Formal Systems. Basically that's what the chapter is about. Introducing us to what that is. One of the characteristics of such a system is conformed with rules. The user of the system creates theorems based with the axioms that are defined by the rules of the game.

In order to understand a little more of Formal Systems, Hofstadter introduces us to the MU system. The only elements I have are M, U  and I. With a series of rules, I have to turn MU into MI.

• 1st rule: If the string ends with an I, one can add a U
• 2nd rule: One can add the same characters written after the M. Mx can be Mxx and can be transformed after to Mxxxx and so on.
• 3rd rule: If you have 3 consecutive I, they can become a U
• 4th rule: If 3 consecutive U, they can become just one U

So using these rules I got into the game. The fun thing about it is that, once one starts looking into the rules by trial and error or purely observation one notices that certain things are not possible with those rules.

In my opinion, one of those impossibilities is making MU out of MI.

So I was driving to school today, after reading this first chapter. I knew these rules (for they are very simple) and got to this conclusion:


Using rule 1, I'll transform my pattern in an irreversible way: if I get a "MIU" for example, I can use rule 2 infinitely solely.
Using rule 2, my patterns will grow exponentially, increasing my digits 2, 4, 8, 16 and so on.
Rule 3 and 4 only work with three digits.

For this, I will need then a number divisible under 3 out of an exponential curve that just starts from 1 or 2. But it will bring me at the end of the day to the same pattern of groups: 2,4,8 and all the heritage of those. I need patterns that gather 3 letters. But that is not possible because of the way numbers increase.

Numbers increase in pairs exponentially, and decrease to one out of triads of consecutive "I"s or "U"s. 

So for this, I would say this is not possible. I'll see what happens...
Interesting is how I got to see this patterns and discount probabilities that might be a "waste of time".

Hofstadter made a beautiful introduction to "Godel, Escher, Bach". He introduces us to three geniuses and how they represented the strange loops:

• Bach, a musician whose Canons represent a strange loop.
  
• Escher, artist, whose drawings represent the impossible geometry (strange loops)
• Godel; logician, mathematician and philosopher that questioned the foundation of mathematics introducing his "incompleteness theorems"

In order to give some kind of notion of what a strange loop is, I'll post an example that Hofstadter gives in the introduction:

The following sentence is false.
The preceding sentence is true.

So here we have a sense of infinity, of something that won't stop. Something that can't be measurable. That's where I got interested in how that makes us "mediocre" as humans beings searching for truth in a system which we have created, but how can we prove that system outside that system? Are we really understanding reality if our minds are the beginning and ending point?

Oh, I missed Amable so much. One can learn so much from him and his stories! Today he told us how he ran away from home when he was 16. He wanted to be a preacher, but when he arrived to the church, he was told that he was to young. Then, he went back home and everyone was looking for him! After that, his father understood that he really wanted to study religion.