Ysi Earth world map II

[Naeddyr]

Karro, the sign on the middle pole (the South Pole shared by both hemispheres) is just the abugida consonant+vowel for the word "south". Remember, guys, that the "down" hemisphere is rotated 180 degrees!



I will also say that Karro is much closer to cracking this than alta, sorry about that.

Are these numerals unique to this map with respect to placement on meridians/parallels, or are they generalized. I.e. if you had a map with a different projection, would the same numerals represent the same lines? A number of things seem to be relative to the point shared between both maps.

These are numbers for a general graticule numbering system.

I've noticed that you guys seem to miss some of the numbers. I will say here that if you can't find the numbers at the equator, it's usually up or down the meridian because there has been too much geography at the equator. And remember, zero is marked by the lack of zero, so there is one unmarked meridian and one unmarked longitude...

Only one of guyanonymous's guesses is correct, but it's exactly spot on.

[altasilvapuer]

D'oh! I forgot all about the rotation. I'll go back and double-check my numbers.

-asp

[Karro]

Well, a few additional observations and thoughts:

First, I missed earlier on in the thread when Naedyr stated unequivocally that zero was represented by the absence of a numeral. This hinted very strongly at a number system that lacked the concept of a zero, and thus is not ordered in a fashion like the arabic decimal system.

Another thing that's been pointed out: the latitude of the north pole is denoted by a single character, while the south pole is denoted by the word for "South", and no numerical figure.

Next: I had a look at the character set for the Phelthie writing system, and it does not include any numerals, further, comparison to between the numerals and the abjad characters does not reveal any clear duplicates. So they are not using their phonetic characters in a double-duty role as numerals as well (common in many ancient numeral systems, including the roman system and the hebrew system).

One last observation: it appears that the fifth line of longitude from the right on the northern-facing continent lacks a numeric designation. The first line of longitude to its right is designated with the carotid symbol (a heart-shape on its side) followed by the S-shaped symbol: the same numeric designation as is given to the first line of latitude north of the South Pole.

Now, an assumption: we are going to assume that in this numbering system a circle has 360 degrees, as it does for us, and that a semi-circle has 180. This may be a faulty assumption - if you view the world a different way, you could easily divide a circle into a different number of segments. But this assumption will drive some of the following conclusions:

Conclusion 1: the symbol at the North Pole represents, on its own, the value 180.

Conclusion 2: since we know that the S-symbol represents 3, then the carotid symbol most likely represents either 12, 5, 18, or 45. 12 would be reasonable for an additive representation: 12 + 3 = 15 (assuming the first line of latitude and longitude are at 15 degrees). 5 would be for a multiplicative system. 18 if our representation is subtractive (18 - 3 = 15) or 45 if this system goes the really unusual route of being divisionary (45/3 = 15). Now, in the representation of the number 412, we see the carotid symbol used in the penultimate (L-to-R) position. If we were dealing with a strictly additive system, if the carotid were to represent 12, we would expect it in the ultimate position (either L-to-R or R-to-L) and for the other figures to somehow represent the value of 400. But there is a different glyph in the final digit location, instead. This suggests that the character we are looking at does not represent 12. This leaves us with the possibilities of 5, 18, or 45. A divisionary system seems rather cumbersome and highly non-intuitive. Although it meets Naedyr's criterion of "a system that does not occur in nature", it would be sufficiently complex and unwieldy that I believe it is very unlikely that this is the system being used. (Besides, just using an unusual numeric base would be sufficient to fulfill this criterion.) This leaves us with the possibilities of 5 or 18.

Now, returning to the numerals representing 412, and assuming we read these symbols from L-to-R, let's examine the symbol following the carotid that looks like a 3 with a long curly-que on the bottom stroke. We know this symbol does not mean 2; we are given that 2 is represented by the small circular symbol that has circling arm that branches off it's right side and curves around to its underside (we'll say this symbol looks like a 9, although it doesn't quite, really). So, we can assume this symbol either represents 12 by itself or represents 12 in conjunction with the symbol to its left: the carotid. Now, from above, we have demonstrated that, at least in some cases, when a numeral follows something to it's left, it is not always additive. We believe the carotid represents either 5 or 18, and in the case of 5 we are further stating that we believe that the system is multiplicative. If the carotid represented 5, however, there is no whole, real number by which we can multiply 5 to reach the value of 12 (or 412, for that matter). From this, we can pretty definitively conclude two things: the carotid does not represent 5, and the system is not multiplicative (or at least, that it is not always multiplicative). So... this suggests that the carotid represents the value of 18. This means the curly-3 represents the value of 6, for 12 is 6-less than 18.

However, we run into a problem, here. We've just delineated a subtractive system, where a numeral to the right of a greater-valued numeral is subtracted from the value of the larger numeral. If this is the case, however, then why wouldn't the value of the carotid be subtracted from the value of whatever lies to it's left? And what does the carotid represent in the representation for 989, where it is the second glyph of four? I feel like I'm getting close, but not quite there.

Summary: I believe that the position of the numerals impacts greatly what we are going to do with that numeral. In the roman system, reading L-to-R, if the next number is of a greater value, then we will subtract the current numeral from the value of the greater. If it is of equal or lesser value, then we will add the value of the next numeral to the value of the current numeral. From there, we have unique glyphs only for 1, 5, 10, and multiples thereof. I think there are similarities in this system.

So far, in this system, we've been shown that there are unique symbols specifically for 2 and 3. We've also followed a logical path, based on a few assumptions that are perhaps faulty, that there are unique symbols for 18 and 180. If the latter two are true, we might also guess that we will encounter unique symbols specifically for 36 and 360, though this is obviously a leap in judgment.

My guess, and this will be a wild guess here: we read the numerals from left to right. If the next numeral is greater than the current numeral, we multiply. If it is less than the current numeral, we subtract. I also guess, based on a certain reading of Naedyr’s response to guyanonymous’s guess, that we will have unique numeral characters for values ranging from 1 through 6, as well as for certain multiples of 6. OTOH, I haven't accumulated quite enough evidence to really assert this as a conclusion (although I do believe that the carotid-symbol represents 18, and that a lesser numeral following after a greater, at least in some cases, is subtracted from the greater). However, this would imply a unique character for 12, which would have to factor into the discussion above on the value of 412, so it’s not worked through completely clearly.

So, in conclusion, Word tells me that I have written over 1,200 words, so this is officially a very long post. Thank you.

[Naeddyr]

Oh god, you are so close, yet. Yet! I was all like warm warm hot hooooot hoooooooooot COLDCOLDCOLDCOLDCOLDCOLDCOOOOOLD.

Here's a big present from Hinterklaas.

[Karro]

Oh god, you are so close, yet. Yet! I was all like warm warm hot hooooot hoooooooooot COLDCOLDCOLDCOLDCOLDCOLDCOOOOOLD.

Here's a big present from Hinterklaas.

Yeah, at the end, I lacked some crucial details to make a better determination.

However, this latest number still fits roughly into this scheme, so it doesn't help much. If the lower-case-e symbol represents 24 (a multiple of 6) 21 will be 3 less than 24.

[Ramah]

I think my brain just melted trying to even follow what is being said, never mind actually taking part. :s

[Karro]

Oh god, you are so close, yet. Yet! I was all like warm warm hot hooooot hoooooooooot COLDCOLDCOLDCOLDCOLDCOLDCOOOOOLD.

Here's a big present from Hinterklaas.

You know, I have to wonder aloud at what point I went from being warm to cold. (That would be a huge clue.) My assumption is that the multiplicative aspect is probably wrong. That was really just a wild stab, and I knew it, as it wasn't based on a build-up of reasoning like I used to arrive at the subtractive element.

I think my brain just melted trying to even follow what is being said, never mind actually taking part. :s

Yeah, thinking about numeral systems is a pretty niche-interest that's largely academic. I myself am not an expert, but just a random joe with a passing interest. I've thought a bit about numeral systems for my own world, but not actually done any work to develop one.

[Naeddyr]

You know, I have to wonder aloud at what point I went from being warm to cold. (That would be a huge clue.) My assumption is that the multiplicative aspect is probably wrong. That was really just a wild stab, and I knew it, as it wasn't based on a build-up of reasoning like I used to arrive at the subtractive element.

How interesting that bit about subtractive systems, hmm. So you're still thinking that, hmmm.

Hmmmmmm.

[Karro]

How interesting that bit about subtractive systems, hmm. So you're still thinking that, hmmm.

Hmmmmmm.

Hmm. Well, if I'm wrong about the subtractive element, then that throws out a lot of the reasoning I built up to in my oversized post.

So, if subtractive is out, the cardioid symbol (I was calling it carotid by mistake; cardioid means heart-shaped, carotid is a major artery supplying blood to my brain, which apparently it wasn't supplying enough blood to my brain) certainly can't represent 18.

So, we're back at square one: additive or multiplicative (or divisionary, if you want to throw that back into the mix, although I can't imagine a society or frame of mind that loves math so much they count by division), with the cardioid representing either 5 or 12. But this leaves us back with the same conundrum of what the cardioid is doing in the number 412. If the system is additive and the cardioid means 12, why is the twelve lodged in the middle of 4 digits to represent 412? And if multiplicative, how does 5 factor into 412?

Concerning the multiplicative aspect, again, one thing we can guess almost for certain is that the system can't be purely multiplicative, because there is a large family of numbers that can't easily be represented in a purely multiplicative system (i.e. Primes). In such a system, each prime number would have to be represented by its own unique symbol (and this could get unwieldy, as there are a lot of primes). This might be possible in a primitive system that never deals with overly large numbers and so might view the total number of primes as finite; but it's also unlikely that a primitive culture would strike upon the concept of primes ex nihilio in the first place. So, although the few digits we've identified with complete certainty (i.e. 2 and 3) are both primes, and none of the multi-digit numbers we've seen represented so far are known to be primes, and also given that we're fairly sure that at least one unique symbol represents a non-prime number (i.e. the symbol for the North Pole, which I still think means 180), I think we can easily assert that the system, if it is multiplicative, is not purely multiplicative.

Anyway, if we’re dealing with either a multiplicative (plus additive) or purely additive system, I’m going to have to think about the implications for the characters the numbers that we do know… And right now I don’t think I have time to devote fully

edit: if we're dealing with either a multiplicative or additive system, we now also know the "e" symbol represents either 7 (multiplicative) or 18 (additive). But since we don't see the "e" represented anywhere else, we can't really use this to build up any additional logic - although assuming it to be 18 would be a possible affirmation of the "base-6" theory, while assuming it is 7 a possible rejection of the same.

[altasilvapuer]

I can't believe I didn't consider the possibility of the North Pole being 180, rather than 90. All of a sudden all the weird patterns I was trying to explain make sense. I'll have to do some more work on this when I get home, and take another stab. For now, though, I'm stuck in and out of classes/rehearsals for another 5 hours or so, with my notes at home.

-asp