artists mentioned by Boards of Canada in their interviews
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=== The Campfire Headphase === | === The Campfire Headphase === | ||
β | [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 [[ | + | [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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<gallery> | <gallery> | ||
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Image:1979yearbook_excerpt.jpg | Image:1979yearbook_excerpt.jpg | ||
</gallery> | </gallery> | ||
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=== Trans Canada Highway Cover === | === Trans Canada Highway Cover === | ||
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Image:1977dodge_instruction_manual.jpg | Image:1977dodge_instruction_manual.jpg | ||
</gallery> | </gallery> | ||
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=== Various === | === 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). | [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]] | [[Image:Rainbow-chakras.jpg]] | ||
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== Numbers & Patterns == | == Numbers & Patterns == | ||
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=== Various Math Related Pictures === | === Various Math Related Pictures === | ||
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[[Image:Bocmath_misc01.gif]] | [[Image:Bocmath_misc01.gif]] | ||
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A visual illustration depicting a facet of Einstein's theory of relativity. | A visual illustration depicting a facet of Einstein's theory of relativity. | ||
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[[Image:Bocmath_misc02.gif]] | [[Image:Bocmath_misc02.gif]] | ||
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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. | 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]] | [[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. | A demonstration that the maximum number of regions into which you can divide a plane using 6 lines is 22. | ||
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[[Image:Bocmath_misc04.gif]] | [[Image:Bocmath_misc04.gif]] | ||
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β | The formula 3n(n-1)+1. This gives the sequence 1, 7, 19, 37, 61, 91, .... These are the centered hexagonal numbers | + | The formula 3n(n-1)+1. This gives the sequence 1, 7, 19, 37, 61, 91, .... These are the centered hexagonal numbers. 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]] | [[Image:Boc_hexnum.gif]] | ||
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[[Image:Bocmath_misc05.gif]] | [[Image:Bocmath_misc05.gif]] | ||
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A graph of changes in life expectancy. | A graph of changes in life expectancy. | ||
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[[Image:Bocmath_misc06.gif]] | [[Image:Bocmath_misc06.gif]] | ||
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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! | 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]] | [[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 Ο. | 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 Ο. | ||
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[[Image:Bocmath_misc08.gif]] | [[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". | 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]] | [[Image:Bocmath_misc09.gif]] | ||
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β | 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 | + | 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 gemetria, 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. 703 is the 37th triangular number, 1+2+...+37 = 703. |
β | Triangular numbers have the general formula | + | Triangular numbers have the general formula nΓ(n+1)/2. E.g. the 37th triangular number is 37Γ38Γ·2 = 703. 37 crops up a lot here: not only is 703 is the 37th triangular number, but 407, 296, and 703 are all divisible by 37. |
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β | 37 crops up a lot here | ||
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[[Image:Bocmath_misc10.gif]] | [[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. | 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]] | [[Image:Bocmath_misc11.gif]] | ||
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A clockface flanked by angelic figures. Perhaps taken from the frontispiece of a book. | A clockface flanked by angelic figures. Perhaps taken from the frontispiece of a book. | ||
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[[Image:Bocmath_misc12.gif]] | [[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. | 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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Here's a picture, using some frames from one of my own animation sequences, to show how this works, geometrically: | 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]] | [[Image:Trirhomb.jpg]] | ||
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