Are Super-Problems a Thing?

Can we know everything, as a species?

Humans are smart. It is astonishing the amount of progress we have made in the understanding of the puzzle that is our universe. Back in the days of hunting and gathering, even banal natural events like thunder or rain cause great feelings of reverence in us. These phenomena were so beyond our understanding that we attributed them to gods, spirits and other entities larger and more powerful than ourselves.

Normally, when humans reach the dead end on a problem of the natural world, we tend to follow the same old steps. First, we don’t even know how to approach it, it is just a feature of the universe in which we live. Then, some smart chaps realize that there are some regularities here and there. Give it a bit more time and maybe someone will figure out a story that fits the data, providing an underlining explanation. Finally someone turns that story into mathematical rigor and now we can make predictions, quantitative prediction about how things are gonna go.

The thing is that most of the mathematical descriptions are just statements about what is known. In order to actually make the predictions we need to solve mathematical sets of equations, most of which have no analytical solutions except for the most simplified and ideal of cases. It turns out, however, that even for the instances where a solution cannot be properly found, we still can find approximate solutions with the aid of a computer or an abacus and some paper.

So far we have only stumbled upon problems that defy our ingenuity not our intelligence. The difference is that the first kind of problem is, in principle, understandable to a human, even if it might be hard to tackle. The second type of problems is absolutely beyond us and it would require a more powerful intellect to even begin sorting it out, perhaps to even notice that they exist. It is arguable whether problems that defy our level of intelligence even exist, because the very concept of intelligence has not reached its final form just yet.

Since several fragmented definitions of intelligence exist accross such a wide range of areas such as formal logic, computation theory and neurobiology, it is easy to see why a consensus has not yet been reached. If problems of this nature do exist, I think we might be swimming in them right the now without ever even noticing.

There might be simpler, easier, more cohesive and ingenious solutions to everything we have just solved but which requires a super-intellect to figure out and, even if figured out, would require a super-intellect to implement because trying to explain these solutions to us would be as productive as trying to explain the internet to a dog.

Are these a thing? If so, then super-intelligent AIs are absurdly scary and a little bit magical. They would be unintelligible on principle. No matter how fancy our tools for reading its mind were, its thoughts would be entirely incomprehensible, just because they would be considerations about things we can’t even articulate.