Does anyone know the source of the phrase or idea "any creature whose brain is simple enough to fully understand, does not have the brain-power to understand it himself"?

I believe the correct phrasing is:

"If the human brain were simple enough for us to understand we would be too simple to understand it"

That should help your search.

Quick googling found one attribution to "Ken Hill". Another said it was a researcher who helped develop Prozac (no name given).

Kurt Gödel's incompleteness theorem is the basis of that colloquialism. The math just says that a complete description of a system will always take more bits than the system it describes.

However, in practice, this is only a restriction if a system is already completely random. No system you would ever want to understand or describe would be random information, certainly not a system of any complexity, certainly not the human species or its brain.

Complex systems are built up as layers of causal grammar (quantum, atoms, molecules, cells, functional parts, bodies, culture, etc.). Each of these gross layers can be subdivided again and again into causal hierarchies of influence (each with their own organizational and behavioral rules or grammars), and as such the whole system can be modeled in a far smaller abstraction space than represented by the original physical entity being abstracted.

Because of this repetitive information that is any inherited causal chain, you don't need to be as smart, or as complex, as the things you set into motion. That is what evolution does. The actions you take today (mental or physical) provide new bricks from which new buildings can be built tomorrow.

So long as there is a ready and proximal flow of energy, a system can set into motion, indeed be a part of, complexity that exceeds over time, their own (at any moment in the present or past).

Of course there is no free lunch. An increase in complexity in one concentrated location, means a decrease in complexity everywhere (including the newly more complex locality).

What is of interest here isn't the math which is well understood and both logically and empirically proven, but the motivations that drive a tendency in some humans to gravitate towards rhetoric meant to derail what they see as dangerous or emotionally uncomfortable.

The bullshit alarms in me all go off at once when I see single sentence memes dropped on the all to ignorant masses. Humans come ready-built for certain kinds of evolution-derived tendencies and emotional grand attractors. These can overwhelm logical thought and allow people to 'believe" things despite absolute evidence and logical causal knowledge of the opposite.

When someone like Kurt Gödel or Allan Turing or Burtrand Russel or Albert Einstein uses a colloquialism as cognitive aid they do so as metaphor, as armature, even at times as ironic over-simplification, to make a point. When we as audience, as lay-people, or as people outside of direct intimacy with the subject material run with these metaphors as fact, we do so at great peril to the truth from which the colloquialism first arose. This is especially true if we have a particular axe to grind.

I ask the originator of this thread to go the distance and explain the rhetoric that drove them to post the original question.

Randall Reetz

Monica Andersen refers to this information elegance as "salience". The concept that from which salience precipitates is this: despite the fact that a system may have thousands of simultaneous behaviors or structures, some of those are more reactive and predictive of that system"s arch of influence and some are simply noise or support. To the extent that one structure or behavior overwhelms the others, that structure or behavior can be said to be salient (the others less so).

Salience is a property of a hierarchically organized universe (such as the one we inhabit).

Randall Reetz

Lets look at the difference between a theory as abstraction and a system for which that theory is true. Take for instance E=mC^2. This formal logical statement has been shown empirically to describe to many decimal places of accuracy to describe the exact relationship between energy, mass, time and distance. Both the equation and the processor necessary to interpret and apply it (the mind) are finite and much much smaller than the total sub-set of the universe that it describes. That is the thing. In a system that is not random, the order present allows a description and potential prediction based on that description that is at least potentially smaller than the "universe" it abstracts.

However, if one expects to be able to use an abstraction, no matter how valid, to "compute" the state of a system at any given instance, one is faced with a computational resources limit. This limit is not the same though almost always confused with the validity of formal abstraction problem.

It is important always to keep these two problems separate when talking about limits. Patterns are describable in much less information and computation than are required to perform an analogue computation based on those formal abstractions.

The fact that we as humans don't seem to be able to keep these two classes of limits separate does not inform either limit class… and only reflects on the limits of our own human brains as "computational machinery".

Randall Reetz