My attempt at a general technical definition of 'Friendliness'

From: Marc Geddes (
Date: Wed Jan 19 2005 - 20:28:01 MST

I'm glad I'm not the one working on FAI all day. I'd
have gone mad by now. Lucky I'm only looking into it
as hobby. I can see why Eli called FAI theory
'friggin hard' (big understatement!).

None the less, I think my understanding has improved
to the point where I at least understand in general
terms what the concept 'Friendliness' mean. So here
I've had a go at attempting to give, in my own words,
a technical definition of 'Friendliness'. Admittedly
it's only a very general definition, but I don't think
it's vacuous or gibberish. That is, I think I'm
actually defining something meaningful here. If you
disagree by all means please tell me.

For background you just need to understand basic terms
from maths (functions, computability, uncomputability,
prospective attributes, listable attributes etc) and a
bit of cosmology too ;)

So here goes:



Marc Geddes, 19th Jan, 2005

* 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.

The 'Omega Point' condition requires that the rate of
information processing (computation) within the
universe approaches infinity as time approaches the
end. The idea is that a concept is no different to
the computational function existing in the mind of a
super-intelligence which generates a list of all
things possessing the attribute, in the limit that the
Omega Point condition is approached.

Example: The concept 'Beauty' is defined as being
equivalent to the mathematical function which
generates a list of all beautiful things. This is an
uncomputable function, since beauty appears to a
prospective attribute: the function to recognize or
generate beautiful things cannot be finitely

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.

Concept x=
Omega x =
Utility function generating all things with attribute
x in the limit that the universe becomes Omega Point

Partial x =
Utility function which is a finitely specified
approximation to function Omega x

* Propositions: All concepts in reality can be
interpreted as utility functions. 'Friendliness' is a
concept; therefore Friendliness is a utility function.

The class of friendly sentients appears to be
potentially infinite, making 'Friendliness' a
prospective attribute. Therefore the exact
Friendliness utility function is uncomputable.

All friendly sentients will consist of finitely
specified approximation functions to the exact
utility function. But by definition, a truly friendly
sentient aims to become as friendly as possible.
Therefore all finite approximations to 'Friendliness'
must have the property that they are recursive and
converge on the ideal utility function.

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.

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.
A PF function is itself a finitely specified function
approximating the uncomputable function Omega Friendly
(OF). So PF (PF) approaches OF as number of
iterations approaches infinity.



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