2023·08·19 Joe Biden Didn’t Win Daily Thread

A Caution

Just remember…we might replace the RINO candidates. (Or we might not. The record is mixed even though there is more MAGA than there used to be.) But that will make no difference in the long run if the party officials, basically the Rhonna McDaniels (or however that’s spelled–I suspect it’s RINO), don’t get replaced.

State party chairs, vice chairs, secretaries and so on, and the same at county levels, have huge influence on who ultimately gets nominated, and if these party wheelhorses are RINOs, they will work tirelessly to put their own pukey people on the ballot. In fact I’d not be surprised if some of our “MAGA” candidates are in fact, RINO plants, encouraged to run by the RINO party leadership when they realized that Lyn Cheney (and her ilk) were hopelessly compromised as effective candidates. The best way for them to deal with the opposition, of course, is to run it themselves.

Running good candidates is only HALF of the battle!

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

I normally save this for near the end, but…basically…up your shit-kicking barbarian asses. Yes, barbarian! It took a bunch of sailors in Western Asia to invent a real alphabet instead of badly drawn cartoons to write with. So much for your “civilization.”

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

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

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

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

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

OK, with that rant out of my system…

Biden Gives Us Too Much Credit

…we can move on to the next one.

Apparently Biden (or his puppeteer) has decided we’re to blame for all of the fail in the United States today.

Sorry to disappoint you Joe (or whoever), but you managed to do that all on your own; not only that, you wouldn’t let us NOT give you the chance because you insisted on cheating your way into power.

Yep, you-all are incompetent, and so proud of it you expect our applause for your sincerity. Fuck that!!

It wouldn’t be so bad, but you insist that everyone else have to share in your misery. Nope, can’t have anyone get out from under it. Somehow your grand vision only works if every single other person on earth is forced to go along. So much as ONE PERSON not going along is enough to make it all fail, apparently.

In engineering school we’re taught that a design that has seven to eight billion single points of failure…sucks.

Actually, we weren’t taught that. Because it would never have occurred to the professors to use such a ridiculous example.

Justice Must Be Done.

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

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

Kamala Harris has a new nickname since she finally went west from DC to El Paso Texas: Westward Hoe.

Lawyer Appeasement Section

OK now for the fine print.

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

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

And remember Wheatie’s Rules:

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

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

Spot Prices

All prices are Kitco Ask, 3PM MT Friday (at that time the markets close for the weekend).

Last Week:

Gold $1,914.10
Silver $22.75
Platinum $921.00
Palladium $1,338.00
Rhodium $4,750.00

So here it is, Friday, 3PM MT after markets closed and we see:

Gold $1,890.50
Silver $22.86
Platinum $923.00
Palladium $1,288.00
Rhodium $4,550.00

Gold sliding. I guess to Wall Street things are just fine. Meanwhile we work for bullshit pay and inflation keeps on going…

Watch Me Pull A Rabbit Out Of My Hat

Last week we left off showing that it’s possible using the Maclaurin series (a special case of the Taylor series) to compute sines and cosines of angles. The closer the angle is to zero, the easier it is to do.

Technically you don’t get an exact answer unless you run the series out forever, but you can typically get acceptable precision in just a few terms.

Here they are, sine and cosine:

sinx = x – x³/3! +x⁵/5! – x⁷/7!…

cosx = 1 + –x²/2! + x⁴/4! + –x⁶/6! + x⁸/8! +…

But if you recall, from way back, there is another such series for the exponential function, i.e., e^x.

(It’s so much nicer when I can find an image of a properly typeset formula, ain’t it?)

Can We Tie Trig and Exponentials To Each Other?

Take a really close look at these three formulas. Compare like terms…and by that I mean x³ in one formula should be compared to x³ in another, and so on.

You’ll notice that the formula for e^x contains terms for every power of x. Sinx, on the other hand contains only the odd-power elements, and cosx contains only the even-power elements.

It’s almost as if you could somehow combine sine and cosine to get the exponential function.

But if you add the sine and cosine functions together you get this:

sinx + cosx = 1 + x – x²/2! – x³/3! + x⁴/4! +x⁵/5! – x⁶/6! – x⁷/7! + x⁸/8! +…

Well…it’s almost right. Except for one rather awkward problem. The terms have two positive signs, then two negative signs, then two positive signs, then two negative signs. and so on, whereas the exponential series has nothing but positive signs.

And you can’t fix this by subtracting cosine from sine (or vice versa), thereby flipping some signs, because some of those errant negative signs come from sinx and some from cosx.

For example:

sinx – cosx = -1 + x + x²/2! – x³/3! – x⁴/4! +x⁵/5! + x⁶/6! – x⁷/7! – x⁸/8! +…

You still have an alternating sequence of two positive numbers then two negative numbers, then two positive numbers, and so on; you’ve just shifted where the pairs of negatives and positives are in the sequence.

So what looked like something that would have been a really cool way to tie trigonometry to the exponential function, fails.

Tying Up A Loose End

I mentioned here: https://www.theqtree.com/2023/06/24/2023%c2%b706%c2%b724-joe-biden-didnt-win-daily-thread/ that complex numbers, i.e., numbers of the form a + bi, where i is the square root of -1, could have all sorts of things done to them, addition, subtraction, multiplication, division…and you could even raise other numbers to complex powers. I said that last part, but then I said I’d have to talk about it some other week.

Well, this is that week.

Nothing says that the x in the Maclaurin series has to be a real number.

So why don’t we plug a complex number into the Maclaurin series for e^x to see what happens?

Well I can tell you beforehand what will happen if we plug a + bi into it…we’re going to have to square that expression, then cube it, then raise it to the fourth power, and the fifth, and we will have a gawdawful mess on our hands very, very quickly.

But really, that would be a chimpanzee move.

e^a+bi, after all is e^a x e^bi. By splitting it up this way, we can handle the two pieces separately and then (at the end) multiply them together. We already have a handle on e^a but we should check on e^bi since the power we are raising e to is an imaginary number. So let’s set e^a aside (but we will not forget it’s there).

Using the e^x Maclaurin series:

…and setting x = bi, we get:

e^bi = (bi)⁰/0! + (bi)¹/1! + (bi)²/2! + (bi)³/3! + (bi)⁴/4! + (bi)⁵/5! + (bi)⁶/6! + …

This doesn’t seem to do much for us; you could put anything in for x and you will be raising it to all those powers. But i has a very interesting behavior when you raise it to successive powers, and we can use that here:

i⁰ = 1, i¹ = i, i² = -1, i³ = –i, i⁴ = 1, i⁵ = i, i⁶ = -1 i⁷ = –i ….

In other words it goes through a 1, i, -1, –i cycle, over and over again. So we can go back to the expansion above and replace all of the i-to-the-somethingth powers with the appropriate value (and do more simplifications….0! is defined to be 1, and any number raised to the 0th power is also 1). Also, when we do this if there is an i or –i we’ll bring it to the front.

e^bi = 1 + ib – b²/2! – ib³/3! + b⁴/4! + ib⁵/5! – b⁶/6! – ib⁷/7! …

Now some of the terms have i in them and some do not, which makes this the epitome of a complex number. It’s a little hard to deal with this in this form, so let’s collect all the real terms together, and all the imaginary terms together–like we would for any complex number. We end up with the sum of two series:

e^bi = 1 – b²/2! + b⁴/4! – b⁶/6! + … (first series)
+ ib – ib³/3! + ib⁵/5! – ib⁷/7! + … (second series)

And we can factor out the i from the second series:

e^bi = 1 – b²/2! + b⁴/4! – b⁶/6! + … (first series)
+ i (b – b³/3! + b⁵/5! – b⁷/7! + …) (second series)

Does anything look familiar?

I ask again, DOES ANYTHING LOOK FAMILIAR?!?

It better.

The first series is the same as the expansion of cosx from earlier, except of course it’s on b instead of x. Makes no difference. They’re the same.

The second series, moreover is i times the sinx series from above (again with b substituted for x).

In other words, switching back to x:

e^ix = cosx + isinx.

Well, well, well. We can connect exponentials and trig functions after all! We just needed a bit of (I can’t resist) imagination, taking the exponent of an imaginary number and getting a result that has both a real and imaginary component.

This is known as Euler’s equation, after Leonhard Euler (1707-1783) who first noted it. Euler is arguably the greatest mathematician that ever lived though he has plenty of stiff competition from others.

It would be hard to overstate the importance of this result. It underlies much of physics, and is all over the place in electrical engineering.

And yet you never hear about it in the popularizations of science (well, not until now).

This is largely because, in order to get here, you need a pretty solid advanced math background. Or someone who’s willing to skip over a lot of formal proofs as he presents it to you. Most math educators won’t do that, and rightly so. Mathematics education relies on proving everything along every step of the way. It’s bullshit-free, everything is proved based on what comes before and you don’t have to trust the perfessor or take his word for anything. And here I am giving it to with little in the way of proofs and enough hand-waving that I am raising myself off the floor from flapping my arms so hard. (As such, if you find this interesting, I ask that you at least ask someone else with the right knowledge if it’s true. DO NOT just take my word for it. Better yet, take a bunch of math courses.)

Putting It Back Together

But there’s one little detail that must be dealt with. We got here by trying to raise e to the a+bi power, and we set aside the e^a that we must multiply e^bi by. So let’s put them back together.

e^a+bi = e^ae^bi = e^a(cosb + isinb)

But now, the last thing should remind you of something. (Though this time I will not jump on the table and yell that it should do so.)

It looks a bit like how you convert polar to rectangular coordinates.

<r, θ> = (rcosθ , rsinθ)

And if you consider your rectangular coordinates to be complex number in a complex number plane, you get:

<r, θ> = r(cosθ + isinθ)

So another way to represent e^a+bi is:

e^a+bi = <e^a, b>

I’ve said before that the angle brackets < and > are not standard mathematical notation. I just use them as a visual cue that the coordinates are polar coordinates. Mathematicians generally don’t bother with that, they just use parentheses for both cases. But sometimes (actually rather often) they will write polar coordinates like this:

<r, θ> as: re^iθ

(And need I remind you: the angle must be expressed in radians. e^iθ will give you the sine and cosine of θ, but only if θ is radians. Another reason why mathematicians prefer radians.)

A Maximally Geeky Bonus

What if θ is π? (I.e., what if θ is 180 degrees?)

The sine of π is zero. The cosine of π is -1.

So if e^iθ = cosθ + isinθ, and θ = π, then e^iπ = cosπ + isinπ = -1 + 0.

e^iπ = -1

Adding 1 to both sides we get:

e^iπ + 1 = 0

Note the beauty of this. It contains all three of the numbers I introduced you to, e, π, and i, plus the numbers 0 and 1–which I sure hope I did not have to introduce you to (though maybe some reader of this took woke mathematics and got to hear about “saving the planet” instead of actual math).

Arguably these are the five most important numbers in mathematics, and one formula ties them together, and no other more mundane number appears in the formula.

This is known as Euler’s identity, and it’s a favorite. There’s absolutely no way anyone can see this intuitively, no way to see that e, i, and π should be related to each other in any way, much less all three of them directly like this.

And yet they are. And much of our modern world depends on this crazy little fact.

Obligatory PSAs and Reminders

China is Lower than Whale Shit

Remember Hong Kong!!!

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

China is in the White House

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

Joe Biden is Asshoe

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

But of course the much more important thing to realize:

Joe Biden Didn’t Win

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

2023·07·08 Joe Biden Didn’t Win Daily Thread

A Caution

Running good candidates is only HALF of the battle!

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

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.

Yep, you-all are incompetent, and so proud of it you expect our applause for your sincerity. Fuck that!!

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.

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:

(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).

Last Week:

Gold $1,920.80
Silver $22.85
Platinum $913.00
Palladium $1,260.00
Rhodium $4,700.00

So here it is, Friday, 3PM MT after markets closed and we see:

Gold $1,925.40
Silver $23.16
Platinum $920.00
Palladium $1,278.00
Rhodium $5,250.00

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

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 after π/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 !!!

2023·06·03 Joe Biden Didn’t Win Daily Thread

A Caution

Running good candidates is only HALF of the battle!

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

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.

Yep, you-all are incompetent, and so proud of it you expect our applause for your sincerity. Fuck that!!

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.

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:

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

Spot Prices

All prices are Kitco Ask, 3PM MT Friday (at that time the markets close for the weekend).

Last Week:

Gold $1,946.20
Silver $23.41
Platinum $1,033.00
Palladium $1,458.00
Rhodium $7,900.00

So here it is, Friday, 3PM MT after markets closed and we see:

Gold $1,948.50
Silver $23.68
Platinum $1,015.00
Palladium $1,459.00
Rhodium $7,450.00

Again, gold being kept below 2000 at all costs. It took a 30 dollar hit Friday after climbing on Thursday. So things ended up almost exactly where they were a week ago.

Pi…or π if Greek Floats Your Trireme

I probably should have done π before doing e. It’s a lot more relatable for most people, who find compound interest magical…and if they don’t find that magical, the idea of continuously compounding it might induce a headache if they think about it too much. (The way out involves concepts verging on calculus.)

But who the heck can’t visualize a circle?

Pi is, of course, the ratio of the circumference of a perfect circle, to its diameter.

The ancients wrestled with this. Pi isn’t quite 3. Nor is it 22/7ths (or 3 1/7 if you can’t stand so-called “improper” fractions and have to see it as a “mixed number” [an integer plus a “proper” fraction]). [An “improper” fraction is any fraction where the top number is at least as large as the bottom number, e.g., 22/7 or even 5/5.]

Perhaps they just needed a different fraction. 333/105 is closer to π, 355/113 is closer still…but neither are spot on. Nor are 52163/16604, 103993/33102, 104348/33215 nor even 245850922/78256779.

There is no possible fraction with integers top and bottom (numerator and denominator) that will represent π. It cannot be expressed as the ratio of two whole numbers. It is ir-ratio-nal. Which leads to “irrational” numbers being a term. It’s unfortunate, because it makes them sound crazy, woke, Leftist, or something.

However, if you truly want a crazy number, consider either the number of illegal “immigrants” coming through…or the US Federal debt.

Pi works out to 3.14159265358……approximately.

There are plenty of irrational numbers out there. For example, if a number isn’t a perfect square (e.g., 1, 4 (2×2), 9 (3×3), 100 (10×10), or 3721 (61×61), then the square root of that number is irrational. So the square root of 3 is 1.732050807…. (easy to remember the start of this, as George Washingon was born in 1732 (new style)).

An irrational number can’t be written as a fraction, and if written as a decimal never ends.

But wait, 1/3, when written as a decimal never ends, either. And 1/3 is clearly a ratio-nal (rational) number.

But a rational number written as a decimal will fall into a repeating pattern if it doesn’t actually end. 1/3 = 0.33333…. (obvious repeat), 1.6 = 0.166666 (repeats, after the first digit). 1/7th = 0.142857142857…. (a seven digit group, repeating forever). In fact the maximum number of digits before repeating is the denominator itself minus 1; 1/7th is at that maximum since it repeats after 7-1=6 digits. So does 2/7, 3/7 and so on (in fact the repeating digits form the same sequence, just started in different places. 5/7= 0.714285714285…. In fact fractions n/7 start with every single one of the numbers in the sequence ending with 6/7=0.857142857142.

[This repeating nature of some fractions…but not 1/2, 1/4, 1/5, 1/8, 1/10, 1/16, 1/20 and so on, is an artifact of our decimal system, operating in base 10; 10 expressed as the product of primes is 5 x 2. As a result, if the denominator is a number that factors completely into 2s and 5s (i.e., any number of 2s and any number of 5s, in any combination), the decimal point representation will eventually end. But if the prime factors of the denomination include any other number…the decimal will never end, but will repeat. So, for instance, 60 (2 x 2 x 3 x 5) has that one 3 in it, so fractions with sixty in the denominator may not end. They will end if the numerator also divides by 3; then the 3s cancel out, e.g., 42/60s also equals 14/20ths or 7/10ths. The denominator is only 5s and 2s and so that fraction is just 0.7.]

So e and π are both irrational numbers, along with almost every square root, cube root, fourth root, and so on.

But π and e are also members of a class known as transcendental numbers. These are numbers that are irrational and can’t be found by solving a polynomial (which can involve taking a root of some other number). In other words, you cannot write a formula like this:

xⁿ – m = 0

Where m and n are any integers you care to pick, and have x equal to π or e or any other transcendental number, whereas the square root of 2, which is also an irrational number, isn’t transcendental because it solves this problem with m and n both set to 2:

x² – 2 = 0

(By the way that’s true even if you combine different powers of x; I just gave a simple case.)

Pi can now be computed to billions of digits, and there’s no sign of it ever ending (nor is it expected; it has been proved to be transcendental, and in math you can actually prove things to be solidly, incontrovertibly true).

Pi is hugely important in mathematics; it shows up all over the place. And in the sciences just about anything having to do with geometry will have π in it. It shows up in Maxwell’s equations and in Einstein’s equation describing general relativity, both of which involve geometry.

Pi also shows up in measuring angles. Consider a circle of radius 1. (We don’t care about whether that’s a meter, furlong, line, chain, light year, or parsec, though the last two would be a bit unwieldy in a diagram.)

Now imagine starting at the right side of the circle (3 o’clock), and going counterclockwise, measuring the length of the arc. If you go all the way around the circle, your total length is 2π. (Remember the radius is 1, not the diameter.) Since this is based on the radius of the circle, we say you have measured an angle of 2π radians. And this works as an angle (not a linear measurement) because it doesn’t matter what the size of the circle is; the full trip around the circumference is of course 2π times the radius, a full circle is 2π radians as well as being 360 degrees.

This sounds like it should be a solid pain in the butt. A 30 degree angle is 1/12th of the full circle, so that works out to π/6 radians or 0.5235987755982987307710723054658…radians. Most people would give up sooner than I did. But who wants to write that out even to five digits?

So they don’t. They’ll write that angle as π/6.

Since radians are simply one length divided by another, without any sort of constant fudge factor thrown in, they’re dimensionless (in physics) and for mathematicians are the “natural” way of working with angles, just like e is the natural base of logarithms.

OK, so how about, instead of stopping after traveling around the full circle, you stop after some other, arbitrary angle? Where are you? You start at one unit to the right and zero units up. After a quarter circle (π/2 radians), you’re now at zero units to the right, and one unit up.

How about that thirty degree angle? Which is to say, 1/12th of the way around the circle, which is to say π/6 radians? Well it turns out you are 1/2 a unit up (exactly), but the square root of 3, divided by 2 a/k/a sqrt(3)/2 units to the right. So yes most of the places on a circle have coordinates that are irrational (but not necessarily transcendental) numbers. Some few places have “special” coordinates, like 45 degrees (π/4 radians), where both sine and cosine are the square root of 2, divided by 2 or sqrt(2)/2; most are just some irrational number you can’t relate to the square root of some nice tidy little number like 2 or 3.

You can conceive of a function that will tell you how many units to the right you will be for any given angle…and another that will tell you how many units up you are for any given angle. You could even give these functions names, like, oh, say…cosine and sine.

Of course, I didn’t just pull those names out of my rectal database. Those are the actual names, and they get abbreviated cos and sin. (So somebody else pulled those names out of his rectal database, and managed to get everyone else to go along with it.)

It seems like this is a contrived situation, but this is astoundingly useful. First objection: Not all circles have a radius of 1. In fact most of them don’t.

So what? It scales. If a circle has radius 1.945, you can compute those positions by simply multiplying the sin and cosine of whatever angle, by 1.945.

[Or you can look at it another way…all circles have a radius of 1…provided you can pick whatever measuring system you want!]

So you will see sines and cosines all over the place in physics; just for instance the way you break a vector up into its components uses the sine and cosine of the angle the vector is pointing towards. A vector of length 10 pointing off at a 60 degree…ahem, π/3 radians) angle will have an x component of 5 (i.e., 10cos(π/3)) and a y component of 10 sqrt(3)/2 (i.e., 10 sin(π/3)). (Note that the cosine and sine of 60 degrees are swapped from the cosine and sine of 30 degrees.)

So sine and cosine can be very useful. And mathematically speaking, if you just take the cosine of some number…that number is assumed to be in radians. (Even deep in the bowels of your computer, in the arithmetic coprocessor, the sine function will take radians as its parameter. What you see on your spreadsheet when you ask for sin(30) is computed only after turning 30 degrees into radians.

And again radians are the natural way to do this. So much so that when taking about, say, the sine of some number, mathematicians don’t even bother to specify “radians” because a radian is simply a dimensionless ratio of arclength to radius without a fudge factor in it, like there would be for degrees.

Now there’s one more thing, and I will give my fingers (and your brains) a rest. The names cosine and sine imply a connection between the two functions, one is the co– of the other.

And that’s true. Let’s switch to degrees for a moment and check a few key values. The cosine of zero is 1. The cosine of 90 is 0. The cosine of 180 is -1. The cosine of 270 is 0 again. And the cosine of 360 is 1 again. And you can fill in the halves, the northeast, northwest, southwest and southeast: The cosine of 45 is sqrt(2)/2, the cosine of 135 is -sqrt(2)/2; the cosine of 225 is again -sqrt(2)/2, and the cosine of 315 is sqrt(2)/2. Merging the two sequences, and writing them out in order: 1, sqrt(2)/2, 0, -sqrt(2)/2, -1, -sqrt(2)/2, 0, sqrt(2)/2 and back to 1, after which 405 degrees is basically the same as 45 degrees, so we repeat the same cycle, over and over again.

Now let’s do the same thing for sines. We get: 0, sqrt(2)/2, 1, sqrt(2)/2, 0, -sqrt(2)/2, -1, -sqrt(2)/2, and back to 0.

Note that they are the same sequence…just starting at different places. If you were to actually graph these functions, they’d look identical…just one would be shifted compared to the other. So there’s definitely a connection worthy of deeming one of them to be the co– of the other.

The sine and cosine are important concepts, and although you can learn to play all kinds of tricks with them–enough so to be worthy of a full semester of math class–really what you’re going to need if you haven’t already rage-quit reading my posts, is to remember that the cosine is the distance to the right of zero (so it’s negative if you’re to the left of zero), and the sine is the distance above zero (so it’s negative if you’re below it), of a point on the “unit circle” (radius 1).

[And yes, being to the left of 0 as in 0bama is pretty far left.]

One last note. The full circumference of a circle is 2π. And because of that, a lot of formulae in physics have a 2π in them. So much so that some argue that the more natural constant is the one we think of as 2π, the ratio of the circumference of a circle to its radius rather than its diameter. That, of course would be 6.283…rather than 3.1415926…and those who make this argument advocate for calling this number τ, i.e., the Greek letter tau. (It rhymes with how.) This position is becoming increasingly popular but I doubt it will ever supplant pi. On the other hand, it’s natural to talk of τ/4 radians and have that be a quarter circle (rather than half of a half circle); that’s more intuitively a right angle than π/2 is.

OK, so far we’ve discussed numbers that show up on a number line. They may be transcendental, impossible to write out in full even as a fraction, but you can say that e is between 2.71828 and 2.71829, and that π is between 3.1415926 and 3.1415927.

Our next number, however, will be one you cannot do that with.

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 !!!

2023·04·29 Joe Biden Didn’t Win Daily Thread

A Caution

Running good candidates is only HALF of the battle!

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

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.

Yep, you-all are incompetent, and so proud of it you expect our applause for your sincerity. Fuck that!!

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.

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:

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

Spot Prices

All prices are Kitco Ask, 3PM MT Friday (at that time the markets close for the weekend).

Last Week:

Gold $1,984.90
Silver $25.17
Platinum $1,134.00
Palladium $1,682.00
Rhodium $9,000.00

So here it is, Friday, 3PM MT after markets closed and we see:

Gold $1,991.60
Silver $25.15
Platinum $1,084.00
Palladium $1,588.00
Rhodium $9,300.00

Things aren’t moving around all that much lately.

Globular Clusters

Time for a wrenching change of subject…because JWST took a picture of a globular cluster.

I was pretty much done with orbits anyhow.

A globular cluster is a grouping of stars, tens of thousands or even millions of them, forming an approximate sphere. The stars are very closely packed in the center and as you move away from the center the density decreases markedly.

This is Messier 2, a globular cluster that (as seen from Earth) is in the constellation Aquarius. (Note this is not the JWST’s image–it’s from Hubble.)

Charles Messier in the 1700s was interested in comets. In telescopes, before they get close to the sun and (possibly) become bright enough for people to see with the naked eye, they simply look like fuzzy blobs. Also, since they orbit the Sun, they move against the background stars (which are at least ten thousand times further away). So Messier would record a fuzzy blob in a certain location then check that location again a few days later. If the blob had moved, he likely had a comet. Otherwise, it was a permanent feature of the nighttime sky.

There were enough permanent blobs that Messier made a list of them, so when he stumbled across that blob again, he’d know he could ignore it. This is now the Messier catalog of about 110 objects. Many of the most famous nebulae in the night sky are Messier objects; many nearby galaxies are too. (Andromeda, for instance, is M-31, and the 800 bazillion ton gorilla of the Virgo cluster, M87 (the one with the really, really big black hole in its center), well, is a Messier object.

Many of Messier’s blobs were fuzzy spheres in his telescope (which was fairly primitive); as optics got better it became apparent they were clusters of tens of thousands or even millions of stars.

It also became apparent that there were quite a number of these in our galaxy…but they do not lie in the plane of the galaxy like the spiral arms do; they are in a swarm in what’s called the galactic halo, a spherical region centered on the bulge at the center of our galaxy. So if you imagine the Milky Way galaxy as, say a CD, some of the clusters are above it, and some below, most are just a few inches from the center of the cd. Other galaxies have them too, and they’re readily visible in powerful telescopes.

Another quirky feature about globular clusters is that the stars in them tend to be very old, over ten billion years old. For a while, astronomers would measure the age of a globular cluster, and come up with a number greater than the cosmologists’ number for the age of the universe. Of course this was absurd…how can an object in the universe be older than the universe. Over a number of decades as measurements were refined the discrepancy went away, but nevertheless, globular clusters are old.

Probably the most famous globular cluster (often just called “globulars”) is Omega Centauri. It’s so bright it was mistaken for a star by the ancients. It does not have a Messier number as it’s not readily visible from northern Europe where Messier worked–but folks living in Australia get to enjoy it. Another famous one is the Hercules cluster, M 13. It’s an easy one to find even with binoculars since it lies on a line between two stars in the Hercules “keystone” pattern (four stars that look like they outline a keystone).

JWST took the following picture of M 92, which is also in Hercules. It’s one of the brighter and more spectacular ones but is overshadowed by M 13. It’s particularly interesting because it’s one of the oldest globular clusters, somewhere between twelve and 13 billion years old. (The universe itself is presently believed to be 13.787 billion years old, give or take 0.02 billion years.) Scientists hope to learn something new about the universe as it was back then.

(We already know from spectrographic analysis the stars shown have almost no “metals” (astrophysicist terminology for elements other than hydrogen and helium) in them…they formed before the elements themselves were formed in more massive stars.)

The first thing you’ll notice is that the center of the cluster is missing. This was deliberate. The astronomers using JWST were interested in the outlying stars and the millions of stars clumped together in the center would have washed them out. They were able to use a gap that exists between two of the NIRCam long wavelength detectors. Talk about making lemonade from lemons!

M92 is about 27,600 light years away. It’s 16,000 light years outside of the plane of the Milky Way and 33,000 light years away from the galactic center. (We are about 27,000 light years from the center.)

This is of course a false-color image, because it’s JWST. None of what you see in this picture is actually visible to the human eye. Rather, this image was taken at four infrared wavelengths we can’t see, then the four each given their own color of visible light and the group combined together into one image. From the NASA website: “This image is composite of four exposures using four different filters: F090W (0.9 microns) is shown in blue; F150W (1.5 microns) in cyan; F277W (2.77 microns) in yellow; and F444W (4.44 microns) in red.” For reference, red light is about 0.7 microns and blue light is 0.4 microns. All of the things seen in the picture are therefore “redder than red.”

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 !!!

2023·03·25 Joe Biden Didn’t Win Daily Thread

A Caution

Running good candidates is only HALF of the battle!

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

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.

Yep, you-all are incompetent, and so proud of it you expect our applause for your sincerity. Fuck that!!

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.

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:

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

Spot Prices

All prices are Kitco Ask, 3PM MT Friday (at that time the markets close for the weekend).

Last Week:

Gold $1,990.30
Silver $22.70
Platinum $985.00
Palladium $1,495.00
Rhodium $10,000.00

So here it is, Friday, 3PM MT after markets closed and we see:

Gold $1,978.30
Silver $23.31
Platinum $993.00
Palladium $1,507.00
Rhodium $9,300.00

After dropping substantially earlier this week, gold reversed course by Thursday and spent most of Friday getting close to $2,000 but not over, then dropping down again. It ended up net down -15.20 for the day, which means it was over 1990 at close yesterday. I can’t see it going down much, honestly; the dollar is circulating the drain, and to keep it from going down the drain they would have to crater the economy. Because our “betters” play stupid games with the currency…we all win stupid prizes.

Galilean Relativity

Well, let’s give this a go, on short notice.

I like to write a first draft of science posts a couple of days beforehand. I’ll then come back in a couple of days and see a much better way of organizing it, or perhaps a more useful analogy, or other things like that.

I don’t have that luxury today; it’s 8PM mountain time already. So here’s hoping I’m organized from the get-go, because I am going to give it a go.

I’ve been planning to cover “gravitational slingshots” (the click-baity name) or “gravity assists” since much of what NASA has been doing is utterly dependent on them. That’s going to be a big topic, but I realized I can at least lay some groundwork tonight.

Consider a typical two body problem: some small satellite or even a space probe, and a big honkin’ planet.

I’ve been talking as if the probe orbits a point at the center of the planet. Technically that’s not true. The two bodies both orbit the “barycenter.” That’s basically the center of gravity of the system. Imagine the planet and the satellite on a seesaw, at whatever their “current” distance is. A million miles? five thousand? Ten billion? Whatever.

The barycenter is the point at which you’d want to put the fulcrum of the seesaw.

Now when it’s Earth and, say, a GPS satellite, that point turns out to be so close to the center of the earth that it’s likely immeasurable, because the earth is about 1.5 septillion times more massive than the satellite (6×10²⁴ kilograms versus 4 kilograms; a one with 24 zeros after it is a septillion). And the GPS satellite orbit is about 20,000 km in radius (it’s a circular orbit so we can speak of a radius here).

So the “balance point” between Earth and the satellite is 1/1,500,000,000,000,000,000,000,000th of the way in from one of the ends. Which works out to 13 and a third femtometers. Recall that a femtometer is roughly the size of a proton or neutron; much much much smaller than an atom, and you’ll see the difference between the barycenter and the center of the earth Just. Doesn’t. Matter.

It can matter, though when the two bodies are closer to each other in mass. The sun-Jupiter barycenter is significantly far from the center of the sun (the mass ratio is almost exactly a thousand to one, the sun is almost half a million miles in radius, Jupiter’s orbit is a bit over half a billion miles in radius). In fact the barycenter is actually outside of the sun. Earth and Moon are closer together in mass, but much closer together, so the Earth/Moon barycenter is still a thousand miles or so down below the surface. Pluto and Charon are more nearly the same mass…they’d be a double planet if they were planets. The barycenter of that system is out in space.

When New Horizons was still far out from Pluto it took the pictures that were assembled into the GIF above of Pluto and Charon. The white x marks the barycenter.

OK, so now that I’ve set the record straight and planet and satellite both orbit a barycenter, I’ll now pose a question that is going to sound like it comes completely out of left field.

What if the barycenter is moving?

Take a space probe doing a flyby of a planet. It’s an escape orbit…it’s flying by never to return, so we are talking about a hyperbola. Under the circumstances the barycenter is effectively at the center of the planet.

So what if the planet is moving? They do move you know.

It turns out that this makes absolutely not a shred of difference. The spacecraft will move along a neat hyperbola as seen from the planet, no matter how fast the planet is moving.

The deep reason for this is that one level, it’s meaningless to talk about a planet or a star moving.

Einstein didn’t quite invent the concept of relativity; rather he refined it. Galileo truly originated it, to cover cases where (for instance) you’re in a moving railroad car tossing a ball in the air, and you have no way to tell the railroad car is moving. In fact, you could claim the railroad car is stationary, and the world is moving. As long as the train isn’t accelerating, you will feel like you aren’t moving.

It turns out that all of the mathematics of speed, velocity, and so on, is exactly equivalent no matter whether you regard the train car as stationary and the earth moving, or vice versa. The signs (plus or minus) on all the numbers are different, but the moving objects behave the same way either way. Galileo realized that there’s no absolute motion, only relative motion. The train is moving? Relative to what? The earth? Or the passengers on the train? Or the bug flying into the locomotive’s windshield?

It’s even more true out in space. Who’s moving, and who’s stationary. Is anything stationary?

You pick a frame of reference and go from there. Since they’re all equivalent, pick a convenient one. And it turns out in the case of the spacecraft flying by a planet, the convenient frame of reference is the center of the planet (I mean the barycenter of the planet/spacecraft system…here let me find my atom-sized measuring stick to correct it). In that frame of reference, draw a hyperbola, that’s what the spacecraft does.

Even though the planet is moving in orbit around the sun. Well, from the planet’s point of view the sun is going in circles around the planet.

[I remember in a college class discussing the sun as seen from Earth; the professor described the sun’s apparent path through the sky as if it were in a one year orbit around the earth. He gave us orbital elements just like I discussed a few weeks ago. And it worked, because…Galileo. We could compute where the sun would appear on any particular day. Of course some satellite in a 150,000,000 kilometer orbit around Earth is not going to complete that orbit in a year…not even in a thousand years. So we had to pretend the sun was closer than it is. The reason why is that in analyzing an orbit we need the combined gravitational parameters of the planet and the satellite…but again the satellite’s contribution is twenty or so digits past where you round off, so we don’t bother adding them together. Similarly, with the sun-earth system, the gravitational parameter that matters is the sun’s, not the earth’s; our gravitational parameter is a rounding error. So we can either put the sun closer to the earth for this analysis…or use the sun’s gravitational parameter in place of our own. The prof went with putting the sun closer.]

OK, we’re halfway to understanding the “slingshot.” I can’t say “see you next week” with a perfectly straight face, so I’ll settle for “see you next time.”

[PS: So what did Einstein add? He added that the rules change when the relative velocity between two objects gets close to the speed of light, and later on he incorporated accelerations into the mix–Galileo specifically excluded them.]

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 !!!

2023·02·18 Joe Biden Didn’t Win Daily Thread

A Caution

Running good candidates is only HALF of the battle!

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

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.

Yep, you-all are incompetent, and so proud of it you expect our applause for your sincerity. Fuck that!!

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.

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:

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

Spot Prices

All prices are Kitco Ask, 3PM MT Friday (at that time the markets close for the weekend).

Last Week:

Gold $1,866.50
Silver $22.08
Platinum $956.00
Palladium $1,614.00
Rhodium $12,950.00

So here it is, Friday, 3PM MT after markets closed and we see:

Gold $1,843.20
Silver $21.81
Platinum $930.00
Palladium $1,583.00
Rhodium $11,900.00

Everything trending down. I don’t think I’ve seen palladium or rhodium this low in a long, long time. And those are likely to be good economic indicators as their uses are industrial.

Hyperbolic Orbits

We now turn to the remaining two-body case, the hyperbolic orbit. This is the sort of orbit an object is in whenever it is moving at above escape velocity.

You get a hyperbola whenever you slice through both “halves” of a cone. It doesn’t have to be vertically as shown in this diagram, the plane just has to be “vertical” enough in the diagram to not miss one of the two “halves” of the cone.

More formally, it’s going to look like this:

Note that this curve has two parts. An orbit will only be one of these two lines–the other is physically meaningless–and the focus for that line (F1 if it’s the right line, F2 if it’s the left) will be where the primary is. You can sketch a hyperbola by crossing two lines (the asymptotes) as in the diagram, then drawing a curve that never quite reaches the asymptotes (it gets closer and closer without ever reaching it, which is where the term “asymptotic” appears, as in “Trump’s administration asymptotically approached being able to actually arrest one of the people in the Deep State”) on either the left or right side of the X. Actually a not-uncommon trick is to draw a rectangle, make the crossed lines the diagonals of the rectangle, then sketch the hyperbola, with the vertex touching the middle of the sides of the rectangle. That point where it touches (and is closest to the focus) is the vertex and of course corresponds to periapsis. Apoapsis is at the ends of the line…which is infinitely far away. Mathematically speaking one end of the line is infinitely far in the past, the other infinitely far in the future, but of course in reality the object has to have come into being more recently than that, and closer than infinity, too.

Another way to draw a hyperbola is to graph the function 1/x. At 0, it’s undefined (or infinite, if you want to stretch a point), the line drops down from infinity until it reaches x=1, y=1, then zooms off to the right…but never reaches y=0. Though it can get so close you’d never be able to tell it wasn’t straight there. The asymptotes are the X and Y axes, and of course the thing is tilted at a 45 degree angle counterclockwise to the one in the diagram above.

And yet another way is to plot all of the points, whose distance from F1 minus their distance from F2 is some constant…and that constant is the distance between the vertices, or 2a. (And a here functions in many ways identically to the a in an elliptical orbit.) This is weirdly analogous to an ellipse, where the sum of the distances from any point on the ellipse to both foci is 2a.

The net effect of a “flyby” on a hyperbola is the object’s direction of travel is bent at some angle (the angle between the two asymptotes). To try to make this visualizable, imagine you are that object, just zipping along through space. If not interfered with, you’ll go in a straight line, at a constant speed (no friction to slow you down). But as it happens some large object (a star, say) is almost in your path. As you get closer and closer, it is pulling you towards it, so you speed up, and you pull off your path a bit; as you get closer and closer, you move faster and are pulled more and more off that straight line you were moving along. Then you fly past it. At that moment you’ve been bent pretty far off your former straight line path, and you are moving really, really fast. But now the process runs in reverse; the object pulling at you almost from behind slows you down and bends your path even more…but once you’re far away, you’re back to traveling a straight line, and nearly constant speed. But it’s a new straight line; the star bent your path.

You can determine whether or not you are in a hyperbolic orbit by measuring your speed and distance from the primary; just plug that distance into the escape velocity formula from last week; if your speed with respect to the primary is higher than that, you’re in a hyperbolic orbit, and you will escape from that primary. And furthermore, this is the only time you’ll encounter it. (To know the exact trajectory an object will follow, of course we will need its direction at that time, best determined with multiple measurements.)

This was famously demonstrated by ‘Oumuamua, an object that zipped through our solar system in a hyperbolic orbit back in 2017. It came from some other star, or maybe from the interstellar void. It was the first time we detected anything like that. It was discovered by the Pan-STARRS telescope on Maui (which spends a lot of time searching for comets and asteroids). ‘Oumuamua is the Hawai’ian word for “scout,” which was a perfect choice.

Here is a video AND a static diagram.

And here is another view…zoomed out quite a bit, Neptune’s orbit at about 30 AU is visible, whereas before Mars at 1.52 AU is the outer orbit in the diagram above. Mars is red in both diagrams. In the diagram below ‘Oumuamua is about to leave the upper left side of the picture. Also note the vertical lines which help give you a sense of ‘depth’ looking at the picture. The lines end at the plane of the planets’ orbits.

Here, from Wikipedia, are the orbital elements plus a few other things. The “epoch” for this is the 23rd of November 2017. (Other objects will pull on ‘Oumuamua and alter its orbit…I’ll have more to say about that sort of thing in future posts.)

Perihelion	0.255916±0.000007 AU
Semi-major axis	−1.2723±0.0001 AU^[b]
Eccentricity	1.20113±0.00002
Average orbital speed	26.33±0.01 km/s (interstellar)^[10] 5.55 AU/year
Mean anomaly	51.158°
Mean motion	0° 41^m 12.12^s / day
Inclination	122.74°
Longitude of ascending node	24.597°
Argument of perihelion	241.811°
Earth MOID	0.0958 AU · 37.3 LD
Jupiter MOID	1.454 AU

An AU is the average distance between the Earth and the sun, so basically this thing got four times closer to the sun than Earth does; this was inside the orbit of Mercury. Note the inclination, the longitude of the ascening node, the argument of perihelion, all explained in past posts. And the eccentricity is greater than 1, just like for any hyperbola. The kicker, though, is the average orbital speed…26.33 kilometers per second. But that was its speed “way out there” (‘Oumuamua will spend 99.99999999999% of its existence out there) not its speed as it flew by the sun! Its maximum speed was 87.71 kilometers every second. To put that in perspective, earth’s orbital speed is about 29.7 kilometers per second. When it was the same distance from the sun as Earth is, it was moving at 49.67 km/sec–comfortably above the escape velocity here which is about 40 km/sec.

This encounter bent ‘Oumuamua’s straight line trajectory by 66 degrees.

Even at its interstellar speed of 26.33 kilometers per second, it covers 5.5 AU in a year, which means it covers the distance from the Sun to Jupiter (5.2 au) in less than a year.

The MOID numbers are how close the line of the orbit of ‘Oumuamua comes to the line of orbit of Earth and Jupiter. This is not how close the asteroid came to either planet though, because when ‘Oumuamua was closest to those orbits, those planets were nowhere near that point in their orbits. (MOID is used to assess the possible future risk of a collision. When both objects are in elliptical orbits and keep coming back to the same place time after time, they could, sometime perhaps millions of years from now, be at the points nearest each other’s orbits at the same time.)

‘Oumuamua turns out to be quite a puzzler. They’re not sure what it is made of; it didn’t outgas much like a comet would, but that doesn’t mean it isn’t made largely of ices; nitrogen ice is a candidate. And we simply don’t know whether it formed near some other star and got ejected from that star’s planetary system, or whether it might have coalesced deep in the interstellar void far from any star. (Wikipedia has more info than I have time this evening to read, much less relate.)

And that touches on a topic. I’ve described these orbits as if they will persist forever. They would, actually, if only there were just two bodies–primary and satellite–involved (there would be a minuscule amount of energy slowly radiated away by gravity waves, an effect not accounted for in Kepler’s and Newton’s work, but that is immeasurable over billions of years for planets and the like).

So how do things get ‘ejected’ from planetary systems? How do comets get kicked into the central part of the solar system where they get to play pinball with planets? How do comets’ orbits get altered so they are short period comets that come back again and again every few years or decades?

One answer, that applies mainly to comets is that as they heat up and outgas, the jet of gas acts like a rocket and nudges the comet into a slightly different orbit.

But that’s not the full explanation, nor even one that applies in all but a minority of cases (though it did affect ‘Oumuamua).

Satellites in orbit around Earth will be affected by the equatorial bulge; this effect can sometimes make 500 miles’ difference after one day of orbiting. The bulge affects, and is very definitely acted on by, the moon. But those effects are small for large orbits, like those of the planets around the sun.

No the real explanation is that there are more than two bodies in the universe, and sometimes that can make a big difference. And, just to make life interesting, those calculations are very time-intensive to do. (As the joke goes, “This is why God made computers.”)

We’ll take that up next time.

Obligatory PSAs and Reminders

China is Lower than Whale Shit

Remember Hong Kong!!!

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

China is in the White House

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

Joe Biden is Asshoe

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

But of course the much more important thing to realize:

Joe Biden Didn’t Win

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

2023·01·14 Joe Biden Didn’t Win Daily Thread

A Caution

Running good candidates is only HALF of the battle!

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

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.

Yep, you-all are incompetent, and so proud of it you expect our applause for your sincerity. Fuck that!!

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.

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:

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

Spot Prices

All prices are Kitco Ask, 3PM MT Friday (at that time the markets close for the weekend).

Last Week:

Gold $1,866.70
Silver $23.92
Platinum $1,100.00
Palladium $1,889.00
Rhodium $13,250.00

So here it is, Friday, 3PM MT after markets closed and we see:

Gold $1,921,60
Silver $24.38
Platinum $1,073.00
Palladium $1,863.00
Rhodium $13,000.00

Gold is going somewhere–we’re not at record levels (~$2070), but at the rate things are going it won’t be long, unless of course it reverses course (let’s face it: “they” will do their darndest to make that happen). Silver is too, though not as much. The others…not very much at all. This looks like the prime “pusher” is people worried about the economy. They will tend to pick gold over silver…and the other metals won’t share in that.

My gut feel is that it will end up dropping again, hard. If I am wrong and the dollar is going to collapse to the point where you can pay off your house with a silver dime because silver is at a million toilet-paper bucks an ounce…well, so be it.

If inflation gets THAT bad, expect your credit card companies to amend their agreements so as to index your balance to inflation. And certainly any other new loan. But old car and house loans cannot be amended!

How Far Are the Stars?

Thanks to Hollywood, it’s easy to imagine that since we’ve gone to the Moon (and yes, we have gone to the Moon), the planets are just one step away–one we inexplicably didn’t just take right after Apollo–and the stars one more step after that.

The moon’s orbit’s semi-major axis (which is one half of the length of the elliptical orbit, measured across the longest part; this serves as a good average distance) is 384,399 kilometers. But you should subtract the earth’s radius from that, as well as the moon’s, as it’s center-to-center. Let’s call it, very roughly, 375,000 kilometers.

Compare that to the distance between the earth and the sun, one “astronomical unit” of 149,597,870.7 kilometers. It’s 398.9 times as far…call it four hundred times. And these are the sorts of distances we’d have to travel to get to Mars. Sure it gets closer to us than 150 million kilometers, but we would not be traveling that shortest distance; we’d be using a “Hohmann Transfer” or something very similar to that (because it would take a lot less delta-V to do that; i.e, a lot less fuel), and that would easily be over 300 million kilometers.

Traveling 400-800 times as far is not a “small step.”

Compare Columbus traveling 3000 miles or so (one way) to the sorts of things people did before him, where they hugged the coastline but often traveled thousands of miles. Comparatively speaking, that’s a much smaller jump than going to Mars, having gone to the Moon, would be.

This is in large part why we’ve been doing everything with robot probes. It takes them as long as it would take astronauts, but they don’t have to bring along food and life support for months or years of travel…so that makes it possible to do it with smaller rockets…smaller meaning rockets smaller than a mountain.

Neptune, the outermost planet, is at about 30 AUs distance; that’s a 15-fold jump over a trip to Mars. Significant, especially when you consider the time it would take, but not that big a jump from getting to Mars. If we can start sending people to Mars, it won’t be that much harder to go other places (assuming there’s something there at the other end that’s not instantly lethal…and let’s face it Jupiter’s moons are mostly close enough to Jupiter’s radiation belts that astronauts would be broiled alive without a lot of heavy shielding…and that word “heavy” is a deal breaker). But, nonetheless, the planets are at similar distances to each other…compared to the jump it will be to go from moon travel to planetary travel.

What about the stars?

Proxima Centuari is the nearest star. And it is 268,000 AUs away. In other words it’s basically ten thousand times as far as Neptune.

We could have Southwest Spaceways running daily (except when their computers go tango uniform) trips to Neptune for tourists…and we’d be nowhere near ready for star travel. For a number of reasons, the main one of which would be having to go a thousand times as fast just to get there in a lifetime. But that’s just a consequence of the YUGE jump in distance.

That day we first set out for the stars, will represent a “giant leap for mankind” bigger than everything before it, put together.

Calculus Made Easy (No Joke)

This is a conceptual introduction to calculus; the meat of it starts about three minutes in–assuming, of course, that it posts at all! There’s no actual math drudgery involved for the conceptual part (though he does start flinging it at you around 12 minutes or so), though you do need to understand graphs. You should come out of it with an understanding of what integration and differentiation are, even if you don’t actually know how to do them.

If it buggers up here’s the link: h ttps://www.youtube.com/watch?v=kuOxDh3egN0 (remove the space).

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 !!!

2022·12·10 Joe Biden Didn’t Win Daily Thread

Another Twitter Censorship Drop.

I must admit it’s having more of an effect than I expected. The Left is having to squirm really hard to pretend it’s not there, meaning it’s penetrating their MSM armor…somewhat.

We got another dump Friday night, and this time more directly to do with the 2020 election, instead of some very-well-connected shit-for-brains’s laptop.

May the Left go apeshit and stroke out. They deserve worse, so I guess I’ve practiced charity/mercy just this once.

A Caution

Running good candidates is only HALF of the battle!

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

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:

https://youtu.be/WjM26GWWoGk?t=21

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.

Yep, you-all are incompetent, and so proud of it you expect our applause for your sincerity. Fuck that!!

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.

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:

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

Spot Prices

All prices are Kitco Ask, 3PM MT Friday (at that time the markets close for the weekend).

Last Week:

Gold $1,798.30
Silver $23.19
Platinum $1,023.00
Palladium $1,974.00
Rhodium $14,100.00

So here it is, Friday, 3PM MT after markets closed and we see:

Gold $1,798.90
Silver $23.56
Platinum $1,034.00
Palladium $2,026.00
Rhodium $13,350.00

It looks like gold didn’t move, to speak of! Actually it dropped and (unusual for a Friday) came back up. It’s trying to bust through $1800 but hasn’t done so. In a normal (non-manipulated) market, you would expect it to either bust through and then just keep going, or turn around and go the other way. In this distinctly not non-manipulated market, who knows?

Artemis I Coming Home

The unmanned Artemis I mission is on its way back, after three weeks in space. In the days of the Space Shuttle going just to orbit (instead of to the ISS) that was a fairly long mission. But this time it not only went to the moon it went significantly farther. It even took a picture of the (round) Earth behind an (also round) Moon, the sort of view you would expect if you were arriving from interplanetary space.

This is the furthest any spacecraft designed to carry people in it has ever gone from Earth. And, presuming that the manned flight slated for 2024 follows the same path, those four people will set a record for furthest distance from Mother Earth, ever. And even before they are more than a thousand miles above the surface they will have been further than anyone has been in half a century.

Apollo only took roughly three days to go to the moon (each way); Artemis was about as fast, actually, but took some side trips once it got there. (It would actually be harder to go to the Moon more slowly…orbital mechanics can be surprising sometimes.) But the fact that the missions are slated to take three or more weeks is an indication we have deep space exploration in mind now…as in other planets, as in Mars. (Which sucks, but much less than anywhere else other than Earth.)

The Orion module has a solar array, there are cameras mounted on it so it’s possible to see the spacecraft from the outside. No need for NASA animations like they did for Apollo, and if something like Apollo 13 should happen [I certainly hope NOT], they’ll be able to actually look at the outside of the spacecraft to see what happened. In the actual Apollo 13, the astronauts couldn’t see the damage until they separated from the service module to start re-entry.

Which brings me to today’s topic.

I have to explain something up front, and that is: how a rocket works. It’s not rocket science (seriously; I tell people that rocket science isn’t rocket science, at least it sure ain’t compared to particle physics). In essence a rocket moves because of Newton’s third law…every action comes with an equal but opposite reaction. If you push something away from you in the direction opposite of the one you want to go, you react by going the direction you want to go. A rocket functions by adding a bunch of energy to a bunch of mass and letting that mass go out one end…the rocket goes the other way. The rocket changes speed; and that’s the goal…the change in speed is called delta V, delta V costs reaction mass, and the heavier you are at the time, the more reaction mass it costs.

With nothing to grab onto in space–like, say, tires on pavement, that’s pretty much the only way to get moving (with the exception of a solar sail). You can’t push on something outside your spacecraft, so you have to push on something you brought with you. But that means you must carry a bunch of mass with you for the sole purpose of throwing it away en route! (It is called “reaction mass” for that reason.) And that mass requires even more mass to get moving. The engineering trick is to find the fuel (as it turns out liquid hydrogen and liquid oxygen are the best readily available) that will generate the most impulse (change in momentum) for the least amount of weight. (Heating it up by burning it and letting it blast out the back end under high pressure is basically how we do it.) And to design your rocket to be as light as possible and as efficient as possible. That is hard, and we seem to be doing it as about as well as can be done; there’s little room for improvement without an (likely as yet unimagined) radically different way.

We’ve done halting experiments with using a nuclear reactor to heat the reaction mass hotter than burning it would; that would help but few people relish the thought of setting up an almost-explosion under a nuclear reactor and sending that reactor up into the air.

Anyway, in a nutshell, and without supplying numbers, that is the “30,000 foot” “granular” view of what rocket science is trying to overcome.

Apollo was just barely possible. The biggest rocket we could build could barely do the job. Think of it in terms of how many times you have to change velocity, each of which requires reaction mass. And you need to think of it back-to-front. You have to change velocity to safely land on Earth (rather than go splat! and leave a very Moon-like crater), after traveling through space at, basically escape velocity because you just did a ballistic orbit from somewhere far away. That takes reaction mass–a lot of it because the delta-V is something like 25,000 miles per hour. (Except we found a way to avoid that…but I am getting ahead of myself.) That fuel has weight, just like the capsule and astronauts do; in fact it would weigh many times as much as the astronauts and capsule. But in order to get to Earth from the Moon, they have to leave Lunar orbit and get to escape velocity. So you need enough fuel to push the astronauts, and that fuel being brought along for landing, through a second-to-last delta V. That’s much more fuel than you would need if it was just the astronauts and spacecraft you needed to push. And then, you have to get off the Moon in order to be in lunar orbit. More fuel, and it’s like compound interest, all the way back through landing on the moon, entering lunar orbit, leaving earth orbit, and getting to Earth orbit…such that it would require a truly gigantic amount of fuel for the initial boost off of Earth, because most of what you’d be lifting was…fuel. The rocket would be as big as a mountain. And that is not that much of an exaggeration; it might not be any exaggeration at all.

We couldn’t do that then. And we can’t do that now.

No I am not claiming we never went. I am claiming we did a lot of creative engineering, instead of just building a massive one-piece rocket. We set things up in such a way as to save fuel. We didn’t, for example, land the whole spacecraft on the moon, just a very tiny, fragile part of it, and we only sent two of the three astronauts down. We also threw away empty fuel tanks (i.e., rocket stages) on the way (a trick we need to do just to get to Earth orbit, unfortunately), so at least we weren’t coming back to earth with a gigantic (read massive) spacecraft that was mostly empty fuel tanks, then trying to land it gently. We were coming back with the bare minimum mass. And of course one other thing, perhaps the most essential, which I’ll get to very shortly.

Even with all those savings, it’s insane. Artemis weighed 5,750,000 pounds at launch. What’s coming back to us in Sunday weighs 18,200 lbs, less than 1/300th as much. That’s 99.7% overhead or 0.3% payload. And they did their best to make sure as much of that was fuel as possible. If you want to double the weight of that capsule, you don’t just add another 18,200 pounds to Artemis’s liftoff weight…no, you make Artemis 11,500,000 pounds. Every pound sent to the moon and then back to Earth requires 300 pounds of rocket plus fuel. (I expect they make sure the astronauts don’t eat too much the night before launch.)

You are, I hope, beginning to understand why space travel costs so damned much.

I promised to tell you about one more savings, and I saved it because it’s going to cover the rest of this post: The most critical and scariest thing we did was to come up with a way to make the final delta-V–the one that would make the rocket as big as a mountain–without expending any fuel at all! That was a yuge savings, because that gets compounded through all of the phases of the mission, not just the first two or three of them. And that alone might just have reduced Apollo to one 1/4 the size it would have been, otherwise–changing 25,000 miles an hour into zero miles an hour takes a lot of fuel there at the end.

I refer, of course, to slamming into the Earth’s atmosphere at escape velocity and letting air resistance slow the capsule down for us. No fuel burned.

The trick was (and is) to do so in a way that didn’t result in spacecraft+astronauts burned instead. Slamming into the atmosphere at 32 times the sea-level speed of sound will heat things considerably; five thousand degrees Fahrenheit is quite toasty. (And incidentally, this is one of the major reasons hypersonic travel in the atmosphere is a challenge.)

It’s called aerobraking, when it isn’t called “bring me my brown pants.”

Because the rocket equation (which implies all that compounding) was well known since WWII if not earlier, we knew we’d have to do this if we were to go to the moon, and tests had been done well before Apollo 11. The first thought was to make the spacecraft extremely streamlined, but that turned out to be a bad idea. So instead a nearly flat face with as much air resistance as possible would be presented to the atmosphere smacking into the vessel at 25000 miles per hour. (And I thought the wind here was bad.) But it had to be a material that wouldn’t just burn away, so that took a lot of materials engineering. In the case of the Space Shuttle the heat-resistant tiles did the job (though the Space Shuttle didn’t come back at nearly as high a speed).

But that wasn’t the only issue. We had to hit the atmosphere at an almost perfectly precise angle. Too steep, and the spacecraft would burn up anyway. Too shallow and the spacecraft would actually skip off the atmosphere like skipping rocks off a pond. (Before you object that the air–certainly not the thin upper atmosphere–isn’t as substantial as the water, try hitting it at 25,000 miles per hour and report back.)

Skipping off the atmosphere would not be instantly fatal, but the spacecraft would now be moving away from Earth at escape velocity and there’s be absolutely no way to rescue the astronauts and (remember, no fuel) no way for them to turn around and come back.

As the spacecraft is approaching Earth, which presents a circular cross section to it, it has to aim near the edge of that cross section…somewhere in a ring about 22 miles thick (but thousands of miles cross). Outside the ring…skip. Inside…slag.

The movie Apollo 13 had one clip in it from an actual newscast at the time, where a blowtorch was aimed at a model of the capsule as the “news”reader talked about what had to happen. I tried to find that clip and failed, but it was an understatement of the peril they had to go through.

So you gotta hit the right angle. And you have to hit the right part of the arc of the ring, too, or you end up landing in Antarctica or Siberia instead of near the Navy ships sent to retrieve you.

Your arrival time at the ring (hopefully not ‘of fire’) is dictated by one thing: the time you left lunar orbit. Because once you’ve done that, you’re basically a bullet, only much bigger and much faster. (Yes, you can make tiny course corrections…but those are basically windage and elevation, not arrival time at target. And you need windage and elevation, because that’s how you make sure you’re going to hit that ring.) So where the astronauts came down was dictated days in advance and they didn’t have much in the way of choices, which is why they came down at the corner of No and Where out in the Pacific. It was a matter of which way the Earth was facing when they hit that ring, which, again, depended on when they left lunar orbit.

And yet, we did this nine times for Apollo 8, 10, 11, 12, 13, 14, 15, 16, and 17. (As well as for Apollo 7 and 9, but only from Earth orbit.) Nary a hitch. The Columbia disaster was a failure of the Shuttle tile system and is similar, but Apollo had a perfect record handling a tougher problem.

In the last fifty years almost nothing has changed. We still have to play meteor to get back to Earth. We’ve gotten better at building spacecraft, but we didn’t use the mass savings on fuel to brake at the return; we just made the spacecraft bigger. Artemis is supposed to hold at least four astronauts, not just three. And it has to do the same trick the Apollo astronauts had to do.

We have a couple of advantages they didn’t have though, and they all boil down to better computing. The computers on Apollo were extremely primitive by today’s standards; you have thousands of times more computing power in your phone. More computing power means finer control over those tiny midcourse corrections, which means more control over how you come back.

The other one, which also comes back to computing power, is that Artemis actually will, deliberately, skip off the atmosphere…but very late in the process, after it has slowed down to merely a nice suborbital velocity. It’ll do this by tumbling in just the right way at just the right time. Once it’s back up in space it can cool off a bit, but then it will come back at a slower speed (typical of mere low-earth-orbit craft) and there will be a lot of control over where it comes down. In fact, they’re going to splash down just off of San Diego. This reduces the maximum g-force during reentry from 6.8 g to about 4 g. (And I’ve actually been on amusement park rides at 4 g.)

This is, as far as I know, a first time trying this, so keep your fingers crossed on Sunday.

Obligatory PSAs and Reminders

China is Lower than Whale Shit

Remember Hong Kong!!!

https://youtube.com/watch?v=L3tnH4FGbd0

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 !!!

2022·11·05 Joe Biden Didn’t Win Daily Thread

A Caution

Yes, it’s great that one of the most rancid cunts in US politics is destined to leave office on January 3rd of next year, having been primaried out…by a great big (but not big enough) margin.

But just remember…we might replace the RINO candidates. But that will make no difference in the long run if the party officials, basically the Rhonna McDaniels (or however that’s spelled), don’t get replaced.

Running good candidates is only HALF of the battle!

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

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:

https://youtu.be/WjM26GWWoGk?t=21

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.

Yep, you-all are incompetent, and so proud of it you expect our applause for your sincerity. Fuck that!!

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.

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:

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

Spot Prices

All prices are Kitco Ask, 3PM MT Friday (at that time the markets close for the weekend).

Last Week:

Gold $1,646.70
Silver $19.34
Platinum $952.00
Palladium $1,981.00
Rhodium $15,000.00

So here it is, Friday, 3PM MT after markets closed and we see:

Gold $1,682.60
Silver $20.98
Platinum $974.00
Palladium $1,950.00
Rhodium $14,300.00

With one exception everything went up, 3-7+ percentage points today, after a relatively flat or even declining rest-of-the-week, silver moving the most, percentage-wise. Rhodium is the exception; it didn’t change today and had (obviously) dropped over the course of the rest-of-the-week.

Obligatory PSAs and Reminders

China is Lower than Whale Shit

Remember Hong Kong!!!

https://youtube.com/watch?v=L3tnH4FGbd0

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 !!!

2022·10·01 Every One Knows Joe Biden Didn’t Win Daily Thread

Was I The Reason?

I’m skipping all the boilerplate invective this week, as fun as it is. Because something just occurred to me.

Let me quote, at length, from my own post about January 6. Or you can look at the original: https://www.theqtree.com/2021/01/09/2021%c2%b701%c2%b709-kmag-daily-thread/ (On the sidebar it’s “Steve’s House Rally Photo Thread”

At some point I got hit with a light dose of something or other. I beat a bit of a retreat but someone got to the top of the scaffolding with an American flag.

Fourth And Final Dump of Pictures

The next thing I remember, after getting close in, is a gas cartridge landing about ten feet away from me. I had already gotten light exposure twice to something that made one cough, and once to something that also stung when you inhaled it. Sticking around here would no doubt entail more than light exposure. I backed away.

This photo was timestamped six second later than the previous one.

When the smoke cleared, I noticed people charging up the steps. Lots of people charging up the steps. In fact I can see them in the prior picture too if I blow it up.

OK, that ends the quote.

Note that I missed the key moment…the moment the people on that stairway started to pour through.

They got through, right after the tear gas landed right next to me.

Let me remind you what I was doing…I was near that stairway, with a camera.

Not a phone, a “real” camera, with an 18-200 mm lens. It’s a lot smaller than it sounds but still, it’s gear in a way that a phone is not. Also, but not visible from the outside (unless someone recognizes the camera model), this little camera takes 32 megapixel pictures. (What I posted on the thread was considerably reduced in size!)

Was that tear gas canister…which landed less than ten feet away from me…fired specifically for the purpose of distracting me while they let the stairway people breach the line?

Maybe, maybe not. But the timing and placement of that canister and the “breach” sure makes me wonder.

The timestamp for the first picture I took after the gas canister hit was 1:19:36 MST. This picture is the first one above with the cloud of tear gas. The camera numbered it #3175.

(Note: That is almost certainly not the right time. I routinely forget to adjust the clock on my camera when I bring it out for use…which is sporadically. And the camera’s clock isn’t all that accurate, it slips from the correct time greatly over the span of a few months. But the time stamps can be used to establish relative timing.)

The timestamp for the last picture I took before that (#3174) was 1:17:46. It’s similar to the last one in my post before the tear gas, which was #3157…that was taken at 1:17:30. (Yes, I took seventeen 32 megapixel pictures in 16 seconds…and the camera didn’t break a sweat; it can do 15 per second for half a minute before the buffer fills up and it chokes. And, by the way, this is not even, by a long shot, the best camera that company makes. This is a fairly small camera whose design emphasis was portability.)

It’s a damned shame I wasn’t taking video. (The last video I took, 2:22 seconds worth, was of the stairway, culminating in some guy in a blue coat getting pepper sprayed. Screen capture (also in my original post) below):

The video (numbered #2944) is time stamped 1:00:58…almost nineteen minutes before the grenade. I don’t know if that’s the start time or the end time. The video is 1080p and you will never see a Bigfoot video of remotely that quality.

Like I said it’s a damn shame I wasn’t videoing at the right time.

Of course these days everyone has a camera with them, in their cell phone, so a lot of cops abusing citizens (and “model citizens” abusing cops) get filmed by passers-by these days, to say nothing of dash cams, body cams, and so on. But at this rally, only a small fraction of people were using their cameras. Most were busy waving flags, and yelling and screaming. Some people put gopros and similar things on poles, but for all I knew they were “media” or Antifa plants or even undercover cops, and therefore harmless to “them.” In fact, I’m at least a bit confident that those guys with cameras on poles were gone by the time the grenade hit.

So anyone else with a “real” camera (interchangeable lens) might have stuck out like a sore thumb.

Out of all those people, did I have to be distracted?

Like I said, I’ll never know.

Ayaan Hirsi Ali on Countering Wokeism

Article is behind a “you get two free articles” paywall. The Objective Standard is a quarterly written from an Objectivist point of view; Objectivism is the philosophy originated by Ayn Rand.

https://theobjectivestandard.com/2022/08/wokeism-and-how-to-counter-it/

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:

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

Spot Prices

All prices are Kitco Ask, 3PM MT Friday (at that time the markets close for the weekend).

Last Week:

Gold $1,645.40
Silver $18.93
Platinum $864.00
Palladium $2,153.00
Rhodium $14,500.00

So here it is, Friday, 3PM MT after markets closed and we see:

Gold $1,662.10
Silver $19.13
Platinum $869.00
Palladium $2,244.00
Rhodium $14,900.00

Gold seems to be stabilizing a bit; it has climbed a bit for the past few days.

Obligatory PSAs and Reminders

China is Lower than Whale Shit

Remember Hong Kong!!!

Whoever ends up in the cell next to his, tell him I said “Hi.”

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

China is in the White House

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

Joe Biden is Asshoe

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

But of course the much more important thing to realize:

Joe Biden Didn’t Win

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