Dual Frontier Analysis

I. Introduction, with Example in Population and Area of Countries and Country-Like Entities

In this post, I introduce a way of looking at correlated data I will term “dual frontier analysis”.

What motivates this idea? Often, we like to compare entities via a certain “rate”, how much of one quantity there is for a unit amount of another quantity, across a set of entities. One example of this is population density. But if you, like me, have glanced at a population density chart of, say, the countries, you may have had one of the same first reactions as I have had: “the top of the chart is pretty much just a listing of city-states!” You might then proceed with questioning whether it really makes sense to compare this quantity for city-states versus for “more normal” countries. Maybe we want a way of looking at this data that better captures what our prior idea of what an “impressively high” or “impressively low” population density is: Bangladesh’s population density definitely “feels” more impressive, even if it’s not as numerically high as Bahrain’s.

There are probably solutions to this problem involving designing a prior distribution of likeliness of one variable in terms of the other, and then comparing percentiles along respective distributions, but going down this path requires crunching a lot of numbers and, more importantly, extensive knowledge in the ideas being analyzed already.

Here is another solution: output the data on the dual frontiers. If two attributes are somewhat correlated, a scatterplot for entities in these attributes probably looks something like this.


What we’re outputting is this.


That is, we’re outputting entities for which no other entity has both more of one attribute and less of the other attribute than this entity.

In this way, we would capture, for instance, the country with the highest population density among countries of similar size. (We could even extend this to become a quantitative metric for entities not on this frontier: the percentage of the way an entity is from one frontier to the other.)

One could also look at an entity in this data and compare it to neighboring entities and see how much larger in one attribute another entity must be to be larger in the other attribute as well (as otherwise, this entity would also be in the frontier), which shows how prominently impressive a particular entity is in the ratio.

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The Sun Actually Still Hasn’t Set on the British Empire (as well as some others)

The expression that the sun never set on the British Empire reflected the fact that Britain’s empire consisted of land all around the world, such that it was always daytime somewhere in the British empire. Since then, the British Empire has fallen, but actually even until today not far enough for the sun to not set on it. Believe it or not, with the UK’s present-day territories, it is still daytime somewhere in the UK all the time.

A sufficient (but not necessary) condition for the sun to not set on a country is for there to exist no 180° span of longitude in either hemisphere without land belonging to the country. The UK accomplishes this among its territories in the Southern Hemisphere with the British Indian Ocean Territory (BIOT)* (72°E), Ascension Island** (14°W), and Pitcairn Island*** (130°W).

*This is, by the way, the place for which .io is intended to be the top-level domain.
**I purposefully chose Ascension Island rather than the Falkland Islands to represent this portion of the world to more respect the disputed status of the latter with Argentina.*****
***Since I decided to make asterisked remarks for each of the previous two items in this list, I’ll also make one for the third for symmetry, which is just going to be this vacuous remark since I don’t think I actually have anything to say about Pitcairn Island. ****
****Although I seem to have successfully made each asterisked remark take as many lines as there are asterisks to denote that remark, at least on compatible systems until I change the font for my blog again, which I’m fairly sure I won’t do, but for which now you, future reader, will know what to look out for.
*****It turns out the BIOT is also disputed land. In fact, it is land that imperialist powers have managed to evict the native population from, so it’s arguably a more thirdraily case than the Argentinian dispute. Should the BIOT gain independence or come under Mauritian sovereignty, the sun will set on the British empire for sure. This would also happen if Pitcairn Island declared independence.

Unfortunately, the UK does not have this for the Northern Hemisphere. Fortunately (for the empire), this condition is sufficient but not necessary. We must now ensure that on the Northern-hemisphere summer solstice (the peak of Southern-hemisphere winter), the Southern hemisphere lands span enough longitude for there to always be some land in daylight even with the reduced day lengths. Indeed, this is the case. Pitcairn Island, the further south of these three territories, is only 25°S, thus on the shortest day still having 10.5 hours of sunlight. The other two territories, at only 7°S, have more than 11.5 hours of sunlight on their shortest day. Thus, the 158° longitude gap between the BIOT and Pitcairn Island is minded and even in June the sun never sets on the UK by the skin of its teeth (a few degrees of longitude).

The UK is in fact not the only present-day country the sun never sets on. New Caledonia (22°S,166°E), Réunion (21°S,56°E), French Guiana (4°N,53°W), and Tahiti (18°S,149°W) prevent the sun from setting on France.

There are also several countries for which the sun doesn’t set for a significant amount of the year. Since Russia spans from 20°E to 168°W, nearly half the Earth longitudinally, the sun never sets on Russia for a substantial amount of the year, that is, nearly all days in the Northern-hemisphere spring and summer. All eight countries with land north of the Arctic Circle (Russia, Canada, United States, Denmark, Norway, Sweden, Finland, Iceland) experience the sun not setting on them at least one day of the year. If one recognizes Antarctic territories, then Argentina, Chile, Australia, and New Zealand may join this party as well.

Disregarding territories, the smallest pair of countries that together the sun never sets on is {Ecuador, Singapore}, followed by {Taiwan, Paraguay}, assuming an independent Taiwan. The latter pair is rather fitting, as Paraguay is one of only a couple dozen countries in the world that recognize the Republic of China as the legitimate government of China.

You Keep Using That Word

Define the following terms. Then, determine which of the items listed below each term are examples of the term, based on your definition.

1. continent

Mars’ surface
New Guinea

(If you changed ‘continent’ to ‘island’, what would change?)

2. country

Costa Rica
European Union
Hong Kong
Islamic State
Northern Ireland
Vatican City

(If you changed ‘country’ to ‘nation’, what would change? What about to ‘state’?)

3. digestive organ

lymph node
salivary gland

4. Eastern Europe


5. fruit


(If you changed ‘fruit’ to ‘berry’, what would change?)

6. functional language


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Reflections on The Martian

(Why doesn’t WordPress allow italicizing in the title?)

About 48 hours ago, I watched The Martian. I almost cannot express how immensely I enjoyed the film.

Some of you may know that I have three favorite movies, of which I can’t really decide which among the three I appreciate the best (the one to which people respond “Yessss.”, the one to which people respond “Ooooohhh.”, and the one to which people respond “What?”). The Martian is in a place where I’m unsure if those are my favorite movies anymore and instead The Martian singularly takes that place.

I was actually pretty sure that was where my opinion is ending up through the first half of the film, and felt its quality slightly tapered as it neared its end. Now, I think there’s still a good chance it actually is my favorite film, but I need to wait to see if it remains that way in my opinion in a few days, since I could still be surging on just-watched hype.

What was I not that much a fan of later on in the film? I found that the plot went through too many incredible heightenings of tension. I don’t have a very high tolerance for suspension of disbelief, and get disappointed by lack of acknowledgement of probable realistic outcome when too many things go wrong and things end up actually going well without a good explanation. Many action movies have their plot enter too improbable a state for the good outcome to happen, and especially when one is reasonably anticipating a good outcome, this generates, at least for me, not excitement but incredulity. The latter portion of this film poked a bit far into this territory, though I’d acknowledge it could have been a lot worse.

The video-diary-like entries were curiously reminiscent of Dr. Horrible’s Sing-Along Blog. Quality humor helped solidify a dubious but piquing connection. Does Matt Damon look that much like Neil Patrick Harris? No, although I’m more face-blind than most people. Okay, so I can be fairly sure I’m not just using physical comparisons and there’s something connecting things on a deeper level?

I approve of the care to get substantial amounts of science right. There were still questionable and incorrect aspects, and I wish they didn’t happen, but the respect for science in the film was definitely appreciable. I also think this film exhibits a rare case of relatively approvable portrayal of nerdy people.

Here’s a big thing I appreciated: minimal romance. I find that far too many films decide that a romantic plot is a requirement for a good movie, and push romance into a storyline that could have been perfectly nice (and sometimes better) without.

There was one thing that bothered me, though, and it’s analogous to one of the things that bothered me the most about biographical film Theory of Everything. The letter board with colors presented to Hawking in the film grouped Y and Z in one square and put more letters in other squares. This is quite easily recognizable as suboptimal: squares with fewer letters should have more common letters, to optimize efficiency of selection by reducing number of actions needed to communicate intent. In fact, I’m pretty sure that at the number of different squares that board had, E should’ve had one square all to itself, because E is so common that it ought to just take that short of an amount of time to express it.

Likewise, when Watney chose to set up the signs around the circle in hexadecimal, he solved a problem with arc length being too small, but my hunch is that the letter groupings by hexadecimal weighted by frequency are not even, and thus it is questionable whether hexadecimal is the right way to compress the alphabet in that communication medium. With 17 signs around the circle like Watney had, it would’ve been substantially more efficient to dedicate one entire sign to characters like a space, e, t, and s, and to either group very rare letters together since it’s probably easy to guess which one fits, or have a sign that’s like a shift key for the next character that chooses among rarer letters redistributed over the signs.

But hey, this is just a you-could’ve-done-better. Major props, Mr. Watney, for surviving as long as you did on Mars.

And overall, big thumbs up to this really great film.

One Twist Further

Many people know certain facts.
> Fewer know a certain twist.

East Timor covers the eastern half of the island of Timor.
> The name of the island, “Timor”, comes from Malay for “east”.

Negative forty degrees is where Celsius and Fahrenheit agree.
> It’s also about when mercury freezes.

“Maine” has one syllable.
> All of the US’s four-letter states are polysyllabic.

Tiananmen Square is the site of a brutal massacre of protesting students.
> “Tiananmen” means “gate of heavenly peace”.

The same side of Charon always faces Pluto.
> The same side of Pluto always faces Charon.

A and M are letters representing the universal vowel and the universal consonant, that is, the most commonly found vowel and consonant sounds in natural languages.
> A and M are the only letters in the same places on the QWERTY and Dvorak keyboards.

Same sex relationships are still not recognized by most countries.
> This is one of those countries’ flags.

Kentucky Fried Chicken is not from Kentucky.
> Arizona Iced Tea is not from Arizona either.

Nepal is the only UN-recognized country with a non-rectangular flag.
> Nepal is the only UN-recognized country exclusively in a quarter-hour time zone.

The tallest mountain on Mars is taller than the tallest mountain on Earth.
> The tallest mountain on Iapetus is taller than the tallest mountain on Earth.

North Korea’s official name is the Democratic People’s Republic of Korea.
> North Korea’s official motto translates to “Powerful and Prosperous Nation”.

This exists.
> This exists.


Land Area: Russia/Earth: 11.4%
Land Area: Russia and Antarctica/Earth: 20.3%

Land Area: Sakha/Russia: 18.3%
Land Area: Nunuvut/Canada: 23.0%
Land Area: Alaska/United States: 16.1%
Land Area: Xinjiang/China: 18.7%

Human Population: China/Earth: 19.1%
Human Population: China and India/Earth: 36.4%

Human Population: Guangzhou/China: 7.8%
Human Population: Uttar Pradesh/India: 16.5%
Human Population: California/United States: 12.1%
Human Population: Jawa Barat/Indonesia: 18.1%

Human Population: New York City/New York State: 42.4%
Human Population: New York City in 1950/New York State in 1950: 53.2%Human Human Population: Chicago/Illinois: 21.1%
Human Population: Chicago in 1950/Illinois in 1950: 41.6%

Cities of Population >100000: California/United States: 23.9%

Subcountry Political Divisions of Population >50000000: India and China/Earth: 90.9%

Mass: Sun/Solar System: 99.9%

Mass: Jupiter/Planets of the Solar System: 71.2%
Mass: Gas Giants of the Solar System/Planets of the Solar System: 99.6%

Mass: Ganymede/Moons of Jupiter: 37.7%
Mass: Galilean Moons/Moons of Jupiter: >99.9%

Mass: Titan/Moons of Saturn: 95.7%
Mass: Spherical Saturnian Moons/Moons of Saturn: >99.9%

Mass: Titania/Moons of Uranus: 38.6%
Mass: Spherical Uranian Moons/Moons of Uranus: 99.8%

Mass: Triton/Moons of Neptune: 99.6%

Mass: Charon/Moons of Pluto: >99.9%