Number Systems Ancient to Modern 2: the Babylonians | Sociology and Pure Maths | N J Wildberger

[@robharwood3538]

Love these topics! Super fascinating! Human history is so incredible when you start to really think about it. Even just the 'history of clay' turns out to play a huge role in our intellectual development!

[@brendawilliams8062]

Tobekie Tepee even has arrows on so much. So interesting.

[@mrborisak]

Love to see videos like this, thank you

[@njwildberger]

Thanks and you’re welcome!

[@someoneanonymous7380]

Why base 60 would be chosen in the first place is still a bit mysterious. That 60 is simply a highly composite number with many factors and therefore convenient is a common theory offered but it leaves me unsatisfied because it doesn't put into context what was being done that made 60 and its factors highly desirable to work with. The ideas offered by Siemen Terpstra and Ernest McClain are the most compelling I've read so far. To keep it short, the Babylonians were a musically oriented culture. They needed regular numbers to handle a 5-limit tuning system, and supposedly they were in the habit of visualizing tone numbers (or musical notes) on a hexagonal grid. With 60 in the center of the hexagonal grid, 6 other whole numbers surround it. With 3600 in the center, 18 other whole numbers surround it, and so on. 1st axis: 60 * 3/2 (perfect fifth) = 90 60 * 4/3 (perfect fourth) = 80 2nd axis: 60 * 5/4 (major third) = 75 60 * 8/5 (minor sixth) = 96 3rd axis: 60 * 6/5 (minor third) = 72 60 * 5/3 (major sixth) = 100 Each axis represents a complementary pair within the octave, because for example 3/2 * 4/3 = 2. One reason these hexagonal grids are nice musically is that they allow one to easily locate all possible 5-limit chords, especially the major and minor triads. Is music really important enough to determine your culture's preferred numerical base? Maybe not now, but back then it was often seen as the framework for everything and shaped cosmology. Ancient metrology and calendars are often compatible with musical thinking for better or for worse.

[@njwildberger]

There are a lot of potential reasons that people have put forward for them adopting a base 60 systems. I think however the metrological explanation is probably the most convincing. Perhaps multiples of 6 got involved because of same taxation law: maybe the local king or temple wanted one sixth of your grain etc. My own guess is that the musical explanation would not be powerful enough.

[@michielkarskens2284]

@@njwildbergeryou give the answer yourself. They are purely number theoretical. A true floating radix point/ komma system. Base 60 is the only base which in place value notation has a floating point. The reasons why are all number theoretical.

[@michielkarskens2284]

@@njwildberger They chose b60 because it reveals a perfect order of primes and complete predictability of all primes >5. The problem/ question of the irregular primes is reduced to a matrix of 16 columns ordered by the minute. The same 16 seconds of every minute are not the product of 2, 3, and 5. These 16 are the 14 primes 7-59, *.01 and *.49. Coincidentally the n^2 of the 16 are exclusively numbers ending on *.01 and *.49 in base 60.

[@peterjansen7929]

This is a very interesting video - thanks a lot! The system has its advantages, but obviously also its limitations, many of them severe. It isn't exactly difficult to divide 7 by 7, but the need for reciprocals might have led to even trivial problems not being solved, unless they had special procedures for dealing with exceptions. But even if they did, then it is unlikely that they would have managed to divide a multiple of 7 by 7 if it had lots of digits, and here "lots of" means 3 or possibly even 2, with the first digit large enough. Sociologically, it is an interesting question what Babylonian teaching was intended to achieve: The problem with the quadratic equation is good at getting a procedure into a pupil's head, but it raises the suspicion that the reason why the procedure works was never taught. If so, the pupil was regarded as a programmable instrument, taught to function, not to understand. That would explain the Prussian style of presentation of not leaving out the obvious statement that the reciprocal of 1 is 1. Is there any known evidence either way? Perhaps there are also writings explaining how the pupil can solve problems involving quadratic equations in more general cases and why these procedures work. Alternatively, perhaps there are written records that urged teachers to act more directly in the Prussian way, whiich was to tell future instuments that they should leave the thinking to the horses, as those have bigger heads. Whether there is a further similarity with old Prussia in most of the teachers themselves also being clueless instruments is something we will probably never know. On the whole, though, I am glad that my computer never returns a message "Division by 7 error" instead of showing the result, but it would be great if computers and calculators were to display whether results are fully accurate or approximations..

[@NuYiDao]

Perhaps base 60 derives from the early notion that a year was 360 days in length. This was expressed in the word Mithras (360) which was modified to Mithrais (extra i=5) in gematria when accuracy improved.

[@KaiseruSoze]

I agree with what you're saying. Numbers are context dependent and arise in different ways depending on the need. Number systems are systematic ways of "naming" or refering to stuff in concise & useful ways. The choice of a base & "decimal" placement provides a way to render the concept of a number in physical & transportable way (communicates the concept.) E.g., the number 2 under the radical sign is an exact representation of whereas 1.41421356237 is not. Same with pi, 1/3 or 1/7. Nature doesn't have any problems with doing it's thing. It is exactly what it is & does exactly what does just fine. And real numbers do fall short of the "exactness" that nature seems to work with. QM is proud of having measured properties of the atom to 12 & even 22 decimal places. Math can measure pi out to ... decimal places. Something seems out of place to me.

[@ali51717]

as someone from Iraq, I am really proud of it!

[@njwildberger]

@Ali Abdul-Kareem It is indeed something to be proud of. I only hope that large scale archeological investigations will continue in the years to come in your country -- there is so much more there to be discovered, of the foremost importance I would imagine.

[@robertnottoprefer2957]

Helle sir can u make video about universals and particulars i mean is there numbers length beauty as real object in other world or its made of our brain it is philosopical but related with math

[@Marvelous771]

Remarkable lecture... I enjoyed it very much .. Konwing that Babylobians were using base-60 number system is astonishing. I'm not sure if Babylobians had come up with some concepts in group theory... let's know if there are something relevant in some sense

[@brendawilliams8062]

They had 0. It just was different in it’s way of getting to it.

[@gems34]

Using the sexagesimal system to divide by seven would Babylonians, perhaps just multiply by 2 and divide by 14?

[@Drbob369]

Amazing

[@tagadasir]

Nice teach you .

[@brendawilliams8062]

Thankyou

[@arekwittbrodt]

And I thought that dozenal system is beautiful ;-)

[@whig01]

Base 420 would have taken care of those pesky divide by seven cases.

[@santerisatama5409]

At 420 I was too busy doing my munchies to be able to think that far...

[@whig01]

It's a green number system.

[@sharonjuniorchess]

Hang on a second I just need a minute to let that sink in. It might take me an hour or two to puzzle out just what is going on here. Lets start with a circle. Round and round we go. My head is dizzy with all the possibilities.

[@arjyadebsengupta8159]

Maths is the language of reality