> Spatial relationships are just another type of logical relationship and we should expect AGI to be able to analyze relationships and generate algorithms on the fly to solve problems.
Not really. By that reasoning, 5-dimensional spatial reasoning is "just another type of logical relationship" and yet humans mostly can't do that at all.
It's clear that we have incredibly specialized capabilities for dealing with two- and three-dimensional spatiality that don't have much of anything to do with general logical intelligence at all.
Yes really. Problem solving on the fly doesn't mean the algorithm can instantly learn anything. Reality is HEAVILY biased towards two and three spatial dimensions so our brains have hours and hours of training on that dataset. But, with time, humans can learn to be good at all sorts of things.
It's important that we try to think from the perspective of an algorithm, not a human. And it's also important that we don't jump to extremes.
It seems like you interpreted "solving problems on the fly" to mean "instantly being an expert on a completely different and novel domain". What it does mean is flexibility, resilience to novel situations, and being able to adapt over time.
Complex numbers are just 2d numbers and they are mapped on a 2d plane, yeah. They are just a 2d vector. Callling them imaginary numbers is silly in the first place, 2+i is just the vector (2,1), all we mean here are the two numbers are orthogonal, i.e they are destinguished by some independent factor. The imaginary component is no more imaginary than the real component.
I mean what problems does physics solve not with just complex number but with even more complex vectors? Problems of...space-time.
Aliens in a SF book. What do you imagine? I see some kind of physical entity having geometric compomnents in some kind of space.
Context free grammers are represented by...trees where one side of a spatial relationship maps to one idea and the other to another. What is context? Things surrounding something, where something is.
Come up with any idea, it can be represented in space and time.
Not really. By that reasoning, 5-dimensional spatial reasoning is "just another type of logical relationship" and yet humans mostly can't do that at all.
It's clear that we have incredibly specialized capabilities for dealing with two- and three-dimensional spatiality that don't have much of anything to do with general logical intelligence at all.