"Fries anyone? Ketchup crash snarls traffic in Nevada"
Lucky volume 13 of the ketchup journal of past-post replies, begun from 13 NewPages in the past...
ucim wrote:It's actually pretty easy.lmjb1964 wrote:[...] my physics class was the first one to use calculators. They were certainly in common usage by then, of course, but our teacher thought the students should learn how to use slide rules. Kind of sorry I missed it, actually. I would have liked to learn how to use a slide rule.Spoiler:There are two things you do with it.... operations with one number (what is the tangent of 43 degrees?, what is the cube of 6.34?) For that, you just move the cursor to the "question" number on one scale, and it points to the "answer" number on a different scale. There are separate scales for common "questions".
The other is doing multiplication by doing addition, but doing it in disguise. To see this in action, first, do addition with two rulers. What's 3+7? Put the "0" of one ruler on the "3" of the other ruler. Then, on the first ruler, move over to the "7". The answer ("10") is right below the "7", on the other ruler. That's all a slide rule is, with one twist, for which I'll have to take a little detour.
Explanation of multiplication using logarithms: How much is (7+7) + (7+7+7)? Don't do the actual arithmetic, but can you tell that it has to be the same as (7+7+7+7+7) ?
In shorthand, 7x2 + 7x3 = 7x5 You're just adding up five sevens... and you can do it in any order you want, even all at once.+
How much is (7x7) x (7x7x7)? Don't do the actual arithmetic, but can you tell that it has to be the same as (7x7x7x7x7) ?
In shorthand, 72 x 73 = 75
You're just multplying five sevens together, and you can do that in any order you want too.x
See what we just did? We multiplied by adding (the exponents)!
It only works because I picked special numbers in this illustration (integer powers of seven) but it actually works for any real number!
All real numbers can be expressed as seven to some power! (That power doesn't have to be an integer - there are a lot of numbers between seven squared and seven cubed, and they can be expressed as seven raised to some power between two and three. This number is called the logarithm. Any number can be used as the base; we don't have to use seven. You just have to be consistent (because the logarithms are different for different bases). 10 is a common base to use.So...
If we were to multiply this way by hand, without a slide rule...
step 1 is look up the logarithm of the two numbers you want to multiply
step 2 is to add them up.
step 3 is to raise your base (probably ten) to that power, and you have your answer! You've multiplied by adding!1
The slide rule combines all these steps into one, by labeling the two scales with the original numbers you wanted to multiply, saving yourself step 1 and step 3, and doing step 2 for you like when you did addition using two rulers, above. And that's why the scales on the slide rule look funny (they are "logarithmic").2,3
+ For the nitpicky, addition is binary, but associative and commutative, which essentially lets you accomplish what I just said.
x Same goes for multiplication. It shares these properties with addition.
1 Step 3 is usually "profit!", but this is math. That's why mathematicians never get rich!
2 See, math is the opposite of profit! The only steps left are the ones that are left blank in the classic profit sequence!
3 Oh... you have to supply your own decimal point. Math is like music - the numbers come in octaves (powers of ten) where the notes (digits) are the same, but the actual number (frequency) is different. The slide rule only displays one octave.
4 Of course, "improve" is a matter of opinion.
edit to add decimal point note.
edit to explain edit.
edit to improve explanation4
Great explanation! Nicely written! I remember using slide rules, but I've always preferred digital tools. The resolution and variation in how accurately you positioned the slide rule always bothered me. Even though I know there's internal rounding and loss of precision with each operation, I always got a warm fuzzy feeling in seeing all those displayed digits of not-quite accuracy from digital results: "The slide rule just says '7.2-ish'; the calculator says '7.17845620972196'. That's got to be better."
Kieryn wrote:Spoiler:yappobiscuits wrote:Kieryn wrote:Dracomax wrote:Stop Chasing me! I am NOT a molpy! I am not tiny! I'm just farther away!
Sorry, dragging forward from several pages back, but i just wanted to show what this reminded me of.
Teehee, before I even clicked the link I had a hunch it would be that
I felt it had to be said. I'm sad to see it went so many pages without a mention... I prescribe all three seasons to everyone that doesn't know what we're talking about. You can just about do one episode between each newpix
I have not seen the series, but I have heard of it -- usually accompanied with comments of "You should definitely watch it!" I'll take this one as a final push to bump it to the top of my Netflix queue, once I get caught up on Doctor Who.
ChronosDragon wrote:Spoiler:StratPlayer wrote:But as always, I'm glad that:
-- I didn't miss the big End of Time.
-- The OTT is still here and still active, and
-- Peaceful Waiting in the OTT hasn't degenerated into "Oh yeah?!? Well, you're completely wrong, you drooling imbecile! And also, your mother eats carbonated toadstools, you cretinous collection of clueless carbon!" flame-war.
And so backwards I go to get current...
I wonder what a carbonated toadstool tastes like...I'll have to ask her some time.
You know, I'm not certain. A Google search mainly only points to "Heidi Deus Sparkling Toadstool crystal pin" jewelry... I'd assume that it's a form of fungus that induces hallucinations, convulsions, seizures, and eventual death, but with a effervescent and bubbly taste that tickles your nose.
BlitzGirl wrote:Thanks, yappo! That would be Trajan Pro.Spoiler:NG:
At first, I misread that and thought you were referring to some sort of prophylactic not recommended for use by amateurs...
ChronosDragon wrote:As promised...Spoiler:
Wonderful! Great job! (But I still say the
...and again two NP's ahead, one NP back -- 12 NP's to go...