“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
This Stormwatch Monday Open Thread remains open – VERY OPEN – a place for everybody to post whatever they feel they would like to tell the White Hats, and the rest of the MAGA/KAG/KMAG world (with KMAG being a bit of both).
Our various sister sites, listed in the Blogroll in the sidebar
Our beloved country is under Occupation by hostile forces.
Daily outrage and epic phuckery abound.
We can give in to despair…or we can be defiant and fight back in any way that we can.
Joe Biden didn’t win.
And we will keep saying Joe Biden didn’t win until we get His Fraudulency out of our White House.
Word of The Week:
precinct
noun
A subdivision or district of a city or town under the jurisdiction of or patrolled by a specific unit of its police force.
The police station situated in and having jurisdiction over such a district.
An election district of a city or town.
Precinct map of Manhattan
More country music!
This one helps me get it. SEEING the lyrics helps to make sense of the sentiment.
I love the way his “round up” verb doesn’t have an object. That’s very important. The object could be anybody. Very important to remember.
As I see politics more up-front and personal, but also PEOPLE, I’m seeing where things are both breaking and healing, and it’s hard for me to communicate the hope and frustration.
I also see the specialness of this place, and how the world needs more of what we have here – a kind of deep honesty without prejudice (used in all senses of the word).
Be the Q Tree, people!
I am beat from local work. But it’s good, too. Resting now, relaxing, and saying thank you for being here.
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 !!!
This Stormwatch Monday Open Thread remains open – VERY OPEN – a place for everybody to post whatever they feel they would like to tell the White Hats, and the rest of the MAGA/KAG/KMAG world (with KMAG being a bit of both).
Our various sister sites, listed in the Blogroll in the sidebar
Our beloved country is under Occupation by hostile forces.
Daily outrage and epic phuckery abound.
We can give in to despair…or we can be defiant and fight back in any way that we can.
Joe Biden didn’t win.
And we will keep saying Joe Biden didn’t win until we get His Fraudulency out of our White House.
Word of The Week:
Dunning–Kruger effect
noun
The Dunning–Kruger effect is a cognitive bias whereby people with low ability, expertise, or experience regarding a type of task or area of knowledge tend to overestimate their ability or knowledge. Some researchers also include the opposite effect for high performers: their tendency to underestimate their skills. In popular culture, the Dunning–Kruger effect is often misunderstood as a claim about general overconfidence of people with low intelligence instead of specific overconfidence of people unskilled at a particular task.
People are actually fairly good at estimating relative abilities, but they are not as good at estimating actual abilities – and the fit is increasingly bad at lower abilities, where people overestimate their own competence.
The effect is commonly used as a justification of authoritarianism by leftists and elitists, and as an argument in favor of the anti-popular positions of scientism.
In words
“The more you know, the more you know that you don’t know.”
“The less you know, the less you know that you don’t know.”
Relevance
There is a fake news site that exists for the purpose of fooling conservatives, and thereby discrediting them in the eyes of everybody else. As a form of insult to its victims, this website calls itself the “Dunning-Kruger Times”.
While the Dunning-Kruger Times (DKT) website claims that its stories are satire, the stories are always remarkably unfunny, and IMO are clearly not intended to be funny.
They are intended to be believable.
True satire sites of a similar nature typically run stories which slowly increase the level of absurdity until the reader recognizes hyperbole and begins to get the joke. These sites can be incredibly (no pun intended) funny, and have often had me breathless with laughter.
DKT never crafts funny satire. The goal appears to be to get reasonable people to see the story and recognize that the story is reasonable, likely to have occurred, and affirming of conservative values. The stories are easily posted to social media. The trouble is, the stories are never true.
As I have said, the stories are discrediting of whoever posts them, and many famous conservatives (Gov. Greg Abbott and Juanita Broaderick, most recently) have been fooled.
The stories are ALMOST libelous, but under the cover of satire, they remain protected and legal speech. Moreover, because the false allegations are very plausible, the accusations anticipate likely real positions by the people who are libeled, and are thus unlikely to be argued against.
It is my belief that these sites and stories are the work of the 3-letter agencies and/or the DNC, both as a psychological operation against Americans, and in particular as a way of discrediting those who would be expected to post or “like” the stories on social media.
For example, Juanita Broaddrick posted this valid tweet, showing significant public sentiment in favor of country music artist Jason Aldean.
Personally, I think that the DKT needs to be investigated all the way back to their (IMO) CIA, big tech, or DNC roots.
DKT is a discreditation site – a psy-op – and NOT a regular satire site.
Hey @elonmusk! Should @Twitter do something about "fake satire sites" that are designed to discredit target groups under the undeserved protection of "parody"? The very unfunny nature of DKT stories gives away their game of psy-op and plausibility.https://t.co/pu0tenqmhl
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 !!!
This Stormwatch Monday Open Thread remains open – VERY OPEN – a place for everybody to post whatever they feel they would like to tell the White Hats, and the rest of the MAGA/KAG/KMAG world (with KMAG being a bit of both).
Norgestrel is a synthetic progestin comprising a 50% racemic mixture, in which levonorgestrel is the biologically active form. Levonorgestrel’s most common use is as a contraceptive agent either alone or in combination with the synthetic estrogen ethinyl estradiol.
For your enjoyment, some country music!
As the election season approaches, I will be getting more and more involved in local politics. I may do some more placeholders, particularly for the final weeks before the election. I’ll just have to see how much time I have. My top priority on this site will be interacting with people, and reading the content that people bring here, rather than bringing my own content.
I just want to make sure people know that I’m not losing interest in this site, by my not being here or by my not doing more analytical posts. Between necessary time for health, family, and local politics, something has to give, and it will typically be posting my own content on this site.
But like Wheatie always said. We WILL get through it!
This Stormwatch Monday Open Thread remains open – VERY OPEN – a place for everybody to post whatever they feel they would like to tell the White Hats, and the rest of the MAGA/KAG/KMAG world (with KMAG being a bit of both).
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 !!!
This week, we begin a new half-year of Monday posts.
I am returning the post format to “Wheatie-style brevity” while sometimes adding short topics or notifications.
This Stormwatch Monday Open Thread remains open – VERY OPEN – a place for everybody to post whatever they feel they would like to tell the White Hats, and the rest of the MAGA/KAG/KMAG world (with KMAG being a bit of both).
For your enjoyment, some epic heroic orchestral music in Wheatie’s favorite style.
I will soon be publishing a statement on the end of Affirmative Action in university admissions. I thought that I might include that statement with this open thread, but I wish to do a better job and not rush it into print. Please bear with me.
Thank you, and God bless you all! -W
ENJOY THE SHOW
Have a great week!
W
Thanks to Valerie for this and other images.
PS – may you have a very, very patriotic Fourth of July!
Today is Canada Day. Something once worth celebrating.
Oh, well.
Speaker Dungsmear? Or?
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 2022 or 2024 is pointless otherwise. Which is not to say one must never talk about this, but rather that one must account for this in ones planning; if fixing the fraud in the system is not part of the plan, you have no plan.
This will necessarily be piecemeal, state by state, which is why I am encouraged by those states working to change their laws to alleviate the fraud both via computer and via bogus voters. If enough states do that we might end up with a working majority in Congress and that would be something Trump never really had.
Lawyer Appeasement Section
OK now for the fine print.
This is the WQTH Daily Thread. You know the drill. There’s no Poltical correctness, but civility is a requirement. There are Important Guidelines, here, with an addendum on 20191110.
We have a new board – called The U Tree – where people can take each other to the woodshed without fear of censorship or moderation.
And remember Wheatie’s Rules:
1. No food fights 2. No running with scissors. 3. If you bring snacks, bring enough for everyone. 4. Zeroth rule of gun safety: Don’t let the government get your guns. 5. Rule one of gun safety: The gun is always loaded. 5a. If you actually want the gun to be loaded, like because you’re checking out a bump in the night, then it’s empty. 6. Rule two of gun safety: Never point the gun at anything you’re not willing to destroy. 7. Rule three: Keep your finger off the trigger until ready to fire. 8. Rule the fourth: Be sure of your target and what is behind it.
The platinum group metals are taking an absolute beating right now. Especially for palladium and rhodium.
Those metals’ primary use is industrial. Everything from catalytic converters to other uses as catalysts in chemical plants. A collapse in demand for these could indicate the actual productive economy is tanking.
A Small Science Post
I finally have a free moment to write this post…and midnight, Swamp Time, is only half an hour away.
So it will be short.
Valerie will not doubt express relief!
We left off having introduced i as the square root of minus one (√-1), pointing out that this number does not appear on the number line and therefore isn’t in the broad group of numbers that we call “real” numbers, which includes integers, fractions, irrational numbers, even the irrational numbers that are also transcendental. It’s therefore an imaginary number…but no, that doesn’t mean it’s made up. It ends up being very useful indeed not just to mathematicians (who work in a very abstract world that can sometimes be quite disconnected from reality), but to engineers, who absolutely must deal with reality.
Imaginary numbers are those which are multiples of i. Because you can do any sort of algebra or arithmetic on i that you can do on real numbers. But you cannot simply mix them with real numbers interchangeably; that’s bigtime apples-and-oranges. But nothing says you cannot make a fruit salad, where they each retain their identity but work together. When you do that, you have a “complex number.” For example, 5+3i is a complex number, as it has both a real part, 5, and an imaginary part, 3i. (But note that pure imaginaries and pure reals are also considered part of the complex numbers…as is zero. If this bothers you realize that reals can all be expressed as <real number> + 0i; we just choose to leave off the zeroed part. We do a lot of things like this, such as expressing 1x1/1 as simply x. Similarly a pure imaginary number can be expressed as a complex number having zero for the real part.)
I mentioned earlier that i is not on the number line. I hope it’s of no surprise to you that no complex number that has an imaginary part is on the number line, either.
So when thinking about number lines, or things like number lines, aids to visualizing sets of numbers, how do complex numbers fit in? As it happens, it’s more the other way around. The real numbers, those on the number line, are part of the complex number set, not the other way around.
Think about the set of all possible complex numbers. The real part can be any number that actually is on the number line. The imaginary part can be i times any number that actually is on the number line. Any real part can be combined with any imaginary part. They are independent of each other…they are independent variables or they are orthogonal to each other.
If you have a STEM background, there’s probably something the size of a gorilla jumping up and down in your mind shrieking “Two dimensions!!! Two dimensions!!!” If you don’t, and you’re wondering why your STEM friends are acting so weirdly right now, well now you know about the jumping gorilla.
Because that’s exactly what we are going to do. The number line has one dimension, left-right. There is a complex plane with two dimensions, left-right and up-down (on the sheet of paper) or east west and north-south (if you’re imagining looking down on the plane from above).
So now we have a new mental picture, the complex number plane, where the old real number line runs side to side and is in the plane, and another line, the imaginary number line, runs vertically, and they intersect at 0 + 0i.
Here’s a picture, with a few sample complex numbers pointed out and ℝ and I axes labeled:
Next time, we’ll see how well it works. And it works very, very well, leading you to some very interesting places.
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 !!!
Next week, we will start a new half-year of Monday posts.
I may take some liberties with the format! Be brave!
This Stormwatch Monday Open Thread remains open – VERY OPEN – a place for everybody to post whatever they feel they would like to tell the White Hats, and the rest of the MAGA/KAG/KMAG world (with KMAG being a bit of both).
And yes, it’s Monday…again.
But we WILL get through it!
‘Cuz Wheatie Sez!
Just like Trump!
So HOLD ON for the ride of your life!
Dedication
WHEATIE – OUR WARRIOR ANGEL
by Duchess01
Please forgive us, Wheatie, we did not know That you had left us with armor in tow We had no idea with what you dealt We did not know the pain you felt And now we can only imagine With you what really did happen Cause rarely did you complain And/or share your personal pain Of one thing we are most certain You are flying high behind the curtain Watching over us above the crowds Our Warrior Angel above the clouds Thank You, Wheatie, for caring for us While you were here among the fuss We miss you dear you have no idea Since time began in the pangaea With you there was no time In your wisdom you would chime To clarify and magnify The what where how and why We did not question when you left We were not slightly bereft But over time we wondered why You did not at least stop by Now we know where you have gone With the break of this new dawn We could be angry but are not Tho with an arrow we’ve been shot Rest peacefully Warrior Angel dear Send us a sign that you are near A butterfly a flower a kiss of rain From your love do not refrain God sends Angels to watch over us And now we have an Angel Plus A Warrior Angel of Magnificence From today and forward hence
Boilerplate, more or less, but worth reading again and again, if only for the minor changes, and to stay out of moderation.
MINOR CHANGE NUMBER 1
Now shortened.
Give them nothing.
Play smart. Every minute, the COUPISTS who stole the election – who lied – who deserve to be at the business end of the very same laws they are using so wrongly against the January Sixth defendants – are trying to set you up. Don’t be a chump. Turn everything back against THEM. Every day, every hour, every minute, every second.
YOU are responsible for your own comments, if they come knocking. YOUR choice. Just remember this…..
For an updated version…..
And for a version that includes your having righteously defended yourself…..
OTHER THAN THAT…….
The bottom line is Free Speech. Theories and ideas you don’t agree with must be WELCOME here, and you must be part of that welcoming. But you do NOT need to be part of any agreement.
Bottom line – respect other people’s FIRST AMENDMENT RIGHTS.
Our only additional requirement is that you do so NICELY. Or at least try to make some effort in that direction.
SO….. [ENGAGE BOILERPLATE…..]
We must endeavor to persevere to love our frenemies – even here.
Those who cannot deal with this easy requirement will be forced to jump the hoops of moderation, so that specific comments impugning other posters and violating the minimal rules can be sorted out and tossed in the trash.
In Wheatie’s words, “We’re on the same side here so let’s not engage in friendly fire.”
That includes the life skill of just ignoring certain other posters.
We do have a site – The U Tree – where civility is not a requirement. Interestingly, people don’t really go there much. Nevertheless, if you find yourself in an “argument” that can’t really stay civil, please feel free to “take it to the U Tree”. The U Tree is also a good place to report any technical difficulties, if you’re unable to report them here. Please post your comment there on one of Wolf’s posts, or in reply to one of Wolf’s comments, to make sure he sees it (though it may take a few hours).
We also have a backup site, called The Q Tree as well, which is really The Q Tree 579486807. You might call it “Second Tree”. The URL for that site is https://theqtree579486807.wordpress.com/. If this site (theqtree.com) ever goes down, please reassemble at the Second Tree.
If the Second Tree goes down, please go to The U Tree, or to our Gab Group, which is located at https://gab.com/groups/4178.
We also have some “old rules” and important guidelines, outlined here, in a very early post, on our first New Year’s Day, in 2019. The main point is not to make violent threats against people, which then have to be taken seriously by law enforcement, and which can be used as a PRETEXT by enemies of this site.
In the words of Wheatie, “Let’s not give the odious Internet Censors a reason to shut down this precious haven that Wolf has created for us.”
A Moment of Prayer
Our policy on extreme religious freedom on this site is discussed HERE. Please feel free to pray and praise God anytime and anywhere.
Thus, please pray for our real President, the one who actually won TWO elections.
By grace you have been saved through faith; not of yourselves. It is the gift of God. Ephesians 2:8-9
You expect me to believe that Ben Brody a political science student at UCR, a liberal college in California who was unmasked at a protest event is a member of the “far right” organization Patriot Front? Yea right, this guy is an Antifa crisis actor hired by the Feds. pic.twitter.com/BkBNJsO4Jf
— Only God can save us (@godoverpolitics) June 25, 2023
I’m proud to say that Peter Hotez has blocked me. 🤣🤣🤣 Given that he has a PhD in propaganda, I’m going to take this moment to reflect on what I did that was so effective. I will then do more of the exact same thing. Tyrants might be liars, but at least they’re cowards too. pic.twitter.com/pYnsE4m7dk
What is an implosion, and what would it have been like for the Titan sub passengers?
The Titan submersible was so deep, experts told NBC News, that the forces crushing it would have been equivalent to the weight of the Eiffel Tower.
The deep-sea water pressure that appears to have crushed the 22-foot craft would have been roughly equivalent in weight to the 10,000-ton, wrought-iron Eiffel Tower, experts told NBC News on Friday. The colossal forces would have acted so quickly that it would be like the vehicle’s carbon-fiber hull “suddenly vanishing” before anyone inside knew what was happening, one expert said.
“They would have known nothing — the minute this body of water hit them, they would have been dead,” said Paul White, a professor at England’s University of Southampton, who specializes in underwater acoustics and forces.
…
“The air inside would compress down to a point, and the forces of the water rushing in and the collapse would be enormous,” he said. “Structurally,” he added, it would be equivalent of the capsule housing the crew “suddenly vanishing.”
“This whole process from start to finish is happening in the blink of an eyelid, the click of a finger,” he said. “I don’t think there would have been any suffering or any knowledge of what happened.”
