From: Marc Geddes (marc_geddes@yahoo.co.nz)
Date: Fri Jan 21 2005 - 20:46:29 MST
O.K, take out the word 'technical' from my subject
header. Then it reads '...a general definition....'
Satisfied?
--- Harvey Newstrom <mail@HarveyNewstrom.com> wrote:
>
> > * Proposition: A mind is a utility function. The
> > universe itself could be interpreted as a kind of
> mind
> > in the limit that it formed a super-intelligence
> at an
> > Omega Point. Therefore any concept within reality
> > could be interpreted as a 'utility function'
> within
> > the universal mind.
>
> These are very controversial and non-obvious
> propositions on which to
> base your definitions. Is friendliness really
> dependent on the
> universe being a "mind"? If I dispute that the
> universe is a "mind",
> does that mean friendliness doesn't exist? Your
> evidence that all
> concepts in reality can be coded as utility
> functions within an AI is
> based on the fact that the universe is a mind which
> codes all reality
> at the omega point? This is more of a religious
> faith-based assumption
> than a basis for an engineering design of an AI.
> Besides requiring the universe to be a mind, your
> definitions seem to
> require a Tipler-type omega point to occur for your
> definition. Since
> this is unknown and unproven at this point, it
> sounds like your
> definition must be unknown or unproven for now as
> well. Since the
> Omega Point won't occur until the end of the
> universe, it is unclear
> that your explanation applies to anything today.
> Can't you base your
> examples on physics existing now?
What I was suggesting was a 'strange loop' (backward
causality). I was putting forward the proposition
that for sentience to exist now, the Omega Point
condition has to hold. If I can provide some evidence
to support the proposition, this would be indirect
evidence for the Omega Point, since of course we know
that sentience *does* indeed exist (humans are an
example of sentient beings after all).
>
> > Example: The concept 'Beauty' is defined as being
> > equivalent to the mathematical function which
> > generates a list of all beautiful things.
>
> This is a circular definition. You defined beauty
> by using the word
> "beautiful" in the definition.
A mathematical function can be (at least
approximately) implemented as a computation. I
defined beauty to be a *process* - I said it was
equivalent to the *process* of a certain kind of
compuation - the computation which would generate an
awareness of all things that a sentient mind would
judge to be beautiful. This is not circular.
>
> > This is an
> > uncomputable function, since beauty appears to a
> > prospective attribute: the function to recognize
> or
> > generate beautiful things cannot be finitely
> > specified.
>
> I don't like where this is going. We can't develop
> coherent plans for
> achieving something we can't define. I doubt (and
> hope) that
> "friendiness" is not such a function. Otherwise, it
> boils down to
> "friendliness is in the eye of the beholder". You
> end up saying that
> people will call the system friendly if they like it
> and unfriendly if
> they don't. You can't engineer to such a spec, and
> it ends up being a
> democracy with people voting on what they want for
> friendliness. If
> you can't define it precisely, how can it be a
> requirement? How do you
> know it even exists, if you don't know what it is?
> This isn't some
> observation that we haven't pinned down an
> explanation for yet. This
> is our instructions and requirements to people
> trying to build AI
> systems. How can our request be vague and
> ill-defined, but we'll know
> it when we see it?
I *didn't* say it was undefinable! I said it was
*uncomputable*. In the technical sense of the word,
uncomputable simply means that no finitely specified
algorithim can compute it *exactly*. But it would
still be totally objective and definable! A finite
algorithim can still *approximate* an uncomptable
function.
>
> > But if the Omega Point condition holds for our
> > universe, then the function can be defined to be
> the
> > one that a super-intelligence (Universal Mind)
> would
> > hold, in the limit that the rate of information
> > processing was approaching infinity (Omega Point).
> So
> > all concepts can be thought of as 'utility
> functions'
> > in the universal mind.
>
> Again, circular logic. You define the universe as
> mind. Everything is
> in the universe (which equals mind, which equals
> universal mind).
> Therefore everything is in this universal mind.
> Therefore all concepts
> are held in this mind. Therefore a concept is what
> this universal mind
> holds. There are no definitions here. You are
> stating circular
> relationships and tautologies that do not
> distinguish between items
> within the definition and items without it.
What I said is not circular. I said that *if* the
universe is like a mind under certain conditions (and
I gave the Omega Point as the required condition
-mathematical limit), *then* we can define all
concepts as utility functions. This is definitely
saying something meaningful. It is stating the
condition required for concepts to be defined as
functions.
For instance I put forward as a proposition earlier
that any concept (and I gave 'beauty' as an example)
can be approximated by a computation (making
*concepts* identical to the *process* of computation).
I'm now stating the limiting condition required for
this to work ( the Omega Point )
>
> > * Propositions: All concepts in reality can be
> > interpreted as utility functions. 'Friendliness'
> is a
> > concept; therefore Friendliness is a utility
> function.
>
> This is not a proposition. You are labeling
> something with a name you
> want to call it. This is not the same thing as
> defining it or
> explaining it. A label is not a testable theory.
> There is no validity
> or truth test as to whether these things are what
> you say or not. You
> merely coined a term. Besides using circular logic
> to reach this
> point, you still haven't defined it. You merely
> labeled it.
No, I am saying that all concepts (like beauty) are
equiavlent to the *process* of computation which
generates an awareness of them in the mind of
sentients, in the limit that the Omega Point is
approached. This definitely has a precise technical
meaning and is falsifiable.
>
> > The class of friendly sentients appears to be
> > potentially infinite, making 'Friendliness' a
> > prospective attribute. Therefore the exact
> > Friendliness utility function is uncomputable.
>
> The first part of you sentence says "it appears...",
> then you jump to a
> more assertive "making...." Vague appearances
> don't make anything
> true. This argument is beyond weak. It doesn't
> actually explain
> anything at all.
I'm putting forward an axiom here. Argument require
assumptions. I'm simply stating an assumption. I say
that it seems likely that a endless diversity of
sentient minds is possible. This seems very
reasonable given that when we observe human beings, we
see that we are not all identical.
>
> The last sentence seem to sum up most of your
> "definition". Instead of
> giving a strong definition, you seem to be spending
> most of your words
> giving excuses for the weakness of any definition.
I'm putting forward reasonable assumptions, then
stating in general terms the conditions required for
them to work.
>
> > Therefore all finite approximations to
> 'Friendliness'
> > must have the property that they are recursive and
> > converge on the ideal utility function.
>
> The only thing you have defined in the end is that
> friendliness is
> recursive. This is not a definition either. It is
> an implementation
> method for encoding the process toward friendliness.
> This is about as
> useful as defining Bayes Theorem as being
> mathematical notation. It
> tells us how it is implemented or expressed, but
> tells us nothing about
> what you are implementing.
It does tell you something. I'm saying that the
mathematical function representing the Friendliness
program has the property that it is recursive.
>
> > Let Partial Friendly (PF) = finitely specified
> > approximation to the Friendliness function.
> >
> > Omega Friendly (OF) = exact Friendliness
> > function (uncomputable)
> >
> > PF must be a recursive function such that PF (PF)
> > outputs PF’ which approaches OF as number of
> > iterations approaches infinity.
>
> Assigning variables (or abbreviations) to terms
> sounds like a lead into
> a rigorous definition, like a mathematical formula
> or technical
> specification. But you fizzle off and don't
> actually use these
> abbreviations you define. They sound good, and look
> rigorous, but
> aren't actually used anything. This is about as
> useful as padding a
> glossary with technical words that aren't actually
> used. It adds
> nothing.
The terms are defining a particular kind of recursive
function. I'm assigning lablels to the particular
kind of recursive functions that I'm interested in -
namely the one's that approximate uncomputable
functions.
Remember, maths functions are equivalent to
computations.
So I'm actually labelling certain kinds of programs -
I'm giving a name to recursive programs that take in
particular other functions as input data and modify
them then give back the modified version as output.
>
> > Definition of Friendliness
> >
> > A computable 'Friendly' function (PF) is a
> function
> > which takes any finitely specified function
> Partial x
> > as input and modifies it such that the outputted
> > function Partial x' is a better approximation to
> Omega
> > x. Successive output used as input for the next
> > iteration has to cause Partial x' to converge on
> Omega
> > x as the number of iterations approaches infinity.
>
> This definition of "friendliness" merely says it is
> will have a
> recursive implementation. There is no definition
> here. You have
> described one attribute (recursiveness) of another
> attribute
> (friendliness) without defining that other
> attribute. There is also no
> measurement method of friendliness here, to
> calculate how friendly we
> are getting. Nor is there a test to define whether
> we are friendly or
> not.
>
> Any recursive function, such as factorial, would
> seem to meet your
> definition above. As such, it fails to define or
> distinguish between
> friendly and non-friendly items.
Not so! A recursive function such as factorial does
not have the property that it takes in the particular
kind of functions I labelled as input data, modifies
them, then outputs the improved version.
The functions operated on by my Friendliness function
were defined to be a very particular kind of function.
Let's why I used the labels I did previously. It is
those specific functions that I defined and labelled
previously that my Friendliness function operates on.
Go back to the definition I gave. I defined a
'Partial function' to be a finite function which is an
*approximation* to an uncomputable function.
Then I said that what Friendly fuctions do is take in
these Partial Functions as input data, modify them and
then output improved versions. My 'improved' I mean
that the outputted Partial function is a closer
approximation to the uncomputable function that the
Partial function was approximating.
If you don't think my statements make precise
mathematical sense please continue to explain why not.
=====
Find local movie times and trailers on Yahoo! Movies.
http://au.movies.yahoo.com
This archive was generated by hypermail 2.1.5 : Tue Feb 21 2006 - 04:22:51 MST