News Flash

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.

Spot Prices.

Kitco Ask. Last week:

Gold $1,960.40
Silver $24.41
Platinum $945.00
Palladium $1,280.00
Rhodium $4,800.00

This week, markets closed as of 3PM MT.

Gold $1,943.60
Silver $23.73
Platinum $930.00
Palladium $1,290.00
Rhodium $4,750.00

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!!!

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 !!!