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 Post subject: D'ni Mathematics
PostPosted: Thu Nov 16, 2006 7:39 pm 
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A civilization as advanced as the D'ni must've had a very good grasp of math. They were without a doubt familiar with decimal numbers and special numbers like pi or e. If so, how did they represent them? And their values? Did they choose a random letter from the alphabet to indicate variables like we do with x and y and whatnot? How come there aren't any references to mathematical documents? Were none found by the DRC? Just a few questions I'd like to share with everyone :3


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PostPosted: Thu Nov 16, 2006 9:27 pm 
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if you think about it though, there really isn't need for mathematics in a civilization like that. Everything is based off of descriptive writing. I'm sure they used simple math for making tools, homes, and other structures. But, I don't think they concentrated on complicated math. I'm just taking a wild guess, but that is a good question, didn't think about that.


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PostPosted: Thu Nov 16, 2006 9:28 pm 
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I'm sure the Great Zero needs complicated math.


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PostPosted: Thu Nov 16, 2006 9:29 pm 
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The D'ni were very advanced engineers, probably more advanced than we are, so they certainly knew advanced mathematics. However, in their guild-based education system, it's not clear if the average person would be familar with things like calculus, or if it would only be taught by certain guilds. Assuming that advanced math was only taught to certain segments of the population, books about it would probably be found mostly in a few specific guild buildings, in the posession of certain professionals, and possibly in some libraries.

Considering the state of destruction in D'ni, I would guess that there are advanced math texts in some or all of those places that simply haven't been discovered. The excavations have opened up mostly average neighborhoods, where they're not very likely to be found. The vast majority of the city is still blocked off, or lies in ruins.

On an interesting tangent, things as simple as fractional numbers are terribly difficult for us when computed in D'ni, since we're so used to our base-10 system.

Base 10 ~ 100.11 = 1(10^2) + 0(10) + 0 + 1(1/10) + 1(1/(10^2))

Base 25 ~ 100.11 = 1(25^2) + 0(25) + 0 + 1(1/25) + 1(1/(25^2))
= 625 + 0.04 + 0.0016

so 100.11, base 25, is 625.0416 in base 10. I never want to take a D'ni math class.


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PostPosted: Thu Nov 16, 2006 9:39 pm 
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According to DRC records, the D'ni actually had a public educational system similar (I'm assuming) to public education on the Surface. I imagine students would be taught the basics in as many fields as possible (language, math, physical sciences, etc.), after which they would enter the Guild's training system for a specific talent (this seems to fly in the face of the Guild system as depicted in BoT, but what else is new?). While I'm sure the D'ni knew of calculus-based concepts, whether the entire culture was capable of performing them is another question entirely (and I dare say that if you ask 10 random people on the street, most of them won't know calculus either ;)).

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PostPosted: Thu Nov 16, 2006 9:53 pm 
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Ah, I did base my assumptions off the book. Even so, we tend to get into higher math mostly in late high school and college (in the USA. Presumably other countries start around age 8, since I'm always hearing how abysmal our education system is). It seems like guild training would be the equivalent of college for the D'ni, so I would still bet that the people who knew a lot were still limited to certain guilds.

It would be interesting in Live if we happened across some 'ordinary' D'ni books. Unfortunately, probably not a high priority on the development list.


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PostPosted: Thu Nov 16, 2006 11:48 pm 
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Amazing coincidence. I was just thinking about this topic today as I was writing an article on the D'ni numbering system for a help file. But, I thought it was rather futile to wonder about calculus, statistics, trigonometry, or even basic algebra when we're so lacking in the most fundamental knowledge of their system.

We don't even know how the D'ni indicated simple arithmetic operations: addition, subtraction, multiplication, and division. We don't know how they indicated equality, nor what punctuation they used to indicate the position of the radix point, or if they used some other convention to separate fractions from whole numbers. We have all the words needed to describe positive integers, but don't know how negation was indicated. We don't have a single word used to describe fractional values, either in base 25 (25ths, 625ths, etc.) or in general language (halves, quarters, thirds, etc.).

RAWA had better get cracking on this stuff! And Cyan's going to need to re-design the dnifont to add the necessary symbols. :) (But, the font needs a re-design anyway. It just doesn't seem to be as good as it could be. They ought to go over to myfonts.com and check out some of the talented amateur designers over there. Maybe one would be interested in helping them out.)

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PostPosted: Fri Nov 17, 2006 1:35 am 
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Some of you, who know a bit less, might be interrested in this page...
http://www.dpwr.net/archive.php?showarticle=631

and this one...
http://www.geocities.com/drumguy42/numbers.html


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PostPosted: Fri Nov 17, 2006 3:13 am 
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I'm not much into D'ni grammar, but could leeahun be used for fraction? (I realize is just speculation at this point)


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PostPosted: Fri Nov 17, 2006 3:46 am 
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I would not be surprised if the D'ni understanding of mathematics is similar to the Greek understanding of mathematics.

The Greeks used numbers as quantities of objects or to denote values, basically as adjectives (we use numbers as their own idea, basically a noun). This limited Greeks in many different ways mathematically speaking. The most famous of these limitations was through the idea of rational numbers. As we have seen that the D'ni are capable of building structure we can assume that they did have the concept of a ratio. However, they might not have realized that not every value (or number) can be represented as a ratio between two numbers. This was realized through the application of the pathagorean theorem: a^2+b^2=c^2. If a,b = 1 then there does not exist a rational number c. (There is a nice proof of this but it is even further off topic.) An early mathematician who proved this was, according to legend, thrown off a ship and drowned for his discovery. Anyway, without the ability to comprehend irrational numbers we lose very important fields such as the Real Numbers and the Imaginary Numbers. Abstract Algebra and Number Theory wouldn't really get too far off the ground that way.

Instead I find it likely that the D'ni veiwed math as a tool instead of a science. If math worked well enough to keep an Age in balance or a building standing or a bank account in decent order (without the use of e, of course) then that was good enough for them. This means that exploration into D'ni will not give us insight into advanced math and Cyan is off the hook for solving Riemann Zeta to keep cannon.


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PostPosted: Fri Nov 17, 2006 5:37 am 
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well they didn't use mathematics when writing a linking book did they? I know they used descriptive words, but did they use numbers or math in the writings?


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PostPosted: Fri Nov 17, 2006 6:36 am 
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Atrus says in his Gravitation Age Journal that he spent months of calculations in preparation for writing the Age. I'd say the d'ni knew some pretty complex math.

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PostPosted: Fri Nov 17, 2006 6:38 am 
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ah ok, I just never knew what it is that they write in the books. I always thought they were just descriptive words, but it would make much more sense if they used numerical descriptions in order to get certain aspects of an age to match properly.


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PostPosted: Fri Nov 17, 2006 6:48 am 
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Interesting topic :D.

Atrus made a lot of stuff that required some impressive engineering skills (especially if you have to know exactly how something works to write it effectively). The question is, did he learn math from Ghen, or from Tianna? Is there any evidence one way or the other?

One thing we know is that they had a concept of numerical zero, which was rather a big advent in the history of math, but beyond that...I'm afraid we're mostly just guessing...


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PostPosted: Fri Nov 17, 2006 6:48 am 
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Since we don't really know exactly what sort of descriptive text is in a descriptive book, we can't tell exactly how numerical formulas would be encoded into the description. I suspect that, instead of a finite number of Gahrohevtee, there is a continuum of symbols with subtley shifting meanings. For example, it would be very hard to write down an exact color in English without resorting to technical notation (RGB value 60,70,49). But in d'ni, it would be comparatively easy: just write down the symbol corresponding to the exact hue (think of the zoetropes in Riven), and then use another pair of symbols to describe the saturation and value. Bingo! The nice feature is that colors that are close together would have similar symbols - a quality that even technical jargon lacks - allowing the Writer to make the description as precise as desired.. (This, incidentally, is why I prefer reading analog clocks to digital ones. I find it nicer to tell the approximate time, then refine my reading if necessary, which is that much harder with an digital reading.)

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