Ian EDCP 442 2020

 Its December already! Time flies, and another term has past. For a lot of people, including me, this course began as just another course to take in the program. Granted, it was related to math so I thought it would be less boring. As we met weekly and discussed various interesting methods and stories about mathematics in the past, this class quickly became the most interesting class of the semester. I love how we explored so many different ideas from the past that have been buried under the Eurocentric view of the world. It is easy to believe that just about anything is created somewhere in North American or Europe. Big names like Edison, Newton, Gauss, and they are all very white. It is not a surprise that the richest countries in the world at various times were also the centre of research, discovery, and innovations. The presentations, readings, and reflections that the class has asked me to do prompted me to think about how math fits in our society. The presentations and storie...

 After my presentation, it made me think more about the history of scientific innovations and discoveries and whether or not it is biased. My presentation revolved around Alan Turing and his life, and unfortunately Alan did not live a rich and long life. Computer industries are in the trillions and it has revolutionized every aspect of how we live. The problem is that the richest companies or individuals are often not the ones who have created all the theories and technology required for the boom. I think this extends equally well in other fields: fundamental research is often funded by government and not much financial gain comes out of it. Practical, profitable adaptations come in later on top of the hard work built previously and become the winners. Like one of the course readings, the ancient Greeks treated theory and thinking highly, and practical careers were considered low-class. Today seems to be the opposite: we reward those that commercialize products and services, and ou...

 As a group (Ian, Ealin, Mariana) we have chosen tow write a short story on the life of Alan Turing and his contribution to the modern world. Our short story (A clickable link). https://docs.google.com/document/d/1jfDYDyK-tOTb9baDtN9_-PbIMbMVTYFB3ef2qSi48s0/edit?usp=sharing (if you cannot click the link, you can copy this and paste into the browser of your choice) Our presentation (A clickable link) https://docs.google.com/presentation/d/1TE2YRjlo5P95dFc6Xq-zM49bjyhZwmytjG_eXiVRstU/edit?usp=sharing (if you cannot click the link, you can copy this and paste into the browser of your choice)   Group Explication of Research     As a group, we chose to write a story about Alan Turing, an aspiring mathematician who contributed an enormous amount during the WWII period, but died as a criminal. Through our research of Alan Turing using the references below, we thought his life story and mathematical contributions would best be told in the artistic format of a short sto...

 The first thing that surprises me is how early people have started wondering about the shape of earth and the circumference. An extraordinary force of curiosity must have been present for people to go and tackle these problems that most of us today would not bother. Maybe physics major would design their experiment on measuring such a thing, but most of us is content with our ground being flat because that's what it appears to us. Another surprising thing is the Islam's desire to learn from other culture. It was mentioned that they sent out people to gather and translate copies of works that are important to the Greeks, and that doesn't seem to immediately benefit them in some way. Again, it seems to be some intellectual thoughts that drive them to do so. Even today, when translating might not be as tedious or difficult, quite a lot of work remains in their own language because we don't actively seek to translate everything (though I'm sure small groups of people a...

Group: Ealin, Mariana, Ian Topic: The History/Contributions of Alan Turing  Artistic Format : Short Story Draft References (at least 2 articles, books, or book chapters & 3 other sources)  Cooper, S. B., & Leeuwen, J. van. (2013). Alan Turing: His Work and Impact. Elsevier Science. https://doi.org/10.1016/C2010-0-66380-2   Cowell, A. (2019, June 5). Overlooked No More: Alan Turing, Condemned Code Breaker and Computer Visionary . The New York Times. https://www.nytimes.com/2019/06/05/obituaries/alan-turing-overlooked.html   Hodges, A. (2013). Alan Turing . Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/entries/turing/    O’Connor, J. J., & Robertson, E.F., Alan Mathison Turing. Maths History St. Andrews MacTutor. https://mathshistory.st-andrews.ac.uk/Biographies/Turing/   Teuscher, C. (2004). Alan Turing: Life and Legacy . Springer Berlin Heidelberg. https://doi-org.ezproxy.library.ubc.ca/10.1007/978-3-662-05642-4

 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...

 1 9 5 6 2 7 8 4 3               The first square is attached above. Surprisingly it did not take too long and I did not write it down as a formal problem. Rather, I simply noted that the numbers 1+2+3+...+9 = 45 exactly. The connection is that we are told (actually we don't need to be told) that each column and row has to sum to 15. This is 45/3, so that seems to be useful. I started by putting 1 in the upper left corner, and hence I need bigger numbers on the row to make 15. I chose 9 and then 5. Now working down at the first column from the left, since I have used 9 I want something big so I pick something like 8. This seems to work fine and I was able to complete them row and column wise. The problem arises when considering the diagonals, they are way off at 1 + 2 + 3. To try it more, I start by considering the diagonals, and complete an X in th...