No, the Science Nerd’s Fight is Still Uphill

There is now a common complacency among many STEM nerds that science and technology are more respected in the modern world and that the general public is more willing to acknowledge heroes in scientific fields, that we have gained an upper hand or even a privilege in society and thus should recognize this and partake less in acts like shunning sports.

I write a bit about this illusion in the linked article. Public skepticism towards technology is as high as ever, and public suspicion towards people still defaults higher (and respect lower) for those in science and technology, but I found a truly stark case of where the public sees science today.

collins

A user would arrive at this disambiguation page upon a Wikipedia search for “Michael Collins”. The Apollo 11 astronaut is listed further down than “Politics”, “Sports”, and “Arts and entertainment”, in a location scientists are usually relegated to on Wikipedia (and other platforms).

The truth is, it will still be a long fight until someone instrumental to discovering the cure to cancer or designing a system for delivering a universal world-class education will earn either the salary or the public respect as an NFL quarterback or Hollywood star.

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Making a Metric for the Brightness of Constellations

Orion is often described as the brightest constellation. For a star, apparent magnitude tells its brightness as it appears from Earth, but what does it mean to consider a constellation bright?

One would clearly say Orion is brighter than bordering constellation Monoceros, with Orion’s brightest stars being that much brighter than Monoceros’ brightest stars, but could we develop a quantitative metric for a constellation’s brightness?

Since apparent magnitude is on a logarithmic scale, we can exponentiate apparent magnitudes of individual stars to get a relatively comparable brightness quantity, a relative flux. We can then sum this across the stars of a constellation to get a total brightness flux, how much light the stars that constitute a constellation beam towards us.

But some constellations are way larger than others, and this value would be larger for them not necessarily because their stars are actually brighter, but because they have more stars. So let’s do something more: like how with country populations one could divide by area to acquire a population density, let’s divide by the area occupied by the constellation (since there’s actually official boundaries) to get a brightness density. Let’s compute these numbers and see what they say the brightest constellations are.

(Note that resulting numbers are pretty much useful mostly as a linear relative quantity. Even though area below is in fraction of a hemisphere occupied [hemisphere simply because a visible field of view of the night sky is a hemisphere], brightness is a relative quantity, and so the numbers for density are mostly helpful only in the relative sense. I only included stars of magnitude brighter than 6 because around where human eyes stop perceiving the stars seems like a good cutoff.)

Rank Constellation Brightness Area (Hemis) Density
1 Crux 1.349 0.0034 396.7
2 Canis Major 5.435 0.0184 295.4
3 Carina 3.892 0.0240 162.2
4 Orion 3.760 0.0288 130.6
5 Canis Minor 0.974 0.0088 110.7
6 Scorpius 2.602 0.0240 108.4
7 Lyra 1.386 0.0138 100.4
8 Triangulum Australe 0.496 0.0054 91.9
9 Centaurus 4.405 0.0514 85.7
10 Vela 1.862 0.0242 77.0
11 Gemini 1.679 0.0250 67.2
12 Musca 0.446 0.0068 65.6
13 Lupus 1.039 0.0162 64.1
14 Auriga 1.988 0.0318 62.5
15 Taurus 2.304 0.0386 59.7
16 Perseus 1.687 0.0298 56.6
17 Puppis 1.778 0.0326 54.5
18 Corvus 0.467 0.0090 51.8
19 Sagitta 0.197 0.0038 51.7
20 Ara 0.584 0.0114 51.2
21 Cygnus 1.964 0.0390 50.4
22 Boötes 2.208 0.0440 50.2
23 Lepus 0.695 0.0140 49.7
24 Piscis Austrinus 0.572 0.0118 48.5
25 Corona Borealis 0.404 0.0086 47.0
26 Ursa Minor 0.582 0.0124 46.9
27 Circinus 0.208 0.0046 45.3
28 Scutum 0.235 0.0052 45.2
29 Cassiopeia 1.288 0.0290 44.4
30 Sagittarius 1.842 0.0420 43.9
31 Corona Australis 0.272 0.0062 43.8
32 Grus 0.776 0.0178 43.6
33 Aquila 1.345 0.0316 42.6
34 Eridanus 2.284 0.0552 41.4
35 Leo 1.848 0.0460 40.2
36 Columba 0.497 0.0130 38.2
37 Andromeda 1.324 0.0350 37.8
38 Triangulum 0.239 0.0064 37.3
39 Reticulum 0.208 0.0056 37.1
40 Ursa Major 2.297 0.0620 37.0
41 Cepheus 1.046 0.0284 36.8
42 Volans 0.249 0.0068 36.6
43 Pavo 0.663 0.0184 36.0
44 Lacerta 0.345 0.0098 35.2
45 Ophiuchus 1.516 0.0460 33.0
46 Aries 0.677 0.0214 31.6
47 Capricornus 0.627 0.0200 31.3
48 Draco 1.610 0.0526 30.6
49 Chamaeleon 0.194 0.0064 30.3
50 Hydrus 0.349 0.0118 29.6
51 Equuleus 0.095 0.0034 28.1
52 Dorado 0.241 0.0086 28.0
53 Vulpecula 0.351 0.0130 27.0
54 Hercules 1.602 0.0594 27.0
55 Serpens 0.794 0.0308 25.8
56 Libra 0.657 0.0260 25.3
57 Hydra 1.588 0.0632 25.1
58 Monoceros 0.588 0.0234 25.1
59 Delphinus 0.229 0.0092 24.9
60 Phoenix 0.564 0.0228 24.7
61 Pegasus 1.338 0.0544 24.6
62 Virgo 1.537 0.0628 24.5
63 Aquarius 1.152 0.0476 24.2
64 Norma 0.182 0.0080 22.8
65 Tucana 0.323 0.0142 22.7
66 Cetus 1.312 0.0598 21.9
67 Apus 0.203 0.0100 20.3
68 Telescopium 0.247 0.0122 20.3
69 Lynx 0.527 0.0264 20.0
70 Pyxis 0.210 0.0108 19.5
71 Pictor 0.230 0.0120 19.2
72 Octans 0.269 0.0142 19.0
73 Leo Minor 0.207 0.0112 18.5
74 Coma Berenices 0.336 0.0188 17.9
75 Cancer 0.436 0.0246 17.7
76 Indus 0.245 0.0142 17.2
77 Pisces 0.743 0.0432 17.2
78 Microscopium 0.171 0.0102 16.7
79 Camelopardalis 0.589 0.0366 16.1
80 Crater 0.198 0.0136 14.5
81 Antlia 0.162 0.0116 14.0
82 Canes Venatici 0.311 0.0226 13.7
83 Horologium 0.156 0.0120 13.0
84 Mensa 0.093 0.0074 12.6
85 Caelum 0.065 0.0060 10.9
86 Sculptor 0.250 0.0230 10.9
87 Fornax 0.196 0.0192 10.2
88 Sextans 0.108 0.0152 7.1

There are some incredibly questionable results in these numbers. Triangulum Australe manages to claim the #8 spot, managing to outrank, say, Gemini and Auriga. Musca, Lupus, and Ara are constellations an experienced stargazer may expect to rank in the lower half, yet are in the top quarter. And Ursa Major is as far down as #40, in fact lower than Ursa Minor? (I personally expected the bottom of the list to comprise of Caelum, Mensa, and Norma; well, two of them got quite close to the very bottom.)

Returning to an analogy with countries and population density, one could remember that many countries on Earth have absurdly high population densities mostly because it’s that much easier to crowd a small amount of space, and thus, for instance, Monaco and Bahrain have substantially higher population densities than Bangladesh despite Bangladesh’s crowdedness being very arguably more impressive. The constellation at the top of the list, Crux, is the area-wise smallest constellation on the night sky, and thus experiences benefits from this lack of need to make very much very bright, just happening to be defined as a notable small piece of terran night sky. Notably, in both of these cases, if a smaller region was indeed an independent unit, it is more likely to contain an interesting segment than a boring segment.

Another important contribution is the effect of the galactic plane of the Milky Way. Since we’re summing all stars of magnitude at least 6, there is a lot more background going into the numbers for constellations along the galactic plane. In fact, the top-ranked constellation in the list that doesn’t either intersect the galactic plane or come close enough to have background effects is…Corvus, at #18. In fact, this effect helps explain why constellations like Triangulum Australe and Musca are so far up in this list: they experience the significant bump of the background light of the Milky Way, which makes our statistic increase, but what causes this increase is what stargazers would view as noise, interfering with the process of recognizing the constellations. Thus, if wanted a metric that better captured the stargazer’s experience, perhaps raw brightness is not what we want to look for, but rather some sense of salience, and it’s very unclear how that would be measured.

More curious to me, it appears that both the bright and dim ends of the list are Southern-hemisphere dominated, whereas Northern-hemisphere constellations tend to more frequently fall in the center. I am rather curious as to what causes this. Since dividers in constellation space are artificial structures on a naturally continuous space, like country borders, we’d want to question effects in the decision-making of the constellation coiners. I wouldn’t be surprised if some explanation lies within the stages in which the constellations were decided.

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.

scatterplot_example

What we’re outputting is this.

scatterplot_example_2

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.

Continue reading “Dual Frontier Analysis”

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

Africa
Antarctica
Australia
Borneo
Europe
Eurasia
Eurafrasia
Greenland
Kerguela
Madagascar
Mars’ surface
New Guinea
Oceania

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

2. country

Abkhazia
Antarctica
Chechnya
Costa Rica
England
Estonia
European Union
Gibraltar
Hong Kong
Islamic State
Kosovo
Kurdistan
Monaco
Nauru
Northern Ireland
Palestine
Quebec
Sealand
Taiwan
Texas
Vatican City

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

3. digestive organ

appendix
brain
gallbladder
kidney
mouth
liver
lymph node
nose
salivary gland
spleen

4. Eastern Europe

eastern_europe

5. fruit

acorn
artichoke
banana
beet
blackberry
blueberry
corn
hazelnut
mango
peach
strawberry
tomato

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

6. functional language

C#
Haskell
Java
Javascript
Julia
Lojban
Python
R
Rust
Scala

Continue reading “You Keep Using That Word”

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.
nwangle1
> This exists.
nwangle2