Final Blog Post

As I look back on my blogposts for 442 there are two themes that stick out to me - practicality and simplicity. Maybe the simplicity of the lives of ancient civilizations allowed for practical mathematics. I in no way express any negative connotation by saying such a thing; in fact I think the simplicity is something lost in today's world. Regardless, I find the importance in such a fundamental approach to exploring mathematics. This course has taught me to not neglect the origins of math concepts and perhaps starting at these places where mathematics originated can make for a more fulfilling lesson. If we take something such as quadratic equations and just move forward with applications and how to solve such equations without first exploring how Al-Khwarizmi came to discover it, we would be eliminating a potentially interesting historical lesson for students. We also get to do math through investigation and exploration. 

I'm realizing now that this is because of the realizations that we had as students in 442. We also learned about the origins of so many math concepts we knew no history about. We got to learn about ancient Chinese mathematics and about the many contributions that were made through these ancient civilizations. We were able to learn math history from a lens outside the perspective of one that is Eurocentric and that is so, so important. 

I'm realizing as well the importance of math history in terms of critical mathematics education. It takes a deconstructing approach and an important step in deconstructing current worldviews is to offer accurate representations of history that haven't been distorted by colonization. 

It was wonderful to see all these things of whose history I knew nothing about and furthermore thought that they were only created by Europeans in ancient Greece. I got to see that there is rich history in other places in the world and more importantly, places that actually relate to my own identity.

Multiplication Tables of 45

I recall sitting in (I think) the garden with Nanxi trying to solve through what these numbers could mean. Intelligently, she figured out how the Babylonians were doing this table of multiplication on base 60 - I'm kicking myself now that I didn't take a picture of her work because she also discovered how the decimals worked as well. As we go down the table from the beginning we see that 2 times 30 equals 60, 3 times 20 equals 60 and so on. When we get to 8, we find our first decimal which is interpreted as 8 times 7 equals 56 and 8 times 30/60 is 4; 56 plus 4 is equal to sixty. I believe there are certain numbers missing because they are prime or have these prime numbers as their factors. For example, 11 is missing and 22, 33, 44 and 55 are also missing. Although, I am not sure why they are missing but I think I just thought of an idea while writing this sentence out. 

If we take the number 11, we could say that whole number wise, it fits into 60, 5 times (which would give 55). Now we need 5 more, the closest to which we could get by multiplying 11 by 27/60 (which gives 4.95). We are still left with 0.05 to make up and our current answer would look like 5, 27. We can already see that to get to 0.05 we would be doing another 27/60 at the third (or fourth?) place value which would yield another decimal value with 5 - we end up having a repeating decimal similar to the fraction 1/3. Babylonians I'm thinking, must have identified that there would be numbers with repeating decimals and thus excluded them from the table. What I think is fascinating is that they also identified that other numbers that are multiples of these numbers would also end up with repeating decimals and chose to exclude them as well. 

Their fraction notation is similar to ours with the exception that they only simplify as far as base-60. Our 3/4 is their 45/60, our 1/2 is their 30/60 and so on. Wait, then there is a difference because our 3/4 is represented as 0.75 while theirs is represented as ", 45". Because we use a base-10 system, our decimals are over powers of 10 while Babylonians construct their decimals over powers of 60. 

A table of 45 would look (I think) like this:

Interestingly enough, I'm not sure if I'm correct but I was noticing that with this odd-number base, the answers in the right side could only contain odd numbers. As soon as you encountered an even number, the decimal would most likely start repeating itself. 

Art History Project Reflection

For our art history project, Brandon and I decided to present on the history of the Monty Hall Problem. When we were first tasked with this assignment and told it would be done in partners, with no hesitation I knew that I wanted to be partners with Brandon. For two reasons, one being that he wasn't in class that day and I didn't want him to be stressed about not having a partner but more importantly, Brandon and I get along really well. There's many ways that we relate to each other and I think the common ground of both working full-time is a channel of empathy that cannot be overlooked. Going through this program while committing such hours to work out of necessity is not something many can understand but Brandon and I are on the same boat with that. This showed in the way that we collaborated with each other. We split up the work, offered each other help and and took autonomy over our work. We didn't hassle each other and we trusted one another. The funnest part about this project was honestly standing at the white board with Brandon working through all the probabilities, explanations and extensions. 

As much as I've heard the Monty Hall Problem, I never fully understood the proof for it until I did this project with Brandon. It was also extremely interesting to learn about the Bertrand's Box Paradox from which this problem originated. 

I'm also really glad the class liked our little presentation bit in the beginning. I was thinking it might be a little corny but hearing everyone laugh and compliment us was a wonderful feeling. A big shout out to Jacob as well - what a guy right? Ask him to speak any prize and his wholesome self said, "a hug".