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| A Thread For The Counters | |
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| Tweet Topic Started: May 24 2007, 02:46 AM (1,706 Views) | |
| leaf | May 31 2007, 04:44 PM Post #16 |
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Hello, regarding the Atevi preference for odd numbers - could it be based around the idea of the "deciding vote" ? I wondered if it related to the social structure being based on group actions/decisions being defined/driven by those of an accepted dominant individual. If loyalty is to a person and that person directs the group to maintain harmony, then could it be that has led to the evolution of a system reflecting this so an odd number is better than a potentially unresolved "unstable" choice where the group could be evenly split? |
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| Saidaro | May 31 2007, 05:08 PM Post #17 |
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At least in the design of engineered objects, the atevi seem to put great store in things that are proven to work. They accept human technology (and the numbers behind it) because it is known to work. Being a numbers nut myself, I often find myself frustrated at the lack of reference in the Foreigner books to common physical constants like pi and phi (a.k.a the Golden ratio). The latter plays an aesthetic role for humans that is nearly unconscious. But these numbers are culture-less constants - they are common to both human and atevi, even before contact. I am also frustrated by the lack of discussion of number theory among the atevi. Who was the atevi Fermat or the atevi Pythagorus? And do the atevi have a proof of Fermat's last theorem that could indeed fit in a margin? And if the atevi are so good with numbers, what effect does that have on their cryptography? Are they able to factor numbers that are the product of 2 or 3 large primes? I also have the sinking feeling that if such topics were woven into the Foreigner fabric, the books wouldn't be nearly as popular! :lol: |
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| Reptile | May 31 2007, 08:07 PM Post #18 |
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Saidaro: In principal I might agree. But I think the Goddess may be a bit a-mathematical. Check out her complaints about doing her accounts on her blog. I think I also read a comment by her somewhere where she admitted that math was not her supreme talent or intuition. I think the fact that mathematics plays such a large role in framing the atevi world view may, in part, be a joke on herself. On the other hand, number plays a very important, though varying, role in human linguistics, certainly in the Indo-European languages. And she is a former Latin teacher, and is probably at least familiar with several other languages (Greek?) with synthetic rather than analytical syntaxes (relationships among words governed by the form of the word--prefixes, suffixes, etc--rather than word order in a sentence as in English). Point being, it is possible that number theory might fly right over her ... well, you get the point. If so, choosing a a sensitivity towards numbers and numerology ("counters") as a marker of an alien mentation seems very brave. It also might reflect a reality that attending to numbers in this way may be a VERY alien way of thinking for the Goddess. Have to ask her to know for sure, I suppose. |
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| hrhspence | May 31 2007, 09:11 PM Post #19 |
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Hani Assassin
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I think reptile, that you are spot on, on this one. |
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| Neco the Nightwraith | Jun 1 2007, 01:35 AM Post #20 |
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Living the Right Life
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for some reason I like things in sets of fives, because they can be so well arranged into nice patterns. Like stacking cookies. *random...* |
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| magicdomino | Jun 1 2007, 02:13 AM Post #21 |
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Cookies are an instability of five, which quickly become a stability of zero. At least, if they are freshly baked chocolate chip. :innocent |
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| Saidaro | Jun 1 2007, 01:58 PM Post #22 |
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I agree with much of what you say, Repti-ji. And your comments put my in mind of a further point - Arithmetic is not Mathematics. There is a difference between facility with numbers and Number Theory. Mathematics makes it possible for humans to increase their facility with numbers. What's 79 times 81? Atevi may be able to calculate that out very quickly. Humans may not, except that they may remember that (x-1)*(x+1) = x^2 - 1 and may be able to answer "6399" just as quickly, using the mathematical crutch. Is it possible that the inate numerical facility of atevi made the development of mathematics unnecessary? |
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| rosebladeaureliuskcir | Jun 2 2007, 02:11 AM Post #23 |
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Machimi Writer in Hiding
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Or perhaps there is the possibility that atevi number theory, proofs, etc., are much like nand'Grigiji's proof of folded space--so far above even our darling Bren that he accepts the things exist, but sees no need to delve in to anything other than the philosophical aspects he can understand. As for the mathematics-arithmetic disparity...what I remember of either would fit in a very small book. Not even a novella-sized book. With large print. I can understand referring to alien philosophies that deal with numbers without delving into the math/arithmetic of the subject at hand. Having a handful of constants, such as one group insisting that nothing can move faster than the speed of light, is enough to say without adding in the exact number of the speed of light and the human Relativity (Einstein), etc. Having atevi mathematicians, of the "Charles Epps" caliber(TV show Numb3rs), but less easily understood by his students, solve it with math that leaves Bren in the dark is a very neat way of getting around explaining anything and leaving it as an article of faith that everything gets fixed by atevi. Besides, if they did not have mathematics and arithmetic, how could the children's language be considered simplistic next to adult Ragi, formal or informal? Between that and the fact that the professor emeritus's students are working through the theories he has put forth over the years, that they are producing elegant solutions to our classical problems argues that both aspects are there. It does beg the question, though, what about atevi students who are not considered capable of understanding the higher maths/adult Ragi? So far we have not encountered any of those citizens, but it is not possible for every single member of a population to be extremely or even of average intelligence. |
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| Aja Jin | Jun 2 2007, 02:57 AM Post #24 |
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number one good, A ?
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I would argue that there is a distinction between pi, e, Planck's constant, c, and other physical constants (presumably measurably the same for humans and atevi), and things like the golden ratio. Beyond the math, the golden ratio is considered to be aesthetically pleasing to humans, but I don't see why that would be extended to the Atevi. After all, humans tend to like pairs of things --- the Atevi find pairs and other even combinations to be irritating at best. |
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| camilla | Jun 2 2007, 10:04 AM Post #25 |
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Things like the Fibonacci sequence show up in nature, in stuff like flower seed arrangements, in fact, all kinds of spirals like on pineapple skins, certain sea shells. I'm far from a numbers expert but I think it has to do with the maximum amount of overlapping things you can fit into a particular space. I wonder if this holds true on the earth of the Atevi. Would their equivalents of daisy and sunflower seeds be packed in a Fibonacci sequence? Do humans only pay attention to the Fibonacci sequence because it exists in our biological world? And would Atevi find it felicitous or not? Would they use it in their arch architecture like the 9th century Arabs did? Are Fibonacci sequences in the art at Tirnamardi? For that matter, what about primes? Would they be infelicitous given that they can only be divided by 1 and themselves, a duality of a kind? Or would they make some kind of stability of one, since they avoid pairs by being indivisible by 2 (well, except for 2 itself) and therefore each one is essentially unique? I like the concepts behind number theory. I find stuff like non-Euclidian geometry fascinating but I never took the math courses so I can't work out the problems. Due to life and disasters intervening, I never studied math beyond very basic algebra and geometry. (I've used calculus, but only in formulas in my chemistry classes that were just applied, not understood. It's amazing how far you can get in chemistry with just memorized formulas and a good calculator.) In this thread, I will always bow to those who actually can work out the numbers. Still, I think perhaps most amazing thing about the universe is that the universe is mathematical. (Well, that and that life should exist at all...life is pretty amazing too). WHY should it be mathematical? How is it that this thing we've invented in our heads should describe the orbits of planets and so much else? I mean, to people who love math, it's a game, especially higher math, where you just invent things to play with the rules. Then 50 or a 100 years later, some physicist playing with superstrings, or quantum loop gravity or quantum mechanics (which in and of itself is just probability) finds some phenomenon that just happens to work by an old arcane type of math. Like there was this female mathematician, Emmy Noeller, early 20th century. Influenced Einstein's work. She figured out that if you have a certain kind of parity or symmetry in an equation, there is always a conservation law of nature that corresponds to it. WHY should that be so? She wasn't looking for conservation laws, she wasn't a physicist or engineer. She was just playing mind games and stumbled on this. Or there was this person who decided, just for the hell of it, let's change one of the basic rules of algebra, I never get the name of the law right, but it's the one that says a+b = b+a. Let's make a game where a+b does NOT = b+a. Fun to do, didn't have any obvious practical application at the time. Today, lo and behold, people are using this math to see if cause and effect is real. Trying to disprove Hawking when he said time flowing forward is just an illusion. (I liken it to a woman who gets pregnant and then has a baby NOT being the same as a woman having a baby and then getting pregnant. In the first case you have one kid, in the second case 2 kids and the forward flow of time most certainly makes a difference. OK, not your average analogy, but since I've never gone beyond basic algebra I can only grasp it by analogy.) I'm an atheist, but I swear, if there is any evidence for a designer behind the universe, this is it. To me at least, it seems to go beyond just our preferences or aesthetics. |
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| Saidaro | Jun 2 2007, 04:06 PM Post #26 |
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Like pi, but perhaps not as easy as, you do see the Golden Ratio in geometry - (Warning - if you are subject to unpleasant word problem flashbacks, proceed with caution!) Suppose you have a rectangle. Now you make a square with sides equal to the long edge of your rectangle and tack it onto the long edge of the rectagle. Posted Image You look at the new, bigger rectangle and notice that its dimensions are just like the rectangle you started out with, only bigger! What was the ratio between the width and height of the rectangles? The Golden Ratio. Because of this geometric relationship, the Golden Ratio shows up in nature, as Camilla points out:
The Golden Ratio is the limit of the ratio between successive members of the Fibonacci sequence. As camilla observes, things like plants and seashells grow subject to geometrical constraints, though iterations that build upon previous iterations, whether on the human earth or atevi earth or in freefall in space. The Golden Ratio is the mathematical embodiment of those processes.
That's a fascinating question. I think that the aesthetic considerations would indeed translate. First, there's the fact that atevi have a keen appreciaton for nature, and would extract the numbers from natural processes. But also there's the fact that humans find atevi to be beautiful. Certainly, atevi find beauty within their species - one would think that's a natural evolutionary trait that gets abstracted once a species reaches a certain level of sentience. So one might conclude that atevi might share some basic concepts of aesthetic beauty with humans. |
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| hrhspence | Jun 2 2007, 04:54 PM Post #27 |
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Hani Assassin
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I agree with Saidaro. Fibonacci numbers show up because of basic geometry, and are not specific to our own evolution. I am convinced that basics like this would show up in either environment, human or ateva. |
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| camilla | Jun 3 2007, 12:02 PM Post #28 |
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Further considering my question about whether Atevi find primes felicitious: I think they must. They find 1 an acceptable stability, 3, 5, and 7 are very felicitous and multiples of primes (3 * 7 = 21) positively give them wet dreams. :) Of course we never hear of 11, 13, 17 et al, let alone the really large primes but there must be applications: is the ideal population of the station supposed to be a large prime? :baji |
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| camilla | Jun 3 2007, 12:07 PM Post #29 |
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Which physical constant is e? Is it the natural log? And if so, can someone explain natural log to me? And if it's something else, can someone please explain both? Thanks. |
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| Saidaro | Jun 3 2007, 07:20 PM Post #30 |
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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. |
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8:47 AM Jul 11