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A Thread For The Counters
Topic Started: May 24 2007, 02:46 AM (1,705 Views)
Aja Jin
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number one good, A ?
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Saidaro,Jun 3 2007
02:20 PM
To my knowledge, e is not a "physical" constant, per se. I don't know of any naturally occurances of e outside of mathematics. Inside of mathemetics, it's everywhere, especially in calculus.

It's the base of the natural logarithms. Perhaps the simplest definition is that it is the number for which the derivative of e^t = e^t itself. (If you graph the function e^t, the slope of the tangent line at any point on the graph will equal the value of the function at that point.) And, no, that's not all that simple.

Refer to the wikipedia page linked above for more information about e. The most fascinating fact about e was something I didn't know: Jacob Bernoulli discovered this constant by studying a question about compound interest. Suppose you have an account of $1 receiving 100% interest per year. If the interest is compounded once a year, after a year you have $2. If the interest is compounded every 6 months, you have $2.25. If the interest is compounded monthly, after a year you have $2.61. If the interest compounds continuously, you have $e (almost $2.72).

I wonder whether the concept of interest existed in the atevi world before human contact. It's an ancient concept for humans (going back to biblical times at least), but in some circumstances it's considered immoral (see Exodus 22:24 - "If you lend money to any of My people,[..] you shalt not [...] lay upon him interest").

If the concept of compound interest existed in the atevi world, they may have derived "e" independently of the calculus. But once again, even though atevi have prodigious arithmetical ability (or perhaps because of it), I wonder if the atevi had advanced mathematics before human contact.

^good post, thanks, I didn't know the Bernoulli part either, very interesting.

e and pi are closely related mathematically --- ie, Euler's forumula e^(pi*i) = -1?

"i" is the square root of -1

you can google "e pi" and "math imaginary numbers" to read all aboot it

I got plenty getting a Physics degree :atwink
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moira
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I recommend this book on e; I enjoyed it. Eli Maor is a pretty good writer (To Infinity and Beyond), etc).

also, The Golden Ratio.

and (has nothing to do with anything but numbers I suppose) Zero: The Biography of a Dangerous Idea. (esp that one)


I love numbers.
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Surtac
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Interesting links. Thanks Mia. I've just ordered the book on e through my local library system - surprisingly there were two copies available.

:invert

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moira
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yw. I myself just ordered Journey Through Genius yesterday.
people rave about this William Dunham... I must see for myself.

they esp rave about his book Euler: The Master of Us All.
(but that one is $35 or so; I thought I'd try the other first. haven't checked with the library yet.)
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rosebladeaureliuskcir
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You know, it has occurred to me more than once that the bodies of atevi and humans are made of completely infelicitous pairs. Arms--2. Legs--2. Two sets of fingers, toes. Two eyes, etc. Two sexes.

So far, all of the creatures we've seen for the atevi world are also bisymmetrical in nature.

Does this make life inherently infelicitous, by the numbers?

*bumping a thread I've missed, and shamelessly*
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hrhspence
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2 legs + 2 arms + 1 head = 5 (a very felicitous number)
2 ears + 1 face = 3 (a very felicitous number)
2 ears + 2 eyes + 2 nostrils + 1 mouth = 7 (a very felicitous number)

need we go on?
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griffinmoon
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Thank you nand'Spence, I was about to say the same thing!
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rosebladeaureliuskcir
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Ah, but we're not talking about the finished product. We're talking about the pairs that appear as a part of, well, existence. Two eyes cannot be mitigated with a third eye, but by another body part? Two knees, one stomach? Going that route is far too easy. The devil's in the details: The design itself is infelicitous.

How about this one...

10 toes + 2 ankles + 2 calves + 2 knees + 2 thighs = 2 LEGS...now, how does one make this pair felicitous, since the hips are only the means of attachment to the body, NOT a "whole".

and if you use only the single set of toes, ankles, etc., you get only one leg. While this is felicitous from a numerical standpoint, it rather sucks for walking around. So...a pair is required.

And you forgot something, spence-ji:
2 legs + 2 arms + 1 head + 1 torso= 6 (not five, and not a very felicitous number)
Even atevi would look pretty weird running around without a body.

Let me put it another way: Functioning without all of these pairs, without this symmetry, creates something that is, from the numerical standpoint, less than whole. Functionally sound, most likely-absolutely, but less than whole in the physical sense. With these infelicitous pairs, there is a whole, but there is also the fact that the body is made up of exactly that: pairs. Can a whole be felicitous if the parts building it are infelicitous? Wouldn't that, for strict counters, create the idea that some sort of modification would be required to create a felicitous whole? Lose a finger to preserve felicity?

This isn't just for the Ragi atevi, but for the "less civilized" groups as well...perhaps some strange swamp-dwellers in the East.

And how, exactly, does one skim over the fact that there are two sexes? A spirit and an intellect--even by atevi standards, re: info about ghosts and burial from the books?

Devil's Advocate and Resident Pot-Stirrer
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hrhspence
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Rose, rose, rose! You are wanting to make it infelicitious! But the Atevi want to make it the other way. They will add one thing else to it to make the numbers work. They will find a rock in the shoe, if they have to, to make it match!

Remember, if it works, it is automatically felicitous.
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Felicitous Sk8er
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Nadiin,
Don't fuss! Don't fume! The very felicitous Rule of Nines can always be invoked!
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rosebladeaureliuskcir
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Actually, Spence-ji, I was looking at the previous information from Foreigner. Changing the slosh baffles from four to five to preserve felicity in the solid-booster rocket. Adding a million or subtracting a million from the budget to make the budget itself felicitous. Certain hours where things cannot be begun, ended, or worked upon. Certain hours in which one must not eat. Debates even in Inheritor about changing the numbers of exits and aisles in Shai-Shan from two to a more felicitous three, before the historical numbers of the design were considered too good to screw around with--but still the debate.

It's not a stretch, and if they've gotten so far in their society, it's come up at some point and, in some schools of thought, is probably still a very important distinction. To treat it so quickly is to miss the inherent question in the numbers of life.
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hrhspence
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I am not dismissing it at all. The official position on the Human technology is that since it obviously works, then it is felicitous. But that makes the superstitious very uncomfortable. You are right.

But, the issue of the ateva body having unfelicitous numbers is countered by redoing the addition. I asked ms. cherryh this very question when I asked if the two colors of a house were infelicitous and she said "two ribbons and the person wearing them make three."

Adding ME into the mix is where an even number becomes a harmonious number.
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Winchester

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I crammed the whole series this weekend and wound up joining the forum when I found out we're definitely getting (at least) three more books....

The whole thing with Atevi, as has been pointed out, is that they are masters of fudging the numbers until they get something acceptable. If you're faced with an even number of servants, include their master when choosing the right pronoun. If they're an odd number, omit him. If you're counting the wheels on a car, include the steering wheel. Don't count the wheels on a train, count the wheeled axles. It's never a pair of tracks, it's a *set* of tracks. Et cetera.

It's the stuff that can't be fudged like this that causes trouble. The shuttle had only two hatches, and there was nothing that could be proxied into the count to make three, so one had to be added. (they did change the design, after much debate). Likewise, the baffles on the lift rocket - nothing else could be construed as part of that count, so they debated whether to add an extra. (This decision was mooted since they scrapped the program in favor of the shuttle...)

Also, IIRC it's demonstrated in a couple of places that if you can't get around an even number, split it into groups of odd ones. Not a dozen, but seven and five. Find a reason, even if it's weird, to separate any big even number into smaller odd ones - that is, if you have to be exact about it.

A big issue among all of this is that there are two ways of handling all this - some people start out with the idea that things are wrong, and they're not going to be able to convince themselves different by someone else's fudging (and some of these people will fudge just to get infeliticious numbers so they can crow about it), and some people will accept that the numbers must be right since things are obviously working.

With all that said, however, I'm pretty sure that the most common engine configurations are inline three and five cylinder engines, and that there's the odd three-bank nine or fifteen cylinder engine in use in sports cars or boats...

...and that an Atevi would scream and run in the other direction if faced with a Harley Davidson. (Two wheels, two cylinders, two-stroke operation... :shoot: )
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Arianne_Luinithil
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Hmm...one hesitates to ask, but would odd numbers of pairs be considered felicitous?
Also, one :rofl: when imagining a 'counter faced with a Harley. And Winchester-ji, one salutes your dedication to the series. Perhaps Sk8er-ji should mention this to nand'Cherryh as an example of a dedicated fan.
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Winchester

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Aww, I wouldn't call myself dedicated to the series - it's just that Cherryh was the flavor of the week. I go through books faster than a .303 bookworm (the native habitat of which is the Library of the Unseen University), and I plum ran out of McCaffrey books... :grin:

I had a rather insane thought last night after I wrote this, and I thought I'd share - Atevi society rather bluntly discourages curiosity, you know? It's impolite to question why things are, since it challenges authority - which Atevi can't do, unless they're Aijin. And even Aijin have much of their curiosity sealed away as children, due to having "proper upbringing".

On the other hand, if someone in authority asks a question, they'll fall over themselves to answer it, due to man'chi. Like the students at the observatory, when nand'Bren asked about FTL. Hand them a piece of technology and ask them to improve it, and they will, if it's possible.

This is why the Atevi have been able to adapt so rapidly to the introduction of technology - and why they never overtook the humans on their own, despite having the raw ability to do so.

Enter Cajeiri. Who hasn't had the curiosity beaten out of him, and only restrains it in polite company. Who is only adverse to even numbers because he's expected to. Who knows that the secret to human progress has been to ask why and why not to precisely everything. And who will be the next Aiji... The galaxy has no idea what's about to hit them.
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