Base 12 - Numberphile 

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

Screw that lets use base 5040 for the ultimate dividing experience

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

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

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

base 12 is called base 10 in base 12

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.

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.

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

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

10 year anniversary. What a wild ride.

2:26 dodos are extinct :(

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

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

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.

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

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

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

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

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.

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

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

Imagine in old Babylon they used base 60. :O

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

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

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

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

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

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

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.

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. 🙏🏼

why can't we just retain the names "tens", "hundreds", "thousands" etc? so why not dozenal 26 (which would be decimal 30) called "twenty six" instead of "two-do-six"? And 102(146) called one hundred and two instead of "gro-two"?

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

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

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! :)

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

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

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.

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

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

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.

Casually including an analog clock behind him

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

I really like all the Numberphile crew, awesome job.

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

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

thank you for your videos it’s always fascinating

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.

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

the US would use base 10

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

i could watch this man enthuse about numbers all day

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

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

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.

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.

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

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.

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.

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

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

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

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

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.

So with this system 9+10 woud be 21?

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

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.

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

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...

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?

That imperial system was one step ahead of us

7:33 "Maybe they made the wrong choice" perfectly describes just about everything that had to do with the French Revolution.

Why not embrace our computer life and use hexadecimal?

pretty sure base infinity has all those advantages and more

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

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

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)

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

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

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

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)

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

To still be able to show someone a number with your hands in base 12, you start by balling your hands into fists and holding them in front of you with the back of your hand facing away from you. You count from 1-5 by holding up each finger; to count six, you turn your open hand away from you so the back of your hand is now facing toward you. To count from 7-12, do the same on the other hand.

the french wanted to DECImate things

Metric system is really convenient though

The week is also dozenal in its roots: 6 (= half of a dozen) working days followed by an extra free day that does not count.

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.

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

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

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

3 segments in each finger, count with your thumb. Right hand does the 1s place and left does the "10s".

Screw base 12 we should have base 60

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).

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 ;)

Schoolhouse Rock already covered this back in the '70's. "Hey little Twelvetoes I hope your thriving. Some of us ten-toed folks are still surviving"

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

use 5040 it has much more factor

He blew my mind at the end with counting the finger segments for base 12

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.

This was mind blowing! I'm starting to question my everyday activities and how they would be if we used dozenal system. :S