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Map of the World's Countries with Mathematically Objective Borders
These international borders follow mathematically impartial pathways, laid out by so-called Voronoi diagrams named after the Ukrainian mathematician Georgy Voronoy.
Planet Voronoi looks almost exactly like our own Earth. The continents are all in the same place. The number of countries hasn't changed, nor has the location of their capitals. But the international borders are all wrong. Interestingly wrong.
Just take a look at those straight borders, all patterned after some abstruse logic. The result is a global ensemble of lines and angles with a weird structural beauty, as if Planet Voronoi were an intricately, delicately cracked Christmas tree ornament.
On our own planet, international borders are the detritus of history, reflecting ancient battle lines or the more recent twin triumphs of diplomacy and trigonometry. They can follow cultural and religious fault lines or ignore them at their peril. They may be familiar to us, but essentially our borders are completely accidental – which explains why they're so often contested, and occasionally changed.
But on the other planet, borders follow mathematically impartial pathways, laid out by so-called Voronoi diagrams. Named after the Ukrainian mathematician Georgy Voronoy, such diagrams are used to divide a space containing a number of points or 'seeds' into an equal number of zones, with each zone containing the entire area closer to a particular seed than to any of the other ones.
So on Planet Voronoi, the international borders are fixed – so long as the number and location of international capitals also stays the same. There can be no argument between countries over territory, no land grabs, no secessionist insurrections. It sounds like Ukraine could use a few latter-day Voronoys, Kiev being closer to both the Crimea and the self-declared Donetsk People's Republic than Moscow.
As an added advantage to mathematically inviolable borders, the Voronoi solution provides each state with territorial compactness and proximity to its capital. It's an oft-cited problem in countries with an extremely elongated shape (Chile, Norway, Indonesia) or with eccentric capitals (like London, tucked away in the south east corner of the UK): The capital is so far away, they don't even know we exist.
So it seems the Voronoisians have it made in the shade. But their idea of efficiency and security comes at a cost. Their international borders ignore the many histories, cultures, languages and religions so jealously guarded and protected by our own lines on the map. Such a degree of demarcational abstraction horrifies most of us – even though it can't be said the idea has never been entertained here (see #18 and #159).
Still, it's an interesting experiment to look in that cracked mirror, see this alternate set of international borders and think that perhaps the Voronoisians too have some reason to think that it's our borders that are all wrong.
South America: a Downsized Brazil
Despite the prescience of moving its capital in 1960 from coastal Rio de Janeiro to Brasilia deep inland, Brazil loses more than half of its territory to its neighbours – a large chunk to Guyana and Suriname, no longer South America's smallest countries.
Still, it could have been worse. Like Argentina: reduced to a shadow of its former self, mainly by eternal rival Chile, expanding from a pinstripe to the continent's cricket bat.
Some of the winners might feel historical justice is being restored: Ecuador regains some of the hinterland it once claimed, Bolivia regains the access to the sea it lost to Chile. Wait a minute: are there two Bolivias? Yes: the northern (green) one is centred on La Paz, its seat of government; the southern (blue) one on Sucre, its official and judicial capital. Now that's prescient – having two capitals instead of one.
North America: Cuba Takes New Orleans
In the new world's northern half, the United States is the biggest loser, suffering for the eccentricity of its national capital (see #389), located on its eastern shore in Washington DC instead of somewhere near Belle Fourche, South Dakota, its geographical centre (or somewhere in between, see #492).
Remarkably, here too old wrongs are righted: Mexico reclaims all that was lost in the war of 1846-'48, from Oregon to Louisiana. Ottawa takes the top off the Lower 48: Seattle and Boston become Canadian cities. The Maple Leaf flag flies over most of Alaska. But the Canadians lose their own High North to Iceland, which also takes over Greenland from Denmark – and even annexes the northern part of Alaska (the western part of which turn Japanese).
In the former USA's Deep South, the Cuban bandera flies over the Gulf Coast from west of New Orleans all the way down to Tampa. Florida is sliced in two by the Cuban-Bahamian border, with Miami ruled from Nassau across the water.
Africa: Grand Maroc, Tiny Algeria
In Africa, at first sight a familiar pattern: relative density of capitals on the coast, especially in West Africa, and relative scarcity of capitals inland, especially in the Sahara. Some of the most remarkable gains are made by two of the continent's smallest countries: Rwanda and Burundi, each taking over massive slices of the DR Congo and Tanzania. Some might say that this is what actually happened over the last decade and a half, at least as far as Rwanda is concerned, if only in the DRC.
Another remarkable fit: Voronoi Morocco resembles the borders of le Grand Maroc of centuries past, when the Kingdom comprised a larger part of North Africa. Could it be that these Voronoi diagrams unwittingly reflect such 'ideal' country sizes and shapes that they resemble reality, if only historical reality in this case? Case in point: Namibia, almost contiguous with its Voronoi projection.
Could this be the country with the stablest borders in Africa? (We're forgetting for a moment the Caprivi Strip – not included in Voronoi Namibia, and indeed the locus of a separatist movement). If the theory holds, that spells trouble for Algeria, reduced from an entire pizza to a single slice by its hungry neighbours. And of course Congo, a pitiful triangle dangling from the coast and no longer a proud parallellogram at the centre of the continent.
Asia: a New Mongolian Empire
Siberia is no longer Russian, but at least Moscow can draw comfort from the fact that it wasn't gobbled up by the likeliest of its arch enemies, the Chinese. No, Russia's hold over northern Asia has been broken by the Kazakhs, the Mongols and the Koreans, with the Japanese reclaiming Sakhalin and annexing Kamchatka.
China itself is reduced to a fragment of its former self, by the Taiwanese (finally back on the mainland), the Vietnamese and, in the most audacious annexation of all, by the Bhutanese. The home of Gross National Happiness now is a landlocked superpower.
India too has been curtailed, by Nepal, Bangladesh and Sri Lanka – Pakistan finally managed to annex Kashmir (see also #692), but lost much of its other border area to Afghanistan, and its south to Oman (again, not without historical precedent). Oh, and did we say Korea takes over part of Siberia? We ment North Korea. South Korea, hemmed in on all sides, only gets to annex the southern tail of Japan, and a little nibble out of China.
Oceania: Timor, Papua and Brunei Rule
Splendid or not, New Zealand's isolation means things in the land of the long white cloud stay exactly how they are. Australia, on the other hand, splits into three (its division slightly resembling the Czech flag): the lower third remaining within the governmental orbit of Canberra, the northwestern half reverting to East Timorese rule, and the remainder in the north owing allegiance to Port Moresby, the capital of Papua New Guinea.
PNG also takes over most of the island from which it derives its name, while Brunei now rules most of Borneo. Indonesia retreats to its main island of Java and a few surrounding snippets. Singapore expands across Sumatra, while Malaysia takes over that island's northern third.
Middle East: Riddle of the Sands
It's good we have the dispassionate logic of maths to back us up. Very few sane people dare suggest border changes in the Middle East, wary of the cartographical equivalent of a fatwa, though again, some have tried (see #8), and other claim - with some justification - that the trouble started because some succeeded (see #70).
The biggest loser in the Middle East of Planet Voronoi appears to be Saudi Arabia. No wonder: one landlocked capital, surrounded by a lot of desert, ringed by the coastal capitals of its neighbours. The Saudis even lose the Holy Places of Islam, Mecca and Medina, to the Eritreans, just across the Red Sea. Yemen and Jordan are the biggest winners, eating up the Saudi south and north, respectively. Kuwait is another remarkable winner, expanding into a window enclosing the entire western end of the Gulf. The Emiratis are also eating into both Saudi Arabia and Iran.
Iraq is a net winner, Syria a net loser. Lebanon has extended deep into Turkey, Israel is pronging far into Saudi Arabia (and has retaken half the Sinai desert). Turkey is besieged on four sides, by a resurrected Armenia in the east and an irredentist Greece in the west, with Cyprus nibbling at its southern coast and Bulgaria and Romania at its European bits.
Europe: Georgia, douze points
Finally, Europe: the continent that invented – or at least perfected – both the sanctity of borders, and the deadly wars fought over them. The continent's many pocket-sized states are the obvious winners in a Voronoi scenario and France, surrounded by so many of them, a clear loser. Monaco now includes large chunks of southern France and northern Italy. Andorra has rolled deep into French and Spanish territory, and is as big as its two chopped-to-bits former masters. Luxembourg is the regional power it always dreamt of being. Liechtenstein, San Marino and the Vatican complete the chain of not-so-small mini-states.
The UK is reduced to England by an Ireland that has taken in the entire Celtic Fringe (even including Cornwall [see #13]). France has shrunk back to the Ile de France it once was. The Netherlands have lost the south to Belgium, but annexed a large part of Germany (as some had suggested at the end of World War II [see #65]). Poland has moved east again – and so has Germany. Denmark has re-attached Skåne, the southern bit of Sweden that had been Danish centuries earlier.
Hungary grows, as does Serbia, but not necessarily in the areas they would want to. Macedonia enacts Greece's worst nightmare, and takes over... Greek Macedonia. Ukraine, in spite of current tribulations, annexes adjacent parts of Russia and Belarus – but still loses Crimea (and southern areas), albeit this time to Moldova. Nobody saw that coming. And see what Georgia did? When nobody was looking, the country that got its behind kicked by Russia in the war of 2008 has annexed the entire Russian salient south towards the Caucasus, and even part of Kazakhstan.
Austria and Lithuania on the other hand have given up playing for territory, and are trying to win the Triangle Lookalike Contest. Portugal has given Spain a little but taken lots, and Morocco has regained a toehold on the European continent, ending a 5-century absence.
These maps are the work of data visualisation specalist Jason Davies, who also repeated the exercise on a state capital level, creating a United States of Voronoi. See below. And check out his website for a host of other cool maps, Voronoi-based and otherwise.
United States: New York, New Jersey?
Strange Maps #657
Certain water beetles can escape from frogs after being consumed.
- A Japanese scientist shows that some beetles can wiggle out of frog's butts after being eaten whole.
- The research suggests the beetle can get out in as little as 7 minutes.
- Most of the beetles swallowed in the experiment survived with no complications after being excreted.
In what is perhaps one of the weirdest experiments ever that comes from the category of "why did anyone need to know this?" scientists have proven that the Regimbartia attenuata beetle can climb out of a frog's butt after being eaten.
The research was carried out by Kobe University ecologist Shinji Sugiura. His team found that the majority of beetles swallowed by black-spotted pond frogs (Pelophylax nigromaculatus) used in their experiment managed to escape about 6 hours after and were perfectly fine.
"Here, I report active escape of the aquatic beetle R. attenuata from the vents of five frog species via the digestive tract," writes Sugiura in a new paper, adding "although adult beetles were easily eaten by frogs, 90 percent of swallowed beetles were excreted within six hours after being eaten and, surprisingly, were still alive."
One bug even got out in as little as 7 minutes.
Sugiura also tried putting wax on the legs of some of the beetles, preventing them from moving. These ones were not able to make it out alive, taking from 38 to 150 hours to be digested.
Naturally, as anyone would upon encountering such a story, you're wondering where's the video. Thankfully, the scientists recorded the proceedings:
The Regimbartia attenuata beetle can be found in the tropics, especially as pests in fish hatcheries. It's not the only kind of creature that can survive being swallowed. A recent study showed that snake eels are able to burrow out of the stomachs of fish using their sharp tails, only to become stuck, die, and be mummified in the gut cavity. Scientists are calling the beetle's ability the first documented "active prey escape." Usually, such travelers through the digestive tract have particular adaptations that make it possible for them to withstand extreme pH and lack of oxygen. The researchers think the beetle's trick is in inducing the frog to open a so-called "vent" controlled by the sphincter muscle.
"Individuals were always excreted head first from the frog vent, suggesting that R. attenuata stimulates the hind gut, urging the frog to defecate," explains Sugiura.
For more information, check out the study published in Current Biology.
Are "humanized" pigs the future of medical research?
The U.S. Food and Drug Administration requires all new medicines to be tested in animals before use in people. Pigs make better medical research subjects than mice, because they are closer to humans in size, physiology and genetic makeup.
In recent years, our team at Iowa State University has found a way to make pigs an even closer stand-in for humans. We have successfully transferred components of the human immune system into pigs that lack a functional immune system. This breakthrough has the potential to accelerate medical research in many areas, including virus and vaccine research, as well as cancer and stem cell therapeutics.
Existing biomedical models
Severe Combined Immunodeficiency, or SCID, is a genetic condition that causes impaired development of the immune system. People can develop SCID, as dramatized in the 1976 movie “The Boy in the Plastic Bubble." Other animals can develop SCID, too, including mice.
Researchers in the 1980s recognized that SCID mice could be implanted with human immune cells for further study. Such mice are called “humanized" mice and have been optimized over the past 30 years to study many questions relevant to human health.
Mice are the most commonly used animal in biomedical research, but results from mice often do not translate well to human responses, thanks to differences in metabolism, size and divergent cell functions compared with people.
Nonhuman primates are also used for medical research and are certainly closer stand-ins for humans. But using them for this purpose raises numerous ethical considerations. With these concerns in mind, the National Institutes of Health retired most of its chimpanzees from biomedical research in 2013.
Alternative animal models are in demand.
Swine are a viable option for medical research because of their similarities to humans. And with their widespread commercial use, pigs are met with fewer ethical dilemmas than primates. Upwards of 100 million hogs are slaughtered each year for food in the U.S.
In 2012, groups at Iowa State University and Kansas State University, including Jack Dekkers, an expert in animal breeding and genetics, and Raymond Rowland, a specialist in animal diseases, serendipitously discovered a naturally occurring genetic mutation in pigs that caused SCID. We wondered if we could develop these pigs to create a new biomedical model.
Our group has worked for nearly a decade developing and optimizing SCID pigs for applications in biomedical research. In 2018, we achieved a twofold milestone when working with animal physiologist Jason Ross and his lab. Together we developed a more immunocompromised pig than the original SCID pig – and successfully humanized it, by transferring cultured human immune stem cells into the livers of developing piglets.
During early fetal development, immune cells develop within the liver, providing an opportunity to introduce human cells. We inject human immune stem cells into fetal pig livers using ultrasound imaging as a guide. As the pig fetus develops, the injected human immune stem cells begin to differentiate – or change into other kinds of cells – and spread through the pig's body. Once SCID piglets are born, we can detect human immune cells in their blood, liver, spleen and thymus gland. This humanization is what makes them so valuable for testing new medical treatments.
We have found that human ovarian tumors survive and grow in SCID pigs, giving us an opportunity to study ovarian cancer in a new way. Similarly, because human skin survives on SCID pigs, scientists may be able to develop new treatments for skin burns. Other research possibilities are numerous.
The ultraclean SCID pig biocontainment facility in Ames, Iowa. Adeline Boettcher, CC BY-SA
Pigs in a bubble
Since our pigs lack essential components of their immune system, they are extremely susceptible to infection and require special housing to help reduce exposure to pathogens.
SCID pigs are raised in bubble biocontainment facilities. Positive pressure rooms, which maintain a higher air pressure than the surrounding environment to keep pathogens out, are coupled with highly filtered air and water. All personnel are required to wear full personal protective equipment. We typically have anywhere from two to 15 SCID pigs and breeding animals at a given time. (Our breeding animals do not have SCID, but they are genetic carriers of the mutation, so their offspring may have SCID.)
As with any animal research, ethical considerations are always front and center. All our protocols are approved by Iowa State University's Institutional Animal Care and Use Committee and are in accordance with The National Institutes of Health's Guide for the Care and Use of Laboratory Animals.
Every day, twice a day, our pigs are checked by expert caretakers who monitor their health status and provide engagement. We have veterinarians on call. If any pigs fall ill, and drug or antibiotic intervention does not improve their condition, the animals are humanely euthanized.
Our goal is to continue optimizing our humanized SCID pigs so they can be more readily available for stem cell therapy testing, as well as research in other areas, including cancer. We hope the development of the SCID pig model will pave the way for advancements in therapeutic testing, with the long-term goal of improving human patient outcomes.
Adeline Boettcher earned her research-based Ph.D. working on the SCID project in 2019.
Satellite imagery can help better predict volcanic eruptions by monitoring changes in surface temperature near volcanoes.
- A recent study used data collected by NASA satellites to conduct a statistical analysis of surface temperatures near volcanoes that erupted from 2002 to 2019.
- The results showed that surface temperatures near volcanoes gradually increased in the months and years prior to eruptions.
- The method was able to detect potential eruptions that were not anticipated by other volcano monitoring methods, such as eruptions in Japan in 2014 and Chile in 2015.
How can modern technology help warn us of impending volcanic eruptions?
One promising answer may lie in satellite imagery. In a recent study published in Nature Geoscience, researchers used infrared data collected by NASA satellites to study the conditions near volcanoes in the months and years before they erupted.
The results revealed a pattern: Prior to eruptions, an unusually large amount of heat had been escaping through soil near volcanoes. This diffusion of subterranean heat — which is a byproduct of "large-scale thermal unrest" — could potentially represent a warning sign of future eruptions.
Conceptual model of large-scale thermal unrestCredit: Girona et al.
For the study, the researchers conducted a statistical analysis of changes in surface temperature near volcanoes, using data collected over 16.5 years by NASA's Terra and Aqua satellites. The results showed that eruptions tended to occur around the time when surface temperatures near the volcanoes peaked.
Eruptions were preceded by "subtle but significant long-term (years), large-scale (tens of square kilometres) increases in their radiant heat flux (up to ~1 °C in median radiant temperature)," the researchers wrote. After eruptions, surface temperatures reliably decreased, though the cool-down period took longer for bigger eruptions.
"Volcanoes can experience thermal unrest for several years before eruption," the researchers wrote. "This thermal unrest is dominated by a large-scale phenomenon operating over extensive areas of volcanic edifices, can be an early indicator of volcanic reactivation, can increase prior to different types of eruption and can be tracked through a statistical analysis of little-processed (that is, radiance or radiant temperature) satellite-based remote sensing data with high temporal resolution."
Temporal variations of target volcanoesCredit: Girona et al.
Although using satellites to monitor thermal unrest wouldn't enable scientists to make hyper-specific eruption predictions (like predicting the exact day), it could significantly improve prediction efforts. Seismologists and volcanologists currently use a range of techniques to forecast eruptions, including monitoring for gas emissions, ground deformation, and changes to nearby water channels, to name a few.
Still, none of these techniques have proven completely reliable, both because of the science and the practical barriers (e.g. funding) standing in the way of large-scale monitoring. In 2014, for example, Japan's Mount Ontake suddenly erupted, killing 63 people. It was the nation's deadliest eruption in nearly a century.
In the study, the researchers found that surface temperatures near Mount Ontake had been increasing in the two years prior to the eruption. To date, no other monitoring method has detected "well-defined" warning signs for the 2014 disaster, the researchers noted.
The researchers hope satellite-based infrared monitoring techniques, combined with existing methods, can improve prediction efforts for volcanic eruptions. Volcanic eruptions have killed about 2,000 people since 2000.
"Our findings can open new horizons to better constrain magma–hydrothermal interaction processes, especially when integrated with other datasets, allowing us to explore the thermal budget of volcanoes and anticipate eruptions that are very difficult to forecast through other geophysical/geochemical methods."