Complexity and Useful Intelligence

To breifly summarize a fragment of what Gödel's incompleteness theorems mean to the world:

80 years ago, before the dawn of the computer age, Gödel proved that it is impossible to create a system that only made true statements unless such a system was also very incomplete. And that no system could prove its own consistency.

However, few people are aware of the incompleteness theorem. In fact, in the world at large, we observe that many people under the impression that sometime in the "near future", scientists will create a machine that is infallible. Or that machines are already infallible. But as Gödel's theorems show, infallibility is impossible. So, based on Gödel's theorems, a usefully intelligent machine would not be infallible. A usefully intelligent is necessarily different.

In fact, a useful intelligence would need organize and rank the clutter of information it takes in, just as we do. To do this, uses combinations, permutations, probability, and statistics. But it does so at amazing speed and today with a wide access to information.

Remarkably, many people are also likely to believe, based on how advertising and lobbying use them, that statistics is a form of evil. That chief among its uses is to convince people of something, to sell them on an idea that is in fact marginally useful at best; to basically lie to them.

However, within the world of advanced computing combinations, probability and statistics, in complement to logic, are the skill set that make computer programs more capable of intelligent skills: planning, organizing, interpreting, learning, predicting, navigating, and of solving a wide variety of problems. Problems few of us dreamed a computer program could ever usefully solve are being addressed today.