Astrophysics Corner, Part 7 - Happy Pi Day, from Dodecahedron Books (and a bit about Pi and Astrophysics, with a side-trip to the Dodecahedron)

As everyone no doubt knows, today is Pi Day.  That is, March 14 is Pi Day (it’s the fourteenth day of the third month, which is sometimes written as 3.14, the value of the transcendental number Pi, to two decimal places).

Speaking of Pi, here’s a bit from The Witches’ Stones Book 1: Igniting the Blaze that actually references Pi:

“I think I can get us into orbit before the Organization ship catches us,” Steph said.  “That might buy us some time, if I can keep the planet between us and the hounds’ ship.  We used to call it playing orbital tag back in training.  It’s a matter of matching speed and maneuver.”

Steph entered some commands into the navigation computer.  “It’s pretty simple, really.  When the distance between us and that ship is the same as pi times the distance between us and the planet, we break off into a circular orbit.  The hounds will have to do the same – they’ll have too much momentum to alter course and try to cut in front of our bow as we finished the first orbit.  Besides, even if they could do that, we’d see what they were up to right away and be in the better firing position to take them out with our bow-chaser laser cannon.  In the olden days, I think they called it having the weather gauge on the opponent’s ship.”

Basically, he is ensuring that he can maneuver his ship in such a way that he can get the Planet of the Amartos between himself and the better armed pursuing enemy ship, thus screening his ship from his enemy’s  fire.  Then, as long as he can keep the planet between them, his ship is safe, orbit after orbit (adjusting his orbit as necessary, when he detects that his opponent is doing so).  So, a bit of simple Pi-based  geometry still comes in handy in the 30^th century.

http://www.amazon.com/Witches-Stones-Book-Igniting-Blaze-ebook/dp/B008PNIRP4

Anyway, that’s the Pi-related book plug.  Now onto other interesting astrophysical and Dodecahedron Books related matters involving pi.

Naturally, astrophysics is full of matters that involve Pi (via circles, spheres, spirals, etc):

·         The fundamental forces, such as gravity and electromagnetism are 1/R**2 laws, that fall off equally in all directions (i.e. with spherical symmetry).  That’s the underlying cause of a lot of the things mentioned below.

·         Many orbits are circular, or close to it.

·         Same with ring structures, such as the rings of Saturn.

·         Stars, planets and other large bodies tend to become spherical if they have enough mass.  Indeed that’s one of the defining features of a planet, rather than an asteroid.

·         The rotation of astrophysical bodies around their spin axes is usually some variation of circular motion.

·         Galaxies often have a beautiful spiral symmetry.

·         The coordinate systems used to locate object in the sky are based on something called the celestial sphere, so Pi comes in there too.

·         Not surprisingly, much of the math used to analyse astrophysical data involves Pi, from geometry to trigonometry to advanced techniques like Fourier analysis and power spectrum analysis.

But what about Pi and the dodecahedron, you ask?  Is there a connection?  That’s a good question for a Dodecahedron Books blog on Pi Day, which we will address below.

Dodecahedron Books is named after the three dimensional geometric shape, the dodecahedron.  This is composed of 12 equal pentagons, which are folded up together into a beautiful characteristic shape.  A pentagon, of course is the two dimensional shape that is made of 5 equal sides, which is itself redolent of fascinating bits of mathematical arcana, mostly connected with a number known as Phi, or the golden mean.  There is a fair bit of lore, ancient and modern, about these shapes, which we will explore in a later blog.  For now, though, let’s focus on Pi, rather than Phi, and see if we can find a connection between Pi and the pentagon and/or dodecahedron.

You can inscribe a polygon (a regular two dimensional shape) in a circle, then inscribe that circle into another polygon.  Using the example of the pentagon, that process looks something like the picture below:

 

As you can see, the perimeter of the inner pentagon will be less than the circumference of the circle in which it is inscribed, while the perimeter of the outer pentagon will be larger than that same circle.  So, we would expect that the average of those two pentagon’s perimeters should approximate the circumference of the circle, more or less.

Let’s assume that the radius of the circle is equal to exactly 1 unit.  With a little high school geometry and trigonometry, we can see that the perimeter of the inner pentagon is given by:

2 X sin(36 degrees) = 2 X .58799 = 1.775571

There are five sides to a pentagon so the perimeter is =  5.877853

A little more high school geometry and trigonometry shows us that the perimeter of the outer pentagon is given by:

2 X tan(36 degrees) = 2 X .72654 = 1.453085

 

There are 5 sides to the outer pentagon, so that gives a total perimeter of 7.265425.

If we average those two, we get 6.571639.

The value of the perimeter of the circle is of course twice the radius times Pi, or:
2 X 3.1459 = 6.283185.

So, sadly our estimate isn’t really very close, differing from Pi by about 5%.  Oh, well let’s try something with more sides than dodecahedron, say an octagon (8 sides).  If we go through the same process, adjusting the size of the angles accordingly, we get an estimate for Pi of 3.18759.  So, that is considerably better.

Using a spreadsheet to carry this on, we get the following table for various numbers of sides for our polygons:

Number of Sides	Pi Estimate	Diff from Pi	Pct Diff
3	3.897114	0.755521663	24.049001%
4	3.414214	0.272620909	8.677793%
5	3.285819	0.144226797	4.590882%
6	3.232051	0.090458154	2.879372%
7	3.204104	0.062511599	1.989806%
8	3.187588	0.045995325	1.464077%
9	3.176957	0.035364046	1.125673%
10	3.169683	0.028090799	0.894158%
20	3.148189	0.006596400	0.209970%
50	3.142630	0.000330092	0.010507%
100	3.141851	0.000258602	0.008232%
500	3.141603	0.000010336	0.000329%
1000	3.141595	0.000002584	0.000082%
5000	3.141593	0.000000103	0.000003%
10000	3.141593	0.000000026	0.000001%

 

 

So, as you can see, the estimate gets better and better as we add more sides to our polygon.  By the time we have arrived at the 500-gon (100 times our original pentagon, which we could call the hecto-pentagon, because that sounds cool), the estimate for Pi that we get is almost indistinguishable from 3.14159, at 3.14160.  We are within one part in three million.

Interestingly, a graph of the above shows a function that looks a lot like our old friend, the power function.  It is interesting how that comes up in all sorts of places.  Of course, a mathematician might say that is a result of the fact that the trig functions can be approximated by power functions.  Indeed, you might say in this case, that Pi is baked right into the pie.

If we used this estimate of Pi for some simple geometry on astrophysical scales:

·         At the distance of the Earth to the Sun (one astronomical unit, about 93 million miles or about 150 million kilometres) we would be out by about 30 miles or 50 kilometres.

·         At the distance of four light years (a trip to the nearest star besides the sun), we would be out about eight million miles, or about twelve kilometres.

·         At the distance from the Earth to the center of the galaxy, we would be out about 40 billion miles or 60 billion kilometres.

·         At the distance to the Andromeda galaxy, we would be out about 4 trillion miles, or about half a light year.

 

So, if you are planning a really long trip, perhaps you should think of approximating Pi with a little more accuracy than the 500-gon can give you.

Whither Chapters 2 (and Whither Barnes and Noble too)

Whither Chapters 2 (and Whither Barnes and Noble too)

Indigo Books and Music Inc is the major corporation behind Canada’s big book chains - Chapters, Coles, Indigo and the World’s Biggest Bookstore.   I have written a couple of blogs about the fate of Chapters (or at least their recent results).  In this blog, I will update some data on them, and also add some data on the U.S. giant, Barnes and Noble.

Chapters

The first graph below shows the sales trajectory for Chapters from 1999 onwards (this data is widely available from online stock market information sources such as the Globe and Mail).  I show sales in both current dollars, and in inflation-adjusted dollars (in this case using 1999 as the base year).  As we can see, sales grew fairly nicely until about 2008 in inflation-adjusted dollars, then plateaued for a few years, before turning downwards in 2011.  With nominal dollars (not inflation-adjusted) the growth continued until 2011, then also turned downwards.  In that case, the growth from 2008 to 2011 was just books keeping up with general inflation.

The fact that sales in inflation-adjusted dollars hit their peak in 2008, then stayed there for a few years is probably a reflection of the worldwide financial crisis that happened about that time.   But the downturn from 2011 onwards is more likely due to the disruption of the book market by the widespread adoption of ebooks, which would have cut sharply into print-book sales.    A significant increase in self-publishing and Indie publishing went along with that, and Chapters has probably not seen much of that revenue, though they might have benefitted from some Indie sales through Kobo, as they do  continue to have close business ties with Kobo.  For those who don’t know, Kobo originated with Chapters, who then sold them to Japanese retailer Rakuten in 2011.

I should note that Dodecahedron Books published our first books, Kati of Terra Book 1 – Escape from the Drowned World  and The Witches’ Stones Book 1 – Igniting the Blaze in 2012, the first year of the major drop in Chapters’ revenue.  Is it mere coincidence that Chapters’ troubles started then?  I wonder J.

http://www.amazon.com/Kati-Terra-Book-One-Drowned-ebook/dp/B00811WVXO

http://www.amazon.com/The-Witches-Stones-Book-Igniting-ebook/dp/B008PNIRP4

We next look at operating expenses versus sales, and consequent operating income (operating profit or loss), in the graph below.  I have just included the inflation-adjusted graph lines, so as to simplify the picture.  As you can see, Chapters operating income dropped during the 2010 to 2012 period, eventually dipping below 0 in 2012, for an operating loss.  In 2013 they ground out a small profit, as their cost-cutting measures managed to overtake their revenue declines.  (Note - not sure if this graph will load properly into blogger).

The third graph shows operating income (profit or loss) at a more useful scale.  It is pretty clear that things took a nosedive after 2010, with a bounce back up in 2013.  Is this the infamous dead cat bounce?  (That’s a financial term that implies that one shouldn’t get too excited about a turnaround, because even a dead cat will bounce a bit after a big fall, but it doesn’t mean it’s getting back on its feet).

It’s hard to know that for sure.  Perhaps Chapters will be able to turn things around, though given the technological disruption that they are facing, it might not be a smart bet, if you are thinking of investing for the long term.  Companies can cut costs faster than they lose sales at the beginning by closing marginal stores, laying off inessential staff, selling unnecessary equipment (not sure if they have a corporate jet), and similar measures.  But most of those things can only be done once, so if sales don’t turn around, it just delays the inevitable.  As they say, you can’t shrink your way to greatness.

Barnes and Noble

Now, let’s look at the same set of graphs for the major bookseller chain in the U.S., Barnes and Noble.  The first graph shows sales (note that I could only find data from 2009 onwards for B&N).  It seems to be undergoing a similar trajectory to Chapters, with sales peaking in 2011, then dropping off.  The fact that their sales kept increasing for a year longer than Chapters’ sales did is probably due to the bankruptcy and closure of Borders, in 2011, which was their major U.S. competitor.   This may have only been a false bloom of health, though, given what happened in the next couple of years.  That is shown in the next graph, showing sales versus expenses and consequent operating profit or loss. (Note - not sure if the second graph will show - eating my graphs seems to be a law of the blogger software).

 

The third graph focuses in on the Operating Income figures (profit or loss).  It appears as if Barnes and Noble has not been quite as successful as Chapters at cutting costs faster than revenues fell.  There is no bounce, dead cat or otherwise in evidence.

So, what’s in store in the future for these major bookselling outlets?  Nobody can be sure, but below are some snips from recent European experiences (by the way, updated financials for Chapters Canada should be out in early April, 2014):

Chapitre (France)(Prensa Latina, Nove 28, 2013)

Paris, Nov 28 2013 (Prensa Latina) The French bookstore chain Chapitre announced today that it is filing for bankruptcy because it cannot maintain its book-buying and selling activities in the country.

The chain, which has 53 stores in France and some 1,200 employees, faces a difficult financial situation because of constantly falling sales, according to chairman Michel Resseguier.

Chapitre ranks second among businesses of its kind in France. It announced a restructuring program in April, including the sale of 12 facilities and staff cuts, but in late November it had only managed to sell four bookstores.

Its failure follows the liquidation of 26 stores of the Virgin Megastore chain in June, leaving 1,000 people jobless in several cities countrywide.

 

Weltbild (Germany) (Jan 14, 2014, Alex Shepard)

Weltbild, one of Germany’s largest publishers and booksellers, has begun insolvency proceedings, citing online competition—the Financial Times reports that it had initially warned investors in September “that high initial investments in its transition to online retail was resulting in temporary losses.” Last week, board member Peter Beer told the FAZ that the company’s struggles are a direct result of its failure to transition into the digital marketplace and compete with Amazon. Beer is also a priest—in fact, he’s vicar-general of Munich; Weltbild is owned by the Catholic Church.     

            
According to Weltbild’s website “every fifth book in Germany is sold through Weltbild.” The company currently employs 6,800 people and serves millions of Germans in its 300 shops. As of 2012 it had a yearly revenue of 1.59 billion Euros. Weltbild has previously claimed to be Germany’s second biggest online book retailer (Amazon.de is first) and its best known publishing company.      

Helena Puumala's romantic short story "Love at the Lake" , now on Amazon

Helena Puumala's romantic short story "Love at the Lake" just went live on Amazon. It's about 6000 words, with an awesome cover and available for Kindle/iPad/iPhone/smartphone for the princely price of 99 cents.

http://www.amazon.com/dp/B00IPSZKLS

A Conversation with Helena Puumala, author of the Kati of Terra Series - What is success for a writer, Part 2

February 26, 2014 Plato’s Pizza, Edmonton Alberta

What is Success for a Writer Part 2?

Question:  Here’s a quick review of our topic.  Last week, I received this work-spam email from the Educational Policy Institute, that included a list of Richard St. John’s Eight Secrets of Success.  Though they do have the flavour of standard business school fluff, the general topic is of “success’ is of widespread interest and this list provides a framework around which to discuss the concept.  So, we thought it might be interesting to discuss them at some length, particularly from the perspective of a writer.  Obviously,  though, any of these thoughts could probably apply to the rest of the creative arts, whether that be writing, drama, painting, music, what have you.  And naturally they apply to other career or life goals, in general.

In Part 1 of our blog (on this site), we discussed the first four general items: Passion, Work Hard, Be Good at what You Do, and Focus.   In this blog we will review the last four major items, indicated below.

Answer: Ok, let’s have a go the remaining items.

Push Yourself

Question:  The first major item is called “Push Yourself” and the first sub-theme is “physically and mentally push yourself to your limits.”  What do you think?  Is this good advice for a writer?

By the way, just as context for blog readers, I know for a fact that you have written over half a million words in the past two years (Kati of Terra 2, published May 2013 and Kati of Terra 3 soon to be published).  If we go back a bit further, you are closing in on a million words written in the past five years (Kati of Terra 1 published May 2012, Witches’ Stones 1 published July 2012 and a collection of short stories, Northern Gothic Stories, published December 2012).  So you are no slacker, and are quite well qualified to comment on this issue.

Answer: Thanks for the literary synopsis.  To be fair, a few of those were based on drafts that I had done when I was younger, as well.  That does sound like a lot, but it’s not so hard if you enjoy what you are doing.

 Anyway, as for pushing yourself to the limits, it’s probably good advice as long as it is interpreted reasonably.  There’s no point in pushing yourself until you have a breakdown.  And with writing, it is more of a mental thing than a physical thing.

Question:  Do you say that because writers just “sit in a chair” while they work, which physically isn’t too difficult.  Because that can be tough on the body too, as a lot of people can attest to.

Answer: I suppose that’s true.  It’s helpful in novel writing, that you can get up and move around at will, which is not generally true of most office jobs.  But I was thinking more about the danger of burning the midnight oil to the point where you just exhaust yourself entirely.  That’s probably counterproductive.  You have to pace yourself, even as you push yourself.

Question:  What about the mental aspect?

Answer: You do have to push yourself mentally, because that’s the way you expand your mind, and you need to expand your mind so that it can hold the contents of your book.  You want to be able to hold a lot of the contents in memory but it’s more than that - you want to be able to mentally inhabit your created world, really immerse in it.  That makes writing easier.

Question:  It sounds a bit like how the best actors try to “live their character” while filming or during the course of the play’s run.

Answer: That’s probably not a bad analogy.

 Question:  You have mentioned previously that you felt that your mind really was expanding, as a result of writing long-form novels.  What’s that feel like to you?

Answer: I can hold more of the book in my head now.  I don’t have to consult notes as much as I did at the beginning.  It just feels like there is more room in my head than there was before I got serious about my writing again.

Question:  That reminds me a bit of studying advanced calculus in my undergraduate days.  When things went well, it felt like your mind could hold things that seemed impossible before.  It could almost feel effortless sometimes.  You were surprised at yourself.  Unfortunately it didn’t always go that well J.

Answer: I agree.  The feeling of your mind expanding can come as a shock at the beginning.  But it is a nice surprise.

Question:  Ok, here’s the next sub-item: “push through shyness and self-doubt.

Answer: I am not sure that shyness applies for most of the writing process.  After all, it’s pretty solitary.

Question:  Oh, I don’t know about that.  What could be more truly the essence of “pushing through shyness” than having the audacity to write a novel or short story, then actually pushing the publish button.  Same thing for “pushing through self-doubt”.

Answer: I guess that’s true in a way.  You are not speaking in front of a big crowd, so the shyness concept doesn’t apply in that way.  But you are expressing yourself and trying to entertain and/or educate.  So, you can’t be shy in a certain sense, to do that.  You can’t be self-effacing.  You have to have an ego and confidence in your right to make your statement. 

Serve

Question:  The next general category is called “Serve”.  The first sub-theme is “make it a privilege to serve people.”

Answer: In writing, you are trying to entertain and perhaps educate, so in that sense you are serving people.  But the way it is phrased has a sort of elitist connotation, like a bit of noblesse oblige.  Plus it can be an ego trip - “I serve”.  So I have some issues with the terminology.  The word serve is a loaded one.

Question:  It can come off as a little bit “business school goody two-shoes”, though there is something there.  The next sub-item is “serve other people something they will find of value”.

 Answer: As a writer, you want to offer for peoples' consumption, the products of your imagination.  Naturally you hope they find it of value.  But it should be a transaction among equals, so again “serve” seems like the wrong word for that.

Question:  The third sub-item is “think more about the needs of your stakeholders than your own needs”.   It sounds like Spock's famous line from The Wrath of Khan -“the needs of the many outweigh the needs of the few”.

Answer:  Well, then I will counter with Kirk's quote in the next movie, The Search for Spock.  In writing, “the needs of the one must outweigh the needs of the many”.   Your production comes from your own innermost intuitive self, so you have to give that first priority.  If you are going to cater to anyone, it has to be to your own muse.  You have to assume (or at least hope) that your audience will follow you to the places where your imagination leads them.

Question:  So, don’t try to slavishly write to some intended audience, because it will just get in the way of your creativity.

Answer:  Well you do want to keep your market in mind, but you can’t really know for sure what they want, so you should offer what comes from within you.   That way it’s sincere and genuine.

Have Ideas

Question:  The next major category is called “Have Ideas”.  The first sub-theme is “you must find the time to think.”

Answer:  Well, that’s self-evidently true for writing.  Even bad writing requires some thought.

Question:  That brings up the question of how much time you should devote to thinking versus how much time you should devote to writing versus how much time you should devote to editing.  There is a school of thought current now, that says writers must push out a lot of product in order to have a reasonable chance of commercial success.  Conversely, in the old days, there was perhaps too much emphasis on re-writing, re-editing and re-polishing.  Obviously there is a trade-off inherent in the quantity versus quality argument.  Where do you stand on that?

 Answer:  I can’t speak for others, but I have never tried to measure the amount of time I spend on one versus the other.  But a good book does require a lot of thought and creativity, in my opinion. And that does take time.  Writers shouldn’t stint on that for the sake of publishing some set amount of product per year.  You can’t get too rule-bound about productivity - that can interfere with the natural rhythm of creativity.

Question:  The next sub-item is “seek inspiration from whatever and whomever you can: books, TED, mentors, gurus”.  This is another one that seems self-evidently true for writers.  You have to beg, borrow and steal from everyone you can.

Answer:  That’s true, but footnote and cite and say thanks.  And try to respect copyright, unless you have a lawyer in the family.  But seriously, you want your ideas to be respected, so you have to respect the ideas of others.  And always remember, the depths of your creative self are the best source of material that you can come across.  Try it, it’s really amazing.

 Question: Obviously in all endeavours, we borrow from the past and lend to the future - that’s Newton’s “standing on the shoulders of giants”.   The last sub-theme of this category is “listen, observe, be curious, ask questions, problem solve, make connections”.

Answer: I would just add: If you are a writer, create, create, create. 

Persist

Question:  The final major category, and perhaps the one most salient for the arts or indeed many careers is “Persist”.  The first sub-item is “persist through failure”.

Answer:  As a writer, you will get the chance to practice that a great deal J.

Question:  Of course, leaving aside money as a scorekeeper, you never really know when you are succeeding or failing.

Answer:  And you have to accept that.  If you throw in the towel, you might do so just before the book or short story that breaks through for you.  It may be the tenth or twentieth book that makes you an overnight success.

Question:  The final sub-item is “persist through CRAP: Criticism, Rejection, Assholes, Pressure”.  That sounds like submitting query letters to agents.

Answer:  Doesn’t it though.  That’s assuming you could find one that was even willing to give you the courtesy of paying attention to you long enough to reject you.  Yes, that’s the beauty of self-publishing, at least at the moment.  Nobody can stop you from expressing yourself.

Question:  But there is still criticism, rejection, assholes and pressure out there.

Answer: True, but that is all easier to ignore now.  I LOVE self-publishing.

 

Richard St. John’s Eight Secrets of Success

1. Passion
1. do it for love not for money.
2. if you do it for love the money will follow.
3. passions are the first thing you thing of in the morning and the last thing you think of at night.
2. Work hard
1. the harder you work the more you will achieve
2. success rarely comes without hard work; lucky winners are few and far between.
3. Be good at what you do
1. work long and hard to be good at something
2. practice; practice; practice
3. when it comes down to it if you aren’t good at what you do you can’t be a success and sustain it
4. Focus
1. concentrate all your efforts into one or two goals.
2. without focus your resources will be too thinly stretched to achieve real success.
5. Push yourself
1. physically and mentally push yourself to your limits
2. push through shyness and self-doubt
6. Serve
1. make it a privilege to serve people
2. serve other people something they will find of value
3. think more about the needs of your stakeholders than of your own needs
7. Have ideas
1. you must find the time to think
2. seek inspiration from whatever and whomsoever you can: books; TED; mentors; gurus
3. listen; observe; be curious; ask questions; problem solve; make connections.
8. Persist
1. persist through failure
2. persist through CRAP: Criticism; Rejection; Assholes; Pressure