Formal systems

I'm afraid that, at least for these first few posts, it's going to sound a lot like a summary of a chapter of Godel, Escher, Bach (GEB).  Hopefully my essay isn't like that.

Hofstadter begins the book with a puzzle of his own invention, which I will reproduce here.  The MU-puzzle includes three and only three letters:  M, I, and U.  Groups of these three letters are referred to in the system as "strings" (which include MIU, IMMUMMU, MIUIUIUIU, and such).  The puzzle consists of beginning with a given string, MI, and trying to produce the string "MU" within the limits of the following rules:

1.  If the string's last letter is "I", you can add a "U" to the end.
2.  You can produce a new string by duplicating everything after the "M".  For example, MI can become MII, MUIUI can become MUIUIUIUI, MUU can become MUUUU, etc.
3.  You can replace "III" with a "U" at any point in the string if you wish.
4.  If you have a "UU" anywhere in the string, you can delete it (the "UU", not the string).

If you're a total nerd like I am, you might actually find some enjoyment in trying to produce the string "MU".  I didn't, but Hofstadter explains in GEB that he doesn't mean for the puzzle to be solved (although he says the solution is later in the book).  Solving the puzzle itself gives you experience with some of the workings of formal systems.

Hofstadter refers to given strings like "MI" as axioms, statements that you must assume to begin with since they cannot be proven.  Strings produced from the axiom are called theorems, since they are provable on the basis of the axiom and the given rules.

The reason that formal systems are such a frequently-used tool of GEB is because humans and computers treat them so differently.  I played with the MU-puzzle for maybe five to ten minutes before giving up.  I don't know if there really is an answer, or if the author will present some "cheater" solution later in the book.  But if it is truly impossible to produce "MU", a computer would continue attempting the theorem indefinitely, whereas a human would, eventually, give up.

In Hofstadter's words, jumping out of the system is a skill that seems almost wholly unique to humans.  Humans "jump out of the system" by giving up on a task, postponing a task, trying to change the rules, etc.  And jumping out of the system isn't always bad; in fact, exiting a system is many times an intelligent move.  Computers inherently have a problem with exiting systems because staying in the system is usually what they are programmed to do.

Hofstadter then uses the three letters of the MIU-system to describe three different ways to approach a task or a system:

-Mechanical mode (M-mode), in which the task is carried out systematically much like a computer would do,
-Intelligent mode (I-mode), in which the subject learns how to use the rules and creates new ways of solving the task, much like a human would do, and
-Un-mode (U-mode), which Hofstadter doesn't describe at this point, but I assume involves jumping out of the system or changing the rules, thereby altering the internal system you began with.

Bored yet?

Godel, Escher, Bach

Well, I'm back.  I decided to resurrect this blog because of something I'm starting to work on in college.  I'm involved in the honors program at my school, and part of the program is completing what's called a great questions essay.  I'm mainly using this blog right now to have a place to gather and organize my thoughts.  I want to have a better idea of exactly how I want to approach this, and writing about it helps.  I don't think much of this will appeal to a wide range of people, and I don't know how much I expect it to be read.  Frankly, I think a lot of people will find it boring.  However, it would be helpful for me to have this as a sounding board where others could give me ideas or opinions I can use, but I guess we'll see how well that pans out.

The essay I'm going to write will be based largely on a few themes from the book "Godel, Escher, Bach" by Douglas Hofstader.  I was introduced to this work while reading a spinoff of Harry Potter called "Harry Potter and the Methods of Rationality".  And yes, it is at least as geeky as the title implies.  I like it because I'm a science nerd and so is the pseudo-Harry in the story.  Anyway, the story references "Godel, Escher, Bach" (hereafter referred to as GEB) several times.  Some time after starting to read this, I was looking at some things I could do to complete other requirements of the honors program, and reading GEB was one of them.  I thought I would give it a try.

It's a tough book.  It's tough no matter who you are.  One distinguishing feature of GEB is just how familiar the author is with many academic disciplines.  His main background, as evident from the book, is mathematics, computer science, physics, and philosophy; but he is also quite adeptly acquainted with life sciences, music, literature, art, and even Zen.  I especially enjoy how much effort Hofstadter puts in to "dumbing down" the subject at first just enough for me to understand it.  It makes it an interesting read for me because it's a challenge, as if the author is daring me to intellectually keep up and try to understand what he's explaining.  What impressed me the most is how smoothly he incorporates all these areas of study to describe one of the overarching themes of the book:  consciousness.  He often explores this through the question:  "Can a machine be programmed to think, act, or operate the way humans do?"

This is the great question I plan to address in my essay.  Because GEB covers this topic so thoroughly, most of my posts here are going to be a sort of commentary about principles Hofstadter discusses in the book.  However, I may later depart from those more often, since I plan in my essay to address the theological perspective of the issue, which Hofstadter never touches.  To those reading this post, I would recommend trying to read a couple posts if you're interested, and if you're still bored after that, give up.  I don't want to waste anyone's time with this blog if what I discuss isn't what you're interested in.  But if it does appeal to you, it would be helpful to have additional feedback.  So here goes.