Monday, 13 July 2020

July 2020 Update: Covid-19 Death Rates Correlate Highly with a Country’s Level of Globalization

July 2020 Update: Covid-19 Death Rates Correlate Highly with a Country’s Level of Globalization

In an earlier blog, I had provided some evidence that the Covid-19 pandemic really can be considered a “Disease of Globalization”.  In that analysis, it was clear that there was a high correlation, at the country level (some 175 countries were used in the analysis), between deaths from Covid-19 and various measures of globalization that had been calculated by the very reputable KOF Swiss Economic Institute.  These included measures of Political, Economic and Social Globalization, as well as an overall summative measure derived from these sub-indexes.

Here is a brief explanation of these globalization measures, as stated on the KOF website:
“Economic globalization is composed of trade globalization and financial globalization, of which each gets a weight of 50 percent. Social globalization consists of personal contact, information flows and cultural proximity where each contributes one third. Economic, social and political globalization are aggregated to the Globalization Index using again equal weights. The overall KOF Globalization Index is calculated as the average of the de facto and the de jure Globalization Index.”

The Covid-19 Deaths per Million Population figures were taken from the reputable Worldometer website, which has been tracking the pandemic closely since early 2020.  

The correlations were exponential in nature, which indicated that as globalization became greater, the death rate from Covid-19 increases drastically, at a much greater than a linear rate.  As I had stated in that blog:

“It is a bit like compound interest – two bank accounts may grow at the same interest rate, but the bigger account will always have an advantage, which grows over time.  In this case, though, it is a disadvantage rather than an advantage.”

That analysis was based on data on Covid-19 Deaths per Million from the start of the pandemic (about Feb 2020 or so) until early May (May 3, 2020).  This update is for deaths from early May (May 4, 2020) to early July (July 6, 2020.  So, one might think of that as the early and middle stages of the pandemic (or at least the first wave of the pandemic).

1) Covid-19 Death Rates and Social Globalization.

In the earlier analysis, it turned out that the relationship between Covid-19 Deaths per Million Population and the Social Globalization measure was highest, with an R-square of nearly 0.60.  This is a measure of the association between two variables, that  can be though of as the percentage of change in one variable that can be accounted for by the change in the other variable (i.e. 60% of the variance in country Death Rates (after a logarithmic transformation) is explainable by their level of Social Globalization).

The graph below shows the new data and the old data, plotted in separate colours and data point symbols (earlier Feb-May3 data is orange and dots, while the later May4-July6 data is blue and triangles).

As you can see, there is still a fairly strong relationship between Covid-19 Death Rates and Social Globalization, though it has attenuated somewhat from the first analysis.  Three features of the data are:

  • The points have tended to shift upwards, with the blue pints mostly being above the orange points.  In other words, the Covid-19 Deaths per Million Population have risen overall, when looking at the world as a whole.  It should be noted, however, that the Death Rate has come down in some countries.
  • The strength of the functional relationship (a power law) has declined somewhat (the slope of the blue line is less steep than the orange line).  This is also indicated by the magnitude of the exponent in the functional relationship (.097 vs .062).
  • The strength of the correlation has declined, from about 0.60 in the earlier data to about 0.32 in the latest data.  Though it isn’t easy to see this visually, that also means that the orange dots are closer to the orange line, on average, than the blue triangles are to the blue line.

2) Covid-19 Death Rates and Economic Globalization.

In the earlier analysis, the relationship between Covid-19 Deaths per Million Population and the Economic Globalization measure was second highest, with an R-square of nearly 0.36.   

As was the case with the Social Globalization measure:
  • Death Rates have drifted upwards (that will of course be common to all of these sub-analyses).
  • The strength of the power law is attenuated (exponent has gone from .077 to .049).
  • The strength of the correlation is attenuated (R-square has gone from 0.36 to 0.18).

3) Covid-19 Death Rates and Political Globalization.

As in the earlier analysis, the relationship between Covid-19 Death Rates and Political Globalization is weak.

Death Rates have trended higher, the power law is slightly weaker and the R-square is down a bit.


4) Covid-19 Death Rates and Overall Globalization.

Lastly, here is the graph for Death Rates vs the Overall Globalization Measure.

As would be expected, this graph is a mid-way result between the other three:
·       Death Rates are up in general.
·       The slope of the line (exponent of the power law) is down, from .098 to .066.
·       The R-square is lower, from 0.40 to 0.23.


Below are some overall remarks and conclusions that can be drawn from the updated data.

  • It would appear that the formal political relationships between countries are not nearly as strong a driver of Covid-19 Death Rates as are the social relationships and the economic relationships.  One might say that the virus prefers to travel on people, then goods, then abstractions like treaties.
  • When looking at the set of countries as a whole, the relationship between Globalization and Covid-19 Death Rates is still relatively robust, though it has attenuated between the first part of the pandemic so far (Feb – May 3), and the second half (May 4 – July 7).  This was seen for all of the Globalization measures.
  •      o   One plausible explanation for this attenuation might be called “pandemic catch-up”.  The countries that were first hit by the pandemic (those that were most highly plugged into the Globalization phenomena) have been able to take measures that have reduced the Death Rate or at least kept it from growing.  Conversely, those that weren’t hit very hard early in the year have now entered the phase of the pandemic that the more globalized countries had entered earlier in the year.
  •      o   So, the countries that were high on the graph earlier haven’t moved up by much, but many of those that were low on the graph have moved up.  That is probably why the slope of the regression lines has gone down and why the R-square has fallen.
There are also some interesting geographical results that show up in the data (relating to hemisphere and latitude) that I will explore later.  Below is an example:

There are, of course, cautions about any results of this sort, especially those that relate to sensitive subjects such as a pandemic.  Many people have doubts about the Covid-19 numbers from some countries, and they might also have doubts about the KOF globalization numbers.  That’s natural.  However, the fact that numbers taken from two very different sources support the theoretical hypothesis of a relationship between the disease spread and globalization is a pretty clear indication that these numbers probably are reasonably reflective of the underlying reality.  

It could also be argued that countries that are low on Globalization Measures are generally not very good at accurate data reporting.  That could be true in some cases, but it is doubtful that it would invalidate these conclusions overall (i.e. the relationships still seem to hold for countries in the mid to high ranges of the various measures).

Some earlier Covid-19 blogs:

And, here’s a more pleasant travel story than anticipating the worldwide journey of a virus.

A Drive Across Newfoundland

Newfoundland, Canada’s most easterly province, is a region that is both fascinating in its unique culture and amazing in its vistas of stark beauty. The weather is often wild, with coastal regions known for steep cliffs and crashing waves (though tranquil beaches exist too). The inland areas are primarily Precambrian shield, dominated by forests, rivers, rock formations, and abundant wildlife. The province also features some of the Earth’s most remarkable geology, notably The Tablelands, where the mantle rocks of the Earth’s interior have been exposed at the surface, permitting one to explore an almost alien landscape, an opportunity available on only a few scattered regions of the planet.

The city of St. John’s is one of Canada’s most unique urban areas, with a population that maintains many old traditions and cultural aspects of the British Isles. That’s true of the rest of the province, as well, where the people are friendly and inclined to chat amiably with visitors. Plus, they talk with amusing accents and party hard, so what’s not to like?

This account focusses on a two-week road trip in October 2007, from St. John’s in the southeast, to L’Anse aux Meadows in the far northwest, the only known Viking settlement in North America. It also features a day hike visit to The Tablelands, a remarkable and majestic geological feature. Even those who don’t normally consider themselves very interested in geology will find themselves awe-struck by these other-worldly landscapes.

On the Road with Bronco Billy

Spring is on us now, and that brings on thoughts of ROAD TRIP.  Sure, it is still a bit early, but you can still start making plans for your next road trip with help of “On the Road with Bronco Billy”.  Sit back and go on a ten day trucking trip in a big rig, through western North America, from Alberta to Texas, and back again.  Explore the countryside, learn some trucking lingo, and observe the shifting cultural norms across this great continent.  Then, come spring, try it out for yourself.

Wednesday, 1 July 2020

Mind the Gap - A High Mass Neutron Star or Low Mass Black Hole?

Mind the Gap - A High Mass Neutron Star or Low Mass Black Hole?

This month’s Astrophysical Journal published a discovery of a binary black hole merger/collision of two highly dissimilar objects, as identified by the LIGO and VIRGO gravitational telescopes (GW190814: Gravitational Waves from the Coalescence of a 23 Solar Mass Black Hole with a 2.6 Solar Mass Compact Object, The Astrophysical Journal Letters, 896:L44 (20pp), 2020 June 20).  This is actually quite a big deal, both in terms of the mass of the objects detected (one object was a about 24 times the mass of the sun and the other was about 2.6 solar masses) and its possible impact on astrophysical theory and even nuclear physics.  That’s because the smaller object is in the gap between the highest mass neutron stars so far confidently discovered and the lowest mass black holes discovered.

To quote the Astrophysical Journal paper:

“The highly unequal mass ratio of -0.112 +0.009 or -0.008 and unusual secondary mass of -2.59 +0.09 or -0.08 Solar mass make the source of GW190814 unlike any other compact binary coalescence observed so far. The average mass ratio for BBH (binary black hole) coalescences detected by the LVC during O1 and O2 is 0.9 (Roulet & Zaldarriaga 2019), and an inference of the underlying population predicted that 99% of detectable BBHs have mass ratios q>=0.5 (Fishbach & Holz 2020). However, the paucity of events from O1 and O2 means that this picture is limited. Indeed, the discovery of GW190412 has already changed the picture substantially (Abbott et al. 2020d).”

When stars reach the end of their main sequence life (when most of their nuclear fuel has been exhausted) they will undergo a collapse, due to the intrinsic high gravitational field created by their mass.  Nuclear burning (note that people often say burning, though it is actually nuclear fusion) prevents this from occurring during their time on the main sequence as the outward pressure from the energy caused by the fusion reaction counterbalances the inward pressure of gravity.  But when that stops, something has to give.

What the end point of that collapse is, depends on a number of parameters, with the most important one being the mass of the original star. 

·       It is thought that the smallest stars, red dwarfs, can last for extremely long periods (on the order of a trillion years) of time, as they burn their nuclear fuel relatively slowly.  They eventually probably collapse into white dwarf stars.

·       Smaller stars, like the sun, eventually go nova (after billions of years), expanding outward, but not explosively, losing some mass.  In time the core of the star contracts to a “white dwarf”, about the size of the Earth, a highly compressed object.  The contraction is stopped by something called electron degeneracy, which puts a brake on the gravitational collapse.

·       Larger stars also burn through their nuclear fuel, though at a much faster rate (tens of millions of years).  After a series of stages of nuclear fusion, which create the various different lighter elements (iron and lighter), they run out of fusional fuel and a supernova results.  This is a massive explosion, truly astronomical.  These last moments also create the elements that are heavier than iron, and it is thought that all of these elements that we see in the universe ultimately came from supernovae.

·       It is these large stars which leave behind either a neutron star or a black hole as supernova remnants.  Depending on the mass of the originating large star, the result may be a neutron star (the smaller massive stars) or a black hole (really big massive stars).

o   If a star is not too large, the neutron star is formed, as the collapse is stayed by neutron degeneracy.  An over-simplified way to think of this is as one mass of huge nuclear material, where the nuclear matter is so close together (“touching” so to speak) that only nuclear repulsion (quantum neutron degeneracy) stays the collapse.  Up until this discovery, the largest neutron stars that had been discovered were thought to be about 2 solar masses or a bit over.

o   However, for really massive stars even nuclear repulsive forces won’t stop the collapse.  It is thought that the collapse continues until a singularity is reached, a strange object of “infinite density” (again over-simplifying), where the laws of physics as we understand them don’t apply.  Up until this discovery, the smallest black holes that had been discovered were thought to be about 5 solar masses or a bit under.

It is possible that this recently discovered object could be a “heavy” neutron star or a “light” black hole.  The authors of the paper are inclined to the latter explanation, though the mechanism through which such a relatively small black hole could form is not well established.

On the other hand, it could be a “heavy” neutron star.  If so, it might have significant implications for our understanding of the atom itself (i.e. the “standard model”).  Most currently plausible theories of the neutron stars don’t allow for a neutron star of this size (i.e. the currently accepted neutron star equations of state don’t predict this).  Since the equation of state relies on evidence and extrapolations from evidence of investigations of nuclear reactions here on Earth, it throws in some doubt our understanding of those fundamental atomic interactions.  Thus, the standard model itself might require some significant alterations.

The finding also upsets some astrophysical expectations.  Basically, it was thought that a merger/collision of very high mass stars, where one star was so much larger than the other, would be a rather rare occurrence.  The fact that this one showed up relatively early in the observing history of the LIGO-type gravitational telescopes upsets that assumption.  To use Bayesian-speak, this will definitely result in updating some priors.

From the Astrophysical Journal paper:

“GW190814ʼs secondary mass lies in the hypothesized lower mass gap of 2.5–5Me (Bailyn et al. 1998; Özel et al. 2010; Farr et al. 2011; Özel et al. 2012) between known NSs and BHs. It is heavier than the most massive pulsar in the Galaxy (Cromartie et al. 2019), and almost certainly exceeds the mass of the 1.61–2.52 solar mass primary component of GW190425, which is itself an outlier relative to the Galactic population of BNSs (Abbott et al. 2020a). On the other hand, it is comparable in mass to two BH candidates: the 2.7 solar mass merger remnant of GW170817(Abbott et al. 2019b) and the 2.6–6.1solar mass compact object (95% confidence interval) discovered by Thompson et al. (2019).  It is also comparable to the millisecond pulsar PSR J17482021B (Freire et al. 2008), whose mass is claimed as 2.74+/- 0.21 solar mass at 68% confidence. However, this estimate, obtained via measurement of the periastron advance, could be inaccurate if the system inclination is low or the pulsar’s companion is rapidly rotating (Freire et al. 2008). In sum, it is not clear if GW190814ʼs secondary is a BH or an NS.”

It  is also worth noting that what I called a “LIGO-type telescope” isn’t a telescope in the usual sense of the word.  It actually detects the effect of gravitational waves on space-time, via careful measurements of distances, which indicate a perturbation in local space-time as the gravitational waves pass by.  But, since it’s purpose is to detect a form of radiation (gravitational radiation in this case), the term telescope seems fair.

It is also worth noting that this merger/collision is thought to have occurred in a galaxy about 240 million parsecs from Earth (or about a billion light years).

Note: The BBC website had a good article on this, which is where the images in this blog originated.

So, that was interesting, but you should think about reading a nice SF book that features a neutron star:

The Witches’ Stones Book 1: Rescue from the Planet of the Amartos

 So, go on a romantic science fiction adventure with an agent of Earth’s Terra Federation’s counter-intelligence group “The Agency”, to prevent the mystical and powerful Witches’ Stones from falling into the hands of the shadowy power-mad developing galactic empire, known to Earthlings only as The Organization.  Key to this mission is the rescue of an apparently unassuming Earth girl, who holds the key to the galactic balance of power, via her ability (unknown to her) to psychically unlock the energies of the Witches’ Stones. 
Amazon U.S:

Witches’ Stones Book One – Rescue from the Planet of the Amartos

Sarah Mackenzie had trained as a space ship mechanic at the Space Port of her home city on Earth. She left Earth to explore the galaxy, and, some months later, landed a dream assignment, to become the ship mechanic of an Explorer ship, the Beth 117.

The Beth was on its way to a planet at the edge of the galaxy, where its crewmembers were to search for the Witches’ Stones, or amartos, the mysterious crystals, which the Witches of the world, Kordea, use to channel and augment their psychic energies.

Sarah has no idea that she, herself, happens to be Stone-sensitive, just like the Witches are. Under perilous circumstances, she comes across the cache of the Stones which the Explorers are looking for, and, unwittingly, “keys” them, igniting a psychic blaze that attracts the attention of The Organization, the implacable foe of the Terra Confederation, the centuries-old star-spanning government of most of the human race, and its non-human allies. To make use of amarto-energy, The Organization needs, not just the Stones, but also amarto-sensitive individuals whom they enslave to the devices which they have developed in their pursuit of galactic domination. Thus, they want not just the cache of Stones; they also want Sarah.

To forestall galactic war, rescuers, from a counter-intelligence group, known as The Agency, are sent to the Planet of the Amartos. A fast scoutship, manned by an Agent and a Pilot, must try to fetch Sarah and the amartos, bringing them to a safe haven among the Kordean Witches.

Sarah, herself, has to deal with serious conflicts. In the psychic realm she must choose between The Organization and the Kordean Witches, while retaining mastery over her own mind. In the physical reality, she has become the centre of an armed battle between the Terran scoutship and a military task force sent by The Organization to capture her and the Stones. Her determination to keep control of her own self sends her into unexplored mental realities, while exciting but dangerous physical events swirl around her and the crew of the scoutship, Camin.

To further complicate things, she senses within herself, the beginnings of an attraction to the handsome Agent sent to rescue her. However, she’s merely a naive young woman from Earth; surely, her hopes are beyond realization....

The novel is about 100,000 words, or 250 pages. It is the first book in the Witches' Stones series, which explores the struggle for power among the Terra Confederation, the Kordean Witches and The Organization, as well as the personal and romantic entanglements of the characters. Book 2  and Book 3 complete the series.