INVENTING A NUMBER SYSTEM 2 ft. Conlang Critic
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- Опубликовано: 2 окт 2024
- All of the number nerd-ery.
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Thanks for watching everyone. It means a lot. :)
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
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?
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
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
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
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
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!
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
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
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.
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.
1:28 "...only has words for 1, 2, 5 and 20"
**happy toki pona noise**
0, 1, 2, a lot...
And 100!
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.
"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?
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...
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.
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
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.
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
baker's dozenal amirite
the base to drive americans away from you
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
That end was great.
I'll use nullary as a base in my conlang!
Me too! I love its simple explanation XD
I actually worked Balanced Septadecimal into my D&D setting because I hate my players. And my Gnolls now use a semi-bijective ternary base with the numerals 0,1,2,and 3, with 3 literally meaning "many" and stands in for an estimation. For example, the number 123 would mean "nine plus six plus a few more".
@@noahegler9131 That's so cool! :O :D
I use 1/4^3 as base
Caveat observator: sudden volume jump around the thirteen-minute mark.
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.
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.
The memes in this one
thank you for these information
im From EGYPT
Hi From EGYPT! I'm dad.
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
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.
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
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.
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...
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!
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.
this video: inventing a number system
also this video: nuclear explosion on repeat.
"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.
The editing in this video is fantastic. You're doing great Edgar and I'm really looking forward to your next video.
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
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.
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.
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.
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
I was really scared there wouldn't be an outro after that finale!
5:23 There's one zero missing for jo. A jo is the same as a trillion. Because it's 10⁴×10⁴×10⁴
Math and linguistics. Yes!
: Electric Boogaloo
5:10 one billion. no, one billion.
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.
5:26 WHAAAAT?! I'm totally doing that for my conlang now! I never knew that was a thing! That's incredible!
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.
I think this is the silliest video you've ever made and I love it
Here's an idea: base infinity
Every single number has its own, seemingly random, name.
Even fractions needs their own names.
3:00 nice
*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'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.
Thanks for these videos they're really fun and inspiring!
My conlang uses seximal with only 5 digits (0 technically exists, but is not used as a digit), it's semi positional, if there would be a zero, you write how big the gap is as a small number to the right above. In canon this came to be, because somebody wanted to save space writing big rounded numbers and placed the vertical line that indicated 0 small to the right above, this tally mark later got simplified into numbers. This change also reflected in language where you say how many places are left every few places (0s are skipped).
13:10 yep. this is how i feel after this video.
I just invented this centered place value numbering system. Powers of 10 start out at 0 in the middle and spread out either side in both directions. So a 3 digit number would go 1 0 1 in powers of 10, a 5 digiter 2 1 0 1 2, 3 2 1 0 1 2 3, and so on. For example 293 would be 2*10 + 9*1 + 3*10 = 59 in our present system. So would 392 of course, but although the same quantity could be represented by at least two numbers, I don't think two different quantities can be represented by the same number. Addition? 293 + 7. Place the 7 under the 9, get 6 and carry the 1 to either the 2 on the left or the 3 on the right. Answer: 363 or 264. Must be other cool things you can do.
"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
It just annoys me how nobody pronounces Tagalog correctly. It's taGAlog, not TAgalog. It's vowels are exactly like the IPA.
Love it
4:55 I was thinking "hm thats an interesting way of doing things" until he mentioned milliard and billiard and I realized that's literally how Swedish works
2???
My, that's nice.
The algorithm went to an ad right when you guys went to that div-by-zero NaN error.... Zeroth LOL!
2:54 Nice!
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
13:00 = RIP headphone users XD
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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
Didn't expect this to come out so soon...
About danish, halvtreds (fifty) means half of treds (sixty), which makes no sense, but I assume that it means something like "two and the third one is a half".
A number like 74th would be "fireoghalvfjerdsindstyvende", meaning "four and a half times three twentieth"
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.
They should make a language using the Danish counting system in base (pi + e*i) :>
10:07 I count my fingers from the little end. Weirdo?
i like how he used 420 for almost every language possible
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.
The best number system not mentioned: each of the first (or most convenient) 16 consonants in the alphabet is an increasing power of two; in English, that'd make B=1, C=2, D=4, F=8, G=16, etc. Then, each among eight vowels and diphtongs is equal to a power of (2 to the 16th power) - that is, a=2^0, no change, while A=2^16, e=2^32, E=2^48, etc. Then, a number is expressed by speaking the binary consonants, surrounding a vowel of the appropriate magnitude. 13 is 8+4+1, so that's FaDaB. 147 is 128+16+2+1, or LaGaCaB (assuming K is skipped, sounding just like C). This is notably different than plain old binary: it is hyper-compact, easy to say large numbers in a few memorable syllables; and, more importantly, addition and multiplication are vastly improved. When you see a consonant in two numbers that you are adding, then you swap that pair out for a single instance of the next consonant -> (DaB + FaD) has a D in each, and D=4, so 4+4=8, which is F... To add numbers together, you just play a pair-matching game, which is MUCH easier to learn, and faster, less error prone. Multiplying is even better: (Fa * Ga) is 8 multiplied by 16, giving 128, or La. Fa is only three 'hops' away from the starting position...that is, Ba -> Ca -> Da -> Fa is three arrows. Because of the way exponents work, that means you only need to take three 'hops' from Ga -> Ha -> Ja -> La to get the answer! Addition is just pair-matching, and multiplication is just adding! Exponents are just multiplication, by this same process. The alphabet is a SLIDE RULE that you can teach in a month to 5 year olds.
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
You should now do a measuring system... for volume, weight and length...
Misali saying hello with "toki!" is immensely adorable of him
In PT-BR we use short scale, even though PT-PT uses long scale.
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.
Pedestrian:
Normal:
Fiućik sitedźane
Simplified:
*Ę* fiok sizene
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3 comments"
Thank you RUclips, very cool
I'm Reminded by this of Terry Pratchet and his trolls counting in One, Tun, Tree, Many, Lots, terra - which in his own comments in his books (he made lots of comments on background stuff) he said that trolls used this in their own counting system based on multiples of those numbers. He said "some people may realize you can get to lots, and one lots and one, lots and two, etc, but this isn't the only way. For example tun tree and tun could = 9, etc. With the biggest troll number being tuntun terra lots - or 4 x 5 x 10 = 200
..... Just wanted to point this out!
If you haven't thought of a base to use yet, you're not lazy, you're using nullary!
The Danish works more backward so 70 is the slightly more confusing “four and half twenties” as I suppose the last one is considered half as big.
You can see this in writing as 50 is written like “half 60” and 70 like “half 80”.
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.
One of my conlangs uses a bijective base-20 numeral system.
Another one uses a base 36 system with a sub-base of 6.
One of my older ones used base 200.
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.
70 in danish actutally doesn't mean three and a half times twenty, it means one half from being four times twenty or (4-1/2)*20.
Ah yes, nullary, the number system where writing anything takes infinite space.
Some nightmare blackhole stuff at the end
My conlang has a vanilla base 10 but also has remains of an older base 8 system. 9 is eight plus one, 16 is two eights, 24 is three eights, 320 is four-eights tens and so on
That's what I'm doing with Xalnish, which uses both a base 6 and a base 10 system
That's okay, I didn't need to sleep tonight anyway...
I miss the quater-imaginary number system. Also, one should be able to extend the base to more than just complex numbers, by using a quaternion base (or a octonion one, or sedenion, or trigintaduonion and so on).
About the million/billion thiing: European Portuguese uses the long scale and Brazilian Portuguese uses the short one, so you could even have dialects influencing stuff like that.
Jan sounds like Tristan from StepBack History.
Jan Misali just loves the Peggle 2 meme. it's great