From: Christian Szegedy (szegedy@or.uni-bonn.de)
Date: Thu Feb 28 2002 - 02:51:11 MST
Ben Goertzel wrote:
>I did NOT say that I could create a pragmatically feasible, 100% accurate
>algorithm for measuring the level of self-modification being displayed by a
>given system.
>
Of course an algorithm would be very far fetched, but it I think the
following much much simpler
theoretical problems are also out of reach:
a) Show two self-modificating systems which are provably different. I
mean by different that
one of them can perform some tasks more effectively than the other.
It seems to be still hopeless, so it would be great if you could:
b) Give precise mathematical definition of two systems, and some
evidence (not proof) that the
one system is significantly more efficient in some way than the other.
(Part of the problem
is of course to define some efficiency measure which has some slight
correspondence with real-word
efficience. Normally, one considers two algorithms equally efficient if
the running time is within a
constant factor of the running time of the other, and vica versa. This
distinction is of course
too fine for most cases, but sometimes the constants involved are soo
huge, that you can't say
anything about the real time performance.)
While reading your three different types of self modificating systems,
my first thought was:
are they different at all? Does not allow the first type of self
modification the same degree of
flexibility and the effectiveness for all learning tasks? Of course you
are allowed to be 1000000000
(or whatever) times slower (simulations always have overhead...), but if
you never get slower,
then the two types are not at all distinct from a theoretical point of
view. In this case your
three cases are not at all different from the mathematical point of
view. To be more concrete:
does not lead the learning process of type 1) to a higher level learning
(i.e. to an improvement
in the learning process itself), if your system is large enough? There
are good chances that you could
simulate learning systems of type 2) by sufficiently complicated systems
of type 1). Of course
I can't support this intuition, because you have not even clearly
defined the difference between
type 1) ,2) and 3) systems. Even a precise mathematical definition would
be of great value.
>Indeed, the mathematical formalization I have in mind will involve some
>very-hard-to-compute quantities, and hence will be of value only
>
>a) conceptually
>
I would not neglect the conceptual value. I think you could happily
write down your thoughts
if you had the slightest evidence the the different types of self
modifications you proposed are
basically different.
Of course I can't blame you. Developing ground breaking theories is
hard, the chances of
success are uncalculable and it costs lot of time. At this stage of the
development, the time may
be better invested in practical (engineering) work.
On the other hand, having the basic definitions and at least a basic
mathematical formulation
can be of great deal of help in guiding the practical process, and for
an effective communication
on the subject.
Normally I am quite irritated by people stating that they could
formulate something mathematically,
and use this as an argument. It is nornally used when running out of
real arguments.
I am not against working using mostly intuition, In most of my time, I
also work on producing efficient
but hard to prove solutions for huge problems, so I know the gap between
the theoretical
and practial world, but I also love mathematics, so my first commandment is:
Do not take the name of Mathematics in vain!
Best regards, Christian
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