Not So Common Sense 70-86

Hofstadter starts this section by talking about what seperates great mathematicians from ordinary mathematicians. He claims that an ordinary mathematicians ask themselves "how can I prove this to be true" after discovering something new, but great mathematicians ask themselves "how interesting is this idea, and by fiddeling around with it, could I find ideas that are even more interesting." I agree with Hofstadter on this, it seems that he is trying to say that great mathematicians try to better the understanding of the world by thinking of new ideas while ordinary mathematicians only care about how they can prove that what they discovered is true so they can get credit, while they don't really care about new interesting ideas.

Hofstadter goes on to discuuss what he calls 'conceptual spheres' which he describes as being a family of concepts that lie in our collective consciousness that applies to a central concept. He then generalizes it saying that conceptual spheres don't apply just in mathematics but in everyday thought. An example of one of these conceptual spheres coming into existence involves the "Tylenol murders" that took place in Chicago. Someone planting poisonous pills in bottles of Tylenol which were consumed by custumors who were then poisoned to death. The FDA, in response to this, established new rules and regulations pertaining to drug packaging. The FDA thought very narrowly, as they did not extend the new regulations beyond the domain of drugs. It is as if the FDA's thought process was trapped in a box and made a generalization that the only way someone else could do a similar thing was by tampering with drugs.

Hofstadter then discusses the "me too " phenomenon. This is an unconscious process, in which people draw analogies from other peoples lives and relate it to their own. He gives a great example which is as follows:

Carol - I often forget my last name, still.
Peter - How long have you been married now - nine months
Carol - About.
Peter - I have that trouble every year in January (referring to writing last years date)

Peter related his forgetting the date when the new year comes to Carol forgetting her last name, this makes me think how often humans really do this. Hofstadter says that the "me too" phenomenon defines thought and I can see why he would say that.

Lastly, he discusses how his prevoius findings in the math world helped him better understand theoretical solid-state physics, which came to him as a surprise. It's very interesting when two things relate to eachother when you least expect it, this applies to everything, not just math and physics.