sidenote, the number system isn't the best for dyslexics because of it having a lot of very similar symbols. I might have a go at creating a conlang that would be as easy as possible to read
as a person with dsycalulia i found the KI numerals much easier as it simplifies what is required to remember. basically now i only really have to think 0-5 the rest is just about knowing your multiplications for 2,'s and 5s
One thing I like about this notation: is easier to "write" numbers on stones, or any other hard material. In fantasy settings, that is what I spec to be in "dwarven math"
As someone who has done engraving and dabbled in runes, and is a massive Dwarf nerd, a system like this or the 13th century Cisterian monk system would be amazing for it.
You could also count using nothing but matchsticks (or any sticks for that matter), no writing or engraving required at all and no mechanisms like an abacus.
@@danielsteel5251 But not all pattern recognition is mathematics. If I recognize that evey time a stoplight turns red, cars stop, and every time it turns green, cars go, I've recognized a pattern but have done no math.
The way you wrote eight seems to indicate that numbers are read in the opposite direction to our usual way. You seem to have put the 1s place on the left, with the 8s place on the right, and I find that very interesting and cool. Also, all your digits have 2 axes of symmetry, so extra cool.
Inigo Diaz yes, thank you. i wanted it to be a right to left number system because my friend is a lefty and used to write backwards, as for the symmetry, it was purely coincidental at the beginning of making it but i decided to keep it that way.
Ha, he says "Maths without maths" when sound is just the wave functions of air to create frequencies. Sound is obviously math. Seriously people need to chill out.
I'm just imagining the Katovik Iñupiaq inventors are like "woah these are really famous now" Also I hope people will learn about the featural abugidas of the Arctic peoples
@@Alice-gr1kb oops i replied to the wrong comment..... how did that happen o.O but yeah the KI numerals are awesome! it inspired me to make a featural number system myself
Huh, I'm already subbed to you, but that made me respect you more than before, answering to comments and owning up to mistakes made (and recognizing when the fault isn't yours too), it's really nice! I'm a fan of world building (I've been building worlds since the age of 7, but it kinda slowed down because no one but me recognized it was a concrete thing) so you can be sure I'll watch more of your videos!
No joke, I’m watching this in a parking lot and i looked up into my mirror. I saw a license plate that starts with 7777 and was like “WOAH! You can get these crazy numbers on license plates?” Also I’m super glad he explained larger numbers in greater detail
I'm coming back years later to say thank you. I've been working to revitalize my language, another indigenous one (Abenaki), for years. We also have a penta-vigesimal system in our language and using the Kaktovik numerals has made teaching it so much easier: Our first five break down into: abstract, animate, inanimate: Pazekw, pazgo, pazgwen (One, s/he is one, it is one); \ Nis, nisoak, nisnol (Two, they are two, those are two); \/ Nas, nloak, nhenol; \/\ Iaw, iawak, iawnol; \/\/ Nôlan, nonnoak, nonnenol; - But then we go into + -ôz(ek): Ngwedôz (a single + 5) -> 6; -\ tôbawôz (a double + 5) -> 7; -\/ Nsôzek -> (three + 5) -> 8; -\/\ Noliwi -> one short of the next ; -\/\/ Mdala -> ten; > Continue to -ônkaw: Ngwedônkaw; >\ (11) Nisônkaw; >\/ (12) Nsônkaw; >\/\ (13) Iawônkaw; >\/\/ (14) Nônônkaw; z (15) Then back to: + -ôzek + -ônkaw (literally kassônkaw "So many -ônkaws"): ngwedôz kasônkaw; z\ (a single + 5 + so many teens) (16) Tôbawôz kasônkaw; z\/ (a double + 5 + so many teens) (17) nsôzek kasônkaw; z\/\ (3 + 5 + so many teens) (18) noliwi kasônkaw; z\/\/ (falling short of the next + so many teens) Nisinska: |o (two pair of hands; two units of 10) (20) Then they hold steady until hundred (Ngwedatgua), thousand (ngwedômkwaki), million (kchinguedômkwaki).
I love this numbering system, and kind of wish I had thought of it when I was doing my worldbuilding. I did something sort of similar: I gave every prime number in the base digits a unique symbol, and every other digit is built out of those. Not quite featural, nor as clean and simple as these, but I'm still fairly proud of it. (I did stay boring base-10, but I'm okay with being boring)
glad you cleared stuff up, the previous vid was rather short and left me with a lot of questions so thanks for making a follow vid and for addressingf the comments that some people.
I should've sent in my "baseless numeral system" or more accurately, base 4 additionative numeral system. That and my infinite numeral system (specifically designed for infinites and the various kinds).
OH YEAH I FORGOT YOU I CAN WRITE MY BASE 4 ONE WITH ASCII 1 is /, 2 is - and 3 is | and every other number is a combination of those added together. So after 3 it becomes however you want to write it. / - | , = + || И Н ||| ++ +/+ (or -И-) |||| |И| ИИ +++ (or |||||) HH H/H |||||| # ... For note И is |/| and H is |-|
@@water594 So 4 could be = or |/ or -// or ////? Interesting, that means |-/ is 6 and ||-// is 11. So if there's no base, is there a standard order to the placement? Does the bigger number go first, like |-/or the smaller number first, like /-|? Or is it free moving, like /-/ or -|-? And what are the rules on stacking in the same cell? Does = equal 4 or does it have to be --? Could I write 5 like + or T or * (okay, that asterisk should look like >|
@@josephschubert6561 These are all problems I origionally encounteted when making it and to be fair I made it when I was sixteen and haven't worked on it for like two years. My biggest problem I never adressed was "crossing rules". Why are | and - allowed to be crosssed to make +? It adds another layer of complication. Perhaps I should ban crossing and five should be |- or T. Although it wouldn't be * or >|< because there is no backslash \ number. I guess you could add one and ir would increase the number of possible combinations and thats a valid choice. You interpreted completely correctly for everything else though. I agree larger numbers become unweildy but stacking rules are quite simple, you just put it together however fits best. I never made a culture to go with this but I imagined it would be almost like an artform. A mathematician would have the task of representing a number in the most elegant way possible. So instead of 20 being ///////////////////// which is unelegant TTTT is way more elegant and understandable and if I wasn't constrained to this format I might stack the Ts in ways that make more sense. Maybe extra rules you could add would be face rules meaing a /-| can only contact a fact of another one once so =| is kinda an illegal number. That'd be another choice.
Divisibilty Rules. Traditional results of number theory. A counterintuitive surprise is that they actually depend on the numeral system used. Some numbers are easier to divide by others depending on which base (base-10/base-2, etc) and symbols to express them you use. For example, 1/3=0.33333... af infinitum only because 10/3 is not an integer. 10000/100=100 is easy because you only had to coun the zeroes, there are other symbolic tricks you can use depending on the rules you use to represent the quantities
2:15 this is nitpicky for sure, but of you wanted to use a prime base, such as 11, you couldn't do something like this, specifically it works for any number base with a 'small' factor (like 3 or 4 as shown).
Generally the more factors a base has, the better it is. Of course, bases shouldn't be too large either. Which is why Base 12 should've been adopted by humankind centuries ago, but we missed that part of the Science tech tree by now I'm afraid lol
I don't think it'd look nice or be intuitive, but typically base systems in large primes aren't used because they're prime (they have no terminating fractional numbers).
0:57 i think the two should be either two horizontal lines, or the six and four should have an extra vertical line and lose their horizontal lines. Its annoying me that for two they did, you have zero and an extra vertical, but six and four you keep the horizontal. Its like 1X or 20, both are fine but you have to stick with one. Also eight, the reverse order of the digit kinda threw me off. But its cool. (the high digit is on the right not left).
You still can recognize them from each other and also 1 = ---- 2 = | 3 = (--|--) = 1 + 2 4 = (=|=) = 1 + 1 + 2 5 = (-|-|-) = 1 + 2 + 2 Ect it's just repeating after If you change 2 to || then their system wouldn't make that much sense
3:50 not quite - using a higher base the record is shorter, easier to remember. Looking at different civilizations depending on the size of the base of the system, they achieved different mathematical successes - the Mayas with the 31th system were good mathematicians, Indians with the binary system - bad. It is influenced by the fact that mathematical operations for humans are simpler on a higher bases. This is due to the fact that we process more data with one digit
I would argue that it isn't geometry. We're not measuring the sizes, angles, or anything really. We're counting specific objects. So to say this is geometry would be to say that counting sheep and pigs is geometry because we have to recognize the shape of the sheep and the pigs.
@@joalampela8612 False. Trigonometry measures sizes and angles of triangles, contradicting my argument "We're not measuring the sizes, angles or anything really".
I once made a hangeul inspired featural numeral system. It had both easy recognition of numbers, but you also grouped every 100 into a block, so it was possible to get up to 999 with just one character. ㅇ = 0, ㅣ= 1, ㅡ = 2, ㄱ = 6, and ㄴ = 8, 이 = 10, 잉 = 100, 댱 = 590, etc (my symbols weren't the same as in hangeul, but I used it to demonstrate the logic).
Math with this is not geometry, but grouping. You group things in multiplication and it matters little whether your number-symbols have an obvious featural system or whether it is arbitrary symbols and you have to learn a multiplication table to know how many times something goes into something else. It's just more blindingly obvious in a featural system. I tried long-division in the base-20 featural system and tried 69 divided by 8. I went into decimals, of course, but it worked out to 8.625 or more correctly in the base-20 system 8.(12)(10). You still need to know a multiplication table, adjusting for base 20, but subtracting at each step to get a remainder was much easier.
@@Otome_chan311 1. It's not necessarily harder, your just used to base 10. 2. See 1:25. It translates perfectly fine to base 10 as it has a sub-base of five. IMO, it looks better in base 10 as you will only ever have one line on top.
I've used Kaktovic vigesimals for years, I know the symbols, but the native names are too challenging for me, so I use them with the Yan-Tan--Tethera, which is also a Base 20 system.
I thought about it and found very simple methods to do any substraction (even with x - y where x < y) and multiplication. And if you know how to divide with an abacus, it works the same way. So yes, it makes maths REALLY easier.
Well, there are a lot of cases where Arabic numerals permits superb tricks. Take 3651:3, it's simply 1217. The trick is to recognize that it's "36" concatenated with "21", so you can divide each part individually, then concatenate the result. Let say you've 1818:3, there, you've to remind you that your two concatenated numbers are 18, so 18:3=06. Which yields 0606 or 606. You just keep the same number of digits for the result and pad with zeroes if required.
I think the biggest issue with these numbers and I probably already said it in the previous video is that they have basically zero error tolerance. You can't have them overlap or be too close together, you can't rotate them, you can't write them sloppy, they also take a lot longer to write (since they require far more strokes), they work much worse in bad lighting conditions or when you need to see them at a glance, they are much less resistant to random alterations (like damage or dust), and are much harder to display and parse in small font sizes. So overall I don't think this font is very practical.
Since September 2022, these numerals are officially part of Unicode 15.0! And the Rust programming language version 1.66 (December) has officially added Unicode15 support!
I would really like to see you do a complex example. Your last video inspired me to learn it and practice with it , and I've kind of developed my own ways about doing it from what wasn't covered in the video. I think you should totally get a random number generator and do some multiplication and division on camera.
What do you think of the number system that goes... 0,1,2,3,4,5 -0,-5,-4,-3,-2,-1 where the minus sign means 12-n where -0 = six where -5 = seven where -4 = eight where -3 = nine where -2 = ten where -1 = eleven where 10 = twelve. Obviously this system might require a better numeral system than Arabic. I'd want one that would count up to 3. Similar to the system on the video. I think the system I made up would reveal more patterns in the numbers. Since this system is a prototype it will have different enough symbols for the negative numerals of the modular base and negative numbers of the reals; ie it will be clear unlike how it is written in Arabic numerals. For arabic numerals you could just cross out the numeral to get the opposite. Can we discuss this?
You can. Maths basically does not care about the way numbers are displayed, althought they may make arithmatics easier, especially in everyday live. At the and of the day, calculation are done in the Natural Numbers (most likely by your intuitive interpretation of the Peano-Axioms) and they don't care how one writes them down.
Very interesting thanks for making the video. Reminds me of Asian children being taught with the abacus, they develop "muscle memory" in their hands from moving the beads. They end up being able to do math as instinctively as most people use a pen.
Dear Artifexian, Could you please create a video on conjunctions and causes but most importantly converbs? I really need help in this area for my conlang.
I have found this very interesting and tried exploring it a bit. The biggest issue for me is while the trick you give for long division is great it can't always be used to get the correct result and I personally have not found a way to determine when you can or cannot use it. Even when a number divides another it isn't guaranteed to work. Try doing 35 / 7 in KI using the trick as an example. Is there a way to know if it will work without already knowing the result? Because if that is not the case it isn't really that useful of a trick.
The guy never explained how borrowing works, but once you know how to borrow you can indeed find patterns just like the examples he provided. I've done a few explanations of how borrowing works and we'll go over 35/7 really quick so you can see. 35 looks like 1 vertical mark followed by 3 horizontal marks and 0 vertical marks, and we're dividing that by a number that looks like 1 horizontal mark and 2 vertical marks. At first I thought I could just rotate the number and everything works out, but the patterns don't quite match out. Instead, I needed to borrow 4 horizonal lines from the left most vertical line, giving me a number with 7 horizontal lines. Then I needed to borrow two of those horizonal lines to make 10 vertical lines for a final number that looks like 5 horizontal lines and 10 vertical lines. THAT matches up 5 times, for our final answer 1 horizontal line. But dang that looks messy when I write it out on paper.
DoomRater in fairness the only way to do 35/7 with the Roman system is to memorize the result or that 5*7 is 35. There is no aspect of our number system that could make solving that problem any easier.
@@ItsAllEnzynes Think of it this way. Base 10 doesn't handle divisions by 7 with terminating fractionals. The smallest base that can is Base 7 (next is 14). This is an interesting phenomenon that I believe cryptographic systems actually rely on to stay secure, though I don't understand the mathematics behind to fully grasp.
@@DoomRater You could in theory do something very similar our base 10. You are basically just breaking division down into multiple subtractions, which it effectively is, you break some of the rules of what is "allowed" in certain places to do so. We do this a lot when we first learn about these ideas. You could say you know that 7 is 3 less than 10. So you could exchange every digit in the tens place for a 1 in the quotient and a +3 to the ones place. 35/7 = 1+ 28/7 = 2+1(11)/7 = 3 + 14/7 = 4+ 7/7 = 5. Here I break a rule by putting for than 9 in the ones place temporary, you make use of this type of idea by writing some of the digits "incorrectly" for lack of better word. In your example you make use of the fact you know multiplication and skip straight there, If I did the same my process would be 35/7 = 3 + 14/7 = 4 + 7/7 = 5 making use of 3x3=9. We can do this because we know the transfer between the values, KI or base 10. You write 35 as 5 horizontal lines (5x5x1) + 10 vertical lines (10x1x1) = 35. (The notation I use here, and later, is ( [number of lines] x [value of that type of line] x [value of that place in the number] ) But this number is not correctly written this way, you just fit 35 into a place that should never have more than 19 in it. I determined when you can use the trick he shows. I (wrongly) thought I could take my 7, 1 horizontal line and 2 vertical lines, and fit it into the 35, 1 vertical then 3 horizontal. Here I think I could fit it in once but rotated which I would denote by placing a singular horizontal line in the 1's place. It then looks like I have a remainder of 5 which is smaller than my 7 so I stop. So just trying to follow the video without doing this in the context of math. I would've guess 35/7 = 5 + 5/7 using this system. The reason this doesn't work is because with vertical lines we can go up to 4 in a single place, but horizontal we can only ever go up to 3. Thus we cannot do this mixing of vertical and horizontal lines while rotated. Making the system base 25 or base 16 would allow me to do this because the ration of 1 vertical line to a horizontal line in a previous place is the same as the ratio from a horizontal line to a vertical line in the same place. Does that make sense? I know it's correct, just not sure how well I explained it. Maybe doing our example problem, 35/7, in these new bases would help. In base 25, so we can have up to 4 horizontal lines and 4 vertical lines in each place, we would write 35 as 1 vertical line (1x1x25 no longer 20 cause we changed base) + 2 horizontal lines (2x5x1). We would write 7 the same and get a perfect fit as we had hoped for. Just rotate and it fits perfectly, we mark our 1 horizontal (rotated) mark and see the value is 5. Similarly in base 16, so only up to 3 horizontal (keep in mind each of these are 4 now, not 5) and 3 vertical lines in each place, we would write 35 as 2 vertical lines (2x1x16) + 3 vertical lines(3x1x1), now 7 would be written as 1 horizontal line (1x4x1) and 3 vertical lines (3x1x1). Here we cannot fit any together natively. But we could do the ole trick you used and take 1 from the 16's place and write it as 4 horizontal lines in the 1's place. So now we can mix the horizontal and vertical values correctly. Our 35 is now written as 1 vertical (1x1x16) + 4 horizontal (4x4x1) and 3 vertical lines (3x1x1). Here again we write the number "incorrectly" as we fit 19 into a place that should only ever store 15. We can now fit in our 7's, once using 1 vertical and 3 of the 4 horizontals to give us a horizontal in the ones place, cause we had to rotate so we rotate the value in the quotient and again as we are left with exactly out value remaining so 1 vertical in the ones place. We are left with 1 horizontal (1x4x1) plus one vertical (1x1x1) = 5. The biggest flaw with the trick in the current KI system is a direct result the horizontal and vertical values being on different footings, one counts up to 4 in a slot the other up to 3. So the ratio of a rotated numbers are different if they have horizontal and vertical lines, I will call these numbers with a "mixed representation". If at any point you have a divisor that has a mixed representation you may no longer use the rotating trick unless you do some manipulation to make them all one type of line (which lets be real is most likely going to be vertical, you could only make them all horizontal if its a multiple of 5). Everything else works just no rotating. If however, you build the base to be a perfect square (i.e. 4^2=16 or 5^2=25) rotating is allowed with mixed representations and it fixes a lot of issues I had with the KI numbers. KI is really closer to a base 5 system but every 5th 5 value is in base 4 which causes the mess you went through to solve 35/7. You still have to do some borrowing from higher digits to write the number "incorrectly" like I showed, but you can now rotate all numbers even if they have mixed representation. I know this was a long rant/explanation but I felt compelled to share what I figured out with everyone that was willing to learn. IKI (Improved KI) uses base 25 as displayed and has all the features of KI but with an extra bonus.
@@chammy2812 Writing numbers incorrectly, or improper numbers as I referred to them in other comments, is exactly the idea their numeral system seems to lend itself well to. After all, it makes the pattern matching easier and it does indeed seem to be possible to do in our number system, if it's broken down into other bases. And borrowing is still necessary no matter the base anyway, so might as well take advantage of the intuitive meaning of marks.
That first video you made was amazing, and inspiring. I find it incredible that the internet has given us the facility to increase our personal knowledge and education more than anything else in human technology, yet rather than use this resource for learning new viewpoints and broadening our general outlooks, one of the most popular internet pass times is to start arguments with strangers about how right our existing opinions are. Anyhow if you’ll excuse the repetition: that first video you made was excellent. Please keep making good videos and thank you.
i HAVEN'T EVEN WATCHED THE WHOLE VIDEO... in fact, I am at timestamp 0:02, But I mashed that LIKE button as soon as I saw your new video. I need more linguistic and world-building. Thank you for feeding my addiction!
You earned my subscription for your honesty. I think your first video may have been a bit misleading but then again people were nitpicking for accusations if you ask me. It's not like you said "hey let's start a revolution and only use this system because it's flawless" you were just saying "hey people this system is amazing and deserves more attention". I honestly think this system is better than the one we have atm so i would without a doubt teach it to my kids. Why? Because it's more intuitive. This is really, and I mean really important for kids. I have a little sister that just entered elementary school and has problems with the simplest of maths just because she is an artistic soul. She became less confident in herself and automatically said to herself "i am not a person for math" when that's completely bogus since she is amazing at geometry. Why? Because geometry is intuitive for us and she can express her sense of logic thinking better in that environment. I will try to teach her this system in order for her to get back on track in the world of mathematics.
People talking about being early so I thought I'd leave my mark. I loved the video, I've been thinking about base systems nonstop ever since, which, math is not actually what I like. Just add language and culture to a topic and I'm hooked I guess!
From the perspective of mathematicians, "mathematics" can refer to pretty any kind of logical thinking that isn't strictly dependent on observed reality, but other people often have narrower ideas about what "mathematics" is, and also often have a different perspective because they're often more familiar with "mathematics" as methods for calculating things using rules learned by rote, rather than a system of connecting ideas using mostly deductive proofs.
Sad to see Base 6 (or 36) didn't get featured; this seems like a pretty great way to show it. Thanks for showing it to us, and featuring the responses you got!
It would have to be base 6 with a sub-base of 3, unless you want to add more strokes to the top and bottom. I think more than 4 strokes on the bottom, and more than 3 on top, would quickly become illegible. Base 36 with a sub-base of 6 would require 4 top strokes and 5 bottom strokes, which would crowd things pretty quickly.
5:02 Regarding cherry picking numbers and your 80% awkward guess. I did the math and when multiplying two 2-digit numbers, (or when a/b=c where b,c are 2 digits), the visual tricks only work 3.5% of the time or 97.5% awkward. In decimal, if we define awkward as never having to add two single digit numbers to get a 2 digit number, it's clean 8.7% of the time or 91.3% awkward. Sure, you could argue that my definition of "decimal awkward" is bad, but I'd say that a 3.5% success rate is barely bigger than 0% and isn't enough to count it as a feature for long division.
I just discovered this numerals yesterday and I'm very curious about using them more frequently in my life but I don't handle them very easy because when the numbers goes bigger I struggle with the base of twenty. Also I want to show them to my teacher like a class work. I don't know if you can make a larger tutorial to start from zero or something like that
I bet mixed radix would be confusing in this base if you literally alternated between base 10 and base 12 for Decadozen because you could decide to use the sideways glyph for 5 in 10 and 4 in 12. You would have something that looks like 55 or 52 but it's actually 64.
It should'nt be to bad, if you are used to it. Most peolpe can "see" amounts up to four, so once the brain automatically divides the number to the subbase and 0ne-digit the numerals, those can instinctively be read.
Picking random number for division without using "math" is still doable. A bit tricky as you have to re-visit how to write your number but doable. Take 28/4 for example.
Years ago I came up with a base 6 number system for my conculture. Zero is just a zero. 1 is an I, 2 is a V, 3 is a V with an I between its "legs," 4 is a +, and 5 is a pentagram. Also things were written backwards to how we do it, so instead of 1 + 5 = 10 (in base 6 normally), it was 0I = (pentagram) (a different symbol for plus) I
This system but block 10 is the way to go...block 20 makes it to a clusterfxck of many additions and multiplications when calculating 4036774 ÷ 6037 for example.
My mom, a math and science teacher, loved it and said she’d like to learn it and mentioned “you can’t teach an old dog new tricks” but she’s going to try.
The visual tricks for addition and subtraction are cool; the long division, however, only works under the assumption that your division works out nicely and every leftmost digit is effectively negated at the end of each geometric step. Changing one digit in one of the examples in the first video illustrates one counterexample to the visual trick for long division: i.imgur.com/xq0pjPU.png It can be shown here that, exclusively using the visual references, one would come up with the same answer of 501 (or "150" in base 20) because the technique doesn't really address the additional digits in the, in this case, 20^2's place. This may be remedied by keeping track of how well each number geometrically lined up during each step, but requires a bit more thought than may be suspected. My main issue is how visually confusing this number system is at a glance. When the cool tricks don't work out, you're essentially left with really claustrophobic symbols that look very similar to each other at a glance and require a lot more counting than our number system, where each number is easily identifiable by shape alone. If we ever were to adopt a number system similar to this, each stroke would probably have to be more distinctive rather than just straight lines (maybe the distinctive features would denote different prime (and 1) quantities, like straight lines for 1, curves for 2, edges for 5, etc.?) just so they're both intuitive when doing arithmetic and identifiable when you're not just crunching numbers. Either way, it's a fun thought, so thanks for sharing.
I learned Mayan numerals back in 1980 while working on film strips for my professor in collage. I could do + - * / like a fiend with 'em when I couldn't do math for shite in our Arabic numerals. Yea, I feel like an idiot.... LOL
Mayan numerals: **Mayans numerals deciding their symbol** All the numerals:So we have a plan to make a pattern Zero:Bread All the numerals:Bu- Zero:BREAD
It's not just that 80% times it's just as awkward as with Arabic numerals and 20% it's easier - some things are easier with Arabic numerals. For example, little things like if the digit sum of a number is divisible by 3, then the number itself is divisible by 3. Only works with 3, but then the examples with division in the previous video seem only to work with _some_ numbers, too. There is no explanation of what to do if the math-less method doesn't work - or how to identify when it doesn't work. But problems manifest themselves clearly when you take simple examples, such as 8/2 or 6/3. With such small numbers you can "cheat" by substituting the 5s with 1s, but how will you know when to do that for larger numbers? And personally I find the base 20 system extremely cumbersome. Now I have to use maths just to write 1000.
I mean it's basically just tally marks with 4 fewer marks on a group of 5. I'm still not convinced that easy math tricks are worth the loss in visual clarity. There is a reason I don't just use tally marks for everything, and part of that is that it get's visually cluttered quickly.
3:55 As a fun fact, I think this would be clearer in Spanish. While "Math" in Spanish is "Matemáticas", the term "Doing math" in Spanish would be translated as "Hacer cuentas" which refers specifically to counting, doing arithmetic and stuff. Though, you would've lost the pun.
I don't know why some folks are picking on the way you worded things or used simple examples to make a point. I understood it PERFECTLY. I am starting my 5 year old in home school this year and THIS is how she's learning math. I HATED math growing up because THIS didn't exist!
Kind of late to the party, BUT wouldn't the system be better if it was base 25? This way you could multiply by 5 just by turning the digits 90°. As the system is now, it would break down as soon as you multiply 4, 9, 14 or 19 because you can't have a W at the top, so you'd have to convert stuff. Personally I'd even go to base 36, because if you use your fingers you can show 0-5 fingers and need a transition at 6 and not 5, so you could count to 35 with two hands. Also 36 has 1, 2, 3, 4, 6, 9, 12 and 18 as divisors. Another improvement: Mirror the digits. This way you can start at the left and write them in one go. As an added bonus you can instantly see if a number is odd or even IF you go to base 36 (or 16), by checking if it starts up or down.
I watched a video on the Numberphile channel a year or three ago on a project the brilliant mathematician, John Conway (he of The Game Of Life fame) and another mathematician collaborated on called "abstract math(s)/numbers". This other mathematician (whose name is lost to me) was the principal creator of this number/math system with Conway acting as an adviser, encouraging him to publish it in book form.
I really like this system! I'll probably show this to my students once I'm confident with it. But how would you do multiplication? Follow-up video to this follow up video?
The insinuated "FU" was not all that clever or appreciated. You did clarify a few points of confusion though and that was greatly appreciated. It was unclear to me if your proposed system is counting in base 4, 5, or 20 and you sort of clarified that. However, in the end, I gave both videos a thumbs down because of the title. I hate how people use titles like this. I know they're generally click-bait or at least exaggeration but when it involves a topic I'm really interested in I'll click hoping the title is honest but then it isn't. The system you proposed is essentially like Korean mixed with Roman numerals or more like Mayan. I fail to see how there is anything unique or useful in this way of writing over others. You could make the counter argument that it makes division "easier" than what most of the western world currently uses( visually-speaking) though that is countered by the fact that the larger bases actually generally make division more difficult, not easier. In my opinion, for an example, the reason why hexadecimal is generally easy to work in despite being a larger base than base 10 is the same reason octal or binary are easy, they're powers of 2 and pretty simple. They're 1 or not 1 plus some multiple/power of 2. Pretty simple. They're less simple in base 4, 8, 16 etc than base 2 but the conversion between them is mathematically easy for computers to handle. Of all the bases of 2^n, binary is the simplest and best (in terms of simplicity (but it takes much more space or digits obvious, that's the trade off)). It doesn't get much simpler than being in base 1 or 2 and using slashes or no slashes. The same arguments you used for KI could be used for base 1 or 2 just slashes. Essentially, the advantage if any of the KI and other similar systems is that it have slashes going two different directions orthogonal to one another. But, this can lead to confusion is reading/writing. These sorts of topics are really interesting so I'd love to thank you for sharing and give your videos both thumbs up despite disagreeing with some of your points but still gave them thumbs down for the title and the (FU lol). Have a wonderful day.
I suppose Sumerian numerals and the Chinese "counting rod" numerals are also featural. Basically, the first ways people invent of writing numbers are often, if not usually, featural. The other way is to base symbols on the words for the numbers used in speech of some language. This is also partially used in some ancient "Middle Eastern" systems, and is at least part of how we got the Roman, "Hindu-Arabic", and Chinese (Han character) numeral systems we that together are used to represent almost all numbers (for reading by humans) today. (I guess tally marks and similar are probably the most common fully featural system today, and they're used only because adding to them is easy.)
My conlang Muipidan has a featural numeral system in base 60, with two sub-bases of 5 and 20. These videos make me want to play more with how arithmetic works in the system!
I kind of feel like instead of 'base 20', it's more of a 'base 5'... (the original system you highlighted) and that the others shown (mostly for base 12) were a base 3 or 4... In English, the numerals were originally based on the angles in the symbol. IE 0 has no angles, 1 has one angle, 2 (if you count the round at the top as an angle as it was originally) has two angles, 4 has four angles (if you don't count the little tail sticking out of the other side, as it originally didn't) and so forth. So it is a true base 10, while I feel the others have a smaller base and even their base 12/8/10/20 had those smaller bases. So wouldn't it just make more sense to make a base system off of smaller numbers? I know binary is a base 2 system, so I know I'm not the only one who thought of simplifying their numeral system, but binary has it's own problems in that it can get terribly long and space-consuming. Are there other problems that crop up in simpler/smaller based systems? Are there ways to circumvent that? Does this question even make sense?
Somebody made a video with the notion that Arabic numerals (sure, borrowed from India) were originally a variant of this. A number is drawn with a straight-line script, and recognized by counting the angles. 1 is drawn with a hook, one angle. 2 is drawn Z with 2 angles. 3 is drawn like a sideways W with 3 corners. 4 is a right triangle with a base extension, 3+1 angles. 5 is squared 5 with an up hook at the bottom left. 6 is a squared 6, closing off the 5's final line. 7 has a cross line (still used in some countries) and an extra top hook. 8 is a double square. 9 gets a bit carried away with cornering.
So if a condensed / altered version of KI can be used with base 10, I'm wondering if there would be a mathematical advantage to using the base 20 or if it's just a language difference where base 10 would be better for English speakers?
sidenote, the number system isn't the best for dyslexics because of it having a lot of very similar symbols. I might have a go at creating a conlang that would be as easy as possible to read
OMG, YES! Someone thinking about the often forgotten 20% of the population...I want to see what you come up with
that sounds really cool.
as a person with dsycalulia i found the KI numerals much easier as it simplifies what is required to remember. basically now i only really have to think 0-5 the rest is just about knowing your multiplications for 2,'s and 5s
I don't have dyslexia, I just fucking suck at reading.
But the similarities are the key
One thing I like about this notation: is easier to "write" numbers on stones, or any other hard material.
In fantasy settings, that is what I spec to be in "dwarven math"
Is it easier because it is more angular?
@@holdthatlforluigi it's easier because has a lot of straight strokes, that's simplify engraving on hard materials
thats how our numbers looked at the start bruh we just changed since writinh on paper and stuff became accesible
As someone who has done engraving and dabbled in runes, and is a massive Dwarf nerd, a system like this or the 13th century Cisterian monk system would be amazing for it.
You could also count using nothing but matchsticks (or any sticks for that matter), no writing or engraving required at all and no mechanisms like an abacus.
I guess pattern recognition is geometry now lol
Mathematics itself is mostly (if not entirely) pattern recognition.
@@danielsteel5251 But not all pattern recognition is mathematics. If I recognize that evey time a stoplight turns red, cars stop, and every time it turns green, cars go, I've recognized a pattern but have done no math.
@Yevhenii Diomidov What? Lol
@@danielsteel5251 I'm pretty sure that's not the case, but maybe I'm wrong.
Tautological. Because pretty much all learning is pattern recognition.
The thumbnail: "FU"
Me: "ok, rude"
:P
It’s fallow up
Alex Milonopoulos r/woooosh
FFFFFFUUUUUUUUUUUU-
@@alexilonopoulos3165 *follow :)
It's a Follow-Up. :-)
0:57 yo thats me, i never expected to be featured in an artifexian video thx so much
ohw cool that's pretty close to what i had in mind
Eyyy good job making it in!
The way you wrote eight seems to indicate that numbers are read in the opposite direction to our usual way.
You seem to have put the 1s place on the left, with the 8s place on the right, and I find that very interesting and cool.
Also, all your digits have 2 axes of symmetry, so extra cool.
Inigo Diaz yes, thank you. i wanted it to be a right to left number system because my friend is a lefty and used to write backwards, as for the symmetry, it was purely coincidental at the beginning of making it but i decided to keep it that way.
post more of your conlang :)
Ha, he says "Maths without maths" when sound is just the wave functions of air to create frequencies. Sound is obviously math.
Seriously people need to chill out.
We do indeed have a sound for sarcasm. Unfortunately I chose the absolute worst type of humor, an obscure joke from a flash game.
I'm just imagining the Katovik Iñupiaq inventors are like "woah these are really famous now"
Also I hope people will learn about the featural abugidas of the Arctic peoples
ohw cool that's pretty close to what i had in mind
Fuseteam about the abugidas? Because yeah they look really cool and work really interesting with the rotation thing
@@Alice-gr1kb oops i replied to the wrong comment..... how did that happen o.O
but yeah the KI numerals are awesome! it inspired me to make a featural number system myself
Fuseteam oh lol that's ok. I'm thinking about doing a featural system or maybe making a system like in Greek where letters were numbers
@@Alice-gr1kb yeah i'm thinking of a featural system myself with just 5 numerals for finger binary xD
Huh, I'm already subbed to you, but that made me respect you more than before, answering to comments and owning up to mistakes made (and recognizing when the fault isn't yours too), it's really nice! I'm a fan of world building (I've been building worlds since the age of 7, but it kinda slowed down because no one but me recognized it was a concrete thing) so you can be sure I'll watch more of your videos!
No joke, I’m watching this in a parking lot and i looked up into my mirror. I saw a license plate that starts with 7777 and was like “WOAH! You can get these crazy numbers on license plates?”
Also I’m super glad he explained larger numbers in greater detail
I'm coming back years later to say thank you. I've been working to revitalize my language, another indigenous one (Abenaki), for years. We also have a penta-vigesimal system in our language and using the Kaktovik numerals has made teaching it so much easier:
Our first five break down into: abstract, animate, inanimate:
Pazekw, pazgo, pazgwen (One, s/he is one, it is one); \
Nis, nisoak, nisnol (Two, they are two, those are two); \/
Nas, nloak, nhenol; \/\
Iaw, iawak, iawnol; \/\/
Nôlan, nonnoak, nonnenol; -
But then we go into + -ôz(ek):
Ngwedôz (a single + 5) -> 6; -\
tôbawôz (a double + 5) -> 7; -\/
Nsôzek -> (three + 5) -> 8; -\/\
Noliwi -> one short of the next ; -\/\/
Mdala -> ten; >
Continue to -ônkaw:
Ngwedônkaw; >\ (11)
Nisônkaw; >\/ (12)
Nsônkaw; >\/\ (13)
Iawônkaw; >\/\/ (14)
Nônônkaw; z (15)
Then back to: + -ôzek + -ônkaw (literally kassônkaw "So many -ônkaws"):
ngwedôz kasônkaw; z\ (a single + 5 + so many teens) (16)
Tôbawôz kasônkaw; z\/ (a double + 5 + so many teens) (17)
nsôzek kasônkaw; z\/\ (3 + 5 + so many teens) (18)
noliwi kasônkaw; z\/\/ (falling short of the next + so many teens)
Nisinska: |o (two pair of hands; two units of 10) (20)
Then they hold steady until hundred (Ngwedatgua), thousand (ngwedômkwaki), million (kchinguedômkwaki).
I guess that your goal was about the "Hangul" of numbers.
Haha funny haha.
I love this numbering system, and kind of wish I had thought of it when I was doing my worldbuilding. I did something sort of similar: I gave every prime number in the base digits a unique symbol, and every other digit is built out of those. Not quite featural, nor as clean and simple as these, but I'm still fairly proud of it. (I did stay boring base-10, but I'm okay with being boring)
glad you cleared stuff up, the previous vid was rather short and left me with a lot of questions so thanks for making a follow vid and for addressingf the comments that some people.
oOOOOOohhh, "FU" stands for Follow Up, not- okay. XD
1:27 Hey! That's me! :D
I should've sent in my "baseless numeral system" or more accurately, base 4 additionative numeral system.
That and my infinite numeral system (specifically designed for infinites and the various kinds).
OH YEAH I FORGOT YOU I CAN WRITE MY BASE 4 ONE WITH ASCII
1 is /, 2 is - and 3 is | and every other number is a combination of those added together. So after 3 it becomes however you want to write it.
/ - | , = + || И Н ||| ++ +/+ (or -И-) |||| |И| ИИ +++ (or |||||) HH H/H |||||| # ...
For note И is |/| and H is |-|
@@water594 So 4 could be = or |/ or -// or ////? Interesting, that means |-/ is 6 and ||-// is 11. So if there's no base, is there a standard order to the placement? Does the bigger number go first, like |-/or the smaller number first, like /-|? Or is it free moving, like /-/ or -|-? And what are the rules on stacking in the same cell? Does = equal 4 or does it have to be --? Could I write 5 like + or T or * (okay, that asterisk should look like >|
Commenting to see the replies because this is interesting
@@josephschubert6561 These are all problems I origionally encounteted when making it and to be fair I made it when I was sixteen and haven't worked on it for like two years. My biggest problem I never adressed was "crossing rules". Why are | and - allowed to be crosssed to make +? It adds another layer of complication. Perhaps I should ban crossing and five should be |- or T. Although it wouldn't be * or >|< because there is no backslash \ number. I guess you could add one and ir would increase the number of possible combinations and thats a valid choice.
You interpreted completely correctly for everything else though. I agree larger numbers become unweildy but stacking rules are quite simple, you just put it together however fits best.
I never made a culture to go with this but I imagined it would be almost like an artform. A mathematician would have the task of representing a number in the most elegant way possible. So instead of 20 being ///////////////////// which is unelegant TTTT is way more elegant and understandable and if I wasn't constrained to this format I might stack the Ts in ways that make more sense.
Maybe extra rules you could add would be face rules meaing a /-| can only contact a fact of another one once so =| is kinda an illegal number. That'd be another choice.
@@josephschubert6561 Also feel free to steal this and call it the Water Scale if you like it enough :), not sure if I'm ever gonna use it
How can I know beforehand if a division will be solvable using the "visual trick". Which kind of divisions work that way?
I think anything from the denominator being 5 to 10 would be pretty easy.
Divisibilty Rules. Traditional results of number theory. A counterintuitive surprise is that they actually depend on the numeral system used. Some numbers are easier to divide by others depending on which base (base-10/base-2, etc) and symbols to express them you use. For example, 1/3=0.33333... af infinitum only because 10/3 is not an integer. 10000/100=100 is easy because you only had to coun the zeroes, there are other symbolic tricks you can use depending on the rules you use to represent the quantities
2:15 this is nitpicky for sure, but of you wanted to use a prime base, such as 11, you couldn't do something like this, specifically it works for any number base with a 'small' factor (like 3 or 4 as shown).
Generally the more factors a base has, the better it is. Of course, bases shouldn't be too large either. Which is why Base 12 should've been adopted by humankind centuries ago, but we missed that part of the Science tech tree by now I'm afraid lol
@@Reydriel Why base 12 and not base 6?
@@TaiFerret Base 6 does not divide evenly by 4
@@Reydriel we all know base 6 is the superior base, we've all seen the conlang critic video
I don't think it'd look nice or be intuitive, but typically base systems in large primes aren't used because they're prime (they have no terminating fractional numbers).
0:57 i think the two should be either two horizontal lines, or the six and four should have an extra vertical line and lose their horizontal lines. Its annoying me that for two they did, you have zero and an extra vertical, but six and four you keep the horizontal. Its like 1X or 20, both are fine but you have to stick with one.
Also eight, the reverse order of the digit kinda threw me off. But its cool. (the high digit is on the right not left).
Digi that does masked sense. Still, they could’ve chAnged the two. But anyways thanks for your reply :)
You still can recognize them from each other and also
1 = ----
2 = |
3 = (--|--) = 1 + 2
4 = (=|=) = 1 + 1 + 2
5 = (-|-|-) = 1 + 2 + 2
Ect it's just repeating after
If you change 2 to || then their system wouldn't make that much sense
3:50 not quite - using a higher base the record is shorter, easier to remember. Looking at different civilizations depending on the size of the base of the system, they achieved different mathematical successes - the Mayas with the 31th system were good mathematicians, Indians with the binary system - bad. It is influenced by the fact that mathematical operations for humans are simpler on a higher bases. This is due to the fact that we process more data with one digit
I didn't get what FU in thumbnail meant at first and thought you were giving a "f*ck u" to the number system
Aren’t Sumerian/Babylonian sexagesimal numerals also featural?
"FU" gave off the wrong message
W.,h,.W
You're last video got me infatuated with the kaktovik Iñupiaq numbers I love your content please keep I up
I would argue that it isn't geometry. We're not measuring the sizes, angles, or anything really. We're counting specific objects. So to say this is geometry would be to say that counting sheep and pigs is geometry because we have to recognize the shape of the sheep and the pigs.
well, it's more about the spatial reasoning, but you are correct that it is definitely not geometry
I would argue that based on this, trigonometry isn't geometry. All the same arguments apply. Reductio ad absurdum.
@@joalampela8612 False. Trigonometry measures sizes and angles of triangles, contradicting my argument "We're not measuring the sizes, angles or anything really".
@@yuirick But this number system is all about the relationships of shapes. The angles and sizes of triangles are the same thing.
@@joalampela8612 Possibly, yeah.
I once made a hangeul inspired featural numeral system. It had both easy recognition of numbers, but you also grouped every 100 into a block, so it was possible to get up to 999 with just one character.
ㅇ = 0, ㅣ= 1, ㅡ = 2, ㄱ = 6, and ㄴ = 8, 이 = 10, 잉 = 100, 댱 = 590, etc
(my symbols weren't the same as in hangeul, but I used it to demonstrate the logic).
7:05 "have a wonderful 2020"
That last comment didn't age well
Hi Enjoy your time here in the comments.
Want some cookies and hot milk?
🍪🍪🍪🍪🥛🥛
Mmm. Thank you!
Thank you
I'll add some oranges in the mix too 🍊 🍊 🍊
How 'bout some cake too, 🍰 🍰 🍰
thank you
Math with this is not geometry, but grouping. You group things in multiplication and it matters little whether your number-symbols have an obvious featural system or whether it is arbitrary symbols and you have to learn a multiplication table to know how many times something goes into something else. It's just more blindingly obvious in a featural system.
I tried long-division in the base-20 featural system and tried 69 divided by 8. I went into decimals, of course, but it worked out to 8.625 or more correctly in the base-20 system 8.(12)(10). You still need to know a multiplication table, adjusting for base 20, but subtracting at each step to get a remainder was much easier.
I wanna learn it so I can confuse my calculus teacher. I'll practice some limits, derivatives and integrals with KI numerals
You also have to get comfortable in base 20, which is way harder than just doing regular math in base 10.
@@Otome_chan311 Not necessarily, he could just adapt the numerals to base 10 as Artifexian described.
@@Otome_chan311 1. It's not necessarily harder, your just used to base 10.
2. See 1:25. It translates perfectly fine to base 10 as it has a sub-base of five. IMO, it looks better in base 10 as you will only ever have one line on top.
@@wesleykronmiller390 except the "rotate it and look for how many times it appears" shit doesn't actually work at that point.
I've used Kaktovic vigesimals for years, I know the symbols, but the native names are too challenging for me, so I use them with the Yan-Tan--Tethera, which is also a Base 20 system.
I thought about it and found very simple methods to do any substraction (even with x - y where x < y) and multiplication.
And if you know how to divide with an abacus, it works the same way.
So yes, it makes maths REALLY easier.
6:18
i wouldn't say 0%. Any division by 10^n can be solved only using visual tricks in decimal.
But those aren't visual tricks of the digits themselves, which is the thing in question here.
Digit Shift Left and Digit Shift Right, as a programmer used to doing the same thing but in binary might say
Over an infinite amount of examples, the amount of examples of the form 10^n tends towards zero
I would convert it to base 16 with a sub base 4, that should br great for computer coding.
Well, there are a lot of cases where Arabic numerals permits superb tricks.
Take 3651:3, it's simply 1217. The trick is to recognize that it's "36" concatenated with "21", so you can divide each part individually, then concatenate the result.
Let say you've 1818:3, there, you've to remind you that your two concatenated numbers are 18, so 18:3=06. Which yields 0606 or 606.
You just keep the same number of digits for the result and pad with zeroes if required.
I think the biggest issue with these numbers and I probably already said it in the previous video is that they have basically zero error tolerance. You can't have them overlap or be too close together, you can't rotate them, you can't write them sloppy, they also take a lot longer to write (since they require far more strokes), they work much worse in bad lighting conditions or when you need to see them at a glance, they are much less resistant to random alterations (like damage or dust), and are much harder to display and parse in small font sizes.
So overall I don't think this font is very practical.
it's useful for basic arithmetic
Since September 2022, these numerals are officially part of Unicode 15.0! And the Rust programming language version 1.66 (December) has officially added Unicode15 support!
That must be how americans see the metric system
I would really like to see you do a complex example. Your last video inspired me to learn it and practice with it , and I've kind of developed my own ways about doing it from what wasn't covered in the video. I think you should totally get a random number generator and do some multiplication and division on camera.
Own methods? How do you perform borrowing? I want to see if it's what I came up with
1 minute and there's already a dislike. wow
Wasn't me I swear
49
What do you think of the number system that goes...
0,1,2,3,4,5
-0,-5,-4,-3,-2,-1
where the minus sign means 12-n
where -0 = six
where -5 = seven
where -4 = eight
where -3 = nine
where -2 = ten
where -1 = eleven
where 10 = twelve.
Obviously this system might require a better numeral system than Arabic. I'd want one that would count up to 3. Similar to the system on the video. I think the system I made up would reveal more patterns in the numbers. Since this system is a prototype it will have different enough symbols for the negative numerals of the modular base and negative numbers of the reals; ie it will be clear unlike how it is written in Arabic numerals. For arabic numerals you could just cross out the numeral to get the opposite. Can we discuss this?
Cool vid! I just have a question, can I use these numbers to solve operations like tetration or even higher???
You can. Maths basically does not care about the way numbers are displayed, althought they may make arithmatics easier, especially in everyday live.
At the and of the day, calculation are done in the Natural Numbers (most likely by your intuitive interpretation of the Peano-Axioms) and they don't care how one writes them down.
Very interesting thanks for making the video. Reminds me of Asian children being taught with the abacus, they develop "muscle memory" in their hands from moving the beads. They end up being able to do math as instinctively as most people use a pen.
Dear Artifexian,
Could you please create a video on conjunctions and causes but most importantly converbs? I really need help in this area for my conlang.
I have found this very interesting and tried exploring it a bit. The biggest issue for me is while the trick you give for long division is great it can't always be used to get the correct result and I personally have not found a way to determine when you can or cannot use it. Even when a number divides another it isn't guaranteed to work. Try doing 35 / 7 in KI using the trick as an example. Is there a way to know if it will work without already knowing the result? Because if that is not the case it isn't really that useful of a trick.
The guy never explained how borrowing works, but once you know how to borrow you can indeed find patterns just like the examples he provided. I've done a few explanations of how borrowing works and we'll go over 35/7 really quick so you can see.
35 looks like 1 vertical mark followed by 3 horizontal marks and 0 vertical marks, and we're dividing that by a number that looks like 1 horizontal mark and 2 vertical marks. At first I thought I could just rotate the number and everything works out, but the patterns don't quite match out. Instead, I needed to borrow 4 horizonal lines from the left most vertical line, giving me a number with 7 horizontal lines. Then I needed to borrow two of those horizonal lines to make 10 vertical lines for a final number that looks like 5 horizontal lines and 10 vertical lines. THAT matches up 5 times, for our final answer 1 horizontal line. But dang that looks messy when I write it out on paper.
DoomRater in fairness the only way to do 35/7 with the Roman system is to memorize the result or that 5*7 is 35. There is no aspect of our number system that could make solving that problem any easier.
@@ItsAllEnzynes Think of it this way. Base 10 doesn't handle divisions by 7 with terminating fractionals. The smallest base that can is Base 7 (next is 14). This is an interesting phenomenon that I believe cryptographic systems actually rely on to stay secure, though I don't understand the mathematics behind to fully grasp.
@@DoomRater You could in theory do something very similar our base 10. You are basically just breaking division down into multiple subtractions, which it effectively is, you break some of the rules of what is "allowed" in certain places to do so. We do this a lot when we first learn about these ideas. You could say you know that 7 is 3 less than 10. So you could exchange every digit in the tens place for a 1 in the quotient and a +3 to the ones place. 35/7 = 1+ 28/7 = 2+1(11)/7 = 3 + 14/7 = 4+ 7/7 = 5. Here I break a rule by putting for than 9 in the ones place temporary, you make use of this type of idea by writing some of the digits "incorrectly" for lack of better word. In your example you make use of the fact you know multiplication and skip straight there, If I did the same my process would be 35/7 = 3 + 14/7 = 4 + 7/7 = 5 making use of 3x3=9. We can do this because we know the transfer between the values, KI or base 10. You write 35 as 5 horizontal lines (5x5x1) + 10 vertical lines (10x1x1) = 35. (The notation I use here, and later, is ( [number of lines] x [value of that type of line] x [value of that place in the number] ) But this number is not correctly written this way, you just fit 35 into a place that should never have more than 19 in it.
I determined when you can use the trick he shows. I (wrongly) thought I could take my 7, 1 horizontal line and 2 vertical lines, and fit it into the 35, 1 vertical then 3 horizontal. Here I think I could fit it in once but rotated which I would denote by placing a singular horizontal line in the 1's place. It then looks like I have a remainder of 5 which is smaller than my 7 so I stop. So just trying to follow the video without doing this in the context of math. I would've guess 35/7 = 5 + 5/7 using this system. The reason this doesn't work is because with vertical lines we can go up to 4 in a single place, but horizontal we can only ever go up to 3. Thus we cannot do this mixing of vertical and horizontal lines while rotated. Making the system base 25 or base 16 would allow me to do this because the ration of 1 vertical line to a horizontal line in a previous place is the same as the ratio from a horizontal line to a vertical line in the same place. Does that make sense? I know it's correct, just not sure how well I explained it. Maybe doing our example problem, 35/7, in these new bases would help.
In base 25, so we can have up to 4 horizontal lines and 4 vertical lines in each place, we would write 35 as 1 vertical line (1x1x25 no longer 20 cause we changed base) + 2 horizontal lines (2x5x1). We would write 7 the same and get a perfect fit as we had hoped for. Just rotate and it fits perfectly, we mark our 1 horizontal (rotated) mark and see the value is 5. Similarly in base 16, so only up to 3 horizontal (keep in mind each of these are 4 now, not 5) and 3 vertical lines in each place, we would write 35 as 2 vertical lines (2x1x16) + 3 vertical lines(3x1x1), now 7 would be written as 1 horizontal line (1x4x1) and 3 vertical lines (3x1x1). Here we cannot fit any together natively. But we could do the ole trick you used and take 1 from the 16's place and write it as 4 horizontal lines in the 1's place. So now we can mix the horizontal and vertical values correctly. Our 35 is now written as 1 vertical (1x1x16) + 4 horizontal (4x4x1) and 3 vertical lines (3x1x1). Here again we write the number "incorrectly" as we fit 19 into a place that should only ever store 15. We can now fit in our 7's, once using 1 vertical and 3 of the 4 horizontals to give us a horizontal in the ones place, cause we had to rotate so we rotate the value in the quotient and again as we are left with exactly out value remaining so 1 vertical in the ones place. We are left with 1 horizontal (1x4x1) plus one vertical (1x1x1) = 5.
The biggest flaw with the trick in the current KI system is a direct result the horizontal and vertical values being on different footings, one counts up to 4 in a slot the other up to 3. So the ratio of a rotated numbers are different if they have horizontal and vertical lines, I will call these numbers with a "mixed representation". If at any point you have a divisor that has a mixed representation you may no longer use the rotating trick unless you do some manipulation to make them all one type of line (which lets be real is most likely going to be vertical, you could only make them all horizontal if its a multiple of 5). Everything else works just no rotating. If however, you build the base to be a perfect square (i.e. 4^2=16 or 5^2=25) rotating is allowed with mixed representations and it fixes a lot of issues I had with the KI numbers. KI is really closer to a base 5 system but every 5th 5 value is in base 4 which causes the mess you went through to solve 35/7. You still have to do some borrowing from higher digits to write the number "incorrectly" like I showed, but you can now rotate all numbers even if they have mixed representation.
I know this was a long rant/explanation but I felt compelled to share what I figured out with everyone that was willing to learn. IKI (Improved KI) uses base 25 as displayed and has all the features of KI but with an extra bonus.
@@chammy2812 Writing numbers incorrectly, or improper numbers as I referred to them in other comments, is exactly the idea their numeral system seems to lend itself well to. After all, it makes the pattern matching easier and it does indeed seem to be possible to do in our number system, if it's broken down into other bases. And borrowing is still necessary no matter the base anyway, so might as well take advantage of the intuitive meaning of marks.
Could we all work on something for base 60 like Babylonian system?
You like linguistics. So what do you think about Polish language?
7:05 "Have a wonderful 2020"
Mission failed.
Can you make a video about non-word characters that communicate things? Like punctuation, parentheses, the / for "or", the & for "and", etc.
That first video you made was amazing, and inspiring. I find it incredible that the internet has given us the facility to increase our personal knowledge and education more than anything else in human technology, yet rather than use this resource for learning new viewpoints and broadening our general outlooks, one of the most popular internet pass times is to start arguments with strangers about how right our existing opinions are. Anyhow if you’ll excuse the repetition: that first video you made was excellent. Please keep making good videos and thank you.
i HAVEN'T EVEN WATCHED THE WHOLE VIDEO... in fact, I am at timestamp 0:02, But I mashed that LIKE button as soon as I saw your new video. I need more linguistic and world-building. Thank you for feeding my addiction!
You earned my subscription for your honesty. I think your first video may have been a bit misleading but then again people were nitpicking for accusations if you ask me. It's not like you said "hey let's start a revolution and only use this system because it's flawless" you were just saying "hey people this system is amazing and deserves more attention". I honestly think this system is better than the one we have atm so i would without a doubt teach it to my kids. Why? Because it's more intuitive. This is really, and I mean really important for kids. I have a little sister that just entered elementary school and has problems with the simplest of maths just because she is an artistic soul. She became less confident in herself and automatically said to herself "i am not a person for math" when that's completely bogus since she is amazing at geometry. Why? Because geometry is intuitive for us and she can express her sense of logic thinking better in that environment. I will try to teach her this system in order for her to get back on track in the world of mathematics.
People talking about being early so I thought I'd leave my mark. I loved the video, I've been thinking about base systems nonstop ever since, which, math is not actually what I like. Just add language and culture to a topic and I'm hooked I guess!
Early gang! How’s it going conlangers
Nathan E it's going very interesting as I'm wondering if I should make a featural system or how normal systems evolve
I wouldn’t say so :) שחר א.
my favourite number symbols are dot, line, triangle, square, pentagon, hexagon and then just basically tile these numbers together for higher numbers.
Now I need to make one for seximal ;)
From the perspective of mathematicians, "mathematics" can refer to pretty any kind of logical thinking that isn't strictly dependent on observed reality, but other people often have narrower ideas about what "mathematics" is, and also often have a different perspective because they're often more familiar with "mathematics" as methods for calculating things using rules learned by rote, rather than a system of connecting ideas using mostly deductive proofs.
We could have made a 10 minutes video but you didn't,
Respect for that
Sad to see Base 6 (or 36) didn't get featured; this seems like a pretty great way to show it. Thanks for showing it to us, and featuring the responses you got!
It would have to be base 6 with a sub-base of 3, unless you want to add more strokes to the top and bottom. I think more than 4 strokes on the bottom, and more than 3 on top, would quickly become illegible. Base 36 with a sub-base of 6 would require 4 top strokes and 5 bottom strokes, which would crowd things pretty quickly.
Wonderful 2020
Ha
Haha
Hahaha
Hhahahahahahahahaha
(Proceeds to loose mind)
5:02 Regarding cherry picking numbers and your 80% awkward guess. I did the math and when multiplying two 2-digit numbers, (or when a/b=c where b,c are 2 digits), the visual tricks only work 3.5% of the time or 97.5% awkward. In decimal, if we define awkward as never having to add two single digit numbers to get a 2 digit number, it's clean 8.7% of the time or 91.3% awkward.
Sure, you could argue that my definition of "decimal awkward" is bad, but I'd say that a 3.5% success rate is barely bigger than 0% and isn't enough to count it as a feature for long division.
ah yes, 3.5 + 97.5 = 100
I just discovered this numerals yesterday and I'm very curious about using them more frequently in my life but I don't handle them very easy because when the numbers goes bigger I struggle with the base of twenty. Also I want to show them to my teacher like a class work. I don't know if you can make a larger tutorial to start from zero or something like that
I bet mixed radix would be confusing in this base if you literally alternated between base 10 and base 12 for Decadozen because you could decide to use the sideways glyph for 5 in 10 and 4 in 12. You would have something that looks like 55 or 52 but it's actually 64.
If you make a quick glance into these symbols, you could easily mistake numbers due to the incredible visual similitude there is between all these.
Which would also make it a very bad system for security purposes
It should'nt be to bad, if you are used to it. Most peolpe can "see" amounts up to four, so once the brain automatically divides the number to the subbase and 0ne-digit the numerals, those can instinctively be read.
I love the base 25 number system in riven
Picking random number for division without using "math" is still doable. A bit tricky as you have to re-visit how to write your number but doable.
Take 28/4 for example.
Why aren't there any comments here?
Years ago I came up with a base 6 number system for my conculture. Zero is just a zero. 1 is an I, 2 is a V, 3 is a V with an I between its "legs," 4 is a +, and 5 is a pentagram. Also things were written backwards to how we do it, so instead of 1 + 5 = 10 (in base 6 normally), it was 0I = (pentagram) (a different symbol for plus) I
Someone should start a petition to get these numerals in Unicode form
This system but block 10 is the way to go...block 20 makes it to a clusterfxck of many additions and multiplications when calculating 4036774 ÷ 6037 for example.
Not sure how new it is, but I love the new(?) profile icon
This was a good follow up, glad to get some input on that messy comment section. Thanks for doing this.
My mom, a math and science teacher, loved it and said she’d like to learn it and mentioned “you can’t teach an old dog new tricks” but she’s going to try.
How do you multiply? 😅
The visual tricks for addition and subtraction are cool; the long division, however, only works under the assumption that your division works out nicely and every leftmost digit is effectively negated at the end of each geometric step. Changing one digit in one of the examples in the first video illustrates one counterexample to the visual trick for long division: i.imgur.com/xq0pjPU.png
It can be shown here that, exclusively using the visual references, one would come up with the same answer of 501 (or "150" in base 20) because the technique doesn't really address the additional digits in the, in this case, 20^2's place. This may be remedied by keeping track of how well each number geometrically lined up during each step, but requires a bit more thought than may be suspected.
My main issue is how visually confusing this number system is at a glance. When the cool tricks don't work out, you're essentially left with really claustrophobic symbols that look very similar to each other at a glance and require a lot more counting than our number system, where each number is easily identifiable by shape alone. If we ever were to adopt a number system similar to this, each stroke would probably have to be more distinctive rather than just straight lines (maybe the distinctive features would denote different prime (and 1) quantities, like straight lines for 1, curves for 2, edges for 5, etc.?) just so they're both intuitive when doing arithmetic and identifiable when you're not just crunching numbers.
Either way, it's a fun thought, so thanks for sharing.
Word of advice: When showing "here's the proof" like the "2x20²+10x20¹+0x20⁰" you should also display what the values are below them, "800+200+0"
I learned Mayan numerals back in 1980 while working on film strips for my professor in collage. I could do + - * / like a fiend with 'em when I couldn't do math for shite in our Arabic numerals. Yea, I feel like an idiot.... LOL
Mayan numerals:
**Mayans numerals deciding their symbol**
All the numerals:So we have a plan to make a pattern
Zero:Bread
All the numerals:Bu-
Zero:BREAD
shout out "Ultra Gamer" for being a doofus
What would a mix between KI numerals and Roman numerals (XIV, XCIX, etc) be like?
It's not just that 80% times it's just as awkward as with Arabic numerals and 20% it's easier - some things are easier with Arabic numerals. For example, little things like if the digit sum of a number is divisible by 3, then the number itself is divisible by 3. Only works with 3, but then the examples with division in the previous video seem only to work with _some_ numbers, too. There is no explanation of what to do if the math-less method doesn't work - or how to identify when it doesn't work. But problems manifest themselves clearly when you take simple examples, such as 8/2 or 6/3. With such small numbers you can "cheat" by substituting the 5s with 1s, but how will you know when to do that for larger numbers? And personally I find the base 20 system extremely cumbersome. Now I have to use maths just to write 1000.
1:00 Holy carpp!!! I finished the previous video, read the comments, and wished for an easier and efficient system I myself could use!!
Thank you so much for these videos! I am researching Kaktovik numerals for a school project and this really helps!
Its a tally mark system
Looking forward to switch to a dozenal system. Base 12 is so much more practical
I mean it's basically just tally marks with 4 fewer marks on a group of 5. I'm still not convinced that easy math tricks are worth the loss in visual clarity. There is a reason I don't just use tally marks for everything, and part of that is that it get's visually cluttered quickly.
3:55 As a fun fact, I think this would be clearer in Spanish. While "Math" in Spanish is "Matemáticas", the term "Doing math" in Spanish would be translated as "Hacer cuentas" which refers specifically to counting, doing arithmetic and stuff. Though, you would've lost the pun.
I don't know why some folks are picking on the way you worded things or used simple examples to make a point.
I understood it PERFECTLY.
I am starting my 5 year old in home school this year and THIS is how she's learning math.
I HATED math growing up because THIS didn't exist!
Kind of late to the party, BUT wouldn't the system be better if it was base 25? This way you could multiply by 5 just by turning the digits 90°. As the system is now, it would break down as soon as you multiply 4, 9, 14 or 19 because you can't have a W at the top, so you'd have to convert stuff. Personally I'd even go to base 36, because if you use your fingers you can show 0-5 fingers and need a transition at 6 and not 5, so you could count to 35 with two hands. Also 36 has 1, 2, 3, 4, 6, 9, 12 and 18 as divisors.
Another improvement: Mirror the digits. This way you can start at the left and write them in one go. As an added bonus you can instantly see if a number is odd or even IF you go to base 36 (or 16), by checking if it starts up or down.
I watched a video on the Numberphile channel a year or three ago on a project the brilliant mathematician, John Conway (he of The Game Of Life fame) and another mathematician collaborated on called "abstract math(s)/numbers". This other mathematician (whose name is lost to me) was the principal creator of this number/math system with Conway acting as an adviser, encouraging him to publish it in book form.
I don't understand the geometry argument from people. Drawing sticks is not geometry
It’s easy to figure out how well the KI numerals translate to bases 6, 8, and 16.
I really like this system! I'll probably show this to my students once I'm confident with it. But how would you do multiplication? Follow-up video to this follow up video?
Remember, multiplication is just the opposite of division
The insinuated "FU" was not all that clever or appreciated. You did clarify a few points of confusion though and that was greatly appreciated. It was unclear to me if your proposed system is counting in base 4, 5, or 20 and you sort of clarified that. However, in the end, I gave both videos a thumbs down because of the title.
I hate how people use titles like this. I know they're generally click-bait or at least exaggeration but when it involves a topic I'm really interested in I'll click hoping the title is honest but then it isn't. The system you proposed is essentially like Korean mixed with Roman numerals or more like Mayan. I fail to see how there is anything unique or useful in this way of writing over others. You could make the counter argument that it makes division "easier" than what most of the western world currently uses( visually-speaking) though that is countered by the fact that the larger bases actually generally make division more difficult, not easier.
In my opinion, for an example, the reason why hexadecimal is generally easy to work in despite being a larger base than base 10 is the same reason octal or binary are easy, they're powers of 2 and pretty simple. They're 1 or not 1 plus some multiple/power of 2. Pretty simple. They're less simple in base 4, 8, 16 etc than base 2 but the conversion between them is mathematically easy for computers to handle. Of all the bases of 2^n, binary is the simplest and best (in terms of simplicity (but it takes much more space or digits obvious, that's the trade off)). It doesn't get much simpler than being in base 1 or 2 and using slashes or no slashes. The same arguments you used for KI could be used for base 1 or 2 just slashes. Essentially, the advantage if any of the KI and other similar systems is that it have slashes going two different directions orthogonal to one another. But, this can lead to confusion is reading/writing.
These sorts of topics are really interesting so I'd love to thank you for sharing and give your videos both thumbs up despite disagreeing with some of your points but still gave them thumbs down for the title and the (FU lol). Have a wonderful day.
I suppose Sumerian numerals and the Chinese "counting rod" numerals are also featural. Basically, the first ways people invent of writing numbers are often, if not usually, featural.
The other way is to base symbols on the words for the numbers used in speech of some language. This is also partially used in some ancient "Middle Eastern" systems, and is at least part of how we got the Roman, "Hindu-Arabic", and Chinese (Han character) numeral systems we that together are used to represent almost all numbers (for reading by humans) today. (I guess tally marks and similar are probably the most common fully featural system today, and they're used only because adding to them is easy.)
My conlang Muipidan has a featural numeral system in base 60, with two sub-bases of 5 and 20. These videos make me want to play more with how arithmetic works in the system!
I kind of feel like instead of 'base 20', it's more of a 'base 5'... (the original system you highlighted) and that the others shown (mostly for base 12) were a base 3 or 4... In English, the numerals were originally based on the angles in the symbol. IE 0 has no angles, 1 has one angle, 2 (if you count the round at the top as an angle as it was originally) has two angles, 4 has four angles (if you don't count the little tail sticking out of the other side, as it originally didn't) and so forth. So it is a true base 10, while I feel the others have a smaller base and even their base 12/8/10/20 had those smaller bases.
So wouldn't it just make more sense to make a base system off of smaller numbers? I know binary is a base 2 system, so I know I'm not the only one who thought of simplifying their numeral system, but binary has it's own problems in that it can get terribly long and space-consuming. Are there other problems that crop up in simpler/smaller based systems? Are there ways to circumvent that?
Does this question even make sense?
Somebody made a video with the notion that Arabic numerals (sure, borrowed from India) were originally a variant of this. A number is drawn with a straight-line script, and recognized by counting the angles. 1 is drawn with a hook, one angle. 2 is drawn Z with 2 angles. 3 is drawn like a sideways W with 3 corners. 4 is a right triangle with a base extension, 3+1 angles. 5 is squared 5 with an up hook at the bottom left. 6 is a squared 6, closing off the 5's final line. 7 has a cross line (still used in some countries) and an extra top hook. 8 is a double square. 9 gets a bit carried away with cornering.
So if a condensed / altered version of KI can be used with base 10, I'm wondering if there would be a mathematical advantage to using the base 20 or if it's just a language difference where base 10 would be better for English speakers?
I was hoping for "heres more cool stuff it can do!" but its mainly respnding to people that missed the point or just "um, ACTUALLY!"
Mindblowing