A Political Statement

One of my stock jokes is to say, as I head off to the bathroom or washroom or restroom, “I’m going to go make a political statement.”

It certainly seems like urinating is a good way to make a statement about the YSM, and defecating works for politicians. Or the other way around is good too, though “#1” just never seems emphatic enough.

Maybe “#1” is just being polite, and “#2” is telling the fixtures what you really think.

Anyhow, I pretty much do plan to be polite to RINOs that electioneer or fundraise. I’ll tell them, Sorry, but I need to GO Pee…

The Twenty Stand-Up Shitbags (Plus Five More Who Were Just Cowardly Shitbags)

Twenty were stand-up shitbags, who actually voted against punishing Adam Schitt, leaving no doubt where they stood. Five more voted present or were sure to be elsewhere…effectively helping shut down justice, but without being overt about it.

At least the first 20 weren’t weasely about it; we know how the insides of those bags stink.

But it won’t work, you Cowardly Five. We’re onto you.

But then…

I read something in the YSM today that suggested that the 20 who voted against censuring, ejecting. and fining Adam #2 (see above if you’re wondering who Adam #1 is–there isn’t one) were mostly concerned about the constitutional propriety of the fine.

OK, fair enough. I can actually see that being an issue; one I’d want to hear arguments on, pro- and con-.

We’ll get some clarity as to the real reason soon. Next week will be a simple censure motion. I’d like to see the little pencilneck turd kicked out as well, but let’s see how “The Twenty” vote this time around.

Language Warning

In the next piece I had to discuss a particular topic. Unfortunately, I couldn’t discuss it without naming it. Therefore I apologize in advance for having to do so, and apologize to anyone offended by the sight of the name.

RINO McDaniel

RINO McDaniel continues to infest the GOP. But RINO McDaniel isn’t the problem.

Let me be crystal clear on this, RINO McDaniel is a lower-than-whale-shit, piss guzzling ratfucking shit eating traitorous rancid syphillitic cunt. Her worth as a human being is substantially less than zero, any oxygen sucked into her lungs is wasted, and it would be, no matter what job she had.

I fear I haven’t been clear enough, but that will have to suffice.

But she is not the problem…or rather, she would not be a problem were it not for others. She’d still be as I have described, but we wouldn’t know who she is and would not care, because she could do no damage. She’d just be anonymous human refuse.

No, the real problem is the fact that a majority of the 168 top GOP people voted for her. And now that has happened five times so they cannot claim they didn’t know what she was.

In spite of the fact that under her “leadership” the party has deliberately sabotaged the will of its base, has deliberately refused to challenge blatant election fraud, had gone out of its way to ensure certain candidates do not get nominated, has diverted donor money to namby-pamby candidates who have all the electoral appeal of a puddle of dog vomit…and in general has done nothing whatsoever to help fix the problems that plague America.

However that last is to be expected; I cannot expect anyone who IS the problem to help FIX the problem.

RINO McDaniel would be powerless without an entire party leadership of the same mind as her. They want this dismal performance; they want to ignore the party base.

If she were to drop dead this instant, it would solve nothing as someone just like her would be elected by those same pustulous people.

According to Charlie Kirk, about 55 people voted against her, 10-12 wanted something different but were too chickenshit to do the right thing, and roughly 100 people voted for her enthusiastically, and even had the unmitigated gall to complain to Kirk about US. Fuck ’em. Rusty 12 gauge bore brushes would be too good for these arrogant pricks and cunts.

Every single one of those hundred is just as bad as she is. In other words, they are all worse than I described at the beginning of this piece. And no doubt those people in turn have people who supported them to be state party chairs and whateveritis they call the other two people from each state and territory who were voting.

It’s time to face up to the fact that the Republican party is effectively owned by the shit-eating RINOs. We’ve got more work to do, a lot more work, to make the GOP an instrument for the restoration of the United States of America. And that’s in addition to cleaning up our elections.

There’s no point in cleaning up elections just to elect ratfucking RINOs.

OK, hopefully now you will have some inkling of my true attitude towards RINOs. Sorry that words were inadequate to give you the full picture.

The Real Fascist is His Fraudulency Joe Biden*

*Or whoever has his hand rammed up that meat puppet’s ass.

Brandon (which I will use as a term for whoever is the power behind the Porcelain Throne) has thrown down the gauntlet…but in a way where most of America will never see it. The networks didn’t carry his tirade. CNN air brushed it (or whatever you call editing the red background) for its five viewers (who aren’t trapped in airports).

Luckily for me I live in Colorado, and therefore, despite my best efforts, I probably didn’t vote for Donald Trump.

Of course, for this purpose who I actually did try to vote for will be essential, and they undoubtedly know.

Come and get us, asswipes!

https://www.youtube.com/watch?v=3h6ZZ28QtX4

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.

Small Government?

Many times conservatives (real and fake) speak of “small government” being the goal.

This sounds good, and mostly is good, but it misses the essential point. The important thing here isn’t the size, but rather the purpose, of government. We could have a cheap, small tyranny. After all our government spends most of its revenue on payments to individuals and foreign aid, neither of which is part of the tyrannical apparatus trying to keep us locked down and censored. What parts of the government would be necessary for a tyranny? It’d be a lot smaller than what we have now. We could shrink the government and nevertheless find it more tyrannical than it is today.

No, what we want is a limited government, limited not in size, but rather in scope. Limited, that is, in what it’s allowed to do. Under current circumstances, such a government would also be much smaller, but that’s a side effect. If we were in a World War II sort of war, an existential fight against nasty dictatorships on the brink of world conquest, that would be very expensive and would require a gargantuan government, but that would be what the government should be doing. That would be a large, but still limited government, since it’d be working to protect our rights.

World War II would have been the wrong time to squawk about “small government,” but it wasn’t (and never is) a bad time to demand limited government. Today would be a better time to ask for a small government–at least the job it should be doing is small today–but it misses the essential point; we want government to not do certain things. Many of those things we don’t want it doing are expensive but many of them are quite eminently doable by a smaller government than the one we have today. Small, but still exceeding proper limits.

So be careful what you ask for. You might get it and find you asked for the wrong thing.

Political Science In Summation

It’s really just a matter of people who can’t be happy unless they control others…versus those who want to be left alone. The oldest conflict within mankind. Government is necessary, but government attracts the assholes (a highly technical term for the control freaks).

A Few Things We Cannot Blame on His Fraudulency

I am pretty sure Joe Biden had nothing whatsoever to do with the 30 Years War that ran from 1618-1648 and probably killed about a third of the people then living in what is now Germany.

Nor did he cause the collapse of either Roman empire (Western, 476 CE, Eastern 1453 CE). Nor the ignominious failure of most of the Crusades. Nor the collapse of Bronze Age civilization around 1200 BCE (including the collapse of the Minoans and the blowup of Santorini).

However, my utter lack of ability to imagine how he could possibly be responsible for these things is not a valid argument against them, so I await correction if appropriate.

His Truth?

Again we saw an instance of “It might be true for Billy, but it’s not true for Bob” logic this week.

I hear this often, and it’s usually harmless. As when it’s describing differing circumstances, not different facts. “Housing is unaffordable” can be true for one person, but not for another who makes ten times as much.

But sometimes the speaker means it literally. Something like 2+2=4 is asserted to be true for Billy but not for Bob. (And when it’s literal, it’s usually Bob saying it.) And in that sense, it’s nonsense, dangerous nonsense. There is ONE reality, and it exists independent of our desires and our perceptions. It would go on existing if we weren’t here. We exist in it. It does not exist in our heads. It’s not a personal construct, and it isn’t a social construct. If there were no society, reality would continue to be what it is, it wouldn’t vanish…which it would have to do, if it were a social construct.

Now what can change from person to person is the perception of reality. We see that all the time. And people will, of course, act on those perceptions. They will vote for Trump (or try to) if their perception is close to mine, and vote against Trump (and certainly succeed at doing so) if their perception is distant from mine (and therefore, if I do say so, wrong). I have heard people say “perception is reality” and usually, that’s what they’re trying to say–your perception of reality is, as far as you know, an accurate representation of reality, or you’d change it.

But I really wish they’d say it differently. And sometimes, to get back to Billy and Bob, the person who says they have different truths is really saying they have different perceptions of reality–different worldviews. I can’t argue with the latter. But I sure wish they’d say it better. That way I’d know that someone who blabbers about two different truths is delusional and not worth my time, at least not until he passes kindergarten-level metaphysics on his umpteenth attempt.

Lawyer Appeasement Section

OK now for the fine print.

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

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

And remember Wheatie’s Rules:

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

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

(Paper) Spot Prices

Kitco “Ask” prices. Last week:

Gold $1,961.70
Silver $24.38
Platinum $1,018.00
Palladium $1,356.00
Rhodium $7,100.00

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

Gold $1,959.20
Silver $24.29
Platinum $992.00
Palladium $1,449.00
Rhodium $7,100.00

Gold took a thumping earlier this week, but recovered almost completely. Silver, similarly. Platinum’s beating was more permanent. Palladium is actually moving up. Rhodium is flat at levels that, though quite low compared to a couple of years ago, still make me wish I had bought some in $400/ozt days.

The problem was, I would have needed to buy it a kilogram at a time, so minimum investment was north of $12K which I sure as heck didn’t have back then. But when it was at $30K I would have made nearly two orders of magnitude on it.

Speaking of orders of magnitude…

Logarithms and Slipsticks

“Slipstick” was apparently American slang…not recognized in the UK. So apparently part of the reason we fought the War of Independence was so that we could call slide rulers “slipsticks” especially when the middle bit fell completely out and clattered on the floor (and probably got a ding that would make it harder to use in the future).

I said last week I wasn’t going to cover logarithms, because they were off the path I wanted to follow in this little math “mini series” (all series are mini- compared to the 30 part physics series plus additions). But there was so much discussion. The subject was beaten until the horse was dead.

Never wanting to let a dead horse remain unpureed, I thought “maybe I should cover logarithms after all.” You didn’t ask for it…but you got it.

What a Logarithm Is

A logarithm is the reverse of raising a number to a power.

To recap: If I have some number…call it b, and want to raise it to some power, like, say, 3, I need only multiply it by itself 3 times: b✕b✕b = b³. (It’s slightly preferably to think of it as starting with 1, then multiplying by b three times.) We were able to establish that even though you can’t multiply things a fractional number of times, it does make sense to speak of a negative power, or a fractional power, or even an irrational power [remember that an irrational number is just one that can’t be expressed as a ratio of two integers, it is not ratio-nal]: e.g., b^-3, b^2.4, b^sqrt(2). Nor does b have to be a nice clean integer, it can be a fraction or an irrational number. (Though if we’re going to play with fractional/irrational powers, we should stick to b being a positive number of some kind.)

Some notational matters to take care of (and sorry to those of you who find this stuff obvious). Raising a number to the second power is often called squaring it; raising a number to the third power is often called cubing it. You’ll note I’ve used the ✕ symbol to denote a multiplication. It’s also possible to use this symbol: · and I will do so. And when dealing with symbols (as opposed to actual numbers) oftentimes you won’t see a multiplication sign at all. So: ab = a·b = a✕b. You’ll also see b^x meaning “b raised to the power x” but when superscripts are unavailable (or someone is lazy) you will see b^x to mean the same thing.

OK with notation out of the way, the key insight here is that, b raised to some power x, multiplied by b raised to some (other) power y, is the same as b raised to the power of x + y. In other words:

b^x·b^y = b^x+y

Note that b (the “base”) has to be the same for this to work. (That’s implicit in the formula, because b can’t change meaning halfway through it; that’s not necessarily implicit in the English language version if not stated (and listened to) precisely enough.)

This seems like something that might only be useful while doing algebra, but no it isn’t.

Why Anyone Ever Gave a Damn About Logarithms

Consider that, since we’re allowing any “real number” power, from minus infinity to plus infinity, including fractions and irrational numbers, any positive number can be expressed as b^x. Pick your base, b, and there is some x you can raise it to. so as to get to your positive number. More than likely x will be an irrational number, but sometimes it’s not. And some other positive number can be expressed as b^y. But remember that you can multiply two exponents by simply adding them together. And you can divide by subtracting.

So if your first number is (capital) X and is equal to b^x, and your second number is (capital) Y and is equal to b^y, then:

X·Y = b^x+y

And

X/Y = b^x-y

Now, given how much of a pain long-hand long-division is, perhaps you can see an application for this…especially more than 50 years ago when electronic calculators could cost a significant fraction of the price of a car, or 60 years ago when they could cost much more than a car.

Little x and y are logarithms. They are the number, you raise your base to, to get some other specific number. so x is the logarithm of X, and y is the logarithm of Y.

It does matter, a lot, what your base b is. So technically, one should say that x is the logarithm, base b, of X, and y is the logarithm, base b, of Y.

[In practice, only three different bases are used even somewhat commonly. The first is e, and logarithms to the base e are called natural logarithms, and are abbreviated ln, as in lnX = x, meaning that e^x = X. The other base you will see a lot is 10 (ten), and that’s usually abbreviated “log”, so logY = y meaning that 10^y = Y. However, sometimes mathematicians will write “log” when it’s the base e, so there’s now an ISO standard (a good one IMHO) that log base e is to be written ln, and log base ten is to be written lg, and any other base, like 2 (the third most commonly used base) should be written like log₂. (Logs base ten and e can also be written that way, of course.)]

So in order to multiply or divide, take the logarithm of X, and the logarithm of Y (in some base…it doesn’t matter, just so long as it’s the same base both times). Add (or subtract) those two numbers. Then raise b (the same base) to that power. The answer is your result.

That doesn’t seem to gain you much. Taking a logarithm, then raising a number to a likely-irrational power, sounds like more work than just the multiplication or division would be.

Except that you can make a table, and look up the logarithms you need in it. Then when you have the logarithm of the final answer, you can use the table backward…find that value in the table, and go back to the number it “stands for.”

But wait, you object: You can use a multiplication table as well!

Yes, you can. But that table has to be two dimensional.

A logarithm table with ten thousand entries, can be used to multiply (or divide) any one of ten thousand numbers, by any other one of those thousand numbers, because you look them both up separately. As long as your result appears in the table (and there are ways to ensure that it will, see below), you can find your answer in the table and read backwards to find your number.

To do the multiplication of any one of those ten thousand numbers, by any other one of those ten thousand numbers, you need to look up a pair of numbers both at once, and you need a table 10,000 x 10,000 in size, and that is a hundred million entries. Do you want that thing straining your bookshelf? And yes; it would be in a book…or many books in this case. Unless you want to paint the thing on your living room floor. (Sorry, no one is that hard core.)

The next objection, though, seems to be a strong one: Numbers cover an infinite range (even if they are positive), they can also be arbitrarily small. What table is going to cover all of the useful values from ¹/_{100,000,000,000,000,000,000,000} to 100,000,000,000,000,000,000,000? And what if you need to go beyond that range? (Note that this applies to multiplcation tables, too…only much worse because the table has to quadruple in size to double its range.)

The answer to that involves using logarithms base 10, also called common logarithms, and abbreviated (often) log, but now officially and pedantically, lg.

Consider: Here is the common logarithm of 15 (to five decimal places): 1.17609.

Now, here is the common logarithm of 150: 2.17609. And 1500: 3.17609. And 1.5: 0.17609.

Do you see the pattern? The logarithm base 10 has a whole number part which differs for each of these numbers, but the part after the decimal is always the same based on what the leading digits are, for digits 1 and 5, it’s always going to be .17609. The number in front of the decimal point on a log (base 10) is called the characteristic. The part after the decimal is the mantissa.

[What about 0.015? It turns out the log of that is -1.82391. What happened? But that is -1 – .82391, or -1 plus negative 0.82391. Rewrite that as -2 + .17609. In other words your characteristic goes negative, but your mantissa should remain positive. Logarithms like this would be written with a bar over the characteristic, and so you’d say the logarithm of .015 was “bar 2 point .17609” meaning the characteristic was negative but the mantissa was positive. That sounds complicated, but it actually simplifies things.]

This means all we have to do is create a table covering .1000 through .9999 (8999 entries) and it can cover all cases. Or if you want more accuracy, 0.10000 through .99999. And so on. In other words, you just need a table for the mantissa. If you can remember the characteristics and add or subtract them, you can do that in your head. (However beware of carrying and borrowing, if your logs are 1.5 and 1.5, your mantissas add to 1.0 and you’d better add that one to the sum of your characteristics; 1.5 + 1.5 = 3.0.)

If you’re wondering why that table doesn’t start at .0000, well the logarithm of zero is undefined. (Fortunately, multiplying by zero is pretty simple, dividing by zero is forbidden; maybe Trump can do it while he’s being Batman.) And a number like .0001 can simply be expressed as .1 but with a different characteristic. So no entries are needed for leading zeros.

Before the days of cheap electronic calculators, no engineer or scientist tried to do precise work without a table of logarithms, generally a fairly thick book because the more entries, the better. It makes for boring reading, but engineering was utterly dependent on logarithms, and for precision the book was necessary.

The table is (structurally) one dimensional: you look up one number and get one answer. However, formatted in the book, you’d see something looking pretty doggone two dimensional. Here’s an example, one page out of an eighteen page table:

This was done to save space, paper and bindings. This is a four decimal table, covering 1000-9999, this page only goes to 1500 so we need another 17 pages.

Nonetheless, we can work an example (as long as I’m careful to pick one where both numbers and their product will show up here.

What is 11 x 13?

Start by realizing that 11 is between 10 and a 100. Its characteristic will be 1, because it’s more than 10¹ but less than 10². Likewise with 13. Remember those characteristics.

To look them up seek out 1100 in the table above. It’s in the row marked 110 and the column marked 0 (110 (as a string of symbols) with 0 tacked onto the end is 1100.) That’s 04139, meaning our mantissa is 0.04139 (space is saved by omitting the leading zero, which is always a zero, and the decimal place, which is always there). Then seek out 1300, the same way, and it gives 11394.

OK, add the two mantissas, 04139 and 11394 to get the mantissa of the answer, 15533. Now you can hunt for it in the body of the table, and you’ll see that it’s in row 143, column zero. Almost. The number shown is 15534, but that’s much closer than the numbers either side of it (15503->1429 and 15564->1431) So your answer is 1430.

But you’re not quite done. This number did not “roll over”, the sum of the mantissas stayed less than 100000. So simply add the two characteristics, 1+1 = 2. Your answer is greater than 10², but less than 10³. So with an answer of a “bare” 1430 you need to stick the decimal point after the 3, to get 143.0, a number between a hundred and a thousand.

And indeed 11 x 13 = 143.

There are more nuances to the table, including ways to squeeze one more digit of precision out of it by interpolating (and the table gives you little “cheat tables” off to the right margin to help with that). But you should get the general idea and I don’t want this to be a class on how to use the table.

A table is good for lots of precision, one part in ten thousand or even a hundred thousand with a big enough table (and even better if you interpolate).

But it takes time, you have to thumb through the book three times for every multiplication, and you have to very carefully guard against reading from the wrong column or row (and that is very easy to do!).

[By the way, one of my tables…is actually an Army technical manual from the early 1960s. It’s full of logarithms of sines and cosines…because artillerymen need to multiply sines and cosines of angles. In 1960 the army was still focused on breaking things and killing people, rather than on “woke” crap…so if they put a technical manual’s cover around tables of logarithms and tables of logarithms of trig functions…you can bet this stuff was genuinely useful for things Deplorables should care about.]

Mechanical Help for Addition

If you don’t want to be as accurate, you can use a mechanical aid…its precision will be limited by how good your eyeball is, and how many marks are on the mechanical aid.

So how would such a thing work?

Let’s start by imagining a mechanical aid for addition and subtraction.

You can sort of fake this with two rulers…for this centimeters is better, but just make sure both rulers use the same unit of measure.

What’s 5.5 + 3.7? Set your first ruler down on the desk. Find 5.5 centimeters on this ruler (and now you see why metric rulers are better for this). Now set the second ruler on top of the first ruler, so that zero on the second ruler is directly on top of the 5.5 on the first ruler. Now on the second ruler, find 3.7. Now very carefully figure out what number on the first ruler is under that 3.7, it should be 9.2 centimeters.

Below is a schematic diagram…pretend they’re transparent rulers and I’ve flipped one over (so the numbers are backwards). The black line is how you read off the answer.

Similarly, to subtract 4.6 from 6.2, put the 4.6 on one ruler, over the 6.2 on the other, then go to the zero point on the first ruler; it’s over 1.6 on the second ruler. You’ve now subtracted lengths to do subtraction.

What you’ve done is added two lengths together to get a third length, but it’s on a ruler so you’ve automatically measured that length, and it represents your answer.

A slide rule simply has two outer “rulers” and a middle “ruler” that slides back and forth between them, so you can readily position 0.0 on the slidey part over 5.2 on the stationary part, then go look to see what is next to the 3.7 on the slidey part.

Slide rule manufacturers even have standard names for those two scales, they call them A and B (and in fact they’re often not present on a real slide rule).

Mechanical Help for Multiplying and Dividing

OK, but I wanted to multiply and divide, not add and subtract.

Yeah, but I really hope you didn’t sleep through the part about how you can add logarithms to multiply numbers.

So use your A-B scale slide rule to add the logarithms–or rather the mantissas. That way all you have to do is find a trained chimp to look up the logarithms in the book. (You might need a slightly smarter chimp to translate the result back because you will likely want to interpolate. Since chimps might fight over the books, you will want two copies of the table.)

But…we’re missing out on the true power of the thing.

Let’s multiply 800 x 60. Log(800) is 2.90309. Log(60) is 1.77815. So line up your rulers at 9.0309 and 7.7815 centimeters. Actually, you’re going to want meter sticks, to get more precision…and since this will run off past the end of the ruler you’ll want a double length ruler, if one of them has twice the range of the other it can’t “overflow” but if your answer is in the second half of the big stick, you need to add an extra one to your characteristics, you get 4.68124.

However…ANY time you go to 7.7185 on the ruler…it’s because you’re really interested in 6.0000. and ANY time you go to 9.0309 on the ruler, it’s because you find 8.0000 fascinating at that moment. That’s true whether the 6 (or 8) is one of the numbers you’re multiplying…or the answer (product).

So take a bit of whiteout, put a dab on that spot of the ruler, and write a dang 6 (or 8) there! Let the ruler do the lookup for you! You want an 8, find it on the damn ruler instead of discovering you want 9.03!

Go through and re-work the scale so it’s not marked in logarithms, but rather the numbers they are the logarithms of. You end up with a scale that runs from 1 (the logarithm of which is zero) through 10 (the logarithm of which is 1). But you know how to make that work for numbers outside that range, right? Characteristic and mantissa.

Now you can go directly to the slide rule, find your numbers (not their logarithms) marked on the ruler where their logarithms would be ordinarily, slip the sticks as described, and your answer is the product, no need to go do a reverse-lookup in the tables. You follow the same procedure you did for adding…but you get the product not the sum. Pretty slick, huh?

Now of course writing the scale this way gives you this funky-looking scale where the numbers close to 1 are spaced far apart, 3 is almost halfway between 1 and 10, and 7, 8 and 9 are bunched up together at the right end. This is called a logarithmic scale, because the numbers are spaced according to their logarithms, rather than their actual values (which makes the ordinary arithmetic scale).

These paired logarithmic scales, called C and D by the manufacturers (who apparently all followed the same standard), appear on just about every slide rule ever made.

Logarithmic scales in general (and not just on slide rules) have all sorts of other interesting properties, to the point where graph paper can be set up this way instead of as an even “grid,” and people used to seek that out, calling it “log paper.” [If Johannes Kepler had had some and a bit of training on what a straight line on such paper meant, he could have saved himself YEARS of work.] Well, maybe some other time.

Well…just one. If you double the length of your 1-10 logarithmic scale, you can simply duplicate the first scale into the second. The second part actually runs from 10 through 100, not ten through 20. 20 is actually at 2 on the second half of the scale. The distance from 1 to 10 is the same as the distance from 10 to 100, which is the same as the distance from 100 to 1000. Or you can check, the distance from 1-2 is the same as the distance from 2-4, which is the same as the distance from 4-8. These actually represent different bases; the difference in the bases is manifested in the relative length on the rule. A slide rule for actual use by engineers will have the C/D scales run from 1 to 10.

By putting other scales on slide rules, you can do square and cubes, and square and cube roots on them (and you don’t even need to slide the stick). A scale, the same physical length as the main scale but which runs from 1-100 will help you with squares and square roots, just for instance.

The downside is, no slide rule you can hold in your hands can reliably give you more than three digits of precision. (If you’re lucky and your numbers are closer to 1 and 2 than to 8 and 9, you can often squeeze another digit out of the thing.) And it takes skill to truly use one…there is a video out there of someone raising a fractional number to a power that is itself the quotient of two non-whole numbers, and he did it pretty fast, in fewer steps than I would have guessed. I am no slide rule virtuoso by any means…though I could use one half-assedly if I had to.

On the upside the user had to know what you were doing. You had to keep in mind what numbers you were actually multiplying and would likely catch one that was off by a factor of ten…or a hundred…because it was on you to track it. Unlike the guy asleep behind the modern adding machine/cash register/calculator who might not have any idea he accidentally fatfingered an extra zero as he tells you your burger and fries will cost you $67.90. Yes, that’s an advantage, not a disadvantage, in spite of the fact it meant that a lot of people had to learn more math in order to use the things. And by “learn” here, I mean truly understand it, not just be able to parrot it until memory-holing it after the exam.

Love them or hate them, slide rules are no joke…we won two world wars with engineering made possible by them–and understanding them can deepen your appreciation of mathematics.

OK…that’s enough digressing (I hope). Back to the “main” story next time.

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 !!!