Artificial intelligence: A look at things that neither we nor computers can discover

Recently (April 15, 2008), Robert J. Marks II, Distinguished Professor of Electrical & Computer Engineering at Baylor University in Texas, addressed a joint meeting of the local American Scientific Affiliation and the Baylor Society for Conversations in Religion, Ethics and Science, on the limitations of computer models of life and mind:

Computing has no theory of everything (T.O.E.). We're uncertain whether physics has a T.O.E. as revealed in M-theory but, due to the genius of Kurt Godel 75 years ago, smart people like Stephen Hawking are starting to doubt it.

This is because of a new startling mathematical idea from algorithmic information theory (AIT): There exist things that are true that cannot be derived from fundamental principles. Some things are true simply because they are true.

Many claim God cannot be proved. (Although I'll show you Godel's short mathematical proof of God's existence). There are some things we know exist that we can prove we will never know.

Most doubt a computer program will ever write a deeply meaningful poem or a classic novel. How about something simpler? Can we look at an arbitrary computer program and decide whether or not it will ever print out the number 3?

We can for some programs. But Alan Turing, the founder of computer science, proved it is impossible to write a program to analyze another arbitrary program to tell us whether or not a 3 will be printed.

In fact, we can't write a computer program to determine anything another arbitrary computer program will do. (This is called Rice's theorem.) To find out, we need to run the program.

We can also prove there are numbers of finite precision numbers a computer can't compute. One of these is Chaitin's number, an astonishing constant between zero and one we know exists.

If we knew Chaitin's constant to finite precision - one single number - we could solve many open problems in mathematics. These include the Riemann hypothesis, Goldbach's conjecture and whether or not there is an odd perfect number.

Chaitin's constant exists, but we can prove we will never know it. These and other mind bending properties in the field of AIT [artificial intelligence theory] seem too far fetched to be true, but with a minimum of math, I will convince you otherwise.

Sounds interesting. I have written to ask him how it turned out.

By the way here are some other Mindful Hack stories on how the human brain differs from a computer:

Mind vs. meat vs. computers - the differences

Let the machine read your mind (We offer an installment plan!)

Free will: In fruit flies yet?

Emotion machines - so that's what we are! (?)

Mind-computer blend: Who believes in this?

Artificial intelligence: Making the whole universe intelligent?

Brain cells release information more widely than previously thought.