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Jean Valjean

What makes sense for a Matoran numeral system?

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:kaukau: This was something that I was thinking a little bit about lately while looking at highly divisible numbers.  And then, today, I was thinking about how Tolkien (the BZPer, not the original) started developing the Matoran language based off of canon materials.  It actually just occured to me, though, that the original canon didn't really do justice to how the Matoran would have likely had a very different view of numbers than humans do.

Let's consider: in just about every set, Matoran don't have ten fingers.  The Miramax films gave them ten, but that's just one interpretation.  Eight seemed to be the norm once 2010 rolled around.  Why would they use Base 10?  Culturally, could something else have sufficed?  And what would have been the most fun learning.

This ties in with a question someone on BZPower asked a few years ago (okay, over a decade ago): Why six sets?  Why not five?  Or seven?  Four?  Why that seemingly arbitrary number?  It wasn't something that I had much of an answer for at the time, but now that I think about it, I realize that it has a lot to do with six being a strong composite number, the product of the first two prime numbers.  There are nice advantages to being able to divide your lineup into either two groups of three or three groups of two.  That sort of happened with the three virtues, in a way, as each village began breaking them down into subcategories of thought.

With that in mind, I would imagine that the most appropriate base for the Matoran would be Base 6.  It simply matches their culture.  It also would have been the simplest for kids to learn.  Alternatively, I could also see Base 12 or 36.  Given their astronomy, I actually kind of like Base 36.  It's 6^2, and I can imagine a month on Mata Nui lasting for about that long.  I know, I know, it was later revealed that they didn't come from Mata Nui, or that planet at all.  I guess that picking a numeral system based off of time and astronomy depends on whether or not you think that it would have been cool for the first three years, or for the entirely of the G1 run.  Assuming the latter, a unique number system and means of keeping track of time might have been interesting foreshadowing for later revelations of the Matorans' history.  For example, a base 36 system might have been an possible early hint that there were more Toa teams.

Of course, their writing system doesn't make this particular base system ideal.  I did always wish that the Matoran number system wasn't almost exactly like their alphabet.  I think that it would still be great if it incorporated circles into the number writing system, but not as framing devices.  Rather, I would want to see circles being a strong, consistent feature throughout the numbers, but used in a different way than the letters, such as how circles have formed a unique part in representing the various virtues and values of the Matoran villages*.  Or, perhaps they wouldn't use circles, and they would resemble variants of the Toa's symbols.  Or it could be a mixed radix system, or a combination of things.  It doesn't have to be a positional notation system at all.  It could potentially use a far more poetic way of representing large numbers, and they wouldn't necessarily require a base at all.  At least, not in their written language.  Perhaps they would still speak in something such as 6, 12, or 36.

However they wrote it down, it would probably be a very good featural, logical writing system.  While their alphabet isn't featural, being essentially a carbon copy of the arbitrary Roman alphabet, their number system was.  There were pretty consistent patterns behind their numbers.  I thought that it said something about their culture, too.  Still, what if it hadn't been simple numeral and positional notation?  Kids across the world were scrapping to translate Matoran signs on MNOG.  Translating the letters was a little hard, but translating the numbers was easy.  What if something had been done about those to make them their own separate puzzle?

Alternatively, because they're kind of robots, sometimes depicted with four or eight, they speak in hexadecimal.  That would be interesting, and also fitting, although I like the highly composite numbers more.  As I said, I think that it fits with their overall culture more.

 

24601

*The alliteration was purely an accident, I swear.

 

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Have you ever looked at the Great Sundial from MNOG? Notice it has 18 slots. Greg confirmed based on it that Spherus Magna has a 36-hour day, with 18 hours of light and 18 hours of darkness.

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:kaukau: Thanks.  That's some pretty awesome information, and a detail that I actually quite like.  Personally, that settles it for me that I like Base 36 the most for Bionicle.  If there's ever a G3, I would love to see them incorporate that in somehow.  Combining LEGO and math games for the win.

 

24601

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I've also thought about this before. I think the circular writing system lends itself to a base-12 number system. It seems really weird that digits 0-5 use a single circle in the middle, but the double circle symbols only cover 6-9 rather than 6-11.

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I assume you're talking about this?

Just as well, I forgot the BBCode anyway. 

I never realized there were canonical number symbols. the ones being referred to are on The BioMedia Project, right?

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Come to think of it, it's possible the BIONICLE characters only use base 18 for time, and base 10 for everything else, kind of like how we use base 12 for time but base 10 for everything else.


"You are an absolute in these uncertain times. Your past is forgotten, and your
future is an empty book. You must find your own destiny, my brave adventurer.
"
-- Turaga Nokama

nichijou2.jpg

Click here to visit my library!

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On 9/24/2019 at 12:36 AM, Master Inika said:

Come to think of it, it's possible the BIONICLE characters only use base 18 for time, and base 10 for everything else, kind of like how we use base 12 for time but base 10 for everything else.

:kaukau: Yes, that was clearly the case, canonically.  Were a G3 to get a little more imaginative with the Matoran language, I would change that.  Within the context of the Bionicle universe, something divisible by 6 makes more sense, so I'm imagining either base 12 or base 36.  My preferences are for 36, although as Planetperson said, the writing system as it currently stands really lent itself to 12.  Were a reboot to write numerals in essentially the same way, then 12 would probably make the most sense, and it would also probably tie more into the sets, since there are 12 released per year.

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On 9/21/2019 at 8:47 AM, Master Inika said:

Have you ever looked at the Great Sundial from MNOG? Notice it has 18 slots. Greg confirmed based on it that Spherus Magna has a 36-hour day, with 18 hours of light and 18 hours of darkness.

[citation needed]

I've seen this information passed around a few times, but I've never actually seen any proof of Greg saying that.

In fact, I remember that Greg at one point clearly stated that he did NOT want to canonize 1 day = 36 hours based on the sundial. Obviously, that doesn't mean he didn't just change his mind later, but I've never seen a quote actually confirming that. Does anyone know where/when he said this?

Edited by Toa-Kal

No, I don't speak English... :( :P

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I like the idea of Matoran number systems being based around the number 6, since that number kinda defined G1 in almost every way. I've actually been trying to crank out some stuff for a G3 idea, and I've toyed with the idea that, in Matoran religion, 6 is actually considered a sacred number because it is both a multiple and factor of many important numbers in their lives; 7 is considered evil because it is associated with Makuta, whom I've assigned a pseudo-Satanic role in the lore.

For writing numbers, I thought to use hexagons. It would be much like writing numbers in G1, with just a dot in the middle to represent 0 and a line going out to each corner to represent additional numbers up to 6. The character would gain a ring in the center for every full count of six when writing numbers higher than six. So, to write the number 13, you'd draw a hexagon, put 2 rings in the center, and draw a line to one of the corners. This would give an excuse to use both the round letters of '01-'05 and the hexagons of '06; the former would be the alphabet, and the latter would be numbers.

Bear in mind, assuming early G1 lore is applied, the Matoran would have been in a tribal stage of civilization, so they wouldn't have had huge, sprawling empires and, as such, wouldn't need to have a number system that's good for really big numbers. The Egyptians were among the first to write down the number 1,000,000 because they needed to keep track of that many slaves. However, assuming a big island (let's say no bigger than Greenland in terms of size) with 6-12 big ethnic groups that comprise communities smaller than a Greek polis is what the Matoran have, you're not gonna see a massive slave trade or any sort of economy requiring these huge numbers. One might even wonder if they'd bother to use 0 as a number, an innovation that was a big deal by the time the Mayans came up with it.

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