The notion of complexity classes is well defined in an abstract mathematical sense. Its just that the abstract mathematical model is sufficiently different from an actual real world AI that I can’t see any obvious correspondence between the two.
All complexity theory works in the limiting case of a series of ever larger inputs. In most everyday algorithms, the constants are usually reasonable, meaning that a loglinear algorithm will probably be faster than an expspace one on the amount of data you care about.
In this context, its not clear what it means to say that humans can solve all problems in P. Sorting is in P. Can a human sort an arbitrary list of values? No, a human can’t sort 3^^^3 values. Also, saying a problem is in P only says that there exists an algorithm that does something, it doesn’t tell you how to find the algorithm. The problem of taking in a number, totally ignoring it and then printing a proof of fermats last theorem is P. There is a constant time algorithm that does it, namely an algorithm with the proof hardcoded into it.
This is especially relevant considering that the AI isn’t magic. Any real AI we build will be using a finite number of physical bits, and probably a reasonably small number.
Suppose that humans haven’t yet come up with a good special purpose algorithm for the task of estimating the aerodynamic efficiency of a wind turbine design. However, we have made a general AI. We set the AI the task of calculating this efficiency, and it designs and then runs some clever new PDE solving algorithm. The problem was never one that required an exponentially vast amount of compute. The problem was a polytime problem that humans hadn’t got around to programming yet. (Except by programming a general AI that could solve it.)
There might be some way that these proofs relate to the capabilities of realworld AI systems, but such relation is highly non obvious and definitely worth describing in detail. Of course, if you have not yet figured out how these results relate to real AI, you might do the maths in the hope that it gives you some insight.
The notion of complexity classes is well defined in an abstract mathematical sense. Its just that the abstract mathematical model is sufficiently different from an actual real world AI that I can’t see any obvious correspondence between the two.
All complexity theory works in the limiting case of a series of ever larger inputs. In most everyday algorithms, the constants are usually reasonable, meaning that a loglinear algorithm will probably be faster than an expspace one on the amount of data you care about.
In this context, its not clear what it means to say that humans can solve all problems in P. Sorting is in P. Can a human sort an arbitrary list of values? No, a human can’t sort 3^^^3 values. Also, saying a problem is in P only says that there exists an algorithm that does something, it doesn’t tell you how to find the algorithm. The problem of taking in a number, totally ignoring it and then printing a proof of fermats last theorem is P. There is a constant time algorithm that does it, namely an algorithm with the proof hardcoded into it.
This is especially relevant considering that the AI isn’t magic. Any real AI we build will be using a finite number of physical bits, and probably a reasonably small number.
Suppose that humans haven’t yet come up with a good special purpose algorithm for the task of estimating the aerodynamic efficiency of a wind turbine design. However, we have made a general AI. We set the AI the task of calculating this efficiency, and it designs and then runs some clever new PDE solving algorithm. The problem was never one that required an exponentially vast amount of compute. The problem was a polytime problem that humans hadn’t got around to programming yet. (Except by programming a general AI that could solve it.)
There might be some way that these proofs relate to the capabilities of realworld AI systems, but such relation is highly non obvious and definitely worth describing in detail. Of course, if you have not yet figured out how these results relate to real AI, you might do the maths in the hope that it gives you some insight.