User blog:DecskySikh34311/Googology Bookclub Meeting I - (One to Infinity: A Guide to the Finite/1.1.1 Welcome to the Numberscape)

For this gathering of the Googology Bookclub the reading material was part one of chapter one of section one of Saibian's online web-book, One to Infinity: A Guide to the Finite. Firstly, before providing my thoughts on it I must apologize for not specifying that only this part of chapter one will be considered, rather than the entirety of chapter one, which may be a lot to read in one day.

Well, firstly let me say my favorite part was the last section, The Call to Adventure... at the end. It really gave me a feeling of excitement to know that I was embarking on a journey of knowledge that spanned across the months it must have taken to write this and polish it, and that here was a person who was willing to explain everything out as if I had never heard of googology before, and did a very good job at it to! What makes Sbiis' explanations good teaching material is that he is telling how he learned these concepts, and also how an inexperienced person might view them at first, so that any beginner questions the reader has are instantly and lucidly addressed.

Particularly I enjoyed this passage:

"The numberscape has attributes similar to those of fractals. Like fractals the numberscape begins with a very simple definition which leads to infinite complexity. Like fractals numbers will contain features of self-similarity, and resemble super-sets of smaller numbers. Lastly, like fractals it contains much that appears random and chaotic, even while being completely deterministic. In short, we discover that even the simple counting numbers have infinite mysteries for mathematicians to solve."

At the moment I'm reading Gödel, Escher, Bach: an Eternal Golden Braid, and in that book the idea that a simply defined structure could have mysteries eluding discovery by the most adept mathematicians boggles the mind. It's not as if the structure "pops out of nowhere", but it seems to build itself and in doing so build up the way it builds itself. Googology is about the study of large numbers, and as most frequently recursion is used to bring these numbers about, Googology is really a matter of layers and the study of how things next, which in turn becomes a study of ordinals. So I can see why Saibian mentioned infinity so much, because if I'm correct he's going to talk more about it and how it can be used for making large numbers later on in the book.

Well, those were my thoughts! If you have anything you'd like to say, ask, or muse on do so below without hesitation!

Oh, and in a week on this exact date we'll be considering 1.1.2 Number Sense from Saibian's webbook.