Mind-boggling Facts

october 2, 2013

It is amazing how much we have improved in our Euclid/Galileo classes. I keep on thinking how last year it was hard for everyone to be engaged and to be excited about presenting a proposition. We also seem to understand the propositions much deeper and we seem to want to know more about them.

Last Monday we didn't have a great time with our Galileo propositions, so we had decided to make up for that time by taking our chosen work time in order to work on those propositions. Well today was all about Galileo, Euclid and Newton, since after our make up period we also had our Galileo period and we also had lab in the afternoon.

Most of us seemed prepared for the classes today, but still none were eager to present Galileo’s second lemma. After one of us volunteered we made great progress in the proposition and everyone seemed engaged. But suddenly, we hit an obstacle, we didn't seem to follow were the conclusion had come from, and this was my favorite part of the proposition. We all started going up to the board and trying to solve it, giving our own ideas. What I loved the most was that when someone said they thought they knew how to solve it and went to the board, everyone else paid very close attention; and if some didn't agree with the proposed solution we would ask questions. If everyone still wasn't convinced of the solution, then someone else would work on it. I also liked this very much, because it showed me that we were really taking into account each others proposals. Well, we finally figured it out and it felt like great team work.

We later presented another proposition, and even though we got a little bit stuck, we all ended up understanding it completely. Although during this presentation I was a little confused, not about the proposition but about the process of the presentation. While my classmate was presenting, I knew all the steps that she had to take in order to reach the conclusion, so when she got stuck I didn't whether I should tell her what she was missing or whether I should ask her questions in order for her to figure it out. It was really hard for me to decide what to do, but I ended up just trying to help out by asking questions and guiding her in the right path. At the end I was grateful that I had chosen this because my classmate thanked me for my contributions and for helping her learn and understand the proposition. This wasn't the first time that I had battled with myself in order to figure out how to contribute to a presentation if you have the answers, but now I know how to act under these circumstances, I’ll just ask questions. 

We are still missing a lot in order to have great presentations but I think that reading the preliminaries of Newton helped us all. And of course, I think that most of us learned that if we approach Newton with an adventurous spirit it will make our experience a hundred times better.

For the second half of our day, our lab, I learned a lot of things. Most of all I learned about knowledge and some ways by which we can obtain it: axioms, deductive inference and empirical knowledge. One of the most incredible things I learned about the ways, and which probably mixed up my brain a bit, was that there are some thing that we know that are self-evident, for example, if we know that a = b, and b = c, then a = c (Euclid’s Common Notion 1). There is no way to explain this, well I mean is that if we try to explain it we end up saying the same thing but in different words. This was really an eye opener for me and it made me start thinking about things differently.

But this wasn't the most mind messing thing I learned (and I mean this in a good way). Something that has left me thinking was that we can’t even imagine Euclid’s definitions for a point and a line, we can only conceive it. So the point and the line, in Euclid’s sense, don't even exist in the world. This made me feel like if all of the time I did Euclid I was lied to, and I was trying to prove something that doesn't exist anyways, and that there was no point in going through Euclid’s proofs. I guess I never really understood what a line and a point really were. But after a while and a couple of chats, I understood that what Euclid does, his drawings, are only representations of the line and point that he describes. This eased me a bit, but every time I think about it again, it end up being mind-blogging.