Mass Shootings in the US

Tragically, we have had another mass shooting in the US. The chart above summarises deaths from such events (data collated by Mother Jones). It is clear that the problem has been getting worse since about 2005 (statistically significant at p < 0.00001).

Social factors appear to be blame, since there has been no signficant change in the availability of weapons in that time. Those social factors might include mental health policy, education policy, social media, video games, drugs, the decline of religion, media coverage of past shootings, etc. It seems to me that serious study is urgently required. Some things we do know: psychiatrist Ragy Girgis suggests:

With exceptions, many of these [perpetrators] tended to be younger males who were empty, angry, and nihilistic, felt rejected by society, were socially, occupationally and/or academically unsuccessful, and blamed society for their failures. These individuals tended to have very fragile egos and were highly narcissistic, feeling they were much more special than they actually were and deserving of fame and notoriety. They harbored a strong desire for this notoriety and infamy. Committing a mass shooting instantly produces these results in today’s culture.

In the Mother Jones dataset (for 1982 onwards), 13 states have never had a mass shooting (Alaska, Delaware, Idaho, Maine, Montana, New Hampshire, New Mexico, North Dakota, Rhode Island, South Dakota, Vermont, West Virginia, and Wyoming), while in 13 other states, the chance of dying in a mass shooting exceeds 0.1 per million per year:

State Total Fatalities Annual Deaths per million
California 175 0.11
Nebraska 9 0.11
Oklahoma 19 0.11
Wisconsin 28 0.12
Washington 37 0.12
Hawaii 7 0.12
Texas 151 0.12
Florida 126 0.14
Virginia 53 0.15
Colorado 53 0.22
Connecticut 41 0.27
DC 12 0.43
Nevada 63 0.48

The relevant social factors are therefore not uniform across the United States. The map below shows the mean annual death rate per million for mass shootings in each state (for 1982 to 2023, excluding Alaska = 0 and Hawaii = 0.12):

Edit: Ragy Girgis, quoted above, notes that perpetrators tended to be “occupationally and/or academically unsuccessful.” Consequently, state unemployment rate is a statistically significant risk factor (p = 0.0148):

Even more significant (p = 0.0046) is the correlation with the Social Support Index from the US Joint Economic Committee Social Capital Project. Better social support helps to reduce the risk of mass shootings.

Do gun laws save lives?

Do gun laws save lives? The chart above shows homicide rates for U.S. states (data from here) together with an A to F ranking of state gun laws from the Giffords organisation. As with my post from 2017, there is actually no statistically significant correlation (this is particular noticeable among the F’s, which include both the seven states with the highest murder rate and the two states with the lowest). In other words, the answer seems to be no.

Rather, it seems that guns don’t kill people, people kill people. The murder rate in the U.S. is driven by social factors which differ from state to state – factors which make New Hampshire and Maine pretty safe, but which produce a murder rate ranging from 14 per 100,000 to 20.5 per 100,000 in Missouri, Alabama, Louisiana, and Mississippi. For comparison, New Hampshire has a murder rate similar to that of Australia, but Louisiana and Mississippi, if they were countries, would rank among the most murderous 20 countries in the world.

There is some evidence that keeping guns out of the hands of criminals would reduce the murder rate in the U.S., but this is extremely difficult to do. The U.S. has a lengthy, porous southern border, across which there is a free flow of people, guns, and illegal drugs.

In addition, a concept from catastrophe theory is useful here. In the cusp pictured below, it is possible to “drop” from the top of the fold to the bottom, but a long roundabout journey would be required to get back up. Similarly, it is very easy to introduce guns into a society, but very difficult to remove them. Although such removal has been done elsewhere, laws forbidding gun ownership are likely to be ignored by precisely those violent criminals that one would not wish to carry them. And, of course, there is the 2nd Amendment.

COVID-19 and Vitamin-D

The chart above shows national Covid mortality against latitude of national capitals (open circles are for the Southern Hemisphere, solid circles for the Northern). The trend line in blue has a correlation of 0.50 (with p < 10−13). Countries further away from the equator are definitely reporting more Covid deaths.

It is possible that these numbers reflect under-counting in the tropics (although this is unlikely for Singapore = SG) and over-counting in wealthier countries away from the tropics (e.g. by reporting deaths of patients with positive Covid tests as Covid deaths, even if the actual cause of death is unrelated). However, it seems unlikely that under-counting and over-counting can explain everything here.

This paper in The Lancet notes that “It has long been clear that groups that traditionally exhibit vitamin D deficiency or insufficiency, such as older adults and nursing home residents, and Black, Asian, and minority ethnic populations, are the same groups that have also been disproportionately impacted by COVID-19. Additionally, increased time spent indoors due to strict lockdowns and shielding triggered concerns that some people might not obtain the necessary physiological levels of vitamin D from sunlight.

My chart above is consistent with this: decreased sunshine away from the equator appears to increase Covid mortality, presumably due to vitamin D deficiency. This study in QJM notes, “vitamin D supplementation is effective in reducing COVID-19 severity. Hence vitamin D should be recommended as an adjuvant therapy for COVID-19.” Personally, I have been taking this advice for quite some time.

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 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?’
‘Or to sell England to the Germans?’
‘Or to print lies as serious research in a scientific periodical?’
‘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