Jim,
FIRST PART. UNCERTAINTY, CAUSALITY, AND SCHROEDINGER'S CAT.
You are very poor and your only hope is to sell your cat. You put it in a
box to take to the market. But you start thinking. What if the cat dies in
the box? I can't sell a dead cat. But if it is still alive when I get there,
how am I going to sell it? Your brain is effectively considering two
different universes. You can't decide between them so you consider both.
>From your perspective, you are living in two different universes at the same
time.
We say that your brain is the system, and the system has only two states:
cat dead, or cat alive. We call this situation an uncertainty, you are not
certain which way it is. So you need an answer to your uncertainty. You go
after the answer, and you choose a behavior that is independent of the
uncertainty. We say that your behavior is invariant under a transformation
from one state to the other. You take the box to the market and open it. The
cat is alive.
As a result of your invariant behavior, you have now acquired new
information: the cat has survived. Your two universes collapse into one. But
you start thinking again. If my cat looked better I could get more money.
Again you have two universes, it either looks well or it doesn't. You seek
an answer. You need an invariant behavior. You take the cat out of the box
and put it in the light. Now you acquire more info: the cat doesn't look
well. Again, you are left with only one universe. And so on.
In Physics, we describe a system by means of a set of variables, and we say
that each possible combination of values of the variables is a state of the
system. The variables can be boolean, or have integer values, or anything
appropriate. Then, we specify an initial state, and a dynamics for the
system. A dynamics is a rule or set of rules that specify how the system
transitions from one state to another. And the rules account for the
uncertainty. If the system is in state A, it can transition to state B, or
C, or D. We don't know which one it will be. And if the system transitions
to B, then it can transition from there to X or to Y or to Z, again we don't
know which. The dynamics is not *causal* because the state and the rule to
do not add up to a transition. Yet, the response behavior, an algorithm,
should be causal so it can be executed. Where does the algorithm come from?
The algorithm comes from what we know, from the information we have. So here
is what we do know. We know that states B, C, or D can not exist unless
state A has existed before. So we say that A *precedes* B, C, and D. We
also know that X, Y, or Z can exist only if B has existed. And this is the
precise point where *causal sets* come in. We formalize our knowledge by
writing:
A<B, A<C, A<D, B<X, B<Y, B<Z.
which, together with the set of states, {A, B, C, X, Y, Z} in this case, is
known as a causal set (read the '<' sign as "precedes"). We can write a
computer program for this. It would look as follows:
if(A) then
{
if(B) then
{
if(X) then ...
else if(Y) then ...
else if(Z) then ...
}
else if(C) then ...
else if(D) then ...
}
which means that if A has existed then either B, C, or D can exist, and in
the case where B has existed then either X, Y or Z can exist, and so on
until the program stops because there are no more state transitions left.
But what have we achieved by writing the program? Nothing. The uncertainty
is still there, only now it has been transferred to the data. In order to
run the program we have to specify all the uninitialized variables as data,
for example we could specify A, B and X, or A, C, etc. In other words we
have to specify the exact sequence of state transitions. Guess, rather than
specify.
There are many possible sequences of execution that satisfy the constraints
in the causal set, and no apparent reason to prefer one over the other. But
our brains make a unique solution, every time, when in possession of certain
information. For example, if I want to travel from Houston to Dallas I can
fly first to San Francisco and from there to Dallas, or I can fly directly
from Houston to Dallas. And brains are very consistent. Every person would
choose the second alternative, unless they have some other reason to go to
San Francisco first, in which case they would have additional information.
So how do our brains make that unique selection? Obviously, we are missing
something here. How does the brain do it?
SECOND PART: ENTROPY AND SELF-ORGANIZATION.
This is now the heart of my work. The brain doesn't do "it". It does
something else, and "it" follows as a result. The brain must satisfy its
never-ending hunger for energy. Information carries energy. Yes, information
itself. In March 2012, they have actually measured the amount of heat
generated by erasing one bit of information, thus confirming the 50 years
old Landauer's prediction. When the brain learns something, that is, when it
receives information, it supplies energy to its memory so it can store that
information. As it stores, it immediately recovers any energy it can from
the stored information, so it can use that energy to store more information.
And here is some Physics. When energy is extracted from information, then
entropy is also extracted. This is the Second Law of Thermodynamics. But
entropy is the measure of uncertainty in the information. The uncertainty is
reduced by the removal of energy because high energy states are no longer
accessible to the system. The state space actually shrinks, and the system
converges to its attractors, which is how self-organization takes place.
And, as if that were not enough, the transformation induced in the
information by the removal of entropy is behavior-preserving. The result is
an algorithm, and the algorithm is causal. In the brain, by the simple act
of conserving energy, also removes all the uncertainty from the information
and results in the unique, invariant behavior.
In AI/AGI, the energy consumption by computers has been the focus of
attention for decades. But few seem to have noticed that the brain goes
beyond that point, and reduces the energy consumption of the information
itself, not just the machine. Removing energy from information also removes
entropy, and casues it to self-organize into invariants. That's what the
brain does, all the time, create invariants, or invariant representations of
the information it has acquired. That's how 100,000,000 dots of light in
your retina become "hi, mom." We use the invreps for everything, to think,
to communicate, to create more invreps. Every word I write here is an invrep
in my mind. A language is an invrep. There can be no intelligence without
invreps.
It generally seems to me, but I can't promise, that little will be left to
explain intelligence once the invresps are understood. There is an infinite
numerable quantity of causal sets, there is and infinite numerable quantity
of invariants, and there is a bijective correspondence between each causal
set to each invrep. What is left? Of course, understanding the
implementation details of the brain is another matter.
AIers and AGIers alike try to process information while leaving all the
entropy in it. Alternatively, they pass the information to humans and use
the human brain to remove the entropy and create the invreps, which are then
fed back to computers, but also results in the familiar man-machine
inter-dependency perpetuated in both fields. We all remember the quest for
the perpetual motion machine, which stopped only when the energy-entropy
interplay was understood in thermodynamic machines. AI/AGI is the pursuit of
the perpetual certainty machine, one that can make its own uncertainty
disappear. It has been going on for 60 years. It is time to understand the
more complex energy-entropy-structure interplay in information.
Sergio
-------------------------------------------
AGI
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