P=NP is indecidable (conjecture)

"P equals NP?" is a million dollars unsolved problem.

"P" is the class of problems where we have algorithms that solves the problem in polynomial time.

"NP" the class of problems that can be proven in polynomial time once you "guess" the solution.

This is analogous with the sorting problem: it's easier to check the sorting of a list than to actually sort a list.

Of course, if you can fully solve the problem in polynomial time, you can also prove it in polynomial time, so P is included in NP. However, NP seems to contain some very hard problems that cannot be currently solved in polynomial time. It is believed that NP contains some problems that can never be possibly solved in P.

I will not do a formal proof, more like an argument or a sketch. You might have more patience and skills to develop some of this ideas even if they might have flaws in the current form.

You can take it as a conjecture, a mathematical joke or "food for thoughts".

Let's see how it goes:


On "morality derived from space colonization"

"Morality derived from space colonization" defines as the highest "Good" the survival of humans in case of an eventual global Earth cataclysm. I believe that such goal (humanity preservation) is likely to be acceptable for many people, but why only by space colonization?

There are arguments that an event that could destroy human life on Earth is likely to happen. We don't need to go until Sun depletion, it is more likely that a big enough asteroid will fall in the next thousands of years. Even without this, life of Earth might be threatened by local events like nuclear accidents, major climate change (it happened before). Even destructive diseases might not be contained in a certain Earth region. If not this, we might also face resource depletion if the population continues to grow.

It seems reasonable that saving humanity from a global Earth cataclysm depends on... finding another planet capable to sustain human life. It's like in the saying "don't put all your eggs in the same basket". It's always good to have a backup plan.

But how can this define Morality and Ethics?


On "competency living" and intelligence

I will call "competency living" the sum of behavioral competencies that allows an organism (in particular a human) to adapt to environment through learning.

"Competency living" will not cover simple bacterial strategies like "eat and multiply". However it is not limited to human level intelligence like abstract thinking. In my definition "competency living" will also cover complex animal behaviors like learning to jump over a rock, learning to climb, recognize good food, recognize dangers, flight maneuvers for birds, etc. Only in particular it also covers abstract human thinking.

I would speculate that abstract human intelligence is based and emulated on "competency living". Also, I would appreciate that the informational complexity of "competency living" is far greater than the additional needed for implementing abstract thinking. A consequence of this would be that abstract thinking is only gradually more complex than "competency living" and for making an artificial intelligence the biggest challenge is to emulate "competency living".


Simple patterns of intelligence

This is an idea about how intelligence could emerge from simple biological patterns. If confirmed, this could have direct impact about how we understand the human brain and how we can design new Artificial Intelligence systems.

There is now a wide spread belief that human brain intelligence is based on very simple structures (neurons) that can implement various thinking processes, based on location and structure. This belief is sustained by researches that shows how brain can learn to perceive with regions that were not initially related to that sensing type (like "seeing with your tongue"). This is the approach taken by various researches that are trying to reproduce human-like brain processes  (like recognizing objects) with general purpose neural networks.