World Solar Challenge Speeds

The chart above (click to zoom) summarises speeds for WSC cars, as per the WSC website.

Update: A few people have pointed out some problems with the numbers behind this chart.


World Solar Challenge Cruiser Scores

The chart above (click to zoom) shows scoring for Cruiser class cars arriving at Adelaide, in a modified version of my “tuning fork” style. The score is calculated as a product S = D × H × (1 / E) × 0.99l. The chart shows the components of the score on a logarithmic scale, so that multiplying and dividing score components corresponds to adding and subtracting bars. For each team, there are 6 bars (the 6th bar, in a darker colour, is the total score):

  1. The distance travelled in km (D). Teams completing the entire course score ahead of others.
  2. The weighted average number of humans (H) in the car (so that the product D×H is the number of person-kilometres). A small tick mark above the bar shows the number of seats in the car, which is the maximum possible value of H for that team.
  3. The nominal external energy usage (E) in kWh (initial battery capacity, plus metered charging along the way). This bar is negative, because we are dividing by E.
  4. The fourth place, labelled P, is reserved for the incorporation of practicality in the final score.
  5. The lateness factor (0.99l), where l is the number of minutes of late arrival, plus the number of demerit points.
  6. The total score (S). The score itself is shown over the bar. It can be seen by inspection that this bar is the sum of the others.

Well done, Eindhoven!

Update: I note that Sunswift’s car has been modified to have 2 seats, rather than 4.

Some Oldest Manuscripts

The chart below (click to zoom) shows the dates of ten significant written works:

Each work is indicated by a vertical line, which runs from the date of writing to the date of the oldest surviving complete copy that I am aware of (marked by a dark circle). Open circles show some of the older partial or fragmentary manuscripts (these act as important checks on the reliability of later copies).

Two threshold periods (marked with arrow) are worth remarking on. First, Gutenberg’s printing press – after its invention, we still have at least one first edition for many important works. Second, the invention of Carolingian minuscule – many older works were re-copied into the new, legible script after that time. They were then widely distributed to monasteries around Europe, so that survival from that period has been fairly good. In the Byzantine Empire, Greek minuscule had a similar effect.

The Bible is a special case (I have highlighted one particular gospel on the chart). It was copied so widely (and so early) that many ancient manuscripts survive.

World Solar Challenge: statistics and recent news

Top left: Onda Solare revealed their modified Cruiser Emilia 4 LT on 31 July (credit); Top right: Western Sydney revealed their new monohull Challenger Unlimited 3.0 on 7 August (photo: Anthony Dekker); Bottom left: STC revealed their unusual passenger-behind-driver Cruiser on 8 August (credit); Bottom right: Durham revealed their asymmetric Challenger Ortus on 12 August (credit)

We have had a few new solar car reveals recently (see above – click to zoom). The pie chart below shows current statistics (excluding #67 Golden State and #86 Dyuti, which do not seem to be active teams). Among the Challengers, the designs for #4 Antakari, #10 Tokai, and #18 EcoPhoton are still unknown.

Monohulls remain a minority among the Challengers (though a minority that has doubled in size since 2017). I am using the term “outrigger” for cars with monohull bodies but wheels sticking well out to the sides (the two new Swedish teams, #23 HUST and #51 Chalmers). There are also two quite different wide symmetric cars (#22 MDH and #63 Alfaisal). Among the Cruisers, 4-seaters remain a minority, in spite of the substantial points benefit for carrying multiple passengers. As always, see my regularly updated illustrated teams list for details.

Mathematics and Art: Why can’t we be friends?

The figures of Geometry and Arithmetic by the Coëtivy Master, late 15th century (detail from Philosophy Presenting the Seven Liberal Arts to Boethius)

For most of history, mathematics and the visual arts have been friends. Art was not distinguished from what we now call “craft,” and mathematics – geometry and arithmetic – provided both a source of inspiration and a set of tools. Polykleitos, for example, in the 5th century BC, outlined a set of “ideal” proportions for use in sculpture, based on the square root of two (1.414…). Some later artists used the golden ratio (1.618…) instead.

Symmetry has also been an important part of art, as in the Navajo rug below, as well as a topic of investigation for mathematicians.

Navajo woollen rug, early 20th century (Honolulu Museum of Art)

The Renaissance saw the beginning of the modern idolisation of artists, with Giorgio Vasari’s The Lives of the Most Excellent Painters, Sculptors, and Architects. However, the friendship between mathematics and art became even closer. The theory of perspective was developed during 14th and 15th centuries, so that paintings of the time have one or more “vanishing points,” much like the photograph below.

Perspective in the Galerie des Batailles at Versailles (base image: 1890s Photochrom print, Library of Congress)

Along with the theory of perspective, there was in increasing interest in the mathematics of shape. In particular, the 13 solid shapes known as Archimedean polyhedra were rediscovered. Piero della Francesca rediscovered six, and other artists, such as Luca Pacioli rediscovered others (the last few were rediscovered by Johannes Kepler in the early 17th century). Perspective, polyhedra, and proportion also come together in the work of Albrecht Dürer. Illustrations of the Archimedean polyhedra by Leonardo da Vinci appear in Luca Pacioli’s book De Divina Proportione.

Illustration of a Cuboctahedron by Leonardo da Vinci for Luca Pacioli’s De Divina Proportione (1509)

Some modern artists have continued friendly relations with mathematics. The Dutch artist M. C. Escher (reminiscent of Dürer in some ways) sought inspirations in the diagrams of scientific publications, for example.

Tiling by M. C. Escher on the wall of a museum in Leeuwarden (photo: Bouwe Brouwer)

Today it is possible to follow in Escher’s footsteps by studying a Bachelor of Fine Arts / Bachelor of Science double degree at some institutions. There is also a renewed interest in the beauty of mathematical objects, whether three-dimensional (such as polyhedra) or two-dimensional (such as the Mandelbrot set). The role of the artist then becomes that of bringing out the beauty of the object through rendering, colouring, choice of materials, sculptural techniques, and the like.

View of the Mandelbrot set at −0.7435669 + 0.1314023 i with width 0.0022878 (image: Wolfgang Beyer)

Artistic techniques such as these (“must we call them “craft” or “graphic design”?) are also important in the field of data visualisation, and are recognised by the “Information is Beautiful” Awards. Speaking of which, this year’s awards are now open for submissions.


The 2019 Eurovision Song Contest is on right now. Above (click to zoom) is a combined word cloud for the songs (or English translations of the songs).

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).

Good luck to everyone for the final!

Exploring the moral landscape with recursive partitioning

I’ve mentioned the World Values Survey before. Lately, I’ve been taking another look at this fascinating dataset, specifically at the questions on morality. The chart below provides an analysis of responses to the question “Is abortion justifiable?” These responses ranged from 1 (“never justifiable”) to 10 (“always justifiable”). I looked at the most recent data for Australia and the United States, plus one European country (the Netherlands) and one African country (Zambia), using recursive partitioning with the rpart package of R, together with my own tree-drawing code.

Attitude data such as this is often explained using political orientation, but political orientation is itself really more of an effect than a cause. Instead, I used age, sex, marital status, education level, language spoken at home, number of children, and religion as explanatory variables, with some grouping of my own. Demographic weightings were those provided in the dataset.

For the United States (US), the overall average response was 4.8 (as at 2011, having risen from 4.0 in 1995). However, among more religious people, who attended religious services at least weekly, the average response was lower. This group was mostly, but not entirely, Christian, and the area of the box on the chart gives an approximate indication of the group’s size (according to Pew Forum, this group has been slowly shrinking in size, down to 36% in 2014). The average response was 3.0 for those in the group who also engaged in daily prayer, and 4.3 for those who did not. Among those who attended religious services less than weekly, the responses varied by education level. The average response was 4.8 for those with education up to high school; 6.9 for those with at least some tertiary education who were Buddhist (B), Hindu (H), Jewish (J), Muslim (M), or “None” (N); and 5.4 for those with at least some tertiary education who were Catholic (C), Orthodox (Or), Protestant (P), or Other (Ot).

For Australia (AU), the overall average response was 5.8 (as at 2012, having risen from 4.3 in 1981), with a pattern broadly similar to the US. Here the “more religious” category included those attending religious services at least monthly (but it was still smaller a smaller group than in the US). The average response was 2.7 for those in the group who also engaged in daily prayer, and 4.6 for those who did not. The group most supportive of abortion were those attending religious services less than monthly, with at least some tertiary education, and speaking English or a European language at home. Those speaking Non-European languages at home clustered with the religious group (and those with at least some tertiary education speaking Non-European languages at home are a growing segment of the population, increasing from 6.2% of adults in the 2011 Census to 8.3% of adults in the 2016 Census).

For the Netherlands (NL), the overall average response was 6.5 (as at 2012). Those most opposed to abortion either attended religious services at least weekly (3.2), or were Hindu or Muslim (3.3). Then came those who either attended religious services monthly (5.2), or who attended religious services less often, but were still Catholic (C), Orthodox (Or), Protestant (P), or Other (Ot), and had not completed high school (5.3). The group most supportive of abortion were those attending religious services less than monthly, with at least some tertiary education, and who were Buddhist, Jewish, or “None” (7.9).

For Zambia (ZM), opposition to abortion was strong, with an overall average response of 3.2 (as at 2007). It was highest for those whose marital status was “separated” (4.5), and lowest for those aged 28 and up whose marital status was anything else (2.8).

Of the explanatory variables I used, all except sex, age, and number of children were important in at least one country. However, sex was important for “Is prostitution justifiable?” or “Is violence against other people justifiable?” Age was important for “Is homosexuality justifiable?” or “Is sex before marriage justifiable?” Number of children was important for “Is divorce justifiable?” or “Is suicide justifiable?” For example, here is an analysis of attitudes to divorce: