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
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%.
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
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".
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
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.
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.
@@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 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.
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.
@@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.
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.
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.
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.
+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.
+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)
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.
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.
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.
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
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.
@@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
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...)
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.
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
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.
@@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
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
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
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.
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)
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"
@@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] ^^
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.
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.
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.
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.
@@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.
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)
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).
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?
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. 🙏🏼
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).
***** 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)
***** 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.
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
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!
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"
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.
Imperial isn't based on 12s either, though. The only unit that divides into 12s is the foot (12 inches). A gallon is divided into 8s, a pound is divided into 16s, a stone is divided into 14s, a mile is divided into 10s, 11s and 16s... Where's the logic in that?!
@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 TH-cam channel explaining my discoveries. There's lots of interesting stuff about it. For one, our numerals were designed by someone using base twelve geometry.
1/5 = 12/60. 60 in dozenzal is 50. 12 in dozenzal is 10. So it would be 10/50. That equals 1/5. What the heck? I have no idea what I am even calculating. Need help...
+xXSpacejumperXx Really what you want to do is long divide 1 by 5. You have to be careful, though, as the addition and multiplication tables are all very different.
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"?
BPA-Free Plastic Water Bottle 1023 is 1111111111 (ten 1's) in binary. For that you would hold up all ten fingers. For a binary number like 10011011 you would hold up your 1st, 4th, 5th, 7th and 8th fingers (depending on how you order them). You'd basically be stating all of the digits with your fingers where a raised finger means 1 and a lowered finger means 0
As true as this is... could you actually count that high easily, sure, you might know what fingers to put up, but then you still need to count it in denary to understand it (unless you're fluent in binary). Unless you learnt all 1024 permutations, it would be difficult to know what number you had on your hands.
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.
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! :)
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.
+TheDatolo97 Maybe because they look like digits.... or they found them in a Unicode set or something, I do use letters for larger digits because they're so quickly accessible, instead of fussy things like superscritps, italics, tildes, etc.
I remember being in a Liberal Arts Math class (a fancy name for math history). In it when got into matricies, subtracting only using addition and multiplication and unusual base number systems. Babylonians had a 60 base system (like why?). The Mayan math system had a 20 base system (10 fingers and 10 toes) and that made math very easy for me for some reason. Having the extra divisibles made life so much easier.
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 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.
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: (
I'd prefer a base 6 system. Base 6? Yes, base 6! I'm surprised that nobody ever saw that with 5 fingers a base 6 system is the natural choice. Well, you may argue: It can't really be natural, if nobody ever saw that before. Maybe so, but in our decimal system we don't have single symbol for "ten". We have a word for it and we have a finger for it, but we don't have a corresponding symbol. The symbol that was added by the the Hindu was the "zero" and the symbol for "ten" was abolished. If you add "zero" using one hand with 5 fingers, and you don't abolish the 5, which is the last finger, but the 6, which is the one from your next hand, then you end up with a base 6 system. You even have you second hand free for counting the sixes. This way your hands represent the nature of the number system. You can count up to 35 (base 10) that is 55 (base 6) with 2 hands. Anybody agree? I've never convinced anyone yet. Must be the nature of it. ;-)
Ger Hanssen I was talking about you saying base 11 was horrible because it's prime. 6 does have the most prime divisors until 30, which is too high... so you have a point there.
Ger Hanssen It's very easy to deal with its multiplication table, but do you think it's a high enough base? 10000 in senary is only 1296 (decimal), and the senary version of a googolplex is 6^(6^36) in decimal.
Cooper Gates Now let's be frank about this. Asking people to use senary would have a greater impact than asking them to drive on the other side of the road. It's like asking them to all start speaking Esperanto, which would also be very useful, but not very feasible. Senary has some drawbacks and longer numbers is a major one. Yet, any number can be written, so there is no fundamental problem. It's a matter of getting used to. Binary is even worse.
van LE Quy That's true. I do agree a base 12 number system would be more useful for day-to-day life, I'm just pointing out that there is a downside as well.
Joe Alias Quite a bit more upsides than downsides. But oh well, it will never be changed. We are unlucky enough to have started using base ten due to our finger tally and we will never change that.
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...
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.
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.
+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.
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)
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.
Today is 111111111111111111/11111/11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
It would take me a while to really absorb the base 12 system. However, I can already see from the comments that it would bring it's own problems not mentioned in the video. I have a feeling that base 12 is basically math nerds' (no offense) cute idea. In reality both base 10 and base 12 have some advantages and disadvantages. Humans need to learn math step by step. I highly doubt that base 12 would make any significant difference. A lot of the base 10 regularities become pretty intuitive with use. Base 12 sounds like a solution looking for a real problem.
It only has the same problem for 5 and 7, but base 10 also has the problem for 7. You end up getting 3 divisors and giving up one. Well worth it. I’m not sold on the way they count though because English already has words for it. If I write 0123456789AB (because AB are easier to write on a keyboard, I do think they deserve their own symbol) then that is simply zero, one, two, three, four, five, six, seven, eight, nine, ten, eleven, and twelve is 10. We can use dozen in subsequent counting though. Doone, dotwo, dothree, dofour, etc. 3A is simply thirdoten. We lose the whole awkward -teen thing, which is something we only have thanks to the French.
@T.J. Kong Base 12 keeps having widely popular applications. We have 12 months. We have two sets of 12 hours in the day. We have five sets of 12 seconds in a minute and of minutes in a hour, and so on. We also still use dozens to count certain food and drinks.
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.
+CarolNav Depends on what would be defined differently... if currencies were divided by grosses instead of into hundredths, if there were a dozenal version of metric, etc. etc.
+iafozzac Lollol I know, but if you want to divide $10 among three people and each is supposed to get $3 and 33.3333... cents, or you take a price and want 5/6 of it, say $20 changing to $16.66666...
Cooper Gates Dude, that's the same in base 12, 10$ become x$ but divided by 3 is still 3.333... changing the counting base won't change the value of money
+iafozzac The adoption of dozenal would most likely change the definitions of currencies, metric, etc., a dollar would be divided into fractions out of a gross instead of cents, or maybe even a "new" currency.
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...
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.
But now I'm confused. Yes, we don't end up with 0.3333... when dividing 10 (base 12) by 3, but you still get it by doing the equivalent of 10/3 in base 12. By your logic: 1/3 * X (base 12) = 10/3 (decimal) And that makes sense because we haven't used dozenal symbols or gone past 10 (base 12). So, simplifying it in decimal STILL gives you 0.333... And therefore you haven't actually fixed your problem, just moved it down 2 spaces in dozenal.
There will always be numbers that have ugly fractions, but the key with dozenal is that 3 and 4 will generally produce normal results (like 5 is in decimal).
+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.
Dozenal system still has infinitely repeating decimals for rational fractions of numbers that don't share factors with 12, so you haven't solved that problem.
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.
While base 12 has 2 more factores it also add two more numbers that don't factor still leaving you with 6 numbers that don't factor. Or to put it in a nothere way base 12 has a 50% factor rate and base 10 has a 40% factor rate. So the benefit is not as big as it might seam. I always thorght it would be better if we used base 5 as we could have each hand be a seporate didget allowing us to count to 35 (55 in base 5).
although 1/3 and 2/3 would be calculable evenly the phenomenon would shift to other values like one fifth. the reason 1/3 is .333333 infinity because 3 does not go into 10 evenly. The dozenal system has it's quirks as well, try 5 into 12 or 7 into 12. let me know what you come up with
+Mercure250 in decimal 1/5 is 20% or .2 store sales use 20% or 1/5 off Reply in the U. S the monetary system has 1 dollar 5, 10 20 50 100 and is a fraction of 100 1/100, 1/20 , 1/10, 1/5, 1 each $20 is 1/5 of $100
This video scores 9/10. Just 3 points short of a perfect score.
this comment deserves more likes
Giant Omnipotent Panda agreed
i see what you did there
random wiggle completely unrelated to the actual video/comment
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ayy 77
Screw that lets use base 5040 for the ultimate dividing experience
Tim Gehrsitz Let's go with 3,628,800
Tim Gehrsitz I advocate a system with a base of Graham's number
+Nate Burnett Never stopped the Chinese-they use over 50,000 logographs in their language.
+Seppe De Coninck Phinary for the win!
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%.
11Ɛ8 is 2012, so that means...
11Ɛ9 is 2013,
11ƐX is 2014,
11ƐƐ is 2015,
That makes 2016 = 1200. Happy new century, I guess.
***** You would call it a biquennium, to be exact. I guess you could just call it a "dozenal century."
+Dr Scrubbington 1 gross = 12 dozen = 144 = 100 base 12
I think 100 base 12 years should be called a grosserie
+KWG grocerie XD
+Dr Scrubbington biquennium sounds much more badass than century
Ranillis Agreed
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
that actually is very smart
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".
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
@@Jordan-zk2wd yeah, I usually do actually do that because 0 acts as a place value holder.
@@urusledge this should be the top comment. Someone explain why
12 guys walk in to a bar
the bartender challenge them to drink 100 glass of vines
they all agree that it's gross
This deserves way more likes!!
I didn't get the joke
AutoRB
144 is great dozen or gross
you mean 10 guys
@Zubeen Bhuiyan base 12, since it's a video of base 12.
*WhY dOn’T wE cOmPrOmIsE aNd UsE bAsE 11???*
LOL
i've wondered about this
what would 1/2 look like in base 11?
Rocotu I think it would be 0.555555555555555...
yeah, i thought that too
in base 3, would it look like .111111111111111111?
ooh, that's gross
base 12 is called base 10 in base 12
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
is pi 10 in base pi?
@@05st43 no it would be 10 also. I think any number written in it's own base would be 10.
SinisterNightcore how about binary. 10 will be 2
@@xusun956 Yes and binary means base 2
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.
it is a lot easier to think concisely in base 12 once you understand it
36 fps is better
@@FebruaryHas30Days - where can I see 36fps?
@@DJNicke Just force the video industry to add a 36 fps option
@@FebruaryHas30Days - what are the benefits of 36 fps?
time for an infinite base, where each number has its own unique character regardless of how big it is
Set keyboard to Chinese (Traditional)
So
base
_
10?
The number i just write out's half is 5× bigger lol
Ah the Chinese method.
Who even needs references to figure out what a new thing means?
I wouldn't want to count using 12 cymbals, it would be unnecessarily loud
nice pun tho
I mean you don’t have to strike them, just carry them around and lay them down every time you count. No biggie
I agree, it would be a very unsound counting system.
He said symbols not cymbals
maria fe r/woooosh
There's an alternate universe where this video is about the decimal system.
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.
and this comment claims that "There's an alternate universe where this video is about the dozenal system. "
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?"
MayBE!
Will Barron huh? no lol
Me: The year 2020 in base 12 is 1204.
The people of Constantinople: Aw s**t here we go again.
Actually the Turkish turned Agia Sophia into a mosque
@@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"
Cheer Bear can i ask how you just know this
@@CrowManJoe research
@@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.
5:32
"In dozenal, It dozen happen."
Thank you!! 🙏 I never would have noticed this if not for your comment! Lol 😂 Priceless!! 🤣🤣
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.
Nice. Although you can then even hold 144 on one hand and complete the other again to get to 156.
@@jasonunddasgoldene you mean 168?
@@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.
Up to 156 actually, if you don't use your other hand for the first set.
Sorry, couldn't help myself.
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.
I love how he's practically smiling all the time.
Edit : Thx for the 600 likes!
he's happy with what he does
Combine that with the size of his pupils and it's either adderall, ritalin or coke.
math. not even once
Jay Jay the real drugs is doing what you love in life though man...
with that being said, my moneys on Adderall. 👽
Cos he’s got an el inch piece
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.
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.
+Ｍｒ Msan , even more so than the states going over to metric, it makes sense but it just aint practical
+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.
Finally someone talking sense
Max Bowen
Out of all of us in the chat, who makes the most sense to you?
+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)
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.
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.
Depends on the language and harshly. Also shiyi dian yi sounds kinda fun, if we're talking about common language
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.
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
first second third fourth fith. first teen second teen doesnt sound right like thirteen fourteen fifteen.
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.
It's hard to remember that 10-9=3 in dozenal.
@@AnaseSkyrider why is it not "1"???
@@jannieschluter9670 because 10 in the dozenal system is 12 in the decimal system
@@yirli4176 no.
@@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
10 year anniversary. What a wild ride.
See you at the 12th anniversary. Or the Ɛth.
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...)
*χ year anniversary
In a year IT WILL BE 10
I feel like "dek" would interfere with our standard of using x as a variable name in algebra.
I'm for the use of -| instead.
We could just use a, b, and c instead of x, y, and z
changing dek a little bit would fix this problem. maybe make it an upside-down y?
@@samuelthecamel that's lambda
@@mrs111198 yikes... uh... how about a sideways y
the US would use base 10
wow. Best comment ever! :)
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
@@elijahrodgers9029 3 feet in a yard. Yeah right
@@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.
No because metric is based entirely around base 10. The Imperial system already has lots of base 12 measurements.
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
wouldn't that be base 2
Unless you choose to not have a zero, it is impossible to have anything less than base two.
Base zero is the best obviously
@Hassan Akhtar Base one is precise as long as you stop at one.
Lol
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.
I want to see a pi day special where they calculate pi in dozenal
Pi? The half circle constant? It's wrong. Clearly you want Tau equal to 6.349416967Ɛ635108b2790423ƐX..
Remember to set the day to March 18
@@davidolsen1222 YES! I was wondering what Tau would be...
TAU FTW!
If we had 6 fingers we'd have no middle finger :(
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"
MrSplodgeySplodge now we can flip the quadruple bird
Nice name
MrSplodgeySplodge HAHAHAHAHA best answer ever!
+tom thrusterman Middle digit?
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
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.
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.
@@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
Can imagine the French going 4 dou 2 dou dou for 92...
I'm belgian, and for me it would be said "7 do 6" (sept do six)
Everyone:WHY CAN'T YOU COUNT NOTMALLY
France:*screams in four twenties ten seven*
Pedro Carvalho quatre do deux do do lol
Its do
i'm laughing in french =)
If we did use the dozenal system, the oldest human would still have a double digit age X2 of 122 years.
Exactly
That would certainly make the film X2 different.
144=100
There are DOZENS of us who want the dozenal/duodecimal system!
That doesn't sound like much support
+Chris woosh
DOZENS OF US!!!
Ikr
Not grosses of great grosses?
There are _grosses_ of us.
2:26 dodos are extinct :(
It's actually 1 Gro
Your English is extincted
@@realeyes8199 you're writing extinct wrong my boi
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
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
王庭茂 Lol you copied his and didn't notice it said "a minute has 60 minutes" instead of seconds
Cooper Gates Fixed, thk!
王庭茂 Is it important that those numbers are divisible by twelve?
Cooper Gates Yes, so it will be something like 10, 100, 1000, 10000 instead of 14, 220, 3300, 50400 etc..
Of course, in the docent system there are periodic figures. Deal with 1/5 or 1/7
1/5 isn't a problem. There will only be 1 more decimal. 1/7 though, is still a problem
I believe 1/5 would equal 0.24972497... and 1/7 would equal 0.186X35186X35...
@@vincenzodanello4085 how is 1/5 not a problem?
1/5 or 1/7 are not much used as 1/3 or 1/6 in daily life.
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
Casually including an analog clock behind him
John Vendler I think the double digits on the clock may have confused him.
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.
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)
Yes, I agree, that would be one of the trade-offs, and something that should be pointed out.
0.13Ē is the same as 0.14.
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"
@@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] ^^
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
pifie
Not if you dont use 12edo
True. I've never understood the why the music scale is called an "octave" when there are actually 12 half tones.
@@heronimousbrapson863 Because they only count the 8 notes that make up a common scale.(8 white notes on a piano octave)
more like base 12th root of 2
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.
My reactions were like:
0:40 - WTF?!
4:30 - hey, that's brilliant!
Makes more sense.
We have:
12 hour day
12 hour night
12 months
yes. realized it when I saw that wall clock
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.
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.
12 inches in a foot
And 12 days in a workweek-weekend-workweek. Great system.
F***, now i need to learn my "el" and "doe" times tables.
+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.
+R4V3-0N Did you not have to learn your eleven and twelve times table at school?
Interesting. I didn't know that. I remember having to learn the 11 and 12 times table back in the day.
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.
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. :)
Why not embrace our computer life and use hexadecimal?
Or binary? You can count to 1023 on your fingers in binary (1111111111)
@@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.
@@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
@@KucheKlizma I dunno... Trying to order 4 beers may cause some confusion.
Sounds like a great topic for a different video.
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)
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).
True.
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?
I'm trying to undo whoever marked Cooper Gates' comment as spam but it isn't working... :(
Nevermind
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. 🙏🏼
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).
In dozenal system, 87 is read "eight do seven." Then, in decimal system, it must be read "eight ten seven."
Nayuta Ito That is how Chinese (also Japanese and Koreans) read it, though.
Was that the bite of eight do seven?
So with this system 9+10 woud be 21?
It will be 19 still.
*****
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)
Ramon Geissbühler Exactly. That's what i mean :>
***** 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.
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
"For serious maths, this system will not make any difference."
Me: *angry digit-based mathematics noises*
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!
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"
I feel like I'm watching a video explaining some cult.
I've been counting in base 12 with my fingers, and convert it to decimal afterwards, you can just fit so many more numbers in your hands
Imagine if we used a Base-1 numbering system... "Okay class, today is 00/00/0000."
April 2 in the year 4?
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...
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).
I'm British, we do dates differently ;)
Paul Varjak How do you do it?
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
Same! I started considering it while studying the clock.
same, i remember thinking about how things would work in the shower
Just because a video was made about it, doesn't mean you're not crazy. 🤪
i will never take my meds
144 birds were alive,
144 birds couldn't dive.
144 birds couldn't fly -
144 birds did die.
+Nemo's Channel That's gross.
+Jebusankel That actually made me laugh
you monster
What do you mean by bird??
Goddammit you uploaded this vid the 11/12/12!
You are probably in the wrong time zone.
9/10/10 in dozenal
@@pranav3848 It would be E/10/10 though.
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?
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.
This turned into anti metric propaganda really fast.
Interesting, considering the fractions used in imperial are considered strange by the metric crowd, but they're only strange because of base 10.
Imperial isn't based on 12s either, though. The only unit that divides into 12s is the foot (12 inches).
A gallon is divided into 8s, a pound is divided into 16s, a stone is divided into 14s, a mile is divided into 10s, 11s and 16s... Where's the logic in that?!
Imperial had to go, those inconsistencies nuts. If it was already one consistent base, like 12, it would've been great.
The metric system is for commies.
Metric system put the world back like the burning of the great library
pretty sure base infinity has all those advantages and more
Of course it has... xD
No such thing
how about base pi?
well, im pretty sure infinity is "prime" though...
That description...
"We mark the date 12/12/12 with a video..."
"Published on Dec 11, 2012"
:y
i guess it looks weird if you're in America
@@AokijiTheIceWarrior or in any timezone that's far from Brady's place
Fookin timezomes
You know I came in sceptical but I’ve kinda been converted-dozenal would make life a lot easier, really.
fifths
@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 TH-cam channel explaining my discoveries. There's lots of interesting stuff about it. For one, our numerals were designed by someone using base twelve geometry.
From any points of view base twelve is actually better... But changing it now is drammatic!
"From any point of view"
The problem is the metric system. Base 12 seems very in favour of imperial to me.
Billionaires would be another community
@@jerry3790
Problem is the fact I have 10 fingers and so counting in tens makes biological sense.
@@jeffvader811 You also have two wrists in addition to the ten fingers. Which is also biological sense.
We had been using this system for years. Correct me if I'm wrong but was there not 12 pence to a shilling?
Notice he didn't do 1/5. What does a fifth look like in dozenal?
0.24
+rlrsk8r1 actually, i'm getting 0.249724972497... and so on
+Nail3728 0.24 looks more like 7/36 to me
1/5 = 12/60. 60 in dozenzal is 50. 12 in dozenzal is 10. So it would be 10/50. That equals 1/5. What the heck? I have no idea what I am even calculating. Need help...
+xXSpacejumperXx Really what you want to do is long divide 1 by 5. You have to be careful, though, as the addition and multiplication tables are all very different.
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"?
Why don't we use base 2,520 because it has all factors?
for the best dividing experience :P
No it is 5040.
well better get to memorizing all them symbols.
No.
Do you want us to just have weird alien symbols all over the place or what
Can you make a 995 328 Sub special? (400 000 in base 12)
if you think about it, base 2 is far superior. with base 2 you can count to 1023 with your fingers. or 31 on just one hand.
BPA-Free Plastic Water Bottle 1023 is 1111111111 (ten 1's) in binary. For that you would hold up all ten fingers. For a binary number like 10011011 you would hold up your 1st, 4th, 5th, 7th and 8th fingers (depending on how you order them). You'd basically be stating all of the digits with your fingers where a raised finger means 1 and a lowered finger means 0
And you could add 2 more bits (thus count from 0 to 4095) by facing the palm of each of your hands either towards or away from you.
That would work well until you get to the number 4 and start flicking people off.
Except fingers can't bend independently from each other very well. My fingers already hurt just thinking about if I had to learn counting that way.
As true as this is... could you actually count that high easily, sure, you might know what fingers to put up, but then you still need to count it in denary to understand it (unless you're fluent in binary). Unless you learnt all 1024 permutations, it would be difficult to know what number you had on your hands.
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 like to watch these videos while i paint, so both sides of my brain are working.
Lol this is utterly brilliant. I feel like it would really annoy people if I actually used it but I love how decimals end up working out so elegantly.
What is it then? I thought it was 0,24
Except for fifths.
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! :)
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.
Interesting idea, but the symbols for 11 and 12 are too similar to x and epsilon
+TheDatolo97 You can choose whatever you wish.
Cooper Gates Then why do they choose that two symbols?
+TheDatolo97 Maybe because they look like digits.... or they found them in a Unicode set or something, I do use letters for larger digits because they're so quickly accessible, instead of fussy things like superscritps, italics, tildes, etc.
+jo l S does resemble 5 but Z is more like 2; how often do you confuse one symbol for another?
+Cooper Gates This is not a matter of resembilng a digit. It's about being that digit
I remember being in a Liberal Arts Math class (a fancy name for math history). In it when got into matricies, subtracting only using addition and multiplication and unusual base number systems. Babylonians had a 60 base system (like why?). The Mayan math system had a 20 base system (10 fingers and 10 toes) and that made math very easy for me for some reason. Having the extra divisibles made life so much easier.
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!
So you want a less efficient Roman Numeral system?
elijahpickens It simplifies all of arithmetic! Allowing for faster calculations, and is therefore MORE efficient.
What if it's 123/53 or something like that?
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.
Lol what about square roots, imaginary numbers, etc.?
Imagine in old Babylon they used base 60. :O
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: (
Its divisble by 1,2,3,4,5,6,12,30 and 60 p o g
@@EHMM Also 10, 15, and 20!
@@thehonesthare8119 i knew that,i just didn't include it-
@@EHMM Oh ok then
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
In italian It was "settordici" sett=sette=7
Ordici=quattOrdici=14
exactly what came to my mind
Tbh he instantly adapted to a base 11 system and could solve some pretty complex addition with it
Imagine getting sent to math camp because you did your entire exam in base 11
I'd prefer a base 6 system. Base 6? Yes, base 6!
I'm surprised that nobody ever saw that with 5 fingers a base 6 system is the natural choice. Well, you may argue: It can't really be natural, if nobody ever saw that before.
Maybe so, but in our decimal system we don't have single symbol for "ten". We have a word for it and we have a finger for it, but we don't have a corresponding symbol. The symbol that was added by the the Hindu was the "zero" and the symbol for "ten" was abolished. If you add "zero" using one hand with 5 fingers, and you don't abolish the 5, which is the last finger, but the 6, which is the one from your next hand, then you end up with a base 6 system.
You even have you second hand free for counting the sixes. This way your hands represent the nature of the number system. You can count up to 35 (base 10) that is 55 (base 6) with 2 hands.
Anybody agree? I've never convinced anyone yet. Must be the nature of it. ;-)
Ger Hanssen Binary is a prime base too :P
I never propagated 6-base because 6 is prime. I propagated 6-base because it has relatively the most (!) divisors.
Ger Hanssen I was talking about you saying base 11 was horrible because it's prime.
6 does have the most prime divisors until 30, which is too high... so you have a point there.
Ger Hanssen It's very easy to deal with its multiplication table, but do you think it's a high enough base? 10000 in senary is only 1296 (decimal), and the senary version of a googolplex is 6^(6^36) in decimal.
Cooper Gates Now let's be frank about this. Asking people to use senary would have a greater impact than asking them to drive on the other side of the road. It's like asking them to all start speaking Esperanto, which would also be very useful, but not very feasible.
Senary has some drawbacks and longer numbers is a major one. Yet, any number can be written, so there is no fundamental problem. It's a matter of getting used to. Binary is even worse.
true, 1/3, 1/4 and 1/6 are much easier in base 12, but 1/5 is 0.2497... with the 2497 repeating.
Honestly, how much usual do you use 1/5? Is it much more useful than 1/3?
van LE Quy That's true. I do agree a base 12 number system would be more useful for day-to-day life, I'm just pointing out that there is a downside as well.
Joe Alias Quite a bit more upsides than downsides.
But oh well, it will never be changed. We are unlucky enough to have started using base ten due to our finger tally and we will never change that.
KarstenOkk I agree, I'm not implying anything by pointing that out.
also, 5/12, 7/12, and 11/12 are irrational numbers so there's that too
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...
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.
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.
+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.
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)
Eleven and twelve have a lot of syllables.
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.
I propose that we use the unary system.
I read urinary xDDDD
ft55555 that would make it WAY easier😅😃😉
We did. Then we started counting large numbers.
I said this somewhere else and I say it again. Base e.
Today is
111111111111111111/11111/11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
use 5040 it has much more factor
Too high, too many symbols
Do you want us to just have random weird alien symbols all over the place
It would take me a while to really absorb the base 12 system. However, I can already see from the comments that it would bring it's own problems not mentioned in the video. I have a feeling that base 12 is basically math nerds' (no offense) cute idea. In reality both base 10 and base 12 have some advantages and disadvantages. Humans need to learn math step by step. I highly doubt that base 12 would make any significant difference. A lot of the base 10 regularities become pretty intuitive with use. Base 12 sounds like a solution looking for a real problem.
It only has the same problem for 5 and 7, but base 10 also has the problem for 7. You end up getting 3 divisors and giving up one. Well worth it. I’m not sold on the way they count though because English already has words for it. If I write 0123456789AB (because AB are easier to write on a keyboard, I do think they deserve their own symbol) then that is simply zero, one, two, three, four, five, six, seven, eight, nine, ten, eleven, and twelve is 10. We can use dozen in subsequent counting though. Doone, dotwo, dothree, dofour, etc. 3A is simply thirdoten. We lose the whole awkward -teen thing, which is something we only have thanks to the French.
@T.J. Kong Base 12 keeps having widely popular applications. We have 12 months. We have two sets of 12 hours in the day. We have five sets of 12 seconds in a minute and of minutes in a hour, and so on. We also still use dozens to count certain food and drinks.
Fittingly I'm watching this 10 (or as some call it, 12) years later and still enjoying the video!
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.
11/11 idea
I agree.
Cuts out 3 and 6 from the factors. Too limiting.
"Doh 1 doh 2 doh 3 doh 4..." Sounds like how Homer Simpson counts.
This was mind blowing! I'm starting to question my everyday activities and how they would be if we used dozenal system. :S
+CarolNav Depends on what would be defined differently... if currencies were divided by grosses instead of into hundredths, if there were a dozenal version of metric, etc. etc.
+CarolNav Yeah, because if we use decimal system is impossible to buy half a dozen of eggs in a supermarket... really guys almost nothing would change
+iafozzac Lollol I know, but if you want to divide $10 among three people and each is supposed to get $3 and 33.3333... cents, or you take a price and want 5/6 of it, say $20 changing to $16.66666...
Cooper Gates
Dude, that's the same in base 12, 10$ become x$ but divided by 3 is still 3.333... changing the counting base won't change the value of money
+iafozzac The adoption of dozenal would most likely change the definitions of currencies, metric, etc., a dollar would be divided into fractions out of a gross instead of cents, or maybe even a "new" currency.
I'm watching this video and typing this comment on 12/12, at 12:12pm local time, 12 years after it was uploaded!
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...
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.
Screw base 12 we should have base 60
This video being released on 12/12/12 is a classic Parker Square of an upload :D
Love the videos
Quick question, linguistically if we switch from Decimal to Dozenal what would be the new word for percent?
Perbiqua is also a nice suggestion.
William Bell Cent is also 100 in French
@@keyboardmannow ...which originates from latin, which is why william bell used latin as an example
@@markenangel1813 Never knew that, thanks for telling me!
@@keyboardmannow you're welcome
But now I'm confused. Yes, we don't end up with 0.3333... when dividing 10 (base 12) by 3, but you still get it by doing the equivalent of 10/3 in base 12. By your logic:
1/3 * X (base 12) = 10/3 (decimal)
And that makes sense because we haven't used dozenal symbols or gone past 10 (base 12). So, simplifying it in decimal STILL gives you 0.333... And therefore you haven't actually fixed your problem, just moved it down 2 spaces in dozenal.
If you do it in base 12, wouldn't it be 3.4?
There will always be numbers that have ugly fractions, but the key with dozenal is that 3 and 4 will generally produce normal results (like 5 is in decimal).
So after a while you get a lot of dough ;)
+Paul van Nugteren
Which leads to total 'zen'.
+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.
+TheEternalPheonix Some fail some thrive, what's the point of life?
Please be 🍪 dough I am tired of pizza
wow lol
Dozenal system still has infinitely repeating decimals for rational fractions of numbers that don't share factors with 12, so you haven't solved that problem.
dotwarner17 But thirds and quarters are quite common, so it's better than decimal
Infinitely repeating is better than infinitely non-repeating, which decimal is chock full of.
@@thewizardofthewoods5709 But base 12 also has infinitely non-repeating decimals? Why would converting to base 12 also change the irrational numbers?
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.
Metric system is really convenient though
It wouldn't change anything, the conversion would still be the same, 10(12) - 100(144).
While base 12 has 2 more factores it also add two more numbers that don't factor still leaving you with 6 numbers that don't factor. Or to put it in a nothere way base 12 has a 50% factor rate and base 10 has a 40% factor rate. So the benefit is not as big as it might seam.
I always thorght it would be better if we used base 5 as we could have each hand be a seporate didget allowing us to count to 35 (55 in base 5).
Oh and you would need to lear two more multiplication tables and all of them would be two numbers longer, so there isn't much of a benefit in the end.
I think we should count in binary system, because it's the way how the nature and computers are counting and it has a 100% factor rate ;)
Max Mustermann yeah that would allow us to count to 1023, but having to constantly flip your fingers is kind of strenuous, 1/3 would be 0.010101011
Not including 1 and itself 10 has a 25% factor rate and 12 has a 40% factor rate
***** so then why not base 6?
although 1/3 and 2/3 would be calculable evenly the phenomenon would shift to other values like one fifth. the reason 1/3 is .333333 infinity because 3 does not go into 10 evenly. The dozenal system has it's quirks as well, try 5 into 12 or 7 into 12. let me know what you come up with
+MIch Dax Maybe, but how often do you use 1/5 s?
+Mercure250 in decimal 1/5 is 20% or .2 store sales use 20% or 1/5 off
Reply in the U. S the monetary system has 1 dollar 5, 10 20 50 100 and is a fraction of 100 1/100, 1/20 , 1/10, 1/5, 1 each $20 is 1/5 of $100
And the duodecimal revolution starts by gaming the engagement metrics for this video!