Mars

Why Leap Years?

PNRJ current events , , , , , , , , , , , , , , , , ,

Mar 3 JDN 2460374

When this post goes live it will be March 3, not March 4, because February had an extra day this year. But what is this nonsense? Why are we adding a day to February?


There are two parts to this answer.

One part is fundamental astronomical truth.

The other part is historically contingent nonsense.

The fundamental astronomical truth is that Earth’s solar year is not an even multiple of its solar day. That’s kind of what you’d expect, seeing as the two are largely independent. (Actually it’s not as obvious as you might think, because orbital resonances actually do make many satellites have years that are even multiples of or even equal to their days—the latter is called tidal locking.)

So if we’re going to measure time in both years and days, one of two things will happen:

  1. The first day of the year will move around, relative to the solstices—and therefore relative to the seasons.
  2. We need to add or subtract days from some years and not others.

The Egyptians took option 1: 365 days each year, no nonsense, let the solstices fall where they may.

The Romans, on the other hand, had both happen—the Julian calendar did have leap years, but it got them slightly wrong, and as a result the first day of the year gradually moved around. (It’s now about two weeks off, if you were to still use the Julian calendar.)

It wasn’t until the Gregorian calendar that we got a good enough leap year system to stop this from happening—and even it is really only an approximation that would eventually break down and require some further fine-tuning. (It’s just going to be several thousand years, so we’ve got time.)

So, we need some sort of leap year system. Fine. But why this one?

And that’s where the historically contingent nonsense comes in.

See, if you have 365.2422 days per year, and a moon that orbits around you in every 27.32 days, the obvious thing to do would be to find a calendar that divides 365 or 366 into units of 27 or 28.

And it turns out you can actually do that pretty well, by having 13 months, each of 28 days, as well as 5 extra days on normal years and 6 extra days on leap years. (They could be the winter solstice holiday season, for instance.)

You could even make each month exactly 4 weeks of 7 days, if for some reason you like 7-day weeks (not really sure why we do).

But no, that’s not what we did. Of course it’s not.

13 is an unlucky number in Christian societies, because of the betrayal of Judas (though it could even go back further than that).

So we wanted to have only 12 months. Okay, fine.

Then each month is 30 days and we have 5 extra days like before? Oh no, definitely not.

7 months are 30 days and 5 months are 31 days? No, that would be too easy.

7 months are 31 days, 5 are 30, and 1 is 28, unless it’s 29? Uh… what?

Why this is so has all sorts of reasons:

There’s the fact that the months of July and August were created to honor Julius and Augustus respectively.

There’s the fact that there used to be an entire intercalary month which was 27 or 28 days long and functioned kind of like February does now (but it wasn’t February, which already existed).

There are still other calendars in use, such as the Coptic Calendar, the Chinese lunisolar calendar, and the Hijri Calendar. Indeed, what calendar you use seems to be quite strictly determined by your society’s predominant religious denominations.

Basically, it’s a mess. (And it makes programming that involves dates and times surprisingly hard.)

But calendars are the coordination mechanism par excellence, and here’s the thing about coordination mechanisms:

Once you have one, it’s really hard to change it.

The calendar everyone wants to use is whatever calendar everyone else is using. In order to get anyone to switch, we need to get most people to switch. It doesn’t really matter which one is the best in theory; the best in practice is whatever is actually in use.

That is much easier to do when a single guy has absolute authority—as in, indeed, the Roman Empire and the Catholic Church, for the Julian and Gregorian calendars respectively.

There are other ways to accomplish it: The SI was developed intentionally as explicitly rational, and is in fact in wide use around the world. The French revolutionaries intentionally devised a better way to measure things, and actually got it to stick (mostly).

Then again, we never did adopt the French metric system for time. So it may be that time coordination, being the prerequisite for nearly all other forms of coordination, is so vital that it’s exceptionally difficult to change.

Further evidence in favor of this: The Babylonians used base-60 for everything. We literally only use it for time. And we use it for time… probably because we ultimately got it from them.

So while nobody seriously uses “rod“, “furlong“, “firkin“, or “buttload” (yes, that’s a real unit) sincerely anymore, we still use the same days, weeks, and months as the Romans and the same hours, minutes, and seconds as the Babylonians. (And while Americans may not use “fortnight” much, I can assure you that Brits absolutely do—and it’s really nice, because it doesn’t have the ambiguity of “biweekly” or “bimonthly” where it’s never quite clear whether the prefix applies to the rate or the period.)

So, in short, we’re probably stuck with leap years, and furthermore stuck with the weirdness of February.

The only thing I think is likely to seriously cause us to change this system would be widespread space colonization necessitating a universal calendar—but even then I feel like we’ll probably use whatever is in use on Earth anyway.

Even when we colonize space, I think the most likely scenario is that “day” and “year” will still mean Earth-day and Earth-year, and for local days and years you’d use something like “sol” and “rev”. It would just get too confusing to compare people’s ages across worlds otherwise—someone who is 11 on Mars could be 21 on Earth, but 88 on Mercury. (Are they a child, a young adult, or a senior citizen? They’re definitely a young adult—and it’s easiest to see that if you stick to Earth years. Maybe on Mars they can celebrate their 11th rev-sol, but on Earth it’s still their 21st birthday.)

So we’re probably going to be adding these leap years (and, most of us, forgetting which centuries don’t have one) until the end of time.

The Expanse gets the science right—including the economics

PNRJ futurism, public policy , , , , , , , , , , , , , , , , , ,

JDN 2457502

Despite constantly working on half a dozen projects at once (literally—preparing to start my PhD, writing this blog, working at my day job, editing a novel, preparing to submit a nonfiction book, writing another nonfiction book with three of my friends as co-authors, and creating a card game—that’s seven actually), I do occasionally find time to do things for fun. One I’ve been doing lately is catching up on The Expanse on DVR (I’m about halfway through the first season so far).

If you’re not familiar with The Expanse, it has been fairly aptly described as “Battlestar Galactica meets Game of Thrones”, though I think that particular comparison misrepresents the tone and attitudes of the series, because both BG and GoT are so dark and cynical (“It’s a nice day… for a… red wedding!”). I think “Star Trek meets Game of Thrones” might be better actually—the extreme idealism of Star Trek would cancel out the extreme cynicism of Game of Thrones, with the result being a complex mix of idealism and cynicism that more accurately reflects the real world (a world where Mahatma Gandhi and Adolf Hitler lived at the same time). That complex, nuanced world (or should I say worlds?) is where The Expanse takes place. ST is also more geopolitical than BG and The Expanse is nothing if not geopolitical.

But The Expanse is not just psychologically realistic—it is also scientifically and economically realistic. It may in fact be the hardest science fiction I have ever encountered, and is definitely the hardest science fiction I’ve seen in a television show. (There are a few books that might be slightly harder, as well as some movies based on them.)

The only major scientific inaccuracy I’ve been able to find so far is the use of sound effects in space, and actually even these can be interpreted as reflecting an omniscient narrator perspective that would hear any sounds that anyone would hear, regardless of what planet or ship they might be on. The sounds the audience hears all seem to be sounds that someone would hear—there’s simply no particular person who would hear all of them. When people are actually thrown into hard vacuum, we don’t hear them make any noise.

Like Firefly (and for once I think The Expanse might actually be good enough to deserve that comparison), there is no FTL, no aliens, no superhuman AI. Human beings are bound within our own solar system, and travel between planets takes weeks or months depending on your energy budget. They actually show holograms projecting the trajectory of various spacecraft and the trajectories actually make good sense in terms of orbital mechanics. Finally screenwriters had the courage to give us the terrifying suspense and inevitability of an incoming nuclear missile rounding a nearby asteroid and intercepting your trajectory, where you have minutes to think about it but not nearly enough delta-v to get out of its blast radius. That is what space combat will be like, if we ever have space combat (as awesome as it is to watch, I strongly hope that we will not ever actually do it). Unlike what Star Trek would have you believe, space is not a 19th century ocean.

They do have stealth in space—but it requires technology that even to them is highly advanced. Moreover it appears to only work for relatively short periods and seems most effective against civilian vessels that would likely lack state-of-the-art sensors, both of which make it a lot more plausible.

Computers are more advanced in the 2200s then they were in the 2000s, but not radically so, at most a million times faster, about what we gained since the 1980s. I’m guessing a smartphone in The Expanse runs at a few petaflops. Essentially they’re banking on Moore’s Law finally dying sometime in the mid 21st century, but then, so am I. Perhaps a bit harder to swallow is that no one has figured out good enough heuristics to match human cognition; but then, human cognition is very tightly optimized.

Spacecraft don’t have artificial gravity except for the thrust of their engines, and people float around as they should when ships are freefalling. They actually deal with the fact that Mars and Ceres have lower gravity than Earth, and the kinds of health problems that result from this. (One thing I do wish they’d done is had the Martian cruiser set a cruising acceleration of Mars-g—about 38% Earth-g—that would feel awkward and dizzying to their Earther captives. Instead they basically seem to assume that Martians still like to use Earth-g for space transit, but that does make some sense in terms of both human health and simply transit time.) It doesn’t seem like people move around quite awkwardly enough in the very low gravity of Ceres—which should be only about 3% Earth-g—but they do establish that electromagnetic boots are ubiquitous and that could account for most of this.

They fight primarily with nuclear missiles and kinetic weapons, and the damage done by nuclear missiles is appropriately reduced by the fact that vacuum doesn’t transmit shockwaves. (Nuclear missiles would still be quite damaging in space by releasing large amounts of wide-spectrum radiation; but they wouldn’t cause the total devastation they do within atmosphere.) Oddly they decided not to go with laser weapons as far as I can tell, which actually seems to me like they’ve underestimated advancement; laser weapons have a number of advantages that would be particularly useful in space, once we can actually make them affordable and reliable enough for widespread deployment. There could also be a three-tier system, where missiles are used at long range, railguns at medium range, and lasers at short range. (Yes, short range—the increased speed of lasers would be only slight compared to a good railgun, and would be more than offset by the effect of diffraction. At orbital distances, a laser is a shotgun.) Then again, it could well work out that railguns are just better—depending on how vessels are structured, puncturing their hulls with kinetic rounds could well be more useful than burning them up with infrared lasers.

But I think what really struck me about the realism of The Expanse is how it even makes the society realistic (in a way that, say, Firefly really doesn’t—we wanted a Western and we got a Western!).

The only major offworld colonies are Mars and Ceres, both of which seem to be fairly well-established, probably originally colonized as much as a century ago. Different societies have formed on each world; Earth has largely united under the United Nations (one of the lead characters is an undersecretary for the UN), but meanwhile Mars has split off into its own independent nation (“Martian” is now an ethnicity like “German” rather than meaning “extraterrestrial”), and the asteroid belt colonists, while formally still under Earth’s government, think of themselves as a different culture (“Belters”) and are seeking independence. There are some fairly obvious—but deftly managed rather than heavy-handed—parallels between the Belter independence movement and real-world independence movements, particularly Palestine (it’s hard not to think of the PLO when they talk about the OPA). Both Mars and the Belt have their own languages, while Earth’s languages have largely coalesced around English as the language of politics and commerce. (If the latter seems implausible, I remind you that the majority of the Internet and all international air traffic control are in English.) English is the world’s lingua franca (which is a really bizarre turn of phrase because it’s the Latin for French).

There is some of the conniving and murdering of Game of Thrones, but it is at a much more subdued level, and all of the major factions display both merits and flaws. There is no clear hero and no clear villain, just conflict and misunderstanding between a variety of human beings each with their own good and bad qualities. There does seem to be a sense that the most idealistic characters suffer for their idealism much as the Starks often do, but unlike the Starks they usually survive and learn from the experience. Indeed, some of the most cynical also seem to suffer for their cynicism—in the episode I just finished, the grizzled UN Colonel assumed the worst of his adversary and ended up branded “the butcher of Anderson Station”.

Cost of living on Ceres is extraordinarily high because of the limited living space (the apartments look a lot like the tiny studios of New York or San Francisco), and above all the need to constantly import air and water from Earth. A central plot point in the first episode is that a ship carrying comet ice—i.e., water—to Ceres is lost in a surprise attack by unknown adversaries with advanced technology, and the result is a deepening of an already dire water shortage, exacerbating the Belter’s craving for rebellion.

Air and water are recyclable, so it wouldn’t be that literally every drink and every breath needs to be supplied from outside—indeed that would clearly be cost-prohibitive. But recycling is never perfect, and Ceres also appears to have a growing population, both of which would require a constant input of new resources to sustain. It makes perfect sense that the most powerful people on Ceres are billionaire tycoons who own water and air transport corporations.

The police on Ceres (of which another lead character is a detective) are well-intentioned but understaffed, underfunded and moderately corrupt, similar to what we seem to find in large inner-city police departments like the NYPD and LAPD. It felt completely right when they responded to an attempt to kill a police officer with absolutely overwhelming force and little regard for due process and procedure—for this is what real-world police departments almost always do.

But why colonize the asteroid belt at all? Mars is a whole planet, there is plenty there—and in The Expanse they are undergoing terraforming at a very plausible rate (there’s a moving scene where a Martian says to an Earther, “We’re trying to finish building our garden before you finish paving over yours.”). Mars has as much land as Earth, and it has water, abundant metals, and CO2 you could use to make air.Even just the frontier ambition could be enough to bring us to Mars.

But why go to Ceres? The explanation The Expanse offers is a very sensible one: Mining, particularly so-called “rare earth metals”. Gold and platinum might have been profitable to mine at first, but once they became plentiful the market would probably collapse or at least drop off to a level where they aren’t particularly expensive or interesting—because they aren’t useful for very much. But neodymium, scandium, and prometheum are all going to be in extremely high demand in a high-tech future based on nuclear-powered spacecraft, and given that we’re already running out of easily accessible deposits on Earth, by the 2200s there will probably be basically none left. The asteroid belt, however, will have plenty for centuries to come.

As a result Ceres is organized like a mining town, or perhaps an extractive petrostate (metallostate?); but due to lightspeed interplanetary communication—very important in the series—and some modicum of free speech it doesn’t appear to have attained more than a moderate level of corruption. This also seems realistic; the “end-of-history” thesis is often overstated, but the basic idea that some form of democracy and welfare-state capitalism is fast becoming the only viable model of governance does seem to be true, and that is almost certainly the model of governance we would export to other planets. In such a system corruption can only get so bad before it is shown on the mass media and people won’t take it anymore.

The show doesn’t deal much with absolute dollar (or whatever currency) numbers, which is probably wise; but nominal incomes on Ceres are likely extremely high even though the standard of living is quite poor, because the tiny living space and need to import air and water would make prices (literally?) astronomical. Most people on Ceres seem to have grown up there, but the initial attraction could have been something like the California Gold Rush, where rumors of spectacularly high incomes clashed with similarly spectacular expenses incurred upon arrival. “Become a millionaire!” “Oh, by the way, your utility bill this month is $112,000.”

Indeed, even the poor on Ceres don’t seem that poor, which is a very nice turn toward realism that a lot of other science fiction shows seem unprepared to make. In Firefly, the poor are poor—they can barely afford food and clothing, and have no modern conveniences whatsoever. (“Jaynestown”, perhaps my favorite episode, depicts this vividly.) But even the poor in the US today are rarely that poor; our minimalistic and half-hearted welfare state has a number of cracks one can fall through, but as long as you get the benefits you’re supposed to get you should be able to avoid starvation and homelessness. Similarly I find it hard to believe that any society with high enough productivity to routinely build interstellar spacecraft the way we build container ships would not have at least the kind of welfare state that provides for the most basic needs. Chronic dehydration is probably still a problem for Belters, because water would be too expensive to subsidize in this way; but they all seem to have fairly nice clothes, home appliances, and smartphones, and that seems right to me. At one point a character loses his arm, and the “cheap” solution is a cybernetic prosthetic—the “expensive” one would be to grow him a new arm. As today but perhaps even more so, poverty in The Expanse is really about inequality—the enormous power granted to those who have millions of times as much as others. (Another show that does this quite well, though is considerably softer as far as the physics, is Continuum. If I recall correctly, Alec Sadler in 2079 is literally a trillionaire.)

Mars also appears to be a democracy, and actually quite a thriving one. In many ways Mars appears to be surpassing Earth economically and technologically. This suggests that Mars was colonized with our best and brightest, but not necessarily; Australians have done quite well for themselves despite being founded as a penal colony. Mars colonization would also have a way of justifying their frontier idealism that no previous frontiers have granted: No indigenous people to displace, no local ecology to despoil, and no gifts from the surrounding environment. You really are working entirely out of your own hard work and know-how (and technology and funding from Earth of course) to establish a truly new world on the open and unspoiled frontier. You’re not naive or a hypocrite, it’s the real truth. That kind of realistic idealism could make the Martian Dream a success in ways even the American Dream never quite was.

In all it is a very compelling series, and should appeal to people like me who crave geopolitical nuance in fiction. But it also has its moments of huge space battles with exploding star cruisers, so there’s that.

Why does nobody want to become a teacher?

PNRJ public policy , , , , , , , , , , , ,

JDN 2457366

The United States is currently suffering a large and growing shortage of qualified teachers, particularly in grades K-12. In some particular areas, this shortage is extremely acute; high schools are not able to teach some courses because there is simply no one qualified to teach them. Science and math teachers are in particularly high demand, because these programs are being expanded even as the people qualified to teach them are shifting over to working at the college level or in the private sector.

Other countries are also suffering severe teacher shortages, including the UK and several other countries in the EU.
The problem is projected to get worse: Enrollments in teacher training are rapidly declining. Meanwhile, because somewhere along the way people got convinced that the problem with education is that our teachers aren’t smart enough (this is completely, totally wrong by the way), standards for becoming a teacher are becoming ever more stringent, narrowing the pool even more.

This is a very serious problem, because education—often called “human capital investment” in economic jargon—is one of the most important investments any society can make. Indeed, it may be the most important, the one factor of production that is absolutely indispensable. If you run out of one raw material, you can make products out of something else. Manual labor can be replaced by machines. If you don’t have enough machines, you can build more. But if you find yourself without anyone who knows how to read and do arithmetic, how are you going to replace that? If we imagine a scenario like being trapped on a desert island or colonizing Mars where we have to start from scratch and we are only allowed to have one factor of production, education is the one we would want to have. (I guess if it’s Mars you do need a certain bare minimum of physical capital, like a spacesuit.)

The teacher shortage is most acute in high-poverty areas, where educational outcomes are terrible. Indeed, the most important cause of the failings of the US education system has always been poverty.

Why are teachers in poor schools so underqualified? Because their working conditions are terrible. Turnover is extremely high because teachers are underpaid, the schools are undersupplied, and their administrators do not support them.

Why are there so many teachers not qualified to teach their subjects? Because people who are qualified can find better jobs in other places. Jobs just as rewarding, that make just as large a contribution to society, which are more pleasant, offer more autonomy, and pay a lot better.

If you are an expert in physics, you could become a physicist and make a median income of $106,000.

If you are an expert in economics, you could become an economist and make a median income of $92,000.

If you are an expert in biology, you could become a biochemist and make a median income of $81,000.

Or, instead of all those things, you could become a high school teacher and make a median income of $55,000. Gee, I wonder which one you’re going to do?

Keep that in mind if it sounds ridiculous to you to pay teachers $100,000 salaries.

Even in wealthy schools, teachers are miserable; I have this on direct testimony from my father, who has taught high school in Ann Arbor for almost 20 years now. There are a lot of teachers who believe in making a difference through education, but quickly become burnt out and leave for better working conditions.

I know in my own case that I’m not planning on teaching high school, even though I know I’d be very good at it and I’ve always found teaching very rewarding. I’d actually be qualified to teach several subjects, from mathematics to social studies and even including physics and Latin. Any public school would be thrilled to have me—but probably not thrilled enough to pay me as much as I’d get from a university, international institution, or policy think-tank. So it’s hard for me to justify the career decision of going into public education.

The absolute highest-paid teacher in the Ann Arbor Public Schools is paid $109,000 gross—and Ann Arbor is one of the highest-paying school systems in the nation, and not coincidentally also one of the best. Most of the professors at the University of Michigan are paid over $100,000 gross and some are paid over $300,000. (As a public school, the University of Michigan releases all its salaries.)

So, you’re living in Ann Arbor… you have a graduate degree… you want to work in education; you could either start at $40,000 and maybe work your way up to $100,000 by teaching high school, or you could start at $100,000 and maybe work your way up to $300,000 by teaching college. (Admittedly, to teach in college you generally also need to do research work and probably get a PhD; so it’s not quite an equal comparison. But the most-qualified educators would be good at either job.)

Economics, along with most science and math fields, pays particularly well outside education. This senior economist position at the World Bank pays at grade GG, which is a minimum starting net salary of $102,000.
How can we solve our teacher shortage? It’s really quite simple: Offer higher salaries for teachers. If you want the best-qualified people in your classrooms, you must pay salaries that attract the best-qualified people. If you pay substandard salaries, you’re going to attract substandard talent. “Those who can, do; those who can’t, teach” isn’t a law of nature; it’s a result of public policy decisions to keep teachers systematically underpaid.

Most of the time when people say “It’s just ECON 101”, they don’t actually understand economics very well and likely have not actually taken ECON 101. But this really basically is a question of ECON 101: Supply and demand. If you have a shortage of something, not enough people willing to produce it compared to the number of people who want to buy it, you must raise the price.

Would that be expensive? Yes it would. Doubling the salary of every teacher would raise total spending on education by about 75%, because teacher compensation is about three-quarters of education spending. This would raise US K-12 education spending from about $600 billion per year to more like $1.05 trillion per year, an additional $450 billion per year in public spending, or a little less than $1,500 per American per year. That is not a small amount of money; indeed, it’s about three times what we’d need to end world hunger. And this is actually an underestimate, since we also hope to hire more teachers and should also improve facilities while we’re at it. So a truly comprehensive educational reform project could very well double our total spending on K-12 education to $1.2 trillion.

And if you want to go up there on a podium and actually tell people, “It would be nice to improve our educational system, but we simply can’t afford to do it without raising taxes unreasonably high!” then that is absolutely a reasonable argument to make. There are always tradeoffs in life. At some point, maybe it really isn’t worth spending an extra million dollars to educate one more child. (Is it worth an extra million dollars to educate two more children? Based on net present value of earnings, yes. And frankly I don’t think net present value of earnings even gets close to assessing the true value of an education; it’s a very weak lower bound.)

But I am sick and tired of people saying “Education is our highest priority!” and then refusing to actually spend the money it would take to improve our educational system. This is not a question of “finding solutions”; we know what to do. Raise teacher salaries. Improve schools. Buy new textbooks. People just aren’t willing to actually pony up the cash to do it. They want an easy way out, some simple way of making education better that somehow won’t cost anything. But we’ve been searching for that for awhile now—don’t you think we’d have found it by now?