Base 12 - Why Counting In Twelves Would Make Life Easier
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- Опубліковано 18 кві 2017
- How has the human body made maths more difficult, and how would counting in twelves make life easier?
This video looks at the differences between base 10 and base 12 (also known as dozenal or duodecimal) and explains why some mathematicians believe a switch to base 12 would make our everyday maths much easier to learn and use.
If you liked this video then check out the book which inspired it:
UK: amzn.to/2oMi0jx
US: amzn.to/2olQbgT
Music:
"Deadly Roulette"
Kevin MacLeod (incompetech.com)
Licensed under Creative Commons: By Attribution 3.0
creativecommons.org/licenses/b...
Website: www.smartbydesignstudio.com
Facebook: goo.gl/cBvvZj
The most common bases are 5 10 and 20
Binary: Am I a joke to you
Also hexadecimal 😂
Is binary base 1 or base 2?
@@isaiahrosner3780 base 2, digits 1 and 0
Shrumz I guess if it was base 1 it would just be 1, 11, 111, 1111, 11111 etc.
@@isaiahrosner3780 I think more like 0,00,000,0000 but I think base 1 doesn't exist
Counting in base 12 may be easier, but switching from a long established base 10 system to base 12 would be horrendously difficult.
Possibly, but we have examples already of countries switching from Imperial to Metric, so it’s not impossible.
@@baoyouming , and that is actually counterproductive in terms of switching to base 12, because metric is based entirely around base 10 while imperial already uses conversions that go with base 12 (like 12 inches in a foot and 3 feet in a yard).
I did this easy.
@@Reginald_Ritmo , an individual switching over is nothing compared to switching an entire society over.
I'd be fine with base 12 getting integrated, but it MUST NOT HAVE any characters that we currently use. I would say we should use 11 entirely new characters to denote that it's base 12. Otherwise, the new "20" is the same as the old "24." In addition, we should change the actual name of the numbers if needed too. It would take some learning but you'd never have confusion about which counting system a person refers to.
I use base -37. It's not too hard to learn, it only took about 111 hours of studying and 148 hours of practicing.
You saved so much time by switching :O
Nothing beats base 1
@@saminhaque13-52 idk I'm partial to a bit of base pi, or maybe base i if I'm feeling adventurous.
Ytf -37
You mean 4071 hrs of studying and 5188 hrs of practicing?
"Some mathematicians believe...." yeah that's a selling point for me.
I am not sure if that was sarcasm or not
@@StRanGerManY likewise, most likely because of the vagueness of the original comment. It was probably meant to be taken as a joke.
Numberphile made a video about it
chk it out ua-cam.com/video/U6xJfP7-HCc/v-deo.html
Explain yourself
Base 12 is easier for every day use. You can divide by 1,2,3,4 &,6 without decimals. That’s really handy once you get your head around it. Multiplication goes the same, the easy patterns are way simpler to remember. So it’s really quick when trying to work stuff out. Very hard to explain how it is, but it is.
I came up with this idea independently as a kid and I was so proud of my realization. When I learned that the concept was already existing, my intellectual ego took a big hit.
Should've just looked at your clock.
You were a smart kid! Too bad you didn't see it as a confirmation of your intellect.
Lol.
Ok but do you realize the larger a prime number gets, the closer we are to calculating a perfect circle?
@@mrsamamorris Maybe I should start seeing it that way
Perfect circles and spheres are impossible. But the primary requirement for long-distance space travel is near-perfect circles.
I had a computer engineering professor a few semesters ago who used to make us switch bases all the time to show us how arbitrary base 10 is. It was a pain in the butt, but I'm glad he made us practice it! Great video!
Its just like railways. They are 4 feet 8 and one half inches wide. It would behoove us especially in the modern world had we used a wider track. Something like 6' feet would have been preferred as broad gauges can handle more weight and the trains can move much faster. Why did we end up getting stuck with 4 feet 8 and one half inches?
Because that’s the way they built them in England, and English expatriates built the US Railroads.
Why did the English build them like that?
Because the first rail lines were built by the same people who built the pre-railroad tramways, and that’s the gauge they used.
Why did “they” use that gauge then?
Because the people who built the tramways used the same jigs and tools that they used for building wagons, which used that wheel spacing.
Okay! Why did the wagons have that particular odd wheel spacing?
Well, if they tried to use any other spacing, the wagon wheels would break on some of the old, long distance roads in England, because that’s the spacing of the wheel ruts.
So who built those old rutted roads?
Imperial Rome built the first long distance roads in Europe (and England) for their legions. The roads have been used ever since.
And the ruts in the roads?
Roman war chariots formed the initial ruts, which everyone else had to match for fear of destroying their wagon wheels. Since the chariots were made for Imperial Rome, they were all alike in the matter of wheel spacing.
And why were roman war chariots 4 feet 8 and one half inches? Because thats just wide enough to accommodate the ass of a horse, and a smaller war chariot is easier and cheaper to build, and is faster and more mobile on the battlefield. Those considerations are very important to a warring empire.
So the next time you ask why something is done the way it is and somebody tells you thats the way its always been done. And you wonder who's horse of an ass thought of that idea? Remember this history, it may very well have been a horses ass that determined the way things are done.
MindfulThinks But don't you hate it when professors mess with students for no real purpose?
lol Alright class, today we are going to be using base 13. " D': " - Every Student in the Class. XD lol
Br!an Delta V thank you for this comment.
What a fucking asshole
I couldn’t help having a stroke when I saw X and E as numbers and 2x9 made 16 not 18. Or that 6 can now go into 50 easily.
yeah, I had a stroke when I saw 1 ninth of 100 being 14
If we used base 12 we would be using special symbols for 10 and 11, because if we used letters we could not use algebra
Idk how old are you or where you're from but as a uni student in south asia it's been such a long time since I've seen x as a symbol for multiplication. Everyone uses brackets/parenthesis [ 2(2), in maths] whenever they wanna multiply something, use a dot (2•2, usually only in physics) or when writing using a computer use a star (2*2) or if there is a coefficient and an unknown of course they won't write anything (2y or 2x). Seriously no one uses it anymore.
@@beluwuga2573 they're not talking about x as an operator for multiplication though, but as a number itself
@@beluwuga2573 it's just a way to write, no need to freak out over someone writing 9x2 = 18 instead of 9*2
Okay, can you imagine if some parents taught their kids other bases for counting, and then in school the kids used them with the teachers, who I'm guessing have no idea about other bases. I can only imagine the argument over who is right.
I mean you still get the same result
@@evilhutdug4665 no, for example, 9x9 is 81 in base ten, and 69 in base 12
Taylor Huisman in binary(base 2) 1+1 = 2 same goes with base 10 why should base 12 be different
@@ZaHandleactually, 1+1 is 10 in binary
Opecuted the number you used is too small try this with 6+ 6
A third of ten is free point free, free, free...
Don’t you dare... get that ad... BACK IN MY HEAD AHHHH
I don't get it
@@nessfinesse3195 at 2:37 it sounds like free instead of three
@@pkawesome6230 there's a difference between free and three?
@@nessfinesse3195
The pronunciation.
As someone who works in music and animation, I count in 12s, and some of its factors, a lot. 3/4 and 4/4 time, as well as 24 frames per second in animation has me using the numbers 2, 3, 4, and 12 a lot. But I still like base-10 for math in general.
Part 2: Why counting in base 12 would make life harder
This might get you much more content!
If you try to redeem a code and a character is "X", you will not know if it is a letter or number.
How about hexadecimal
32lizOtuseM Similar story with “I”, “l”, and “1”
The transition is what would be hard
@@butterbluemchn that. if we are to switch lets switch right so there will be no more need to switch. There is no better base, despite maybe 8
The Sumerians actually used base 60, around 5000 years ago for some of these same reasons. That's why there are 60 seconds in a minute, 12 hours in a clock, and 360 degrees in a circle.
This had some wrong parts that make the whole thing a lot more confusing than it has to be.
"Ten is now called do" Wrong. Ten is called dec, like you said yourself. 10 is a do, but the notation of 10 has very little to do with ten in base twelve. And the concept of ten is the same across bases.
Similarly "1/3 is now forty percent, or forty pergro, as it would now be called". Once again this is wrong and confusing. 1/3 is thirty three point three percent in all bases, because you are saying what it is: per CENT, that is in a hundred! You can mix the names like this, it gives the impression that the number is some mutable thing, when the number is the same, what is changing is the NOTATION of the number
Hi, I will explain it to you how it is actually not wrong. Let's not confuse ourselves with names. In base 12, the new hundred will be actually 144 of base 10.
So, (100) base 12 = (144) base 10.
Now, if we divide them by 3, we will get:
(40) base 12 = (48) base 10.
Note: in base 12, 40*3 = 100.
So, in percentage, a third will actually be equal to 40% 🙂
Kunal Kashelani I believe he’s referring to the incorrect use of the word ‘perCENT.’ This word is specific to the use of 100 as we know it in base 10. However, like you said, our new “hundred” would be 144 (as represented in base 10), so we would have to instead use another word to represent this ratio in base 12, such as ‘perGROSS.’
@@kunalkashelani585 yes, I understand that, but (40) base 12 is not "forty percent", it is "four-do pergross". Reading the number as if it was in base 10 is confusing, because it gives off the false impression that the values somehow changed
@@SKyrim190 Ahh! I get it now, Thanx for explaining 🙂
@@jonathancamarena1938 Thanx for the explanation.. I understand the difference 🙂
Personally I really like base 6. You can divide it up just as easily as 10 (10 divides by 1, 2 and 5. 6 divides by 1, 2 and 3). It doesn't require us to invent any new symbols. Plus, counting on your hands means you can express the entire range of 0-5 on just one hand, meaning with two hands you can express any two-digit base-6 number, or any decimal number up to 36.
I prefer base 8. Same reason, we already have enough digits available. And most of us have exactly 8 fingers. And, most important of all, a 36 bit number if represented by 12 digits, none of the partial digits as with other bases.
I'm a big fan of base 6 too !
- using fingers as you described -> easy to show numbers up to 35
- small multiplication table -> easy to learn
- very efficient divisibility rules (2 and 3 -> look at last digit ; 5 -> sum of digits ; 7 -> alternating sum of digits)
- 6 faces dices is already the standard
Of course, numbers would require more digits to be written, but the increase (about 29% on average) is very reasonable in my opinion.
@@y.kennard3381 Who cares about standard we already threw out the number system. Just change the standard die to that one shape with 12 sides. Or switch to binary so you can count to 31 on one hand and 1,024 on two hands. (Of course, if you're trying to communicate, you'd have to establish which way is 2⁰ and which is 2⁴.)
Base 10 is good, because it has a gap between the two primes it is a composite of. No one mentions this.
with base 12 if you use one hand to count groups of twelve you can count up to 156
0:50: most common bases are 5, 10 and 20.
2: am i a joke to you?
He also missed 16
He was talking about historical bases specifically, where binary and hexadecimal never were used.
Base 60 was extensively used historically if I’m not wrong
Omg...he said the MOST COMMON bases THROUGHOUT HISTORY used are base 5, base 10, and base 20. Unless you have reliable data that prove that any other bases were used more commonly throughout history, then his statement was accurate. No, base 60, though it would most likely come in 4th place here, in my estimation does not outrank the others. He did not say these were the only bases extensively used. He did not "forget" any bases. Binary is becoming increasingly important, but nothing comes close to counting based on fingers and toes. Every binary function a computer does, is based on someones base ten reckoning of something. When I use electronics to get my bank balance, it uses binary to do this, but it still uses base 10 to present this to me. I still speak it out loud as base ten. And no, the sheer amount of numbers processed by electronics does not count. That's like saying the most common human language on earth is the series and patterns of electric pulses between the synapses in our brains.
@@Jimbo-de7ww Hexadecimal was used in ancient India long long time ago. The Indus Valley Civilization people who lived at era contemporary to ancient Egypt and Mesopotamia were definitely the first people to use this system. The stone weights found at the IVC sites are perfectly in the order of 16, 64 and 160 units.
Person 1: I count my 5 fingers on one hand
Person 2: I count my 10 fingers on my two hands
Person 3: I count my 20 fingers on my hands and feet let me take off my shoes
The Mayas did base 20, because of exactlly this reason. 🤗
The people from Papua can count upto base 20 with 1 hand. I wonder how the maths can be advance by the level of Incest.
I can count to 21 ;)
Person 3 can count 20 **fingers**. Does that mean person 3 has fingers instead of toes?
Meh... I was born with 11 fingers and 11 toes.
I have a head start :-)
I like base 6 better, you can count ones on one hand and tens in the other. This is good for reading from a distance. Plus, 6 has 4 factors, which is close to 12's 6.
Nice
i prefer base 8, it has the same nuber of factors, (1,2,4,8) with the ability to *infinitely divide by 2 intuitively* and simple converson to base 16 (by converting through base 2)
@@Gregory_12 well it cant do thirds which is a little inconvenient
@@Gregory_12Actually factors for 8 are... 2,2,2. So only one. Has all the problems of binary, but numbers are just shorter.
For base 6, factors that matters are 2 and 3 - a bit of an improvement over base 8, and easier to count on hands.
@jarlsofenrir so 12 is best? Plz no 60
Don't waste your time with base 12. We live in a digital age, and binary switches still are the cheapest and fastest way to store numeric values in a machine. Base 2 and base 16 FTW!
Real men count in binary
@@dovahkiin52 Yes!
@@dovahkiin52 Amen.
Make someone learn base 69 when they lose a bet
Doesn't dealing with base 10 make dealing with money in programming problematic? It's the whole deal of having to deal with money as integer values rather than floats. Although one would always find fractions with infinite expansions, which is what makes the aforementioned thing problematic, it seems like the usual fractions are easier.
Just makes me think how much humans love zeros. . .
Zeroes are awsome
Bcs you want 434,123,123 instead of saying 434,000,000..with the new zeroes, nothing woulc change, only different numbers owuld have plenty zeros after them
The symbol 0 as in 'your balance is 0' and the symbole zero used in '100’ are actually different concepts. One means no value in that position in that notation, the other means no value at all. You could have ∅ for the latter and it wouldn't change much. You could then omit all 0's from your notations and replace with whitespace or dashes. 100 = 1--
In computer sciece, you have hexadecimal base 16, octal base 8 and binary base 2. Once you start adding and multiplying with them you'll understand why we stick with the decimal system.
I was thinking the same...
It doesn't disprove the video.
The reason why it is so awful for us to do math with other systems is that we simply lack the experience and ABCDF still feel like weird placeholders and not like real numbers. It is also extremely difficult to not fall back to base 10 math when doing calculations.
It is not the fact that the system are base 8 or base 16 what makes math with it hard, it is the fact that we humans are just not used to deal with those number systems.
Blame the humans, not the numbers ;)
You just find them weird because you didn't grow up learning them.
@@tzarcoal1018 no it kinda does
Base 10 is so much easier for bigger number calculations
Imagine being an accountant for a big company using base 12
Even if you learnt it from the start it would be horrible
As its impossible to form intuitions on bases that arent base 10
I used to be a math prodigy
And i had methods to speed up calculations
Patterns i found when certain things interact
These patterns are stable in base 10
But whilst base 12 has patterns(so does base 8 and 16)
They arent stable forcing you to do calculations in lots of cases where you wouldnt need to in base 10
@@TheMe26 hey math prodigy, you understood nothing of what it means for base 12 to be a different number system
3:06 - Base 10 seems simpler... Yes, there are more infinite fractions in base 10, but they're all simple, 1/3 is just threes (0.333...) and 1/6 is almost the same (0.16666...). By contrast, 1/5 in base 12 looks terrible (0.2497...), so does 1/10 (0.12497...). The only fraction that really looks bad in base 10 is 1/7 (0.142857...), which is also bad in base 12 (0.186A35...). So some fractions like 1/3 become a bit easier, and others like 1/5 become a lot harder, is that really worth it?
Correction: 0.186Χ35…
What You Put: 0.186A35…
@@keonscorner516 I know, but using A, B, C, ... for 10, 11, 12, ... is the standard notation for any base other than 12 so i'm used to writing it that way
Probably not.
Fractions don't represent the same numbers in base 10 as they do in base 12. You got those numbers because you tried to directly convert base-10 decimals into base-12 duodecimals. In proper dozenal arithmetic, 1 divided by 10 is still 0.1 since 10 represents the number 12 in base-10. In base-10, fractions have terminating digits if the denominator factors into 2s and 5s. In base-12, you get terminating digits when the denominator factors into 2s and 3s. Notice how there's a lot more terminating denominators for base-12 than for base-10. Try using a dozenal calculator and you'll see how neatly everything lines up in base-12.
@@scylecs You have misunderstood what he was saying. In both decimal and duodecimal systems, 1 means one and 5 means five. However, in decimal system, 1/5 looks like 0.2 ; and in duodecimal system 1/5 looks like 0.2497...
Also, if there is a lot more non-terminating denominators for base-12, shouldn't it make a base-12 system a lot worse than base-10?
“Free point free free free free free free free”
You named the numbers the decimal way even when you were using the dozinal system. That's very confusing, should try and fix that
"Most common systems: 5,10,20"
*Cries in Binary and Hexadecimal*
Current number systems: Binary, Octal, Decimal, Hexadecimal
*Cries in Dozenal*
Guess ya never heard of the sumerians.
Yeah those buggers were possibly Way ahead of their time only to have the bazentines rip them off and to a far worse job.
Commmander 64 This is a great comment.
The niburu guys.
Anyone who thinks base 12 is easier has clearly never measured things in inches and factions of inches as opposed to centimeters and milimeters.
Having to memorize that after 5/32" comes 3/16", then 7/32" and then 1/4" sure sounds simpler than counting 4mm, 5mm, 6mm etc doesn't it?
Yes; thank you! Try making something, like you would in a wood shop & use each system for real-world experience. It made me appreciate the metric unit of distance.
This is because it requires a decimal system to count a dozinal scale, but if they were both dozinal then it would be easy as multiplying by 10 in decimal scale
@@netherworldofmind7402 Excellent point.
The point flew so far over your head it reached orbit.
you don't have to memorize those things ... it is not hard at all
I’m always found it interesting that, when written in its own base, every base can be called base “10”, for example binary is base 2, but 2 written in binary is 10. This works for all bases because there is one more than the biggest number characters (because of zero) by definition and to add one more you must use 1 and 0
It's also important to consider that "10" as a 2 digit symbol is possible thanks to the concept of zero. Before the placeholder of zero, civilizations had to use a specific symbol to represent the "10" or complete value in their bases. In a base 10 counting system, we use "11" and "12" to represent those values, but in a base 12 system, the counting would use 11 symbols to represent 11, and a higher magnitude symbol to represent 12. What we see as 17, the old systems would represent with 1*12 + 1*5 which they would see as 17 units in their minds.
@@SerunaXI yep! Numbers are awesome
3:10 "Franctions of 12 are easier"
Fraction of 10: One non-periodic number
Fraction of 12: THREE NON-PERIODIC NUMBERS
Like honestly, as an Computer Science Student, Base 10 isn't the best, but Base 12? Come on, if we want to have some good and usefull system to learn, at least pick Base 16
What do you mean by non-periodic number? Any non-periodic number which is not finite is actually irrational.
@@StarryNightGazing a periodic number for example is 8.3333333.... because it repeats a pattern of numbers, in this case the '3', and never stops to repeat them. Another good example is the number (45/99), that's equal to 0.45454545.... and it repeats '45' endlessly, so it's periodic.
But π for example is non-periodic, it is an endless number but never has a repeating pattern, so no pattern of numbers that is just repeating, so it's non-periodic, like sqrt(2) for example as well
@@hohesc-gangstah1012 I know, that's why fractions of 12 cannot be non-periodic. No such thing exists.
@@StarryNightGazing oh, well, you're right and I'm a complete idio... fractions are rational.... i keep forgettinf because like 7th and stuff look so irrational....
@@hohesc-gangstah1012 no worries, and thanks for acknowledging of being wrong. Not a widely spread virtue these days 👍🏻
the most confusing thing about it is keeping all of the regular base 10 numbers together with the 2 new digits, one of them (X) even looks like 10 in the roman system, and "Dek" also makes you think 10, so there's 2 10-like digits right after each other, kind of confusing. Completely new symbols would be preferable I think, but that would take a bit of working out.
if you use a different base than 10, you usually prefix it with a 0 and the symbol for the appropriate system.
0h10 would be 16 in base 10 (h for hex/base 16)
0b10 would be 4 in base 10 (b for binary/base 2)
Another thing that many people don't think about is endianness. Is the most significant digit of a number at the beginning or the end? For example, westerners use Big Endian in human interaction while Arabs use Little Endian.
The digits 0-9 have precisely the same meaning in both systems, so your point is pointless.
Was it just me? or did he make a mistake at 1:45, saying “do-one for eleven, do-two for twelve”, etc...
I think do-one is thirteen and do-two is fourteen. Am I getting it mixed up?
No, you are right.
That's somewhat of a mistake, though in base 12 system the "Twelve" = Do-two = 14 in decimal
Your are correct.
it’s not a mistake cuz when he wrote 11, he wrote it in terms of the dozenal system. So when he wrote 11, in the decimal system, that would’ve been 13. so he was right. it’s confusing though in the beginning so I understand where you got confused
Your right
He was speaking by the looks of the numbers, not their decimal base equivalents.
Actually, there's yet another number system that no one's talking about when a extra number is placed in between 5 and 6. Its called *Derf.*
Luciano Martinez haha I was literally just thinking that👍
wouldnt that be base 11?
Which is base 11
Neekk0 not necessarily.
@@jackcallister78 why not? :O
Why not just use your fists like:
1✊2☝️3👆 and so on that's way easier than to imagine some lines on your fingers
I was thinking the same...
Isn't ✊ actually 0?
@@User-bx3xw no cause you could simply spin your fist. Let's say you start counting so that the back of you hand is facing you. That would be 0 then 1✊ 2☝️ 3✌...
@@ivankapetanovic4070 Ohhhhhhhhhh, I see.
@@LlamaNeck yes but 1st you only count on one hand
2nd it's harder to communicate over greater distance
And 3rd but that's only my opinion, you can easier get lost when your distracted.
Number of hours, mins, secs falls nicely into the base 12 system too.
Though that isn't because those things are naturally this way, but because they're hangovers of old numeric systems that got grandfathered in. Change the lengths of what we call "hours" and "minutes" and we already could have 20 hours in a day and 50 minutes in an hour even with base 10, no problem.
Because it's already in that system lol
And months
That's right
That's from the sexagesimal system (base 60) that has carried through all the way from the ancient Babylonians. The sexagesimal system is useful as it's highly composite (no surprise that it divides neatly into 12 either).
Their understanding of astronomy was so good and precise for that time and limited technology, that their method of measuring angles in the sky (using 'degrees', 'arc-minutes' and 'arc-seconds') was adopted by the ancient Greeks, Romans, and thereby through the Arabs and eventually the Europeans. They are the reason our hours are still 60 mins, our minutes are 60 seconds, and most likely why we measure angles as 360 (something that fits as part of the sexagesimal system, and therefore the base 12 system too).
Another fun fact about the ancient Babylonians is that our signs of the Zodiac were created by them. They mapped the sky by dividing it into 12 bands of an ecliptic coordinate system. They assigned the exact animals or objects for each part of the year, e.g. a sheep for Aries, a bull for Taurus, twins for Gemini, crab for cancer, etc. So that little animal you learned about as your 'star sign' as a kid was devised by some random guy in 'Iraq' 4000 years ago just trying to understand the sky above him :)
(If I'm wrong on any of this please correct me! I'm going off of memory so there may be some mistakes)
Really interesting video! I'm going to test it out and see if it makes my life easier. As I'm terrible at maths so hopefully this will make my mental sums a little better :D
Try Tau instead of Pi...
- Cogito - Probably not. I recommend sticking with base 10.
Any advantages now? No?
how has it gone?
I've thought of this idea myself, but people keep getting confused when I try to explain it to them. Nice to know it's a real thing.
It wouldn't be as hard as people say. Hard for many adults but not for the new generation. They would excel faster than we did counting in Base 10 if anything. Also we think in Base 12 a bit already more than people think.
If i am 6 ft 2, I am not 62 inches tall. We must convert that to base 12 - I would be 74 inches tall.
If the big hand of a clock is pointing at 3 it's quarter past because 3 =1/4 of 12.
Likewise if it points at 6, it's half past as 6 = 1/2 of 12.
"base" 12 counting has also been one of the more common systems in the west. Many germanic tribes, some greeks, and even the Romans (to some extent) used it. It became common due to uncial counting, that is, counting using the segments of your fingers, (called phalanges, or uncia in Latin), using the thumb as a pointer. there are 3 segments per finger, 4 per hand, thus you can count to 12 on one hand.
I think it is a really important lesson to be aware that some of our concepts are totally arbitrary. As this also is valid for cultural, religious and scientific "certainties" that are very hard to recheck from inside.
This is blowing my mind right now
Regardless of which base you use, some things will get easier, others harder. In practice everything will get harder, because now there needs to be a switch that is counter-intuitive to the norm that also needs to be taught and will come into conflict with the older norm, while fixing some things and creating issues for the same number of things so what ends up happening is problems get shifted around, the total sum results in nothing getting fixed in reality and all you have is the monumental problem of having a base switch resulting in a net negative solution.
I didn't even know this was possible until now
It's the same principle as the binary and the hexadecimal system
We don't need new names for 10, 11, 12 because we already have individual names for it. Ever wondered why it's not oneteen and twoteen? The dozenal system is the reason why. At least that's what I assume. I'm Austrian and in German it's the same way. Pretty fascinating I think.
I remember something similar
I tought it was a dream or something
But I clearly remember it for some reason,
During my kindergarten, the teacher was teaching us the number in the 'BASE 12'
and then I stand and ask "we only have 10 fingers,why don't we just count till 10?"
This video brought back that memory... or dream.
Please think harder, and find out whether it's a dream or real memory, trace yourself
We have 10 fingers, but we have 12 sub-fingers (I don't know what the proper term is) per hand, and thumbs to indicate which subfinger we've gotten to. In this way base60 is base12 multiplied by base5.
Good points made here. You raised some of the points that I realized on my own and I did not realized were considered by others, and I learned a few things. Some of the points made in favor of a base 12 system (i.e. simple divisibility) can also explain advantages of the English vs. Metric system of units, although there is commonly talk about why the U.S. should switch to Metric (which would have advantages as well).
Too many people advocating for base twelve, not enough people advocating for base SIX.
ua-cam.com/video/qID2B4MK7Y0/v-deo.html
Quote:
"For any given base, an integer whose reciprocal has a simple expansion is an integer that base considers important, whereas an integer whose reciprocal has a complicated expansion is an integer that base considers not as important."
― jan Misali
Great ! thank you it answers very well the question of one of my pupil !
2:40 free point free free free
It seems base 12 is a more alien form of counting as you said we would be doing the 6 n 12 base if we had three fingers and toes. Yes base 10 is a bit messer but it is easier and more organized in practice not paper (this may be because everyone does B10 and not 12 idk)
It is definitely only easier because you grew up with it. There really is no objective way to say any base is easier than another base. While higher ones would have you memorize more symbols, lower ones would have you writing longer strings of symbols (base 2 only has 2 symbols {0 and 1} but it can take 4 digits to write numbers that can be written with just a single digit in base 10).
You missed the entire point of what a different number system is
@@SgtSupaman You can codify that concept as "digital efficiency", which is the number of digits you need to write a number multiplied by the number of digits you have to choose from for each place. And if you do that, you find that base 3 is actually the sweet spot, because it's closest to _e_ .
This is why constructing with feet and inches is easier than metric. Cutting things into halves and thirds, etc is easier, divisions that are common everywhere.
Nice Video. Its hard to imagine cause im so used to group the numbers into tens.
Meanwhile Binary: *laughs in 0,1*
1000101 + 110100100 = 111111000
@@oscwavcommentaccount shouldn't that be 111101001 or 489[10] or 349[12]
Base 6 would be better because in base 12 1/5 is written as .1297 repeating
In the language i wrote for my book series i'm working on i made the numbering system in base 12 (so 100 turns into 144) because it makes so much sense, you can quarter, third and half.
Anyone remember the School House Rock song "Little Twelve Toes" which explores this exact thing, even naming the "ten" and "eleven" stand-ins "dek" and "el" and the new "twelve" "do," while also listing the products of multiplication by 12.
This change sounds like itd be super easy, barely an inconvenience!
Base 12 is tight!
It's a little more complicated than you think. In the video he stated do-one is 11, but what he means it's written like 11. It's actually value is 13. All numbers above 9 would have to have their value changed. For example, 25 would have a value of 29, and a value of 25 would be written as 21. Since we're just changing the base number, how you write math stays consistent, so you would still write an equation like this: 11+12=23. But the actual values would be 13+14=27. The difference seem small now, but the difference increases ever do. Ex) 51+24=75 is actually 61+28=89.
Edit: Also, the metric system would need to be adjusted because 1m would now equal 84 cm, etc.
Nice breakdown! You seem to have put some thought into it! Thank you for the explanation!
Until you try dividing by 5 or 7 or 10, it becomes a horrible base...
Me in 50 years:
"Back in my days we had only 10 base numbers!"
From genetics, we know that humans have a dominant allele that codes for 6 fingers on each hand. But only the recessive lived longer and now we are pure bred recessive meaning we only have 5 digits.
So if the dominant allele remained present, or even became the norm. Would we have adapted 12 base instead of 10?
A base 12 system would also make things easier because our clocks use it. Also, we say "dozens" to literally or figuratively refer to a large number, we don't say "tens".
At 3:04 once we started counting in twelves, we dont use fraction of 100 anymore but 144
100 in this case means 144
@@kaloca i thought throughout the whole video, those numbers are in denary so “100” only means 100 but not 144
Base 60 is where it's at. But the reason for everything coming out "clean" is simply the prime factorization of the base. 12 has, 2^2, 3 which allows for more clean fraction representations than 10 = 2^5.
Babylon used base 60 and it was from them that the 360 degree rotation for the circle was implemented. Also, the year is technically a cycle of 360 days and that is truly the number that everything quite literally revolves around. So base 60 is the most appropriate since it uses 2^2, 3 and 5 as its prime factors.
But if cleanliness is of utmost importance then all we need to do is follow the 7 limit system of numbers which would be: 2^4, 3^3, 5^2, and 7^1 which comes out to be a base 75600.
We could easily create a cyclical symbolic notation that allows us to recognize each value based on a recursive structure, which means we would have a base system built into a base system through some recursive definition of a geometric representation that would allow us to quickly recognize the value once we saw it...
Of course, there is a reason we choose not to have perfectly clean numerological representations of value and that is complexity.
So an optimization for complexity:cleanliness would have to be made for the best base N counting system and that would simply be base 60 as it was thousands of years ago and it matches the universe's solar and lunar cycles, music and everything. So we need not go too far to have a perfect world. The reason we don't is that we don't want a perfect world because we don't want to do the work to have it. And perfection starts from within. For some reason, we'd like a perfect world without starting with ourselves but treating us last instead. And this is obviously the problem with human psychology, is the unwillingness to be corrected for even obvious contradictions, let alone the non-obvious ones.
If you want an extremely large base, 55440 is objectively better than 75600. They both have exactly 120 factors, but the latter is 36% larger. And if you don't care about multiples of 11, your best bet for a large base is 5040, which has 60 factors, only half that of 55440 while being 1/11 the size. 5040 was plato's favorite base
So what I’m hearing is the answer to life, the universe and everything is 42
If any one of you can explain why an average person like me should care enough, and then you can also truly define what a base system is and how it matters, then I would consider changing the world for humanities betterment. Because, this video did a horrible job of explaining to a layman like myself of any importance of change, or even a graspable understanding of what exactly the base system functions as,...as far as I can tell, we all use the same numbers and can count to any number, and there isn't a limit to only using 0-9,.... basically, I am lost on the first part 😂
All I know is that 6 is afraid of 7, because, 7, 8, 9,...and if 7 did eat 9, then it's actually a base 9/or 8🤔🤫... And #9 was probably the key to getting out of here, and 6 is our way out the wrong direction, so it may just be that we are in an infinite loop ➿ 8 of some sort, or cycle or spiral of some sort, and doesn't that mean that 0-9 best represent this fact?
@giant9833 Listen, if you don't care, then why are you watching this video? Hmm? Shouldn't you do something "better" with your time and brainwash yourself with mindless ASMR videos? HMM?
@@MarloTheBlueberry well, I did find a video that explains more of the details in a better way, and I do care to a point, but do believe that the base 10 system does make the best sense for us in the end, when considered for the masses...and I was partially joking, and this is evident in reading my comment in it's wholeness...but, either way, maybe I came across too condescending, and I apologize for that.🙏👍
Fun fact: Front-end web developers generally use 12 column grid for developing web apps. This UA-cam page itself might be using 12 column grid. It's coz, 1/4, 1/2, 3/4 of the screen realestate is 3, 6, 9 columns respectively (nice non-fractional numbers).
We do use it to a certain extent when measuring in fractions, inches to feet, etc
Ok, UA-cam is scary, yesterday I thought that it would actually be better if ppl count to 12 and today this was in my recomendation. Has anyone ever had a similiar situation?
I will not have this imperial system propaganda in my recommended.
This has literally nothing to do with it
@@StarryNightGazing Imperial system largely revolves around 3s 6s and 12s. Whereas the metric system is all tens.
You bloody idiot, this has nothing to do with the Imperial System. I was born in a country that uses decimal btw, have used it all my life. I still prefer the dozenal system. Perhaps if your myopic eyes and prejudiced mind would stop judging everything ´12´ as inherently Imperial. Do some research and judge by yourself.
@@fernwehn5925 wooooooooooosh
This is not imperial system propaganda. I love the metric system for how it deals with quantities in base ten. But a dozenal system would make everything even easier.
Try dividing into units of 5 in base 12
Base 10 and base 12 both have two prime factors and prime factors determine whether a fraction is periodic or not. In base 10 it's all combinations of 2 and 5 (2, 4, 5, 8, 10, 16, 20, 25, 32, 40...) that result in non-periodic expressions. In base 12, it'd be all combinations of 2 and 3 (2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27...).
They might be closer in the beginning but pretty soon are just spaced apart as much as with bases 2 and 5. If you want to decrease the periodic fractions, you'd have to go with base 30, or it's more common brother, base 60.
So youre saying not only is it going to be harder but its going to be expensive.....well im convinced
Americans: *laughs in feet
Sorry, but I would rather move a decimal point for converting values vs the mathematical acrobatics required for the more inferior imperial system. How quick can you mentally convert 20 yards to inches vs 20 meters to centimetres? There's not even any reason to debate it. Metric is simply more superior. If it wasn't, NASA wouldn't use it. Keep laughing in feet, while the rest of the world laughs at you.
@@angelus_solus so, you got offended by a metric system joke?
@@angelus_solus The poster didn't say they laughed in feet! They said Americans did. Why are you getting so triggered at a simple joke at Americans by the original commenter?
@@angelus_solus r/woosh
@@angelus_solus r/woosh
It is hard to count in duodecimal so we need 2 more symbols, A & B. There are called [dek] & [el] 10 is which we represent in dozenal: [do]
I've been counting in 3's on my fingers like in the video since I was 5 and I have no idea why I was doing it but it always made math easier for me. I wish I knew who taught me that
I guess the biggest problem I've always found with base 12 is the problem of 5.
5 is pretty common and very easy to work with in base ten. In base 12, it's as difficult to use as 7.
In base ten, there's only one "problem number". In base 12, you have 5, 7 and El.
El isn't a problem number in base 12. 1/E = 0.11111... pretty much as complicated as 1/3 in decimal. 5 and 7 are though.
If you're looking for a system that handles threes well but doesn't have serious issues with five and seven, I'd suggest taking a look at base six
1/5 = 0.1111...
1/11 (seven) = 0.0505...
You can get up to a tenth before things start getting complicated
1/15 (eleven) = 0.0313452421...
Its small size also means it is ridiculously easy to do arithmetic, and there are neat patterns like all primes besides 2 and 3 ending in 1 or 5
@@YourAverageLink Hi, I'm jan misali, and seximal is a better way to count.
"5 is pretty common..." 3 and 4 occur with greater frequency than 5. Outside the context of base 10, 6 occurs more frequently in nature than 5.
Many thanks! I've long thought that Base 12 math would be simpler, but never taken the time to sort out just why. You might want to explore a similar topic. I've heard that Chinese speakers have an easier time with math because the language uses short, one syllable words for numbers and is rigorously logical in how it expresses larger numbers, not having inconsistencies like our eleven and twelve. That makes numbers easier to retain in memory while calculating. There's no need to translate eleven into "ten-one."
I'll also comment on this comment, "Lol here in US we can’t even switch to the metric system like the rest of the world not to mention base 12."
Actually, one reason the U.S. hasn't changed is that much of the English system of measurements are in base 12 (inches in a foot) or variations of it (36 inches in a yard). That's actually better and for reasons much like those that make base 12 math better. And the U.S. hasn't totally rejected metric. We use it where it works well, but ignore it where it is stupid. For instance, in construction the ease of being able to divide by half, third and fourth is a big plus. That's where a base twelve system of length shines. I would not want to build a home using metric.
Too many people advocating for base twelve, not enough people advocating for base SIX.
ua-cam.com/video/qID2B4MK7Y0/v-deo.html
Quote:
"For any given base, an integer whose reciprocal has a simple expansion is an integer that base considers important, whereas an integer whose reciprocal has a complicated expansion is an integer that base considers not as important."
― jan Misali
Guys I thought about this a few months before and now I am seeing this video
I am not the only one , thanks for this video
Im curious how would a number system change impact measurement systems?
"...and other hilarious jokes you can tell yourself"
I had always thought of this as a child. And 13 day calendar is interesting also. Thank-you. I believe if we start using these higher systems of counting and they become in the mainstream curriculum and if society can adapt as a whole (generationally and slowly)then this would mean great evolution for the human being and planet earth. However, there are so many greater matters of urgency to tend to:(
what is 13 day calendar?
"Higher systems" LMAO
What about just teaching about different numbering systems and when some of the more common ones are applicable and continually build on that in school
If we used base 12 then the year 2016 in base ten is 1200 in base 12, this means we have recently experienced what is analogous to the turn of a century
A fird of ten is free point free free free repeating.
Yes, he needs to sort that out. Very grating!
WHY DIDN'T WE THINK TO USE OUR HANDS/PALMS/FISTS?!?!?!
1 Hand + 5 Fingers = 6
2 Hands + 5 Fingers on each Hand = 12
The first one is correct, 1+5 = 6
But how does 2+5 = 12 ?
For real?!...Fine...edit! :)
@@hellodavey1902 I'm still confused lol
@@hellodavey1902 oh wait nvm I saw it ;)
Because its easier to just count the sections of finger on each hand, and use your thumb as a bookmark/pointer.
3 sections per finger, 4 fingers per hand. 5 digits per hand. This means any product of the multiplication of 3, 4 and 5 can be counted on your hands, such as ((3*4)*5)=60 and 3*4=12
And if you used the dozenal system, where you count using five fingers and your palm for six, the primes only show up at finger 1, 5, 7, and 11. Those numbers are never divisible by 2 or 3. They are either primes or products of primes not including 2 and 3.
You should have mentioned that the dozenal system has been in fact in use. There is a 12-hour clock, one foot equals 12 inches, one shilling was a unit of currency worth 12 pence etc.
This is inadvertantly a perfect endorsement for the Imperial measuring system.
Ew gross
Except some imperial units don't use twelve, 3 feet in a Yard, this can be somewhat justified as it is a quarter of twelve.
However weight cannot be justified at all, 16 Oz in a pound and 14 pounds in a stone.
@@matthewloughran73 This is literally the first time I have heard of the stone, but 16 ounces in a pound is as good as 12, because 12 divides into 1, 2, 3, 4, and 6, but 16 divides into 1, 2, 4, and 8, which are also used in binary numer systems.
This comment is inadvertently a perfect example of someone who doesn't even know how their own system works
@@fudgerounds91 it literally means that
I feel like at 1:38 he is using the wrong terminology or I’m just hearing it wrong :) Makes it sound incorrect. How about?
...9(nine), X(dek), E(el), 10(do), 11(do-one), 12(do-two)...1E(do-el), 20(two-do), 21(two-do-one)...
“..nine, dek, el and then for the symbols (10)‘one zero’ we use ‘do’, which is equal to a dozen or decimal ‘twelve’. From there we have ‘do-one’ for (11)‘one one’, ‘do-two’ for (12)‘one two’... and ‘two-do’ for (20)‘two zero’, that is equal to two dozen or decimal ‘twenty four,.
What a to-do to die today at a minute or two to two.
... a thing distinctly hard to say but harder still to do.
Along with number of fingers, isn't the compatibility (or sometimes lack there of) of the number 0 another reason to take base 10. (For eg, elimination of decimals). Though I understand this function can still be used with base 12
Like many other conventional notations and systems. There might be better ones but the transition is hard to implement. How do you change something that people use and learn continuously on different levels?
The most common bases are 5, 10, and 20.
Ancient Sumerians & Babylonians: We don't do that here.
We’ll get on that right after the USA goes metric. ;)
Year 2200, humans have colonized Mars, split into several sub-species with wildly varying abilities, everyone can merge with AI from birth. The New Americans are still debating whether to switch to the metric system. But nobody cares, the AI chips do all calculations for them anyway...
Are there any decent books out there that go into using base 12 for arithmetic, which would provide a sufficient foundation for exploring more advanced mathematics?
The finger counting method is the way my parents taught me to count. They weren't like "oh use base 12 over base 10", but moreso, it's easier and less energy used. Also, in elementary school our teachers were trying to get kids to stop using fingers for math and do it on our head. I got away with this for years by doing this.
It's not mentioned in the video, but you can use your non-dominant hand to count the "10s" place and your dominant hand to count the ones place.
So, in base 10, can count up to 144.
"The most popular number bases are base 5, 10, 20"
Base 2: Am i a joke to you?
Yes. Every computer (unless its quantum) uses base 2
"A third is 40%"
Should be four-do per gross 😉
@@StarryNightGazing The Dozenal Society of America used to use p/g for pergross, but I don't know what the current consensus is. So in base 12, 1/3= 4/10= .40= 40 p/g
@@isaacbruner65 There's no consensus, which is the entire problem with the dozenal movement - nobody could ever agree on anything. Even the thing about which digits to use for ten and eleven was a constant argument between the American and British groups. ↊ and ↋ eventually got into Unicode and it looked like the other side pushing X and E started to switch over, and then there wasn't much discussion about it since. (Even these past couple weeks we have some new person inventing new digits for it in their Reddit posts!)
Then you have the "how to read the numbers" issue, which some people want to say "do", "mo", "gro", other people want to say things like "thirzeen" or "forzy-five", yet other people want to say all numbers in SDN.
I can't remember whether anyone discussed what to use for pergross/perbiqua but I have always just used % because % means "/100" which is still true in dozenal.
I use base 69, it might seem chellanging but once you get used to it it's pretty nice.
personally I use base pi (base 3.14159265359...ect) took a while to learn but I think it makes the most sense
any carpenter can tell you that 12's are much easier to use once you get used to it. If measurements were in 10's it would be a nightmare
I guess they don't have carpenters in Europe.
No, we dont
That's right. People that do the same thing like a carpenter they are called tischler. And they also know that a quarter is 25% and not 30. Haha
I blame the French!
You mean cm, mm, micron, micrometer etc? Yeah, that's so difficult to understand that we use it for space travel...
the octal system cleans up fractions too. Can you talk about that?
AnteConfig Octal is also easier for converting to binary.
But 8 only has four factors where 12 has six
Base 8 is actually worse than 10
1/3 = 0.252525252525...
1/5 = 0.1463146314631463...
1/7 in octal system = 0,111111111111111... 😂
People that use inches and feet: "Way ahead of you"
I used to work in a club, stocking up the bars. A case of beer came with 24 bottles. My maths really improved through thinking in terms if 24.
I've never really considered that the reason we use base 10 is because of our anatomy (though I have often wondered why we didn't use higher bases with better fractions). But, the fingers on our hands would be base 11 (with 10 different fingers and putting them all down to mean zero)... Perhaps even our ancestors realized how stupid base 11 would be, though (1/4 would be .282828... 1/3 would be .373737... and 1/2 would be .555..., and the multiplication tables would look like 2x4=8; 2x5=A; 2x6=11; 5x3=14; 5x4=19; 5x5=23).
SgtSupaman this is very long of repeating decimal
Nope, you just described base 10. Base 11 would be if all fingers down somehow represented 1 unit.
@@StarryNightGazing , you aren't quite understanding what I'm saying (or what you're saying). Having base x means using x unique digits (including 0) before you move to the next place (x^0, x^1, x^2, and so on). For instance, base 10 has 10 unique digits from 0 to 9 before it starts repeating digits (10 is made of the digits 1 and 0). Because the basic way we count on our fingers can uniquely represent 0 (with all fingers down) to 10 (all fingers up), we have 11 unique digits, which means the typical way of counting on our fingers is base 11, not base 10.
Decimal: I'm the best numbering system.
Dozenal: No, I'm the best!
???: Amateurs.
Decimal: What was that punk?
Seximal: Amateurs.
We should all be counting in base 120. It's dvisible by 2,3,4,5,6,8,10,12,15,20,24,30,40,60. You could divide your pizza pretty much in any number of slices and still calculate fractions without decimals. And we do have a bunch of alphabets to chose from for the symbols.
So are x and e variables? What values do they represent