Undertale headcanon: Monster society uses a base higher than 10
My biggest source of evidence for this hypothesis is Papyrus. In his room he says:
The intended gag is clearly "haha, he has negative two followers!" But Undertale jokes generally have a layer of seriousness under the initial humor. I don't think analyzing the joke is a misunderstanding of its intended purpose.
While Papyrus is very prone to exaggeration, he rarely outright lies. When he does, it's clearly something he wishes were the case. (For example: "I don't ever wonder what having lots of friends is like.") It doesn't seem in-character for him to lie about something in a way that's mathematically impossible to make himself look worse.
So, if the initial reading of the gag isn't technically the truth, how else could we interpret this? How could Papyrus be "a dozen away from a double-digit follower count"? Simple. The base system that monsters use is higher than ten.
In any base system, there are [base] unique digits, and the base itself is represented as "10". In base ten ("decimal"), which we're all familiar with, there are unique digits for numbers zero through nine (which makes ten unique digits total), and the number ten is represented as "10". In smaller bases, e.g. base six, there are six unique digits (0,1,2,3,4,5), and six would be represented "10".
For larger bases, there need to be more digits. Many other societies have had other number systems, and constructed languages that use other bases can invent their own from scratch, but we modern humans generally represent higher bases by adding more digits to our existing arabic-numeral repertoir. A boring, but effective, way of doing this is to add letters, which you might be familiar with from hexadecimal, which is used for color codes. In hexadecimal (base sixteen), the digits for ten through fifteen are A,B,C,D,E,F, and sixteen is written "10".
If I had to take a wild guess based on no other evidence than this one scene, I'd say the most likely number for Papyrus's character given these lines is that he has 1 follower. He proactively talks about fame, which implies he has any followers at all. But he's clearly also the sort of person who would look at an empty glass with one tiny drop of water clinging to the side and call it "a glass of water" on that technicality. So, if we assume "dozen" means "twelve", then one plus twelve = thirteen, and if thirteen is double-digits ("10"), that means the counting system being used is base thirteen.
Another possibility for the base is thirty-four. For this, I'll call your attention to the date we see in several places in the game, most prominently in the intro movie:
The common assumption is that "201X" refers to an intentionally-ambiguous year between 2010 and 2019 in the Gregorian calendar. It's tempting to insert our calendar into this fantasy universe, given that it appears to have many things in common with our world, but I don't think that's a valid assumption to make. It seems too specific. If the writer were trying to obscure the year, it's strange to only obscure the last digit. "20XX" would make more sense, if "X" was intended that way. Instead, I think the more reasonable (and interesting) interpretation is that X is actually a digit in and of itself.
There are two ways to interpret this as it factors into the numbering system. Either the digits after 9 are X(ten), Y(eleven), and Z(twelve), or ten is A, as in hexadecimal. If ten is A, then X would be thirty-three. And if that's the highest single digit (and we have no evidence with which to say it's not), then the base would be thirty-four.
In such a case, "a dozen away from a double-digit follower count" would be twenty-two followers, which in the monster universe (where 3 dozen members counts as a huge fan-club), is an objectively brag-worthy number. And Papyrus does occasionally brag about things that are objectively very cool. His "fabled blue attack" being one. So this isn't an out-of-character interpretation, either.
I think either idea is valid: base thirteen or base thirty-four. It just depends on whether "X" is the first digit of the letter-based digits or the last.
