“The Crest of the Peacock” Babylonian Algebra Reflections

 It’s honestly quite difficult to think about mathematics at this point in our lives and try to ignore the existence of algebra. We’ve come to understand the significance of algebra in representing patterns, interpolating and extrapolating information, and logically illustrating the core information of problems in a universal and concise manner. However, when trying to explain the same mathematical concepts to students that haven’t experienced algebra, we employ the use of imagery and clearer explanations to relay the same ideas. In the same effect, I think that pre-algebraic mathematics would have relied more heavily on the use of effective depictions. When thinking of most everyday mathematics, such as algebra, the Shakespearean quote, “A rose by any other name would smell as sweet”, often comes to mind. That’s simply because basic algebra is a fairly intuitive concept that we use often in many scenarios, and often don’t realize that what we’re applying is math! 

Factors of 45 using Base 60

Below, I've attempted writing some factors of 45 using the Babylonian base 60. I was a bit stumped by 90 since they did not have a 0 place holder, for 0.5. I ended up trying 11 different pairs because I was curious about how this would look for numbers from 1 to 10 and for a number twice the size of 45. 

“The Crest of the Peacock” Reflections

 The Crest of the Peacock was truly an impressive, enjoyable read! While there were many striking points, I’ve discussed my top three below. 

The ‘Trajectory of Mathematics during the Dark Ages’ diagram was the most interesting (page 10). In our British Columbian education, we learn a lot about Europe’s Dark Ages; however, what we weren’t taught was that it coincided with the Golden Age of Arabia! It was surprising to see that Western Europe only had three arrows pointing at it, while Iraq, for comparison, had an impressive four arrows pointing to it and three arrows pointing outwards, really establishing itself as a central hub for mathematics at the time. Arabia’s dominant presence on the diagram demonstrated that Europe’s stagnance had little effect on the rest of the mathematical world, which shifted my euro-centric understanding of the development of mathematics, technology, and education. In fact, I do feel a bit guilty that my level of surprise was a result of many years of Western and European media immersion, but at this point my curiosity has been piqued enough that I intend to look more into the Golden Age of Arabia and the nearby civilizations. 

Babylonian Base 60 Reflections

 Speculative Phase:

Base 60 has some obvious advantages as opposed to base 10. For one, its factors are comprised of: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60, which includes the first 6 countable numbers, and the wondrous digit 10 itself; meaning that base 60 has the convenience of being easily divided into halves, thirds, quarters, fifths, and sixths, and is the smallest possible number that can do so! So, in a time where mathematics was most societally necessary for various types of bookkeeping, it makes sense that the base number is one that can be broken into so many sections. Another convenience to base 60 has to do with our basic anatomy as well- humans have 2 hands, and 2 feet (adding to 4 main limbs); 5 fingers per hand and 5 toes per foot (adding to 10 appendages per group, or a collective 20); and, each finger is subdivided into 3 sections (for 1 hand, 4 fingers x 3 groups = 12 subsections, plus the thumb- which makes 15 subsections; and 2 hands make 30). So right off the bat, the numbers 1, 2, 3, 4, 5, 10, 12, 15, 20, and 30 appear, making tallying an effective and tangible process. 60 offers a tremendous amount of flexibility when it comes to counting and grouping, which I think could have familial significance in terms of sharing and dividing basic needs, and societal significance in regards to distributing resources. 

“Integrating history of Mathematics in the classroom: an analytic survey” Reflection

Over the years I have taken a number of math courses in secondary school and in my mathematics major. Mathematics is the focus of my studies, and in some ironic or modest way, I’d like to admit that I’m not actually very good at it. My passion for math instead lies in satisfying an innate curiosity towards amateurly painting the abstractness of reality with profound numbers and logic, rather than solving homework questions one exam to another. So, I’ve always believed that in my future math classrooms, the emphasis would be placed on understanding how ideas came to be, allowing students to be inspired by that process, and giving them a space to apply logic to their imaginations. Because, mathematics at its heart really is much more than just numbers and equations- it’s a systematic way of thinking and presenting ideas that has influenced the development of so many fields, from fashion, to forestry, physics, and beyond.