Happy New Year!

I’ll wear both the pessimist and optimist hats.

Pessimist first.

Remember how we thought 2021 couldn’t get worse and got disabused of that idea in only six days?

(Yeah well we sort of stepped into that burning bag of bearded dragon poo.)

A friend of mine, who could be a bit of a wiseass at times (and pessimism was part of his schtick), would tell me something sometimes when I was a bit bummed out about something that had just happened.

And it bears remembering, especially with the usurpatious vacuum skull still in the White House:

“It’s never so bad that it can’t get worse.”

OK, on the optimist side. OK, this is cautious optimism, rather than full frontal unicorns and rainbows optimism, but here it is:

I think both the pessimist side and the optimist side can agree this will be a very eventful year. But if things actually work well in November, even a horrific year might contain the seeds of a reversal of fortune.

Let’s go back to 1979. Carter. Malaise. Soviets surging all over the world. 50 Americans held hostage by a bunch of neolithic barbarians.

The man, I think, might actually have meant well. (I was more certain of that a few years ago than I am today.) But he was not competent in that job.

But then, irony of ironies, there was this song. If you do NOT like 1970s/1980s Swedish popular music, skip the next video. Otherwise, the gratuitous fireworks display ends at 57 seconds and the music starts shortly thereafter.

Note the video is set in 1979 New Year’s eve and they actually ask what it will be like in 1989/90.

Quite a bit different, thanks to Ronaldus Magnus! We went from Jimmy Carter Malaise to seven years of economic growth and The Wall coming down! Unimaginable in 1979!

But, we did have to get through the highest misery index ever in 1980, first.

And we have to get through 2022. Which will likely make 1980 look like child’s play. Let’s just hope it doesn’t make 2021 look like child’s play, too.

The Chinese Should Think Before Wiping Us Out As Sometimes They Need Us To Solve Their Problems For Them

Okay you knuckledragging ChiComs trying to take us down…here’s a history lesson for you.

For millennia, you had to suffer from this:

Yep. Steppe Nomads. They laid waste to your country, burned, raped and pillaged (but not in that order–they’re smarter than you are) for century after century.

You know who figured out how to take them on and win? The Russians.

Not you, the Russians. And it took them less than two centuries. And Oh By The Way they were among the most backward cultures in Europe at the time.

You couldn’t invent an alphabet, you couldn’t take care of barbarians on horseback, and you think you can take this board down?

HAHAHAHAHAHAHA!!!! We’re laughing at you, you knuckledragging dehumanized communists…worshipers of a mass-murderer who killed sixty million people!

I mean, you still think Communism is a good idea even after having lived through it!

By my reckoning that makes you orders of magnitude more stupid than AOC, and that takes serious effort.

His Fraudulency

Joe Biteme, properly styled His Fraudulency, continues to infest the White House, and hopium is still being dispensed even as our military appears to have joined the political establishment in knuckling under to the fraud.

All realistic hope lies in the audits, and perhaps the Lindell lawsuit (that will depend on how honestly the system responds to the suit).

One can hope that all is not as it seems.

I’d love to feast on that crow.

“No Chemicals”

A detailed analysis of the contents of His Fraudulency’s skull was performed.

Absolutely no chemicals found!

(That one’s for you, Gail!)

Justice Must Be Done.

The prior election must be acknowledged as fraudulent, and steps must be taken to prosecute the fraudsters and restore integrity to the system.

Nothing else matters at this point. Talking about trying again in 2022 or 2024 is hopeless otherwise. Which is not to say one must never talk about this, but rather that one must account for this in ones planning; if fixing the fraud is not part of the plan, you have no plan.

Political Science In Summation

It’s really just a matter of people who can’t be happy unless they control others…versus those who want to be left alone. The oldest conflict within mankind. Government is necessary, but government attracts the assholes (a highly technical term for the control freaks).

James Webb Space Telescope Update

JWST deployed both booms on the 31st. The first one took quite a long time because some of the sensors that were supposed to show the cover unfurled weren’t working right.

So here’s what it looks like now.

Over the course of the weekend the sheets will be separated and tensioned, at which point the sun shield will be fully functional and the JWST should really start to cool off (though they have been heating things up to ensure they will deploy properly). -370 F is the goal temperature though it will take weeks to get there.

Lawyer Appeasement Section

OK now for the fine print.

This is the WQTH Daily Thread. You know the drill. There’s no Poltical correctness, but civility is a requirement. There are Important Guidelines,  here, with an addendum on 20191110.

We have a new board – called The U Tree – where people can take each other to the woodshed without fear of censorship or moderation.

And remember Wheatie’s Rules:

1. No food fights
2. No running with scissors.
3. If you bring snacks, bring enough for everyone.
4. Zeroth rule of gun safety: Don’t let the government get your guns.
5. Rule one of gun safety: The gun is always loaded.
5a. If you actually want the gun to be loaded, like because you’re checking out a bump in the night, then it’s empty.
6. Rule two of gun safety: Never point the gun at anything you’re not willing to destroy.
7. Rule three: Keep your finger off the trigger until ready to fire.
8. Rule the fourth: Be sure of your target and what is behind it.

(Hmm a few extras seem to have crept in.)

(Paper) Spot Prices

Last week:

Gold $1810.20
Silver $22.96
Platinum $981.00
Palladium $2036.00
Rhodium $14,975.00

This week, 3PM Mountain Time, markets have closed for the weekend.

Gold $1830.80
Silver $23.40
Platinum $973.00
Palladium $1995
Rhodium $15,300

Now THIS is a little more like it!!!

Let’s see if “they” manage to push it down again. Palladium actually went down sixty bucks Friday, it was over 2000 bucks earlier.

More On Time

(Please note, this is not titled “Moron Time.” We’ve had quite enough moron time, thankyouverymuch.)

[And speaking of morons, I somehow posted the original of this on January 1 of last year…I thought I had checked that but it did somehow goof up the time of day and I had to fix that…it probably took that opportunity to “correct” my year.]

Happy New Year!!!

It’s New Year’s Day. It’s an arbitrarily picked day, based (somewhat) on Ancient Roman (and Pre-Christian) practice. And a suitable day for more information on our calendar.

The Year

Last time I told the story of Julius Caesar’s reform of 45 BCE, and how it ended the practice of entire intercalary months–months added every now and again to keep the calendar roughly lined up with the seasons. This had had to be done because months were true to their origin back then, matching the phases of the moon. But 12 of these “moonths” didn’t make up a year, not really, and thirteen of them was too much. The Jewish calendar has the same issue; they have to add entire months fairly often.

Julius Caesar made the twelve months longer, and set things up to add a leap day every four years to account for the fractional day over 365 in the tropical year. It wasn’t quite right; I told that story last year.

But that calendar has come directly down to us with only the minor adjustment made originally in 1582 by order of Pope Gregory XIII, and eventually adopted by Protestant and Orthodox countries, and it’s pretty much either official worldwide, or well known.

The months and days of the month set by Julius Caesar seem set almost in concrete; only one lasting change has been made to them in the last two thousand years (even if that change wasn’t done at the same time everywhere).

But the numbering of the years–and even the choice of when the year should begin–has changed a lot.

When Caesar was in charge, the calendar year was generally identified by who was consul at the time, which makes modern historians’ lives a bit of a pain, but we do have a fairly detailed list: https://en.wikipedia.org/wiki/List_of_Roman_consuls and they can generally figure things out.

That list starts in 509 BC because that is when, according to tradition, the last of the seven Roman kings was overthrown and the Roman Republic was established. And the emperors (starting with Octavian/Augustus) kept the office around but they were the real power.

The Romans, however, did sometimes think in terms of something called Ab Urbe Condita, essentially since the founding of the city of Rome, and that was in 753 BCE. Therefore AUC 753 was 1 BCE, and AUC 754 was 1 CE. Were we still using that numbering, 2022 would be AUC 2775.

[Note, by the way, there was no year Zero. 1 BCE was followed directly by 1 CE. Which makes “how many years between” arithmetic a bit hazardous when computing between dates either side of that line. Astronomers, who sometimes have to “backtrack” such things, do use a zero year, then negative numbers, so their year 0 is 1 BCE, -1 is 2 BCE, etc. Archaeologists tend to use “Before Present” but “Present” turns out to be roughly 1950–they fell prey to institutionalizing a “present” by accident (they probably didn’t expect to use “BP” forever) in exactly the same way that “modern” no longer means “modern” because people named a specific time the modern period and we have moved past it, so we sometimes find ourselves using strange terms like “post modern” that shouldn’t be meaningful without a time machine.]

Early Christians actually did not use AD dating. The AD dating schema was first put forward by Dionysius Exiguus in 525. Before that the most commonly used schema was the Diocletian Era used in an old Easter table; he (understandably) didn’t want to commemorate Diocletian, who had instituted the last and worst persecution of Christians in the Roman Empire. (The Diocletian era was, in any case, mostly used in the East.)

The year that is now known as AD 1 (or 1 CE), was almost certainly not the birth year of Jesus. Matthew indicates it was in the time of King Herod (Mt 2:1), who kicked the bucket in 4 BCE. Luke indicates that the census requiring Mary and Joseph to go to Bethlehem occurred while Quirinius was governor of Syria (Lk 2:2) though he talks about other early events happening under Herod. Quirinius became governor in 6 CE. Absent some major historical discovery these two times don’t even overlap; neither includes 1 CE. But it’s certainly close to the right year. Whether it’s close enough for non government work is, I suppose, moot. We’re not likely to change our year numbers right now.

Which is not to say that it hasn’t happened.

The Eastern Orthodox Church and Byzantine Empire used “Anno Mundi,” year of the world. By attempting to fix Year One to be the year of creation, they sidestepped all issues with negative numbers, missing zero years, and so on. So they got hold of their Bibles, laid out a chronology, and fixed creation at 5509 years before Jesus was born. However, they did not at first agree with Exiguus’s dating of when Jesus was born. Their year 1 A.M. is September 1, 5509 BCE through August 31, 5508 BCE. Note their year began (and within the church organization still does begin) on September 1. September 1, of 2021 (i.e., last September) began the year 7530 A.M.

By the way, it’s technically not quite kosher to give a date like that, because the calendar didn’t exist yet on that date–if anything the prior mess of a Roman Republican calendar should be used–if anyone can figure out how it would have worked that year. So they’ll often qualify things by referring to the proleptic Julian calendar; i.e., they extend the Julian calendar back to that date. (In this particular case, remember that it’s not our current Gregorian calendar.)

(Russia switched from this calendar to a January 1 start of the New Year in 1700 CE; they also began to use the AD numbering at that time…but they were still on the Julian Calendar so they were off from the Gregorian calendar by 11 days, then 12 days in the 1800s, then 13 days during the 1900s before and during the ‘October’ Revolution–which happened in November by the Gregorian calendar. The commies switched in 1918, trying to shed the past–they even considered switching Russian to the Latin alphabet.)

You may think that 5509 BCE sounds wrong. It certainly does disagree with the usual Bible-based dating used by many churches here in the United States, which is based on Archbishop Ussher’s (1581-1626) chronology which fixes creation at about 6 PM, on the 22nd of October, 4004 BCE (by the proleptic Julian calendar). This is the chronology most often used by fundamentalists in the US.

That’s a difference of over 1500 years. It’s really difficult to construct an unambiguous chronology from the Old Testament.

I alluded to some disagreement over what date the year started; Russia used September 1 until 1700, one of Peter the Great’s many reforms, the Eastern Orthodox church still uses it internally, but that wasn’t the only difference between past practice and today’s practice. Up until 1752, England (and her colonies, which would include US (as in U.S.) at the time) was on the old Julian calendar; until that time, March 25 was the start of the new year. Not even the beginning of a month! March 24, 1751 was followed the next day by March 25, 1752. In September of that year, things were set to the current January 1 practice; also September 2, 1752 was followed by September 14, 1752; England dropped 11 days there to get in sync with the Gregorian calendar and would follow it from then forward.

If George Washington had had a birth certificate, it would have read 11 February, 1731 (Julian date); unlike many he changed his birthday to 22 February, in other words following the Gregorian calendar, and the year is now given as 1732 to be consistent with a January 1 start-of-year.

There was confusion as to which European gets the credit for ‘discovering’ South America for similar reasons of confusion between countries who didn’t start the year at the same time.

And nothing would astonish me more than to hear that’s a complete list.

What day to call the New Year, is fundamentally an arbitrary decision. But a date has to be chosen and abided by, and today is that date. So get used to writing and typing 2022.

Julian Dates

“Julian Date” means two distinct things. Usually, it’s just a day number within the year. February 3rd, for instance is Julian date 34. It runs all the way up to 365 or 366.

But there’s a different Julian Date used by astronomers. A 365.25 day year is awkward to deal with sometimes, so they’ll sometimes compute the time between two events in number of days. A “day” they can get a handle on; it’s 86,400 seconds and a second is quite thoroughly defined. So they’ll (for instance) compute the period of a planet in days.

Joseph Justus Scaliger (1540-1609) proposed a scheme where days would be sequentially numbered from a start time, then continue counting upward forever. This became the Julian date, named after his father Julius Scaliger. He first suggested it in 1583.

Scaliger chose the day January 1, 4713 BCE as his start date. It was satisfactorily far back in time that negative numbers wouldn’t be referenced often. Why that particular year? It was a leap year, the first year of a solar cycle of 28 years, the first year of a lunar cycle of 19 years, and the first year of an indiction cycle of 15 years. The solar cycle is simply the repeat period of the Julian calendar, the lunar cycle was named such because the moon would undergo the same phases on the same days, every 19 years, and the indiction cycle was an ancient Roman period at the beginning of which taxes would be reassessed. These cycles could be run backward in time, and 4713 BC was the most recent year when all three cycles were in their first year. (Being a leap year was implicit in being the start year of a solar cycle.)

This is, by the way, according to the proleptic Julian calendar, not the proleptic Gregorian calendar.

Astronomers still number their days this way. Their day starts at noon (logical, because that way an overnight period, when they’d be observing, didn’t have a day break in it), so noon, January 1, 4713 BCE was the start of Julian Day 0. (In the Gregorian calendar, this would have been November 24, 4714 BCE.) Scaliger wasn’t familiar with time zones, but the modern definition of this specifies Universal Time (essentially the time at Greenwich without Daylight Saving Time; it’s seven hours ahead of Mountain Standard Time).

And if my arithmetic is right, this post will go “live” on 2459580, almost three quarters of the way into that date; so at 7 AM ET, it will be 2459581. TIme of day is handled as a decimal fraction, so midnight UTC is Julian day [whatever it is].5.

In another common usage, we use a “modified Julian date” that starts at midnight, UT (not noon) and drops the 2,400,000 in front and just goes with 59581. So the Modified Julian Date is the Julian Date minus 2,400,000.5. This will work for another century or so then we’ll have to either restart it at 0 or just start dealing with six digit numbers. It’s handy for computers that might not have the precision to show a seven digit number with multiple digits of precision after the decimal point; we save two digits that way. (This is less of an issue today, with 64 bit computers, than it was with 32 bit computers.)

The following link: https://en.wikipedia.org/wiki/Julian_day gives a lot more information including a way to compute the Julian day for any “regular” date.

Holocene Dating

As an aside, someone came up with an idea called the “Holocene Epoch.” The idea was to simply add ten thousand to all years, so that this would be 12,022. 1 CE becomes 10,001, and 1 BCE becomes 10,000. The idea is not to try to find the beginning of the world, but at least all of human history, almost back to the first buildings that survive, would at least have a positive year number attached to it. And 10,000 BCE is very nearly the start of the present geological epoch, the Holocene, roughly corresponding to the end of the last glaciation, hence the name “Holocene.” (That epoch actually began [best estimate] 11,650 years “Before Present” which makes it 11,722 years ago right now, not 12022 years ago. A three hundred year glitch.)

Yeah, that won’t ever happen.

Leap Weeks?

And on a very different topic. File this one under “won’t ever freaking happen” but I include it because you might find it amusing.

Because, as I’ve pointed out, the shape of our calendar–the configuration and sizes of months–has only undergone one slight adjustment in the last 2000 years. I don’t take this seriously–but I find it amusing.

Many are unhappy with the fact that each year “looks” different. January 1 starts on a different day of the week from one year to the next, that of course throws every other date off as well as compared to the first year. Normally, it’s a one day shift, but if a leap day is in between, it’s two days. It sets up a cycle where you can safely use a calendar that’s 28 (or 56) years old, if you want…but don’t go back past 1900 with this. The real cycle is a 400 year cycle before the pattern repeats.

That’s kind of annoying, in some cases it’s really annoying, but we live with it. However some people have suggested reforming the calendar so it won’t happen. But it’s a bit of a challenge, especially now that there’s an ISO scheme that numbers the weeks within the year; this has to adapt to those weeks that straddle years.

And this is because 365 does not divide by 7, there’s a remainder of 1.

Many would-be reformers say this can be handled quite easily: simply have one day (two in a leap year) that do not have a day of the week assigned to them.

OK, I imagine many readers of this would go find the pitchforks and torches (OK, firearms) if this were adopted, because of course it’d throw your church services off; the Sabbath would either have to move around the week, or it wouldn’t be a seven day metronome any more. (It rather messes with the fourth commandment.)

And you’d have a lot of company from both Jews and Muslims.

So it’s not going to happen.

But someone did come up with an interesting alternative. Get rid of leap day. Have leap week. Start January on (say) Monday. The year ends on a Sunday, 364 (yes FOUR) days later. Very soon, though, in order to align with the seasons, you add an entire week at the end of December (371 days), so that way the next year is lined back up with the seasons, but the year still starts on a Monday. The advantage is that the calendar is the same from year to year (an extra week can go at the end of December with an asterisk next to it), and churches, synagogues and mosques would not be disrupted.

This is the Hanke/Henry calendar. It also changes the lengths of some months so that each quarter is 91 days.

https://en.wikipedia.org/wiki/Hanke%E2%80%93Henry_Permanent_Calendar

http://hankehenryontime.com/html/qanda.html

OK, it’s at least somewhat clever and thinking-out-of-the-box. But these guys also advocate for everyone on earth using Universal time (i.e., Greenwich time) and that, I think, is ridiculous. It would solve nothing because it will still be midnight in some places while it’s 3PM in others. Worse, the sun would rise here in Colorado at 2PM in December. Almost everywhere on Earth, things would be about that ridiculous. And it doesn’t solve the fundamental problem of having to worry about someone else’s time zone, It just changes it to having to know how out of whack their clocks are compared to yours. You’d still have to wonder whether someone was up when making a long distance call, and you wouldn’t be able to look at the time where they were for a clue. [As far as time of day goes, our situation today is pretty optimal. For applications where time synchronization between continents is needed, we have UTC. For everything else our clocks match the time of day pretty well…or only fairly well during daylight saving time.]

The rule for computing leap years actually depends, crazily, on what day of the week the (presumably abandoned) Gregorian calendar begins.

It’s one of those “interesting idea, but no way” types of things, just like the Holocene Era is.

The Day

Enough about years, but there’s a bit more to add about days.

Last week, I posted a graph called “the equation of time.” This one:

It’s the difference between what you sundial says, and what your watch says. (And that assumes you have your watch set to mean solar time for your longitude, which since the advent of time zones, is generally not true. But let’s say you live at precisely 75, 90, 105, or 120 W longitude (or any other longitude that divides by 50). That’s nearly true for me, I live at a bit above 104 W longitude.)

Because your watch is designed to move at a constant rate–whether it actually does so is another matter, and back in the day of mechanical watches there was some correlation between the cost of the watch and how well it did so. But the sundial directly registers the sun…which doesn’t move at a constant rate. So the watch (hopefully) moves at an “average” of the sun’s rate, “mean Solar time.”

[Nowadays even a crappy watch often gets corrected by listening to the “atomic clock” but watch out when that fails…I’ve known two “this is an atomic watch” braggarts to be off the correct time by minutes; but my 1996-purchased Citizen Navihawk keeps plugging away, sometimes even after the computer in it resets.]

The differences are due to two factors: the ecliptic is inclined to the celestial equator, and Earth’s orbit about the sun is elliptical. That elliptical orbit results in the earth travelling faster closer to the sun (Kepler’s second law), which means when the earth is closer to the sun, it has to rotate further to bring the sun to the meridian, more than 24 hours since the last time the sun crossed the meridian.

If noon-to-noon is more than twenty four hours, then, if you’re using a good watch and are monitoring a sundial, you will see it. The watch will be faster (compared to the sundial) the next day as compared to today, because it will get to noon faster than the sun’s shadow will.

In other words, you’re at a time of the year when that squiggly red line is sloping upward, the watch is becoming faster and faster.

As it happens Earth is closest to the sun on about January 6, and the line is really steep there.

During the weeks before and after that time, the time of sunset is changing. You’d expect it to be earliest on December 21, because that is after all the shortest daytime of the year because its the solstice.

But it’s actually earliest a week before that. Check any “sunrise and sunset” table. It doesn’t matter for where, honestly, since you’re looking for the earliest sunset, but the effect is much easier to see the further north the table is for. (And of course this flip-flops in the Southern hemisphere).

So if you’re thinking (like Aubergine said on Sunday) that you’re already “feeling” longer days by the solstice on the 21st, you’re not quite right, but the sun is already setting later by the 21st–the random chart I grabbed showed a two minute difference. (Sunrise is also later but basically forgotten by sunset. In fact sunrise will continue to come later and later all the way through the end of the month and possibly beyond…the chart stops there.)

Another way to visualize this…as well as something else…is a figure called the analemma.

Unlike the previous figure, the horizontal axis/direction shows how far ahead or back of the sundial a watch would be. And this time the vertical axis usually shows how far the sun is north or south of the celestial equator, its declintion. (But in this case it shows how far above the southern horizon in London, though it does show the equator line, labeled φ). So an analemma gives you two pieces of information graphically, but you have to hunt for the date you want on the figure 8.

This has a real meaning. People with a lot of patience and attention to detail will sometimes photograph the sun at the same time each day (or every couple of weeks), from the same spot with the camera pointed precisely the same way each day, and you can see it forming a figure 8 in the sky.

[I had to download from Wikipoo, edit (and shrink), save as a jpg, and upload. Taking one for the team…]

It’s an almost perfect figure 8. If aphelion, the closest approach to the sun, actually fell on the winter solstice, it probably would be. This will happen sometime in the future: the equinoxes and solstices, after all, are moving along Earth’s orbit and if I understand right, we’re heading towards that situation. Give it about a thousand years.

For some reason that graph up above really exaggerated the horizontal direction. The photo, by contrast might look familiar to you as that figure eight that gets printed over the southeastern Pacific ocean on some globes. (There is almost no dry land there so it’s a safe place to print things like that.) Well, now you know what it’s for!

I decided to see what would happen with other configurations. The easiest way to do that is to look up the analemmas for other planets in our solar system, where aphelion is nowhere near a solstice or equinox.

Mars has a very similar axial tilt to that of Earth. Its orbit is more elliptical, though, and so we have:

And in fact here are analemmas and equations of time for all of the other planets, and Pluto. Figure 8s are fairly common it turns out, but just as common is some sort of lopsided quasi-egg-like shape. Saturn appears to be a figure 8 with a very small northern loop.

Well, that’s all for this week. Now I am really going to have to think hard about what to do for next week, other than, of course a JWST update.

Obligatory PSAs and Reminders

China is Lower than Whale Shit

Remember Hong Kong!!!

中国是个混蛋 !!!
Zhōngguò shì gè hùndàn !!!
China is asshoe !!!

China is in the White House

Since Wednesday, January 20 at Noon EST, the bought-and-paid for His Fraudulency Joseph Biden has been in the White House. It’s as good as having China in the Oval Office.

Joe Biden is Asshoe

China is in the White House, because Joe Biden is in the White House, and Joe Biden is identically equal to China. China is Asshoe. Therefore, Joe Biden is Asshoe.

But of course the much more important thing to realize:

Joe Biden Didn’t Win

乔*拜登没赢 !!!
Qiáo Bài dēng méi yíng !!!
Joe Biden didn’t win !!!

SPECIAL SECTION: Message For Our “Friends” In The Middle Kingdom

You knuckle-dragging barbarians are still trying to muck with this site, so I’ll just repeat what I said last time.

Up your shit-kicking barbarian asses. Yes, barbarian! It took a bunch of sailors in Western Asia to invent a real alphabet instead of badly drawn cartoons to write with. So much for your “civilization.”

Yeah, the WORLD noticed you had to borrow the Latin alphabet to make Pinyin. Like with every other idea you had to steal from us “Foreign Devils” since you rammed your heads up your asses five centuries ago, you sure managed to bastardize it badly in the process.

Have you stopped eating bats yet? Are you shit-kickers still sleeping with farm animals?

Or maybe even just had the slightest inkling of treating lives as something you don’t just casually dispose of?

中国是个混蛋 !!!
Zhōngguò shì gè hùndàn !!!
China is asshoe !!!

And here’s my response to barbarian “asshoes” like you:

OK, with that rant out of my system…

Loop it if you like; I will wait.

Richly deserved.

Justice Must Be Done

The prior election must be acknowledged as fraudulent, and steps must be taken to prosecute the fraudsters and restore integrity to the system.

Nothing else matters at this point. Talking about trying again in 2022 or 2024 is hopeless otherwise. Which is not to say one must never talk about this, but rather that one must account for this in ones planning; if fixing the fraud is not part of the plan, you have no plan.

The Audit

The Audit is definitely heating up. Let’s see if the Opposition manages to squelch it and its consequences. I’ll be honest; I expect it to be ignored by anyone capable of ordering Biden/Harris to step down.

Nevertheless, anything that can be done to make Biden look less legitimate is a worthy thing!

Lawyer Appeasement Section

OK now for the fine print.

This is the WQTH Daily Thread. You know the drill. There’s no Poltical correctness, but civility is a requirement. There are Important Guidelines,  here, with an addendum on 20191110.

We have a new board – called The U Tree – where people can take each other to the woodshed without fear of censorship or moderation.

And remember Wheatie’s Rules:

1. No food fights
2. No running with scissors.
3. If you bring snacks, bring enough for everyone.
4. Zeroth rule of gun safety: Don’t let the government get your guns.
5. Rule one of gun safety: The gun is always loaded.
5a. If you actually want the gun to be loaded, like because you’re checking out a bump in the night, then it’s empty.
6. Rule two of gun safety: Never point the gun at anything you’re not willing to destroy.
7. Rule three: Keep your finger off the trigger until ready to fire.
8. Rule the fourth: Be sure of your target and what is behind it.

(Hmm a few extras seem to have crept in.)

Spot (i.e., paper) Prices

Last week:

Gold $1799.70
Silver $22.45
Platinum $947.00
Palladium $1868.00
Rhodium $14,900.00

This week, 3PM Mountain Time, markets have closed for the weekend. Actually it appears they were closed all day Friday for Christmas Eve.

Gold $1810.20
Silver $22.96
Platinum $981.00
Palladium $2036.00
Rhodium $14,975.00

Slow creep upwards.

James Webb Space Telescope Update

Launch is set for TODAY, Christmas Day at 0720 EST.

Which means that as I write this, I don’t know how it went, but perhaps you reading this, do. Of course, there’s always the chance of a last minute delay, that pushes launch time out of the 32 minute window that the spacecraft must launch during.

After launch (assuming a successful one) about a month of nailbiting begins as over three hundred things have to all happen without fail for this bit of high tech origami to unfold properly, because there is no way to fix a spacecraft that is literally a million miles away. The following video shows the sequence.

The next video, which I should have put in last week’s daily (but I did post it in the comments once I found it) also conveys how tense things are going to be at NASA. This mission has sucked all of the oxygen out of the room for nearly 20 years, and to have it fail…well, let’s just hope it doesn’t.

I have no idea if NASA will have a page to visit that will count down all of the events that must happen. But I do have this one for a launch countdown, in case you are either here before 7AM OR the launch slips again:

Launch Countdown Webb/NASA

The Reason There Even Is A Season

Of course I know what day this. That Advent calendar where Hans Gruber is falling to his death is finally complete (but does that calendar have a “thud” sound effect?).

Of course I am committing the cardinal sin of forgetting “the reason for the season.”

Actually I haven’t. I could write something about that, loaded with chapter and verse. But I am sure you wouldn’t like it. So I will leave it to others to do so.

So I thought I’d do something a bit more typical of what you’ve come to expect from my Saturday dailies and talk about why we even have seasons in the first place. (And yes, I am literal-mindedly talking “season” as in “winter” not “season” as in “season’s greetings.”)

I expect most of you know most of what’s in here, so this should be light reading. Actually, you’ll get a twofer, as I’m going to talk about time of day as well (and more of this will be obscure).

[Note: this is written from the point of view of someone in the northern hemisphere. Our friends in Oz will have to adjust what I wrote as they read it.]

The “first order” view of time, surely figured out long before we learned how to bang the rocks together to make fire, of course, is that this big glowing thing (the sun) would come up over the horizon, making everything light, travel across the sky, and drop again on the other side, and after it did so it would become dark. Maybe (or maybe not) there’d be another very noticeable object in the sky (the moon), and maybe not. There would (if the sky wasn’t completely clouded over) also be a lot of stars out. And then, the sky would grow bright in the east, that super bright glowing thing would show up…And the cycle would repeat itself ad infinitum, which is actually the important point.

The bright period and dark period were of very roughly equal length most places.

But thousands of years ago, if not much longer, we noticed some more subtle patterns. This understanding surely predates the invention of writing; we know this because we’ve found plenty of remains of tools to measure these more subtle patterns, left behind by cultures that didn’t write. (E.g., one of many: Stonehenge.)

The sun doesn’t rise and set in exactly the same spot every day. It rises in a general easterly location, but sometimes its a bit north of east, and sometimes it’s a bit south of east; it’s a slow progression from the most northerly sunrise, further and further south each day, until we reach the most southerly sunrise, then the process reverses itself, the sun rising further north each day.

This correlated with the stars that were visible at night. For instance, when the sun is close to rising as far south as sunrise gets, right after sunset the constellation of Orion is visible in the east; it travels across the sky overnight and sets before sunrise. But when the sun is most of the way to its most northerly sunrise (and sunset), Orion is already setting just after sunset; a few dozen days later on, you can’t see Orion at all.

[The above is true for southern hemisphere people as well.]

All of this also correlates with the seasons, at least for places like Europe. When the sun is rising further south, the weather tends to be colder, though the coldest time might be a bit after the sun has started rising further and further north. Nevertheless, it was pretty obvious: The further south the sunrise and sunset, the colder it gets, and it gets cold enough that food is impossible to grow and difficult to find.

Fortunately we did know that the sun wouldn’t just keep drifting further south, that there was a limit to how far south it would get, and we’d celebrate when it got furthest south, because there was the promise that the weather would get better. And so we have all those tools to be able to mark the day the sun would start to return; Stonehenge being probably the most famous of them. We now call that day the “Winter Solstice” and on our present calendar it falls on or about December 21.

[Folks in the southern hemisphere will want to swap things around; for them it gets colder when the sun is furthest north.]

There were a couple of other aspects of this, too. When the sun was further north, the day was very noticeably longer, and also when the sun was further north, it was higher at noon, nearly overhead in fact (in Southern Europe at least), but much closer to the horizon when it rose further south.

This is actually a consequence of the fact that the path of the sun across the sky forms the same angle regardless of where it rises.

And now, I need a diagram.

As I alluded to before, the furthest south the sun gets is called the winter solstice. But also, the furthest north it gets is the summer solstice (roughly June 21). The in-between cases where it rises precisely to the east and sets precisely to the west, which happen twice as often as either one of the solstices, are called equinoxes (roughly March and September 21).

Where did that word “equinoxes” come from?

So glad you asked!

As you can see from that diagram, the three arcs have different lengths, and that manifests itself as differences in the length of the day. Furthermore, in the far north and south, the differences are greater. Certainly people in Europe and other places that far away from the equator did notice that daytimes are shorter, and night times longer, in winter, whereas for summer it’s the other way around.

It was, in medieval times, customary to divide the daytime into twelfths and to divide nighttime into twelfths as well–this is the origin of our modern hour–but of course these daytime and nighttime hours were rarely the same length. (The advantage of this was that the sun always rose and set at six o’clock, by definition.)

Only at the two equinoxes were day and night–and the day and night hours–the same length; equinox comes from Latin for “equal night.” And we have two of them, there’s a vernal or “spring” equinox, where the sunrise position is in the process of moving north, and the sun rises directly to the east, and the autumnal or “fall” equinox where the sunrise is headed south for the winter.

Going back to that diagram, there’s a line across the sky that starts at the horizon due south, climbs straight up until it’s precisely overhead, than continues on to the horizon due north; this is the meridian. It turns out that this line crosses the arc the sun is taking across the sky, at the arc’s highest point. The two parts of the arc, before and after this point, are of equal length. When the sun is at that point, it’s “noon.” And our abbreviations AM and PM come from “ante meridian” and “post meridian.”

And there is one more concept to be introduced here, and that is the length of time between two winter solstices, or spring equinoxes, or summer solstices, or fall equinoxes, and that is a year. To be more precise, it’s a tropical year. (And yes, there are other similar concepts known today, that mean slightly different things. By the time I explain those, the name tropical year might make a bit more sense.)

Our calendar is set up to cycle in one such period. Since it’s the sun’s variations it’s based on, our calendar termed a solar calendar. Some cultures (most notably Islamic ones) operate off the moon instead of the sun, and others work off a mixture of both. A pure lunar calendar will follow the phases of the moon, and may have a number of these moon-cycles bundled together into a year…but it won’t be the same length as the solar year, because the length of a moon cycle doesn’t divide evenly into a solar year. This is why the Islamic year is only 354 or 355 days long…they flat out didn’t care about the seasons (known as “hot” and “even hotter”) in Arabia.

The Jewish/Hebrew calendar is a combination lunar-solar calendar; its months follow the moon cycles, but will try to track with the seasons, too, by adding entire extra months in some years to make up the difference.

This is similar to the way the ancient (pre Julius Caesar) Roman calendar worked, too: months followed the moon strictly, but the priesthood would determine when extra months needed to be added to keep things roughly in sync with the seasons. A year without an extra month was 355 days long; a year with the extra month was 378 days long. This was eventually abused by priests who’d add extra months if the consul in power that year was someone they liked. Eventually it turned into a big mess that Julius Caesar would have to take drastic action to fix. More on that later, perhaps.

Between all of this about the sun’s curious behavior and the way the stars behave over the course of the year, people eventually came up with a mental model of what’s going on behind the scenes. Aspects of this model are still in use in astronomy.

It’s known as the celestial sphere and comes in two slightly different forms.

The idea is that the sphere is centered either on Earth or on the observer, and it’s arbitrarily far away. The position of every object in the sky is projected onto that sphere.

In particular the stars, which (almost) don’t move, are regarded as fixed in place upon the celestial sphere.

Earth is at the center, and there is a north celestial pole and a south celestial pole, directly over the earth’s north and south poles. There is also a celestial equator, above the earth’s equator.

The earth, of course, rotates counter-clockwise as seen from over the north pole, but in this model we pretend the earth is stationary and the celestial sphere is rotating clockwise as seen from “above” the north celestial pole.

The second version you will see of the celestial sphere is with respect to an observer on Earth’s surface. There are still celestial poles and a celestial equator, but in a diagram like this, usually drawn assuming someone in the northern hemisphere, you’ll see the north celestial pole above the horizon, the south celestial pole below the horizon (if it’s shown at all), and half of the celestial equator at an oblique angle to the ground. And the celestial equator will intersect the plane of the ground precisely east and west of the observer. In fact you can consider each star in the sky as having a “latitude” above or below the celestial equator, just as places on Earth do with respect to the earth’s equator. Astronomers actually do this, but they call it “declination” rather than latitude.

In fact this diagram is a gif, and you can see three points on the celestial sphere moving in circles as the celestial sphere rotates. A point sufficiently far north on the celestial sphere never sets…a real life example of this for people in the US is the Big Dipper, which doesn’t set (it might do so in the far south of the US; I don’t know). Similarly, there are stars that never rise in the US, our friends in Oz get to see them, though. (Alpha Centauri, the nearest visible-to-the-unaided-eye star other than our own sun, is permanently below the horizon where I live, as are Canopus and Fomalhaut, two other very bright stars.) But most stars in the sky rise and set, following arcs very similar to the arc the sun follows in its daily journey across the sky.

It turns out that, for all intents and purposes unless you have a true atomic clock (not just a receiver) the stars move across the sky at an absolutely constant rate. You can set your watch by them…and indeed for quite a long time, we did set our clocks by them.

Pick a bright star, and start your stopwatch when it crosses the meridian. Wait a day for it to cross again, and how much time elapses?

By modern units, do you suppose it’s 24 hours? After all the earth spins once every twenty four hours, right? Well…almost.

In fact, it’s 23 hours, 56 minutes, 4.0905 seconds (approximately). Or equivalently, with respect to the stars, the earth rotates once every 23 hours, 56 minutes, 4.0905 seconds. This is the sidereal day, the amount of time it takes the earth to rotate once, with respect to the stars.

Astronomers actually have special clocks in their observatories that measure sidereal time. When a certain point in the sky crosses the meridian, that’s zero hours (0h), then every 24th of a sidereal day another hour has passed…but these hours are slightly shorter than what your watch measures, of course. But you can tell what stars will be “up” at any given time by knowing the sidereal time. In fact they will occasionally set their sidereal clocks by watching the stars. It’s fairly simple to convert sidereal time to “normal” time and that’s why observatories were once the places that would define what time it was.

Huh. Why the difference? Hold that thought!

How about measuring the sun’s time between crossings of the meridian? OK, that’s both better and worse. No, it’s not 24 hours. In fact, it’s not even a constant amount of time! Sometimes it is longer than 24 hours, sometimes less. But it does average 24 hours over the course of a year.

And that is how the length of the day was originally defined.

So how can the sun take 24 hours–on average but not on any particular day–to go around the earth (in celestial sphere terms), but the stars do it almost four minutes faster?

Remember earlier when I talked about how Orion would be just rising as the sun sets in autumn, but during the winter, it would be higher and higher in the sky at sunset, until around about May when it’s about to set just as the sun sets?

That means the sun is moving closer and closer to Orion over the course of the winter. Which means the sun is not nailed to the celestial sphere like the (other) stars are. In fact, it moves in a full circle around the celestial sphere, and it takes a year to do so.

Unfortunately for reasons that I might not get to this week, it doesn’t take a tropical year to do so, it takes a slightly different amount of time, a sidereal year. And you may have noticed a pattern: “Sidereal” means with respect to the stars. The sidereal year is about 20 minutes longer than a tropical year.

So what about this circle on the celestial the sun travels on over the course of the year? It’s called the zodiac, and it’s tilted with respect to the celestial equator, intersecting it at two points. The tilt is about 23 1/2 degrees. When the sun is at one of those intersections, it is of course right on the celestial equator and will rise (or set) directly to the east (or west). When you hear some newscast saying that spring will start at such-and-such a time on March 21st, that’s actually the exact instant the sun crosses the celestial equator.

That crossing point, called the First point of Aries, is where astronmers start measuring celestial “longitude” analogous to longitude on Earth…except they call it “right ascension” and it is measured in hours, not degrees, with 24 hours making up the full circle. In fact, sidereal 0h is when the march equinox location crosses the meridian.

Since the sun takes a full year to travel around the zodiac, on any given day it moves about 1/365th of the zodiac or just under one degree. And at different times of the year, it’s well north or well south of the celestial equator, accounting for those differing-located (and differing length) arcs across the sky that our prehistoric ancestors first noted.

The difference between the sidereal and the (average) solar day of 24 hours is accounted for this way: Noting that the sun crosses the meridian at a particular time, if you wait exactly one sidereal day, the same stars will cross the meridian again [never mind that you can’t see them in broad daylight!]. But the sun will have traveled about a degree to the east in the meantime, and the celestial sphere must rotate (east to west) about one more degree to bring the sun across the meridian again. (A degree is 1/360th of the circle, and with a day being 1440 minutes, it takes about 4 minutes for the celestial sphere to rotate one degree. Actually, it takes exactly four sidereal minutes to do so, but they’re slightly shorter than your wall-clock minutes.)

Part of the reason the time between meridian crossings of the sun varies from 24 hours, is because of the tilt of the ecliptic. Where it crosses the equator, it does so at a slant, so part of the distance traveled is in the north-south direction and the sun therefore moves a bit less in the east-west direction. Which means the celestial sphere has to rotate slightly less to bring the sun across the meridian the next day, making noon-to-noon a bit shorter than average. At the two solstices the sun’s motion along the zodiac is purely along the east-west direction and the right ascension lines are closer together, so the celestial sphere must rotate more to bring the sun across the meridian line, so noon-to-noon duration is a bit longer.

There is a second factor affecting this, which I’m going to ignore for now, I’ll get to it later.

OK, so what are the practical effects of all of this?

First off, ironically the only instrument that actually tracks the sun’s movement is a very primitive one, a sundial. But even here, there’s a subtlety or two you must keep in mind. A sundial always seems to have a triangular or sloped thing to cast the shadow (the “gnomon” from Monday’s daily). Why is that? The sloped side of the triangle is actually parallel to the earth’s axis (or the celestial sphere’s axis), so that there won’t be any weird perspective shifts over the course of the day. You may have noticed me pointing out how steep that one sundial in Canada was in the comments last Monday. That’s why: gnomons will be steeper the further north you go (or further south in the southern hemisphere), and a vertical (plumb) pole in the ground will work perfectly at the north or south pole.

Incidentally, did you ever wonder why we happened to choose the direction we call “clockwise” to be the direction clocks turn? Why not the other direction (which, of course, we’d then call “clockwise” instead of this direction)?

It’s because that’s the direction the sun’s shadow travels on a sun dial. We were making the clocks “backward compatible” in a way by doing that–a shadow to the left of another shadow indicates an earlier time, and hour hands further left also indicated an earlier time.

If modern, watch-making civilization had developed in Australia instead of Europe, chances are good that clocks would run the other direction and maps would have south at the top. If we ever run into aliens who put south at the top of their maps, chances are good their watches will run “backwards.” You wouldn’t think the two arbitrary decisions are related…but they are both more than likely functions of which hemisphere civilization started modern map making and timekeeping.

OK, so we have a sundial which will actually measure the position of the sun in the sky. But we can’t use them for modern timekeeping, even leaving out the fact that they don’t work at night. Because we’d have to deal with the inconsistent length of the sundial day, from one day to the next…remember that bit about the sun crossing the meridian?

We can come up with something called “Mean Solar Time” which is the average time the sun will cross the meridian. And in fact we did precisely that, for centuries. We even had tables and graphics showing how far off of mean solar time the sun’s crossing of the meridian would be any given day of the year, and it’s even called “the equation of time.” People in a certain town would set their watches by mean solar time, and those watches would be off from their sundials by a predictable amount, according to the graph below.

Now you’ll note I said “in a certain town.”

Yes, it matters where you are. The sun appears to travel across the sky east to west. Therefore it stands to reason that someone further east than you are will see the sun cross the meridian earlier than you do. And when he does the whole averaging to get mean solar time thing that you did, he’s going to end up setting his watch a bit faster than you are. In fact, only if two people are directly north-south of each other, under the same meridian line, would their clocks be synchronized.

Until the advent of the railroad, in fact, every single city had its own, distinct local mean solar time.

This didn’t matter much in stagecoach days; a stagecoach could maybe make a few dozen miles in a day, and people’s watches were inaccurate enough they needed to be reset every few days anyway; while traveling they’d just have to set them in every new town…not much more often than they already had to.

But railroads could cover hundreds of miles in a day, and there you could see easily see significant differences between towns’ mean solar times in one day of travel.

And railroads liked to run on a schedule. That schedule was a royal pain to set up when the time of day was shifting depending on your position on the track. A trip east to west would be shorter (by wall clock times at every stop on the route) than a trip west to east at the same speed. Time measured on the train would be identical, of course, it’s just that the train’s clock would seem faster at the west end of the trip than at the east end.

So what did the railroads do? They invented time zones. This began in Great Britain in 1840, where the Great Western Railway simply synchronized all of their clocks with the Greenwich observatory’s mean solar time, which became “Greenwich Mean Time.” In essence all of Great Britain ended up in one time zone, with most public clocks showing GMT regardless of the local mean solar time, though this didn’t become a legal thing until 1880. In fact, many clocks from this time actually have two minute hands; one could be set to GMT and the other could be set to local time.

Britain was a relatively small country. The US is much larger. What happened here?

Well, we could have set every clock at every railway station to Washington DC time, or (more likely back then) New York City time. But the US is wide and clocks on the west coast would have been reading noon when the sundials were saying 9AM. A few minutes like the UK had was tolerable (we’d never have noticed without watches in the first place), but two or three hours would be a problem.

Railroads at first simply used the time at their headquarters, transmitted by telegraph so other stations could synchronize. That led to the spectacle of some stations that served two railroads having to show two clocks, one for each railroad, so that people could know at what time trains were supposed to arrive and depart.

In 1863 Charles F. Dowd proposed a set of standard times for all railroads to follow but no real action was taken until he consulted railroad officials in 1869. In 1870 he proposed Washington DC as the center of one time zone. In 1873, finally time zones began to be used, but the boundaries between them would tend to be in major railway stations–depending on whether the train went east or west through the station, it’d have to set its clocks forwards or backwards at the station. Finally, something very akin to what we have now was adopted by Congress in 1918.

The four time zones we use in the Lower 48 are based on the mean solar time at 75, 90, 105, and 120 degrees west longitude.

If you live right on those longitudes, and your watch is set correctly, it reads mean solar time, and the equation of time in the chart above is correct.

If you don’t live on those longitudes, then you’re east or west of the longitude your watch is set for, and you have to add or subtract a constant to your watch to know mean solar time for your location. And of course if the never-to-be-sufficiently-damned Daylight Saving Time is in effect, you’re still off by an hour.

Interestingly enough, there’s a reverse to this: If you have an accurate clock and do not reset it, you can determine your longitude by observing the sun to determine the local solar time, looking at your watch, taking the difference, and correcting for the equation of time. For instance if you set your clock to GMT, go sailing off, and at some point notice that the sun says it’s 9:50 am when your watch reads noon, and the equation of time says your watch is fast by ten minutes on that day, you know that at that instant a sundial in London would say it’s 11:50 AM, but where you are the sundial would say 9:50 am–you are two hours behind London, and with each hour being 15 degrees on the globe (360/24 = 15), that means you’re at 30 degrees W longitude.

Without that accurate clock, determining longitude is nearly impossible, and in fact the British government sponsored a substantial prize (10 to 20 thousand pounds) for the first person who could invent a clock that would keep accurate time even on the swaying and heaving deck of a ship (which left out any clock based on a pendulum). The amount of the prize depended on the accuracy of the method. The prize was finally collected in 1773.

Columbus and Vasco da Gamma (to say nothing of Magellan) would likely have given up significant body parts for one of those chronometers.

[There are other methods to determine longitude; they all amount to determining an absolute time. One was to observe Jupiter’s moons’ positions, but that depended on Jupiter being visible, and that was essentially seasonal (and subject to cloudy weather). And, one needed to correct for where the earth was relative to Jupiter; it could be further away than average in which case the actual time was later than indicated by Jupiter’s moons because the light took longer to reach you.]

OK, so now it’s time to get back to seasons.

I’ve been talking about the celestial sphere, which is a handy visualization device and is the basis of astronomical (sky-chart) coordinates, but now we need to get back to reality.

The sky doesn’t rotate, the earth does. And the sun doesn’t travel around the earth on the zodiac, the earth travels around the sun in the plane of the zodiac.

The earth spins about its axis, and the axis of the spin is almost stationary. We can, for now, pretend that it is stationary (but–spoiler–the fact that it is not accounts for the twenty or so minute difference between sidereal and tropical years).

The plane of the earth’s orbit about the sun is the zodiac; and as I said before the angle between the zodiac and the celestial equator–i.e., between the zodiac and Earth‘s equator–is about 23.5 degrees. That also means the earth’s axis, rather than being perpendicular to the zodiac, is tilted 23.5 degrees off perpendicular.

At the time of the summer solstice around June 21st, according to the “celestial sphere” visualization, the sun is at the furthest north point on the zodiac. Stepping back and looking at the whole earth/sun system from space, it’s apparent that Earth’s north pole is tipped towards the sun.

There are parts of the far northerly, arctic regions where the sun won’t set at all! [Conversely since the south pole is tipped away from the sun, it won’t see daylight…and large antarctic regions also won’t see the sun around that time.]

A bit further south than the north pole, there are large areas where the sun will ride high in the sky and the daytime will last well over 12 hours. Those areas are getting a lot of sunlight, almost head-on, and that’s why summers are warm. In fact, at 23.5 north latitude, the sun will cross directly overhead, shining absolutely straight down at local noon. Eratosthenes, in Ptolemaic Egypt, records that the sun would shine clear down to the bottom of wells in Syene, to the south of Alexandria (and he used this fact, plus the sun angle in Alexandria that same day, to estimate the size of the earth; he didn’t do too badly).

Waiting three months until the September equinox, the situation looks like this:

Neither hemisphere is favored and the Sun is directly over the equator…and will rise directly to the east that day.

And you can see what will happen; the winter solstice will have the south pole tilted toward the sun, and the north pole tilted away; sunshine will hit the ground at a more oblique angle in the northern hemisphere, and heat the ground less.

Spring will be the mirror image of fall, with neither hemisphere being favored.

Putting it all together, you see the standard diagram, that looks like this:

Note that at all times, the earth’s axis of rotation points in the same direction; the seasons are caused by the differing relation between the direction of the sun (as seen from earth) and that axis.

And that is the reason we even have seasons. The tilt of the earth’s axis is that reason.

Now there’s one more factor I alluded to when I talked about the equation of time. The earth’s orbit about the sun isn’t a circle, it’s very slightly elliptical. Which means at one time of the year, it’s actually closer to the sun than at any other time; six months later, it’s furthest away.

I have to mention this, because many people think the reason it’s hotter in summer is that Earth is closer to the sun then.

Actually, it’s not. It’s actually closest to the sun in January! Yes, it does get a tiny bit more sunlight then, but the effect of the angle of the sun hitting the ground is much, much greater, which is why the northern hemisphere experiences summer when the north pole is tipped a bit towards the sun–even though Earth is further away from the sun at that time.

But this does have an effect on the equation of time. I mentioned that, as seen on the celestial sphere, the sun moves a bit eastward each day, meaning that in order to bring the sun back to “noon” the celestial sphere had to rotate about another four minues / one degree’s worth.

Stepping back, we see what’s actually happening. At noon on one day, you can draw a line from the sun through the earth. Now wait one sidereal day. The earth is oriented exactly the same as it was before–it has rotated once. But over the course of that day, the earth has moved almost one degree along its orbit. In order for the same spot that was facing the sun before, to be facing the sun again, the earth has to rotate one more degree. That accounts for the difference between the sidereal and solar day.

But as I said, the earth is in an elliptical orbit. Even at a constant speed, at the furthest out end of the orbit, the earth will cover slightly less angle of its orbit than it will closer. But in fact the earth moves faster nearer the sun, so this effect is magnified.

So it takes slightly less than four extra minutes to put the sun back on the meridian in July (when earth is furthest away from the sun), and more than four extra minutes to do it in January. That accounts for more off the changes in mean solar time that show up in the equation of time; a couple of those humps and valleys on the graph are due to this effect.

Are you starting to get the idea that simple measuring of time is actually a rather complicated subject?

It gets worse. Let’s go back to the calendar.

The length of the tropical year is 365.24217 mean solar days. Or to put that in long form, the length of time it takes to go from spring equinox to spring equinox is 365.24217 times as long as the average interval between sun crossings of the meridian.

Now, if we’re going to set up a calendar (which will want to be in whole days) and expect it to remain in the same relationship with the seasons, that means some years will have to be 365 days long, and some will have to be 366 days long.

I mentioned the drastic reform Julius Caesar made to the Roman calendar. First he had to restore the traditional alignment of the months to the seasons, which had gotten bollixed up by the priests’ arbitrary insertion of extra months. Then he had to change the lengths of the months so there’d be twelve months, no more, no less in a year. Then he had to do something about that fractional 0.24217 days.

The year 46 BCE was known as the year of confusion. Caesar added multiple extra months that year to get the calendar lined back up with January starting as it should, early in winter. Then the next year he introduced the twelve months we know today, at their current lengths. Those totaled 365 days. He decreed that every fourth year, an extra day be added to February. That would make the average calendar year 365.25 days, which is quite close to 365.24217 days.

There were glitches–for a time people were mistakenly holding leap year every three years, and Caesar Augustus had to straighten that out and re-sync. But after 1 CE, every year divisible by 4 was a leap year, 4, 8, 12, etc.

The “Julian Calendar” held sway for over fifteen centuries.

But after fifteen centuries, the difference between 365.25 and 365.24217 had added up. Consider a century of 36,525 days on the Julian calendar, versus 36524.217 days in an actual tropical century. There’s almost 0.8 days difference. Call it .75 (which is what a certain guy named Gregory did), it becomes apparent that in 1600 years, there’d be a twelve day error.

And indeed, because the year was longer than it “should” have been, spring was now starting on March 12th instead of the 21st, in the 1500s.

Pope Gregory changed the leap year rule from “every fourth year” to one where three of those leap years out of every four centuries would be skipped. And he decreed dropping days to get the calendar back to where it was supposed to be. This is the Gregorian calendar, and it’s the one we use today. Under the Gregorian calendar, every year divisible by 4 is a leap year–except for century years (ending in 00). Those are not leap years even though they are divisible by 4. However, if a century year is divisible by 400 it is still a leap year anyway. The upshot is that 1700, 1800 and 1900 were not leap years, but 2000 was, and 2100 will not be.

This made the average length of a calendar year 365.2425 days, which is a lot closer to 365.24217, and we won’t have to figure out what to do about the difference for at least another thousand years. It looks like we need to ditch three or four more leap days every ten thousand years, or perhaps ditch 33 leap days every hundred thousand years. (On the other hand, Gregory could have come a lot closer if he’d gone with a rule where instead of very 400 years, every 500 years the century leap year is not dropped. Perhaps he didn’t have quite the right number of days in a real tropical year; I imagine it’s tricky to measure accurately.)

Gregory made his change in 1564; but by then the Reformation had happened and Protestant Europe wasn’t going to muck with their calendar because some guy in Rome said to do it. It took until the 1700s to bring them on board (it happened in England and her colonies in September of 1752; in order to get things back in sync 11 days were dropped. The day after September 2, 1752 was September 14, 1752, and occasionally we will refer to dates around then as “O.S.” for “Old Style” and “N.S.” for (wait for it…) “New Style.”

Eastern Orthodoxy didn’t catch up until much, much later (in fact some congregations still haven’t switched). Russia still used the Julian calendar in day-to-day business until the Communists forced the change in 1918. (If you think having to deal with time zones is bad, imagine writing to someone who is thirteen days behind you.)

There’s one last issue. It doesn’t affect our daily lives much…unless we’re astronomers.

Remember how I said the earth’s axis is almost stationary?

In fact, it wobbles, like a top. The angle remains about 23.5 degrees, but it moves around in a big circle, like this:

On the left, a top, wobbling as it spins. On the right, Earth doing the same thing.

Only it takes 25,700 years to do it.

In about 12,850 years, it will have gone 180 degrees around that circle. And the north pole of earth will not point towards Polaris any more. It will be pointing very roughly in the direction of Vega. (Vega is the star in the summer triangle that sets first…it’s probably setting about sunset right now.)

I’ve found it difficult to locate a video that shows this, that isn’t chock full of mystical/astrological woo or other irrelevancies. Many years ago I found a video that would have been perfect…except that the perspective rotated, which made it impossible for someone who didn’t already understand it, to understand the video.

But this one isn’t bad. It’s shown from the perspective of the celestial sphere. The flat grid shown is the plane of the earth’s orbit, i.e., the Zodiac.

What that will mean is that at the spot in the earth’s orbit that is now the summer solstice will then be the location of the winter solstice (and vice versa); the vernal and autumnal equinoxes will also trade places, as seen below, where A shows the current situation, and B shows the situation 12,850 years from now. Note that the orientation of Earth’s orbit does not change, just the locations of the equinoxes and solstices.

In both diagrams, Sagittarius is to the left; at the present time, when the earth is at perihelion, just after winter solstice, the Sun is in Sagittarius. (Not Capricorn, which is the “astrological sign” associated with that date; I’ll explain that below.) The earth’s northern axis is tipped almost perfectly away from the sun. 12,850 years from now, at perihelion, the Sun will still be in Sagittarius, but the date (which is aligned with the seasons) will be July 4th. (Happy Independence Day, if there is still a United States in 14,871 CE.) The earth’s northern axis will be tipped almost perfectly toward the sun at this point, because the axis has precessed since 2021.

The location of the “first point of Aries” (upon which astronomical coordinates depends) will have shifted to the other side of the celestial sphere.

So the first point of Aries moves in the celestial sphere. And since the tropical year depends on the first point of Aries, while the sidereal year is fixed with respect to the stars…that’s why the two lengths are different. The first point of Aries is moving in the direction that makes the tropical year shorter than the sidereal year–the earth hits the first point of Aries in slightly less than one orbit around the sun.

I said before the difference was about 20 minutes. Actually we can come closer than that. Over the course of one full precession of the equinoxes, 25,700 years, the total “slip” has to be a full year. So dividing 25,700/365.25 we get 70.36 years to slip one day; 1/70.36 days is about 1228 seconds. So the difference should be about 20 and a half minutes. This is a back-of-the-envelope calculation, of course, but it turns out the real difference between the sidereal year and the tropical year is 20 minutes, 24.5 seconds, so we were only off by 3.5 seconds. Not bad for the back of the envelope!

Notice I said that the first point of Aries moves, and that astronomical coordinates depend on the first point of Aries. Doesn’t that bollix up astronomical coordinates? Yes it does…and it’s worse. The celestial poles move, which means the celestial equator moves. The only constant is the zodiac in fact, but the point on the zodiac that crosses the celestial equator shifts.

Astronomers have to put an “epoch” date next to their coordinates, because they go out of date every fifty years or so. But since they’re (mostly) stuck on the earth, and have to rotate their telescopes against the earth’s rotation so that the stars don’t drift across their field of view, they really do need to follow the celestial poles. Even though they move.

[As a matter of fact, the “first point of Aries” has, for a long time, actually been in Pisces, and it’s moving into Aquarius (the video shows this). Which is what that insipid early 70s song “Age of Aquarius” was referring to. And this means if your astrological “sign” is Aries…well it really should be Taurus. Or maybe Aquarius. One the one hand astrology looks clueless because of this, on the other hand it’s a lot of astrology weenies who prate about the “Age of Aquarius” in the first place. I’m going to go with “they’re clueless” though.]

One last question you might have is what causes Earth’s axis to precess in the first place. Well, because the earth is rotating, it bulges a bit at the equator; this bulge is of course not pointed at the sun. It’s also not pointed at the moon. So both bodies, especially the moon, tug at that bulge, which is a torque against the earth’s angular momentum. That goes through a cross product to cause an actual motion of the poles at right angles to the tug–it’s a funky “gyroscope thing.”

As I said, measuring time is a complicated business.

And I haven’t even gotten to the truly modern complications…where it turns out the earth’s rotation is slowing down! (This is why we have to add leap seconds every once in a while.) Since the GPS satellites don’t bother with leap seconds, GPS time, which many treat as a de facto standard, differs from “Coordinated Universal Time” (basically a spruced up GMT), which is really the standard, by an increasing amount.

And now, with your head throbbing from all of that, I wish you a Merry Christmas.

Hopefully Santa delivered some nice, dirty sulfur-laden coal to Joe Biden’s stocking.

Fuck Joe Biden

Biden, you don’t even get ONE scoop of ice cream today.

(Please post this somewhere permanent, as it will continue to be true.)

Obligatory PSAs and Reminders

China is Lower than Whale Shit

Remember Hong Kong!!!

中国是个混蛋 !!!
Zhōngguò shì gè hùndàn !!!
China is asshoe !!!

China is in the White House

Since Wednesday, January 20 at Noon EST, the bought-and-paid for His Fraudulency Joseph Biden has been in the White House. It’s as good as having China in the Oval Office.

Joe Biden is Asshoe

China is in the White House, because Joe Biden is in the White House, and Joe Biden is identically equal to China. China is Asshoe. Therefore, Joe Biden is Asshoe.

But of course the much more important thing to realize:

Joe Biden Didn’t Win

乔*拜登没赢 !!!
Qiáo Bài dēng méi yíng !!!
Joe Biden didn’t win !!!