@@johnboy221B Because the numerical representation of our number system is base 10. If we used base 12 (e.g. the digits 0, 1, ..., 9, A, B similar to how hex numbers get displayed), 2*12=24 in base 10 would be "20"=2*12^1+0*12^0 in base 12.
@rwindex I know :D. I guess I should have phrased my question better. I just mean that we use the decimal system simply by convention. A System as you describe above (where 10=a and 11=b) seems equally well suited for multiplication to me. I don't see why the decimal system would be any better for multiplication other than that we are accumstomed to it. For multiplication even base 11 or base 13 seem equally viable. I thought that maybe the author of the original comment had some insight or some interesting reason that I cannot think of.
you can count to 1024 with two hands if you use binary btw. (and to 1.048.576 if you also use your feet). what i want to say is: different systems are good for different tasks. 12/24/60 is great for time related things. 360 is great for circles and navigations 10 is great for counting, distances and volumes 2 and 16 are great for computer science just imperial measurements are crap in everything.
The actual core of the problem is linguistic: the language is decimal, so people naturally find it easier to think in decimal, even if it limits the available easy calculations; it means that you're _not_ having to do non-trivial mental arithmetic as you move up and down throughe units, as that information is encoded in the base of the number system. If we wanted to make the most of divisibility, we should change the base of our number system to a _superior highly composite number_ (to employ a bit of maths jargon), obviating the need for mental arithmetic when moving between units of a particular measure and the numbers we're used to dealing with every day. Of course, this is very unlikely to ever happen; the fundamental components of a language are the most resistant to change, as people use them all the time and it would take a lot of un-learning and re-learning to alter them. I think that's why most of the few remaining irregular plurals in English (notwithstanding later loanwords which retained their foreign plural) are things that would come up frequently in everyday speech: people, (wo)men, children, sheep, oxen, geese, fish, feet, teeth. And if decimalization was expensive, one can only imagine what it would cost to change the number system. It would probably bankrupt the country. And even if it succeeded, unless the whole world follows suit, you've just moved the conversion headaches elsewhere (and multiplied them to an astronomical degree). So it's completely impractical, but if it _were_ possible to somehow magically intervene, the best solution would be to adopt a numerical base of 12 or - at a push - 60 (the other options are probably either too small to be useful, or too large to be manageable).
So in a base 12 we can divide without a remainder by two more numbers. So what? We will also have to use two more digits. Besides, counting fingers is more natural than counting knuckles.
I'd add that time, unlike the other measurements, is based on more celestial and seasonal standards rather than what is conveniently near, like our arms, fingers, or counting stones. A solar day is still better divided into 12 hours, especially based on solar position. By virtue, using a circle for time divides well into degrees (360°) over using radians (2π) or gradians (400), but you still "could" use a different unit of measurement for time. Nowadays, the second is standardized based on the resonance of cesium-133, and since Jan 1, 1970, UNIX has been counting seconds for the use of computers worldwide.
I want to know where the 360 comes from. I suspect it is related to the 12 hour clock, later the 24 hour version, and the most convenient number for converting time into a decimal compatible format, for dividing the equator up into equal segments that align a clock to the stars... ?
@MadScientist267 the greeks first got their sundials (and partly their math) from the Babylonians; the Babylonians used a base-60 number system (see 2:40)
@@cube2fox Base -2 would be even better. It retains the easier Multiplication and division and makes negative numbers very intuitive. Addition is a little harder to intuit than in base 2 (still easier than base 10 but different enough that looking at it with a base 10 coded mind it seems hard untill you redevelop the intuition) but that is almost always rote memorized before the intuition on how it works develops anyways. and subtraction ends up working exactly the same as addition getting rid of an entire course. A highly composite number is still better for fractions though.
Is it though? I understand the logic of having more options for division, but the true is that in most situations the decimal system would give you a simpler time to work on and a simple numbers, even when working decimals, rather than just having more composite and using having a few more options that would expeceficially be useful in certain situations. That is to say, if you don't have a proper composite to work with with the base 12 or base 60, then you are in more problems than with the base 10. Also, in multiplication and measurement, the the system would work much better: Personally, I like base 10. Then again, who know what I would think if I had grown with a better system, whatever shape that might take.
Thanks a lot! I'm semi-retired and my background is teaching English as a foreign language. I had zero experience of making videos but a lot of curiosity and an interest in history
Ok that actually makes a lot of sense. This leads me to an obvious next question... Why are there 360 degrees in a circle? I know they just about have to be related given we originally based time on the behavior of the sky [earth]... but it is peculiar as it would seem to be based on 36, a clean multiple of 12... but not 24... 360 is divisible by 24, giving a clean 15 degrees but we're out in the weeds here... More "legacy shenanigans"? I'd watch a video on it... 🤣
I think that was during the French revolution. A year has 12 months with 30 days and the 5 days that is left by the end of the year would be public holiday. A week would have 10 days, so a month would have 3 weeks. But maybe the sovjets also tried something alike.
@@simplypodly Not just lucky, a holy number. It's likely because they loved astronomy, and you can see 7 major celestial objects with the naked eye: the Sun (Sunday), the Moon (Monday), Mars (Tuesday; dies Martis in Latin), Mercury (Wednesday/dies Mercurii), Jupiter (Thursday/dies Iovis), Venus (Friday/dies Veneris), and Saturn (Saturday).
It's interesting that time is mostly scaled in multiples of a hundred, just like money. 100 milliseconds in a second, 100 microseconds in a millisecond, 100 nanoseconds in a microsecond, etc.
There is alot to be said about the "best base". I have seen decent arguments that 60, 12, 6, 4, 3, 2, -2, and -1-i are all better bases to count in than 10. Paradoxically the large highly composite bases are great at representing fractions and the small low radix bases are better at efficiently representing large numbers. Now we can get away with just writing in bases ten for some systems that actually represent other bases like currency and time, especially when the other base is close to or a multiple of 10, 12 and 60. There are alot of issues with the metric system, that is stemming from the fact that it is created by the same people that brought you the french revolution. It is really just whatever those egotists thought was best and not a system that had evolved over millennium. It isn't even very good for modern science, it isn't as good as the alternative for human usage, the fact that it is still around is a testament to european hardheadedness.
But all you smarty pants learned counting and math in school didn't you? In what base? And for how many hundreds of ages? Instead of using only 1 base you used dozenal decimal 20-nal 60-nal and i don't know what other nals. And now Europe is the culprit.
Do you multiply more or do you divide more? ;) Base 10 is better at going up
Why though?
@@johnboy221B Because the numerical representation of our number system is base 10. If we used base 12 (e.g. the digits 0, 1, ..., 9, A, B similar to how hex numbers get displayed), 2*12=24 in base 10 would be "20"=2*12^1+0*12^0 in base 12.
@rwindex I know :D. I guess I should have phrased my question better. I just mean that we use the decimal system simply by convention. A System as you describe above (where 10=a and 11=b) seems equally well suited for multiplication to me. I don't see why the decimal system would be any better for multiplication other than that we are accumstomed to it. For multiplication even base 11 or base 13 seem equally viable. I thought that maybe the author of the original comment had some insight or some interesting reason that I cannot think of.
you can count to 1024 with two hands if you use binary btw. (and to 1.048.576 if you also use your feet).
what i want to say is: different systems are good for different tasks.
12/24/60 is great for time related things.
360 is great for circles and navigations
10 is great for counting, distances and volumes
2 and 16 are great for computer science
just imperial measurements are crap in everything.
The actual core of the problem is linguistic: the language is decimal, so people naturally find it easier to think in decimal, even if it limits the available easy calculations; it means that you're _not_ having to do non-trivial mental arithmetic as you move up and down throughe units, as that information is encoded in the base of the number system. If we wanted to make the most of divisibility, we should change the base of our number system to a _superior highly composite number_ (to employ a bit of maths jargon), obviating the need for mental arithmetic when moving between units of a particular measure and the numbers we're used to dealing with every day.
Of course, this is very unlikely to ever happen; the fundamental components of a language are the most resistant to change, as people use them all the time and it would take a lot of un-learning and re-learning to alter them. I think that's why most of the few remaining irregular plurals in English (notwithstanding later loanwords which retained their foreign plural) are things that would come up frequently in everyday speech: people, (wo)men, children, sheep, oxen, geese, fish, feet, teeth.
And if decimalization was expensive, one can only imagine what it would cost to change the number system. It would probably bankrupt the country. And even if it succeeded, unless the whole world follows suit, you've just moved the conversion headaches elsewhere (and multiplied them to an astronomical degree).
So it's completely impractical, but if it _were_ possible to somehow magically intervene, the best solution would be to adopt a numerical base of 12 or - at a push - 60 (the other options are probably either too small to be useful, or too large to be manageable).
The french made 10 hour watches, but did'nt succeed.
So in a base 12 we can divide without a remainder by two more numbers. So what?
We will also have to use two more digits.
Besides, counting fingers is more natural than counting knuckles.
Interesting video! Lots of points I've never considered before
Some time guides are metrisised, if that is even a word, where an hour is divided into a hundred. So a time of 1.5 hours would be an hour and a half.
1.5 hours would always be an hour and a half regardless of any metrisisation. That's because we are using normal numbers to count the hours.
I'd add that time, unlike the other measurements, is based on more celestial and seasonal standards rather than what is conveniently near, like our arms, fingers, or counting stones.
A solar day is still better divided into 12 hours, especially based on solar position. By virtue, using a circle for time divides well into degrees (360°) over using radians (2π) or gradians (400), but you still "could" use a different unit of measurement for time.
Nowadays, the second is standardized based on the resonance of cesium-133, and since Jan 1, 1970, UNIX has been counting seconds for the use of computers worldwide.
I want to know where the 360 comes from. I suspect it is related to the 12 hour clock, later the 24 hour version, and the most convenient number for converting time into a decimal compatible format, for dividing the equator up into equal segments that align a clock to the stars... ?
@MadScientist267 the greeks first got their sundials (and partly their math) from the Babylonians; the Babylonians used a base-60 number system (see 2:40)
Australia went metric and decimal isefin five years. We didn’t whinge or complain about it, but it was the best thing we ever did.
Dividing by 3 had always made me uncomfortable for some reason. Now I understand why, and why I found the time division of 3 much easier.
Base 12 in math would be much better for teaching imho
Base 2 would arguably be even better because it simplifies algorithms for multiplication and division.
@@cube2fox Base -2 would be even better. It retains the easier Multiplication and division and makes negative numbers very intuitive. Addition is a little harder to intuit than in base 2 (still easier than base 10 but different enough that looking at it with a base 10 coded mind it seems hard untill you redevelop the intuition) but that is almost always rote memorized before the intuition on how it works develops anyways. and subtraction ends up working exactly the same as addition getting rid of an entire course. A highly composite number is still better for fractions though.
No
That is how I will educate my children
The 360 degree circle convention comes from the Babylonian sexagesimal system as well and is highly composite.
Really good video I had always wondered myself without realising!!
Is it though?
I understand the logic of having more options for division, but the true is that in most situations the decimal system would give you a simpler time to work on and a simple numbers, even when working decimals, rather than just having more composite and using having a few more options that would expeceficially be useful in certain situations.
That is to say, if you don't have a proper composite to work with with the base 12 or base 60, then you are in more problems than with the base 10.
Also, in multiplication and measurement, the the system would work much better:
Personally, I like base 10. Then again, who know what I would think if I had grown with a better system, whatever shape that might take.
Yeah you're right
Metricity is sooooo nice
Warmbru, I love you man! Your videos are the best. What’s your back story?
Thanks a lot! I'm semi-retired and my background is teaching English as a foreign language. I had zero experience of making videos but a lot of curiosity and an interest in history
Ok that actually makes a lot of sense. This leads me to an obvious next question... Why are there 360 degrees in a circle? I know they just about have to be related given we originally based time on the behavior of the sky [earth]... but it is peculiar as it would seem to be based on 36, a clean multiple of 12... but not 24... 360 is divisible by 24, giving a clean 15 degrees but we're out in the weeds here... More "legacy shenanigans"?
I'd watch a video on it... 🤣
The Babylonians used six times sixty as the next step up in counting.
Didn't the Soviets try to implement a new "week" for their calendar?
I believe that is true.
I think that was during the French revolution. A year has 12 months with 30 days and the 5 days that is left by the end of the year would be public holiday. A week would have 10 days, so a month would have 3 weeks. But maybe the sovjets also tried something alike.
Why is the week seven days?
Do you really not know?
No he doesn't know, otherwise he wouldn't have asked. But apparently you do. Enlighten us bbryant460, why are there seven days in a week?
Babylonians thought it was a lucky number.
@@simplypodly Not just lucky, a holy number. It's likely because they loved astronomy, and you can see 7 major celestial objects with the naked eye: the Sun (Sunday), the Moon (Monday), Mars (Tuesday; dies Martis in Latin), Mercury (Wednesday/dies Mercurii), Jupiter (Thursday/dies Iovis), Venus (Friday/dies Veneris), and Saturn (Saturday).
❤
The French, it's always the French! VLLC (Milei). Thank you for the video!
Thanks for watching.
comment for support~
It's interesting that time is mostly scaled in multiples of a hundred, just like money. 100 milliseconds in a second, 100 microseconds in a millisecond, 100 nanoseconds in a microsecond, etc.
That's because "milli", "micro" and "nano" are decimal identifiers, each being 1000 times smaller than the former. It's not specific to time.
There is alot to be said about the "best base". I have seen decent arguments that 60, 12, 6, 4, 3, 2, -2, and -1-i are all better bases to count in than 10. Paradoxically the large highly composite bases are great at representing fractions and the small low radix bases are better at efficiently representing large numbers. Now we can get away with just writing in bases ten for some systems that actually represent other bases like currency and time, especially when the other base is close to or a multiple of 10, 12 and 60.
There are alot of issues with the metric system, that is stemming from the fact that it is created by the same people that brought you the french revolution. It is really just whatever those egotists thought was best and not a system that had evolved over millennium. It isn't even very good for modern science, it isn't as good as the alternative for human usage, the fact that it is still around is a testament to european hardheadedness.
AI trash translation
Because it's stupid
But all you smarty pants learned counting and math in school didn't you? In what base? And for how many hundreds of ages? Instead of using only 1 base you used dozenal decimal 20-nal 60-nal and i don't know what other nals. And now Europe is the culprit.