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

The Old Babylonian arithmetical system was a base 60, or sexagesimal floating point system -- an ancient precursor to the Hindu-Arabic base 10 system that we use today. However there is a big difference, due to the fact that 60 has a factor of 3, while 10 does not! Why should that be so important?

We will explain that, and much more about this remarkable period of time -- ancient Mesopotamia, from the Sumerians to the Akkadians to the Babylonians, culminating in a golden period for clay tablets around 1900 - 1600 B.C.E. A highlight is that we go through an ancient Problem Text that illustrates their concrete approach to arithmetic, their step by step explanations of procedures, and reveals that they had an effective understanding of quadratic equations.

We also discuss the role of multiple or multiplication tables. Daniel Mansfield and I have investigated these and concluded that they should really be called something like "multiplication / division tables" because their use extends to the most difficult operation in elementary arithmetic -- namely division.

There is much to be learnt by modern educators and students of mathematics by appreciating Old Babylonian arithmetic, not just as a curious historical relic, but as a coherent independent system that has demonstrable computational advantages. And that sheds an uncomfortable light on the ambiguities and logical weaknesses in our current arithmetical systems, as we shall investigate in future videos in this series.

Uniformity of thought can be an impediment to our ultimate understanding, and a historical perspective is one of the best ways for recognizing and transcending our own limitations!

The (lovely) paper I reference is by Donald Knuth, Ancient Babylonian Algorithms, Communications of the ACM, vol. 15, issue 7, 1972, 671-677.

A big thanks to all my Subscribers, Members of the Wild Egg Maths channel, and Patreon supporters!

Video Content

00:00 Intro to the Mesopotamians!
05:29 Birth of writing (3500 B.C.E)
10:07 Sexagesimal arithmetical system
16:47 The Babylonian scribes relied on tables
20:15 Old Babylonian reciprocal table
24:57 Multiplication/division tables
30:01 Combined multiplication/division tables

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Solving Polynomial Equations: https://www.youtube.com/playlist?list=PLzdiPTrEWyz7hk_Kzj4zDF_kUXBCtiGn6
Exceptional Structures in Maths and Physics via Dynamics on Graphs" https://www.youtube.com/playlist?list=PLzdiPTrEWyz5HBT_Yo1G4DfeqUfI9zkKM
Triangle Centres: https://www.youtube.com/watch?v=iLBGXDSUohM&list=PLzdiPTrEWyz6VcJQ5xcuqY6g4DWjvpmjM
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Видео Number Systems Ancient to Modern 2: the Babylonians | Sociology and Pure Maths | N J Wildberger канала Insights into Mathematics