Rods and cones in the human eye

I already posted these images (click to zoom) on Instagram. They illustrate the sensitivity to colour of the rods (lower right) and the three types of cones in the human eye. Cone sensitivity data is from CVRL.

Notice that red light is pretty much invisible to the rods. This is why red light does not interfere with night vision, and is used in e.g. this aircraft cockpit:


Eurovision Song Contest and GDP

Following up on my previous post and the one before that, here is some more analysis of Eurovision Song Contest voting for this year. There are some interesting correlations between national tele-votes (not jury votes) and demographic variables, especially per capita GDP. As the map above shows, this is essentially a proxy for the northwest–southeast axis.

Iceland came 4th with the song 10 Years in spite of never actually competing; a positive COVID-19 test result restricted the band to their hotel; and they were judged based on a tape of their rehearsal performance. The richer Nordic countries seem to have been especially generous in this situation (see chart below).

Conversely, the winning song from Italy received generally lower tele-votes from the richer countries (I am not entirely sure why):

The song Je me casse from Malta came 7th overall. As with Iceland, the higher tele-votes came from the richer countries, although the pattern here is fuzzier than for Iceland. There are also some notable outliers: the Australian tele-vote of 8 for Malta probably reflects the 176,000 people of Maltese descent living in Australia.

Russia shows a pattern somewhat similar to Italy (p < 0.004, R2 = 22%), but this is simply because the former Soviet countries that vote for Russia are also the poorer ones. A better predictor can be obtained by counting Russian expatriates (p < 0.001, R2 = 44%).

And finally, here is a plot of tele-vote totals against jury vote totals. They differ substantially:


Eurovision Song Contest: More Analysis

Following up on my previous post, here is some more analysis of Eurovision Song Contest voting for this year. The maps above show a hierarchical clustering analysis on tele-voting (above) and jury voting (below), based on calculating simple Euclidean distance between vote vectors and on an assumption that countries would give themselves 12 points if they could. Some key differences between the four main clusters are highlighted in colour (note that Azerbaijan, Israel, the Netherlands, and the UK clustered alone or in a pair):

Tele-voting cluster 1 (green)

Countries: Australia, Belgium, Denmark, Estonia, Finland, Germany, Iceland, Ireland, Italy, Latvia, Lithuania, Malta, Norway, Poland, Sweden, and Ukraine.

Average votes:  Italy:  8, Iceland:  8, Ukraine:  8, Finland:  8, Lithuania:  8, France:  6, Switzerland:  4, Sweden:  4, Norway:  4, Malta:  2, Russia:  2, Serbia:  1, Belgium:  1, Albania:  1, Germany:  1, Greece:  0, Cyprus:  0, and Moldova:  0.

Tele-voting cluster 2 (purple)

Countries: Austria, Bulgaria, Croatia, North Macedonia, Serbia, Slovenia, Spain, and Switzerland.

Average votes:  Italy:  10, Serbia:  10, France:  8, Switzerland:  6, Ukraine:  6, Finland:  5, Iceland:  4, Russia:  2, Bulgaria:  2, Greece:  2, Azerbaijan:  2, Albania:  2, Spain:  2, Malta:  1, Lithuania:  1, Portugal:  1, Cyprus:  1, and Moldova:  0.

Tele-voting cluster 3 (red)

Countries: Albania, Czech Republic, France, Moldova, Portugal, and Romania.

Average votesMoldova:  10, Ukraine:  9, Italy:  8, France:  8, Switzerland:  6, Finland:  4, Greece:  4, Russia:  3, Portugal:  3, Iceland:  2, Sweden:  2, Albania:  2, Lithuania:  1, Bulgaria:  1, Israel:  1, Azerbaijan:  1, Serbia:  0, and Cyprus:  0.

Tele-voting cluster 4 (yellow)

Countries: Cyprus, Georgia, Greece, Russia, and San Marino.

Average votes:  Italy:  10, Greece:  9, Cyprus:  9, France:  7, Ukraine:  6, Finland:  4, Russia:  4, San Marino:  4, Lithuania:  3, Switzerland:  2, Bulgaria:  2, Moldova:  2, Azerbaijan:  2, Malta:  1, Albania:  1, Iceland:  0, and Serbia:  0.

Check out the disputed songs: Iceland: 10 Years, Lithuania: Discoteque, Serbia: Loco Loco, Moldova: Sugar, Greece: Last Dance, and Cyprus: El diablo.

The map below shows jury voting. For jury voting, there were only two substantial clusters (i.e. containing 4 or more countries – Albania, Malta, Romania, France, Israel, Norway, Sweden, Belgium, and Italy clustered alone or in small clusters of 2 or 3 countries).

Jury voting cluster 1 (purple)

Countries: Australia, Austria, Croatia, Czech, Denmark, Estonia, Finland, Georgia, Germany, Iceland, Ireland, Latvia, Lithuania, Netherlands, NM, Poland, Portugal, Serbia, Slovenia, Spain, Switzerland, Ukraine, and UK.

Average votesSwitzerland:  9, Iceland:  8, France:  7, Italy:  6, Malta:  4, Bulgaria:  4, Portugal:  4, Ukraine:  3, Finland:  3, Lithuania:  2, Russia:  2, Israel:  2, Belgium:  2, Greece:  1, Sweden:  1, Serbia:  1, Cyprus:  1, Azerbaijan:  1, San Marino:  1, Netherlands:  1, Spain:  1, Germany:  1, UK:  1, and Moldova:  0.

Jury voting cluster 2 (red)

Countries: Azerbaijan, Bulgaria, Cyprus, Greece, Moldova, Russia, and San Marino.

Average votesGreece:  9, Moldova:  8, Malta:  7, Bulgaria:  7, Italy:  6, France:  6, Russia:  6, Cyprus:  4, Azerbaijan:  4, San Marino:  3, Portugal:  2, Belgium:  2, Switzerland:  1, Iceland:  1, Ukraine:  1, Finland:  1, Lithuania:  1, Sweden:  1, Israel:  1, and Spain:  1.

Check out the disputed songs: Switzerland: Tout l’Univers, Iceland: 10 Years, Greece: Last Dance, and Moldova: Sugar


Eurovision Song Contest 2021

The Eurovision Song Contest has been on again (strangely, Australia is now part of Europe). On the whole, I didn’t think much of the songs this year, although there were a few gems (like the French entry).

This (revised) chart shows those tele-votes which were surprisingly high, given the total scores (country colours indicate total scores, with grey for non-finalists). Arrows reflect high tele-votes (in a relative sense). Red arrows reflect particularly high tele-votes (in a relative sense), including:

  • Austria, Croatia, North Macedonia (NM), Slovenia, and Switzerland Serbia (Balkan cluster)
  • North Macedonia (NM) and Italy Albania (ditto)
  • Cyprus Greece Cyprus (as usual)
  • Netherlands Greece (the Greek singer resides in the Netherlands)
  • Georgia Greece
  • Russia Cyprus
  • Moldova Russia (former USSR)
  • Czech Republic and Romania Moldova
  • Latvia, Germany, Norway, UK, and Ireland Lithuania
  • Denmark and Iceland Sweden (Nordic cluster)
  • Sweden, Iceland, and Estonia Finland (ditto)
  • Malta Norway
  • Azerbaijan Israel

Regional sentiment and expatriate voting still play a part, I see. Here is the same network overlaid on a map:


Personality Types and Social Media

Following some discussion with friends, I made a chart comparing the general prevalence of MBTI personality types with their prevalence on Facebook (using data from this report). The first of each pair of bars is general prevalence, and the second is prevalence on Facebook.

It can be seen that extroverted types are more likely to be on Facebook than introverted types. However, the IN-J types swim against the tide. The chart below provides a bit of a summary.

The third chart shows the results for Twitter. Here extroverts are also over-represented, especially the EN-P and ESTJ types, but not the other ES– types. Among the introverts, the ISTJ type swims against the type, and is in fact the most common personality type on Twitter.


A Narnian Timeline

I’ve been on a bit of a Narnia binge recently. Continuing that theme, here is a timeline of the Chronicles of Narnia (click to zoom). The Terran time axis has varying scales (although piecewise linear), since 5 of the 7 Narnia books (53% of Narnian history) are set during 1940–1942. For simplicity, I also assume a piecewise linear mapping of Narnian time to Terran time (see graph below), although the text of the books indicate that the mapping is more complex than that. For Narnian events in the chart, only the vertical position has meaning (the sideways curve is only there to create space).

The Crucifixion of Jesus is included as a significant Terran event, since its Narnian parallel is the key event of The Lion, the Witch and the Wardrobe. Some scholars date this to the year 30, rather than 33.

The chart was produced using R. The curved lines are plotted with colours from colorRampPalette(). Images were added using png::readPNG, as.raster(), and rasterImage(), with circles using plotrix::draw.circle(). For the title, the extrafont package was used.


Perelandra: a book review


Perelandra (1943) by C. S. Lewis (1996 cover by Kinuko Y. Craft)

Having blogged about Out of the Silent Planet and That Hideous Strength, the first and last novels of the “Space Trilogy” or “Cosmic Trilogy” by C. S. Lewis, I should also mention Perelandra, the middle volume.

While Out of the Silent Planet is science fiction, Perelandra is better described as religious fantasy (with portions of what could be called supernatural horror). However, in a 1962 discussion with Kingsley Amis and Brian Aldiss, Lewis states that “The starting point of the second novel, Perelandra, was my mental picture of the floating islands. The whole of the rest of my labors in a sense consisted of building up a world in which floating islands could exist. And then, of course, the story about an averted fall developed. This is because, as you know, having got your people to this exciting country, something must happen.” When Aldiss responds “But I am surprised that you put it this way round. I would have thought that you constructed Perelandra for the didactic purpose,” Lewis replies “Yes, everyone thinks that. They are quite wrong.

The basic idea of the floating islands of vegetation on the ocean of Perelandra (what we call Venus) may have came from the novel Last and First Men by Olaf Stapledon (XII§4), after mankind has chosen to exterminate the native civilisation of Venus (something that Stapledon seems to approve of, but which Lewis explicitly criticised in Out of the Silent Planet): “Man now busied himself in preparing his new home. Many kinds of plant life, derived from the terrestrial stock, but bred for the Venerian environment, now began to swarm on the islands and in the sea. For so restricted was the land surface, that great areas of ocean had to be given over to specially designed marine plants, which now formed immense floating continents of vegetable matter.

In Chapter 3 of Perelandra, when Elwin Ransom first arrives on Venus, there are some wonderful descriptive passages, which go far, far beyond Stapledon’s bald statement: “It seems that he must have remained lying on his face, doing nothing and thinking nothing for a very long time. When he next began to take any notice of his surroundings he was, at all events, well rested. His first discovery was that he lay on a dry surface, which on examination turned out to consist of something very like heather, except for the colour which was coppery. Burrowing idly with his fingers he found something friable like dry soil, but very little of it, for almost at once he came upon a base of tough interlocked fibres. Then he rolled round on his back, and in doing so discovered the extreme resilience of the surface on which he lay. It was something much more than the pliancy of the heather-like vegetation, and felt more as if the whole floating island beneath that vegetation were a kind of mattress. He turned and looked ‘inland’ – if that is the right word – and for one instant what he saw looked very like a country. He was looking up a long lonely valley with a copper-coloured floor bordered on each side by gentle slopes clothed in a kind of many-coloured forest. But even as he took this in, it became a long copper-coloured ridge with the forest sloping down on each side of it. Of course he ought to have been prepared for this, but he says that it gave him an almost sickening shock. The thing had looked, in that first glance, so like a real country that he had forgotten it was floating – an island if you like, with hills and valleys, but hills and valleys which changed places every minute so that only a cinematograph could make a contour map of it.

It’s a great pity that Venus is nothing like that at all.


Lewis wrote Perelandra while a Fellow at Magdalen College, Oxford.

Much of the rest of the book consists of conversations about theology and moral philosophy between Ransom, the scientist Weston (who first appeared in Out of the Silent Planet), and Tinidril, one of the two “people” on Venus. Tinidril corresponds to Eve in the Bible, so that we get a sort of alternate history of the “Temptation of Eve.” Weston is possessed by a “Force” that turns out to be Satan or a demon. As a former academic myself, it is interesting to see Lewis’s ascending hierarchy of potential moral failings:

“RANSOM: ‘Does that mean in plainer language that the things the Force wants you to do are what ordinary people call diabolical?’
WESTON: ‘My dear Ransom, I wish you would not keep relapsing on to the popular level. The two things are only moments in the single, unique reality. The world leaps forward through great men and greatness always transcends mere moralism. When the leap has been made our “diabolism” as you would call it becomes the morality of the next stage; but while we are making it, we are called criminals, heretics, blasphemers. …’
‘How far does it go? Would you still obey the Life-Force if you found it prompting you to murder me?’
‘Yes.’
‘Or to sell England to the Germans?’
‘Yes.’
‘Or to print lies as serious research in a scientific periodical?’
‘Yes.’
‘God help you!’ said Ransom.

The chart below shows a chapter-by-chapter frequency analysis of various names and words in the book (some obvious synonyms were also used in counting words, and characters mentioned but not appearing are included). There is also a chapter-by-chapter polarity (sentiment) analysis at the bottom of the chart.

When one considers the theological subject matter, the conflict with the Un-man, and the underground scenes towards the end, the novel is a little reminiscent of Dante’s Inferno, but the final chapters are far more like the Paradiso, and (in a letter) Lewis himself tells us that some of the conversations between Ransom and Tinidril draw on Matilda in the Purgatorio. Aspects of the conflict between Ransom and Weston recall the interaction between Frodo and Gollum in The Lord of the Rings, while other aspects of Perelandra are like visiting the Elves. It is not a simple book.

Goodreads rates the novel as the best of Lewis’s trilogy, giving it 3.99 out of 5. I’m giving it five stars, but readers not interested in theology or moral philosophy would no doubt rate it lower.

5 stars
Perelandra by C. S. Lewis: 5 stars


World Solar Challenge Cruiser scoring

Having participated in some recent discussions about the World Solar Challenge Cruiser Class, I thought I would explore the scoring again. Scoring in the WSC is based on a multiplicative formula (see reg 4.4.7), but as we all learned in high school, multiplying is equivalent to adding logarithms.

By appropriate scaling of logarithms, the chart above breaks down the various components of the multiplicative formula into additive points (black bars are negative numbers).

For example, on this system, in 2019 Eindhoven received a total of 67 points:

  • 100 points for completing all three stages
  • +12 points for an average of 2.6 people in the car
  • −53 points for 71.2 kWH of external energy
  • −0 points for no lateness
  • +8 points for a practicality of 93.1%

Lateness refers to arrival at stage stops after the “soft cutoffs,” which in 2021 will be Sat 15:30 in Tennant Creek, Mon 16:30 in Coober Pedy, and 11:30 Wed in Adelaide (there are also “hard cutoffs” leading to elimination, of 17:00, 17:00, and 14:00 respectively). According to reg 4.4.8, teams are ranked by the number of completed stages, and then by score.

In 2019 Minnesota received a total of 39 points:

  • 86 points for completing only one stage (thus also ranking after all the finishers)
  • +9 points for an average of 2 people in the car
  • −40.5 points for 25.7 kWH of external energy
  • −21 points for 165 minutes of lateness
  • +5.5 points for a practicality of 76.3%

Suppose a larger battery and a longer race had increased Minnesota’s external energy use to 128 kWH (an extra −20 points), but this had removed the lateness factor (an extra +21 points) and allowed achieving all three stages (an extra +14 points). Minnesota would then have been 15 points ahead, for a total of 54. This would have put them neck-and-neck for second place with Sunswift.

This example makes clear how the rules create an incentive for large batteries. It also highlights the difficulty of the second stage from Tennant Creek to Coober Pedy – I wonder if an extension to the “hard cutoff” is possible there?

Technical note: I am multiplying natural logarithms by 12.48 (so that 3020 gives 100), and I have also doubled practicality, and thus the total score (this doesn’t, of course, give practicality any extra weight). Sanity check for Eindhoven: 12.48 × ln(104×2) = 67.


COVID-19 in the UK #4

The chart above (click to zoom) is an updated view of registered deaths in England and Wales according to the ONS up to the end of the year, along with data from previous years.

The difference between the red and black lines (highlighted in yellow and labelled A) indicates deaths where COVID-19 was mentioned on the death certificate.

There was also a spike in non-COVID-19 deaths (labelled B), which seems to reflect under-treatment of cancer and other serious diseases during the lockdown. The Telegraph expressed concern at this some time ago, and I myself know people in this tragic category.

For a while (label C) deaths were actually running slightly below trend, but deaths unrelated to COVID-19 then increased again, perhaps due to the renewed lockdown. More recently, there are now indications of a “second wave” of COVID-19, with a slight increase in deaths where COVID-19 was mentioned on the death certificate (labelled D). However, the increase is significantly slower than the first wave, and (given the dip in the red line) some of these reported COVID-19 deaths may be misdiagnosed seasonal influenza. The overall death rate at the end of the year was much the same as for previous years.

The bar chart at the bottom shows a year-to-date comparison with previous years. The white additions to the bars for previous years show an adjustment to account for population growth.


Board games!

I love board games. I really, really, love them. The chart below shows my least favourite game (Monopoly) and some personal favourites:

The chart shows the rating on boardgamegeek.com, the age range, the number of players, the approximate time to play the game (games with a predictable duration are better in social terms – particularly if you want to finish a game before dinner), and three other quality characteristics:

  • Artistic quality: I am rating this subjectively, but it’s always nice to have something beatiful to look at while you are waiting for your turn.
  • Educational value: Ticket to Ride and Pandemic teach geography, 7 Wonders teaches something about history (especially with the Leaders expansion), and Kingdomino teaches multiplication (I give partial credit to Forbidden Island for being a collaborative game, and negative credit to Monopoly for teaching that money is the most important thing in life).
  • Winning: ideally, all players have a chance of winning right up to the end (I give extra credit to Kingdomino for having a mechanism that helps players that “missed out” on a good tile, and to Pandemic and Forbidden Island for being collaborative).

It can be seen that Monopoly scores badly in every possible way: it can take forever; the artwork is poor; it teaches bad moral lessons; and players are actually eliminated from the game during play. That is why I dislike it.