# Unifying Intelligence and Morality

In Chapter 2 of Gödel, Escher, Bach: an Eternal Golden Braid, Hofstadter writes that the primary purpose of his book is to explore answers to the question "Do words and thoughts follow formal rules, or do they not?" I believe an alternate way to ask the same question is "do our thoughts follow the laws of physics?"1

The answer to this question means that we have to understand what intelligence is. In chapter 1 of GEB, Hofstadter presents the "M-I-U system" which is simple set of rules for transforming certain strings which contain only the letters M, I, and U in well-defined ways. The four transformation rules are:
1. xI xIU
2. Mx Mxx
3. xIIIy xUy
4. xUUy xy
The first rule says that a sequence of characters that end in I can be lengthened by appending U. The second rule says that any string starting with M can be lengthened by appending all of the characters following the M. The third rule says that any three consecutive I's can be replaced with one U. The fourth rule says that any two consecutive U's can be deleted.

Hofstadter then asks: given the string MI can application of the rules result in the string MU? We can attempt to answer the question by applying the rules the to initial string MI and searching for MU. A very incomplete graph is:

If the production rules only lengthened the string, as rules one and two do, then we could generate all strings with the length of the target string and stop once the string was found or there were no more strings of that length. The same is true if the rules always shortened the string. Because the rules lengthen and shorten strings, we don't know if MU exists in the "universe" of producible strings. We could search a long time and find it, or search forever and never find it. The application of the rules does not guarantee that we will discover the answer to the question.

But if we step outside the rules, we observe that I's are produced in powers of two: 1, 2, 4, 8, 16 etc... We also observe that I's are transformed to U three at a time. To get one U we would need a combination of three I's: 3, 6, 9, 12, 15... Because a power of two is not evenly divisible by three, these rules cannot produce MU from MI. We know something about the MIU system that cannot be proven from inside the MIU system. This is a simple example of
Gödel's Incompleteness Theorem.

The key observation is that one of the components of intelligence is the ability to step outside one set of rules into another. Of course the devil is in the details, but this a core principle of human level intelligence.

Hofstadter described this aspect of intelligence in 1979. John McCarthy said the same thing, but in a different way, twenty-one years earlier in his landmark paper
Programs with Common Sense. McCarthy presented five requirements for human equivalent intelligence:
1. All behaviors must be representable in the system. Therefore, the system should either be able to construct arbitrary automata or to program in some general-purpose programming language.
2. Interesting changes in behavior must be expressible in a simple way.
3. All aspects of behavior except the most routine should be improvable. In particular, the improving mechanism should be improvable.
4. The machine must have or evolve concepts of partial success because on difficult problems decisive successes or failures come too infrequently.
5. The system must be able to create subroutines which can be included in procedures in units...
In The Mechanism of Morality I wrote: "If these requirements correctly describe aspects of human behavior, then number three means that humans are goal-seeking creatures with no fixed goal. Not only do we not have a fixed goal, but the requirement that everything be improvable means that we have a built-in tendency to be dissatisfied with existing goal states!"

This is one reason why computers don't typically exhibit intelligent behavior. Computers are well known for their inflexibility; humans for their flexibility. Artificial intelligence is the attempt to make a flexible system from a set of rules. Those rules will need to include rules for changing certain rules.
2

Intelligence: step outside the system
Morality: step outside the system in a "constructive" direction

[1]
Bad Arguments Against Materialism and Atheism, It isn't about evidence assume that our thoughts follow the laws of physics.
[2] This is one reason why the programming language LISP is so powerful -- code is data and data is code.