Interesting Things

Reading chapter 2 of Taming the Infinite I came across many interesting things. 

The first very interesting thing I came across was the second paragraph. It starts talking about how pictures leave more room for differences of interpretation than symbols. It mentions this because mathematicians use various types of visual reasoning, and some are pictures. So it hit me, I started thinking about an essay we read called The Rhetoric of the Image by Roland Barthes. I wonder if this essay has anything to do with this. I guess I will find that out later on. 

The second very interesting thing was the Pythagoreans´ philosophy. I found it very interesting because the Pythagoreans understood that mathematics is about abstract concepts, and not about reality. They also believed that most of these abstract "things" were just a way to get to the ideal of an object. It is very true. For example, when we draw a circle we are actually trying to copy that abstract ideal in our heads  that a circle is perfectly round. Of course our circle isn't perfect, but most of the time we try to perfect it. (Since I am  not very good explaining things I did my best, trying to reach that ideal in my head. haha)

My third very interesting thing was kind of a big slap to my face. When I blogged about Euclid, I was complaining that people where mixing in three dimensions and two dimensions. I thought they hadn't been discovered yet. In page 33 it says that in Euclid's The Elements there a treatment to the geometry of two dimensions and of three dimensions (meaning space). I  guess he did know about dimensions. 

The fourth and last very interesting thing I found in the chapter was the initial statements. By initial statements I think it means the definitions. The book mentions that some of these initial statements can't themselves be proved (I mean, Euclid had to start somewhere). This makes me feel a whole lot better. I don't have to worry that much about understanding what a point is, since I guess even Euclid didn't have tha concept so clear. 

I found many other interesting things in this chapter but these are the ones that really stood out.