Base 12 - Numberphile

We mark the date 12/12/12 with a video about the merits of the dozenal/duodecimal system.
More links & stuff in full description below ↓↓↓
Numberphile regular Dr James Grime makes the case. More about James at www.singingbanana.com/
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[@77gravity]

This video scores 9/10. Just 3 points short of a perfect score.

[@giantomnipotentpanda236]

this comment deserves more likes

[@daveythehand4964]

Giant Omnipotent Panda agreed

[@trapccountant]

i see what you did there

[@felixroux]

random wiggle completely unrelated to the actual video/comment random wiggle completely unrelated to the actual video/comment random wiggle completely unrelated to the actual video/comment random wiggle completely unrelated to the actual video/comment random wiggle completely unrelated to the actual video/comment random wiggle completely unrelated to the actual video/comment random wiggle completely unrelated to the actual video/comment

[@dragonzairlumpus8490]

ayy 77

[@timgehrsitz3267]

Screw that lets use base 5040 for the ultimate dividing experience

[@deeptochatterjee532]

Tim Gehrsitz Let's go with 3,628,800

[@melvinshaw7574]

Tim Gehrsitz I advocate a system with a base of Graham's number

[@JamesDavy2009]

+Nate Burnett Never stopped the Chinese-they use over 50,000 logographs in their language.

[@harry_page]

+Seppe De Coninck Phinary for the win!

[@janisreinberger7724]

You can't just think of 5040 words, but you certainly know way more. But if you took a dictionary (which certainly contains more than 5040 words) you would certainly recognise at least 99.8%.

[@n124ac9]

Me: The year 2020 in base 12 is 1204. The people of Constantinople: Aw s**t here we go again.

[@goatgamer2389]

Actually the Turkish turned Agia Sophia into a mosque

[@VentiVonOsterreich]

@@goatgamer2389 that was after 1453 not during one of the Crusades that led to the sacking of Constantinolple and eventual creation of a "Latin Kingdom"

[@CrowManJoe]

Cheer Bear can i ask how you just know this

[@VentiVonOsterreich]

@@CrowManJoe research

[@m_uz1244]

@@CrowManJoe youtube history videos and all that, some people tend to keep an interest in rome when they grow up from when they were little, and thus usually end up finding out about the 4th crusade, sack of constantinople, and the fall of constantinople in 1453 also.

[@oliverdowning1543]

when I use alternate bases I usually replace the symbols 0-9 as well because I find it hard to get used to numbers that look the same but are different

[@thelickpolice1210]

that actually is very smart

[@urusledge]

I find it interesting that in some languages we actually seem to count to twelve in base 12, since 11 & 12 are spelled/spoken "eleven and twelve" or "elf und zwölf" in German, while 13, 14, and so on all end in "teen" or "zehn", and when you get to 21 it goes back to base ten with "twenty-one" and "einundzwanzig".

[@Jordan-zk2wd]

You could probably keep zero without mucking things up, as long as you change every other number. 0 will still be zero, but 10 won't be 10 because you'll be using a different symbol for 1, etc etc

[@oliverdowning1543]

@@Jordan-zk2wd yeah, I usually do actually do that because 0 acts as a place value holder.

[@lukasschallibaum5046]

@@urusledge this should be the top comment. Someone explain why

[@autorb5188]

12 guys walk in to a bar the bartender challenge them to drink 100 glass of vines they all agree that it's gross

[@minty_drawer6925]

This deserves way more likes!!

[@franzyuri5751]

I didn't get the joke

[@shericestivale7064]

AutoRB 144 is great dozen or gross

[@lovelypotatoes]

you mean 10 guys

[@sicklymoonlight]

@Zubeen Bhuiyan base 12, since it's a video of base 12.

[@DrScrubbington]

11Ɛ8 is 2012, so that means... 11Ɛ9 is 2013, 11ƐX is 2014, 11ƐƐ is 2015, That makes 2016 = 1200. Happy new century, I guess.

[@DrScrubbington]

***** You would call it a biquennium, to be exact. I guess you could just call it a "dozenal century."

[@KWGTech]

+Dr Scrubbington 1 gross = 12 dozen = 144 = 100 base 12 I think 100 base 12 years should be called a grosserie

[@Mercure250]

+KWG grocerie XD

[@sh0ck3r48]

+Dr Scrubbington biquennium sounds much more badass than century

[@DrScrubbington]

Ranillis Agreed

[@DJNicke]

Fascinating! Great video! As a former Disney animator, we worked at 24 frames per second, which was SO MUCH EASIER to animate things on fractions of a second using 2, 3, 4, 6, 12, 24 - as steps in timing for a character or object. I definitely think mathematics would be far simpler using this numbering system, as I still use it to calculate things in my head simply by being exposed to it in my younger years.

[@daddyascii9040]

it is a lot easier to think concisely in base 12 once you understand it

[@FebruaryHas30Days]

36 fps is better

[@DJNicke]

@@FebruaryHas30Days - where can I see 36fps?

[@FebruaryHas30Days]

@@DJNicke Just force the video industry to add a 36 fps option

[@DJNicke]

@@FebruaryHas30Days - what are the benefits of 36 fps?

[@GrayBlood1331]

10 year anniversary. What a wild ride.

[@DoctorLazertron]

See you at the 12th anniversary. Or the Ɛth.

[@ComradeTiki]

There's a big new innovation! Instead of "Two-doh one... Two-doh two... Two-doh three...", you can instead say "Twendy one, Twendy two, Twendy three..." and so on. (Thirdy, Fordy, Fivdy, Sixdy, Sevendy...)

[@nopenuhuhthankyouno]

*χ year anniversary

[@Mintymenty]

In a year IT WILL BE 10

[@thatasiankid45]

There's an alternate universe where this video is about the decimal system.

[@coopergates9680]

Henrique Tomio The multiples of 4 have a pattern after every five numbers (in decimal), which is better than eight or ten. Too bad seven is a spoiler for both bases, since its multiples have a pattern of all twelve ending digits in dozenal.

[@UncopyrightTNT]

and this comment claims that "There's an alternate universe where this video is about the dozenal system. "

[@1spiceatatime]

Henrique Tomio That's nice way to do it; however, the idea of infinity starts with thinking "What is the biggest number I can think of?"

[@CipherA]

MayBE!

[@ayeayre]

Will Barron huh? no lol

[@05st43]

base 12 is called base 10 in base 12

[@oz_jones]

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

[@05st43]

is pi 10 in base pi?

[@sinisternightcore3489]

@@05st43 no it would be 10 also. I think any number written in it's own base would be 10.

[@xusun956]

SinisterNightcore how about binary. 10 will be 2

[@sinisternightcore3489]

@@xusun956 Yes and binary means base 2

[@themustardthe]

And for the hand-counting bit at the end, it’s made even easier to count in 12’s if you use your thumb instead of your other hand to count of the segments. This frees another hand to count off *groups* of twelve, letting you count to 144 on just two hands.

[@jasonunddasgoldene]

Nice. Although you can then even hold 144 on one hand and complete the other again to get to 156.

[@CorgiCorner]

@@jasonunddasgoldene you mean 168?

[@jasonunddasgoldene]

@@CorgiCorner no, I mean that may be equally possible but I meant 156. When you keep track with one hand and you are at 12x12, then the hand you repeatedly count to twelve with is free to count to 12 one more time, amounting to 156.

[@deansprivatearchive]

Up to 156 actually, if you don't use your other hand for the first set. Sorry, couldn't help myself.

[@BonzoDrummer]

Ancient Sumerians, perhaps the 1st civilization, counted the bones in their fingers with the thumb on the other hand, and would pop a finger out on that hand every time they hit a multiple of twelve. Counting the thumb, that gave them the also-highly-divisible 60, which is where we get our number of seconds and minutes.

[@tehalexy]

2:26 dodos are extinct :(

[@mcnole25]

It's actually 1 Gro

[@realeyes8199]

Your English is extincted

[@tehalexy]

@@realeyes8199 you're writing extinct wrong my boi

[@Azide_zx]

time for an infinite base, where each number has its own unique character regardless of how big it is

[@definitelynotobama6851]

Set keyboard to Chinese (Traditional)

[@EHMM]

So base _ 10?

[@EHMM]

The number i just write out's half is 5× bigger lol

[@Nomenius1]

Ah the Chinese method.

[@Mike1Lawless]

Who even needs references to figure out what a new thing means?

[@rogerwang21]

*WhY dOn’T wE cOmPrOmIsE aNd UsE bAsE 11???*

[@jumbo_mumbo1441]

LOL

[@rocotu]

i've wondered about this what would 1/2 look like in base 11?

[@theleftuprightatsoldierfield]

Rocotu I think it would be 0.555555555555555...

[@rocotu]

yeah, i thought that too in base 3, would it look like .111111111111111111?

[@theranger8668]

ooh, that's gross

[@JaveLester]

Makes more sense. We have: 12 hour day 12 hour night 12 months

[@EdwardKennethSolomon]

yes. realized it when I saw that wall clock

[@grantdawson767]

Fun when you get into other values. 265 days in a year. Works out to 10 months with 26 days, with 5.3 days left over. Could also modify weeks to be 6 days, with 5 weeks per month, and 50 weeks per year. That's right...dozenal will get you a four day workweek.

[@luismiranda8944]

Someone sent me this video when I jokingly mocked our time system. I argued we should use base 10 instead of 60 for seconds, minutes and hours. 100 seconds for a minute, etc.

[@justincoleman9776]

12 inches in a foot

[@user-zl9vh2xr6b]

And 12 days in a workweek-weekend-workweek. Great system.

[@pietertalens1256]

I actually wouldn't mind relearning counting as an adult for future generations for this, but I suspect of course most people wouldn't haha.

[@UCkU0SrpEeCdPX-2cBVndj7g]

yeah and that's entirely the problem... it would essentially take an entire generation choosing to sacrifice themselves for all those to come... we've proven as a species to be pretty bad at that :P

[@ilikevideos4868]

I'm surprised how many people in the comments are against this.

[@UCkU0SrpEeCdPX-2cBVndj7g]

@@ilikevideos4868 I'm surprised anyone can be against James. He's so enthralling and charismatic.

[@ilikevideos4868]

@@UCkU0SrpEeCdPX-2cBVndj7g True

[@capitaopacoca8454]

@@ilikevideos4868 I've never seen a single person against base 12 here

[@user-iangramps]

5:32 "In dozenal, It dozen happen."

[@lZEOBA]

Thank you!! 🙏 I never would have noticed this if not for your comment! Lol 😂 Priceless!! 🤣🤣

[@user-zb8tq5pr4x]

I wouldn't want to count using 12 cymbals, it would be unnecessarily loud

[@Kitulous]

nice pun tho

[@natebit7167]

I mean you don’t have to strike them, just carry them around and lay them down every time you count. No biggie

[@alexanderhough9175]

I agree, it would be a very unsound counting system.

[@mariafe7050]

He said symbols not cymbals

[@imaalt1893]

maria fe r/woooosh

[@joegoldsmith3172]

I've been thinking about this concept as a shower thought for years, I had no idea it was this big of a thing, I'm glad I'm not crazy hahaha

[@michaelvoorhis9954]

Same! I started considering it while studying the clock.

[@K0nomi]

same, i remember thinking about how things would work in the shower

[@williammundy6562]

Just because a video was made about it, doesn't mean you're not crazy. 🤪

[@zafuro]

i will never take my meds

[@Leyrann]

There are a number of other things that are also interesting to consider here. For example, it's relatively easy to adjust our calendar to base 12. The easiest options do require SOME changes to what we're used to, but if you have 12 months of 2.5 times 12 days (which could become one week), you're left with 5 days at the end of a year, which you could for example turn into a short holiday, and suddenly the calendar fits with the number system we use. Or timekeeping. There are 86400 seconds in a day. It's kind of a random number, but it's pretty close to 82944, which is 4 times 12^4. And once you know that, it's possible to make an interesting adjustment to our timekeeping: The amount of hours in a day remains the same, 24 (though this is 20 in base 12). The duration of a second can remain ALMOST the same; you increase it by 1/24 (a little more than 4%), and you have 82944 seconds in a day (40000 in base 12), and 3456 seconds in an hour. 3456 somewhat random? No of course not, it's 2000 in base 12. So, what's next? Well, the one change you should probably make is the length of a minute. See, 2000 (in base 12) is 40 (in base 12) times 60 (in base 12), or 48 and 72 in base 10. So an hour has 40 (48 in base 10) minutes, and a minute has 60 (72 in base 10) seconds. Length of an hour remains the same, length of a second remains almost the same, and you have 20 hours in a day, 40 minutes in an hour, 60 seconds in a minute. Nice, round, and only limited adjustment needed from what we're used to, because if you needed 5 seconds for a task, you still need 5 seconds, and if you eat at 6 pm in the evening that's still 6 pm, except now you don't have to adjust with that digital clock that calls it 18:00, because it now says 16:00. The metric system? Can simply adapt along. It's still the biggest change, because a kilo suddenly means 1728 (1000 in base 12) times as many, and so on, but the core of the system remains. The numbers of specific variables (e.g. gas constant, gravity constant, etc) will change, but they will still be one specific number. And then there's prime numbers. In base 10, a prime number can be any number that ends on 1, 3, 7, 9. In base 12, a prime number can be any number that ends on 1, 5, 7, 11 (which becomes the thingy that I don't have on my keyboard). So also four, but there's more numbers. This is because you're automatically excluding any numbers that are divisible by three. It also makes it super easy to see that, for example, all primes are either one more or one less than a multiple of 6 - I actually didn't realize this myself until I wrote down numbers in base 12 and marked primes.

[@ArvindRajAgnosticAtheist]

I love how he's practically smiling all the time. Edit : Thx for the 600 likes!

[@doubleAAbatteries689]

he's happy with what he does

[@JayJay-ki4mi]

Combine that with the size of his pupils and it's either adderall, ritalin or coke.

[@SaftoRangen]

math. not even once

[@lilfr4nkie]

Jay Jay the real drugs is doing what you love in life though man... with that being said, my moneys on Adderall. 👽

[@davidbedder2873]

Cos he’s got an el inch piece

[@prismokz4711]

If we had 6 fingers we'd have no middle finger :(

[@levoGAMES]

The very long and useless username that you just took the time out of our life to read. Double-Middle fingers. You'd show someone the "middle fingers"

[@ikasu00]

MrSplodgeySplodge now we can flip the quadruple bird

[@lilbigness522]

Nice name

[@MrPyroguy1]

MrSplodgeySplodge HAHAHAHAHA best answer ever!

[@TechnoMinarchistBall]

+tom thrusterman Middle digit?

[@yashphatak6260]

Felt great seeing that numberphile has created a video on such a less-thought topic by people, also cuz I have thought about why only 10 is a base? The last trick was classic!! Loved it. 🙏🏼

[@KingstonCzajkowski]

"For serious maths, this system will not make any difference." Me: *angry digit-based mathematics noises*

[@Mnnvint]

What would really make a difference, though, is bijective bases, where every string represents exactly one number. No problems with 0000013 and 13 representing the same number. So every number has a unique reverse, and digits are functions in a simple and lovely way. I hope numberphile makes a video on them one day!

[@jangofet555]

would histograms and other forms of visualizing numbers be different? i just stumbled on this amateur video of a pattern in pi and the fibonacci sequence in base 12. search "Base Twelve Pi: Part Three, The Fibonacci Sequence"

[@gendertoads]

this is like that episode of icarly when carly told some kid they invented a new number called “derf” so he would fail his math test

[@andreacolace8538]

In italian It was "settordici" sett=sette=7 Ordici=quattOrdici=14

[@warnstar1101]

exactly what came to my mind

[@mustlovedonuts9233]

Tbh he instantly adapted to a base 11 system and could solve some pretty complex addition with it

[@orangenostril]

Imagine getting sent to math camp because you did your entire exam in base 11

[@R4V3-0N]

F***, now i need to learn my "el" and "doe" times tables.

[@msolec2000]

+R4V3-0N "el" is simple as nine in decimal, dozens going up, units going down. So: E, 1X, 29, 38, 47, 56, 65, 74, 83, 92, X1, E0.

[@rob876]

+R4V3-0N Did you not have to learn your eleven and twelve times table at school?

[@rob876]

Interesting. I didn't know that. I remember having to learn the 11 and 12 times table back in the day.

[@R4V3-0N]

I do remember my parents saying that. But when I was at school it was 10's, and I moved around to different schools often-ish when I was in intermediate school (In nz, it goes 'primary, intermediate, highschool", in USA I remember and assume you are in, it's "Elementary, middle school, highschool", the years of eneterance and exit is different. Primary goes for 6 years from the age of 5-ish., Intermediate goes for 2, highschool goes for 4.) Granted in highschool they do not even teach times tables and intermediate they do not touch it to much as it goes of the assumption you know it .... by highschool I forgot it because the very important 'times tables' I rarely use now and then... got a job, still don't use it. And it was a source of a lot of suffering for me.

[@msolec2000]

R4V3-0N But what about the table of 13? Or in base 12, 11. So it goes: 11, 22, 33, 44, 55, 66, 77, 88, 99, XX, EE, 110. :)

[@ricoreissmann]

Imagine in old Babylon they used base 60. :O

[@skyemegakitty]

For those curious about how you would remember that many: it iss basically a tally system with a unique symbol only for one and ten, and it uses positional notation. So when you get from 59 to 60 its essentially this, using parenthesis to denote each place: (

[@EHMM]

Its divisble by 1,2,3,4,5,6,12,30 and 60 p o g

[@thehonesthare8119]

@@EHMM Also 10, 15, and 20!

[@EHMM]

@@thehonesthare8119 i knew that,i just didn't include it-

[@thehonesthare8119]

@@EHMM Oh ok then

[@jankima8646]

The best way to count on your fingers is in base 6. You use 1 ha d to count 1, 2, 3, 4, 5 and then your other hand is for the groups of 6. This allows you to count to 35 on your hands (5 groups of six and 5), without having to grow an extra finger and the base 12 counting shown in the video using your finger segments is just impractical

[@jacobzinno8978]

The best way to count on your fingers is base 2. Finger up is a 1, finger down is a 0. You can count to 1023 like this.

[@joshuafury5353]

The "best" way to count with your fingers is in binary you'd hit every combination of fingers like that. 0000000001 0000000010 0000000011 0000000100 0000000101 0000000110 0000000111 0000001000 Bam over 1000 numbers with just your hands. Either way I think the finger segments is a way more intuitive idea than treating our fingers like digits.

[@notEphim]

@@joshuafury5353 Your way is efficient in a sense that this would convey maximum amount of information using our fingers, but reading shown fingers would be super hard. What jan Kima is suggesting is using one hand as a digit -- it's easily readable and covers more information than using both hands as a single digit. Also, jan Kima is referencing a great video "a better way to count" by jan Misali. Highly recommended

[@PedroCarvalhoLC43]

Can imagine the French going 4 dou 2 dou dou for 92...

[@cdemr]

I'm belgian, and for me it would be said "7 do 6" (sept do six)

[@redbaron827]

Everyone:WHY CAN'T YOU COUNT NOTMALLY France:*screams in four twenties ten seven*

[@jakelucena3392]

Pedro Carvalho quatre do deux do do lol

[@Ljossop]

Its do

[@thomasgdg5954]

i'm laughing in french =)

[@syncfish7892]

the US would use base 10

[@kentoutcourt]

wow. Best comment ever! :)

[@elijahrodgers9029]

Lol US would be the ones to use base 12, they already do in measurements. 12 inches equals 1 foot. And the DSA was founded in USA

[@therealdave06]

@@elijahrodgers9029 3 feet in a yard. Yeah right

[@elijahrodgers9029]

@@therealdave06 12 is divisible by 3. 5280 feet in a mile, which12 goes into 440 times. I think they would have an easier time making the switch.

[@bigcat5348]

No because metric is based entirely around base 10. The Imperial system already has lots of base 12 measurements.

[@elijahmasquelier1238]

You know I came in sceptical but I’ve kinda been converted-dozenal would make life a lot easier, really.

[@kornsuwin]

fifths

[@duodecimaldivision783]

@Music Account I spent most of 2020 exploring base twelve using geometry. There are things you can do in base twelve that you can't do in base ten. I just posted two videos on my KZbin channel explaining my discoveries. There's lots of interesting stuff about it. For one, our numerals were designed by someone using base twelve geometry.

[@Emanemoston]

I really like all the Numberphile crew, awesome job.

[@kichrootra]

I feel like "dek" would interfere with our standard of using x as a variable name in algebra.

[@thebronywiking]

I'm for the use of -| instead.

[@linus6718]

We could just use a, b, and c instead of x, y, and z

[@samuelthecamel]

changing dek a little bit would fix this problem. maybe make it an upside-down y?

[@mrs111198]

@@samuelthecamel that's lambda

[@samuelthecamel]

@@mrs111198 yikes... uh... how about a sideways y

[@JoaDrath]

There are DOZENS of us who want the dozenal/duodecimal system!

[@Chris.1812]

That doesn't sound like much support

[@bodenstrich2428]

+Chris woosh

[@SuperStingray]

DOZENS OF US!!!

[@coopergates9680]

Ikr Not grosses of great grosses?

[@kauhanen44]

There are _grosses_ of us.

[@jazzsoul69]

thank you for your videos it’s always fascinating

[@Hect0rxP]

After so long I keep enjoying the video and the idea.

[@theginginator1488]

I want to see a pi day special where they calculate pi in dozenal

[@davidolsen1222]

Pi? The half circle constant? It's wrong. Clearly you want Tau equal to 6.349416967Ɛ635108b2790423ƐX..

[@anirudhsilai5790]

Remember to set the day to March 18

[@thewarlord6529]

@@davidolsen1222 YES! I was wondering what Tau would be... TAU FTW!

[@KuraSourTakanHour]

I can see the benefits, but it would be virtually impossible at this point to get the whole world consensus to switch to duodecimal, since most countries use the decimal system officially.

[@elliotgale470]

+Ｍｒ Msan , even more so than the states going over to metric, it makes sense but it just aint practical

[@yannzul]

+Ｍｒ Msan It just need to start at school... like back in the days when my grandparents where forced to learn French instead of Occitan. We even changed money in 2000, forcing everyone to divide prices by 6,5 or something. At world scale, I can see it would be much harder, but not impossible, not at all.

[@maxbowen6482]

Finally someone talking sense

[@buffoonery5021]

Max Bowen Out of all of us in the chat, who makes the most sense to you?

[@Mercure250]

+Yannzul Gaming FR Si tu veux mon avis, c'est déplorable. L'occitan, comme toutes les langues régionales, contribuent à la diversité linguistique, et n'empêchent pas d'utiliser le français comme "dachsprache" ("langue-toit", une langue commune à un ou quelques pays pour permettre aux gens parlant différentes langues ou différents dialectes de communiquer, à ne pas confondre avec une lingua franca, qui est beaucoup plus universelle) (sorry for those who don't speak french, I'm just a little bit tired, so I went toward the language I master the most =P)

[@catherinedesrochers]

Interesting since the sumerians used a base 60 which works quite great with a base 12. Even with « only » 10 finger, this could have been a possibility! The last part where you explain about counting the segments of the fingers, was a part of it! :)

[@omars0009]

The best is base 1 4: 1111 5: 11111 3+2: 111+11 = 11111 And the joke 1+1=11 would be true Subtraction is removing ones

[@nathancosta2182]

wouldn't that be base 2

[@johnchestnut5340]

Unless you choose to not have a zero, it is impossible to have anything less than base two.

[@jamesyeung3286]

Base zero is the best obviously

[@hassanakhtar7874]

Base one is either just a tally or just doesn't work if you want to be precise. Edit: It doesn't work

[@johnchestnut5340]

@@hassanakhtar7874 Base one is precise as long as you stop at one.

[@johnvendler7061]

Casually including an analog clock behind him

[@princeyama3134]

John Vendler I think the double digits on the clock may have confused him.

[@andreiparaschiv9915]

There were moments when I had a hard time keeping up with the video, because it's a reflex of mine to automatically "complete" a group of numbers at 10. I understand base 12 mathematically, but it takes some effort to use it given that I was raised using a decimal system.

[@AnaseSkyrider]

It's hard to remember that 10-9=3 in dozenal.

[@jannieschluter9670]

@@AnaseSkyrider why is it not "1"???

[@yirli4176]

@@jannieschluter9670 because 10 in the dozenal system is 12 in the decimal system

[@jannieschluter9670]

@@yirli4176 no.

[@yirli4176]

@@jannieschluter9670 The numbers in the dozenal go: 0,1,2,3,4,5,6,7,8,9,X,Ɛ,10 Which, in decimal form, go: 0,1,2,3,4,5,6,7,8,9,10,11,12 So 10-9=3 in dozenal form This in decimal form is 12-9=3

[@yayagingersnap280]

And the duodecimal revolution starts by gaming the engagement metrics for this video!

[@vincent21212]

Finally, a Numberphile episode I'm smart enough to understand!

[@gustavmardby9364]

A clock has 12 symbols :O A day has 24 hours which is 12•2 :O One year has 12 months :O A minute has 60 minutes which is 12•5 :O A circle has a 360 degree which is 12•30 :O

[@maowtm]

Gustav Mårdby A clock has 10 symbols :O A day has 20 hours which is 10•2 :O One year has 10 months :O A minute has 50 seconds which is 10•5 :O A circle has a 260 degree which is 10•26 :O

[@coopergates9680]

王庭茂 Lol you copied his and didn't notice it said "a minute has 60 minutes" instead of seconds

[@maowtm]

Cooper Gates Fixed, thk!

[@coopergates9680]

王庭茂 Is it important that those numbers are divisible by twelve?

[@maowtm]

Cooper Gates Yes, so it will be something like 10, 100, 1000, 10000 instead of 14, 220, 3300, 50400 etc..

[@Liquifiedpizzas]

I feel like I'm watching a video explaining some cult.

[@urielseptim910]

What do you call a fake $20 bill? A pseudo two-do.

[@malikphenix3118]

i could watch this man enthuse about numbers all day

[@MrSal445]

I really like the base 12 number system. But why rename ten, eleven and twelve? They are already unique names without linguistic pattern unlike thirteen (three and ten) fourteen (four and ten) and so on.

[@davidolsen1222]

Because saying "eleven-one" sounds like "111" in common language. When el one does not. The first is equal to 111 the second equal to 121. Since the number means == 12 it would get confusing to change its meaning to being a value in the 12s place or 144s place.

[@TrickyTrickyFox]

Depends on the language and harshly. Also shiyi dian yi sounds kinda fun, if we're talking about common language

[@KusacUK]

Eleven and twelve do have a linguistic pattern. If you go back to pre-Old English they were ain-lif and twa-lif, which you can translate as “one left” and “two left”, i.e. what is left after subtracting ten. So basically they do have base ten implicit in them.

[@noelkahn4212]

I agree and why say “two do” and not “twenty”cause then we just redefine what “20” means. Because when I used base 1,2,3... in school, if we were talking about base 3 and we saw 20 we knew that meant 6 in base 10 but we called it “twenty base 3”. Other then that I am completely for this

[@mariecamille2998]

first second third fourth fith. first teen second teen doesnt sound right like thirteen fourteen fifteen.

[@pifie]

We actually count in base 12 in the western music scale, just as: C,C#,D,D#,E,F,F#,G,G#,A,A#,B

[@EchoHeo]

pifie Not if you dont use 12edo

[@heronimousbrapson863]

True. I've never understood the why the music scale is called an "octave" when there are actually 12 half tones.

[@torin1006]

@@heronimousbrapson863 Because they only count the 8 notes that make up a common scale.(8 white notes on a piano octave)

[@retired5548]

more like base 12th root of 2

[@tuckersmith7991]

Tubmaster 5000 Historically, the western musical scales were usually only divided up into 8 notes, and which note you started on determined which scale you were playing, 7 of them corresponding to each note of the scale minus the octave, which were just called modes. Major and Minor are actually modes in a way, as they correspond to the Ionian and Aeolian modes respectively. This is also where we get the Solfege system, Do Re Me Fa So La Ti, with another Do as an octave. It wasn't until we began standardizing with tuning systems and the creation of 12 tone equal temperament that we settled on 12 half steps, forming the chromatic scale that we know today. So basically, octave is still named octave for historical reasons, and it still kinda makes sense today because most of the common scales (major and minor) today are still divided into 8 notes.

[@davecrupel2817]

Definitely one of the most profound numberphile videos I've ever watched. I think about the dozenal system from time to time. In fact every time I look at my fingers, I look at the segments and I think back to what Dr Grime said at the end. I think I agree with him. I think the dozenal system would have been a better one.

[@Hippeus26]

The Romans told numbers by using the thumb to count the joints of four fingers of the hand - each finger has three joints - a duodecimal system. Their fractions are figured in this way: uncia = 1/12; sextans = 1/6 (2/12); quadrans = 1/4 (3/12); triens = 1/3 (4/12); quincunx = 5/12; semis = 1/2 (6/12); septunx = 7/12; bes = 2/3 (8/12); dodrans = 3/4 (9/12); dextrans = 5/6 (10/12); deunx = 11/12.

[@karlhelm875]

If we did use the dozenal system, the oldest human would still have a double digit age X2 of 122 years.

[@bruce9421]

Exactly

[@TheGerkuman]

That would certainly make the film X2 different.

[@bruce9421]

144=100

[@nayutaito9421]

In dozenal system, 87 is read "eight do seven." Then, in decimal system, it must be read "eight ten seven."

[@weijiafang1298]

Nayuta Ito That is how Chinese (also Japanese and Koreans) read it, though.

[@jondoh2226]

I love this. I wonder how hard it would be to teach my brain to think in base 12. I was thinking about this because everyone is saying we need to go to the metric system but imperial units are more natural. This makes me want to build a base 12 abacus and learn numbers all over again.

[@JesseSierke]

You can use your fingers to count to twelve and even on one hand. The other hand can keep track of the number of “does” all the way up to one number shy of a “grow”. Using your thumb as a pointer, touch each of the soft pads of each finger on the same hand one at a time. There are twelve. The other hand can hold the number of the second digit.

[@DriesduPreez]

About halfway through the video, my mind started seeing 10 as 12. It felt weird. Then while typing out this comment, it suddenly reverted back to 10 being ten, and 12 as twelve. If we were to go over to a dozenal system, then I think the hardest part would be to 'unsee' 10 as ten, and to develop whatrever new symbols for ten and eleven and accept them in the line as numbers. Thanks for the vid :3 Very informative.

[@hlynurgumundsson6979]

Goddammit you uploaded this vid the 11/12/12!

[@marcellkiss-redey8451]

You are probably in the wrong time zone.

[@pranav3848]

9/10/10 in dozenal

[@anonymoususer2756]

@@pranav3848 It would be E/10/10 though.

[@realBeltalowda]

Using dozenal you can count to gross on two hands (144 in decimal). Use one hand to count the number of do’s and the other hand to count through the one’s place of each do.

[@JRLarsen]

I remember watching this video when it came out and I still think about it and bring it up in conversation when anyone talks about the decimal system. lol

[@BluesyBor]

My reactions were like: 0:40 - WTF?! 4:30 - hey, that's brilliant!

[@danielfernandocarballo1890]

Of course, in the docent system there are periodic figures. Deal with 1/5 or 1/7

[@vincenzodanello4085]

1/5 isn't a problem. There will only be 1 more decimal. 1/7 though, is still a problem

[@theleftuprightatsoldierfield]

I believe 1/5 would equal 0.24972497... and 1/7 would equal 0.186X35186X35...

[@abeke5523]

@@vincenzodanello4085 how is 1/5 not a problem?

[@tuncayusta640]

1/5 or 1/7 are not much used as 1/3 or 1/6 in daily life.

[@YourAverageLink]

Guess what deals with both of those? Base 6, referring to them and 0.1111111... and 0.0505050505.... respectively It's better than base 12

[@stelladavis1798]

Octal system ;) We have four fingers. 8 is a power of two and also a perfect cube. It would make learning binary and hex a lot easier for normal people. I like hex too because 16 is the only (natural) number where swapping the exponent and the base yields the same result. It would make root 2 prettier as a decimal (or in this case, an octal or hexadecimal) I think. It has the same number of factors as 10, but with 2*4 instead of 2*5. Which, really, four is a much more useful number. It's not prime, it's even... The only reason we see five as an easy number is because it's half of 10.

[@uhhh_idkwhattoputhere]

11/11 idea

[@cleanerben9636]

I agree.

[@platypuspracticus2]

Cuts out 3 and 6 from the factors. Too limiting.

[@little_isalina]

I keep coming back to thinking about dozens and the dozenal system whenever i buy a package of something i might want to share with friends or my family, and they pack a prime number of those things in the package. Gets my goat every time.

[@NemosChannel]

144 birds were alive, 144 birds couldn't dive. 144 birds couldn't fly - 144 birds did die.

[@Jebusankel]

+Nemo's Channel That's gross.

[@davidwestern3878]

+Jebusankel That actually made me laugh

[@suwinkhamchaiwong8382]

you monster

[@NebulousEnigma]

What do you mean by bird??

[@Agent29416]

Screw base 12 we should have base 60

[@yukaroj]

i love that this video feel just some mathematician that finally got to tell the world about one of his favorite subjects.

[@CrashCubeZeroOne]

5:27 "It's not something that goes on forever. That's the sort of thing Decimal does. In Dozenal, it doesn't happen." *Decimal*: 1/3 = 0.(3) 1/6 = 0.1(6) 1/7 = 0.(142857) 1/9 = 0.(1) *Dozenal*: 1/5 = 0.(2497) 1/7 = 0.(186X35) 1/X = 0.1(2497) 1/Ɛ = 0.(1) Way to go people, you definitely made these easier to memorize. In addition, About the multiplication table thingy. 4 does have a period, it's just a little longer. Instead of 4-8-10 it's 4-8-12-16-20 Decimal does have no visible pattern for 3, 6 and 7, but dozenal does the same with 5, 7 and X. So it does simplify some things, but makes things that were easy hard, like 5 and 10 (aside from 7 it's bad everywhere, unless someone decides to use base 14). So it kind of pays off, and the change won't just fix everything. Also the multiplication table would be 1.5 times larger. Doesn't really seem to make it easier for 2-nd graders.

[@markenangel1813]

7 is not bad using base 6. its only .(05)

[@seraphimwiththecheese5880]

Most kids already learn 12×12 multiplication tables.

[@Torstenr16]

So with this system 9+10 woud be 21?

[@pawelmrowka2454]

It will be 19 still.

[@ramongeissbuhler6566]

***** Actually 9+10 in base-12 would still be 19. But 19 in base-12 is equal to 21 in base-10: 1*12 + 9 = 2 * 10 + 1 So yes for: 9+10 (base-12) = 21 (base-10) But no for: 9+10=21 (base-12)

[@pawelmrowka2454]

Ramon Geissbühler Exactly. That's what i mean :>

[@pawelmrowka2454]

***** There is no base, to 10 would be equal any other number. So don't write "in base-12, 10 is equal 12", plz That's why 10+9 =19 in both (decimal and dozenal) bases.

[@coopergates9680]

Paweł Mrówka I would say to write (Dec.) or (Doz.) after numbers if you keep translating back and forth so fast might be helpful. The same addition in dozenal: 15 + 6 = 1E 15 + 18 = 31 Versus those same numbers in decimal. 17 + 6 = 23 17 + 20 = 37

[@djpgator]

Base ten just makes more sense, the base twelve system was used by the Greeks before al-Khwārizmī made the Arabic(actually the Hindu) numerals popular, not only is it base 10, it also has the concept of zero(WHAAAAAAA?!) We see this in roman numerals, as there is no numeral for zero. So in that aspect the base 10 system is way better. Another aspect is that it makes more sense to roll over into the next base-system once you increase the number of digits, i.e. 10, 100, 1000, 10000, etc. Yeah, 10, 11, and 12 are changed in this method, but you can make infinitely many squiggles and say they have meaning, just look at the number of languages that have existed through out (only man's recorded) history. So why don't we have base 100? Why don't we have base 86593172? I'm sure we can make that many arbitrary symbols. Let's add the Greek alphabet, Let's just throw Delta, Theta, Kappa, Omicron, Psi, and all the others in as well? Because it wouldn't make sense, that's why. The same goes for base 12, is it practical, sure, but does it make sense? No. By making it base 12 at this point, not only would you break every computer, you'd make mathematics more complex. "But 1/3 would be .4 if we switched to base twelve" yeah, and it's be Omicron Upsilon in some other base. Hell, computers operate in an either-or base, let's go binary! We will always have irrational numbers, no matter what base we chose, Pi is going to be irrational and hard to compute(unless we operate in base-pi, in which case, god help us), Base 12 does not make sense when you consider the facts: humans have 10 digits, the numerals are clear, math thus far has been taught in base 10 for centuries, all of our calculations have been done base 10, all of our formulas are base 10, all our lives have been base 10. Base 12 still has irrational numbers: 7/12, 5/12, let's just swap the 5 with a 3 and use base ten: the same number of irrational numericals per base unit! Oh, and should I mention that we can simplify factions in base 10? I'm not an expert in base 12, but I know I didn't see any, so isn't it just simpler to say one quarter rather than 4 over "Do"? Or one third opposed to 3 over "Do"? It just doesn't work, there is a reason we use base 10: more people think it's easier, if it came to vote, base 10 would be picked almost unanimously. edit: fuck base 12, the Gregorian calendar, 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day, 7 days in a week, 52/53(leap year) weeks in a year, which get divided unequally into 12 months... that is the thing that I hate most about base 12. I don't know why but *that* is the bane of my existence. 60 isn't even half "Do", it makes no sense! If it was 72 I wouldn't have that complaint, but it's 60! It just sits there, a base 10 operator for a base 12 unit, and we don't even think about it...

[@davidwuhrer6704]

Dozenal also has 0. The ancient Greeks actually did use their alphabet as numbers. Computers use binary, it makes no difference to them if you print in decimal or dozenal. Irrationals are always irrational regardless of what base you use. A quarter is always a quarter and a third is always a third. 1/4 = ¼, 1/3 = ⅓. 0.25 in decimal is 0.3 in dozenal, still a quarter, 4 quarters is 1 in either case. 0.3333… in dezimal is 0.4 in dozenal, still a third, 3 times a third is 1 in either case. The Gregorian calendar is not base 12, and never has been. Same with the Julian calendar. The hours, minutes, and seconds are from a base 60 system originally, not dozenal. A dozen is a fifth of 60.

[@LolipopLW13]

Oh my goodness - I am 24 and never realised you can do the 12 times table on the segments of your finger. Love it! lol

[@andreaswiklund7197]

Looksbylauralw Too me you don’t look a day older than 20.

[@boboften9952]

Nine Times Table Is Fold The Finger Down . And Count The Finger Positions . Eg 4 x 9 Count Finger 1 , 2 , 3 , 4 .... Fold Down The Fourth Finger ...... Count One , Two , Three Fingers Space . And Count One , Two , Three , Four , Five , Six Fingers Up " Three , Six " Equals Thirty Six

[@lulah3463]

Awesome video. I would like to see a video demonstrating the segment counting. Where's that still done?

[@MS-ib8xu]

Why not embrace our computer life and use hexadecimal?

[@KucheKlizma]

Or binary? You can count to 1023 on your fingers in binary (1111111111)

[@Vezoth56]

@@KucheKlizma Counting with fingers is a bit different from using a certain system. The problem with using binary would be the length of math. As you showed, 1023 would require ten characters in a binary system, but only 4 in our current base 10. I would also argue that it would be a lot easier to mix up with larger values if there wasn't a method of dividing the 1's and 0's into a more readable format, like how we do in base 10 with a space between every thousand/million/billion/etc. Otherwise, you might find yourself lost in a long string of 1's and 0's and have to start over. But for the counting with fingers part, binary is definitely superior to base 10. This is mainly because binary works with the powers of 2 and while counting you can use the same finger multiple times. Assuming that we're counting full fingers and that there are 10 fingers in total, the first finger is going to be used a maximum of 512 times. The second would be used 256 times, third 128 times, and so forth.

[@KucheKlizma]

@@Vezoth56 Idd but it makes remembering 132 really easy if you convert it to binary and count on your fingers. Try both 132 decimal and hex. :p

[@AXes89]

@@KucheKlizma I dunno... Trying to order 4 beers may cause some confusion.

[@JesseSierke]

Sounds like a great topic for a different video.

[@romyrconcepcion5458]

Imagine if we used a Base-1 numbering system... "Okay class, today is 00/00/0000."

[@Monody512]

April 2 in the year 4?

[@DelphinusMAch1]

2nd February, 4 April 2, 4 would be 00/0000/0000 (or 0000/00/0000 if you're a yank) Problems occur at larger numbers...

[@Aleschu]

With base 1 the number 2 would be 00, 3 would be 000. 10 would be 0000000000 and so on. April 2nd would be 00(2nd)/0000(4th)/0000(4th).

[@DelphinusMAch1]

I'm British, we do dates differently ;)

[@Aleschu]

Paul Varjak How do you do it?

[@pbhello]

excellent video, thanks!

[@Theo-pd3ny]

James Grime is so adorable...I have to say it in the comments everytime I watch a video of his, I can't help it! The amazing thing is that I don't understand anything about math, but I don't care. I just look at him and listen to his lovely accent. Grazie James! Your italian n.1 fan ;)

[@user-pl7ch9lo1g]

pretty sure base infinity has all those advantages and more

[@cicciobombo7496]

Of course it has... xD

[@earthchan9171]

No such thing

[@guyda1716]

how about base pi?

[@arkanon8661]

well, im pretty sure infinity is "prime" though...

[@Lightningblade67]

Can you make a 995 328 Sub special? (400 000 in base 12)

[@Arcanefungus]

Awww, James said I am great. Thats it, my life has peaked

[@aFreeDrifter]

If you use your thumb as a pointer to the knuckles of your four fingers for teaching the dozenal to children, it would also help them easily visualize that 3x4=twelve="doe" from the knuckles positions. And with both hands, instead of only counting to ten (as now), they could count to 24 (or 20 in dozenal). If one uses left hand as the 10's (in dozenal) multiplier and the right as the 1's multiplier, and again, the thumbs as pointers and place holders, one can easily count to a gross on their hands. One can do the same with the hex (base 16) system by using the bumps right under your fingers (there are sixteen finger bones in an xray) and count to 256 (decimal) (my son and I have a dispute about that, I like dozenal best, he likes hex best, I think he's winning me over to hex though).

[@MumboJ]

See, I've been an advocate of Base12 for years, but recently I've started to waver when I realised something troubling. Although 12 has more factors, which allows many fractions to look nice, most single-digit fractions which aren't of a factor of 12 look absolutely horrible in Base12. People bemoan 1/3 = 0.(3) and 1/8 = 0.125, but those are nowhere near as horrible to comprehend as 1/9 = 0.13(E) or 1/X = 0.1(2497). (Brackets denote Recurring Digits)

[@johanrichter2695]

Yes, I agree, that would be one of the trade-offs, and something that should be pointed out.

[@grabern]

0.13Ē is the same as 0.14.

[@lucashfaria98]

To be fair, 1/X wouldn't be much used. The reason we use it (and related fractions) is because of percentage, and it wouldn't be a thing. Dozenal 100% would mean decimal 144%. Percentage would become "pergrossage"

[@Xelianow]

@@lucashfaria98 Actually 100 pergross (from now on: §) would mean 100/100 [doz], which is 144/144 [dec], which is a whole, which is the same as 100%. 0 and 1 (0% and 100%, or 0§ and 100§) are values which would be written the same way (all whole numbers which are written the same in Dec and Doz would be the same in percentage and pergrossage, beeing 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9) For example a half is 60§, a third is 40§, but two is still 200§, as its 288/144 [dec] ^^

[@jod6191]

Man, I just saw the uploading date... enormous!

[@nilufarrahaman570]

This video was released on 12/12/12 . Meanwhile Thanos: Perfectly balanced!!

[@donandremikhaelibarra6421]

Or 0/0/0

[@Opiate1987]

also, does this mean that, if we had had 12 fingers, and thus a base 12 system from the very beginning, we would have more 3/4 music?

[@xenomann442]

Why not just use base 1? 1= l. 2=ll. 3=lll. 10= llllllllll. 25= lllllllllllllllllllllllll. Fractions are made easy because you can directly see the ratio. 1/2 = l/ll. 3/4= lll/llll. 3/2= lll/ll. Simplifying fractions is also made easy since you can directly group them into smaller ratios. ie. 6/4 might be confusing to children in base 10. But in base 1 its simple. llllll/llll=(ll)+(ll)+(ll)*/*(ll)+(ll)=lll/ll. ta da!

[@elijahpickens]

So you want a less efficient Roman Numeral system?

[@xenomann442]

elijahpickens It simplifies all of arithmetic! Allowing for faster calculations, and is therefore MORE efficient.

[@elijahpickens]

What if it's 123/53 or something like that?

[@xenomann442]

elijahpickens lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll / lllllllllllllllllllllllllllllllllllllllllllllllllllll equals (lllllllllllllllllllllllllllllllllllllllllllllllllllll)+ (lllllllllllllllllllllllllllllllllllllllllllllllllllll)+lllllllllllllllll / (lllllllllllllllllllllllllllllllllllllllllllllllllllll) So as you can see there are two equal groups of 53 in the numerator with an additional 17. This means it simplifies to 2+(17/53). Or in base 1: ll + (lllllllllllllllll/lllllllllllllllllllllllllllllllllllllllllllllllllllll) See its simple.

[@elijahpickens]

Lol what about square roots, imaginary numbers, etc.?

[@dreadfuloperator5206]

Quick question, linguistically if we switch from Decimal to Dozenal what would be the new word for percent?

[@VesselTrinh]

Perbiqua is also a nice suggestion.

[@keyboardmannow]

William Bell Cent is also 100 in French

[@markenangel1813]

@@keyboardmannow ...which originates from latin, which is why william bell used latin as an example

[@keyboardmannow]

@@markenangel1813 Never knew that, thanks for telling me!

[@markenangel1813]

@@keyboardmannow you're welcome

[@cablestick]

What a brilliant man.

[@KPopsicleSNSD]

Metric system is really convenient though

[@MaxIronsThird]

It wouldn't change anything, the conversion would still be the same, 10(12) - 100(144).

[@aurelia8028]

the french wanted to DECImate things

[@aurelia8028]

Markus - :D

[@coopergates9680]

Hence, that word really does mean to remove one tenth of something.

[@totalsyambles8308]

Dozemate them.

[@FinlayHamm]

That imperial system was one step ahead of us

[@sierra7534]

I never thought in a million years I'd watch more than 20 seconds of this video or ever want to transition to a dozenal based number system. Especially not knowing that that ever even existed until a few minutes ago.

[@jaxonnobles]

That description... "We mark the date 12/12/12 with a video..." "Published on Dec 11, 2012" :y

[@AokijiTheIceWarrior]

i guess it looks weird if you're in America

[@kshitijbenedict8431]

@@AokijiTheIceWarrior or in any timezone that's far from Brady's place

[@imienazwisko8742]

Fookin timezomes

[@GodsMistake]

We had been using this system for years. Correct me if I'm wrong but was there not 12 pence to a shilling?

[@donoroko]

you guys are awesome. I never know if the guy that talks in this video is the channel "boss" or whatever or just a mathematician that appears a lot in it.

[@thenumeratorofficial]

There's a numeral set called Argam, and I have a closely-related set, Numerian Argam, and the two are about as similar as English and Scots, on the border of seperate sets and dialects. Based on Numerian's motifs and goals, I conder it a kind of "cousin" to Argam. Now this comes into play with the digits for 10 and 11. They both use an update down 2 (dess) and a backwards 7 (Ar: ell, NumAr: elv). My set is currently at 960 digits.

[@nutelina]

So after a while you get a lot of dough ;)

[@buffoonery5021]

+Paul van Nugteren Which leads to total 'zen'.

[@TheEternalPheonix]

+Buffoonery How does dough lead to zen? Unless you have completely failed on the level of thinking of dough as money and not realizing the money is not the solution to problems but the cause of them, I fail to see how you got that.

[@nutelina]

+TheEternalPheonix Some fail some thrive, what's the point of life?

[@littleconnormcd]

Please be 🍪 dough I am tired of pizza

[@aurelia8028]

wow lol

[@abcdefzhij]

Base 3 is another one you could make a case for, being the most efficient exponential information storage (which is due to the fact that it is the closest integer to e)

[@coopergates9680]

Not shabby for building hardware (if ternary logic and etc. is made efficient), though it's very poor for strings, using 3 symbols when a character can hold at least 256. Even for odd bases, I prefer complements, such as twos' for ternary... ...222.222... -> 0 -(01211) -> 21011 Overflow: 111111 would be the largest integer in 6 trits and 111112 would be -(111110).

[@abcdefzhij]

True.

[@Improbabilities]

Why would it be so much worse for strings? I don't see how that would cause a problem, aside from the obvious system issues of switching from binary to ternary. 256 isn't that far off from 3^5=243, so a 6-bit ternary system should work fine for strings. Or am I missing something?

[@abcdefzhij]

I'm trying to undo whoever marked Cooper Gates' comment as spam but it isn't working... :(

[@abcdefzhij]

Nevermind

[@fernandomunoz2954]

I love this guy

[@YourAashique]

This is awesome.

[@wasweiich9991]

What bugs me are those made up names. You know you can also just call them "ten, eleven, twelve". That basically also why we have those names for these numbers in the first place...

[@zhiracs]

Dek comes from the latin root which means "ten" El is an abbreviated "eleven" Do is an abbreviated "dozen" Congratulations on proving your decimal thinking. All words are made up.

[@wasweiich9991]

Maxwell M. I know where they come from - but I don't see why there should be new words of them, when we literally have them already. "Congratulations on proving your decimal thinking." Congratulations on putting me off your pet system through your superiority complex.

[@raisins7777]

+Wasweiß Ich You're going to run into gaps either way. If you want to keep saying "twenty", "thirty" etc and call twelve twelves "one hundred", that's fine but then you have to make up language for ten twelves or eleven twelves.

[@keithstathem872]

To use the existing words properly, I believe it would be one through twelve, then "dozen one", "dozen two", etc then "two dozen", "three dozen" etc. (which actually already makes sense to me)

[@habe1717]

Eleven and twelve have a lot of syllables.