MaxPat: The Maximum Pattern Creation Principle

I will argue here that, in natural environments (I’ll explain what this means below), intelligent agents will tend to change in ways that locally maximize the amount of pattern created.    I will refer to this putative principle as MaxPat.

The argument I present here is fairly careful, but still is far from a formal proof.  I think a formal proof could be constructed along the lines of this argument, but obviously it would acquire various conditions and caveats along the route to full formalization.

What I mean by “locally maximize” is, roughly: If an intelligent agent in a natural environment has multiple possible avenues it may take, on the whole it will tend to take the one that involves more pattern creation (where “degree of patternment” is measured relative to its own memory’s notion of simplicity, a measure that is argued to be correlated with the measurement of simplicity that is implicit in the natural environment).

This is intended to have roughly the same conceptual form as the Maximum Entropy Production Principle (MEPP), and there may in fact be some technical relationship between the two principles as well.   I will indicate below that maximizing pattern creation also involves maximizing entropy in a certain sense, though this sense is complexly related to the sort of entropy involved in MEPP.

The setting in which I will consider MaxPat is a universe that contains a large number of small “atomic” entities (atoms, particles,  whatever), which exist in space and time, and are able to be assembled (or to self-assemble) into larger entities.   Some of these larger entities are what I’ll call Stable Systems (or SS’s), i.e. they can persist over time.   A Stable System may be a certain pattern of organization of small entities, i.e. some or all of the specific small entities comprising it may change over time, and the Stable System may still be considered the same system.  (Note also that a SS as I conceive it here need not be permanent; stability is not an absolute concept...)

By a “natural environment” I mean one in which most Stable Systems are forming via heavily stochastic processes of evolution and self-organization, rather than e.g. by highly concerted processes of planning and engineering.  

In a natural environment, systems will tend to build up incrementally.   Small SS’s will build up from atomic entities.   Then larger SS’s will build up from small SS’s and atomic entities, etc.    Due to the stochastic nature of SS formation, all else equal, smaller combinations will be more likely to get formed than bigger ones.  On the other hand, if a bigger SS does get formed eventually, if it happens to be highly stable it may still stay around a while.

To put it a little more explicitly: The odds of an SS surviving in a messy stochastic world are going to depend on various factors, including its robustness and its odds of getting formed.   If formation is largely stochastic and evolutionary there will be a bias toward: smaller SS’s, and SS’s that can be built up hierarchically via combination of previous ones…  Thus there will be a bias toward survival of SS’s that can be merged with others into larger SS’s….   If a merger of S1 and S2 generally leads to S3 so that the imprint of S1 and S2 can still be seen in the observations produced by S3 ( a kind of syntax-semantics continuity) then we have a set of observations with hierarchical patterns in it…

Now, consider the position of an intelligent agent in a natural environment, collecting observations, and making hypotheses about what future observations it might collect.

Suppose the agent has two hypotheses about what kind of SS might have generated the observations it has made so far: a big SS of type X, or a small SS of type Y.   All else equal, it should prefer the hypothesis Y, because (according to the ideas outlined above) small SS’s are more likely to form in its (assumed natural) environment.   That is, in Bayesian terms, the prior probability of small SS’s should be considered greater.

Suppose the agent has memory capacity that is quite limited compared to the number of observations it has to process.  Then the SS’s it observes and conjectures have to be saved in its memory, but some of them will need to be forgotten as time passes; and compressing the SS’s it does remember will be important for it to make the most of its limited memory capacity.   Roughly speaking the agentwill do better to adopt a memory code in which the SS’s that occur more often, and have a higher probability of being relevant to the future, get a shorter code.   

So, concision in the agent’s internal “computational model” should end up corresponding roughly to concision in the natural environment’s “computational model.”

The agent should then estimate that the most likely future observation-sets will be those that are most probable given the system’s remembered observational data, conditioned on the understanding that those generated by smaller SS’s will be more likely.  

To put it more precisely and more speculatively: I conjecture that, if one formalizes all this and does the math a bit, it will turn out that: The most probable observation-sets O will be the ones minimizing some weighted combination of

As KL distance is relative entropy, this is basically a “statistical entropy/information based on observations” term, and then an “algorithmic information” type term reflecting a prior assumption that more simply generated things are more likely.

Now, wha does this mean in terms of “pattern theory”?  -- in which a pattern in X is a function that is simpler than X but (at least approximately) produces X?   If one holds the degree of approximation equal, then the simpler the function is, the more 'intense" it is said to be as a pattern.

In the present case, the most probable observation-sets will be ones that are the most intense patterns relative to the background knowledge of the agent’s memory.  They will be the ones that are most concise to express in terms of the agent’s memory, since the agent is expressing smaller SS generators more concisely in its memory, overall.

Now let us introduce the agent’s actions into the picture. 

If an agent, in interaction with a  natural, environment, has multiple possible avenue of action, then ones involving setting up smaller SS’s will on the whole be more appealing to the agent than ones involving setting up larger SS’s. 

Why?  Because they will involve less effort -- and we can assume the system has limited energetic resources and hence wants to conserve effort. 

Therefore, the agent’s activity will be more likely to result in possible scenarios with more patterns, than ones with less patterns.   That is -- the agent’s actions will, roughly speaking tend to lead to maximal pattern generation -- conditioned on the constraints of moving in the direction of the agent’s goals according to the agent’s “judgment.”  

So, what we have concluded is that: Given the various avenues open to it at a certain point in time, an intelligent agent in a natural environment will tend to choose actions that locally maximize the amount of pattern it understands itself to create(i.e., that maximize the amount of pattern created, where “pattern intensity” is measured relative to the system’s remembered observations, and its knowledge of various SS’s in the world with various levels of complexity.)    

This is what I call the Maximum Pattern Creation Principle – MaxPat.

If the agent has enough observations in its memory, and has a good enough understanding of which SS’s are small and which are not in the world, then measuring pattern intensity relative to the agent will be basically the same as measuring pattern intensity relative to the world.  So a corollary is that: A sufficiently knowledgeable agent in a natural environment, will tend to choose actions that lead to locally maximum pattern creation, where pattern intensity is measured relative to the environment itself.

There is nothing tremendously philosophically surprising here; however, I find it useful to spell these conceptually plain things out in detail sometimes, so I can more cleanly use them as ingredients in other ideas.    And of course, going from something that is conceptually plain to a real rigorous proof can still be a huge amount of work; this is a task I have not undertaken here.