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.
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".
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
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".
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