“We do not believe any group of men adequate enough or wise enough to operate without scrutiny or without criticism. We know that the only way to avoid error is to detect it, that the only way to detect it is to be free to inquire. We know that in secrecy error undetected will flourish and subvert.” –J. Robert Oppenheimer
Today, it is still the case that Joe Biden didn’t Win.
I realize that to some readers, this might be a shock; surely at some point things must change and Biden will have actually won.
But the past cannot actually be changed.
It will always and forever be the case that Joe Biden didn’t win.
And if you, Leftist Lurker, want to dismiss it as dead white cis-male logic…well, you can call it what you want, but then please just go fuck off. No one here buys that bullshit–logic is logic and facts are facts regardless of skin color–and if you gave it a moment’s rational thought, you wouldn’t either. Of course your worthless education never included being able to actually reason–or detect problems with false reasoning–so I don’t imagine you’ll actually wake up as opposed to being woke.
As Ayn Rand would sometimes point out: Yes, you are free to evade reality. What you cannot do is evade the consequences of evading reality. Or to put it concretely: You can ignore the Mack truck bearing down on you as you play in the middle of the street, you won’t be able to ignore the consequences of ignoring the Mack truck.
And Ayn Rand also pointed out that existence (i.e., the sum total of everything that exists) precedes consciousness–our consciousnesses are a part of existence, not outside of it–therefore reality cannot be a “social construct” as so many of you fucked-up-in-the-head people seem to think.
So much for Leftist douchebag lurkers. For the rest of you, the regular readers and those lurkers who understand such things: I continue to carry the banner once also carried by Wheatie. His Fraudulency didn’t win.
Let’s Go, Brandon!!
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 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.)
Tranheuser Busch
Those asshats either get the world, all time record for obtuseness…or this is deliberate somehow. And their namby pamby non-apology that amounts to a “We’re sorry you’re too much of a knuckledragger to appreciate what we did” simply underscores the stupid. It’d be like a 400 pound golfer wearing spikes tromping on your instep and being utterly clueless why you are screaming in pain.
Me
I wrote that months ago, and they are casting about now trying to figure out how to get people to come back. However the one thing that might work (an abject admission that they were wrong to even think of doing this) is the one thing they cannot do. Because the decision makers are woke and cannot conceive that they were actually fuckheadedly wrong to do this.
Silver and platinum took a beating this week. Gold down too but not in “took a beating” territory.
Obligatory PSAs and Reminders
China is Lower than Whale Shit
Remember Hong Kong!!!
Whoever ends up in the cell next to his, tell him I said “Hi.”
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 !!!
One of my stock jokes is to say, as I head off to the bathroom or washroom or restroom, “I’m going to go make a political statement.”
It certainly seems like urinating is a good way to make a statement about the YSM, and defecating works for politicians. Or the other way around is good too, though “#1” just never seems emphatic enough.
Maybe “#1” is just being polite, and “#2” is telling the fixtures what you really think.
Anyhow, I pretty much do plan to be polite to RINOs that electioneer or fundraise. I’ll tell them, Sorry, but I need to GO Pee…
Language Warning
In the next piece I had to discuss a particular topic. Unfortunately, I couldn’t discuss it without naming it. Therefore I apologize in advance for having to do so, and apologize to anyone offended by the sight of the name.
RINO McDaniel
RINO McDaniel continues to infest the GOP. But RINO McDaniel isn’t the problem.
Let me be crystal clear on this, RINO McDaniel is a lower-than-whale-shit, piss guzzling ratfucking shit eating traitorous rancid syphillitic cunt. Her worth as a human being is substantially less than zero, any oxygen sucked into her lungs is wasted, and it would be, no matter what job she had.
I fear I haven’t been clear enough, but that will have to suffice.
But she is not the problem…or rather, she would not be a problem were it not for others. She’d still be as I have described, but we wouldn’t know who she is and would not care, because she could do no damage. She’d just be anonymous human refuse.
No, the real problem is the fact that a majority of the 168 top GOP people voted for her. And now that has happened five times so they cannot claim they didn’t know what she was.
In spite of the fact that under her “leadership” the party has deliberately sabotaged the will of its base, has deliberately refused to challenge blatant election fraud, had gone out of its way to ensure certain candidates do not get nominated, has diverted donor money to namby-pamby candidates who have all the electoral appeal of a puddle of dog vomit…and in general has done nothing whatsoever to help fix the problems that plague America.
However that last is to be expected; I cannot expect anyone who IS the problem to help FIX the problem.
RINO McDaniel would be powerless without an entire party leadership of the same mind as her. They want this dismal performance; they want to ignore the party base.
If she were to drop dead this instant, it would solve nothing as someone just like her would be elected by those same pustulous people.
According to Charlie Kirk, about 55 people voted against her, 10-12 wanted something different but were too chickenshit to do the right thing, and roughly 100 people voted for her enthusiastically, and even had the unmitigated gall to complain to Kirk about US. Fuck ’em. Rusty 12 gauge bore brushes would be too good for these arrogant pricks and cunts.
Every single one of those hundred is just as bad as she is. In other words, they are all worse than I described at the beginning of this piece. And no doubt those people in turn have people who supported them to be state party chairs and whateveritis they call the other two people from each state and territory who were voting.
It’s time to face up to the fact that the Republican party is effectively owned by the shit-eating RINOs. We’ve got more work to do, a lot more work, to make the GOP an instrument for the restoration of the United States of America. And that’s in addition to cleaning up our elections.
There’s no point in cleaning up elections just to elect ratfucking RINOs.
OK, hopefully now you will have some inkling of my true attitude towards RINOs. Sorry that words were inadequate to give you the full picture.
The Real Fascist is His Fraudulency Joe Biden*
*Or whoever has his hand rammed up that meat puppet’s ass.
Brandon (which I will use as a term for whoever is the power behind the Porcelain Throne) has thrown down the gauntlet…but in a way where most of America will never see it. The networks didn’t carry his tirade. CNN air brushed it (or whatever you call editing the red background) for its five viewers (who aren’t trapped in airports).
Luckily for me I live in Colorado, and therefore, despite my best efforts, I probably didn’t vote for Donald Trump.
Of course, for this purpose who I actually did try to vote for will be essential, and they undoubtedly know.
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.
Small Government?
Many times conservatives (real and fake) speak of “small government” being the goal.
This sounds good, and mostly is good, but it misses the essential point. The important thing here isn’t the size, but rather the purpose, of government. We could have a cheap, small tyranny. After all our government spends most of its revenue on payments to individuals and foreign aid, neither of which is part of the tyrannical apparatus trying to keep us locked down and censored. What parts of the government would be necessary for a tyranny? It’d be a lot smaller than what we have now. We could shrink the government and nevertheless find it more tyrannical than it is today.
No, what we want is a limited government, limited not in size, but rather in scope. Limited, that is, in what it’s allowed to do. Under current circumstances, such a government would also be much smaller, but that’s a side effect. If we were in a World War II sort of war, an existential fight against nasty dictatorships on the brink of world conquest, that would be very expensive and would require a gargantuan government, but that would be what the government should be doing. That would be a large, but still limited government, since it’d be working to protect our rights.
World War II would have been the wrong time to squawk about “small government,” but it wasn’t (and never is) a bad time to demand limited government. Today would be a better time to ask for a small government–at least the job it should be doing is small today–but it misses the essential point; we want government to not do certain things. Many of those things we don’t want it doing are expensive but many of them are quite eminently doable by a smaller government than the one we have today. Small, but still exceeding proper limits.
So be careful what you ask for. You might get it and find you asked for the wrong thing.
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).
A Few Things We Cannot Blame on His Fraudulency
I am pretty sure Joe Biden had nothing whatsoever to do with the 30 Years War that ran from 1618-1648 and probably killed about a third of the people then living in what is now Germany.
Nor did he cause the collapse of either Roman empire (Western, 476 CE, Eastern 1453 CE). Nor the ignominious failure of most of the Crusades. Nor the collapse of Bronze Age civilization around 1200 BCE (including the collapse of the Minoans and the blowup of Santorini).
However, my utter lack of ability to imagine how he could possibly be responsible for these things is not a valid argument against them, so I await correction if appropriate.
His Truth?
Again we saw an instance of “It might be true for Billy, but it’s not true for Bob” logic this week.
I hear this often, and it’s usually harmless. As when it’s describing differing circumstances, not different facts. “Housing is unaffordable” can be true for one person, but not for another who makes ten times as much.
But sometimes the speaker means it literally. Something like 2+2=4 is asserted to be true for Billy but not for Bob. (And when it’s literal, it’s usually Bob saying it.) And in that sense, it’s nonsense, dangerous nonsense. There is ONE reality, and it exists independent of our desires and our perceptions. It would go on existing if we weren’t here. We exist in it. It does not exist in our heads. It’s not a personal construct, and it isn’t a social construct. If there were no society, reality would continue to be what it is, it wouldn’t vanish…which it would have to do, if it were a social construct.
Now what can change from person to person is the perception of reality. We see that all the time. And people will, of course, act on those perceptions. They will vote for Trump (or try to) if their perception is close to mine, and vote against Trump (and certainly succeed at doing so) if their perception is distant from mine (and therefore, if I do say so, wrong). I have heard people say “perception is reality” and usually, that’s what they’re trying to say–your perception of reality is, as far as you know, an accurate representation of reality, or you’d change it.
But I really wish they’d say it differently. And sometimes, to get back to Billy and Bob, the person who says they have different truths is really saying they have different perceptions of reality–different worldviews. I can’t argue with the latter. But I sure wish they’d say it better. That way I’d know that someone who blabbers about two different truths is delusional and not worth my time, at least not until he passes kindergarten-level metaphysics on his umpteenth attempt.
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.
Gold barely moved at all, everything else is down except rhodium which moved up by what appears to be the minimum increment (I don’t believe I’ve ever seen a price for it which wasn’t a mulitiple of $50.
So it seems to have been a quiet week, but then again I rarely look during the week.
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 !!!
I start writing a post, usually, by going back five weeks and copying that post. That way I get the same eagle I had back then without having to dig through the uploaded media looking for it. (And I get the same boilerplate too.)
Of course when I do something else instead of an eagle, I then have to go back six weeks the next time (and the times after that) until doing so brings up the “odd” post.
This was the week that, going back six weeks I saw a big yellow weary lizard as the banner.
So back to going back five weeks for my eagle.
In the meantime a belated thank you to everyone who commented and offered condolences and kind words on Darwin’s demise.
This Man is Pissed!
And if you aren’t…what the hell is wrong with you?
Is This Our Anthem?
Or at least our song to march to?
I’m sure most of you know I don’t believe in “devolution” or any variant of “we’re really still in charge” and certainly not the ones that come with “They’re waiting for everyone to wake up.”
No, I don’t think the good guys are in charge. But that makes it even more necessary that people wake up.
This might be the Uncle Tom’s Cabin of our age. (Or perhaps the recent trafficking movie was it. Or maybe both.)
Certainly there seem to be a huge number of people who are finally having the light bulb turning on when they hear this song.
Joining The Herd Of Lemmings
I’ve had cause to consider a few things. Maybe we’re going about it the wrong way, and we need to ditch Trump
Yeah, NO
Trump all the way! Why? Because being hated by the people who hate him is a sign of impeccable character, that’s why.
The haters can go fuck themselves with rusty twelve gauge bore brushes. I’d prefer ten gauge but that’s kind of scarce, so…I’m willing to compromise.
The RINO’s Dilemma
The RINOs who who have burrowed in and taken over most GOP organizations, from the state down to local organizations, have quite a dilemma on their hands, and most of them have their heads too far up their asses to realize it.
OK, I’m not talking about the liberal in a Republican area, who knows they’re in the wrong party, but is there because it’s the only game in their town; they hope to capture a nomination someday, at which point they’re guaranteed to be elected…otherwise, they never will be. These people are a hazard in any heavily conservative area.
No, I’m talking about the guys who are a little bit conservative and want to do some good by going into politics, and they’re in a closely matched area, closely enough that they can join the party they are most aligned with and still have a chance. They think the Democrats…particularly the ones who end up running for office…are nuts.
They don’t think much better of the Deplorable types, either. A bunch of bumpkins whose hearts are in the right place, mostly…OK a bit extreme. But they think Deplorables can’t understand that first you have to get elected, then work within the system to change things…a slow process. They genuinely want many of the things Deplorables want…just not as much. The government is spending too much. Or they need to spend money on highways instead of welfare for illegal immigrants. But they want to work within the system to get these things done.
Or maybe they think things are pretty close to ideal right now, and they want to nail it in place.
The problem is, that means they don’t stand for anything in particular. And it shows. They’re about as unappetizing to the electorate as a puddle of dog vomit. The folks in the middle, who they think they are appealing to because they themselves are not extreme, would honestly prefer a clear-spoken radical to someone who qualifies everything they say to the point where they sound like they don’t believe anything at all.
The problem these “Mild RINOs” have, is they just can’t see that. And the reason they just can’t see that, is their entire sense of self-worth is tied up in not seeing that. In their minds, they’ve worked tirelessly for their party, to keep those crazy Democrats out…only to have to constantly fight with a small number of crazy Republicans–who are only liabilities if they end up as candidates. They’ve fought the good fight, and if they can just find the right candidate, someone with some charisma, they might stop the crazies…without being too beholden to the OTHER crazies. In the meantime it’s not working. What’s a responsible guy in politics to do?
They simply cannot understand that the Republicans can’t succeed as the party of nothing in particular. Not really in the past, and certainly not today when people are starting to realize that no matter what they do in the voting booth, the country is still about to fly off a precipice. If they did see it, they’d suddenly have two choices: Go away and let the GOP succeed, or stay and fight. But “go away” isn’t really an option, because what’s the point of having a party now owned by the crazies, win?
Well, they have a dilemma…and WE, therefore have a problem. And we would have that problem even IF they realized that they had a problem…that they were the problem.
No one ever thinks they are the bad guy. Even Epstein probably thought he was the good guy. Right up to the moment where he didn’t kill himself.
So if you ever wonder why these unappetizing dufuses cling on even when their fingernails are being left behind…that’s why. They don’t understand no one wants them, and can’t imagine that no one should want them. And oftentimes their greatest pride is in all the hard work they’ve done for the party. They’re not going to give that up; it’d be psychological suicide.
If you’ve worked with these people, there’s a good chance you like them and consider some of them your friends. But even if so…we’re going to have to give them a good, hard shove. Because America is more important than those milquetoasts’ egos.
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.
Gold’s decline appears to have reversed…at least for now. Usually when something is moving there’s a sort of three-steps-forward, one-step-backward (or vice versa) thing going on; it’s too early to tell whether this is just the “one step” and gold will resume its downward travel shortly.
But at this instant everything is up versus a week ago–except palladium.
Science Post Place Holder (Under Arrest)
Y’all get a break this week.
Fuck Joe B*d*n
Due to complaints about foul language, I’ve censored the most objectionable word in the title of this section.
B*d*n, 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.)
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 !!!
Just remember…we might replace the RINO candidates. (Or we might not. The record is mixed even though there is more MAGA than there used to be.) But that will make no difference in the long run if the party officials, basically the Rhonna McDaniels (or however that’s spelled–I suspect it’s RINO), don’t get replaced.
State party chairs, vice chairs, secretaries and so on, and the same at county levels, have huge influence on who ultimately gets nominated, and if these party wheelhorses are RINOs, they will work tirelessly to put their own pukey people on the ballot. In fact I’d not be surprised if some of our “MAGA” candidates are in fact, RINO plants, encouraged to run by the RINO party leadership when they realized that Lyn Cheney (and her ilk) were hopelessly compromised as effective candidates. The best way for them to deal with the opposition, of course, is to run it themselves.
Running good candidates is only HALF of the battle!
SPECIAL SECTION: Message For Our “Friends” In The Middle Kingdom
I normally save this for near the end, but…basically…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…
Biden Gives Us Too Much Credit
…we can move on to the next one.
Apparently Biden (or his puppeteer) has decided we’re to blame for all of the fail in the United States today.
Sorry to disappoint you Joe (or whoever), but you managed to do that all on your own; not only that, you wouldn’t let us NOT give you the chance because you insisted on cheating your way into power.
Yep, you-all are incompetent, and so proud of it you expect our applause for your sincerity. Fuck that!!
It wouldn’t be so bad, but you insist that everyone else have to share in your misery. Nope, can’t have anyone get out from under it. Somehow your grand vision only works if every single other person on earth is forced to go along. So much as ONE PERSON not going along is enough to make it all fail, apparently.
In engineering school we’re taught that a design that has seven to eight billion single points of failure…sucks.
Actually, we weren’t taught that. Because it would never have occurred to the professors to use such a ridiculous example.
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.
Kamala Harris has a new nickname since she finally went west from DC to El Paso Texas: Westward Hoe.
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
All prices are Kitco Ask, 3PM MT Friday (at that time the markets close for the weekend).
Gold sliding. I guess to Wall Street things are just fine. Meanwhile we work for bullshit pay and inflation keeps on going…
Watch Me Pull A Rabbit Out Of My Hat
Last week we left off showing that it’s possible using the Maclaurin series (a special case of the Taylor series) to compute sines and cosines of angles. The closer the angle is to zero, the easier it is to do.
Technically you don’t get an exact answer unless you run the series out forever, but you can typically get acceptable precision in just a few terms.
Here they are, sine and cosine:
sinx = x – x3/3! +x5/5! – x7/7!…
cosx = 1 + –x2/2! + x4/4! + –x6/6! + x8/8! +…
But if you recall, from way back, there is another such series for the exponential function, i.e., ex.
(It’s so much nicer when I can find an image of a properly typeset formula, ain’t it?)
Can We Tie Trig and Exponentials To Each Other?
Take a really close look at these three formulas. Compare like terms…and by that I mean x3 in one formula should be compared to x3 in another, and so on.
You’ll notice that the formula for ex contains terms for every power of x. Sinx, on the other hand contains only the odd-power elements, and cosx contains only the even-power elements.
It’s almost as if you could somehow combine sine and cosine to get the exponential function.
But if you add the sine and cosine functions together you get this:
Well…it’s almost right. Except for one rather awkward problem. The terms have two positive signs, then two negative signs, then two positive signs, then two negative signs. and so on, whereas the exponential series has nothing but positive signs.
And you can’t fix this by subtracting cosine from sine (or vice versa), thereby flipping some signs, because some of those errant negative signs come from sinx and some from cosx.
You still have an alternating sequence of two positive numbers then two negative numbers, then two positive numbers, and so on; you’ve just shifted where the pairs of negatives and positives are in the sequence.
So what looked like something that would have been a really cool way to tie trigonometry to the exponential function, fails.
Tying Up A Loose End
I mentioned here: https://www.theqtree.com/2023/06/24/2023%c2%b706%c2%b724-joe-biden-didnt-win-daily-thread/ that complex numbers, i.e., numbers of the form a + bi,where i is the square root of -1, could have all sorts of things done to them, addition, subtraction, multiplication, division…and you could even raise other numbers to complex powers. I said that last part, but then I said I’d have to talk about it some other week.
Well, this is that week.
Nothing says that the x in the Maclaurin series has to be a real number.
So why don’t we plug a complex number into the Maclaurin series for ex to see what happens?
Well I can tell you beforehand what will happen if we plug a + bi into it…we’re going to have to square that expression, then cube it, then raise it to the fourth power, and the fifth, and we will have a gawdawful mess on our hands very, very quickly.
But really, that would be a chimpanzee move.
ea+bi, after all is ea x ebi. By splitting it up this way, we can handle the two pieces separately and then (at the end) multiply them together. We already have a handle on ea but we should check on ebi since the power we are raising e to is an imaginary number. So let’s set ea aside (but we will not forget it’s there).
This doesn’t seem to do much for us; you could put anything in for x and you will be raising it to all those powers. But i has a very interesting behavior when you raise it to successive powers, and we can use that here:
In other words it goes through a 1, i, -1, –i cycle, over and over again. So we can go back to the expansion above and replace all of the i-to-the-somethingth powers with the appropriate value (and do more simplifications….0! is defined to be 1, and any number raised to the 0th power is also 1). Also, when we do this if there is an i or –i we’ll bring it to the front.
Now some of the terms have i in them and some do not, which makes this the epitome of a complex number. It’s a little hard to deal with this in this form, so let’s collect all the real terms together, and all the imaginary terms together–like we would for any complex number. We end up with the sum of two series:
The first series is the same as the expansion of cosx from earlier, except of course it’s on b instead of x. Makes no difference. They’re the same.
The second series, moreover is i times the sinx series from above (again with b substituted for x).
In other words, switching back to x:
eix = cosx + isinx.
Well, well, well. We can connect exponentials and trig functions after all! We just needed a bit of (I can’t resist) imagination, taking the exponent of an imaginary number and getting a result that has both a real and imaginary component.
This is known as Euler’s equation, after Leonhard Euler (1707-1783) who first noted it. Euler is arguably the greatest mathematician that ever lived though he has plenty of stiff competition from others.
It would be hard to overstate the importance of this result. It underlies much of physics, and is all over the place in electrical engineering.
And yet you never hear about it in the popularizations of science (well, not until now).
This is largely because, in order to get here, you need a pretty solid advanced math background. Or someone who’s willing to skip over a lot of formal proofs as he presents it to you. Most math educators won’t do that, and rightly so. Mathematics education relies on proving everything along every step of the way. It’s bullshit-free, everything is proved based on what comes before and you don’t have to trust the perfessor or take his word for anything. And here I am giving it to with little in the way of proofs and enough hand-waving that I am raising myself off the floor from flapping my arms so hard. (As such, if you find this interesting, I ask that you at least ask someone else with the right knowledge if it’s true. DO NOT just take my word for it. Better yet, take a bunch of math courses.)
Putting It Back Together
But there’s one little detail that must be dealt with. We got here by trying to raise e to the a+bi power, and we set aside the ea that we must multiply ebi by. So let’s put them back together.
ea+bi = eaebi = ea(cosb + isinb)
But now, the last thing should remind you of something. (Though this time I will not jump on the table and yell that it should do so.)
It looks a bit like how you convert polar to rectangular coordinates.
<r, θ> = (rcosθ , rsinθ)
And if you consider your rectangular coordinates to be complex number in a complex number plane, you get:
<r, θ> = r(cosθ + isinθ)
So another way to represent ea+bi is:
ea+bi = <ea, b>
I’ve said before that the angle brackets < and > are not standard mathematical notation. I just use them as a visual cue that the coordinates are polar coordinates. Mathematicians generally don’t bother with that, they just use parentheses for both cases. But sometimes (actually rather often) they will write polar coordinates like this:
<r, θ> as: reiθ
(And need I remind you: the angle must be expressed in radians. eiθ will give you the sine and cosine of θ, but only if θ is radians. Another reason why mathematicians prefer radians.)
A Maximally Geeky Bonus
What if θ is π? (I.e., what if θ is 180 degrees?)
The sine of π is zero. The cosine of π is -1.
So if eiθ = cosθ + isinθ, and θ = π, then eiπ = cosπ + isinπ = -1 + 0.
eiπ = -1
Adding 1 to both sides we get:
eiπ + 1 = 0
Note the beauty of this. It contains all three of the numbers I introduced you to, e, π, and i, plus the numbers 0 and 1–which I sure hope I did not have to introduce you to (though maybe some reader of this took woke mathematics and got to hear about “saving the planet” instead of actual math).
Arguably these are the five most important numbers in mathematics, and one formula ties them together, and no other more mundane number appears in the formula.
This is known as Euler’s identity, and it’s a favorite. There’s absolutely no way anyone can see this intuitively, no way to see that e, i, and π should be related to each other in any way, much less all three of them directly like this.
And yet they are. And much of our modern world depends on this crazy little fact.
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 !!!
McCarthy 2.0 seems a vast improvement over Speaker Dungsmear. So here’s the question. Was he once a conservative with a little fire in the belly that got captured by the system and now is finding the bellyfire again? Or is this all completely under duress?
For the moment, it doesn’t matter which one. But some day it will matter, and we will have our answer.
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 our most recent 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?
In Defense of Ranked Choice Voting
One of the biggest obstacles to direly-needed change is RINOs, and one of the weapons in their arsenal is the “Wasted Vote” argument.
Periodically a third party has arisen, trying to hold RINOs to account by putting pressure on them from outside of the party, since doing so from the inside has historically done very little good. But, even if you find a third party candidate who perfectly reflects your views, you’re likely to vote for the RINO anyway. Why? Because if you don’t, the Democrat might win, and that would be even worse. So if you vote for that third party (that few will vote for), you’re throwing your vote away and increasing the likelihood of the Democrat winning. (It’s half as much a gain for the Democrat, as actually voting for the Democrat would be. Not as much, but half as much. Because although you denied the R your vote, you did not flip your vote to the Democrat.)
The Republican Party Establishment knows you don’t love them. But they know you hate the Democrats worse, and they use that to continue to herd you into supporting them. With gritted teeth you cast your vote, but your vote counts the same whether you cast it enthusiastically. And the other alternative, pissing on the voting apparatus to express your actual feelings, is probably a felony.
But what if you could vote for that third party without increasing the chances of the Dem walking away with the prize?
This is what ranked choice voting, or instant runoff voting, can do provided it is properly implemented. (And this includes the votes, and only genuine votes, being counted honestly, of course. However, I’m going to compare it to what we have today, and pretend that is honestly done too. RCV can’t work if it’s not honestly administered, just like our current system isn’t working because it isn’t honestly administered.)
The idea behind RCV is to vote by expressing your order of preference. You could vote for the Patriot Party, then for the RINO Party as your second choice (and ignore the Democrat, the Green, the Overt Socialist Schmuckmonkey Party, etc).
What does this do? It nullifies the wasted vote argument. Your vote will be counted for the Patriot party, first, then instead of it being “wasted” when the Patriot Party loses, it ends up going to the RINO. Actually, it’s just barely possible that the Patriot Party would actually beat the RINO, if people weren’t all individually afraid to vote for it.
It’s just like the famous “Prisoner’s Dilemma” where your fear of other peoples’ actions prevents you from doing the optimal thing–and vice-versa. As long as Job Lowe is afraid to vote Patriot because he’s afraid you’ll vote RINO, you’ll have to vote RINO because you fear that Job Lowe will, because he fears you will.
So on the whole I like RCV. It gives you a no-risk way to vote against the RINO scum, and in favor of someone who deserves your vote.
The problem is, as done here in the US, it comes packaged with a “jungle primary.” A bunch of candidates get to put their name out there, and the top four (or so) candidates get onto the “main” ballot. This gives party establishments their way around the threat of a good third party bumping them off. Because they know that few people bother with primaries, and third parties don’t have the resources to run in a primary…so they throw two or three establishment hacks into the primary and they will probably beat the third party. The result is the RINOs end up with two of the four slots in the general election, and the Dems get the other two. Now there’s suddenly no third party candidate on the ballot at all.
If we were to combine RCV with the present system where each party could nominate exactly one candidate to appear on the November ballot, or at the very least, ensure minor parties could get onto the ballot with at least one candidate regardless of the primary, we would be getting somewhere, but the establishment is smarter than we like to give them credit for. They will support the jungle primary + RCV “solution” rather than the more appropriate one-candidate-per-party + RCV solution.
It’s not RCV that is the problem, it’s the primary structure grafted onto it.
Justice
It says “Justice” on the picture.
And I’m sure someone will post the standard joke about what the fish thinks about the situation.
But what is it?
Here’s a take, from a different context: It’s about how you do justice, not the justice that must be done to our massively corrupt government and media. You must properly identify the nature of a person, before you can do him justice.
Ayn Rand, On Justice (speaking through her character John Galt, in Atlas Shrugged):
Justice is the recognition of the fact that you cannot fake the character of men as you cannot fake the character of nature, that you must judge all men as conscientiously as you judge inanimate objects, with the same respect for truth, with the same incorruptible vision, by as pure and as rational a process of identification—that every man must be judged for what he is and treated accordingly, that just as you do not pay a higher price for a rusty chunk of scrap than for a piece of shining metal, so you do not value a rotter above a hero—that your moral appraisal is the coin paying men for their virtues or vices, and this payment demands of you as scrupulous an honor as you bring to financial transactions—that to withhold your contempt from men’s vices is an act of moral counterfeiting, and to withhold your admiration from their virtues is an act of moral embezzlement—that to place any other concern higher than justice is to devaluate your moral currency and defraud the good in favor of the evil, since only the good can lose by a default of justice and only the evil can profit—and that the bottom of the pit at the end of that road, the act of moral bankruptcy, is to punish men for their virtues and reward them for their vices, that that is the collapse to full depravity, the Black Mass of the worship of death, the dedication of your consciousness to the destruction of existence.
Ayn Rand identified seven virtues, chief among them rationality. The other six, including justice, she considered subsidiary because they are essentially different aspects and applications of rationality.
I’m sure enough of this that I put my money where my mouth is.
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 2024 or 2026 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.
Everything down or flat except palladium. Interesting!
Sines and Cosines from Plain Old Arithmetic
Well after last week’s difficulty with editing I’m going to have another go at it.
I ended by stating that there was a way of computing the sine and cosine of any arbitrary angle, without knowing any other sines or cosines.
This is good because if you do need other sines and cosines as inputs, then roundoff error in the previously determined sines and cosines will start you off wrong, and you’ll be making an roundoff error here (remember you can’t specify most of these numbers precisely, they’re irrational). These errors will only accumulate. A direct method that doesn’t depend on other calculations would be much better.
We have that method. Sort of. There are a couple of caveats: This method will give you an approximation, though you can put more work into it and get it as close to the actual sine or cosine as you want. The more accurate you want, the more work you will need to do. (It becomes precisely accurate if you do infinite work.
And the other caveat is you have to give your angle in radians, because that is the “natural” way to measure an angle: as a distance along the arc of a circle.
OK, here we go:
Remember a few weeks ago (https://www.theqtree.com/2023/06/10/2023%C2%B706%C2%B710-joe-biden-didnt-win-daily-thread/) I talked about the Taylor series, and a special case of it called the MacLaurin series. These can be used, in some cases to compute values of a function that might otherwise seem intractable, and by using pure arithmetic.
The function must be infinitely differentiable, which is a calculus concept. I’m going to try to explain it, but if you don’t want to know it won’t hurt you not to know…much. You may want to skip the next few paragraphs…I’ll put bold where it’s safe to pick up so you can scan for it.
Basically, if you have a function like sinx which is shown below with x in radians.
…you can create another function that gives the slope of sin x at any given point. So what would such a function look like? Well, when x is zero, the slope of the wiggly line is just about 1. Which is to say, right there at x = 0, it’s climbing at the rate of one square vertically for every one unit to the right (in radians). Our new “slope of sin x function” has a value of 1 at x = 0. At π/2 (or 90°), the curve of sin x is level, so the slope is zero. At π, the slope is -1. At 3π/2, it’s zero again. And at 2π, it’s back to being 1 again.
We already know of a function that has these values at these points. It’s the cosine of x. Is that a coincidence? Actually, no. It turns out (after a lot more proof than I am going to show you), that the “slope of sin(x) function” is indeed cos(x). Now for some terminology; the correct way to phrase this is “the derivative of sin(x) is cos(x).”
You can repeat this exercise for cos(x), and you will get -sin(x). So the derivative of cos(x) is -sin(x). But cos(x) is already the derivative of sin(x), so the derivative of the derivative of sin(x) is -sin(x). But we don’t want to say “the derivative of the derivative of..” so we call that the second derivative.
Unsurprisingly, the derivative of -sin(x) is -cos(x). And the derivative of -cos(x) is back to sin(x). In other words, you can keep taking the derivative of the derivative of the derivative…forever. Kind of boring.
But that’s what it means to say that sin(x) is infinitely differentiable. With most functions you’ll eventually end up with a derivative that’s zero for all values of x, and then you’re done. But not with sin(x) and also (since it shows up in the chain) not for cos(x).
Which means that sine and cosine are infinitely differentiable and we can use the Maclaurin series on them.
(OK the calculus-averse are back with us now, and we can continue.)
So here is the Taylor series of any function, f. The idea is to pick a central point, a, and then compute the value of f for some nearby x. Note that all of the terms have x–a in them; you get closer if x is very close to a.
If a is zero, it becomes the Maclaurin series:
And the tick marks denote the first, second, third, and four derivatives.
The 1!, 2!, 3! etc are factorials. You get a factorial by multiplying the number by every smaller number down to 1. So 4! is 4 x 3 x 2 x 1. (Practically, of course, you don’t bother multiplying by 1.)
So if we set a equal to zero (we’re going to be interested in values for x close to zero), the formula can simplify.
I pointed out in the section you skipped over that the first derivative of sinx is cosx, the second derivative is -sinx, the third derivative is -cosx, the fourth derivative is sinx again, and so on…the cycle repeats.
But we know that the sin(0) is zero, and so is -sin(0). So we can simply throw a bunch of these terms out (and as I do so I’ll bring in more terms from where the ellipsis was)
And the others (cos(0) and -cos(0)) can be replaced with 1 and -1 respectively, so simplifying:
sinx = x – x3/3! +x5/5! – x7/7!…
This is a nice pattern. Every odd power of x, divided by the factorial of the power. Every other term gets a minus sign. The further you carry it out, the more accurate you will be. Also, the closer to zero x is, the more accurate it will be, but you can always just carry it out further if x isn’t very close to zero, to make up for it. If you can follow this infinitely far, you can get the correct answers for numbers very far away from 0, as far away as you like.
Here is a graph of sinx, along with a graph of what you get out of the Maclaurin representation taken to the x7 term.
As a practical matter you do not need to go past x=π/2, because the function makes the mirror-image curve going down to π as it did climbing to π/2. So the sine of 89° is the same as the sine of 91°, and so on. And the stretch from π to 2π is also a mirror image, except flipped vertically. After that, it repeats. So even though you can see some difference at x = π, and a lot of difference at 2π, you can probably get everything you need from the range 0 to π/, where this is pretty close.
So you can get pretty close with this function, between –π/2 and π/2. I’ll repeat it with the factorials written out:
sinx is roughly equal to: x – x3/6 +x5/120 – x7/5040.
Certainly the brain inside a calculator should be able to do that very quickly! And so, that’s probably what it does. It might go out one or two more terms:
x – x3/6 +x5/120 – x7/5040 + x9/363,880 – x11/39,916,800
But you can see if x is small you’re not going to get much change from the x11 term.
So let’s do the same thing for cosines. Now when we go back to the MacLaurin series, everything shifts over, it starts with cosine, then -sine, then -cosine, then sine.
And now we know that the cosine of zero is 1, and the sine of zero is zero, so:
cosx = 1 + –x2/2! + x4/4! + –x6/6! + x8/8! +…
So here we have a pattern oddly like, but oddly unlike, the sine version. Now it’s the even powers of x (including x0 = 1) that show up, again with alternating signs.
And we have:
cosx is roughly equal to: 1 – x2/2 +x4/24 – x6/720 + x8/40,320.
So we can get increasingly accurate. Because, remember sine and cosine swap at 45 degrees. The sine of 60° is the same as the cosine of 30°, so if you want the sine of 60°, compute the cosine of 30° instead; your answer will be closer. (Needless to say first, convert to radians!) So we really only need these series to be accurate enough for whatever our purposes are, to 45° or π/4 radians.
Next time: I pull a mathematical rabbit out of my hat!
Obligatory PSAs and Reminders
China is Lower than Whale Shit
To conclude: My standard Public Service Announcement. We don’t want to forget this!!!
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 !!!
Today, it is still the case that Joe Biden didn’t Win.
I realize that to some readers, this might be a shock; surely at some point things must change and Biden will have actually won.
But the past cannot actually be changed.
It will always and forever be the case that Joe Biden didn’t win.
And if you, Leftist Lurker, want to dismiss it as dead white cis-male logic…well, you can call it what you want, but then please just go fuck off. No one here buys that bullshit–logic is logic and facts are facts regardless of skin color–and if you gave it a moment’s rational thought, you wouldn’t either. Of course your worthless education never included being able to actually reason–or detect problems with false reasoning–so I don’t imagine you’ll actually wake up as opposed to being woke.
As Ayn Rand would sometimes point out: Yes, you are free to evade reality. What you cannot do is evade the consequences of evading reality. Or to put it concretely: You can ignore the Mack truck bearing down on you as you play in the middle of the street, you won’t be able to ignore the consequences of ignoring the Mack truck.
And Ayn Rand also pointed out that existence (i.e., the sum total of everything that exists) precedes consciousness–our consciousnesses are a part of existence, not outside of it–therefore reality cannot be a “social construct” as so many of you fucked-up-in-the-head people seem to think.
So much for Leftist douchebag lurkers. For the rest of you, the regular readers and those lurkers who understand such things: I continue to carry the banner once also carried by Wheatie. His Fraudulency didn’t win.
Let’s Go, Brandon!!
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 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.)
Tranheuser Busch
Those asshats either get the world, all time record for obtuseness…or this is deliberate somehow. And their namby pamby non-apology that amounts to a “We’re sorry you’re too much of a knuckledragger to appreciate what we did” simply underscores the stupid. It’d be like a 400 pound golfer wearing spikes tromping on your instep and being utterly clueless why you are screaming in pain.
Me
I wrote that months ago, and they are casting about now trying to figure out how to get people to come back. However the one thing that might work (an abject admission that they were wrong to even think of doing this) is the one thing they cannot do. Because the decision makers are woke and cannot conceive that they were actually fuckheadedly wrong to do this.
Gold and silver still farting about in roughly the same places. Someone with a big futures presence can make some money off of these moves…some poor guy who bought physical metal a few months ago ain’t making squat (it has to rise enough to cover the buy/sell spread, which can be pretty wide). PGMs mixed.
More on Sines and Cosines
As you may have realized, I generally start to write a post by copying the one from five weeks earlier and modifying it…that way I can recycle my eagle pictures. (Right now that’s six weeks, because the Darwin Memorial Post doesn’t have an eagle on it.)
So I get to see an older science (or math) post of mine and I will sometimes read through it. When I did that this time I found multiple typos (not so bad) and also one glaring arithmetic error…that no one one called me on. (I’ve gone and fixed it.)
Makes me wonder.
Anyhow, we left off realizing that a complex number can be thought of as representing an angle, and that multiplying any complex number (including those that are pure real or imaginary) by another complex number, produces a complex number that represents the sum of the two angles. If one of the complex numbers has a magnitude of 1, the effect of the multiplication is to simply rotate the other number by the first number’s angle.
OK, those sentences were a bit complicated, so let’s show some examples: Take two complex numbers:
A = <a, α> B = <b, β>
The first complex number A, is a units long at an angle of α radians, and similarly for B. (And a quick reminder. For clarity, I’m using angle brackets to indicate polar coordinates–a distance and an angle–but this is not any kind of standard notation.)
If you multiply those two complex numbers together, you get <ab, α+β>. The magnitudes get multiplied, the angles get added.
If b just happens to be 1, then you have an answer of <a, α+β>. In other words multiplying by B just means rotating A by the angle β.
And if both a and b are 1, you are simply adding the angles together to get another answer that has magnitude 1; it’s a pure rotation.
As I said before this is not just a geek parlor trick; it underlies much of electrical engineering.
Also discussed, a lot, last time were the sines and cosines of angles. I stated that some angles have obvious sines and cosines. For example, zero degrees measured on the unit circle has no y value, so its sine is clearly 0. And it’s x coordinate is 1, so the cosine is 1. Similarly 90° or π/2 radians is pure y coordinate with no x component, so its sine is 1 and its cosine is 0. You can easily figure out 180° and 270°, and of course 360° is the same as 0°.
But those aren’t the only obvious angles. 45° (or π/4 radians) is another obvious one. Why? Because you know the x and y coordinates of 45° on the unit circle are the same number, so it forms an isosceles right triangle…the two “legs” (the sine and cosine of 45°) are the same.
You can then get the rest of the way with Pythagoras. Squaring the two legs gives you the same number too, and the hypotenuse is 1:
12 = (sin(45°))2 + (cos(45°))2
But the cosine and sine are equal so just replace cosine with sine (and 12 with 1):
12 = (sin(45°))2 + (sin(45°))2 1 = 2(sin(45°))2
Dividing through by 2 we get:
½ = (sin(45°))2
Taking the square root of both sides:
√½ = sin(45°) = 1/√2
So we know that the sine of 45° or π/4 radians is one divided by the square root of 2.
But you do not want to divide by an irrational number if you can possibly avoid it, because they have an infinite number of digits, so think about writing that one out doing long division…you’re going to be multiplying long numbers a lot and subtracting them too.
So for historical reasons mathematicians never let a square root sign be in the denominator. You fix this by multiplying top and bottom by that number:
(√2 x 1) / (√2 x √2) = √2/2
Which works out to roughly .707.
So if you’ve done trig for any length of time when you see 45° (or 135°, or 225°, or 315°) you just automatically know the sine and cosine will be 0.707 (or -0.707).
You can use similar reasoning for 60°. That angle is the angle for an equilateral triangle, one where all three sides are the same length, and all three angles are 60°. So the origin (0,0), the (x,y) for 60 degrees on the unit circle, and (1,0) form an equilateral triangle. But the (x,y) are just (cos(60°), sin(60°)). The top angle of the triangle is half as far to the right as 1,0 is, so cos(60°) must be 1/2. You can then use Pythagoras on half of the equilateral triangle to show that the sine must be √3/2, or about .866.
(I must apologize for this diagram, it only shows half of the equilateral triangle. I found that any diagram that showed the whole triangle made the sides of length 2, and I thought that would be even more confusing than this diagram is.)
For 30° you have a mirror image of 60°, and you can swap the sine and cosine.
OK, what about the other angles?
Not every problem you’re going to want to solve with trig is going to involve one of these angles. In fact, if one ever actually does find oneself doing these angles, one is probably working a story problem!
It turns out that there are formulas for computing the sine (or cosine) of half of a given angle. So you could find the sine and cosine of 15° by running the formulas on 30°, and you could get the sine and cosine of 7.5° by running the formulas on that. You can get as small an angle as you like by repeatedly doing half angles. And then you can add those angles together in some combination with other formulae. For instance to get the sine and cosine of 11 1/4 degrees, run the addition formulae on the sines and cosines of 7.5° and 3.75°.
Actually you know how to do the addition formula: just turn the angles into complex numbers and multiply them together. The real part is the cosine of the sum of the angles, the imaginary part is the sine of that same sum.
Many people spent countless hours building up tables of sines and cosines this way, and back in those days they had to work longhand multiplying six digit numbers together just to get halfway decent results after rounding, and reusing the rounded numbers to do the next computation.
But there IS another way. It may not be easier but you can go directly to the sine and cosine of the angle you want instead of having to build off of other, known numbgers. So maybe it is easier because you could compute the sine and cosine of 11.25° directly instead of first computing the sine and cosine of 7.5° and 3.75°.
And I want to tell you what it is, and I was planning to do so tonight, but for some reason the Wordpus editor is slowing down on me more and more, and I’ve already restarted Firefox four times. It’s now slow enough that backspacing over one letter takes a second or two. And I have to wait for it to catch up as I type.
So I’ve run out of patience. Next time, the direct way to get a sine or a cosine. A hint: the sine and cosine are “infinitely differentiable.” (Not much of a hint, for people who haven’t taken calculus.)
Obligatory PSAs and Reminders
China is Lower than Whale Shit
Remember Hong Kong!!!
Whoever ends up in the cell next to his, tell him I said “Hi.”
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 !!!
One of my stock jokes is to say, as I head off to the bathroom or washroom or restroom, “I’m going to go make a political statement.”
It certainly seems like urinating is a good way to make a statement about the YSM, and defecating works for politicians. Or the other way around is good too, though “#1” just never seems emphatic enough.
Maybe “#1” is just being polite, and “#2” is telling the fixtures what you really think.
Anyhow, I pretty much do plan to be polite to RINOs that electioneer or fundraise. I’ll tell them, Sorry, but I need to GO Pee…
The Twenty Stand-Up Shitbags (Plus Five More Who Were Just Cowardly Shitbags)
Twenty were stand-up shitbags, who actually voted against punishing Adam Schitt, leaving no doubt where they stood. Five more voted present or were sure to be elsewhere…effectively helping shut down justice, but without being overt about it.
At least the first 20 weren’t weasely about it; we know how the insides of those bags stink.
But it won’t work, you Cowardly Five. We’re onto you.
But then…
I read something in the YSM today that suggested that the 20 who voted against censuring, ejecting. and fining Adam #2 (see above if you’re wondering who Adam #1 is–there isn’t one) were mostly concerned about the constitutional propriety of the fine.
OK, fair enough. I can actually see that being an issue; one I’d want to hear arguments on, pro- and con-.
We’ll get some clarity as to the real reason soon. Next week will be a simple censure motion. I’d like to see the little pencilneck turd kicked out as well, but let’s see how “The Twenty” vote this time around.
Language Warning
In the next piece I had to discuss a particular topic. Unfortunately, I couldn’t discuss it without naming it. Therefore I apologize in advance for having to do so, and apologize to anyone offended by the sight of the name.
RINO McDaniel
RINO McDaniel continues to infest the GOP. But RINO McDaniel isn’t the problem.
Let me be crystal clear on this, RINO McDaniel is a lower-than-whale-shit, piss guzzling ratfucking shit eating traitorous rancid syphillitic cunt. Her worth as a human being is substantially less than zero, any oxygen sucked into her lungs is wasted, and it would be, no matter what job she had.
I fear I haven’t been clear enough, but that will have to suffice.
But she is not the problem…or rather, she would not be a problem were it not for others. She’d still be as I have described, but we wouldn’t know who she is and would not care, because she could do no damage. She’d just be anonymous human refuse.
No, the real problem is the fact that a majority of the 168 top GOP people voted for her. And now that has happened five times so they cannot claim they didn’t know what she was.
In spite of the fact that under her “leadership” the party has deliberately sabotaged the will of its base, has deliberately refused to challenge blatant election fraud, had gone out of its way to ensure certain candidates do not get nominated, has diverted donor money to namby-pamby candidates who have all the electoral appeal of a puddle of dog vomit…and in general has done nothing whatsoever to help fix the problems that plague America.
However that last is to be expected; I cannot expect anyone who IS the problem to help FIX the problem.
RINO McDaniel would be powerless without an entire party leadership of the same mind as her. They want this dismal performance; they want to ignore the party base.
If she were to drop dead this instant, it would solve nothing as someone just like her would be elected by those same pustulous people.
According to Charlie Kirk, about 55 people voted against her, 10-12 wanted something different but were too chickenshit to do the right thing, and roughly 100 people voted for her enthusiastically, and even had the unmitigated gall to complain to Kirk about US. Fuck ’em. Rusty 12 gauge bore brushes would be too good for these arrogant pricks and cunts.
Every single one of those hundred is just as bad as she is. In other words, they are all worse than I described at the beginning of this piece. And no doubt those people in turn have people who supported them to be state party chairs and whateveritis they call the other two people from each state and territory who were voting.
It’s time to face up to the fact that the Republican party is effectively owned by the shit-eating RINOs. We’ve got more work to do, a lot more work, to make the GOP an instrument for the restoration of the United States of America. And that’s in addition to cleaning up our elections.
There’s no point in cleaning up elections just to elect ratfucking RINOs.
OK, hopefully now you will have some inkling of my true attitude towards RINOs. Sorry that words were inadequate to give you the full picture.
The Real Fascist is His Fraudulency Joe Biden*
*Or whoever has his hand rammed up that meat puppet’s ass.
Brandon (which I will use as a term for whoever is the power behind the Porcelain Throne) has thrown down the gauntlet…but in a way where most of America will never see it. The networks didn’t carry his tirade. CNN air brushed it (or whatever you call editing the red background) for its five viewers (who aren’t trapped in airports).
Luckily for me I live in Colorado, and therefore, despite my best efforts, I probably didn’t vote for Donald Trump.
Of course, for this purpose who I actually did try to vote for will be essential, and they undoubtedly know.
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.
Small Government?
Many times conservatives (real and fake) speak of “small government” being the goal.
This sounds good, and mostly is good, but it misses the essential point. The important thing here isn’t the size, but rather the purpose, of government. We could have a cheap, small tyranny. After all our government spends most of its revenue on payments to individuals and foreign aid, neither of which is part of the tyrannical apparatus trying to keep us locked down and censored. What parts of the government would be necessary for a tyranny? It’d be a lot smaller than what we have now. We could shrink the government and nevertheless find it more tyrannical than it is today.
No, what we want is a limited government, limited not in size, but rather in scope. Limited, that is, in what it’s allowed to do. Under current circumstances, such a government would also be much smaller, but that’s a side effect. If we were in a World War II sort of war, an existential fight against nasty dictatorships on the brink of world conquest, that would be very expensive and would require a gargantuan government, but that would be what the government should be doing. That would be a large, but still limited government, since it’d be working to protect our rights.
World War II would have been the wrong time to squawk about “small government,” but it wasn’t (and never is) a bad time to demand limited government. Today would be a better time to ask for a small government–at least the job it should be doing is small today–but it misses the essential point; we want government to not do certain things. Many of those things we don’t want it doing are expensive but many of them are quite eminently doable by a smaller government than the one we have today. Small, but still exceeding proper limits.
So be careful what you ask for. You might get it and find you asked for the wrong thing.
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).
A Few Things We Cannot Blame on His Fraudulency
I am pretty sure Joe Biden had nothing whatsoever to do with the 30 Years War that ran from 1618-1648 and probably killed about a third of the people then living in what is now Germany.
Nor did he cause the collapse of either Roman empire (Western, 476 CE, Eastern 1453 CE). Nor the ignominious failure of most of the Crusades. Nor the collapse of Bronze Age civilization around 1200 BCE (including the collapse of the Minoans and the blowup of Santorini).
However, my utter lack of ability to imagine how he could possibly be responsible for these things is not a valid argument against them, so I await correction if appropriate.
His Truth?
Again we saw an instance of “It might be true for Billy, but it’s not true for Bob” logic this week.
I hear this often, and it’s usually harmless. As when it’s describing differing circumstances, not different facts. “Housing is unaffordable” can be true for one person, but not for another who makes ten times as much.
But sometimes the speaker means it literally. Something like 2+2=4 is asserted to be true for Billy but not for Bob. (And when it’s literal, it’s usually Bob saying it.) And in that sense, it’s nonsense, dangerous nonsense. There is ONE reality, and it exists independent of our desires and our perceptions. It would go on existing if we weren’t here. We exist in it. It does not exist in our heads. It’s not a personal construct, and it isn’t a social construct. If there were no society, reality would continue to be what it is, it wouldn’t vanish…which it would have to do, if it were a social construct.
Now what can change from person to person is the perception of reality. We see that all the time. And people will, of course, act on those perceptions. They will vote for Trump (or try to) if their perception is close to mine, and vote against Trump (and certainly succeed at doing so) if their perception is distant from mine (and therefore, if I do say so, wrong). I have heard people say “perception is reality” and usually, that’s what they’re trying to say–your perception of reality is, as far as you know, an accurate representation of reality, or you’d change it.
But I really wish they’d say it differently. And sometimes, to get back to Billy and Bob, the person who says they have different truths is really saying they have different perceptions of reality–different worldviews. I can’t argue with the latter. But I sure wish they’d say it better. That way I’d know that someone who blabbers about two different truths is delusional and not worth my time, at least not until he passes kindergarten-level metaphysics on his umpteenth attempt.
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.
Gold barely moved at all, everything else is down except rhodium which moved up by what appears to be the minimum increment (I don’t believe I’ve ever seen a price for it which wasn’t a mulitiple of $50.
So it seems to have been a quiet week, but then again I rarely look during the week.
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 !!!
I’ve had cause to consider a few things. Maybe we’re going about it the wrong way, and we need to ditch Trump
Yeah, NO
Trump all the way! Why? Because being hated by the people who hate him is a sign of impeccable character, that’s why.
The haters can go fuck themselves with rusty twelve gauge bore brushes. I’d prefer ten gauge but that’s kind of scarce, so…I’m willing to compromise.
The RINO’s Dilemma
The RINOs who who have burrowed in and taken over most GOP organizations, from the state down to local organizations, have quite a dilemma on their hands, and most of them have their heads too far up their asses to realize it.
OK, I’m not talking about the liberal in a Republican area, who knows they’re in the wrong party, but is there because it’s the only game in their town; they hope to capture a nomination someday, at which point they’re guaranteed to be elected…otherwise, they never will be. These people are a hazard in any heavily conservative area.
No, I’m talking about the guys who are a little bit conservative and want to do some good by going into politics, and they’re in a closely matched area, closely enough that they can join the party they are most aligned with and still have a chance. They think the Democrats…particularly the ones who end up running for office…are nuts.
They don’t think much better of the Deplorable types, either. A bunch of bumpkins whose hearts are in the right place, mostly…OK a bit extreme. But they think Deplorables can’t understand that first you have to get elected, then work within the system to change things…a slow process. They genuinely want many of the things Deplorables want…just not as much. The government is spending too much. Or they need to spend money on highways instead of welfare for illegal immigrants. But they want to work within the system to get these things done.
Or maybe they think things are pretty close to ideal right now, and they want to nail it in place.
The problem is, that means they don’t stand for anything in particular. And it shows. They’re about as unappetizing to the electorate as a puddle of dog vomit. The folks in the middle, who they think they are appealing to because they themselves are not extreme, would honestly prefer a clear-spoken radical to someone who qualifies everything they say to the point where they sound like they don’t believe anything at all.
The problem these “Mild RINOs” have, is they just can’t see that. And the reason they just can’t see that, is their entire sense of self-worth is tied up in not seeing that. In their minds, they’ve worked tirelessly for their party, to keep those crazy Democrats out…only to have to constantly fight with a small number of crazy Republicans–who are only liabilities if they end up as candidates. They’ve fought the good fight, and if they can just find the right candidate, someone with some charisma, they might stop the crazies…without being too beholden to the OTHER crazies. In the meantime it’s not working. What’s a responsible guy in politics to do?
They simply cannot understand that the Republicans can’t succeed as the party of nothing in particular. Not really in the past, and certainly not today when people are starting to realize that no matter what they do in the voting booth, the country is still about to fly off a precipice. If they did see it, they’d suddenly have two choices: Go away and let the GOP succeed, or stay and fight. But “go away” isn’t really an option, because what’s the point of having a party now owned by the crazies, win?
Well, they have a dilemma…and WE, therefore have a problem. And we would have that problem even IF they realized that they had a problem…that they were the problem.
No one ever thinks they are the bad guy. Even Epstein probably thought he was the good guy. Right up to the moment where he didn’t kill himself.
So if you ever wonder why these unappetizing dufuses cling on even when their fingernails are being left behind…that’s why. They don’t understand no one wants them, and can’t imagine that no one should want them. And oftentimes their greatest pride is in all the hard work they’ve done for the party. They’re not going to give that up; it’d be psychological suicide.
If you’ve worked with these people, there’s a good chance you like them and consider some of them your friends. But even if so…we’re going to have to give them a good, hard shove. Because America is more important than those milquetoasts’ egos.
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.
Gold creeping upward. Other things decidedly mixed, with little movement, prercentage wise. Except of course rhodium which continues its collapse.
Comparing Cartesian And Polar Coordinates
Last week I introduced polar (circular grid) coordinates as an alternative to (and equivalent of) Cartesian (square grid) coordinates.
I also stated that because they’re equivalent either one could be used at any time, so you could pick whichever one was most convenient at the time.
What did I mean by that? Well, hold that thought.
I was talking about x, y pairs last week, but I could just as easily have been talking about complex numbers. Remember they can be represented on a plane that looks a lot like the Cartesian plane, with the real part taking the place of x, and the imaginary part standing in for y. So you can convert complex numbers to polar coordinates, too…but there’s a hitch. The resulting r and θ do not map nicely to real and imaginary, the pair as an inseparable whole is part imaginary and part real. You just have to remember that the thing represents a complex number, and if you want to split it up, you have to convert to Cartesian.
In polar coordinates, r is often called the “absolute value” of the complex number (or you can think of it as the magnitude or length), while θ can be called the “argument.”
Actually…this is not standard notation, but for clarity I am going to surround polar-style complex numbers with angle brackets: < and >
OK, now let’s consider the complex number plane, in both Cartesian and polar forms. And let’s look at some examples.
We’re going to represent a couple of complex numbers in both ways and do two different things to them in order to see which system is more convenient for each of those things.
The first example number we will call A, and in Cartesian form, it is 1+i. Converting to polar coordinates, it’s <√2, 45°> or <√2, π/4> depending on whether you’re thinking in degrees or radians.
The second pair is B and in Cartesian coordinates, it is √3 + i. Converting to polar coordinates, it’s <2, 30°> or <2, π/6>, depending.
[Angles like 30°, 45° and 60° degrees are the “easy” angles in trigonometry because their sines and cosines are well known and fairly simple; the sine of 30° is 1/2, the cosine is √3/2. For 45° both the sine and cosine are √2/2. For 60°, swap the sine and cosine of 30 degrees. Other easy angles are 0 and 90°, plus of course any corresponding angles in the other quadrants of the plane, e.g. 120° is simply the mirror image of 60° so its sine and cosine are going to be the same except for the cosine changing sign to -1/2. People who have been doing trigonometry for very long simply know these angles, and their matches in other quadrants, off the tops of their heads. So (returning to our two example complex numbers), A is at 45° but its length is clearly not 1 since both the x and y (real and imaginary) values are 1. We can get the length from Pythagoras, though, x2 = 1 and y2 = 1, so the hypotenuse (the length of A) squared is 1+1=2, so the length of A is √2. For B, I simply doubled the well-known sine and cosine of 30°, so I’ve got a 30° angle and a length of 2.]
OK, let’s add A + B. That’s easy to do in Cartesian coordinates, it will be (1+√3) + (1+1)i. (If you remember vector addition from the physics series, this works exactly the same; you can even treat the two numbers as if they were vectors and do a tail-to-head visual addition.) So what do we get in polar coordinates? Well, it’s not obvious how to add things in polar coordinates…but let’s convert the sum into polar coordinates just to see if some sort of pattern suggests itself. Doing so, we find that 1+√3 + 2i converts to <3.3859, 36.206°>…approximately.
Yuck.
There’s no obvious way to get from <√2, 45°> + <2, 30°> to get <~3.3859, ~36.206°>. Not even if you write 1.414… for √2. You can add 1.414… and 2 and get 3.414…but that’s different from 3.3859. It’s close but not close enough. In fact if you actually did do a tail-to-head vector addition diagram, you saw why. The two “vectors” are in almost, not quite the same direction, so the sums of their lengths is not that much greater than the length of their sum. But it’s not the same. And of course the angle 36.206° has no obvious derivation from 45° and 30°. It’s not halfway in between or anything like that.
So it seems that, if you want to addx, y pairs, or complex numbers in Cartesian form…you’d better leave them that way. Adding those is easy. Adding r, θ pairs looks a lot more complicated. So, for addition, the Cartesian form is most convenient.
How about multiplication? Multiplication is defined for complex numbers (but defining it for vectors gets a bit dicey). Okay, so let’s do the multiplication.
(1 + i) x (√3 + i)
Remember for complex numbers, you use “FOIL” (first, outside, inside, last), a generalization of the rule that you multiply everything in the first vector, complex number, or whatever, by everything in the second, then combine like terms.
1 x √3 = √3 (first) 1 x i = i (outside) i x √3 = √3i (inside) i x i = -1 (last)
Gathering like terms together, we have (I’ll put parentheses around the real and imaginary parts for clarity):
(√3 – 1) + (√3+1)i.
This seems kind of almost-symmetrical, but it’s a mess, actually.
OK. It’s not obvious here how we’d use polar coordinates to multiply, so let’s just convert the answer and see what pops out.
The first component, r, is going to be the square root of the sum of the squares of the real and imaginary parts. That’s basically Pythagoras, r2 = (real part)2 + (imaginary part without the i)2
(Note that we don’t include the i in the squaring because we are trying to assess the sizes of the sides of the triangle, and those are all real numbers.)
And lo and behold the 2√3’s cancel and we’re left with r2 = 8 = 4×2, so r = 2√2. Which is sort-of tidy. And the angle turns out to be (I won’t show the work, but I pushed it into a calculator even though I know the answer already because…well, you’ll see): 75°.
Exactly 75°.
OK now set <2√2, 75°> next to the polar version of the two pairs we were multiplying and see if anything strikes you as a pattern.
<√2, 45°> x <2, 30°> = <2√2, 75°>
Now if this were a video, I’d either wait a while or ask you to pause it and think about it.
But really…look. The rs multiplied, √2 x 2 = 2√2…and the angles added.
Geez, that is a lot less tedious than FOIL. In fact it’s almost as easy as adding the numbers is in Cartesian mode!
As it turns out, multiplying any complex number, by some other complex number, gives you another complex number with magnitude equal to the product of the two numbers, and angle the sum of the two angles. Or you can think of it as rotating the first number by the angle in the second, and then multiplying the two magnitudes.
So which mode is more convenient for multiplication? You’ve got it: the polar mode.
And as an extra bonus, we have a way to rotate a complex number. (And similar ways to rotate vectors.) Multiply it by another complex number with the desired angle. And unless we want the magnitude to change, make sure the “rotator” complex number has magnitude, r, equal to 1.
A “rotator” complex number like that will have, as its real component, the cosine of the rotation angle, and as its imaginary component, the sine of the rotation angle. Or in other words, <1, θ> a/k/a cosθ + isinθ will, by multiplication, rotate another complex number on the complex number plane by the angle θ.
This may seem like nothing more than a parlor trick for geeks, but it turns out to be very, very important in the technical realm, particularly with electrical and electronic engineering. Whatever it is you’re reading this on, ultimately depends on this fact.
OK that’s enough for now!
Fuck Joe B*d*n
Due to complaints about foul language, I’ve censored the most objectionable word in the title of this section.
B*d*n, 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.)
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 !!!
I went to a reptile show in Denver on November 11, 2018, quite coincidentally the 100th anniversary of the end of World War I. There were a fair number of bearded dragons for sale there, but I didn’t want a really tiny, young one; it sounded like there were too many ways for them to come to harm. I opted for one about 5 months old, one who seemed to be a mix of green, yellow and orange, without being too garish. At the time he was approximately 14″ long including an unusually long tail for a bearded dragon. (He would eventually reach 21 3/4 inches. Some told me if they hadn’t actually seen him, they would have thought the long tail was a photoshop.)
A wild bearded dragon’s color is generally a mix of grays and dull tans, though the pattern is fairly intricate. But reptile breeders love to select for very unnatural color schemes. Red like flaming hot Cheetoh. Bright yellow like a lemon. Or even an albino. Or different skin textures, such as silky smooth, instead of very rough. (The spikes along the sides are actually pretty soft, but the skin naturally feels like rough grit sandpaper.) They give all of these morphs (and others I haven’t described) names.
I didn’t go too outrageous on the color…I could almost imagine Darwin’s color being decent camouflage in central Australia. That’s where his particular species (one of eight bearded dragon species, and by far the most common of the eight in the pet trade) is from. And it turned out the green coloration is an illusion; he often exhibited spotty gray coloration which when in close proximity to the yellow, looks a drab greenish. When he was upset the gray color would disappear leaving him looking a drab yellow on the head where there is no orange.
It turned out that my lizard was a “hypo, orange tiger stripe dunner.” (Hypo simply meant hypomelanistic, and the prime indicator is clear, rather than black, claws. Dunner has to do with the pattern of scales on the belly.)
I named him Darwin, not after Charles, but after the city of Darwin in Australia, which got its name from the bay it is on, which in turn was named that in the 1830s. Since Charles didn’t become famous until 1859 with the publication of Origin of Species, I concluded the city was not named after him.
Darwin on his first day at my house. Notice the S the seller put on him to mark him as having been sold to me, while I went and visited the rest of the reptile show. (It came off the first time he shed.)
I was wrong. The city was named by the crew of the HMS Beagle, after Charles Darwin who had been on the ship collecting the specimens that would eventually lead him to knowledge of evolution by natural selection. Apparently they had liked him well enough to name places after him–well before he was famous.
Darwin, this time I mean the lizard, had one thing in common with Charles. He was very likeable. To hell with “Everybody Loves Raymond.” Everybody loved Darwin.
A few weeks later, he went through an almost complete shed, starting with his head. He looks for all the world as if he’s disgusted with the fact that his head just exploded.
It is easy (though painful) to eulogize him; there’s no mentally editing out bad personality traits with a “let’s not talk about that” or a “maybe I can make a joke of this.”
Later on during the same December 2018 shed, on his basking rock. Beardies will sometimes get rid of excess heat by opening their mouths, as shown here. To the right you can see the “reverse cape” of the skin that came off. That was the only time he ever shed that much, all at the same time.
Darwin did have a personality, contrary to those who diss reptiles as not having personalities. In fact, his personality was better than that of most people–a sentiment echoed by a condolence card I received after I wrote the first draft of this.
I could show pictures of him on my office chair (or keyboard) during the early COVID lockdown (it was designated “take your lizard to work week” in this house) and people would spontaneously tell me on the basis of the photographs alone that they had never seen such personality in a lizard.
Weirdest cat I ever saw.What’s down there?
I could take him to street markets, perched on my shoulder and people would be delighted to see him, he was a favorite of kids.
Of course the downside is he sometimes proofread my posts.
“Steve, you don’t actually mean that, do you?”
The people at the vet’s office loved Darwin too; they’d fawn over him more than they would most people’s dogs.
His picture is posted in four locations in this county, one a business whose owner would be appalled to find I actually write for a “Trumper” site like this. He’s the unofficial mascot of that store.
Early 2021
Or rather, he was.
A few months ago I noticed he was having trouble with his back legs, which were swollen. I called for an appointment at the vet, and had to wait a month.
The news was grim. He almost certainly had kidney cancer; it was hugely swollen in the ultrasound. However, there was one dim hope: It might only be a kidney infection.
So began a course of fifteen antibiotic shots, two every week. After the fifth shot, though, there would be evaluation, and if there were no improvement, well, it would be the time for that “quality of life” discussion.
An image taken the day of the evaluation trip to the vet…when I thought he might end up being put down. Note how swollen the rear ankle is. He had no use of his rear feet then though at least he could move the leg as a whole by this time.
Well, wouldn’t you know, it seemed to be working. The vet was ecstatic; he truly thought the infection was very unlikely, but since it was treatable and the cancer was not, it had been worth the gamble.
And even though I don’t like driving to the part of town the vet is located at, I was overjoyed to hear I’d be doing it ten more times for the rest of the shots. (I couldn’t get the hang of injecting him. The vet could do it without Darwin even noticing; in my case he’d try to get away from my attempts.)
So we went through the ten remaining shots, and scheduled a follow up for a month after the last shot; that follow-up was this past Thursday.
A week ago I noticed Darwin wasn’t climbing to the top of his basking rock. Basking is a necessity for many reptiles, it helps them digest their food. Now, instead of his rear legs being useless, it was his front legs…which I tend to call arms when I’m not thinking, as he grasped with those feet (“hands”).
And his appetite was off.
He was basically unable to lift himself off the ground. Whereas before he could drag himself up the basking rock with his front legs, he couldn’t do that now with no motion in those legs.
I thought this might be any one of the bugs and other micro-critters that sometimes infest the digestive tracts of reptiles (some of them can get us too: pinworms, for instance). He’d had a lot of difficulty with those in the past. He left me with a sample of well, you know, on Monday which I duly collected and refrigerated, knowing the vet could check it over. (He very uncharacteristically deposited it inside his hide, rather than onto his basking rock. And didn’t move after he left it.)
Alas this past Thursday the verdict was…”And” logic. He had had an infection and cancer. And with the infection gone, the cancer was progressing rapidly now.
It was time to make The Decision. So at roughly 4PM on Thursday, Darwin–who brought a smile if not joy to everyone he met, even to people who don’t like lizards–Darwin was no more.
His light, small as it was, has left this world of gathering darkness.
The photograph at the top of the post is of Darwin being held by a tech at the vet’s office, less than an hour before he was put to sleep. The mere fact that his front legs aren’t gripping something should tell you how bad it was.
I have other pictures of him on the table, and him being held on, then on me.
He found the strength to move from my arm partway onto my chest (which he liked to do), even five minutes before he took his last sleep.
Things up a bit, especially gold. Gold was down for the day on Friday, so clearly Thursday’s numbers were even higher. Silver closed up one cent versus Thursday.
Obligatory PSAs and Reminders
References to our opponents as “Lizard People” are officially in poor taste today.
Darwin had ten million times as much personality as they do.
And not one shred of evil.
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 !!!
Just remember…we might replace the RINO candidates. (Or we might not. The record is mixed even though there is more MAGA than there used to be.) But that will make no difference in the long run if the party officials, basically the Rhonna McDaniels (or however that’s spelled–I suspect it’s RINO), don’t get replaced.
State party chairs, vice chairs, secretaries and so on, and the same at county levels, have huge influence on who ultimately gets nominated, and if these party wheelhorses are RINOs, they will work tirelessly to put their own pukey people on the ballot. In fact I’d not be surprised if some of our “MAGA” candidates are in fact, RINO plants, encouraged to run by the RINO party leadership when they realized that Lyn Cheney (and her ilk) were hopelessly compromised as effective candidates. The best way for them to deal with the opposition, of course, is to run it themselves.
Running good candidates is only HALF of the battle!
SPECIAL SECTION: Message For Our “Friends” In The Middle Kingdom
I normally save this for near the end, but…basically…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…
Biden Gives Us Too Much Credit
…we can move on to the next one.
Apparently Biden (or his puppeteer) has decided we’re to blame for all of the fail in the United States today.
Sorry to disappoint you Joe (or whoever), but you managed to do that all on your own; not only that, you wouldn’t let us NOT give you the chance because you insisted on cheating your way into power.
Yep, you-all are incompetent, and so proud of it you expect our applause for your sincerity. Fuck that!!
It wouldn’t be so bad, but you insist that everyone else have to share in your misery. Nope, can’t have anyone get out from under it. Somehow your grand vision only works if every single other person on earth is forced to go along. So much as ONE PERSON not going along is enough to make it all fail, apparently.
In engineering school we’re taught that a design that has seven to eight billion single points of failure…sucks.
Actually, we weren’t taught that. Because it would never have occurred to the professors to use such a ridiculous example.
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.
Kamala Harris has a new nickname since she finally went west from DC to El Paso Texas: Westward Hoe.
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.)
A Side Rant (not my main science post)
I’ve seen multiple articles now (including one on Friday) that played fast-and-loose with the terms “rare earth element” and “rare earth metal” that I am going to just try (futilely) to set the record straight.
The two articles, one an old one that keeps regurgitating itself on the internet that called lithium a rare earth, and one recently that implied gallium was a rare earth, are the sort of thing that try to sound educated, but the analyst gets some basic facts right. Which is a shame because in both cases the basic conclusion is right. Whether certain metals are rare earth metals or not, it’s nevertheless a really bad idea to rely on China to supply them.
Unfortunately if these guys get this basic fact wrong, many of the other facts they bring to their argument are also suspect, and I’d hesitate to use them in an argument. Which means I can’t use their articles as sources to try to convince someone else that we shouldn’t trust China (because…I seem to recall someone saying China is Asshole).
OK, exhibit One: the periodic table:
Note the coloration, representing different groupings of elements. Red and Orange are the Alkali Metals and Alkaline Earths, respectively. Combined, they are called the “s-block” for reasons I’m not going to go into now. Helium, on the upper right, is also really in the s-block. Note the s-block is 2 columns wide. Over on the right you see another tall area with purple, blue and a green triangle stairstepping downwards. This (minus helium) is the p-block. It’s six columns wide. In the middle you have a great swath of yellow, ten columns wide, it’s the d-block.
That just leaves the bunch at the bottom, which is fifteen blocks wide and called the f block.
In fact, the F block should be wedged in between the s and d blocks, but then you’d have a very wide table and the way it’s done here it fits on an 8½ x 11 sheet of paper or in a book. But I won’t let that stop me, here’s an example.
In this case the S block (other than helium, top right) is blue, the p block is orange (and so is helium), the d block, red, and the f block, green. Note that in the first table, Lu and Lr are in the footnote; but in this diagram, they are directly under Sc and Y in the red block.
Another way to wedge the f block in is shown here:
This is a lower-res image, and color coded quite differently, but you can see they put La and Ac under Sc and Y in the third column. So, basically, the two blank boxes in the first diagram either get replaced by the last column of the footnote, or the first, respectively; and the rest of the columns are dropped in to the left or right of this, as appropriate. If you go with the last diagram, the d block gets split up.
Either way, when you do wedge the f-block in, one of the columns in the f block would fit right under Sc (scandium) and Y (yttrium) at the left and side of the d block, so the f block ends up being fourteen columns wide, not 15. One of the fifteen columns is really in the d block.
Note there’s a sequence: s, two columns wide, p, six columns wide, d, ten columns wide, and f, fourteen columns wide. Each is four more than the one before it. It’s likely the next (undiscovered) row of the table will include a g block with eighteen columns in it (and it will probably fit between the s and f blocks).
OK with that backdrop, let’s talk about the rare earth elements.
The rare earth elements are basically: the top row of the f block, plus the the column with Y, Sc, and either La or Lu in it.
[Scientists until recently argued over which elements belong under yttrium. It was one of those “is Pluto a planet” type debates, and they settled on Lu and Lr being under Sc and Y…in other words like the first, rather garishly colored long table I showed.]
The rare earth elements are sort of like the Holy Roman Empire. The holy Roman Empire was neither holy, nor Roman, nor an empire. And the rare earths aren’t particularly rare in the larger picture, nor are they especially earthy compared to the other elements. (What does that even mean, anyway?)
If you were to grab a notional “average” pile of dirt–average in composition for the entire crust of Earth, that is–and sort it, atom by atom, after you were done, you’d have more of some of the “rare” earths than copper (by weight, not necessarily the number of atoms). Some of the other “rare earths” are quite a bit more scarce but with one special exception that’s due to other factors, all of them would show up far more often than gold or platinum, in fact even silver would be rarer than any of them (see chart below). The rarest “rare earth” (thulium) would be 0.52 parts per million, while the commonest, (cerium) would be 66.5 parts per million. This is not rare when you consider gold, platinum and the like are down in the single-digit or even fractional parts per billion.
In fact chemists sometimes try to school themselves not to use the name “rare earth” at all, since it combines one column of the d block, with one row of the f block.
OK, so where did this name come from? Let’s start with “earth.” These metals began to be discovered in 1787 and originally they showed up as oxides because that was the mineral form, and the chemists of the time couldn’t break those molecules apart. This was before Lavoisier brought order to the naming of compounds, too, and the term for what we now call a metal oxide, was “earth.”
OK, so why “rare” then? Well they did seem “rare” at the time, for reasons I’ll get to. And they’re also oddballs. Some history:
In 1787 a new mineral was discovered in Ytterby, Sweden, and named ytterbite after the town. A sample was sent to chemists at the Royal Academy of Turku, and there was a new “earth” in it; implying there was a new metal in it. The earth was named yttria, and the metal, yttrium (symbol Y). But then things started to get weird.
The more chemists played with this and a few other discoveries of similar minerals around the world, the more elements they kept finding. They were very chemically similar so hard to separate out, and it seemed like each time someone thought they had a pure earth, some wiseguy would come along and prove it was two or even three of them.
Eventually there were 16 of them…and in the early 1900s thanks to Mosely, we realized that there was still one remaining hole, a radioactive element almost totally absent from the earth’s crust (it’s the one exception I mentioned above). It probably wouldn’t be terribly rare, either…if only it would quit vanishing almost as soon as it were formed.
When Mendeleev was first trying to lay out the periodic table as rows of eight or ten elements, the rare earths broke him. Yttrium seemed to fit tidily in the third column of one row, but all the others wanted to wedge into the third column two rows down, breaking the regular sequence of rows of eight or ten. (He laid his table out differently from modern tables, and I wonder whether he’d scream out “of course! Why didn’t I think of that” if he could see today’s table.)
These elements are now the f block row starting with lanthanum, plus scandium (not known in Mendeleev’s day) and yttrium.
Chemists will more commonly call the first row of the f block the lanthanides, since that row starts with lanthanum, but even this is a bit of a misnomer since one of the 15 is really in the d block and shouldn’t be considered a lanthanide. (This would be particularly ironic if it’s actually lanthanum that’s in the d block! You’d be naming a group of elements after an element that isn’t even in the group!) [In case you were wondering, the second row starting with actinium is called the actinides, by analogy.]
As I mentioned before, these elements are very similar to each other chemically, and thus they not only tend to appear in the same ores, but are hard to separate out from each other. It wasn’t until the 1950s or 60s that we finally could get pure samples of them in meaningful quantities.
Before that, they were expensive because what we could do, was laboratory-level-labor intensive. And another factor is, they don’t tend to concentrate locally in ores as much as many better-known elements…so it’s hard to find a good source. Crustally common they may be, but that does no good if you can’t find an economically viable source of ore.
We’re helped somewhat by the fact that there is a gradation through the f-block. Elements on the left end of the lanthanides…the “light rare earth elements” tend to rust and crumble even in dry air; the elements from gadolinium (Gd) rightward can actually form stable pieces of metal that will tarnish, but at least not turn back into earths. These are the heavy lanthanides. Some ores contain mostly “light” rare earths and others will be more “heavy” rare earths. Yttrium and scandium tend to appear in the heavy rare earth ores, which argues for them being above lutetium in the long table.
So these are the “rare earth elements” by present definition, the lanthanides plus scandium, yttrium, and lutetium.
If these elements are so chemically similar, why do they matter so much? It turns out that many of them have unusual magnetic properties, and many have emission lines in places in the spectrum that no other element has, so they’re useful for lighting when you want a balanced spectrum (great for photography). These are differences that aren’t relevant when considering chemical reactions and compounds.
You’ve probably heard of neodymium (Nd) magnets. And if you ever had an MRI done you may have had a gadolinium (Gd) compound injected into you; its magnetic properties make it stand out in the imaging. More mundanely, the red phosphor in color TVs relies on a rare earth, europium (which is the one that rusts and crumbles the fastest, by the way). And there is wiring in front of the light emitting elements of your monitor that is transparent, made partially from lanthanides.
But, to finally get to the point of my rant,
Lithium is not a rare earth. Neither is gallium. Lithium is in the first column, right below hydrogen…no where near the f block. Gallium is tucked in under aluminum, where the d and p blocks meet, even farther from the f block.
Maybe you want to just sweep that aside, and claim that a rare earth is anything that is rare, and then go on to point out that the “real” rare earths aren’t. Aren’t rare, that is.
Well, guess what?
It turns out that gallium (Ga) and lithium (Li) are both more common than the most common rare earth element. [OK, gallium is about tied with cerium, the most common rare earth.]
So if there’s no justification for calling the rare earth elements rare earth elements, there certainly isn’t for misapplying the label to gallium and lithium!
It’s basically an excuse justifying the ignorance of the people writing the articles that others want to post. And a poor one.
The fact that the name “rare earth element” is historically used by the people who know about those elements the most, is ample reason to use it and insist that it be used correctly.
Having said that, however, it’s obvious that the sloppy people are misusing the term in a very specific wa. They definition they are thinking of is something like: “obscure metals Americans are utterly reliant on, but have to buy overseas from shithole tyrannies who would love to put us over a barrel during a conflict by cutting off our supply.”
That’s a valid concept…it needs a label. But it needs and deserves its own label; it shouldn’t hijack an existing one. Now, I’ve seen one that comes close to meaning that already, and that’s “strategic metal.” Strategic metals, however, don’t necessarily come from hostile countries (though Brandon is trying to make that true by making every country hostile). So it’s not quite right, but until we think of something better, it will work…a lot better than the ignorantly-applied “rare earth metal” which means something very different.
Spot Prices
All prices are Kitco Ask, 3PM MT Friday (at that time the markets close for the weekend).
Not much to say here, that hasn’t been said before.
Going Polar
Last week we left off with the notion that a complex number…the general case of any number that contains both a real and imaginary part…can be represented on a plane instead of the number line.
Of course, that’s exactly the same thing as we do with ordered pairs…x and y. In other words, all that time you spent in algebra with graph paper is basically what’s going on here.
The similarity isn’t just superficial.
If you add two ordered pairs together, you get a certain answer. For example (3,4) + (5,-2) = (8, 2). If you write the corresponding complex numbers, 3+4i and 5-2i and add them together you get…wait for it…8+2i. There’s a perfect analogy here.
Those ordered pairs resemble vectors, but they’re not, quite; if you do think of them as vectors, you have to think of them as vectors that must start at 0,0…which isn’t normally a restriction. (Any two vectors of the same length and orientation, regardless of where they are, are considered the same vector. But here the not-quite-a-vector must start at 0,0.)
But…you can multiply complex numbers together, but there’s no really obvious way to multiply the ordered pairs. (There are two distinct ways of multiplying vectors together, but neither of them quite matches, either.)
Well, maybe there is a way. Time to take a cross country digression, that really isn’t.
Polar Coordinates
There is actually another way to represent ordered pairs…and complex numbers.
Instead of putting the number(s) on a square grid, called the Cartesian coordinate system, put them on a radial or circular grid like this:
[Which…alas, should not be in degrees, it should be in radians, with 30° instead being π/6, 60° being π/3, etc., etc. (And 180° is π radians.) But this is what wikipoo dished up for me today so degrees it shall be.]
The red circles represent simple tape-measure distance from the center, denoted r. The blue (and black) lines, indicate the direction from the center, measured as an angle, this is denoted θ, (Greek letter theta, usually mangled by English speakers as “thay-tah” where the first syllable is like “say” with a lithp, not like “they”). This is in contrast to the Cartesian coordinates, where the vertical lines represent the distance to the right of the center vertical axis (without regard to how far up or down), and the horizontal lines represent the distance above the center horizontal axis (without regard to how far left or right).
So we have r, θ, instead of x, y. And this new system is called polar coordinates, likely because of the resemblance to what the latitude/longitude lines look like on a map of the north or south pole.
The same point on the plane can thus be denoted two different ways; they are absolutely equivalent. However, it’s often the case that one of the two is very convenient for what you want to do right now…and the other is profoundly inconvenient. Pick the one you want.
But that implies being able to convert between the two. Put some point “out there” somewhere, if you know its Cartesian coordinates, can you figure out the polar coordinates? Or vice versa?
The answer is yes.
Let’s look at a few obvious examples first.
If the innermost red circle has radius 1, then (1,0) in Cartesian coordinates, is 1, 0° in this diagram, meaning a distance of 1 from the center, at an angle of 0°. Similarly (0, 1) ends up being at 1, 90°.
But what if you want (1,1) translated into polar coordinates?
The answer is not, repeat not, 1, 45°.
You see, the point (1,1) is directly, plumb-line above (1,0) which is also 1, 0°.
And it is directly, spirit level, to the left of (0,1) or 1, 90°. That puts it outside of that innermost, distance=1 circle. Since the first number in polar coordinates is the distance, that tells you that the distance of (1,1) from the center isn’t 1. It’s something greater than 1.
Well, duh.
I say duh, because we’ve had the tools necessary to deal with this distance issue for over two thousand years. It’s the Pythagorean theorem, or those doggone right triangles.
If you start with your Cartesian x and y coordinates, you square each of them. They are the legs of a right triangle; the distance is the hypotenuse. Once you add those two squares, you have the square of the distance:
r2 = x2 + y2
Or
r = √(x2 + y2)
(Which, by the way, means r will usually end up being an irrational number.)
OK, that’s easy, right?
But what is θ? In this case we know it’s 45°, because x and y are the same thing. And of course if either x or y were zero, we’d know it was 0°, 90°, 180°, or 270°.
That doesn’t help us in the general case. What do you do with (3, 4)? We know that r is 5 (since 3, 4, 5 is the cliche Pythagorean triple you see in story problems all the freaking time…except when they get clever and hit you with 6, 8, and 10 or better yet, 5, 12 and 13). But what on earth is that angle?
Well, for that you need…trigonometry.
Yes, trigonometry returns, like a bad penny.
Recap of Trig
I briefly touched on trigonometry a few weeks ago. I’ll recap here.
The start of trigonometry is to consider the “unit circle.” This is the circle of radius 1 (and thus diameter=2) centered on the origin, 0.0. So the right side of the circle touches (1,0), the top edge is at (0,1), the left edge (-1,0), and the bottom at (0,-1).
Consider measuring along the curve of the circle, starting at the rightmost point at (1,0). If you follow the curve exactly one unit, you’ve covered an angle of one radian. If you walk halfway around the circle, to (-1,0) you’ve covered a distance of exactly π, so that’s π radians. It’s simply another way to measure angles, one defined by the ratio of the length of the arc, to the radius of the circle. This is fudge-factor free in technical terms, so it tends to be the way mathematicians and physicists prefer to measure angles.
Now, place the circle on a Cartesian grid. You can go to any point on the circle, and 1) there’s some angle measured from (1,0) counterclockwise that describes that point; that’s actually θ. (r of course is 1 on a unit circle.) 2) that point also has (x, y) coordinates in the Cartesian grid.
You can define a function, where given an angle θ on the unit circle, the function gives you x. You can define another function that, for the same θ, gives you y. These are respectively the cosine and sine, respectively (and are abbreviated cos and sin).
This time the Wikipoo diagram is perfect:
If you were to plot these functions versus θ you would see the following:
for cosine, and for sine:
The graphs stop at θ=2π because the functions simply repeat, over and over. Which is logical because once you’ve gone around the circle once (2π radians), you’re back where you started, and another five degrees after that will just look like the first five degrees did.
If you’re thinking the two curves are identical, just offset from each other, you’re right. The sine lags the cosine by 90 degrees or π/2.
Another thing to notice is that almost any cosine or sine value can come from more than one angle. Looking, for instance, at the sine graph, it hits 1/2 at two places…one just before 1/4π and one just after 3/4π. (In fact it’s at 1/6π and 5/6π.)
There is one more function that will be useful to us shortly, and that is the tangent, abbreviated tan. This is the rise over the run for the angle θ, in other words its grade or slope. You can find this by dividing the sine by the cosine. But be careful, if the cosine is zero, then only Donald Trump (being Batman) can do the computation, the rest of us are not allowed to divide by zero.
Here is the tangent, graphed:
Note that it zooms off to infinity at π/2 (sine is close to 1, cosine is close to zero. Dividing by a small number leaves you with a big one). Right afterπ/2 though it’s a negative number. Because the sine is still positive, but the cosine is now negative–the point is to the left of the y axis. And note these kind of swoopy curves repeat not every 2π radians (360 degrees) but every π radians (or 180 degrees).
OK, we’re actually well on our way to being able to convert polar to Cartesian, and back.
Converting Polar to Cartesian, and Vice Versa
It’s actually easiest to explain this if we go from polar to Cartesian first.
In polar coordinates we have a distance, r, and angle, θ. We just saw that on a unit circle, θ is associated with x and y, which is what we want, by the cosine and sine functions. So, if it just so happens that r is 1, then:
x = cos(θ) y = sin(θ)
Of course, almost all points are not on the unit circle.
Luckily we can just scale things. If r is 2, just multiply your cosine and sine by 2. If it’s 1/8th, multiply your sine and cosine by 1/8.
Bascially, just multiply them by whatever r happens to be.
So we have:
x = rcos(θ) y = rsin(θ)
That’s nice and tidy. It’s a little more complex going the opposite way, from Cartesian to polar.
It’s easy enough to compute r with the Pythagorean trick, as mentioned above:
r = √(x2 + y2)
The angle could be computed by reversing the two formulas above. Divide x and y by r, and you have a sine and cosine for θ. You can reverse these functions, the reverses are called the arccosine and arcsine (arccos and arcsin or cos-1 or sin-1). Each one is likely to give you two answers (remember how 1/2 shows up twice in the sine and cosine graphs, so the arcsine of 1/2 could be two different angles), but only one answer will show up in both places.
But there’s an easier way to do it as long as you keep your brain engaged. Divide y by x, and you have the tangent of the angle. Then just take the arctangent and you have θ.
Well, almost. If x is zero, don’t do this. Instead just look at y, and if y is positive, θ is 90 degrees, if y is negative, θ is 270 degrees.
The other problem is that the tangents of the angles from 180-270 degrees are the same as the tangents of the angles from 0-90. Similarly the angles from 90-180 and 270-360 have the same tangents. So, go ahead and take your arctangent…but then, if y is negative, your angle is between 180-360 not between 0 and 180.
OK…yes, there was a point to this. I’d go on, but I’ve probably already overloaded some brains here. So next week, I’ll continue this.
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 !!!
