Yo, Jim Acosta!

I see from video of your “conversation” with MTG that someone posted yesterday, that you are still a pugnacious, lying, puddle of bearded dragon shit.

How you can look at yourself in a mirror is beyond me, unless your conscience has been replaced by a dedication to Leftist goals. It certainly isn’t dedicated to real adversarial journalism. Much less any kind of journalism.

I will give you this. You have better hair than Brian Stelter. But then, so did Telly Savalas. And Yul Brynner.

RINOs an Endangered Species?
If Only!

According to Wikipoo, et. al., the Northern White Rhinoceros (Ceratotherium simum cottoni) is a critically endangered species. Apparently two females live on a wildlife preserve in Sudan, and no males are known to be alive. So basically, this species is dead as soon as the females die of old age. Presently they are watched over by armed guards 24/7.

Biologists have been trying to cross them with the other subspecies, Southern White Rhinoceroses (Rhinoceri?) without success; and some genetic analyses suggest that perhaps they aren’t two subspecies at all, but two distinct species, which would make the whole project a lot more difficult.

I should hope if the American RINO (Parasitus rectum pseudoconservativum) is ever this endangered, there will be heroic efforts not to save the species, but rather to push the remainder off a cliff. Onto punji sticks. With feces smeared on them. Failing that a good bath in red fuming nitric acid will do.

But I’m not done ranting about RINOs.

The RINOs (if they are capable of any introspection whatsoever) probably wonder why they constantly have to deal with “populist” eruptions like the Trump-led MAGA movement. That would be because the so-called populists stand for absolutely nothing except for going along to get along. That allows the Left to drive the culture and politics.

Given the results of Tuesday’s elections, the Left will now push harder, and the RINOs will now turn even squishier than they were before.

I well remember 1989-1990 in my state when the RINO establishment started preaching the message that a conservative simply couldn’t win in Colorado. Never mind the fact that Reagan had won the state TWICE (in 1984 bringing in a veto-proof state house and senate with him) and GHWB had won after (falsely!) assuring everyone that a vote for him was a vote for Reagan’s third term.

This is how the RINOs function. They push, push, push the line that only a “moderate” can get elected. Stomp them when they pull that shit. Tell everyone in ear shot that that’s exactly what the Left wants you to think, and oh-by-the-way-Mister-RINO if you’re in this party selling the same message as the Left…well, whythefuckexactly are you in this party, you lying piece of rancid weasel shit?

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. (This doesn’t necessarily include deposing Joe and Hoe and putting Trump where he belongs, but it would certainly be a lot easier to fix our broken electoral system with the right people in charge.)

Nothing else matters at this point. Talking about trying again in 2022 or 2024 is pointless 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 in the system is not part of the plan, you have no plan.

This will necessarily be piecemeal, state by state, which is why I am encouraged by those states working to change their laws to alleviate the fraud both via computer and via bogus voters. If enough states do that we might end up with a working majority in Congress and that would be something Trump never really had.

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.)

Mozart

Light this time around. The Turkish March, K331.

The string quartet, consisting of two violins, a viola and a cello, is a sort of economy orchestra. In the days when all music was live, if someone wanted to host a gathering and wanted music, they had to actually pay people to perform it. Except for the most fabulously wealthy hosts, that meant you weren’t going to be hearing symphonies and concertos! The string quartet was a good compromise (and you could even arrange a symphony for it). Each of the four instruments played different parts, so the music could be plenty complex.

Joseph Haydn around 1750 invented the “string quartet” as a compositional form (as opposed to an ensemble) with four movements, and wrote over sixty of them.

Mozart wrote 23 string quartets; this one, #17 “The Hunt,” K. 458 is probably the most famous of the bunch. Quartets 14-19 were dedicated to Joseph Haydn and composed between 1782 and 1785 (i.e., just after we won the Battle of Yorktown and bracketing the time we signed the Treaty of Paris with the United Kingdom).

This video is of The Hunt, in full. Movements are at the following time cues:

• 00:06 – I. Allegro vivace assai
• 13:13 – II. Menuetto. Moderato
• 17:22 – III. Adagio
• 25:05 – IV. Allegro assai

Mozart, in his dedication, admitted to taking “a long and laborious endeavor” with these quartets. Usually, he was able to compose in his head, with seemingly little effort. Putting it on paper was actually “copying it out” once completed, not part of the actual creative process.

To my dear friend Haydn,

A father who had resolved to send his children out into the great world took it to be his duty to confide them to the protection and guidance of a very celebrated Man, especially when the latter by good fortune was at the same time his best Friend. Here they are then, O great Man and dearest Friend, these six children of mine. They are, it is true, the fruit of a long and laborious endeavor, yet the hope inspired in me by several Friends that it may be at least partly compensated encourages me, and I flatter myself that this offspring will serve to afford me solace one day. You, yourself, dearest friend, told me of your satisfaction with them during your last Visit to this Capital. It is this indulgence above all which urges me to commend them to you and encourages me to hope that they will not seem to you altogether unworthy of your favour. May it therefore please you to receive them kindly and to be their Father, Guide and Friend! From this moment I resign to you all my rights in them, begging you however to look indulgently upon the defects which the partiality of a Father’s eye may have concealed from me, and in spite of them to continue in your generous Friendship for him who so greatly values it, in expectation of which I am, with all of my Heart, my dearest Friend, your most Sincere Friend,

W. A. Mozart

Upon hearing the quartets performed, Haydn said this to Mozart’s father, Leopold Mozart:

Before God, and as an honest man, I tell you that your son is the greatest composer known to me either in person or by name. He has taste, and, what is more, the most profound knowledge of composition.

Mozart lived from 1756 to 1791 and it is probably the greatest tragedy of orchestral music that he died so young. Imagine what he could have done in the next twenty years. (OK, honestly no one can imagine it, or they’d be Mozart.) Beethoven got his start shortly after Mozart’s untimely death; what influence would they have had on each other? Beethoven was famous for breaking the rules of the Classical era; would Mozart have been sympathetic? Possibly; a lot of his later works were quite “edgy” by the standards of the day.

Spot Prices

Last week:

Gold $1,933.30
Silver $24.23
Platinum $936.00
Palladium $2,443.00
Rhodium $19,250.00

This week, 3 PM MT on Friday, markets closed for the weekend

Gold $1.897.70
Silver $22.84
Platinum $948.00
Palladium $2,404.00
Rhodium $18,800.00

Everything down, with the sole exception of platinum.

James Webb Space Telescope Update

The mirror is done. Instruments are at proper temperature.

People who have spent half a lifetime working on it now get to move on to their next endeavor, and hopefully will succeed at it as well.

All of the instrument packages now get a crisp image. The mirror is better than they expected!

They will now proceed to commission those packages. That’s expected to take about two months.

The picture above shows the results of aiming the JWST at a part of the Large Magellanic Cloud. This is a small galaxy that is a satellite of our own Milky Way, and is readily visible at night in the southern hemisphere (as is the Small Magellanic Cloud), provided, of course, you’re not in a big city. It’s a good target because, as seen from here there are a lot of stars crammed together in one part of the sky and they’re all at pretty much the same distance from us.

(This is how we discovered that Cepheid variables had an intrinsic brightness proportional to their period of variability–an astronomer looked at a bunch of them in the LMC and SMC and noticed their apparent brightness was proportional to their period of variability; since all were at the same distance, the apparent brightness was directly related to the intrinsic brightness with no possible confusion due to differing distances.)

When Supernova 1987-A blew up in (wait for it) 1987, it was in the LMC.

I’ve never seen the LMC and SMC, though I did look for them when I was a good deal further south than I am now. Alas, the lighting situation was terrible.

Anyhow, the process of commissioning the instruments is expected to take a couple of months, and involves setting operating parameters and the like (the blog doesn’t have a lot of detail, so I didn’t boil it down for you; they did).

NASA’s Webb In Full Focus, Ready for Instrument Commissioning – James Webb Space Telescope

Obligatory PSAs and Reminders

China is Lower than Whale Shit

To conclude: My standard Public Service Announcement. We don’t want to forget this!!!

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 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 !!!

Hey China!

Or rather, “Hey Chinese Communist Party and your entire array of servitors, ass-wipers, and fellators!”

You’re not even worth my time this week. When you decide to act like civilized people, maybe I’ll give you a lesson or two in how non-barbarians behave.

Hey BiteMe!
(Or, Whoever Has Their Hand Rammed Up That Putrefying Meat Puppet’s Ass)

[Language warning]

You and yours have caused a lot of injury. Literal injury with your war on people who don’t want to take an untested vaccine. When people die in an emergency room because a hospital won’t admit them because they haven’t had their clot shot, that’s a crime.

I’m going to address here the insult on top of the injury, because I am among the insulted. I still have my health but apparently you want me to live under the 8th Street Bridge (which actually isn’t on 8th Street, but whatever, that’s what the I-25 overpass over Cimarron is called), so maybe if you have your way that won’t be true for long. Dreadful time of year to become homeless.

No, you’re just trying to make me unemployed, because I won’t take your fucking shots.

Well, that threat is NOT going to work. I. Won’t. Take. Your. Fucking. Shots.

And it looks like enough people agree, that you’re having to back down, you worthless asswipe.

You’re LOSING.

You LOSER.

You Chinese-bought ratfucking traitor.

I would love to see you die an agonizing, humiliating death. (This isn’t a threat, because I am not threatening to cause that death. I am just announcing my intention to party if it happens.) It would be just recompense for the way you’re killing America…and millions of Americans.

His Fraudulency

Joe Biteme, properly styled His Fraudulency, continues to infest the White House, we haven’t heard much from the person who should have been declared the victor, and hopium is still being dispensed even as our military appears to have joined the political establishment in knuckling under to the fraud.

One can hope that all is not as it seems.

I’d love to feast on that crow.

(I’d like to add, I find it entirely plausible, even likely, that His Fraudulency is also His Figureheadedness. (Apparently that wasn’t a word; it got a red underline. Well it is now.) Where I differ with the hopium addicts is on the subject of who is really in charge. It ain’t anyone we like.)

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.

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 Prices.

Kitco Ask. Last week:

Gold $1,975.80
Silver $25.77
Platinum $1,000.00
Palladium $2,436.00
Rhodium $19,900.00

This week, markets closed as of 3PM MT.

Gold $1,933.30
Silver $24.23
Platinum $936.00
Palladium $2,443.00
Rhodium $19,250.00

Everything down except palladium (and it went down on Friday). Silver down a LOT in percentage terms. So I guess the market manipulators (if they aren’t tinfoil hat imaginings, but that’s yet another metal) are at work.

Expect continued inflation and for shortages to not just continue but get worse.

James Webb Space Telescope Update

JWST is still in the last mirror-alignment iteration.

The NASA website is talking about temperature right now. MIRI is keeping chill at 6 or 7 kelvins, but not everything is at final temperature. The mirror, especially, is not quite at its final temperature. The primary mirror segments’ (the segments are the individual hexagonal parts of the big mirror) temperatures vary from 34.3 to 54.5 kelvins, and the secondary mirror (which is at the end of the tripod-like structure; it reflects light back towards the instruments) is at 29.4 kelvins. The primary and secondary mirrors are made out of beryllium, which just takes a long time to cool off. Things are close enough, though, to work on commissioning the instruments, and for that the telescope is oriented to look at the ecliptic poles (i.e., perpendicular to Earth’s orbital plane, or roughly parallel to the sun’s axis of rotation), and in that orientation JWST heats up the most. Which is still not much but at those temperatures any amount of heating could be significant. But the system is working well, and the spacecraft can continue cooling off even in this orientation.

Orthodox Easter

Yesterday was Good Friday. Tomorrow is Easter.

If you’re thinking I’m out of my skull, well, you’re probably right but not on account of this; you see, I am talking about (Eastern) Orthodox holidays.

Easter is supposed to be the first Sunday after the first full moon after the spring equinox (the “paschal moon”, which is why it moves all over the place from year to year, but actually computing that date is a challenge.

Today, of course, we could determine the exact instant of the equinox (start of spring), the exact instant of the full moon, and then go to the next Sunday. But because not every place on Earth is at the same date, that could be problematic. Imagine that first full moon being on Sunday at 11:43 PM ET; that day should be Easter, right? But in Europe and certainly in Jerusalem, that’s Monday, and so Easter should be the next Sunday, not this Sunday.

But in ancient and medieval times, the Church just deemed spring to start on March 21, and counted from there using an algorithm that approximates the phase of the moon. But even March 21 being the first day of spring is a bit slippery, historically, because we began to switch calendars in 1564. Currently, it’s very likely that March 21 will actually be the first day of spring, but before the change spring might start on March 10–but the algorithm said to start with whatever day was called March 21, not the actual day of the equinox.

The algorithm is still being used today, with the “new,” more correct March 21.

Trying to follow the thread of this made my head hurt, but apparently, because (Eastern) Orthodoxy didn’t change calendars when the (Roman) Catholic church did, nor even when the protestant churches did, they don’t agree with the western churches, and usually end up celebrating Easter (and every other thing tied to the date of Easter) a week later.

Now whether they are late (rather than later), or the West jumps the gun and celebrates early, is a fight I don’t have a dog in. But the difference is an interesting historical artifact of how both our knowledge of astronomy and our calendars have developed over the centuries.

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 !!!

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.

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!

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

MIRI (the Midrange InfraRed Instrument) is now at 6K and the final iteration of mirror alignment is in progress. Once this is done, it’s time to work on commissioning the instruments…and I have no idea what that entails, to be honest. My vague notions of what that meant were all taken care of as part of the mirror alignment process.

The NASA blog put out another article on what JWST is expected to do. It’s expected to learn more about extrasolar planets that we have already detected; in particular it will be able to analyze their atmospheres.

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 $1,947.70
Silver $24.86
Platinum $987.00
Palladium $2,503.00
Rhodium $20,000.00

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

Gold $1,975.80
Silver $25.77
Platinum $1,000.00
Palladium $2,436.00
Rhodium $19,900.00

In fact, they closed 3PM on Thursday; the market weenies get Good Friday off and apparently that’s true even in Asia.

Gold is definitely on another upward climb. It was a couple of bucks higher on Wednesday, but that downtick doesn’t cover the fact that it’s distinctly in the upper 19s now. (1975? I remember that year…) The price of platinum can’t get any rounder than it is right now (even rounder than rhodium’s was last week). Palladium and rhodium are the two losers this week, albeit not by very much. But they are the two metals whose price is most dependent on industry.

T4 Combinatorics

If you’re wondering what “Combinatorics” is (and let’s face it, you probably weren’t wondering until you read that title, if even then), it’s the branch of mathematics that has to do with counting things; including counting the number of possible combinations of things. It’s not “hard” to do, but the concepts are a bit abstract sometimes.

If you’ve ever seen those statements about how many different configurations some puzzle (like a Rubik’s Cube) can have (and only one of them is right!), those were computed with combinatorics. (No one went and looked for them all.)

Ancient Indian physician Sushruta in the 6th century BCE asserted that given six tastes, there are sixty three possible combinations total where they are taken one at a time, two at a time, three at a time, and so forth. The ancient Greeks looked into this sort of thing too. During the Middle Ages, more progress was made, but not in Europe. Again in India more general formulas were found.

The specific problem here is precisely the number of combinations of different objects can occur. As it turns out, that’s also the same number as possible sequences of coin tosses.

Going back to Sushutra’s example, if you flip a coin six times, there are 64 possible outcomes. It could come out tails all six times. It could come out tails the first five times, then heads the last time. It could come out tails the first four times, then heads the fifth time, then tails the last time. And so on. If I were to tabulate all 64 of them with 0s (for tails) and 1s (for heads) it would look like someone counting in base 2 or binary.

000000
000001
000010
000011

…and so on.

There’s another method of stepping through all of the possibilities, and that’s to use a sequence where exactly one of the six things changes each time. That’s a bit trickier, but you can get some cool patterns out of it (like the bottom half of the list being a mirror image of the top half…except for the first digit which is 1 instead of 0).

But something may be bothering you….Sushutra said there were 63 combinations; I have just been yapping about there being 64. The discrepancy is because Sushutra didn’t count the case where none of his 6 samples were being tasted.

So far, perhaps not a surprise. The number of possibilities is 2ⁿ, where n is the number of times you toss the coin (or the number of flavors you’re sampling). And this works when the different tries are independent of each other. In the case of the coins, one toss has no effect on any of the others. In the case of the flavors, there are no rules like, for example, that flavor E is forbidden if you are using flavor B.

Slightly more interesting is the question, out of these six possibilities, how many of them have exactly three flavors. Or how many possible sequences of six coin tosses have exactly three heads in them?

Well, it turns out there’s a formula for this. And it involves, interestingly enough, combining formulas for another couple of possible problems.

Let’s say you have six scrabble tiles, A, B, C, D, E, F. How many possible words are there?

You could exhaustively list them all out, but that’s tedious. Instead let’s try thinking about it.

There are six possible choices for the first letter. Once you pick the first letter, though, there are five possible choices for the second letter; so each of the six first possible letter possibilities has five possible second letters. So that’s 6 x 5 = 30 possibilities for the first two letters. You can proceed similarly, 4 possibilities for the third letter, 3 for the fourth, 2 for the fifth, and 1 for the sixth. So we’re looking at 6 x 5 x 4 x 3 x 2 x 1 = 720 possible combinations. (It’s a good thing we decided not to try to list them all!)

This is a common enough thing that we call this the factorial and denote it with an exclamation point, in this case, 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720.

I don’t believe it’s possible to form a good word of English out of those six letters, with all of those six letters and no others (but correct me if I’m wrong!); the best I can come up with is FACED. Or DECAF. I guess if you’re sore at the Federal Elections Commission you could say BADFEC.

But this is a game of Scrabble, and so you might settle for using some of the tiles. For example, how many candidate four letter words are there?

You can follow the same reasoning as above. Six possibilities for the first letter, five possibilities (for each of the six) for the second letter (30). Four possibilities (for each of the thirty) for the third letter (120). For each of those, three possible fourth letters (360). But now we STOP, because we don’t pick a fifth, or sixth letter. The math is: 6 x 5 x 4 x 3 = 360. So it’s like 6! only not taken all the way down to 1. In fact, it’s like 6! divided by 2!. Look: (6x5x4x3x2x1)/(2×1); the twos and ones cancel and we’re left with 6x5x4x3. Note that 2 is 6 – 4, i.e., it’s the total number of titles minus the number of tiles actually chosen.

So there’s a general formula here. You have n objects, you want to choose m of them. The number of possibilities is n!/(n-m)!

One thing that needs to be stressed, though! This formula is for use when you care about the order of the selection. In other words, if you grabbed the letters A, C, E, F, it matters to you whether you grabbed them as F, A, C, E or C, A, F, E or FCEA.

When dealing with Sushruta’s flavors, the first, third, fifth and sixth flavors (combined) taste the same no matter what order you’re adding them. It’s as if you didn’t care what order ACEF was written in.

So how do you adjust your answer to the question of how many possible ways to select four of the six letters if you don’t care about the order?

Well, imagine that you had actually written down all of the possible combinations (all 360 of them). Some number of these would have the letters A, C, E, and F in them. In fact, all possible orders of those letters would appear in the list exactly once. How many possible orderings of A,C,E,F are there? We already know this: 4 x 3 x 2 x 1.

And this is true for any possible grouping of four letters. There will be nine other anagrams of those four letters in the list.

So to get the answer, we start with our 360…and divide by 4! which is to say, 24, and get 15. This is the factorial of the number of objects we are choosing (m).

So, remember we got the 360 with n!/(n–m)!; this new number involves dividing again by m!.

So our number of combinations for an unordered choice of m objects out of a group of n objects is n!/[(n–m)!m!]. My combinatorics teacher called it “n-choose-m” or he’d substitute actual numbers.

We could, for example, figure out how many possible groups of ten letters we could pull out of the alphabet. With 26 letters, we have 26!/(16! x 10!).

So punch that into your calculator.

Well, don’t. 26! is probably too big for your calculator.

But you can probably get clever before you punch the numbers in.

Write those factorials out. It turns out you can do a lot of cancelling! You can skip 10×9…x1 on top, and just divide by 16x15x14…on the bottom. Better yet, you can skip the 16x15x…x1 on top and only divide by 10! on the bottom.

26 x 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 / 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1.

Right off the bat, you can cancel the 20 up top with the 10 and 2 on the bottom, and the 18 up top with the 6 and 3 on the bottom:

26 x 25 x 24 x 23 x 22 x 21 x 19 x 17 / 9 x 8 x 7 x 5 x 4 x 1

Do a bit more cancelling–get rid of the 5, 7, and 4 by dividing them into the 25, 21, and 24 respectively:

26 x 5 x 6 x 23 x 22 x 3 x 19 x 17 / 9 x 8

You have three even numbers on top. Divide them all by 2 and get rid of the 8 on the bottom:

13 x 5 x 3 x 23 x 11 x 3 x 19 x 17 / 9

And you now have two threes, so you can get rid of the 9 and those 3s

13 x 5 x 23 x 11 x 19 x 17

Well, now, we don’t have to do any dividing! In fact, you should NEVER have to do any dividing after you cancel. Why? We’re counting numbers of combinations, and that has to be a whole number. You won’t get a fraction. So if it looks like you’re about to get a fraction, you messed up somewhere–you didn’t do a cancellation you could have, or you made a simple arithmetic error.

So now go to the calculator, and it turns out there are 5,311,735 possible sets of ten letters you could pull out of 26 letters of the alphabet.

Yikes, that’s a lot!

You can get to some really big numbers this way with bigger “pots” of choices; in fact you can easily get to numbers that are larger than the numbers of quarks in the universe without too much trouble.

In fact, consider the number of possible bridge hands, which is 52!/(39!13!). If you think you’ve played enough bridge to repeat a hand…you’re probably wrong! Because there are 635,013,559,600 of them. That’s still more than the US Debt…though ask me again next week.

(And the game would still be different unless the other three players also each got the same hand as before. This could be computed with our n-choose-m formula, too, applied successively (it’ll be that number, times 39-choose-13, times 26-choose-13, times 26-choose-26) to see how many possible bridge deals there are.)

There’s another clever method to compute m-choose-n. It’s very visually oriented, but it does involve computing all of the smaller problems first.

Start with 1.

Then below it, staggered, write 1 1.

So you see:

1
1 1

You repeat this, over and over again. Each number is the sum of the two above it (and “blank” is zero). So you get:

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1

And so on. What good is this exercise (which is called “Pascal’s Triangle”)?

It turns out that if you go to row n, the mth element is n-choose-m. But you have to start counting from zero. That last row is row 4 (not 4). And if you want 4-choose-2 you have to go to the third element on that row, which is 6. This is logical, because the actual first element is always a 1, and that’s how many ways you can pick zero items out of the group of 4. Or 17, or whatever. The last number is choosing all of the elements, and of course there’s only one way to do that (if you don’t care about the order).

Another neat thing about this triangle is if you sum up everything in the row, you get the total number of possible selections in that row, for example, with 4 items, the total is 16…which is 2⁴.

Pascal’s triangle has a whole host of interesting properties, actually.

Once you see this triangle, it’s pretty clear that the biggest single n-choose-m value is when m is half the size of n. (Or if n is odd, when m is either just above or just below half of n.)

So that, if you toss a coin a hundred times, the most likely outcome is 50 heads and 50 tails, (In fact that is possible about 1×10²⁹ different ways!) though a 49/51 split is almost as common (~9.89 x 10²⁸ different ways), and a 48/52 split wouldn’t be all that surprising either (~9.32×10²⁸ different ways). But 100 heads (or tails) in a row? Ridiculously unlikely! Even a 75/25 split can “only” occur 2.42 x 10²³ ways, which sounds like a lot…but is 2 ⁴²/₁₀₀ millionths as common as a 50/50 split. And therefore. 0.00000242 times as likely as a 50/50 split if you try the experiment.

Conversely an exact 50/50 split might be the most likely result, but it’s less likely than a 49/51 and 51/49 split put together, much less if you add all the other near/even splits. There are 2¹⁰⁰ possible sequences, that’s 1.267×10³⁰ possibilities. So there’s roughly 1 chance in 12 ²/₃ you’d get an exact 50/50 split.

The takeaway from this is that an exact “middle” result becomes less and less likely the more things are involved…but a result near the middle becomes overwhelmingly likely the more things are involved.

But what, you might ask, does this have to do with heat and temperature and thermodynamics?

This sort of example does not really have much to do with it, but the general concepts behind combinatorics do have a lot to do with it, as it turns out. Next time…

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.

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 $1,926.60
Silver $24.72
Platinum $994.00
Palladium $2,365.00
Rhodium $20,400.00

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

Gold $1,947.70
Silver $24.86
Platinum $987.00
Palladium $2,503.00
Rhodium $20,000.00

Gold is moving around within a fairly tight range lately.

James Webb Space Telescope Update

A lot of material has been written by the JWST team. The mirrors are lined up and focused, but they need to be focused for all five of the sensors behind the mirror before they can do the next iteration of fine-tuning. But that has only been done for four of them. What’s the issue? The issue is that the Mid-InfraRed Instrument (MIRI) has been blind until very recently.

The other four instruments have gotten down to their desired operating temperatures of 34 to 39 kelvins. (And I discussed kelvins last week. Very convenient timing!) But they all work in either long wavelength visible light (oranges and reds) or “near infrared.” “Near” because it’s right next to visible wavelengths, just a bit longer than our eyes can see. But objects at room temperature actually glow at some of these frequencies, so in order to keep the sensor itself from glowing in the very light it’s trying to see, we keep them cooled off.

But the longer the wavelength (and lower the frequency) we want to see, the colder we have to make the instrument. Mid Infrared is longer than near infrared, so we have to cool MIRI down to about 7 kelvins or less. From MIRIs point of view the rest of the spacecraft, at -390 to -399 F, is scorching hot!

This is done with cryogenic cooling, using helium. Apparently at least some of the power on board the spacecraft runs what is essentially a refrigerator, and we’ve been running that and allowing MIRI to slowly, slowly cool down to -450 F. We don’t want to cool it off too fast lest frost form on the sensor (which would FUBAR it).

This whole process is described here.

From what I can see MIRI is actually at this temperature now, so the mirror adjusting fun can resume.

What use is MIRI? It’s expected to be able to look at stars–and their accompanying planets–as they form. For instance, we’ve all seen “the Pillars of Creation” as imaged by Hubble, which is actually a part of the Eagle nebula.

As presented the pillars run vertically, but the “Eagle Nebula” name was given to it based on the appearance of that area seen rotated 90 degrees clockwise. Or, here is a picture of the entire nebula, rotated only about 45 degrees. The dark area in the center is shaped a bit like an eagle, you can see the wings to the left, the body in the center, and the talons to the right…and of course, blown up, it’s “The Pillars of Creation.”

The Pillars of Creation picture is actually in false color, with green used to show hydrogen, etc., the picture of the eagle nebula is more like what it would look to us if we were close enough to it for it to be bright enough for us to see color.

But here’s what the Pillars look like in infrared:

Of course the colors here are ALL false; an infrared image in true color would look black.

But notice you can see a lot more stars.

Infrared can cut through dust clouds, including the dust clouds that condense to form stars and planets. So MIRI is expected to help us greatly in our quest to study “solar systems” that are forming Out There. This is all described in this blog post, from which I ripped off these pictures.

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; the SOB will never deserve a scoop.)

Incidentally, I’m writing this on Friday. This morning I saw a full-sized pickup truck in the oncoming left turn lane with a forest of flags in the bed. Once he turned and drove left-to-right in front of me, I could see two American flags near the cab, and SIX “Let’s Go Brandon” flags near the tailgate. That was unusual; usually there’s a mix of FJB (only not abbreviated) and “Trump Won” and “Trump 2024” flags when someone does this.

I haven’t seen such a display in a few weeks, by the way. Even the guy at the office complex where I work with the FJB flag on his pickup seems to have removed it (or doesn’t work there any more–trucks all look alike to me from the back, and all crossovers look like cockroaches).

T3 Heat Engines

In the early 1800s, steam engines were the cutting edge tech. We didn’t talk of them changing the world, because before that time, really the world didn’t change much over a person’s lifetime. People in the late 1700s pretty much lived as they had hundreds of years earlier. In fact, living conditions in Europe at the time (for everyone except the nobility and a very small wealthy merchant class) were described as “Third World Europe.” Except that unlike the third world today, we had no concept of sanitation, vaccination (real vaccination, not this current crap), the germ theory of disease, etc., so we had high infant mortality rates and all the rest of the stuff that today’s Third World is getting away from.

The steam engine, and the prosperity it would bring to Europe, would ultimately change that, and usher in an era where we are actually used to seeing rapid technological change generating wealth that even the not-so-rich and not-so-connected could accumulate.

If you recall my first Thermo post, I talked about turning work (energy doing something macroscopic like moving objects around) into heat, and how heat and work were both forms of energy.

A steam engine is one of a large class of devices called heat engines, that turn heat back into work.

A common misconception is that James Watt “invented” the steam engine. No, he didn’t. Actually the first known thing that was something sort of like a steam engine was put together by Hero of Alexandria (10-70 CE), and it’s either called Hero’s Engine or the Aeolipile (from Greek αιολουπυλη). It looks something like this:

A cauldron of boiling water is kept under pressure, steam can only get out by going into an object free to move around a pivot (like a bird on a spit over a fire). The steam can only escape by going through the bent arms; it generates a thrust that causes the doohickey to spin.

So Hero was actually able to get heat to do work–some fifteen or so centuries before we had our scientific concept of “work.”

The next step was to actually put something like this to work. It took a while. In 1698 Thomas Savery invented a pump for water that worked by steam power. Steam was allowed to cool and condense , which created a near vacuum which could be used to suck water upwards against gravity. Then more steam could be used to push that water.

So the first commercial application for steam power was to pump water.

Small copies of this device were reasonably efficient, larger ones were not. And lift height was severely limited (since it was a vacuum pump). And the power wasn’t continuous.

In 1712 Thomas Newcomen came up with a steam engine that could deliver continuous power and it used a cylinder, but was still very inefficient because parts of the engine itself (not just the steam) ended up being heated and cooled, heated and cooled, over and over again…which took time. These things could pump water out of mines…slowly. Still, it was better than paying some grunt to do it.

What Watt did was vastly improve the Newcomen engine. And now it could be used not just to pump water, but to pull trains, and power steamships, and even (very primitive) automobiles. And also to power factory equipment, which up until then had been almost entirely reliant on water power or (worse) animal power.

A good steam engine could supply LOADS of power.

And of course this was something scientists investigated. And what they learned could be used to make steam engines even more efficient, delivering more work for the same amount of fuel, which could be either wood, or coal that was pulled out of some of the mines the steam engine had been invented to pump water out of.

One “model” of an engine that could turn heat into work was the Carnot Engine, basically an idealized model, a thought experiment.

What’s needed is a piston with gas in it, a huge mass at high temperature (called the hot reservoir) that we can attach to the piston, and another huge mass at cold temperature (the cold reservoir) which we can attach to the piston as well. It runs through four phases, then from the fourth phase, it returns to the first phase.

Phase one starts with the piston pushed in all the way. There’s a tiny space inside filled with hot gas, under pressure. The gas is at exactly the same temperature as the hot reservoir.

Now you could let the gas under pressure expand, and push on the piston and use that to do work. But as the gas expands, it will lose pressure and the temperature will drop. Instead, what we want to do is let the gas absorb heat from the hot reservoir, so that it stays at the same temperature as it expands. Ideally the temperature is exactly the same but in practical terms this is unachievable (unless you are willing to take literally forever for it to happen).

Phase 2 is to allow the gas to continue to expand and push the piston, but now you let the gas cool off…until it reaches the temperature of the cold reservoir.

Phase 3 is to compress the gas, and keep it at the same temperature as the cold reservoir. Compressing the gas would normally raise its pressure and temperature, but we let the increased heat bleed into the cold reservoir. Do this infinitely slowly, and the gas in the cylinder stays at the cold reservoir temperature.

Phase 4, finally, is to continue compressing the gas, but let it heat up…all the way up to the temperature of the hot reservoir. We’re now back to having compressed gas at the temperature of the hot reservoir.

So what has happened here? We’ve extracted a net amount of work from the system…more came out letting the gas expand and cool than we had to put into it recompressing the gas. Also, some heat energy has been taken from the hot reservoir and put into the cold reservoir.

In reality, this would result in the hot reservoir cooling off just a tiny bit, and the cool reservoir heating up just a tiny bit, but this ideal model assumes these reservoirs are of infinite size.

So what’s going on here? Heat has moved, and some (notice: some, not all) of that heat got turned into work. The rest simply moved from hot to cold and did no work for us at all. And since heat moves from hot to cold naturally, not the other way, that heat energy we didn’t use is gone for good.

As it turns out this “Carnot Cycle” is the most efficient possible way, even in principle, to turn the heat differential between a hot and cold body into work. And it gets more efficient the greater the difference between the two. (And this is true even for engines that are steam turbines with no piston at all, or where the working fluid changes from a gas to a liquid…they can’t beat the Carnot engine.)

The maximum theoretical efficiency is 1-T_C/T_H. Note that those temperatures need to be measured against absolute zero (so kelvins and Rankines work). You’ll note that if T_C and T_H are far apart, that fraction gets smaller, and the efficiency climbs, if you can make that fraction 0, your efficiency is 1 (i.e., 100 percent). As a practical matter, though, we don’t have a cold reservoir at 0 K, so we can’t reach 100 percent efficiency even in principle. And whatever this number is…our current power plants don’t even achieve that.

But this is why power plants (coal, nuclear, natural gas, even geothermal) run so hot; it’s to raise the temperature of the working gas as high as possible. And this is why geothermal usually sucks as a power source. You have to drill way, way, way down to get to rocks hot enough to be worth the effort. Of course in some places, like Iceland the hot stuff is closer to the surface. Yellowstone has, if anything, even more potential than Iceland does for geothermal power.

And of course with nuclear and fossil fuels, we control the temperature difference and you can bet we run them as hot as we can.

Since a Carnot engine is as efficient as you can get, a lot of engine design since the mid 1820s has been to try to get as close to a Carnot engine as possible. (That was, for example, the initial idea behind the Diesel engine; eventually Diesel had to start making design compromises.)

In every power plant we build (other than geothermal) the heat reservoir is not only not infinite in size, but it’s actually rather small. It would cool off rapidly as the engine cycles, and the heat is transferred out. To keep it hot, we have to burn fuel. So we’re basically burning fuel to create heat to maintain the temperature of the hot reservoir so we can then turn the heat into work.

With geothermal, the reservoir is huge, perhaps even yuge, but still finite; using geothermal does suck heat energy out of the earth and dump it somewhere colder. It’s just that there’s so much of it we’ll never notice.

A typical coal fired plant uses the work extracted from burning the coal (and keeping the hot reservoir hot) to turn a generator. And the efficiency is roughly 30 percent. 30 percent of the energy in the coal becomes electricity. In fact the engineers and designers are overjoyed when they get that number.

But that does mean the other 70 percent is wasted as waste heat…and it can’t be any other way.

Waste heat is inevitable, and it can’t be recovered. Not without reversing the process. We can push heat energy from the cold to hot reservoir by supplying work. If it’s a Carnot engine, we can run the process in reverse, put the work we got out back in, and move all the heat back where it came from. For any real engine, it will take more work to move less heat than we lost creating the work in the first place. In other words, a Carnot engine is a reversible process. But no real heat engine is reversible this way. But if you try, you will move some heat from cold, back to hot.

This is the idea behind a heat pump.

In reality, there are always losses, and (again) there’s no such thing as a Carnot engine. So if, say, you ran your (real) heat engine and got 100 joules of work out of it, and 200 joules of heat ended up in the cold reservoir, you’d probably need to put 150 joules into it to move those 200 joules back to the hot reservoir. Where would you get the extra 50 joules from? Maybe from another engine, which has its own losses and its own inefficiencies, and even more energy flows from its hot reservoir to its cold reservoir.

In fact, there’s no way to completely reverse heat flow from hot to cold. Any attempt actually moves even more heat from hot to cold in the process. Which might be worth it, if you want to cool the inside of your refrigerator. You suck some heat energy out…at the cost of more heat energy being permanently lost somewhere else.

But on net, heat flows one way, one way only: From hot to cold. Even a theoretically perfectly reversible process like a Carnot engine just holds the total flow to zero. Never negative.

This is what was originally behind the concept of entropy. It denotes that fact that as processes go forward, temperatures even out, they get more and more evened out as time goes on, never the other way around.

(If you think you know of a case, like the inside of your refrigerator, recognize that that’s at the cost of more heat flow in the other direction somewhere else. This is why you can’t cool your house by opening the refrigerator door and leaving it open–it dumps the heat through the coils in back…more heat than it sucks out of the inside. Your air conditioner, on the other hand, does work…by dumping the heat (again, more than it removed from your living space) outside your house and making the outside warmer than it was before.)

Entropy is, conceptually, a measure of how much heat energy is irretrievably lost, and it increases. (It can even be quantified and measured…but that’s WAY beyond the scope of this post.) Entropy never shows a net decrease.

(Entropy is also second only to quantum mechanics as a source of pop philosophizing with a scientific/geeky bent to it. More on this in future posts, because the concept of entropy would eventually be greatly extended beyond mere “waste heat” type considerations.)

So what happens at some distant day when all of the energy in the universe has become waste heat and is irretrievably lost? Well, it’s game over.

Thinking in the long term, the big picture is the entire universe is running down. It will ultimately be one big thing of uniform temperature…and though there will be a lot of heat energy out there, none of it will be usable, not just for industry, but for life itself.

The concept of entropy, and the accompanying realization that the universe as a whole must run down, was the dawn of the science of thermodynamics. The true “dismal science.” Economics is sometimes called the dismal science, but it doesn’t hold a candle to thermodynamics when it comes to “dismal.”

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 !!!