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 Post subject: Re: D'ni mathematics
PostPosted: Sun Jul 27, 2014 5:53 am 
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To add to these questions...
How do you represent a fraction or a decimal point in the D'ni numeric system?

David Tierce

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 Post subject: Re: D'ni mathematics
PostPosted: Sun Jul 27, 2014 9:03 am 
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larryf58 wrote:
While I'll grant that "gah" could be used in the sense that we use "two and two equals four", that's not very precise. The only math function I know a D'ni word for is "equals" (pehkai).

I thought about a simple math problem, 15+3=18. In written D'ni, that would be "heebor gah sehn pehkai heegahsehn"... and it sounded kind of silly, since the answer is the same as the problem, minus the -bor suffix.


Well, it’s like “twenty and five gives twentyfive”. This actually strongly support the usage of gah for ‘+’, as it is embedded in the number structure.

As for ‘=’: apparently, for a while, an alternative notation was ‘æ’ (from the Latin aequalis), so I wouldn’t rule out a (limited) use of initials, at least in ‘ancient’ texts.

Decimal point: the apostrophe?
96.6 --> [3] [21] ' [15] (praised be the Internet for online converters)

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 Post subject: Re: D'ni mathematics
PostPosted: Sun Jul 27, 2014 12:42 pm 
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dtierce wrote:
To add to these questions...
How do you represent a fraction or a decimal point in the D'ni numeric system?

David Tierce


Sadly, there are no examples of fractions in any of the source material. However, we know of three punctuation marks and one example of a particle that serves as punctuation.

The three marks are period, en-dash, and apostrophe. Since there is a period, and no proof for or against it, you could use it the same way we do as a decimal point in fractions. Here's an example of how it could work, using the en-dash as a minus sign.

25.5 - 0.75 = 24.75
Image

The one particle we know is "ah", which is a word that serves pretty much the same function as an exclamation point. "Ah" is a suffix appended directly to the word it emphasizes, rather than at the end of the sentence. As an example, "Yahvo is great!" would be written ".yahvo kehn gahroah", and "Give me the book!" is ".tahgehmah b’zoo ah rehkor". Note that there are two examples of "ah" in that last sentence. The "ah" at the end of "tahgehm" is the imperative, and the "ah" before "rehkor" is a preposition that marks it as the object of the verb. In other words, it tells you that the book is what's supposed to be given. So the first sentence is "Yahvo is great!" while the second is "give! to me the book."

I've always wondered how D'ni formed an interrogative, since there is no sign of a question mark anywhere. Problem is, the source material seems to lack any written questions. There is an example of spoken questions. When Keta asks if the imager is ready to record in her speech in Gehn's bedroom imager, she says something like "Kehnehn atsoo? Sheemah?". She uses a rising inflection to show they are questions just like we do in English. The two phrases show no sign of an interrogative particle, so that leads me to believe that a punctuation mark must exist... if only somewhere in the back of RAWA's head.

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Last edited by larryf58 on Mon Jul 28, 2014 2:59 am, edited 1 time in total.

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 Post subject: Re: D'ni mathematics
PostPosted: Sun Jul 27, 2014 4:04 pm 
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Note that 0.5 in base-25 is 1/5; 1/2 is the periodic number 0.CCC (this is why most numbering systems are based on even numbers). Your example would look like (hoping I got the numbers right):

[1][0].[13][13] – [0].[18][19] = [24].[19][19]

I think the ‘period’ might actually be a begin-of-sentence mark, like a capitalization of the following letter, and not an ‘actual’ period; though it might have been used as a separator as well.
The lack of punctuation parallels the way medieval manuscripts were written: until the Middle Ages, reading was done aloud and one word at a time, so a clear division wasn’t necessary. In transliterations, I’d favor using our punctuation for clarity (there was a nice example, Geltahvoy tso Mistireeum, in the old DLF forum):

Kehnehn atsoo? Rahm!

The D’ni seem to be an odd mix of advanced steampunk technology and medieval / early renaissance writing and society :lol:

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 Post subject: Re: D'ni mathematics
PostPosted: Sun Jul 27, 2014 4:50 pm 
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Yeah, I blew it with the math problem because I was thinking in base 10 after the decimal point. I seem to recall saying on my site page that I wasn't at all eager to tackle fractions in D'ni. :roll:

It was just to get the decimal point example on the table for discussion, though, so no real harm done.

This is the corrected version of the problem you put up. I'm using 'p to stand for "equals" this time.

Image

I call it a period just for the sake of convenience, since there's no D'ni word and that's the key used to type it. An alternate word for period is "full stop", so the D'ni character could be thought of as a "full start", I guess.

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 Post subject: Re: D'ni mathematics
PostPosted: Mon Jul 28, 2014 2:12 am 
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larryf58 wrote:
The one particle we know is "ah", which is a word that serves pretty much the same function as an exclamation point. "Ah" is placed directly after the word or words it emphasizes, rather than at the end of a sentence. As an example, "Yahvo is great!" would be written ".yahvo kehn gahro ah", and "Give me the book!" is ".tahgehmah b’zoo ah rehkor".


There's some evidence that ah affects the following word: we have phrases like votahr ah'shem where ah is phonologically joined with shem, and while ah is preceded by various kinds of words, it's followed only by noun phrases. I suspect that it does have some focusing function, but it's hard to tell exactly what.

I'll throw out there that there is a known but unidentified D'ni numerical symbol: Dnifont +. (As seen in this chart).

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 Post subject: Re: D'ni mathematics
PostPosted: Mon Jul 28, 2014 2:49 am 
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Nice. There are two characters I do not recognize in that font. One is mapped to plus, and the other is mapped to equals.

Image

The key mapping is very likely to be meaningless, of course, going by the mapping for the other numbers above 19. Cyan just used them because they were more or less in the right area. but the boxes imply that they are numbers of some kind. Anyone ever seen a reference to them? Just going by appearance, the first one looks like it should be a standalone character for 31, and the other looks like a half mark for 25, which would be 12 and a half. If that's even close, why would they be needed?

And I got mixed up because there are two versions of "ah". The imperative is a suffix, and the one that stands alone is a preposition marking the object directly affected by a verb. I'll edit and correct my examples.

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 Post subject: Re: D'ni mathematics
PostPosted: Mon Jul 28, 2014 5:45 am 
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I have very little knowledge in this area but I wonder if it is right to assume a simple system of mathematical notation from the accomplishments of the D'ni. My college classes in Roman culture leave me with a strong suspicion that those master engineers, the Romans did not use simple symbols like our - and +. I would not be surprised if they just wrote everything out, perhaps with some abbreviations. I don't know what other advanced ancient peoples, such as the Chinese may have done for writing math, but again I suspect they saw nothing awkward about writing things out long hand. The D'ni naturally would have had a very great respect for every word used to define and solve a problem.

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 Post subject: Re: D'ni mathematics
PostPosted: Mon Jul 28, 2014 8:43 am 
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When I wrote the proposal for the inclusion of D’ni in the UCSUR (E830−E88F), I asked RAWA about those two symbols: the ‘31’ represents “infinity”, “something that cannot be numbered”, while the ‘half 25’ is “for cyclical representations where 0 and 25 would overlap”, like 00:00 / 24:00 in a 24-hours clock or 0 / 360 in a compass.

     (you’ll probably see just blocks, of course)

EDIT: Romans weren’t that good at mathematics, compared to the Greeks, but they were very good at putting it into practice. Mathematical notation became a necessity once concepts got too complex to handle with plain words (e.g. electromagnetism would be quite a beast to write about without symbols, and the D’ni seem to know about it).

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 Post subject: Re: D'ni mathematics
PostPosted: Mon Jul 28, 2014 12:02 pm 
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ventris wrote:
I suspect they saw nothing awkward about writing things out long hand. The D'ni naturally would have had a very great respect for every word used to define and solve a problem.


That's actually a good point.

korovev wrote:
When I wrote the proposal for the inclusion of D’ni in the UCSUR


And the chart for the font has an explanation of all the characters, which I believe counts as source material. I'll add them to my page.

The ' . and - marks are the D'ni apostrophe, full stop, and hyphen.
The two numbers are infinity and cyclic zero.

The chart also has the D'ni color symbols, so looks like I need to add another page to the site. I overlooked those.

BTW, how do you use the CSUR font? I downloaded a copy and installed it, but it just shows normal characters when I try to type anything with it.

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 Post subject: Re: D'ni mathematics
PostPosted: Tue Jul 29, 2014 1:26 am 
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An interesting, if trivial point that occurs to me is that although 25 isn't divisible by much, 25-1 is. This means we have quite a few unit fractions with simple repeating decimals.

1/2=0.(12)(12)...
1/3=0.88...
1/4=0.66...
1/6=0.44...
1/8=0.33...
1/12=0.22...
1/24=0.11...

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 Post subject: Re: D'ni mathematics
PostPosted: Tue Jul 29, 2014 2:17 am 
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So that would mean

5/8 = 0.(15)(15)
2/3 = 0.(16)(16)
3/4 = 0.(18)(18)

...is that right?

This isn't the first time D'ni fractions have come up. There's a D'ni Fractions topic from back in 2010/2011, although they didn't really talk about examples like we are. However, explorer Giovanni figured out Pi in D'ni:

Image

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 Post subject: Re: D'ni mathematics
PostPosted: Tue Jul 29, 2014 10:08 am 
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About the UCSUR font: it’s normal to get roman characters because the D’ni letters are in a different code block, as if they were cyrillic or hanzi. I haven’t made yet a proper keyboard layout, mostly because I use search-and-replace macros; you can find Applescript and Notepad++ versions in the same folder as the fonts.
Note that those are whole-document substitutions, and that I didn’t make a direct OTS –> UCSUR conversion.
Moreover, only the letters are converted; I was thinking about making a (perhaps separate) [xx] <–> <digit> conversion.
Oh, and here is the rationale behind my encoding choices.

About fractions: on this point it looks like Gehn was right, the number 5 was indeed pervasive in the D’ni worldview, if they based their numbering system on it instead of 2 and 3.
Here are some constants (I’ve used the converter, too lazy to compute them myself :lol: note that A=10, B=11, etc):

π = 3.3DC9FINDOI
e = 2.HNN3KOD395
√2 = 1.A8M24800F6
φ = 1.FB6JD472F7 (golden ratio)

And in base-10:

c = 110651744 šafítí/goran (roughly)

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