Ian EDCP 442 2020

 The first quote I came across is "Aristotle advanced a similar plan in which the elementary training consisted of reading, writing, gymnastics, and music; and the advanced studies included arithmetic, geometry, and astronomy, with the emphasis on the natural sciences." It was interesting to me since they consider gymnastics and music before arithmetic and natural sciences as elementary. I am not sure whether that necessarily indicate that those are easier topics to study, but basic arithmetic at least to me is quite a lot easier than music which has lots of structure along with hand-eye coordination.  Another interesting note was "[Martianus Capella] rejected medicine and architecture as purely technical subjects, pursued only for practical and not speculative ends and so unworthy of free men". I think this is quite the opposite of what we have today, where medicine is considered one of the most impactful jobs one can take and every year lots and lots of undergradu...

 I think the quote "each of the positive integers was one of [Ramanujan's] personal friends" aligns very well with the results of Alice Major's paper: people tend to associate numbers with properties, an those association tend to be cultural based and not random. It's quite interesting that such a simple association in people that might come off as natural can be so involved in terms of brain structure and how we process and react to information. Neuroscience must be an interesting yet difficult field of study as we try to unfold the mystery of the brain. (Although I have presented already, I just wanted to say that John von Neumann's proposed self-replication machine predicts certain properties needed for it to happen: we need to have blueprints to replicate, the complexity required to self-replicate and self-repair. Even today, we cannot build a robot that fixes itself, but humans have been replicating (though not by oneself) and can self-repair to some degr...

 Reflections and takeaway from Assignment 1: Digging deeper into ancient methods of computing trigonometry is quite interesting. I am not sure if others have the same lingering questions when they have been exposed to topics as such trig functions and exponential function in high school, but I personally do and have no received a good answer up until I took complex analysis. The question is how would I explain sin(sqrt(pi))? Or 2^e. It seems like on the grade 12 level, in pre-Calculus and Calculus, we should just accept that exponential and trigonometric functions are nice and smooth and defined everywhere, but HOW? We can reason about rational exponents, but what about irrational? And the same goes for trig functions. (It's cool that complex analysis gives the answer as Taylor series, and I think we might be too comfortable consulting our calculators for answers. The question is then how do calculators calculate different functions with ease and speed? That's a whole different...

 The first thing that surprises me in the paper is the reference “there are several dance companies who have used Euclid’s Elements as inspiration for abstract modern dance choreography”. I have never really danced or practice dance moves, and it is quite interesting that moves are designed with some mathematical properties in it. Perhaps the paths the body takes, or the arms or legs can have some nice properties that appeal to us without the audience knowing. The second part I find interesting is “Note here that the logic is not exactly parallel to the definitional and axiomatic propositions in Euclid’s proof. Instead, we rely on our intuition that usually a person’s two arms are equal in length, and we rely on our imagination that the dancers’ arms are also equal”. I like how the author brings in the fact that intuition and imprecise imagination is often used to describe or understand difficult mathematical concepts. When we talk about higher level abstract topics often there...

 It has been a while since I sat down ad read a poem. I would probably go back as far as the English 12 provincial that they no longer do now to find my last poem reading. When I tried to look into information about Euclid's life, I was surprised at how little information is retained over the course of time. The same is not true when I look at Pythagoras or Archimedes. where great tales pass down to people that don't study much math. In fact, I saw an interesting argument about Euclid being a pen name, and a group of mathematicians instead published results under this name. While this is not commonly accepted, it shows the lack of information and how little we can know about Euclid's life. The poem makes many references to Beauty. Since it's capitalized, it might be personification (or not, forgive my literature analysis) of some idea. Now normally for poems like this, I would think Beauty refers to maybe beautiful objects, beautiful people, or beautiful scenes or natur...