Kaj,

(Disclaimer: I do not claim to know the sort of maths that Ben and
Hutter and others have used in defining intelligence. I'm fully aware
that I'm dabbling in areas that I have little education in, and might
be making a complete fool of myself. Nonetheless...)


I'm currently writing my PhD thesis at the moment in which, at Hutter's
request, I am going to provide what should be an easy to understand
explanation of AIXI and the universal intelligence measure.  Hopefully
this will help make the subject more understandable to people outside
the area of complexity theory.  I'll let this list know when this is out.


The intelligence of a system is a function of the amount of different
arbitrary goals (functions that the system maximizes as it changes
over time) it can carry out and the degree by which it can succeed in
those different goals (how much it manages to maximize the functions
in question) in different environments as compared to other systems.


This is essentially what Hutter and I do.  We measure the performance
of the system for a given environment (which includes the goal) and
then sum them up.  The only additional thing is that we weight them
according to the complexity of each environment.  We use Kolmogorov
complexity, but you could replace this with another complexity measure
to get a computable intelligence measure.  See for example the work of
Hernandez (which I reference in my papers on this).  Once I've finished
my thesis, one thing that I plan to do is to write a program to test the
universal intelligence of agents.


This would eliminate a thermostat from being an intelligent system,
since a thermostat only carries out one goal.


Not really, it just means that the thermostat has an intelligence of one
on your scale.  I see no problem with this.  In my opinion the important
thing is that an intelligence measure orders things correct.  For example,
a thermostat should be more intelligent than a system that does nothing.
A small machine learning algorithm should be smarter still, a mouse
smarter still, and so on...


Humans would be
classified as relatively intelligent, since they can be given a wide
variety of goals to achieve. It also has the benefit of assigning
narrow-AI systems a very low intelligence, which is what we want it to
do.


Agreed.

If you want to read about the intelligence measure that I have developed
with Hutter check out the following.
A summary set of talk slides:

http://www.vetta.org/documents/Benelearn-UniversalIntelligence-Talk.pdf

Or for a longer paper:

http://www.vetta.org/documents/ui_benelearn.pdf

Unfortunately the full length journal paper (50 pages) is still in review so
I'm not sure when that will come out.  But my PhD thesis will contain this
material and that should be ready in a few months time.

Cheers
Shane

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