Editing Folklore - bocpages

== Artwork Allusions ==
=== Incredible String Band ===
Allusions in the artwork. Particularly referring to the [http://www.discogs.com/artist/Incredible+String+Band,+The Incredible String Band], for whom [[Boards of Canada|BoC]] have a great deal of respect, and whom they apparently see from time to time. The lyrics section reveals that they have sampled the ISB occasionally; there's the old track "ithcus sound", a possible reference to the ISB track "ithkos". There's a general similarity in mood between Geogaddi and such ISB songs as "Waltz of the new moon" (HBD). It has also been observed that the title "Geogaddi" might in part refer to the ISB song "koeeaddi there" (HBD again).

One interviewer comments that the front covers of the ISB's "The Hangman's Beautiful Daughter" and [[Boards of Canada|BoC]]'s "Music Has The Right To Children" would make "a nice pair":
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However, but there is a far more striking similarity between the back cover of the ISB album, and some of the pictures of [[Boards of Canada|BoC]] available elsewhere; if this is any more than coincidence, and it may be no more than that, it makes a nice tribute to the ISB:
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The next pair aren't all that similar, except in their mood, but here they are anyway: 
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=== Geogaddi Cover  ===
[Roger B] has pointed out something about the cover art of the [[Geogaddi]] album: In the scene in the film "The Wicker Man" that features dancing around a maypole, a figure is seen in silhouette (by his shadow on the grass). The pose is very similar to that in the picture used to make the album cover. (Thanks, Roger). Below, is a frame from that film. To the right, the photo on which the [[Geogaddi]] cover is based (the picture was taken by Peter Iain Campbell, as is noted on the back of the album).
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However, [Tonamel Rhysthal] has another suggestion, that the pose mirrors that of Leonardo da Vinci's famous "Vitruvian Man". Wikipedia, always a good resource, has an article on [[wikipedia:Vitruvian_Man|Vitruvian Man]]. The link between this figure and the relation between art and mathematics fits in very well with some of the other images [[Boards of Canada|BoC]] had on their site (see below), and also with one of the themes of Geogaddi (religious iconography and geometry).

=== My Bloody Valentine ===
The following information has been given by [7seals].
The front covers of both albums. Note the very similar font used (Bauhaus). Faces obscured. (in [[Music_Has_the_Right_to_Children|Music Has the Right to Children]], it seems artificial whereas in [http://www.discogs.com/release/217169 isn't anything] it seems to be intentionally caused by overexposure).
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<gallery caption="The front covers.">
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<gallery caption="The inside front covers.">
Image:Mhtrtc_inside_front.jpg
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<gallery caption="The inserts.">
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<gallery caption="The back covers of the albums.">
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=== The Campfire Headphase ===
[Khov] made a post on the watmm forum about one of the small artwork pictures on [[The Campfire Headphase]] cover which obviously has been taken from [[http://www.iit.edu/alumni/updates/yearbook/1970s/images/campus%20and%20student%20in%20computer%20center%201979.jpg this 1979 yearbook picture]].
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=== Trans Canada Highway Cover ===
[Damien] made a post on the [http://fredd-e.narfum.org/formerboc/guestbook/page11/#id714 old guestbook] about the striking resemblance between the [[Trans Canada Highway]] cover and a 1977 Dodge operation manual. No coincidence.
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=== Various ===
[DC] stumbled across this purely by accident: one of the little images in the artwork of the [[In_a_Beautiful_Place_out_in_the_Country_(release)|In a Beautiful Place out in the Country]] single comes from [http://www.healthy.net/rainbowstress/chakras.htm here] (where the image is explained).

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[[Image:Rainbow-chakras.jpg]]
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== Numbers & Patterns ==
=== Pascal's Triangle ===
An older version of the [[Boards of Canada|BoC]] website briefly had some black-and-white drawings on a page, which contained Pascal's Triangle. Alas, the page at [http://web.archive.org/web/20010606214250/http://www.boardsofcanada.com/misc.phpl web.archive.org] is dead.

Some of the pictures that were accessible on that page (and reproduced below) have interesting references that might not be apparent at first glance. Putting his interest in mathematics to use, [DC] submitted the following section about the images; he adds that, while he is interested in maths, and the mathematical patterns to be found in nature, he does not personally believe in the merits of numerology. As former maintainer of this site, he requests that that section, below, be left just as it is as his own lasting personal contribution to the site.

Firstly, there's [http://mathworld.wolfram.com/PascalsTriangle.phpl Pascal's Triangle] itself. Each number is the sum of the two diagonally above it.
If you start at the top and follow it down diagonally:
* the first column consists only of 1's (a single zero-dimensional point),
* the next has the positive integers 1,2,3,.... (dots arranged in a 1D line),
* then triangular numbers: 1,3,6,10,15,21,... (dots arranged in 2D triangles),
* then the tetrahedral/pyramidal numbers : 1,4,10,20,35,56... (dots arranged in 3D tetrahedrons);
* then: 1,5,15,35,70,126... (dots arranged in 4D '4-simplex' arrangements);
and so in, into ever higher-dimensional analogues of the triangle.

Another example - tossing coins: take the row "1,4,6,4,1". If you toss a coin 4 times, the chances of getting 0,1,2,3, and 4 heads (or tails) are, respectively: 1/16, 4/16, 6/16, 4/16, 1/16. If you toss it 5 times, the chances of 0,1,2,3,4,5 heads (or tails) are: 1/32, 5/32, 10/32, 10/32, 5/32, 1/32 (from the next row). And so on.

The total of the numbers in each row is a power of two. There are many more relations - a whole page could be devoted to Pascal's Triangle alone - but I'll let readers pursue this themselves. There's a Dr Math article on it, and another [http://ptri1.tripod.com/ site devoted to Pascal's Triangle] even explains how you can get the Fibonacci numbers from it, among other things.

=== Various Math Related Pictures ===
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[[Image:Bocmath_misc01.gif]]
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A visual illustration depicting a facet of Einstein's theory of relativity.
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The Pioneer 10 plaque: it shows the location of the earth relative to distant pulsars (lower-left of picture), and the height of the woman relative to the space-craft. The two spheres beside each other (top-left) represent the reversal of spin of an electron in a hydrogen atom, which results in the emission of 21cm radio waves. Therefore, all distances on the plaque are indicated in terms of 21cm units.
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[[Image:Bocmath_misc03.gif]]
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A demonstration that the maximum number of regions into which you can divide a plane using 6 lines is 22.
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The formula 3n(n-1)+1. This gives the sequence 1, 7, 19, 37, 61, 91, .... These are the centered hexagonal numbers. The nth centered hexagonal number is 1 more than 6 times the (n-1)th triangular number. You can make a series of hexagons of different sizes using coins (or indeed small hexagons). The first degenerate case is a single coin = 1. You can place six more coins around this one to make a hexagon with 7 coins. You can place twelve more coins around the outside of this hexagon to make a larger hexagon with 19 coins. And so on, adding another eighteen to get 37, then another twenty-four to get 61. My own illustration of this is below.
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[[Image:Boc_hexnum.gif]]
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Whereas centered hexagonal numbers make filled-in hexagons, the "cornered" hexagonal numbers {1, 6, 15, 28, 45, ...} make the outlines of hexagons. They are given by the formula n(2n-1), or every other triangular number (starting with 1 which is by convention the zeroth).
The centered and cornered hexagonal numbers are related by the following formula. Let x be the nth centered hexagonal number and y be the nth cornered. Then x = y + n²
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[[Image:Bocmath_misc05.gif]]
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A graph of changes in life expectancy.
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Possibly, a poem by the Saucepan Man from an Enid Blyton book - from the "Magic Faraway Tree" series of books, I think!
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[[Image:Bocmath_misc07.gif]]
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Presumably making the point that the ratio of the gematria for "Jesus Messiah" and "Holy Wisdom" in Hebrew, namely 116/37 or 3 + 5/37, is a good approximation to π.
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[[Image:Bocmath_misc08.gif]]
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The Greek Sphinx was said to have "the bust and head of a lady, the wings of an eagle, the body and legs of a lioness, and the tail of a snake or dragon".
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[[Image:Bocmath_misc09.gif]]
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A pyramid or triangle of 703 dots made up of 296 dots on top, and a further 407 dots below. The Hebrew words in the picture are the last two words of Genesis 1:1, namely, the word for "and", and the word for "the earth" (Hebrew is written from right to left). The gematria for the words for "and" and "the earth" are 407 and 296, respectively (400+1+6, and 90+200+1+5; for further details on gematria, you can do your own research). The total for these two words is 407 + 296 = 703. As it happens, 703 is a triangular number, meaning simply that 703 dots form a triangle, as shown in the image. Triangular numbers can be expressed in the form 1+2+3+...+n-1. 703 is the 38th triangular number, 1+2+...+37 = 703. The number 38 is the sum of the rows of the magic hexagon; this sum is known as a magic constant.

Triangular numbers have the general formula n(n-1)/2. E.g. the 37th triangular number is 37×36÷2 = 666. Combinatorially, the triangular numbers are the "choose-two" numbers because they count the number of ways to pick 2 objects from a set of N objects (not counting the order by which you pick them).

37 crops up a lot here. Note that 407, 296, and 703 are all divisible by 37. Also note that if, against convention, you were to count 1 as being the first triangular (instead of the zeroth), then 703 would be the 37th triangular number.
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[[Image:Bocmath_misc10.gif]]
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Anatomical diagram with many Fibonacci numbers, powers of two, and so on. Perhaps relates to the work of medieval artists, relating ideal proportions of the body in art to the Golden Section, and so forth.
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[[Image:Bocmath_misc11.gif]]
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A clockface flanked by angelic figures. Perhaps taken from the frontispiece of a book.
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[[Image:Bocmath_misc12.gif]]
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A square, with a dedication to the "Hyperborean Apollo" (in transliterated Greek, which I find more confusing to read than Greek itself, since I expect the letters to have their Greek values). Pythagoras was regarded by some as the incarnation of the Hyperborean Apollo. 296, the figure in the box, is four times 74, the figure at each edge. Pythagoras and his followers: saw a connection between music and mathematics, and discovered that notes in the scale were connected by mathematical ratios. For example, the ratio of the frequencies of two notes separated by a major third (e.g C and E) are 5/4. For a fourth (e.g. C and F), it is 4/3, and for a fifth (e.g. C and G), it is 3/2. Of course, they were quite correct about the mathematical underpinnings of harmony - see Jean-Philippe Rameau's classic text, "A Treatise on Harmony". In that sense, music is, indeed, math.
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An unrelated point I noticed when thinking about hexagonal numbers: a [[Boards of Canada|BoC]] track is called "Triangles and Rhombuses". You can make each hexagonal number from a triangular number plus a square (which can be drawn as a rhombus).I don't know whether [[Boards of Canada|BoC]] had this in mind when they named the track, but I just mention this for interest anyway. Examples of "triangular number" + + square" = "hexagonal number"

0 + 1 = 1, 3 + 4 = 7, 10 + 9 = 19, 21 + 16 = 37, 36 + 25 = 61, and so on.

If you want to work it out for yourself, use: Triangle(n) = n(n+1)/2   ♦   Rhombus(n) = n2   ♦   Hexagon(n) = 3n(n+1)-1
and show that: Triangle(2n-2) + Rhombus(n) = Hexagon(n)

Here's a picture, using some frames from one of my own animation sequences, to show how this works, geometrically: 
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[[Image:Trirhomb.jpg]]
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== Future Releases Theories ==
=== 2016 ===
[[Boards of Canada|BoC]] began 2016 by breaking their silence after "[[Tomorrow's Harvest]]" by releasing two new remixes one month apart from each other, [[NEVERMEN_-_Mr_Mistake|Mr Mistake by NEVERMEN]] and [[Odd_Nosdam_-_Sisters|Sisters by Odd Nosdam]].  The latter was accompanied by a video <ref>https://www.youtube.com/watch?v=yzjoArxwW2E</ref> which was formally released on February 22nd.  This led to some speculation that some new material could be in the works.


After a few months passed, they recaptured the attention of their fanbase with an innocuous post to their generally dormant [[Websites|social media accounts]] on June 6th, 2016, linking to an existing fan made video for "[[Macquarie Ridge]]".  A month later, on July 7th they retweeted another fan video of the "[[Beck_-_Broken_Drum|Broken Drum by Beck]]" remix that had been posted to Twitter on July 2nd.  


They tweeted once again, this time a Youtube link to "[[Peacock Tail]]" on July 31st.  The last post raised some uncertainty as to whether they would continue posting in a 6/6, 7/7, 8/8 type frequency.  


Around this same time, ASCAP entries for a release entitled "Harvest Ritual" and Untitled (Machinedrum reconstruction) were discovered <ref>http://www.twoism.org/forum/viewtopic.php?f=2&t=13437</ref>, but quickly disappeared after they were noticed and the former subsequently waved off <ref>http://www.twoism.org/forum/viewtopic.php?f=2&t=13437&p=264601#p264601</ref> as an old ''[[Tomorrow's Harvest]]'' related entry by someone <ref>http://www.twoism.org/forum/memberlist.php?mode=viewprofile&u=4155</ref> making their first (and still only) post on the [[Twoism (messageboard)]].  After 8/8 came and went, the next known date of interest was 8/22 (the 20th anniversary of the system date on the [[Cosecha-transmisiones.com|Cosecha-transmisiones console]]) but this date also passed without incident.  


With 8/8 and 22/8 eliminated as possibilities, what's the next date that would make sense for them to make another appearance out from the ether?


They finally posted a fan video for "[[Nothing Is Real]]" on August 24th which didn't seem to follow any type of previously speculated upon date related logic.  


They posted again on October 14th, this time for the song "[[Left Side Drive]]".  


Over the span of the few months described above, they had begun liking various fan posts on Twitter, seemingly at random, many of the fan posts including pleas for new material or involving the liking of tweets that included their own music.  This activity slowed down as time went on, briefly peaking at 49 likes before dropping back down to 48 likes, before going up to 49 likes again in February 2017  - the original 49th liked post was deleted by its author, so keeping the tally set to 49 likes seemed important to them at this stage.


They posted a new fan video for "[[Open the Light]]" on December 8th, alongside a simultaneous heavy revamp of their [[Websites|Youtube channel]] playlists, which had been in need of some upkeep as by that time, as there were multiple broken or delisted videos from over the years.  What was interesting about the "[[Open the Light]]" post is that it wasn't cross-posted to Facebook, the same as "[[Peacock Tail]]" back on July 31st.  I feel that these omissions from their Facebook account weren't an accident but rather, those 2 entries were only relevant to a pattern that they were establishing at their Twitter account, but more on that in the Posting Details section.


Rather than a new release announcement at the end of the year, the Youtube video channel revamp seems to have joined the campaign midway to serve as a map of sorts, providing vague hints to assist in navigating the numeric trails being blazed at both their Facebook and Twitter accounts for those who were trying to pay attention.  I'll go into more detail on that as the timeline continues to progress.


After the playlist revamp and the "[[Open the Light]]" posting on December 8th, they went silent for the rest of 2016.

=== Posting Details ===

==== Twitter ====


Now that the events have been summarized, it's time to get to the details.  As described above, each social media network account seems to have its own unique pattern, but the same crucial end points.  Twitter is the most plentiful (and therefore easiest to pick out a method to the madness) so it's best start to start there with a list of the dates and posts so far:


6/6 - Macquarie Ridge - 2:06 AM CET

7/7 - Retweet of Broken Drum from 7/2 - 12:19PM ET (original tweet)

31/7 - Peacock Tail (2005) - 6:25PM GMT

24/8 - Nothing is Real (2013) - 12:57PM UTC

14/10 - Left Side Drive (2006) - 3:11AM MT

8/12 - Open the Light (1998) - 8:57AM UTC


- The main pattern to follow would involve multiplying the date and month together for the posts when both numbers are divisible by 4.  We add up to 24 in other even numbered months.  We subtract down to 24 in odd numbered months, the odd months are also preceded by a retweet.


- "[[Macquarie Ridge]]" is unique (for now).  Add to (12), multiply to (36) and then subtract those sums (36 - 12), we have a sum of 24.  It doesn't have a year tied to its post title either.


- The other hint to multiply is when the timestamp ends in :57.  The timestamp on the Cosecha console was 2:57 - potential nod to the number 70 2x(5x7)
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- The multiplication sum halves with each subsequent step, while alternating with the added/subtracted 24s, and de-increments by 4 hours each time it happens. (12:57 -> 08:57 -> ??:??)


- So far, the multiplication steps include a number from the previous multiplication based step, and carries over the number to the next step (ie. 24 - 8 - 8 - 12) meaning that the month  of the current tweet will be part of the subsequent tweet's date. ie. August 24th means the 8 carries to December, giving us December 8th, etc.


- They specify the year of release for "[[Peacock Tail]]", "[[Nothing Is Real]]", "[[Left Side Drive]]" and "[[Open the Light]]" in the title of the respective tweets.  If treated as two pairs, they are both separated by 8 years.  A look back at their discography determines that 2001 and 2009 as the only other remaining pair of year that functions this way.


- Based on the rules above, omitting any retweets, the main numeric pattern should be read like this:


6/6 - 0


31/7 - 24

24/8 - 192


14/10 - 24

8/12 - 96

==== Broken Drum ====


All recent Twitter posts have specifically been part of this assumed large pattern, or have been related to promotion of a remix or physical release of some kind.  That initial Broken Drum post didn't seem to make much sense in the scheme of things when it first came about, other than being a red herring that initially hinted toward a potentially more straightforward series of posts such as 6/6 7/7, 8/8, etc.


Going back to 2016, the Broken Drum retweet set up its own sub-pattern starting in July 2016.  The original posting date (7/7) is obfuscated on Twitter because it's a retweet, but it was mentioned on the [[Twoism (messageboard)]] <ref>http://www.twoism.org/forum/viewtopic.php?p=263668#p263668</ref> on the day that it was first posted.  This means that there were posts on 7/7, 31/7, and 24/8 - the commonality is that the posts were separated by 24 days each.  The retweet approach seems as if it was intentional, to separate it from the main pattern and hide the existence of the smaller pattern.

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==== Multiplication chain progression ====

Following the logic described previously, the multiplication related posts chain together like this:

24 x 8 | 8 x 12 < > ?? x ? | ? x ?

==== Facebook ====


Much of the chatter from Twitter is omitted, but it seems that it has a potentially identical end goal, even if some of the same numbers are utilized in a different way.  Note that only a single entry per "pair" makes it over to their Facebook account.  This is what we know so far.


2016 - sum = 48

6 + 6 = 12

24 + 8 = 32

14 - 10 = 4


2017

? ? ? = ?

? ? ? = ?

? ? ? = ?

==== YouTube ====


Their approach to their [[Websites|YouTube playlist]] structure has been thoughtful and at times playful.  Try subtracting the numbers of some of the entries from the overall number (145) to se what type of  "companion" you end up with (for example, 72 and 73 are "[[Satellite Anthem Icarus|SATellite ANthem ICarus]]" and "[[XYZ]]", interesting after they spelled out L-M-N-O-P with their first few social media posts) You can also add some of the duplicate song values together to see where you end up.  They might ask you to do something like "[[Split Your Infinities]]" when you find a third instance in the list of the first 2 songs that you added together, for example.


Example of a playlist easter egg:

* 7 ("[[Dayvan Cowboy]]") [https://www.youtube.com/watch?v=A2zKARkpDW4&list=PL221B13914A7EF3A2&index=7]

* 47 ("[[Dayvan Cowboy]]") [https://www.youtube.com/watch?v=ES02mWIJ2Tk&list=PL221B13914A7EF3A2&index=47] 

* 74 ("[[A Is To B As B Is To C]]") [https://www.youtube.com/watch?v=Kg3fsTjEY5c&list=PL221B13914A7EF3A2&index=74]


In the end, it's impressive to witness the care that went into assembling these playlists as a companion to what they have been establishing at their [[Websites|Twitter and Facebook accounts]].  It provides information that leads one to speculate on future posts.  The only drawback to the playlist assembly is that due to the number of repeats, and the proximity of some of those repeats to each other, it detracts a bit from being able to appreciate the playlists at face value.  The playlist construction definitely prioritizes the subliminal/easter egg aspects over providing a good flow for the everyday casual listener.

== References ==
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