Hi Jason, Hi Skeletori,

A short comment, on Jason's comment on Skeletori.

A deeper question is what is the upper limit to intelligence? I haven't yet mentioned the role of memory in this process. I think intelligence is bound by the complexity of the environment. From within the computer, new, more complex environments can be created. (Just think how much more complex our present day environment is than 200 years ago), however the ultimate limit of the complexity of the environment that can be rendered depends on the amount of memory available to represent that environment. Evolution to this point has leveraged the complexity of the physical universe and the presence of other evolved organisms to create complex fitness tests, but evolution would hit a wall if it reached a point where DNA molecules couldn't get any longer.

I would distinguish intelligence and competence;

I would define intelligence by an amount of self-introspection ability. In that case the singularity belongs to the past, with the discovery of "Löbian machine", that is universal machine knowing that their are universal. This makes all humans intelligent, as far as they have the courage and motivation to introspect themselves enough, and be aware of the unnameability of truth and correctness. As far as you are (luckily) 'correct', Löbian machine like PA or ZF are as intelligent than you and me, despite having different knowledge (even different arithmetical knowledge).

I would define competence by the inclusiveness of the classes of (partial) computable functions recognizable by the the machine when in its inference inductive mode (searching programs for matching a sequence of <input-output> presented to it in any order).

Then the notion of singularity points makes no sense, because two inference machines (cooperating or not!) are uncomputably more competent than a unique machine (Blum and Blum non-union theorem(*)). Also machines doing errors are also uncomputably more competent, machines changing their mind (the synthesized program) are also uncomputably more competent 5case and Smith(*).

Competence has a negative feedback on (some) intelligent machine. It may even lead to the loss of Lobianity, making the machine "idiotic", feeling superior, thinking at the place of others, egocentric, and eventually inconsistent. Competence develops from intelligence, but intelligence is restrained by competence. This leads to complex chaotic loops.
Competence can be evaluated by test, exams, etc.
Intelligence cannot.

I think that intelligence entails both consciousness and free-will.


(*) see the precise references in my URL (thesis's bibliography).

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