I agree that, to compare humans versus AIXI on an IQ test in a fully
fair way (that tests only intelligence rather than prior knowledge)
would be hard, because there is no easy way to supply AIXI with the same
initial knowledge state that the human has.
Regarding whether AIXI, in order to solve an IQ test, would simulate the
whole physical universe internally in order to simulate humans and thus
figure out what a human would say for each question -- I really doubt
it, actually. I am very close to certain that simulating a human is NOT
the simplest possible way to create a software program scoring 100% on
human-created IQ tests. So, the Occam prior embodied in AIXI would
almost surely not cause it to take the strategy you suggest.
-- Ben
Richard Loosemore wrote:
Ben Goertzel wrote:
Sorry, but I simply do not accept that you can make "do really well
on a long series of IQ tests" into a computable function without
getting tangled up in an implicit homuncular trap (i.e. accidentally
assuming some "real" intelligence in the computable function).
Let me put it this way: would AIXI, in building an implementation
of this function, have to make use of a universe (or universe
simulation) that *implicitly* included intelligences that were
capable of creating the IQ tests?
So, if there were a question like this in the IQ tests:
"Anna Nicole is to Monica Lewinsky as Madonna is to ......"
Richard, perhaps your point is that IQ tests assume certain implicit
background knowledge. I stated in my email that AIXI would equal any
other intelligence starting with the same initial knowledge set....
So, your point is that IQ tests assume an initial knowledge set that
is part and parcel of human culture.
No, that was not my point at all.
My point was much more subtle than that.
You claim that "AIXI would equal any other intelligence starting with
the same initial knowledge set". I am focussing on the "initial
knowledge set."
So let's compare me, as the other intelligence, with AIXI. What
exactly is the "same initial knowledge set" that we are talking about
here? Just the words I have heard and read in my lifetime? The words
that I have heard, read AND spoken in my lifetime? The sum total of
my sensory experiences, down at the neuron-firing level? The sum
total of my sensory experiences AND my actions, down at the neuron
firing level? All of the above, but also including the sum total of
all my internal mental machinery, so as to relate the other fluxes of
data in a coherent way? All of the above, but including all the
cultural information that is stored out there in other minds, in my
society? All of the above, but including simulations of all the related
Where, exactly, does AIXI draw the line when it tries to emulate my
performance on the test?
(I picked that particular example of an IQ test question in order to
highlight the way that some tests involve a huge amount of information
that requires understanding other minds .. my goal being to force AIXI
into having to go a long way to get its information).
And if it does not draw a clear line around what "same initial
knowledge set" means, but the process is open ended, what is to stop
the AIXI theorems from implictly assuming that AIXI, if it needs to,
can simulate my brain and the brains of all the other humans, in its
attempt to do the optimisation?
What I am asking (non-rhetorically) is a question about how far AIXI
goes along that path. Do you know AIXI well enough to say? My
understanding (poor though it is) is that it appears to allow itself
the latitude to go that far if the optimization requires it.
If it *does* allow itself that option, it would be parasitic on human
intelligence, because it would effectively be simulating one in order
to deconstruct it and use its knowledge to answer the questions.
Can you say, definitively, that AIXI draws a clear line around the
meaning of "same initial knowledge set," and does not allow itself the
option of implicitly simulating entire human minds as part of its
infinite computation?
Now, I do have a second line of argument in readiness, in case you can
confirm that it really is strictly limited, but I don't think I need
to use it. (In a nutshell, I would go on to say that if it does draw
such a line, then I dispute that it really can be proved to perform as
well as I do, because it redefines what "I" am trying to do in such a
way as to weaken my performance, and then proves that it can perform
better than *that*).
Richard Loosemore
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