Today's lesson: our days have 24 hours thanks to Sumerian mathematics

in #mathematics7 years ago (edited)

Another chapter in Today's lesson series, in this opportunity we will be talking about some curious things in relation to the origins of the way we measure time.

time24.jpg

Have you ever thought about why the day have 24 hours instead of 10 or 100, and why one hour has 60 minutes (instead of 100 or another amount), and one minute has 60 seconds?


Well, everything has to do with the Sumerians, a civilization from around 6,000 years ago ...

We will start with the most basic, and leave a surprise for the end: The reason for using 60 is because the numerical system of the Sumerians (which was later passed to the Babylonians) was a "Base 60" system (unlike the Base 10 system we have today).

That is, we have 10 digits (from 0 to 9), the Sumerians had 60 different digits (well, technically 59, since they had not invented zero yet, but we can ignore that detail for today). Which means these people needed to memorize 60 different digits, which certainly was not an easy task, particularly when making heavy calculations (such as memorizing multiplication tables, for which purpose they invented all kind of shortcuts).

These are the digits they used:

Babylonian_symbols.gif

This was not only the first known mathematical system, but also one that gave us... the "place" concept: Just as, (in the decimal system), 2 can be 2 or 20 or 200, depending on the digits place, so could a Sumerian 2 mean 2, or 120 (2 x 60), and so on, depending on the place. | Source


But, why 60? It could have been that they figured out the fact that the number 60 is a practical number for various reasons, for example it has 12 factors (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60) that makes the job of doing divisions much more easy (if you try it, you can see for yourself how easy it is to divide a minute, or an hour between any of said factors), which also, makes facilitates the work when doing astronomical calculations, by the way, the 360 degrees of the circle (which is nothing more than 6 * 60) was also a discovery from the Sumerians.

The accepted reason for the use of a sexagesimal system is that it was based in astronomy and the desire of the Babylonians to develop accurate calendars to chart the turning of the seasons and predict the best times for planting, extremely importantly in a culture with a strong agricultural base | Source

What about the 24 hours? That does not seem to make sense, and I would not have it except for a curious observation.

I need before you continue to follow the flow and put the tip of your thumb together with the tip of the index finger, essentially making a "zero" with your hand. What I am going to teach you today is how the Summaries managed to make their calculations.

Could you live in a world with no digital way of making calculations?
While holding that position, now look at your index finger and you will notice that it is divided into three parts (due to the internal skeleton under the skin), so while touching the tips of the thumbs and forefingers, count "one" out loud (or internally for yourselves).

Now, lower the tip of your thumb to the second part of the index finger and count "two." Now go down to the third part of the index finger and count "three". Repeat now with the other fingers (following with the big finger and ending with the little finger) and you will realize that you can count up to 12 using only one hand, and obviously you can count up to 24 with both hands.

Amazing and very curious, isn’t it?

Additionally, notice that the reason why we now have a decimal system (10 digits) is precisely for a similar reason: Having 10 fingers make it easy to count for us, and so it is natural to use a system based on ten.

Finally, notice that the number of symbols we use to count is something totally arbitrary. It is quite possible that another advanced civilization somewhere in Space with only 6 fingers for example, use a system with Base 6, and the same can be applied to another civilization with 8, 16, 20 or any number of limbs that make it easier to count mentally.

What do you think of today’s lesson? Were you able to learn something new?

Feel free to share your opinions and participate in the discussion

If you enjoy the post, make sure to read the next chapter in where we will be talking about the origins of a year, and what does it means?




References

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Very interesting, we owe much of our current inventions to the creativity of the Sumerians. Math, farming, and writing!

Thanks for sharing

Exactly right! They were pretty advanced for their time.

wow i never knew any of that. fascinating and thank you, will be checking out more of your posts.

The truth that I had never asked these questions, but now that I read it seems incredible to me as everything that started, thank goodness that is 10 digits what we like, imagine memorizing 60?

It would probably be a little more difficult. But I suppose one could get used to it.

This is the stuff I adore to learn about! Thank you for the awesome post! The "12 phalanges" gave me an "Aha!" moment! Can't wait to read more of your posts!

I really appreciate your kind words man!

MIND BLOWN! I love learning shit like this.. the finger counting thing seriously blew my mind! Those damn Samaritans were some smart people.. thanks for teaching me something new.
Knowledge is power

Happy to provide some good knowledge for you pal!

Damn you Sumerians!!!!

This is why I NEVER have time for ANYTHING!!!

Couldn't they have not invented more hours? :p
Cheers!

Do not worry, in the future we will figure out ways to "get" more time, using things like virtual realities with a slower timer.

Happy to see you here man!

I'd really like that... and that is definitely a "deep" thought... makes me wonder no doubt.

Very interesting, there are many numerical systems that we have used throughout history, imagine using the Babylonian or even Roman numerals in modern times, I guess we would get used to it, but I guess it would give us a lot of difficulty when it comes to making some calculations.

I think the same, children would have a harder time in school learning mathematics if we used the old systems.

Luckily we don't! And besides, eventually we will probably make this calculations instantly using synthetic ways.

Hah very clever! The finger counting kind of reminds me of the "hands" measurement which is actually still used in measuring the height of horses. You can measure with whatever you've got handy, really - though it's only a matter of time before someone starts thinking of standardization.

I did not know about the horse measurement style! Damn!

It just shows we can all learn from each others in this community!

Cheers!

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