Sept 30 Blogging for Babylonian ‘algebra’ from Crest of the Peacock

 

"In particular, we own to the Arabs in the field of mathematics the bringing together of the technique of measurement, evolved from its Egyptian roots to its final form in the hands of the Alexandrians, and the remarkable instrument of computation (our number system) which originated in India; and the supplementing of these strands with a systematic and consistent language of calculation which came to be known by its Arabic name, algebra. "

                                                                                      -  from Crest of the peacock, page 7

I like this quote because it show how so many nations gathered together their knowlege to reach an outcome on what we are learning today.  

Before the development of algebra and algebraic notation, Old Babylonians used symbolic notations to state general mathematical principles. They used words in their language to describe the mathematical terms. For example, ush means length, sag means breadth, asha means area. So  ush multiply by sag result asha. The Babylonians were also able to solve quadratic equations in its symbolic variant very similar to our modern day notation. 

Math is certainly not all about generalization and abstraction, it is about the thinking behind these generalizations. Without algebra, we could try stating general or abstract relationships verbally with words (jsut like the Old Babylonians). However, this adds more complication to understanding the gerneralizations or abstractions. 

Sept, 28 Babylonian style base 60 mulitiplication for #45

 Using the example given, I came up with this table below.

The Crest of the Peacock by George Joseph

 

Three things that surprised me were:

  1. European trajectory 

The ideology of European superiority has surprised me. The article mentions "the contributions of the colonized peoples were ignored or devalues as part of the rationale for subjugation and dominance" (p.4) . In other words, Europeans were taking credits for the discoveries done by other nations, and claimed those were their findings. I think we would call this plagiarism in our modern day society. Other nations such as China, India, and the Hellenistic world have contributed to the development of mathematics, and I agree with the main message that "it is dangerous to characterize mathematical development solely in terms on European developments" (p.12).

2. Figure 1.4 The spread of mathematical ideas down the ages

I am amazed by the intelligence of our ancestors. Regardless of time and place, ancient people in Egypt, Greece, Mesopotamia, India, Arab world, China, and Mayan empire were all under construction for mathematical concepts. Each nation had their own way of approaching and understanding mathematics, and they would transmit their ideas to each other, all working towards the development in mathematics. 

3. Cross-cultural contact between China and India

Besides mathematics, works on astronomy and medicine were also exchanged between these two nations as early as 500 BC (which over 2500 years ago). Once again, I am amazed by the intelligence of our ancestors! 

Base 60 !

 

What special meaning did base 60 have to the Babylonians at that time?  Were 60 tribes nearby? Was 60 is the amount in their money system? 

In our daily life, we use the number 60 as a unit in the time-telling system. (60 seconds = 1 minute, 60 minutes = 1 hour). We also use 60 to make reference to the degrees of a circle (360). 

By doing some resarch online, I found some interesting facts about the Babylonian Mathematics and the base 60 system.

- Babylonians adopted the number 60 as base possibly because it has more divisors than any smaller  positive integers.

-The Babylonian math system did not have zero. 

-The Pythagorean theorem we use today is based on Babylonian math multiplication formula.

                                                                                                                                        (Gill, 2020)

In another article by Sweeney, he notes that "the Chinese or Egyptian culture have developed elaborate and highly accurate divination systems to predict the future, all based on Base 60". People in ancient China would predict the best times for planting and harvesting crops based on the traditional Chinese calendar which has some connection to the number 60. Sweeney also mentions the Pisano Periodicity, which indicates that "nature has a law that living things develop to the fullest to the number 60. " 

For those who are intersted, here are the links to the two articles/

https://www.thoughtco.com/why-we-still-use-babylonian-mathematics-116679

https://vixra.org/pdf/1407.0062v1.pdf

Why We Teach Math Reponse