Social Media, Marketing, and the Fyre Festival

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.


Mathematics of the Harp

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 = A ρ, 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):


Image produced in R. Click to zoom.

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:


Image produced in R. Click to zoom.

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:


Inside of a piano (photo: Alexandre Eggert)

And to finish, here is one of my favourite classical harpists in action:


Harp History

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.


Harpist depicted on the Standard of Ur, c. 2500 BC

Later harps were of particular importance to the Celtic people, and the harp is still a symbol of Ireland today.


The medieval Queen Mary harp, c. 1400s (photo: David Monniaux)

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).

Child prodigy Alisa Sadikova playing the pedal harp (at age 9)

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.

Camille and Kennerly Kitt playing “wearable” electric harps

The harp is often seen as a stereotypically feminine instrument – when I look at American harpists on Wikipedia, I count 10 men and 60 women. There are, however, exceptions.

Jakez François (president of French company Camac Harps) playing jazz


The Harp Twins

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).


Congratulations, Toronto!


Toronto’s solar car Horizon comes 12th in the 2015 World Solar Challenge (my photo)

The Blue Sky Solar Racing team from the University of Toronto ( ) had their 20th anniversary on November 18th last year. The video below celebrates their two decades of solar car racing. Congratulations, guys!


The magnificent Doble steam car

The video above shows the beautiful 1920s Doble steam car owned by Jay Leno (see this article). This magnificent vehicle represents the pinnacle of a technology that was already dead when it was built. A front-mounted boiler powers four cylinders at the rear, which drive the back wheels via spur gears (see below). There is no traditional gearbox or transmission. The steam is condensed and recycled, so that water does not have to be constantly replenished. All very efficient.

Leno says that “The last days of an old technology are almost always better than the first days of a new technology,” and aesthetically (in spite of my love of solar cars) he is probably right. Something similar can be said about the ultimate examples of castle-building, which occurred when castles were already obsolete (see below). So watch the video of this wonderful vintage car!