In 1987, my PhD work at the University of Tasmania was beginning to take shape, and I produced a technical report with some preliminary results. I also started a side-project on functional programming language implementation which was to result in the design of a novel computer (a computer, sadly, that was never actually built, although many people joined in on the hardware aspects).
Horror writer Stephen King had a good year, with The Tommyknockers and several other novels being published. The term “steampunk” was coined in 1987, and Orson Scott Card’s Speaker for the Dead, the sequel to Ender’s Game, won the Hugo Award for best science fiction or fantasy novel (it also won the Nebula Award in 1986, the year it was published).
In music, The Alan Parsons Project released their album Gaudi (which included the single below), U2 released The Joshua Tree, and Linda Ronstadt, Emmylou Harris, and Dolly Parton released Trio. The Billboard top song for 1987 was the rather silly 1986 single “Walk Like an Egyptian.”
Underneath (or, perhaps, to the side of) adult culture sits an often poorly documented culture for children alone. There are, of course, many songs and stories directed by adults to children, but true child culture consists of games, riddles, songs, stories, and rules directed from children to other children.
A rather dark example, largely specific to North America, is the Hearse Song below (the video gives a more complete version, but I must warn my readers – it’s really very gross, and not at all suitable for adults):
“Don’t ever laugh as a hearse goes by
For you may be the next to die
They wrap you up in a big white sheet
From your head down to your feet
They put you in a big black box
And cover you up with dirt and rocks …
And the worms crawl in, the worms crawl out
The worms play pinochle on your snout …”
The song is essentially a form of gallows humour picked up by children at around age 10 – about the age that children first come to grips with the inevitably of death (although it is rather surprising, given that the US is a majority-Christian society, that Christian views of death barely appear in the song at all). The excellent article on the song by Charles Doyle also reports military versions of the song from World War I recorded by Carl Sandburg and John J. Niles, but those appear to draw on earlier childhood versions.
I’ve been experimenting with a textual analysis focussing on song snippets containing lines devoted to interment (2 to 6 lines, depending on the version). I compared versions with a variation of the Levenshtein distance at the word level, using a table of related words, and allowing for permuted lines. The multi-dimensional scaling diagram below collapses the calculated distances into two dimensions. The phrase “Doyle var” refers to variants listed by Doyle (e.g. “They put you in a big white shirt / And cover you up with rocks and dirt”), whereas “Alternate” refers to versions I have collected myself on the Internet (e.g. “They wrap you up in a bloody black sheet / And throw you down a thousand feet”). A large amount of mishearing and misremembering seems to be going on.
The numbers in brackets on the chart indicate the number of lines in each snippet. The 2-line child versions form a visible cluster in the diagram, with 4-line versions by modern bands (Harp Twins and Rusty Cage) a little more distant, and the World War I versions on the periphery all quite different:
Distances can also be visualised as an UPGMA tree. However, this cannot really be interpreted as an evolutionary tree, in that the 4-line band versions seem to be combining lines from multiple 2-line versions. Indeed, there seems to be a large pool of rhyming pairs within the culture that is assembled and reassembled in various ways, rather than any canonical song. Perhaps this reflects the character of the verbally innovative child culture in which the song (or, rather, song family) dwells.
Books of 2009 included Wolf Hall by Hilary Mantel (set in 1500–1535; a TV series of 2015), The Windup Girl by Paolo Bacigalupi (dystopian science fiction; Nebula Award winner), and The Maze Runner by James Dashner (young adult dystopian sci-fi; a film of 2014). Books that I later reviewed include The Lassa Ward by Ross Donaldson and God’s Philosophers by James Hannam.
From the point of view of getting into the final, it seems to be bad to sing about Heaven (Montenegro, Portugal), war (Croatia, Finland), cell phones (Belgium, Portugal), or cold (Latvia, Poland, Romania). On the other hand, it’s good to sing about lights (Germany, Norway, Sweden).
The Eurovision Song Contest has been on again (strangely, Australia has now become part of Europe). On the whole, I didn’t think much of the songs this year, although Ieva Zasimauskaite from Lithuania did sing an interesting song about love and marriage:
As usual, the voting is the really interesting aspect. This year, I’ve done an analysis where:
I looked at combined country votes in the final (jury plus televoting)
I assumed that countries would have given themselves the maximum score of 24
The diagram below shows a “cultural map” of Europe produced by multi-dimensional scaling of the votes by each country. That is, countries with similar tastes are located close to each other.
For example, Germany and the Netherlands have similar tastes. They both gave 6 or more points to Germany, Israel, Cyprus, Austria, Italy, Sweden, Lithuania, and the Czech Republic. They both gave at most 2 points to Moldova, Albania, France, Bulgaria, Ukraine, Serbia, Finland, Slovenia, Hungary, Portugal, and the UK. They differed on the remaining seven countries.
Colouring in the diagram is by the second principal component of the voting, which defines a cultural north-south axis.
In traditional Christian theology, Satan is the ultimate marketing genius. Not being able to create, Satan has no actual product to sell – merely illusions. However, being a fallen angel, he does have supernatural intelligence. He also has a large crowd of “influencers” willing to endorse the nonexistent product. The book and film of Stephen King’s Needful Things illustrate the concept brilliantly, as the main character (played to perfection by Max von Sydow) uses his supernatural marketing genius to con people into trading their souls for useless bits of junk:
Of course, that kind of marketing is an ideal that mere human beings cannot achieve. Beneath the ridiculous Kendall Jenner advertisement, Pepsi has an actual product to sell. It may only be flavoured sugar-water, but that’s not a product to be sneered at – I remember a hot day in rural Thailand some decades ago when it was the only safe thing to drink.
Yet we may be closing in on what Max von Sydow could do. Browser history analysis and sophisticated predictive algorithms can stand in for the supernatural intelligence. YouTube helps to sell the illusion. And Instagram provides influencers galore. The recent Fyre Festival is perhaps the closest approach ever to the ideal. The musicians, accommodation, and food promised to the paying clientele do not appear ever to have been organised (although there apparently were a few waterlogged tents and cheese sandwiches). But the promo was great.
After my second harp post, I thought I’d keep going with some mathematics. In particular I want to answer the question: why does a harp have that shape?
A modern electric lever harp (photo: Athy)
The physics of vibrating strings gives us Mersenne’s laws, which tell us that the frequency of a string of length L is (1 / 2L) √T / μ, where T is the tension force on the string (in newtons), and μ is the density per unit length (in kg per metre).
For a string of diameter d and density ρ, we can calculate μ = Aρ, where A = π (d / 2)2 is the cross-sectional area. Nylon has a density ρ of 1150 kg/m3. For a nylon string of 1 mm diameter, we get μ = 0.0009 kg/m. Putting 0.448 m (17.6 inches) of that string under a tension of 140 newtons (31.5 pounds force), we get a frequency of (1 / 0.896) √ 140 / 0.0009 = 440 Hz. That is, the string plays the note A.
The important thing here is that the frequency is inversely proportional to the length. Over an octave the frequency doubles, which means that the string length halves. A 36-string harp covers 5 octaves, therefore if all the strings were made of the same material under the same tension, the longest string would be 32 times the length of the shortest. Doing some calculations in R for strings of diameter 0.8 mm under a tension of 140 newtons (31.5 pounds), we would get the following harp, which has strings ranging from 7 to 224 cm in length (note that the strings run from A to A, and the C strings are red):
You can see quite clearly that, starting at the treble end, there is an exponential growth in string length. That makes for a terribly unwieldy instrument, and creates all sorts of problems in playing. In practice, we make bass strings thicker (and usually of heavier material) and we vary the tension as well – although, to make life easier for the harpist, we want the properties of the strings to vary reasonably smoothly. If we re-do our calculations with string diameters varying linearly from 3 mm to 0.6 mm, and tension varying linearly from 210 newtons at the bass end to 60 newtons at the treble end, we get a much more realistic-looking harp:
We can flatten out the curve at the top a little by changing the way we vary the strings (after all, a guitar manages to span 2 octaves with all the strings being the same length). However, we cannot eliminate that curve completely – it is the inevitable result of spanning so many octaves, combined with the mathematics of exponential growth.
Left: an exponential curve (red) and a similar polynomial (dashed). Right: the quotient of the two functions (green) compared to a straight line (grey). Click images to zoom.
Mathematically speaking, the modifications to the strings have the effect of dividing an exponential function by some kind of polynomial (as shown above). Over a short range of x values, we can find a polynomial that fits the exponential well, and gives us strings of the same length. Over a wide range of x values, however, the exponential wins out. Furthermore, exponential growth is initially slow (sub-linear), so that (starting at the right of the harp), growth in string length is slower than the linear shift provided by the sloping base, which means that the top of the harp curves down. After a few octaves, growth in string length speeds up, and so the top of the harp curves up again.
A similar situation arises with the strings of a piano, although these are usually hidden from view:
After some feedback on my harp twins post, I thought I’d say something about the history of the harp. It’s one of the oldest musical instruments (following the flute and the drum). Harps are known to go back to 3500 BC, in Ur. Harp design has varied considerably over the 5500 years since then.
A limitation of harps has been that the strings correspond only to the white keys on the piano. A significant improvement was the pedal harp – initially the single-action version, and from 1810 the double-action version. The double-action pedal harp is typically tuned to C♭ major, the key of 7 flats. There are 7 pedals, with e.g. the C pedal connecting to all the C♭ strings. Using the pedal can effectively shorten all the strings in this group to give either C♮ or C♯ (and the same for other groups of notes).
The pedal harp is the main concert instrument today. Garrison Keillor once described the instrument as “an instrument for a saint” because “it takes fourteen hours to tune a harp, which remains in tune for about twenty minutes, or until somebody opens the door.”
A modern electric lever harp (photo:Athy)
Smaller harps (including modern electric harps, like the one above) use levers to modify individual strings (which makes key changes much more difficult than with the pedal harp). Electric harps weighing up to 8 kg are described as “wearable,” which reminds me a little of this 11 kg grand-daddy of the laptop.
Someone recently pointed me at Camille and Kennerly Kitt, the so-called “Harp Twins” (above). I admire anybody who “thinks outside the box,” and these young women have clearly left the “box” of traditional harp-playing several light-years behind.
Their rather eclectic oeuvre includes film, game, and TV tie-ins (from e.g. Lord of the Rings or The Legend of Zelda); rock, folk, and pop classics (like “Hotel California” or “House of the Rising Sun”); metal (from bands like Iron Maiden or Metallica); and other music (such as “Amazing Grace” and “Scarborough Fair”). They have just started releasing their own compositions. The chart below summarises their releases by genre (data taken from Wikipedia, so probably incomplete).