AGI,
I have been focusing way too much in my own contribution to AGI, and not
nearly enough in explaining why that contribution is necessary in the first
place. Focusing in one's contribution is not optional but mandatory in
science: you want "the meat", you don't want to read a lot of stuff that you
already know. But AGI is different, perhaps because the "you already know"
part is not yet well established. So I will focus more on what is lacking
from "you already know" and try to expand it and find a place where
contributions are needed. It may be an impossible task, but I'll try, hoping
for your collaboration.
The crude reality is that we are building a machine, a physical system, or
more precisely a dynamical system. Sooner or later, we will all fail or
succeed depending on how well we understand machines.
Consider a discrete state model of dynamical systems. The term "discrete"
applies to the model, not the system. It implies that the granularity of the
model is variable, an outside parameter. For now, we will allow the modeler
to select the degree of detail. Later, when the system is allowed to learn,
there will be no modeler and the granularity will be determined by what the
system has learned.
In a state model, the system is described as a finite set of state
variables, all of them time-dependent. At any particular instant of time,
each variable has a certain value, and the state of the system at that
instant is the set of all those values (I am myself using a coarse-grained
description, there is more to variables and values than what I say here). A
state transition occurs when a variable's value changes. A good example of a
state model is a computer running a program. The state is determined by the
values of all variables in the program. A statement such as a=2 is a
transition to a new state.
The state space of the model is the collection of all states (it's just a
concept to help us think, nobody is going to compute it). In a discrete
model, the state space is discrete. It is customary to represent the state
space as an N-dimensional space, where N is the number of variables, so each
coordinate corresponds to one variable (think 3D to help you understand
this). In the state space, the state of the system at some instant of time
is specified by one point. As time elapses, the point moves in the space.
This is called the trajectory of the system (you can think of a program with
only 3 boolean variables, represented by a point in a 3D coordinate system,
and the point moves as the program executes).
A trajectory in state space may have a start and a finish, say an initial
state I and final state F. This is the case with computers. It's just like
the Turing machine. One starts from state I, and, hopefully, execution will
stop at some state F. The case where execution doesn't halt, is not
considered here. The set {I, F} is called the behavior of the system. No
wonder, you start from I, you end with F, that's how the system behaves. The
same term behavior will appear later in the context of refactoring.
Refactoring is a behavior-preserving transformation.
Action is defined with reference to a trajectory with a behavior {I, F}. The
principle of least-action says that, if there exist many trajectories from I
to F, then the system will follow the one where the action is least. If
there are more than one least-action trajectories from I to F, then the
model has a symmetry of the action. If there exists a symmetry of the
action, then there also exists a conservation law. And the conservation law
says that a pattern (or conserved quantity, or attractor) exists that is
invariant (does not change) in the course of the trajectory. Just so you see
where I am going, I will explain later.
Sergio
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