well the data actually fits the equation.  An R-square near 1.00 implies an excellent fit, while an R-square near 0 implies a very poor fit.  Scores in between those extremes are less clear-cut.

In the graphs, the Amazon data are modelled by quadratic functions.  Though they are very imperfect fits, the quadratic model seemed to capture one very important feature of the Amazon rater data; in many cases, the earlier and later books in the series got the most reviews, while the mid-point books were less likely to be reviewed.  A quadratic function incorporates that well, since the nature of a quadratic is to have one inflection point(a maximum or minimum).  The power-law and straight line function fit R-squares are also shown, to help indicate which functional form best fits the observed data.

As before, the Goodreads data are modelled by power law functions.  You can refer to the earlier blogs on power functions to refresh your memory on those.   The main feature of a power law that is important here, however, is that the series decays, with each book being a (more or less) constant fraction of the one before it.

Note that in both cases, these are standard Excel options for modelling data. 

1 – Harry Potter (J.K. Rowling)

The Amazon data wasn’t particularly well fit by a quadratic, though we do seem to see a general trend where the number of reviews sags in the middle of the series.  As noted previously, the Goodreads data  followed a power law quite closely.

Testing the Amazon data for three different functional forms (power law, quadratic and straight line), it turns out that the R-square is marginally better for the quadratic than the others.

Power law R-square =	0.060
Quadratic R-square  =	0.130
Straight line R-square =	0.003

2 – Robert Langdon (Dan Brown)

In this case, we see that the quadratic function fit the Amazon data quite well, though that was probably mainly due to the influence of the last data point, which refers to the most recent book of the series.   Evidently that book was much more “popular” on Amazon than on Goodreads, at least in as much as people were inclined to do reviews.

Again, when testing the three functional forms for the Amazon data, we find the quadratic has the best fit, somewhat better than a straight-line fit (though that one wasn’t bad, either).

Power law R-square  =	0.490
Quadratic R-square  =	0.872
Straight line R-square =	0.671

 

3 – Twilight (Stephanie Myers)

In this case, the quadratic function was an excellent fit to the Amazon data, with the first and last books getting almost the same level of reviews, both far higher than the middle two books.  As noted previously, the Goodreads data followed a power law very closely.  So this seems to be a textbook case, contrasting the situations in the Amazon world versus the Goodreads world. 

For the Amazon data, the quadratic form is far superior to the others:

Power law R-square =	0.190
Quadratic R-square =	0.997
Straight line R-square =	0.000

 

4 –Hunger Games (Suzanne Collins)
As with the Twilight series, the Hunger Games series demonstrates the Amazon versus Goodreads responses very well.  However, with only three data points we have to be careful not to over-interpret our results.  It is trivially true that 3 points can be made to fit a quadratic perfectly (as long as they aren’t on a straight line), much as a 2 points can be made to fit a straight line perfectly.  Nonetheless, it is notable that the Amazon data fits the general picture that we have seen in the other cases, with the first and last books drawing more interest that the second.
For the Amazon data, the quadratic form is far superior to the others, though the “perfect fit” to three points is no surprise, as noted above:

Power law R-square =	0.850
Quadratic R-square =	1.000
Straight line R-square =	0.535

5 –Wheel of Time (Robert Jordan)
As with the Harry Potter series, the Amazon data for this long series was not particularly well modelled by the quadratic function.  The first and last books of the series were high points in terms of reviews, but some of the middle books also did very well in that regard.  Curiously, those were not books that were notable in the Goodreads data, which was modelled by a power series fairly well.
Nonetheless, for the Amazon data, the quadratic form is superior to the others.  Basically, though, this series was not well represented by any simple functional form.

Power law R-square =	0.000
Quadratic R-square =	0.240
Straight line R-square =	0.099

6 –The Dark Tower (Stephen King)

As with Harry Potter and Wheel of Time, the Amazon data for this series is not particularly well modelled by a quadratic, but it does follow the general trend of the first and last books being reviewed more often than the middle books.   Again, however, one of the middle books was an “outlier”. On the other hand, the Goodreads data was an excellent fit to a power law. 

Once more, though, for the Amazon data, the quadratic form is superior to the others.

Power law R-square =	0.010
Quadratic R-square =	0.348
Straight line R-square =	0.074

7 –Game of Thrones (G.R.R. Martin)
This series seems to follow the same general trend as the Twilight and Hunger Games series, which is to say that the first and last books had much higher numbers of reviews, relative to the middle books.  So, the fit to the quadratic form is very high (though there are only 5 points).  As for the Goodreads data, it is very well fit by the power law.

Once more, for the Amazon data, the quadratic form is far superior to the others.

Power law R-square =	0.090
Quadratic R-square =	0.941
Straight line R-square =	0.040

 

 

8 –Divergent (Veronica Roth)

This series follows a similar pattern to Twilight, Hunger Games and Game of Thrones.  In all of those cases, the first and last books of the series drew more Amazon interest than the middle book(s).  However, as with Hunger Games, we must note that there were only three books in the series, so a quadratic will naturally be a perfect fit.  As for the Goodreads data, as noted earlier, it had a very good fit to a power law.

As noted below, for the Amazon data, the  quadratic fit is superior (trivially so, with three data points).

Power law R-square  =	0.650
Quadratic R-square =	1.000
Straight line R-square =	0.335

9 –Hitchhikers’ Guide (Douglas Adams)

For the Amazon data, the Hitchhikers series is a good fit to a quadratic form.  However, that’s mainly due to the influence of the first point.  It actually appears to conform nearly as closely to a power law fit as the Goodreads data did.

The fits of the various functional forms to the Amazon data make that explicit, below.

Power law R-square =	0.899
Quadratic R-square =	0.808
Straight line R-square =	0.502

10 – Aubrey/Maturin (Patrick O’Brian)

The Aubrey/Maturin series conforms somewhat to the quadratic form in the Amazon data – the first and last books drew the greatest amount of interest.  But, as with Hitchhikers, the Amazon data actually conformed very well to a power law, as did the Goodreads data. 

Once more, comparing the R-squares of the various functional fits brings that out, as shown below.

Power law R-square =	0.795
Quadratic R-square =	0.572
Straight line R-square =	0.259

 

Some Conclusions

·         It appears that the pattern in the number of Amazon reviewers per book is quite different from the trend in the number of Goodreads raters per book.

·         Amazon reviewers seem to be inclined to review the first and last books of a series more than the middle books, resulting in a quadratic fit to the data.  As noted earlier, Goodreads raters tend to drop off continuously as the series proceeds, resulting in a power law.

·         The Amazon quadratic function phenomenon is much more evident in more recent book series, namely:

o   Robert Langdon (Dan Brown)

o   Twilight (Stephanie Myer)

o   Hunger Games (Suzanne Collins)

o   Game of Thrones (G.R.R. Martin)

o   Divergent (Veronica Roth)

·         In some of the older series, the Amazon and Goodreads trends in reviews/raters were quite similar (best modelled by a power law), namely:

o   Hitchhikers Guide (Douglas Adams)

o   Aubrey/Maturin (Patrick O’Brian)

·         The other three series were less clear-cut, but the Amazon data still tended to be modelled somewhat better by the quadratic:

o   Harry Potter (J.K. Rowling

o   Wheel of Time (Robert Jordan)

o   Dark Tower (Stephen King)

·         We can’t be sure whether the tendency for the Amazon reviewers to be more focussed on “first and last” is a reflection of underlying purchasing numbers or a reviewing preference, though it’s probably a bit of both.

·         Some people may be willing to skip some of the middle books in a series.  They may get hooked on the first book, not have time to read some of the middle books (and thus skip them), but want to find out how the story arc went by purchasing and reading the final book.

·         On the other hand, people are more likely to want to weigh in with their opinions at the outset of a series or at the conclusion of the series than they are in the middle of the series.  There is a common human reaction to want to jump on the bandwagon at the start and let the world know about.  People also want to make their “summing up” judgements known.  So this could account for the prominence of first and last book reviews predominating, even if the middle books were purchased and read.

 

The one thing that does seem pretty clear is that the Amazon ebook world has produced quite a different reviewing (and presumably purchasing) pattern than the old world of physical books and bookstores.   In the old world, scarcity was the rule - if you didn’t jump into a series at the start, you might never find the early books of the series (short of haunting used bookstores).  Now, if a series interests you, you can jump in at any time and read the whole series.

In our own small way, we have seen this at Dodecahedron Books in the buying patterns for Kati of Terra series.  When Kati 2 came out, it sparked as many sales of Kati 1 over the following year as it did of Kati 2.  Kati 3 seems to be having a somewhat similar effect.  In this case, at least, it seems that people were seeing Kati 2 and saying “that looks interesting, but I might as well start with the first book of the series”.  Since ebooks are always available (no windowing as with physical bookstores) this is a perfectly logical response.   It will be interesting to see how these patterns evolve over time.