That's already a fraction, you're just switching the terms around. Mandarin does exactly this: 1/4 is called 四分之一 sì fēn zhī yī literally ‘one of four parts’
re: "wait, isn't 0^0 equal to 1?" so, yes, if 0^0 has to be given a value, it's treated as one. BUT that depends on how you approach it. 0^x is always 0 and x^0 is always 1. 0^0 can't be both, so it's undefined. this, of course, doesn't stop mathematicians from sometimes giving a value anyway; it is useful to treat it as equal to one in some contexts. "so then wait, why is it equivalent to 0/0?" great question! the defining property of exponentiation is that a^b is equal to b copies of a multiplied together. to generalize this to work for weirder numbers, we can say that a^b is equal to a^(b-1) · b. in other words, adding one to the b in a^b is the same as multiplying the whole thing by a. from the original limited definition of exponentiation, you'll find that this has to be true. the inverse also has to be true, specifically that SUBTRACTING one from the b in a^b is the same as diving the whole thing by a. so, let's say that you start with a^1, and you subtract one from the exponent. what do you get? you get a^0 = (a^1)/a. a^1 is always a, and a/a is always 1, therefore anything to the power zero is always 1. except! what if you start with 0^1? well, from THERE, subtracting one from the exponent requires dividing 0^1 by 0, otherwise the defining property of exponentiation doesn't work. now, you might notice that this isn't actually a proof. this way of deriving an exponent from division seems to imply that zero to ANY power has to be equal to zero divided by zero, and that can't be right. it is, however, a pretty useful intuition for why 0^0 is undefined. (unless it's one, which it is sometimes.) hope that helps!
There is a really good reason 0^0=1, it's that lim x->0 x^x = 1 And it's a very useful definition pretty much everywhere in math. So you can't really say 0^0 is undefined, most mathematicians define it has 1!
11:27 I love how Artifexian's "strange number" 70 is, according to maths, a "weird number". Look it up in wikipedia if you want, it is a lot of fun (and a very random thing to care about). Edit: 836 from 12:23 is yet another one - and they are the first two weird numbers. This is not a coincidence.
@@oyoo3323 Not usually, or at least in my opinion, no. Mostly because order of operations days that -2² = -4, but (-2)² = 4, which is what was meant in this case. So, instead of -1 * 2ⁿ you would get (-1)ⁿ * 2ⁿ
exponentiation before mutiplication babeyyyyyyyy Seriously though, annoying as it may be it's pretty necessary. Otherwise in order to write -k^n you'd have to write -(k^n) and that's just clunky, especially for something that's so much more common than (-k)^n
I never actually thought about even considering the power of something as something that could be seperate in a power sense, now that i am writing it i realised it for longer strings but not a single number, thats actually kind annoying when its negative xD thanks :)
"Ever wondered what would happen if you chose a negative number as a base?" "Can't say I have, no" Hmm... maybe I'm weird, because I totally have. Especially base (-1) is absolutely insane... and not all that useful...
They probably got that from the Etruscans: ci-em-zathrum is three-from-twenty. (There's a dispute about 4 and 6, huth and se or the other way around. Me, I'm on the 4=huth side.)
Lets hope the universe is a complex function space. Then divisions by zero are while locally undefined, not destructive to the entire system. In fact you if integrate any circle in complex function space the result of the integration is always the exact count of places somebody divided by zero inside the circle.
@@Carewolf Speaking of complex numbers what about a complex number system? Though if that isn't extreme enough there is also quaternions which add two more terms allowing the representation of vectors in the like representing the coordinates of a hypersphere. This is probably the domain the universe uses as it encodes space and time by default, I could see this being the system used by some advanced alien civilization which doesn't have a brain with a hardcoded three dimensional limit.
9:41 That's technically not even the end of it! "Three and a half" in this context is said as "Half four" (think "Halfway to 4 from the last integer"). So really, it's a hyper-abbreviated form of "Halfway to four from the last integer times twenty"
@@sofia.eris.bauhaus Wait does negabinary actually span all the integers? I know binary spans all natural numbers, but with less positive factors wouldn't negabinary miss some?
@@AKhoja it does! :) the thing is that, when adding digits, it 'grows' in both the negative and positive direction. it also 'grows' (on average) half as fast into the positive direction as regular binary does.
@@sofia.eris.bauhaus I wonder how you would go about proving it...I gave it a cursory shot, and came up with nothing :( Probably one wouldn't need more than number theory.
@@AKhoja lemme see: 1 digit: numbers 0 to 1 2 digits: numbers -2 to 1 3 digits: numbers -2 to 5 4 digits: numbers -10 to 5 and so on not sure that's what you had in mind when talking of a proof, but i hope it helps.
6:25 - Yes, humans got along fine without 0 for a long time, but most of what we take for granted in the last couple millennia *requires* a zero. The concept of debt, for example, is unworkable without some way of signifying that a debt is cleared. Mathematics more complex than compass-and-ruler geometry is also nearly impossible without zero. And you can forget any kind of scientific discipline. Also, I'm disappointed that you didn't mention Donald Knuth's en.wikipedia.org/wiki/Quater-imaginary_base
Also it should be noted that while there might not be a symbol for zero the concept of nothing was used in many pre-zero math systems. So there existed at least for those that was dealing with complex math a proto zero concept. I also like how you mention debt would be a problematic concept without zero. It was accounting that help spread the numeral system we use today that made zero a popular concept. So very appropriate. (But hay it was accounting that lead to written language and the concept of money to so it has had a huge impact on our world in general)
@@aaryanbhatia4939 Imaginary numbers are pretty basic. At least if you have heard many of the concepts talk about the video your should be somewhat familiar with them. If not then just mentioning it could lead to some people actually looking it up. I am pretty sure that people willing to watch a video like this would look up a concept like that. (But maybe I am just the weird one and often have Wikipedia up and ready when complex topics are talked about. Can be nice to have a quick lookup if is something you unsure of. As well as double check if they got something correct.)
I thought my phone crashed when he said “zero divided by zero” at 13:00 but actually an ad popped up. Edit: Just finished the video. Okay maybe something did crash there...
I have a personal tally system I use which is base 10 instead of 5. It starts as base 5 tally does, with a single vertical line on the left, and the fifth line diagonal from the upper right. But then 6 is a horizontal line at the top, followed by another below it, then another below it, one at the bottom, and 10 is a diagonal line in the other direction, leaving you with basically a box with a small grid inside, and an x over it to finish it.
Think of how binary is used on the fundamental level here, before things like counting binary is primarily used for logical states of on and off, or signal and no signal. So maybe your culture has a leaning towards this kind of on and off thinking. I would imagine it could evolve from the words yes and no, separate whatever existing numerical system there is... Maybe there comes a situation requiring a combination of yes-no as a third state, after 1000 years imagine that the old counting system fell out of use and the only thing available is this logic based system.
Count each finger separately instead of requiring that all previous fingers are raised. It's possible to count as high as 1023 on 10 (binary) digits. Exclude thumbs and you have a perfect byte with a nybble per hand.
@@dafoexI was... WHAAAAA????????!!!!!!!!! I CAN'T HEAR YOU!!!! was my reaction when someone tried to talk to me... Or, at least, i thought they were, i dunno what they said
Interesting video as always Edgar, it certainly gives a few food for thoughts on number systems that would seem overly complicated and/or convoluted for an advanced civilization would logically utilize that would make them even more noteworthy, like Roman Numerals. Joking aside, these alternate numeral systems can also highlight the world view of the conlang even more. On a side note, I never even considered that Tagalog could even be pronounced like that. My extended family had always pronounced it Ta-Gal-Og. Anywho, thanks for posting the video.
I'm sad you didn't bring up "base fibonacci" when you mentioned base phi. It uses the fibonacci numbers as its place values, and it has the property that every positive integer can be represented as a string of 1's and 0's with no adjacent 1's. I believe base phi shares this "no adjacent 1's" thing because they're pretty similar, but "base fibonacci" can represent integers cleanly.
This is my new favorite conlang-related video, as it combines two of my favorite super nerdy things: conlangs and fun math weirdness. It kinda makes me want to see if I can come up with an interesting counting system that uses balanced base-5 and standard base-5 as needed.
Nice video ! That's some really inventive ways of writing numbers. PS : at 7:36 it's wrong, you need to put the parenthesis : (-2)^n, or else they are all negative.
Ahhhh they mentioned Tongan! Finally! Though I would mention that Tongans usually count how you described, however that’s the informal way of talking. Tongan has words for the multiples of ten (hongofulu - 10, uongofulu - 20, tolungofulu - 30, etc.) and 100 is teau, 1000 is afe, and 10,000 is mano. Formally the number words are conjoined with the word mā, so for 11, for example, you would say (formally), hongofulu mā taha. 77 would be fitungofulu mā fitu. Of course, taha taha and fitu fitu are much easier to say and so almost always are. The year 2019 would be said uaafe taha hiva because that’s easier to say than ua noa taha hiva, but again the forms way would be uaafe mā hongofulu mā hiva.
1:33 Last year, this number system was an amazing question at the Brazilian Linguistics Olympiad. I couldn't find the difference between yott (times one) and rpat (one), since it doesn't appear in any other number.
05:50 Funny you mention it... When I made my conlang, I messed up with the numbering system and made this by accident. So now you have to write 1000 as 900+90+10. I decided that the bug is a feature because I was too far in when I noticed...
Some kind of combination of prime factor notation and a more traditional base system might be quite interesting, e.g. having numerals for 0, 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 30 and +. You could also add special digits representing the reciprocals of the primes, which would make writing fractions very easy and maybe a numeral representing -1 and a numeral representing a very large number like 30^6.
and if he talked to high school and college students who speak tagalog he'd probably also say that tagalog speakers also count grades in spanish (singko to uno or vice versa depending on the school) lmao
One thing that could be cool is if you left the natural numbers completly. i.e. you had a complex base using just i or euler's formula. or even a vector vector baced counting system where the numbers also incode the direction in which the numbers are being counted for example
@@Errenium For Edgar and jan Misali? Yes, naturalism is a consideration, although since jan Misali loves toki pona and auxlangs, I'm not sure exactly how naturalistic his conlang tastes skew. Anyway, my comment is meaning that it would really depend on the type of conlang you wanted to create and its purpose. For something engineered, then the sky is the limit on odd numeral systems. But, as you move toward something naturalistic, then you'll likely need a more natural system. Also, for simplicity's sake, auxlangs tend toward decimal. It all just depends on what you'll do with it.
@@Errenium Edgar has also favored naturalistic and realistic world building, not just a random assortment of "I want a mountain here because it would look cool, but I don't care how it got there." His conlanging has been in service of his world building; therefore I feel that he would still favor a naturalistic conlang. Also, you fail to understand the differences between naturalistic conlangs and other types of conlangs, while also misunderstanding that such bizarre numeral systems are fine for specifically engineered conlangs, but not naturalistic ones. I never said that using base i or such in a numeral system was impossible, stupid, or that it should NEVER be done, only that it wouldn't show up in a naturalistic conlang.
@@Errenium Plausibly real is naturalistic. Naturalistic is plausibly real. And guess what, even if you are making your own world, ANADEW. It is neither naturalistic nor plausibly real for any speaking population to come up with a numerical base of i or Euler's formula, for instance, unless it is a deliberate construction long after that speaking population has discovered complex math. The number i, as an imaginary number, is only used for purposes of math; you can't see i flowers in a field. You can't count e chickens, even after they've hatched. You can't ask that π bakers make confections for your party. I must reiterate that I am not saying that it would be wrong, no matter what, to use base φ, say, for your numeral system. As long as it is an englang, a loglang, a jokelang, or any other non-naturalistic conlang, then fine! go ham on the numbers! It just isn't plausible for a naturalistic conlang. That's all I was saying.
Ancient Chinese had their own "short scale" and stuff as well, above 10000. The number 載 would mean 10^14 in the "low scale"(10-based), 10^44 in the "myriad-based scale"(modern system), 10^80 in the "middle scale"(100000000-based), 10^4096 in the "high scale"(exponential base) As for why, it's just a mathematical representation, albeit a probably overkill one. Actual usage never exceed 兆, though the value of that exact number is now debated because of the scales, and it's usually avoided in modern usage.
6:20 A possible workaround to this is to write 0 as a simple equation (1 - 1) several languages do this for large numbers at least verbally (ex: french 80 = 4 * 20) so zero is by all means possible for a zero - less writing system.
Stellar video! You covered a lot of bases here, but I did notice at least one possible weird number system you missed. Base 3/2 is completely workable if you do it the James Tanton exploding dots way. It goes like this -- instead of just 0 and 1, allow yourself the digit 2. When counting or adding, carry twos instead of ones -- i.e., whenever a digit would need to be greater than two, treat the three as a two in the next highest place value. Counting to ten this way goes 1, 2, 20, 21, 22, 210, 211, 212, 2100, 2101. These are all completely valid base-3/2 expansions. For instance, 2*(3/2)^3 + 1*(3/2)^2 + 0*(3/2) + 1 = 10.
This video is brilliant! I've been thinking about all these weird bases for years, but only in a "shower stall thoughts" kind of way. Hearing you guys discuss them is the video I've been searching for. Thank you!
I've had a crazy number system idea but I will def leave it to math nerd like you two. A system built on squares so : 1, 4, 9, 16, 25 ext. I think it would be fun but I have no clue how to write it much less use it
As a native Tagalog speaker, I've just realized we're generally using Spanish numbers for time or money. Current generation of native speakers tend to use English number terms for time and money.
and you can combine those: in kirxan one uses scientific notation with bijective six for base and almost balanced dozenal for exponent, except when you try to write fraction, then dozenal is for numerator and seximal is for denominator (and integer part).
Now I want a number system with such an inconvenient base so that people have to perform college level calculus just to count out change Cashier: That will be $6.37 hands over $7 Cashier: Sigh (pulls out TI-92), one moment sir
1. I once tried to shoehorn SI binary prefixes into a base-power-of-2 counting system and achieved an inconsistency with how they line up with the powers of 2^10, and just rolled with it. For example: - For base 8, powers of 2^3 only line up with powers of 2^10 whenever the exponent is 30*n, so you either have to give up on kibimeters, kibigrams, and whatever or just accept that the positions are 8, 8, 2, 8, 8, 8, 2, ... times larger than the previous (every 4th position is 2 times larger instead of 8 times larger). - It's a little more merciful with base 16 in that you can at least go by a sub-base of 4, but the positions become 16, 4, 16, 16, 4, 16, 16, 4,... times larger the last (every 3rd position is 4 times larger instead of 16 times larger). 2. I'm sorry but the stresses in "Tagalog" are different from how you said them. 3. You had me at base 0.
Creating a bit of a written conlang for Minecraft (though spoken portions would likely be based on available creature sounds in-game) using in-game items as the base hieroglyph system. I wanted to use sticks as a sort of in-game counter but couldn't quite figure out how to draw glyphs representing them. These videos have been very helpful!
Also, how do the Pirahã people perform complex mathematics and physics and even perform tasks such as dialing someone up on a phone? Said tasks require a comprehension of a finite numeral system. One option could be to use loanwords from Portuguese to express numbers greater than two, similarly to how Korean uses the Chinese number system for numbers greater than 99, but a study has shown that even that would be perplexing to most Pirahã speakers.
I grew up learning what we now call a Billion was actually called a Milliard, So the scale of money that Billionaires really impressed me. Then sometime in 2010 I learned that the short scale was a thing and apparently it's been in use universally in English speaking finance since the 70s.
I want to thank you Artifexian. These videos have been helping me construct the language for my novel, and for helping construct worlds for my Starfinder games.
Another reason to say 0^0=1 is the following. Note that x^y is the number of strings of length y written in an alphabet of x characters. For example 2^2=4 is the number of binary strings of length 2: "00", "01", "10" and "11". And the number of strings you can write of length 0 using an alphabet of 0 zero character is exactly one: "", the empty string. So it makes sense in that regard to say 0^0=1. More formally: the number of functions from a set of y elements to a set of x elements is x^y for all cases where x and y aren't both equal to 0. So consider this set of functions where both x and y are 0. Such functions are formally defined as relations R such that for every a in the domain of R, there is exactly one b in the codomain such that aRb, i.e. every input has exactly one output. For that reason we also write R(a)=b. And a relation R between two sets A and B is formalized as a subset of the Cartesian product A×B. In our case, where we're trying to find a candidate for 0^0, we take both A and B to have 0 elements, aka A = { } and B = { }. Then the Cartesian product A×B is the set of all pairs (a, b) such that a is in A and b is in B. There are no such pairs, so the Cartesian product is also empty: A×B = { }. Then the only subset of the Cartesian product is { } itself, and this is a function: there are no elements in its domain A, so it's trivially true that every input has an output. (All zero of them do.) So there's exactly one function from the empty set to itself. We can then use this to argue that it may be convenient to say 0^0=1.
10 is folly, 12 is jolly, purely on the basis that 9x9 in base 12 is 69, making it square. Also, what makes odd bases peculiar is that even/odds alternate depending on the amount of digits in a number. So 7 is 7 in base nine, but 17 is actually 16, making it even. However, 27 is 25, making it odd again. It goes on. 107 (9x9+7) is even. This provides a situation where if there are an odd number of odds, its odd, but if it's an even number, it's even. We have an equivalent in base 10 where if a negative is taken to a power, it alternates between even an odd. Hell, imaginaries make it even weirder, where it rotates between 4 different number types depending on the power. Positive Imaginary, Negative Real, Negative Imaginary, and Positive real.
In one of my (admittedly not well fleshed out) conlangs, I use base 10 for integers but balanced base 12 for fractions. In addition, the writing system is almost, but not quite, positional, sort of a compromise between positional notation and the Chinese system of dedicated order-of-magnitude symbols. And finally, negative quantities are written upside down, which means that this system has a concept of negative numbers *without* a zero.
"Imagine if like German did this" Well you're in luck cause Icelandic does "One man" = "einn maður" "One woman" = "ein kona" "One child" = "eitt barn" Note the examples are just the standard masculine, feminine, and neuter, this goes for all nouns and other words in other groups but not all from said groups
That's more or less "just" grammatical gender and different forms of numerals. German does it as well, although masculine and neuter are mostly identical (ein Mann, eine Frau, ein Kind). What they're talking about is counting different noun classes with entirely different systems. Like 🙍 1 man, 🙍🙍 2 men, 🙍🙍🙍 3 men, ... 9 men, 10 men, 11 men (decimal) 🙎1 woman, 🙎🙎 10 women, 🙎🙎🙎 11 women, ... 1001 women, 1010 women, 1011 women (binary) 🚗 1 car, 🚗🚗 2 cars, 🚗🚗🚗 3 cars, ... 9 cars, A cars, B cars (hexadecimal) So "10 X" depends entirely on what you're talking about - it's (in decimal) 10 masculine things, 2 feminine things, or 16 neuter things.
Actually, you DID do the tones in Pirahã. The main problem is that you also added a glottal stop between the vowels. Pirahã has contrasive glottal stops, which are written with an . Also, I don't know, but I suspect most of the vowels you said could all be considered long vowels, which would mean that you actually said "hóóxi", and "hooxíí"
I am so stoked about getting so many videos in my feed from all my favorite linguistics/conlang UA-camrs! A little comment on the point about Danish numbers: The underlying logic behind 70 (halvfjersindstyve) isn't exactly (3.5 · 20). Well, sorta: halvfjersindstyve means *something* along the lines of "halfway-until-four twenty" in the sense that there's half a twenty until you've got four twenties. So I'd express it as ((4 - 0.5) · 20).
Ten in base 3/2 is 2101. For rational bases > 1 you can always find not only a terminating expansion, but a "whole number" expansion for integers if the number of symbols you have is the numerator of the base. . To do this in base b=p/q, you can imagine buckets in each position, for any integer you want, put that many things in the b^0 bucket, if this number is smaller than p, you're done, otherwise, take out as many groups of p things from the bucket as you can, and put that many groups of q into the b^1 bucket. Then you repeat with the next bucket and so on until all the buckets have less than p things. . For example with 10 base 3/2, we start with all 10 in the first bucket, so 10*(3/2)^0. We take 3 groups of 3 out of 10, and put 3 groups of 2 in the next bucket, so 6*(3/2)^1 + 1*(3/2)^0. 2 groups of 3 out of 6, and 2 groups of 2 into the next bucket, so 4*(3/2)^2 + 0*(3/2)^1 + 1*(3/2)^0. Once more and we get the final expansion 2*(3/2)^3 + 1*(3/2)^2 + 0*(3/2)^1 + 1*(3/2)^0! . This works for all integers in any rational base >1 because everytime we move to the next bucket we have less things
@@arnouth5260 but if you allow for digits as large as the numerator, then integers still look like integers. That seems like a much better system to me
@@jpamado96 but that’s simply not how fractional bases work. The largest digit in any base b is (b-1), since fractional bases act just like integer bases this stays the same, the only difference is that we then round up to the nearest integer, giving ceil(b-1). Also, then you’d always have to specify that people should use the simples form of the fraction. By your logic base 3/2 would have 3 digits, but base 6/4 would have 6.
@@arnouth5260 fractional bases, or any bases, are just constructions, and we can impose any rules we want in them and see what results from that. I hadn't considered non simplified fraction, so before now i would have said they have to be simplest form, but after thinking on it a bit, you could have base(6/4) and base(3/2) be distinct bases with 6 and 3 digits respectively as you said. Using the method i described in my original comment 10 could be 4*(6/4)^1 + 4*(6/4)^0, or 2*(3/2)^3 + 1*(3/2)^2 + 0*(3/2)^1 + 1*(3/2)^0. Neat!
0^0 is often defined as 1 rather than undefined, because defining it as 1 has many practical uses in various mathematical fields. Most calculators will actually return 1 for this calculation because of that. But this also means that a base 0 system would be equal to unary. Here's the wikipedia article on 0^0 en.wikipedia.org/wiki/Zero_to_the_power_of_zero
it still wouldn't be equivalent to unary, however, because 0^x is always zero (which is why 0^0 is equal to "undefined, but if it is anything it's one" and not just 1)
oh true, I messed up my maths and thought for a moment it would be i^b (index ^ base or radix), but positional systems use b^i, so yeah you're sort of right, however if 0^0 is accepted to be 1, then only the 0th position would have any value in base 0, while all other positions would only have a value of 0, which would make it equal to having a unique symbol for each number. In other words, if 0^0 = 1, then d*b^i would have a value for i = 0 would be equal to d (the digit), but all other positions would always have a value of 0. But ofc this all comes down to how you choose to define 0^0
My conlang uses base-32 because the human hand has 5 fingers and 2^6=32. The last one digit number (31) is ponuced as ʞôn and 32 is ʞá ʞà. Every number starts with "ʞ", the last two binary bits describe the tone, the 2nd and 3rd ones describe the vowel and the first bit adds an -n ending if it's 1
huh... I am just realizing that we do count money and time mostly in Spanish lol also, you read Tagalog as ta-ga-log, not tag-a-log....unless there's an official pronunciation for non Filipinos, in which case, ignore this comment
It's undefined, since the rule that 0^n=0 also applies. n^0=1 doesn't just override it, and it can't have two values at once (that would break _way_ too much stuff), so we just say it's undefined and avoid it altogether.
@@Errenium n^0=1 is accepted for any n ∈ R \ {0}, not just n ∈ R+ (or, since you mention the real component, if you want all numbers, ∀n ∈ C ∧ (R(n) ≠ 0 ∨ I(n) ≠ 0), which I now realise is just n ∈ C \ {0} again) And the fact that 0^0 has contradictory limits is _exactly_ the reason it's undefined. It is not equal to 1.
@@photonicpizza1466 No, 0^0 is taken to be one all the time, you just lose a^b being continuous. It's important for certain branches of probability theory that you let 0^0=1, otherwise lots of things break.
5:29 Oh, YES, this does exist! When I was in primary school I didn't really know how do billion and so forth work, so I came up with more or less something like this. I asked people if what I guess was right, or if you just get a new number for each ×1000 and nobody could understand what I was taking about. It turned out that it's plain boring long scale with -illions and -illiards for ×1000. How mundane…
this is really neat!! a few days ago i just updated the numeral system for one of my conlang (the conlang itself still needs lots of work so shhh) with a base 9 system, and came up with something i thought was pretty smart but was touched on pretty early in this video eheh. i didnt know there was so many options available!! my system uses 9 as a base to write numbers, and every digit added right of it as added, and digits left to it are multiplied, so 291 would be 2*9+1 aka 19. if theres more numbers, each operation is done from left to right. anyway, good videos!! gave me ideas for the system of the other cultures in my world. i hadnt considered at all that one could have different numeral systems that are used for different things, i think i'll use that. thank you for your vids!!!
Alternate idea: an inverse base. Mostly you just switch the denominator and numerator, so 5 would be 1/5th and vice versa, and our plural case would be dropped, while a fractional case would be added (for example, imagine if there was a rule in English where instead of saying "half of my inheritance" or "a quarter tank of gas" you had to say "half of my inheritancey" or "a quarter tanky of gas" because you're talking about something that is not whole, sort of a twist on the whole "diminutive case" concept). I mainly enjoy this idea just because of the thought that someone counting "1, 2, 3, 4, 5..." would be imagining a single thing broken into ever smaller pieces rather than the usual mental image of a rapidly growing group of things, and someone doing a countdown would be imagining a thing becoming unbroken rather than the usual mental image of a rapidly dwindling group of things. I also like how this number system does not conventionally allow for the existence of zero, so I'm curious to see how a culture with this number system would perceive it. I imagine they would understand it, but also consider it a Platonic ideal that can't exist in reality, and what looks like zero avocados is actually just a quantity very close to zero.
I'm working on a base 60 system which is divided in a sub base 12. In the proto language there was only a limited amount of number 1, 2, 3, 4, 5, 6, 12, 60 360/720 and maybe other but I'm not really worked on big numbers. The numbers are formed in this way: from 1 to 6 is pretty straightforward, from 7 to 9 are 6+1 6+2 6+3, 10 is 2*5 and 11 is 12-1, 24 is 2*12 36 is 3*12 and 48 is 4*12. Numbers above 12 are formed generally by adding a number to 12. So 13 is 12+1, 14 is 12+2 etc... five is not used in this numbers so 6-1 or X*12-1 is used. 15, 20, 25, 30-35, 40, 45, 50, 55 are irregulars, 15 is 60/4, 20 is 60/3, 25 is 5*5, 30 is 1/2*60, 31, 32, 33, 34, 35 are 1/2*60+1, 1/2*60+2, 1/2*60+3, 1/2*60+4, 1/2*60+5, 40 is 60/3*2, 45 is 60/4*3, 50 is 5*5*2 and 55 is 60-5. For bigger number I've nothing decided yet.
I'm slightly disappointed that the factorial system never showed up. It has a lot going for it: 1. All rational numbers can be written without repeating numbers; 10. The common irrational number e can be written with just 1 recurring number; 11. Addition and multiplication function similarly to numerical basis systems; 20. It is really good at expressing really large numbers; 21. In many cases it is easy to verify the prime divisors of a number; 100. It makes many calculations in maths even more beautiful; 101. Its one drawback, the requirement of infinite algorisms to express a number, is easily solved with a mixed basis system.
Another possible division of radixes is register. In her Doctrine of the Labyrinths novels, Sarah Monette creates a world where the ruling class uses base 10, and the working and uneducated classes use base 7.
A balance 3 or 5 while problematic when dealing with division, could make sense as an part of a early counting number system with the "middle finger" = 0 meaning you can count on your hands with it, much like how we got our base ten
I once came up with what I call zug notation for balanced ternary. ז is-1, ו is 0, ג is 1. It looks more sensical in handwriting. And of course, it's right to left.
I feel like base 4 is the best idea because 2 using any operation which stems from addition, like multiplication and exponents, to itself is 4. So 2+2, 2x2, 2^2, 2 to the power of itself twice, all 4
The "divide by zero" section just made me think of a sad robot's final words being "divide.. by... z e r o ......." Really cool video! I liked the overview of lots of different languages and how they deal with things, and some of the stranger bases like bijective unary (I'm now going to call it that when I do tally marks).
imagine a system where they said 15 as "quarter of 60" but they didn't invent fractions yet so they say something like "one of the four parts of 60"
That's already a fraction, you're just switching the terms around. Mandarin does exactly this: 1/4 is called 四分之一 sì fēn zhī yī literally ‘one of four parts’
where is the 4
@@ashtarbalynestjar8000 The first character is off; that's the number 2. So here is 1/4: 四分之一
Fixed, I copied the wrong character.
Ondřej Adam I never knew I would find another vocaloid fan here
Nullary: I have no numerals and I must NaN
Alex00712
He is speaking the language of gods.
"The only number we have is not a number." - Nullary
Nullary: All you have is a Math Error :D
You must Sodium Nitride?
re: "wait, isn't 0^0 equal to 1?"
so, yes, if 0^0 has to be given a value, it's treated as one. BUT that depends on how you approach it. 0^x is always 0 and x^0 is always 1. 0^0 can't be both, so it's undefined. this, of course, doesn't stop mathematicians from sometimes giving a value anyway; it is useful to treat it as equal to one in some contexts.
"so then wait, why is it equivalent to 0/0?"
great question! the defining property of exponentiation is that a^b is equal to b copies of a multiplied together. to generalize this to work for weirder numbers, we can say that a^b is equal to a^(b-1) · b. in other words, adding one to the b in a^b is the same as multiplying the whole thing by a. from the original limited definition of exponentiation, you'll find that this has to be true. the inverse also has to be true, specifically that SUBTRACTING one from the b in a^b is the same as diving the whole thing by a.
so, let's say that you start with a^1, and you subtract one from the exponent. what do you get? you get a^0 = (a^1)/a. a^1 is always a, and a/a is always 1, therefore anything to the power zero is always 1. except! what if you start with 0^1? well, from THERE, subtracting one from the exponent requires dividing 0^1 by 0, otherwise the defining property of exponentiation doesn't work.
now, you might notice that this isn't actually a proof. this way of deriving an exponent from division seems to imply that zero to ANY power has to be equal to zero divided by zero, and that can't be right. it is, however, a pretty useful intuition for why 0^0 is undefined. (unless it's one, which it is sometimes.) hope that helps!
Hey Mitch! I find it really cool that you seem to be well versed in math. Do/Did you study math?
@@giladu.6551 only recreationally
I've heard the argument that 0/0 can be any number you want, because all numbers are valid solutions to the equation 0 * x = 0
When I tried to read this I got about halfway through, and then it got really fuzzy. I'm gonna try again.
There is a really good reason 0^0=1, it's that lim x->0 x^x = 1
And it's a very useful definition pretty much everywhere in math. So you can't really say 0^0 is undefined, most mathematicians define it has 1!
Instructions unclear, I invented the alphabet.
You successfully invented base 26
or base x in which x is the number of letters you invented
Welcome to 2 or 3 years ago
*If you accidentally make an alphabet while trying to make a number system, use Gematria
That moment when
I like how this video is done in a hybrid of Edgar and jan Misali's visual styles
Me as well.
Yo I know you from the conlang CDN.
@@zerbgames1478 I knew it was a bad idea to use the same icon on everything 😂
I do as well
LangFocus, Conlang Critic, Biblaridion and now Artifexian; this has to be declared as The Day of Language!
Name Explain published today too!
Wait, langfocus did? Oof
I'm okay with a Conlang Day
I don't see an Albanian video, what? Is it blocked in the UK or something
@@danieldoel6216 nope, only patrons get to view it right now
11:27 I love how Artifexian's "strange number" 70 is, according to maths, a "weird number". Look it up in wikipedia if you want, it is a lot of fun (and a very random thing to care about).
Edit: 836 from 12:23 is yet another one - and they are the first two weird numbers. This is not a coincidence.
ШНАТ
@@gabenugget114 well, they're abundant, but not semiperfect, and that's weird.
@@gabenugget114 Shnat
@@ljr6490 shnat
@@floenele8892shnat
Papua New Guinea: we have the weirdest number systems
Nullary: hold my beer
Ugh, kids these days xan't even count in nullary
but.. how many beers would Nullary have? :P
@@xevira ERR_0⁰=undefined. Beers=0⁰=undefined. Beers=null.
A radix number system, 00=0^0=1
000=undefined
0000=0^0+0^0=2
@@xevira 404 beers because: 404 error brain no found
Highkey annoyed by -2ⁿ not being (-2)ⁿ
@@oyoo3323 Not usually, or at least in my opinion, no. Mostly because order of operations days that -2² = -4, but (-2)² = 4, which is what was meant in this case. So, instead of -1 * 2ⁿ you would get (-1)ⁿ * 2ⁿ
exponentiation before mutiplication babeyyyyyyyy
Seriously though, annoying as it may be it's pretty necessary. Otherwise in order to write -k^n you'd have to write -(k^n) and that's just clunky, especially for something that's so much more common than (-k)^n
@@annabelarduino8548 If it is clear from context it's okay to ignore the default order of operations.
I never actually thought about even considering the power of something as something that could be seperate in a power sense, now that i am writing it i realised it for longer strings but not a single number, thats actually kind annoying when its negative xD thanks :)
@@haraldmbs thus balanced ternary ftw
"Ever wondered what would happen if you chose a negative number as a base?"
"Can't say I have, no"
Hmm... maybe I'm weird, because I totally have. Especially base (-1) is absolutely insane... and not all that useful...
-0?
@@Kassakohl -0 is 0 so that's still nullary
@@aaayaaay5741 Ikr, it was a joke
Bijective base -1 be like:
1+1= 13:03
more useful than nullary though. The concept of negative here is confusing because relatively it's theoretical here, isn't it?
7:50 In ancient Latin, the numbers 18 and 19 have been 20-2 and 20-1 for a long time before switching to 10+8 and 10+9
They probably got that from the Etruscans: ci-em-zathrum is three-from-twenty. (There's a dispute about 4 and 6, huth and se or the other way around. Me, I'm on the 4=huth side.)
@Gregor Kerr I was talking about the words, the name of the number, how they were pronounced, not the numerical notation.
Well done and I like how nullary breaks the universe
Lets hope the universe is a complex function space. Then divisions by zero are while locally undefined, not destructive to the entire system. In fact you if integrate any circle in complex function space the result of the integration is always the exact count of places somebody divided by zero inside the circle.
@@Carewolf Speaking of complex numbers what about a complex number system? Though if that isn't extreme enough there is also quaternions which add two more terms allowing the representation of vectors in the like representing the coordinates of a hypersphere. This is probably the domain the universe uses as it encodes space and time by default, I could see this being the system used by some advanced alien civilization which doesn't have a brain with a hardcoded three dimensional limit.
@@Dragrath1There is a complex number system. Complex quaternary or imaginary balanced nonary.
1:28 "...only has words for 1, 2, 5 and 20"
**happy toki pona noise**
0, 1, 2, a lot...
And 100!
9:41
That's technically not even the end of it! "Three and a half" in this context is said as "Half four" (think "Halfway to 4 from the last integer"). So really, it's a hyper-abbreviated form of "Halfway to four from the last integer times twenty"
Nonov Yurbisniss me when i’m tryna explain 2x2 to my friends
Caveat observator: sudden volume jump around the thirteen-minute mark.
So we’re just not gonna talk about “negabinary” then? Ok.
you mean the fact that you don't ever need a minus sign when working with it? or the fact that it is used by eggman nega aka nega robotnik?
@@sofia.eris.bauhaus Wait does negabinary actually span all the integers? I know binary spans all natural numbers, but with less positive factors wouldn't negabinary miss some?
@@AKhoja it does! :)
the thing is that, when adding digits, it 'grows' in both the negative and positive direction. it also 'grows' (on average) half as fast into the positive direction as regular binary does.
@@sofia.eris.bauhaus I wonder how you would go about proving it...I gave it a cursory shot, and came up with nothing :(
Probably one wouldn't need more than number theory.
@@AKhoja lemme see:
1 digit: numbers 0 to 1
2 digits: numbers -2 to 1
3 digits: numbers -2 to 5
4 digits: numbers -10 to 5
and so on
not sure that's what you had in mind when talking of a proof, but i hope it helps.
French learners: "Sacre bleu! 'Soixante-dix' is such an odd way to say 'seventy'!"
Danish speakers: hold my beer...
Quatre Vingt Onze
@@anselmschueler
Quatre vingt dix sept
@@want-diversecontent3887 Quatre vingt dix neuf
@@anselmschueler et onze*
*Laughs in Belgian French*
Septante ftw
6:25 - Yes, humans got along fine without 0 for a long time, but most of what we take for granted in the last couple millennia *requires* a zero. The concept of debt, for example, is unworkable without some way of signifying that a debt is cleared. Mathematics more complex than compass-and-ruler geometry is also nearly impossible without zero. And you can forget any kind of scientific discipline.
Also, I'm disappointed that you didn't mention Donald Knuth's en.wikipedia.org/wiki/Quater-imaginary_base
Also it should be noted that while there might not be a symbol for zero the concept of nothing was used in many pre-zero math systems. So there existed at least for those that was dealing with complex math a proto zero concept.
I also like how you mention debt would be a problematic concept without zero. It was accounting that help spread the numeral system we use today that made zero a popular concept. So very appropriate.
(But hay it was accounting that lead to written language and the concept of money to so it has had a huge impact on our world in general)
"Some way of signifying that a debt is cleared" --> "Debt is cleared."
@@aaryanbhatia4939 Imaginary numbers are pretty basic. At least if you have heard many of the concepts talk about the video your should be somewhat familiar with them. If not then just mentioning it could lead to some people actually looking it up. I am pretty sure that people willing to watch a video like this would look up a concept like that.
(But maybe I am just the weird one and often have Wikipedia up and ready when complex topics are talked about. Can be nice to have a quick lookup if is something you unsure of. As well as double check if they got something correct.)
Donald Knuth, what have you done
@@aaryanbhatia4939 Well, it wouldn't really take that much time, probably a minute for this style of explanation
I thought my phone crashed when he said “zero divided by zero” at 13:00 but actually an ad popped up.
Edit:
Just finished the video. Okay maybe something did crash there...
I have a personal tally system I use which is base 10 instead of 5. It starts as base 5 tally does, with a single vertical line on the left, and the fifth line diagonal from the upper right. But then 6 is a horizontal line at the top, followed by another below it, then another below it, one at the bottom, and 10 is a diagonal line in the other direction, leaving you with basically a box with a small grid inside, and an x over it to finish it.
no one:
absolutely nobody:
conlang critic: what if *hits blunt* we had a negative base
Not no one. Me for example
Donald Knuth did it before.
This is so fucking stupid even the bare rudiments of language puzzle about it.
@@johannesh7610 No human being*
I think irrational bases are even crazier. Imagine for example a system based on pi.
Question: How would a binary number system naturally arise? What would the conditions have to be?
yeah powers of 2 would have to be a lot more prevalent in nature
Think of how binary is used on the fundamental level here, before things like counting binary is primarily used for logical states of on and off, or signal and no signal. So maybe your culture has a leaning towards this kind of on and off thinking. I would imagine it could evolve from the words yes and no, separate whatever existing numerical system there is... Maybe there comes a situation requiring a combination of yes-no as a third state, after 1000 years imagine that the old counting system fell out of use and the only thing available is this logic based system.
We have decimal just because we have 10 finger, so logicaly you would have to have 1 finger per hand
Aliens with 2 fingers on each hand.
Count each finger separately instead of requiring that all previous fingers are raised. It's possible to count as high as 1023 on 10 (binary) digits. Exclude thumbs and you have a perfect byte with a nybble per hand.
I'm so glad I wasn't wearing headphones at the ending of this video.
I was but I'm low volume crew
@@dafoexI was... WHAAAAA????????!!!!!!!!! I CAN'T HEAR YOU!!!! was my reaction when someone tried to talk to me... Or, at least, i thought they were, i dunno what they said
ki
Interesting video as always Edgar, it certainly gives a few food for thoughts on number systems that would seem overly complicated and/or convoluted for an advanced civilization would logically utilize that would make them even more noteworthy, like Roman Numerals.
Joking aside, these alternate numeral systems can also highlight the world view of the conlang even more.
On a side note, I never even considered that Tagalog could even be pronounced like that. My extended family had always pronounced it Ta-Gal-Og.
Anywho, thanks for posting the video.
baker's dozenal amirite
the base to drive americans away from you
I'm sad you didn't bring up "base fibonacci" when you mentioned base phi. It uses the fibonacci numbers as its place values, and it has the property that every positive integer can be represented as a string of 1's and 0's with no adjacent 1's. I believe base phi shares this "no adjacent 1's" thing because they're pretty similar, but "base fibonacci" can represent integers cleanly.
NAGABINARY 3 IS 111
Rereply
Well, the ratio of each Fibonacci number to the one before it (starting from the second 1) does approach phi.
The editing in this video is fantastic. You're doing great Edgar and I'm really looking forward to your next video.
This is my new favorite conlang-related video, as it combines two of my favorite super nerdy things: conlangs and fun math weirdness. It kinda makes me want to see if I can come up with an interesting counting system that uses balanced base-5 and standard base-5 as needed.
Nice video ! That's some really inventive ways of writing numbers.
PS : at 7:36 it's wrong, you need to put the parenthesis : (-2)^n, or else they are all negative.
Pemdays Shemdas!
thank you for these information
im From EGYPT
Hi From EGYPT! I'm dad.
Ahhhh they mentioned Tongan! Finally!
Though I would mention that Tongans usually count how you described, however that’s the informal way of talking. Tongan has words for the multiples of ten (hongofulu - 10, uongofulu - 20, tolungofulu - 30, etc.) and 100 is teau, 1000 is afe, and 10,000 is mano. Formally the number words are conjoined with the word mā, so for 11, for example, you would say (formally), hongofulu mā taha. 77 would be fitungofulu mā fitu. Of course, taha taha and fitu fitu are much easier to say and so almost always are.
The year 2019 would be said uaafe taha hiva because that’s easier to say than ua noa taha hiva, but again the forms way would be uaafe mā hongofulu mā hiva.
1:33
Last year, this number system was an amazing question at the Brazilian Linguistics Olympiad. I couldn't find the difference between yott (times one) and rpat (one), since it doesn't appear in any other number.
05:50 Funny you mention it... When I made my conlang, I messed up with the numbering system and made this by accident. So now you have to write 1000 as 900+90+10.
I decided that the bug is a feature because I was too far in when I noticed...
Some kind of combination of prime factor notation and a more traditional base system might be quite interesting, e.g. having numerals for 0, 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 30 and +. You could also add special digits representing the reciprocals of the primes, which would make writing fractions very easy and maybe a numeral representing -1 and a numeral representing a very large number like 30^6.
this video: inventing a number system
also this video: nuclear explosion on repeat.
The memes in this one
Me: _scrolling through a conlang in another window_
Edgar: TAAAG-uh-LOG
Me: IT'S PRONOUNCED TAH-*GAH*-LOHG
I doubt there's a lot of Tagalog speakers in Ireland.
Read this comment right when he said it.
and if he talked to high school and college students who speak tagalog he'd probably also say that tagalog speakers also count grades in spanish (singko to uno or vice versa depending on the school) lmao
One thing that could be cool is if you left the natural numbers completly. i.e. you had a complex base using just i or euler's formula. or even a vector vector baced counting system where the numbers also incode the direction in which the numbers are being counted for example
While such a system could be used in an englang, I very highly doubt that it would ever occur in either a natlang or a naturalistic conlang.
@@Errenium For Edgar and jan Misali? Yes, naturalism is a consideration, although since jan Misali loves toki pona and auxlangs, I'm not sure exactly how naturalistic his conlang tastes skew. Anyway, my comment is meaning that it would really depend on the type of conlang you wanted to create and its purpose. For something engineered, then the sky is the limit on odd numeral systems. But, as you move toward something naturalistic, then you'll likely need a more natural system. Also, for simplicity's sake, auxlangs tend toward decimal. It all just depends on what you'll do with it.
@@Errenium Edgar has also favored naturalistic and realistic world building, not just a random assortment of "I want a mountain here because it would look cool, but I don't care how it got there." His conlanging has been in service of his world building; therefore I feel that he would still favor a naturalistic conlang. Also, you fail to understand the differences between naturalistic conlangs and other types of conlangs, while also misunderstanding that such bizarre numeral systems are fine for specifically engineered conlangs, but not naturalistic ones. I never said that using base i or such in a numeral system was impossible, stupid, or that it should NEVER be done, only that it wouldn't show up in a naturalistic conlang.
@@Errenium Plausibly real is naturalistic. Naturalistic is plausibly real. And guess what, even if you are making your own world, ANADEW. It is neither naturalistic nor plausibly real for any speaking population to come up with a numerical base of i or Euler's formula, for instance, unless it is a deliberate construction long after that speaking population has discovered complex math. The number i, as an imaginary number, is only used for purposes of math; you can't see i flowers in a field. You can't count e chickens, even after they've hatched. You can't ask that π bakers make confections for your party. I must reiterate that I am not saying that it would be wrong, no matter what, to use base φ, say, for your numeral system. As long as it is an englang, a loglang, a jokelang, or any other non-naturalistic conlang, then fine! go ham on the numbers! It just isn't plausible for a naturalistic conlang. That's all I was saying.
"836!" XD
Some nations like to use really complicated systems.
I struggle to see why the ancient Chinese had a need to have a word for 10^4096
Same reason anyone needs a word for 10^4096: numerological shenanigans!
Bureaucracy.
They invented fiat money.
Ancient Chinese had their own "short scale" and stuff as well, above 10000.
The number 載 would mean 10^14 in the "low scale"(10-based), 10^44 in the "myriad-based scale"(modern system), 10^80 in the "middle scale"(100000000-based), 10^4096 in the "high scale"(exponential base)
As for why, it's just a mathematical representation, albeit a probably overkill one. Actual usage never exceed 兆, though the value of that exact number is now debated because of the scales, and it's usually avoided in modern usage.
5:23 There's one zero missing for jo. A jo is the same as a trillion. Because it's 10⁴×10⁴×10⁴
6:20 A possible workaround to this is to write 0 as a simple equation (1 - 1) several languages do this for large numbers at least verbally (ex: french 80 = 4 * 20) so zero is by all means possible for a zero - less writing system.
Thanks for these videos they're really fun and inspiring!
Stellar video! You covered a lot of bases here, but I did notice at least one possible weird number system you missed. Base 3/2 is completely workable if you do it the James Tanton exploding dots way.
It goes like this -- instead of just 0 and 1, allow yourself the digit 2. When counting or adding, carry twos instead of ones -- i.e., whenever a digit would need to be greater than two, treat the three as a two in the next highest place value. Counting to ten this way goes 1, 2, 20, 21, 22, 210, 211, 212, 2100, 2101. These are all completely valid base-3/2 expansions. For instance, 2*(3/2)^3 + 1*(3/2)^2 + 0*(3/2) + 1 = 10.
13:10 yep. this is how i feel after this video.
This video is brilliant! I've been thinking about all these weird bases for years, but only in a "shower stall thoughts" kind of way. Hearing you guys discuss them is the video I've been searching for. Thank you!
Didn't expect this to come out so soon...
I've had a crazy number system idea but I will def leave it to math nerd like you two.
A system built on squares so : 1, 4, 9, 16, 25 ext. I think it would be fun but I have no clue how to write it much less use it
As a native Tagalog speaker, I've just realized we're generally using Spanish numbers for time or money. Current generation of native speakers tend to use English number terms for time and money.
and you can combine those: in kirxan one uses scientific notation with bijective six for base and almost balanced dozenal for exponent, except when you try to write fraction, then dozenal is for numerator and seximal is for denominator (and integer part).
Now I want a number system with such an inconvenient base so that people have to perform college level calculus just to count out change
Cashier: That will be $6.37
hands over $7
Cashier: Sigh (pulls out TI-92), one moment sir
Cashiers would be such a high paying job, then.
1. I once tried to shoehorn SI binary prefixes into a base-power-of-2 counting system and achieved an inconsistency with how they line up with the powers of 2^10, and just rolled with it. For example:
- For base 8, powers of 2^3 only line up with powers of 2^10 whenever the exponent is 30*n, so you either have to give up on kibimeters, kibigrams, and whatever or just accept that the positions are 8, 8, 2, 8, 8, 8, 2, ... times larger than the previous (every 4th position is 2 times larger instead of 8 times larger).
- It's a little more merciful with base 16 in that you can at least go by a sub-base of 4, but the positions become 16, 4, 16, 16, 4, 16, 16, 4,... times larger the last (every 3rd position is 4 times larger instead of 16 times larger).
2. I'm sorry but the stresses in "Tagalog" are different from how you said them.
3. You had me at base 0.
2???
My, that's nice.
Creating a bit of a written conlang for Minecraft (though spoken portions would likely be based on available creature sounds in-game) using in-game items as the base hieroglyph system. I wanted to use sticks as a sort of in-game counter but couldn't quite figure out how to draw glyphs representing them. These videos have been very helpful!
: Electric Boogaloo
Also, how do the Pirahã people perform complex mathematics and physics and even perform tasks such as dialing someone up on a phone? Said tasks require a comprehension of a finite numeral system. One option could be to use loanwords from Portuguese to express numbers greater than two, similarly to how Korean uses the Chinese number system for numbers greater than 99, but a study has shown that even that would be perplexing to most Pirahã speakers.
*Tuh-GAW-lug is a more accurate pronunciation of Tagalog.
Ta-GAH-log
/tɐˈɡaːloɡ/
IPA
Learn it.
@@tamaboyle I know what the IPA is. I was writing this comment on the phone however, so I didn't have the liberty to use it.
@@tamaboyle lemme know when everybody ever has a ready-to-use IPA keyboard
@@Geegs /aɪ/ /hav/ /wʊn/
I grew up learning what we now call a Billion was actually called a Milliard, So the scale of money that Billionaires really impressed me. Then sometime in 2010 I learned that the short scale was a thing and apparently it's been in use universally in English speaking finance since the 70s.
2:54 Nice!
I want to thank you Artifexian. These videos have been helping me construct the language for my novel, and for helping construct worlds for my Starfinder games.
13:00 = RIP headphone users XD
x x
\
i saw that papua new guinea image on image search and never knew what it meant until now
Here's an idea: base infinity
Every single number has its own, seemingly random, name.
Even fractions needs their own names.
I have a base-hundred base that has two parts: twenties and units (0-19)
11037 will be written as
1 10 20·17
0^0 is usually taken to be one, for example, when expanding out generating functions. So nah, you can represent 1
Another reason to say 0^0=1 is the following. Note that x^y is the number of strings of length y written in an alphabet of x characters. For example 2^2=4 is the number of binary strings of length 2: "00", "01", "10" and "11". And the number of strings you can write of length 0 using an alphabet of 0 zero character is exactly one: "", the empty string. So it makes sense in that regard to say 0^0=1.
More formally: the number of functions from a set of y elements to a set of x elements is x^y for all cases where x and y aren't both equal to 0. So consider this set of functions where both x and y are 0. Such functions are formally defined as relations R such that for every a in the domain of R, there is exactly one b in the codomain such that aRb, i.e. every input has exactly one output. For that reason we also write R(a)=b. And a relation R between two sets A and B is formalized as a subset of the Cartesian product A×B. In our case, where we're trying to find a candidate for 0^0, we take both A and B to have 0 elements, aka A = { } and B = { }. Then the Cartesian product A×B is the set of all pairs (a, b) such that a is in A and b is in B. There are no such pairs, so the Cartesian product is also empty: A×B = { }. Then the only subset of the Cartesian product is { } itself, and this is a function: there are no elements in its domain A, so it's trivially true that every input has an output. (All zero of them do.) So there's exactly one function from the empty set to itself. We can then use this to argue that it may be convenient to say 0^0=1.
10 is folly, 12 is jolly, purely on the basis that 9x9 in base 12 is 69, making it square.
Also, what makes odd bases peculiar is that even/odds alternate depending on the amount of digits in a number.
So 7 is 7 in base nine, but 17 is actually 16, making it even. However, 27 is 25, making it odd again. It goes on. 107 (9x9+7) is even. This provides a situation where if there are an odd number of odds, its odd, but if it's an even number, it's even. We have an equivalent in base 10 where if a negative is taken to a power, it alternates between even an odd.
Hell, imaginaries make it even weirder, where it rotates between 4 different number types depending on the power. Positive Imaginary, Negative Real, Negative Imaginary, and Positive real.
Misali saying hello with "toki!" is immensely adorable of him
I was really scared there wouldn't be an outro after that finale!
10:07 I count my fingers from the little end. Weirdo?
In one of my (admittedly not well fleshed out) conlangs, I use base 10 for integers but balanced base 12 for fractions. In addition, the writing system is almost, but not quite, positional, sort of a compromise between positional notation and the Chinese system of dedicated order-of-magnitude symbols. And finally, negative quantities are written upside down, which means that this system has a concept of negative numbers *without* a zero.
"Imagine if like German did this"
Well you're in luck cause Icelandic does
"One man" = "einn maður"
"One woman" = "ein kona"
"One child" = "eitt barn"
Note the examples are just the standard masculine, feminine, and neuter, this goes for all nouns and other words in other groups but not all from said groups
That's more or less "just" grammatical gender and different forms of numerals. German does it as well, although masculine and neuter are mostly identical (ein Mann, eine Frau, ein Kind).
What they're talking about is counting different noun classes with entirely different systems.
Like
🙍 1 man, 🙍🙍 2 men, 🙍🙍🙍 3 men, ... 9 men, 10 men, 11 men (decimal)
🙎1 woman, 🙎🙎 10 women, 🙎🙎🙎 11 women, ... 1001 women, 1010 women, 1011 women (binary)
🚗 1 car, 🚗🚗 2 cars, 🚗🚗🚗 3 cars, ... 9 cars, A cars, B cars (hexadecimal)
So "10 X" depends entirely on what you're talking about - it's (in decimal) 10 masculine things, 2 feminine things, or 16 neuter things.
They're not differnt bases, just differnet numbers which is something german already does
Actually, you DID do the tones in Pirahã. The main problem is that you also added a glottal stop between the vowels. Pirahã has contrasive glottal stops, which are written with an .
Also, I don't know, but I suspect most of the vowels you said could all be considered long vowels, which would mean that you actually said "hóóxi", and "hooxíí"
12:50 Correction, my math teacher told us that 0 power 0 is defined as 1. It is the limit of x power x when x tends to 0 that is undefined.
Your maths teacher is wrong
I am so stoked about getting so many videos in my feed from all my favorite linguistics/conlang UA-camrs! A little comment on the point about Danish numbers: The underlying logic behind 70 (halvfjersindstyve) isn't exactly (3.5 · 20). Well, sorta: halvfjersindstyve means *something* along the lines of "halfway-until-four twenty" in the sense that there's half a twenty until you've got four twenties. So I'd express it as ((4 - 0.5) · 20).
In my number system, we call it by how likely you are to encounter this number of cockroaches at once. One and Million are the same.
Ten in base 3/2 is 2101. For rational bases > 1 you can always find not only a terminating expansion, but a "whole number" expansion for integers if the number of symbols you have is the numerator of the base.
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To do this in base b=p/q, you can imagine buckets in each position, for any integer you want, put that many things in the b^0 bucket, if this number is smaller than p, you're done, otherwise, take out as many groups of p things from the bucket as you can, and put that many groups of q into the b^1 bucket. Then you repeat with the next bucket and so on until all the buckets have less than p things.
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For example with 10 base 3/2, we start with all 10 in the first bucket, so 10*(3/2)^0. We take 3 groups of 3 out of 10, and put 3 groups of 2 in the next bucket, so 6*(3/2)^1 + 1*(3/2)^0. 2 groups of 3 out of 6, and 2 groups of 2 into the next bucket, so 4*(3/2)^2 + 0*(3/2)^1 + 1*(3/2)^0. Once more and we get the final expansion 2*(3/2)^3 + 1*(3/2)^2 + 0*(3/2)^1 + 1*(3/2)^0!
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This works for all integers in any rational base >1 because everytime we move to the next bucket we have less things
Base 3/2 doesn’t have the digit 2. The largest digit in any rational (non-integer) base b is floor(b).
@@arnouth5260 but if you allow for digits as large as the numerator, then integers still look like integers. That seems like a much better system to me
@@jpamado96 but that’s simply not how fractional bases work. The largest digit in any base b is (b-1), since fractional bases act just like integer bases this stays the same, the only difference is that we then round up to the nearest integer, giving ceil(b-1).
Also, then you’d always have to specify that people should use the simples form of the fraction. By your logic base 3/2 would have 3 digits, but base 6/4 would have 6.
@@arnouth5260 fractional bases, or any bases, are just constructions, and we can impose any rules we want in them and see what results from that.
I hadn't considered non simplified fraction, so before now i would have said they have to be simplest form, but after thinking on it a bit, you could have base(6/4) and base(3/2) be distinct bases with 6 and 3 digits respectively as you said. Using the method i described in my original comment 10 could be 4*(6/4)^1 + 4*(6/4)^0, or 2*(3/2)^3 + 1*(3/2)^2 + 0*(3/2)^1 + 1*(3/2)^0. Neat!
يلي جاي من طرف الدحيح يحط لايك😂
😂😂😂😂😂😂
✌
مافيش ترجمة عربي😂
Google Translate has failed me
@@OrangeC7 its guy talk about this Channel and we come to it to see it
0^0 is often defined as 1 rather than undefined, because defining it as 1 has many practical uses in various mathematical fields. Most calculators will actually return 1 for this calculation because of that. But this also means that a base 0 system would be equal to unary. Here's the wikipedia article on 0^0 en.wikipedia.org/wiki/Zero_to_the_power_of_zero
it still wouldn't be equivalent to unary, however, because 0^x is always zero (which is why 0^0 is equal to "undefined, but if it is anything it's one" and not just 1)
oh true, I messed up my maths and thought for a moment it would be i^b (index ^ base or radix), but positional systems use b^i, so yeah you're sort of right, however if 0^0 is accepted to be 1, then only the 0th position would have any value in base 0, while all other positions would only have a value of 0, which would make it equal to having a unique symbol for each number. In other words, if 0^0 = 1, then d*b^i would have a value for i = 0 would be equal to d (the digit), but all other positions would always have a value of 0. But ofc this all comes down to how you choose to define 0^0
and tbh, letting 0^0 = 1 would result in the cool property of one symbol for each number be equivalent to base 0, maybe that's just me though heheh
Love it
My conlang uses base-32 because the human hand has 5 fingers and 2^6=32.
The last one digit number (31) is ponuced as ʞôn and 32 is ʞá ʞà.
Every number starts with "ʞ", the last two binary bits describe the tone, the 2nd and 3rd ones describe the vowel and the first bit adds an -n ending if it's 1
huh... I am just realizing that we do count money and time mostly in Spanish lol
also, you read Tagalog as ta-ga-log, not tag-a-log....unless there's an official pronunciation for non Filipinos, in which case, ignore this comment
“But it uses base 6 which makes it cool by default.” The universal truth
0^0=1
Did you know that?
It's undefined, since the rule that 0^n=0 also applies. n^0=1 doesn't just override it, and it can't have two values at once (that would break _way_ too much stuff), so we just say it's undefined and avoid it altogether.
@@Errenium n^0=1 is accepted for any n ∈ R \ {0}, not just n ∈ R+ (or, since you mention the real component, if you want all numbers, ∀n ∈ C ∧ (R(n) ≠ 0 ∨ I(n) ≠ 0), which I now realise is just n ∈ C \ {0} again)
And the fact that 0^0 has contradictory limits is _exactly_ the reason it's undefined. It is not equal to 1.
@@photonicpizza1466 No, 0^0 is taken to be one all the time, you just lose a^b being continuous. It's important for certain branches of probability theory that you let 0^0=1, otherwise lots of things break.
I love when these make me think. It is great seeing how different ways to count across the world there are
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Thank you UA-cam, very cool
5:29 Oh, YES, this does exist!
When I was in primary school I didn't really know how do billion and so forth work, so I came up with more or less something like this. I asked people if what I guess was right, or if you just get a new number for each ×1000 and nobody could understand what I was taking about.
It turned out that it's plain boring long scale with -illions and -illiards for ×1000. How mundane…
this is really neat!! a few days ago i just updated the numeral system for one of my conlang (the conlang itself still needs lots of work so shhh) with a base 9 system, and came up with something i thought was pretty smart but was touched on pretty early in this video eheh. i didnt know there was so many options available!! my system uses 9 as a base to write numbers, and every digit added right of it as added, and digits left to it are multiplied, so 291 would be 2*9+1 aka 19. if theres more numbers, each operation is done from left to right. anyway, good videos!! gave me ideas for the system of the other cultures in my world. i hadnt considered at all that one could have different numeral systems that are used for different things, i think i'll use that. thank you for your vids!!!
Alternate idea: an inverse base. Mostly you just switch the denominator and numerator, so 5 would be 1/5th and vice versa, and our plural case would be dropped, while a fractional case would be added (for example, imagine if there was a rule in English where instead of saying "half of my inheritance" or "a quarter tank of gas" you had to say "half of my inheritancey" or "a quarter tanky of gas" because you're talking about something that is not whole, sort of a twist on the whole "diminutive case" concept). I mainly enjoy this idea just because of the thought that someone counting "1, 2, 3, 4, 5..." would be imagining a single thing broken into ever smaller pieces rather than the usual mental image of a rapidly growing group of things, and someone doing a countdown would be imagining a thing becoming unbroken rather than the usual mental image of a rapidly dwindling group of things. I also like how this number system does not conventionally allow for the existence of zero, so I'm curious to see how a culture with this number system would perceive it. I imagine they would understand it, but also consider it a Platonic ideal that can't exist in reality, and what looks like zero avocados is actually just a quantity very close to zero.
I'm working on a base 60 system which is divided in a sub base 12. In the proto language there was only a limited amount of number 1, 2, 3, 4, 5, 6, 12, 60 360/720 and maybe other but I'm not really worked on big numbers.
The numbers are formed in this way: from 1 to 6 is pretty straightforward, from 7 to 9 are 6+1 6+2 6+3, 10 is 2*5 and 11 is 12-1, 24 is 2*12 36 is 3*12 and 48 is 4*12. Numbers above 12 are formed generally by adding a number to 12. So 13 is 12+1, 14 is 12+2 etc... five is not used in this numbers so 6-1 or X*12-1 is used. 15, 20, 25, 30-35, 40, 45, 50, 55 are irregulars, 15 is 60/4, 20 is 60/3, 25 is 5*5, 30 is 1/2*60, 31, 32, 33, 34, 35 are 1/2*60+1, 1/2*60+2, 1/2*60+3, 1/2*60+4, 1/2*60+5, 40 is 60/3*2, 45 is 60/4*3, 50 is 5*5*2 and 55 is 60-5. For bigger number I've nothing decided yet.
Exceptionally interesting and well executed, well done both of you. 9/10, -1 for not mentioning imaginary/complex bases.
If you haven't thought of a base to use yet, you're not lazy, you're using nullary!
Say the name of every square in your numerical system:
Hindu-Arabic: 1, 4, 9, 16…
Prime Factorisation: Wun, Tu-Tu, Pree-Pree, Tu-Tu-Tu-Tu, Fo-Fo
I'm slightly disappointed that the factorial system never showed up. It has a lot going for it:
1. All rational numbers can be written without repeating numbers;
10. The common irrational number e can be written with just 1 recurring number;
11. Addition and multiplication function similarly to numerical basis systems;
20. It is really good at expressing really large numbers;
21. In many cases it is easy to verify the prime divisors of a number;
100. It makes many calculations in maths even more beautiful;
101. Its one drawback, the requirement of infinite algorisms to express a number, is easily solved with a mixed basis system.
Another possible division of radixes is register. In her Doctrine of the Labyrinths novels, Sarah Monette creates a world where the ruling class uses base 10, and the working and uneducated classes use base 7.
A balance 3 or 5 while problematic when dealing with division, could make sense as an part of a early counting number system with the "middle finger" = 0 meaning you can count on your hands with it, much like how we got our base ten
I once came up with what I call zug notation for balanced ternary. ז is-1, ו is 0, ג is 1. It looks more sensical in handwriting. And of course, it's right to left.
I feel like base 4 is the best idea because 2 using any operation which stems from addition, like multiplication and exponents, to itself is 4. So 2+2, 2x2, 2^2, 2 to the power of itself twice, all 4
i like how he used 420 for almost every language possible
The "divide by zero" section just made me think of a sad robot's final words being "divide.. by... z e r o ......."
Really cool video! I liked the overview of lots of different languages and how they deal with things, and some of the stranger bases like bijective unary (I'm now going to call it that when I do tally marks).
5:26 WHAAAAT?! I'm totally doing that for my conlang now! I never knew that was a thing! That's incredible!