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.


Human embryology again

Returning to the topic of human embryology, here is a human fetal timeline for the first 16 weeks post fertilisation (obstetricians count from the LMP = last menstrual period, which adds about 2 weeks). It is a little disturbing quite how much scientific misinformation is being circulated in regard to the topic. False information is not conducive to honest debate, and is highly corrosive of the trust people have in professionals such as scientists (it’s also unethical on both religious and Kantian grounds). In particular, contrary to what some have suggested:

Fetal length data in the table is mostly from here. Except where indicated, linked images are subsequent to miscarriage or to surgery to resolve ectopic pregnancy, so may be distressing to some readers.

Week post fertilisation Week post LMP Fetal length Image
1 3 0.01 cm / 0.005 inches 8–cell image
2 4 0.02 cm / 0.008 inches
3 5 0.1 cm / 0.04 inches heart begins beating at 21 days
4 6 0.5 cm / 0.2 inches image on flickr
5 7 1 cm / 0.4 inches image on wikimedia
6 8 1.6 cm / 0.6 inches image on flickr
7 9 2.3 cm / 0.9 inches image on flickr
8 10 3.2 cm / 1.3 inches
9 11 4.1 cm / 1.6 inches
10 12 5.4 cm / 2.1 inches
11 13 6.7 cm / 2.6 inches ultrasound image
12 14 14.7 cm / 5.8 inches
13 15 16.7 cm / 6.6 inches
14 16 18.6 cm / 7.3 inches
15 17 20.4 cm / 8 inches ultrasound image
16 18 22 cm / 8.7 inches

Below (from here) is a chart of heart development:


Are there more hurricanes nowadays?


Hurricane Ian approaches Florida (NOAA image)

Florida is counting the cost of Hurricane Ian (above). While we empathise with the people affected by this terrible tragedy, and wish them well, it’s appropriate for a science blog to reflect on what’s happening. The paper “Trends in Global Tropical Cyclone Activity: 1990–2021” by Philip J. Klotzbach, Kimberly M. Wood, Carl J. Schreck III, Steven G. Bowen, Christina M. Patricola, and Michael M. Bell (Geophysical Research Letters, 14 March 2022) is a good guide.

Klotzbach et al. find that global hurricane counts have in fact decreased since 1990. We are not seeing more hurricanes. Restricting attention to Category 4–5 hurricanes (see below) shows no significant change. This overall decrease seems to be driven by more frequent La Niña years, which are associated with fewer hurricanes in the huge Pacific Ocean, and more in the smaller North Atlantic Ocean, giving a reduced total.

Global damage has increased significantly, however, due to having more people and more infrastructure in hurricane-prone coastal areas. It seems difficult to stop people from moving to Florida to live, so there is a clear need to make buildings and infrastructure more hurricane-proof. This document from the government of Queensland (Australia) offers some useful tips for home construction.


Figure 3c from Klotzbach et al. Category 4–5 hurricanes in six tropical cyclone basins during 1990–2021.


Explaining Doppler ultrasound

Recently, I posted something about fetal heartbeats. This seems to be a hot political topic at the moment in the US. Many people don’t seems to understand that, as I noted in my earlier post, the human fetus has a functional (though not yet fully developed) heart from about 21 days after conception.

There seems to be an even greater confusion about the physics of Doppler ultrasound machines. These do not “detect electrical signals,” as has been suggested, but are essentially “speed cameras” for blood (although they use sound rather than radio waves). They detect movement, because movement causes a change in sound frequency, through the Doppler effect. When the heart contracts and the blood is moving fastest, the velocity signal is greater. The pulsing of the resulting velocity signal matches the pulsing of the heart, and can be made audible, although the timbre of the resulting heartbeat sound will not be identical to what a microphone would detect.

The graphic below summarises the operation of the device, at three moments in time (A, B, C). The sound signal sent and received is shown in blue. At the bottom of the graphic is the velocity signal, with the three moments A, B, C marked.


Fetal heartbeat and political debate

Following the recent Dobbs v. Jackson Women’s Health Organization decision in the US, that nation is struggling with two moral/philosophical questions:

  • Is the unborn human fetus a person, and if so from when?
  • Does the unborn human fetus deserve legal protection, and if so from when?

These are independent questions – a puppy or kitten is not a person, but nevertheless has legal protection from animal cruelty. The now-repealed Roe v. Wade (1973) and Planned Parenthood v. Casey (1992) decisions essentially answered the second question as “yes, from viability.”

These questions are moral and philosophical, not scientific. However, scientific questions do arise in the debate. Is the fetus alive? Yes, obviously. Is it human? Well, it has different hemoglobin from adult humans, but the fetus is obviously Homo sapiens. Does the fetus have a heartbeat? Surprisingly, that seems to be controversial, although every textbook I have seen agrees that the heart is functional very early (how else would the developing fetus get oxygen and nutrients?). To quote some sources:

  • “The heart is the first organ to develop. In the human embryo, the heart begins beating at about 21 days after conception [i.e. 5 weeks after LMP = last menstrual period].” (Anatomy and Physiology of the Circulatory and Ventilatory Systems, page 2)
  • “The fetal–placental circulation begins at about 9 days postfertilization … A functional circulation is established by the end of the third developmental week [i.e. 5 weeks after LMP].” (Fetal MRI, page 405)
  • “In a developing embryo, the heart has developed enough by day 21 post-fertilization to begin beating [i.e. 5 weeks after LMP]. Circulation patterns are clearly established by the fourth week of embryonic life. It is critical to the survival of the developing human that the circulatory system forms early to supply the growing tissue with nutrients and gases, and to remove waste products.” (Anatomy and Physiology 2e)
  • “Circulation of fetal blood in the placental circulation begins approximately 21 days postfertilization in humans [i.e. 5 weeks after LMP].” (Handbook of Developmental Neurotoxicology, page 68)
  • “1. Fetal heart development begins during the first month of gestation. At about 21 days of gestation, the fetal heart begins beating, and blood begins circulating [i.e. 5 weeks after LMP]. Between the second and seventh weeks of gestation [i.e. 4 to 9 weeks after LMP], the primitive fetal heart undergoes a series of changes that create the four-chambered heart and its great arteries. 3. During gestation, the lungs are nonfunctional, and fetal oxygenation occurs via the placenta.” (Pediatric Nursing, page 223)

In my view, accurate discussion of the scientific facts is a necessary preliminary to addressing the moral and philosophical questions.

Doppler ultrasound is routinely used to detect fetal heartbeat and the velocity of fetal blood flow. The scientific principle known as the Doppler effect allows the detection of motion. It is the principle behind speed cameras, and it allows bats to “hear” the fluttering wings of a distant insect. During first-trimester screening (at around 11 to 13 weeks after LMP), professional Doppler ultrasound devices are sensitive enough not only to detect fetal heartbeat, but to detect blood flow abnormalities in various parts of the fetal circulatory system.


Fetal heartbeat at 13 weeks (from here). S is the ventricular systolic wave, D the early diastolic, A the atrial contraction.


Some thoughts on Roe

The hot topic at the moment is the recent “repeal” of Roe v. Wade by the US Supreme Court. This topic involves not only legal, but also moral, social, and scientific issues. This blog being a science blog, it’s appropriate to comment on the scientific issues here, and to that end I have produced the chart of human prenatal development above. Horizontal bars show fetal size on a logarithmic scale, and the two images are from Wikimedia and from USAID. Confusingly, two time scales are in regular use for prenatal development, one starting at the last menstrual period, and the other at fertilisation (around 2 weeks later). The chart shows both.

Roe v. Wade had, in fact, largely been overturned by Planned Parenthood v. Casey in 1992. The majority of people in the US (around 63%) believe that abortion should be legal in some cases but illegal in others (although views vary widely between demographic groups and from state to state). Roe v. Wade claimed a constitutional right to an abortion based on a constitutional right to privacy, and attempted to draw a cutoff for abortion legality based on the trimester of pregnancy:

  1. “For the stage prior to approximately the end of the first trimester, the abortion decision and its effectuation must be left to the medical judgment of the pregnant woman’s attending physician.
  2. “For the stage subsequent to approximately the end of the first trimester, the State, in promoting its interest in the health of the mother, may, if it chooses, regulate the abortion procedure in ways that are reasonably related to maternal health.
  3. “For the stage subsequent to viability the State, in promoting its interest in the potentiality of human life, may, if it chooses, regulate, and even proscribe, abortion except where necessary, in appropriate medical judgment, for the preservation of the life or health of the mother.”

Planned Parenthood v. Casey rejected both of these ideas, grounding a right to abortion instead in the due process clause of the 14th Amendment (“nor shall any State deprive any person of life, liberty, or property, without due process of law”), and drawing a new legal line solely based on viability (the age at which the unborn baby can survive outside the womb) rather than on “Roe’s rigid trimester framework.”


The Supreme Court of the United States: the Roberts Court

Viability has some appeal as a guideline, since many people consider it problematic to kill an unborn baby which could be delivered by caesarean and then cared for successfully in the neonatal intensive care unit down the hall. However, as the recent judgement by the Roberts Court in Dobbs v. Jackson Women’s Health Organization notes, viability “is heavily dependent on factors – such as medical advances and the availability of quality medical care – that have nothing to do with the characteristics of a fetus.” In fact, the viability threshold has been dropping at around a week per decade, sitting now at around 22 or 23 weeks (see the chart). Dobbs also took issue with the constitutional aspects of the decision in Casey, overturning it (and what was left of Roe), so that “the authority to regulate abortion is returned to the people and their elected representatives.” Some of “the people” have been very happy about this, while others have protested.

Another scientific (or rather, technological) issue relevant to the decision in Dobbs has been the widespread use of obstetric ultrasonography in the United States. Janelle Taylor notes that “the obstetrical exam has come to incorporate rituals of showing and telling and giving out pictures” (we have all seen them on Facebook). Such images have greatly influenced how the fetus is viewed by the population at large. Unsurprisingly, such images have also lent support to pro-life campaigners, since they give a very clear face to the unborn. This article in The Atlantic notes that “in recent years, pro-life activists have been more successful in using that tool [scientific evidence] to shift the terms of the policy debate.”

More complex has been the debate on whether the unborn human can feel pain. Even in adults, pain is complex, with two separate human pain systems, one more precisely localised, and the other more affective (it “hurts” more). No real scientific consensus currently exists on when a fetus can feel pain (indeed, how could you really prove a hypothesis here?). Various stages are reported in the literature, some as early as 14 weeks, and this literature has been heavily cited as part of the ethical debate on abortion. Other writers have, rather disturbingly, suggested that only adult human beings can truly feel pain. The debate in the US and elsewhere is ongoing.


Pi Day!

Pi Day is coming up again (3/14 as a US date). The number π is, of course, 3.14159265… Here are some possible activities for children:

  • Search for your birthday (or any other number) in the digits of π
  • Follow in the footsteps of Archimedes, showing that π is between 22/7 = 3.1429 and 223/71 = 3.1408.
  • Calculate 333/106 = 3.1415 and 355/113 = 3.1415929, which are better approximations than 22/7.
  • Measure the circumference and diameter of a round plate and divide. Use a ruler to measure the diameter and a strip of paper (afterwards measured with a ruler) for the circumference. For children who cannot yet divide, try to find a plate with diameter 7, 106, or 113.
  • Calculate π by measuring the area of a circle (most simply, with radius 10 or 100), using A = πr2. An easy way is to draw an appropriate circle on a sheet of graph paper.

You can also try estimating π using Buffon’s needle. You will need some toothpicks (or similar) of length k and some parallel lines (such as floorboards) a distance d apart (greater than or equal to k). Then the fraction of dropped toothpicks that touch or cross a line will be 2 k / (π d), or 2 / π if k = d. There is an explanation and simulator here (see also the picture below). And, of course, you can bake a celebratory pie and listen to Kate Bush singing π, mostly correctly!

This picture by McZusatz has 11 of 17 matches touching a line, suggesting the value of 2×17/11 = 3.1 for π (since k = d).

Actually, of course, π = 3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 … (digits in red are sung by Kate Bush, accurately, although some have said otherwise).


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: