Financial status: This is independent research. I welcome financial support to make further posts like this possible.

Epistemic status: This is in-progress thinking.

This post is part of a sequence on the accumulation of knowledge. Our goal is to articulate what it means for knowledge to accumulate within a physical system.

The challenge is this: given a closed physical system, if I point to a region and tell you that "knowledge is accumulating" in this region, how would you test my claim? What are the physical characteristics of the accumulation of knowledge? We do not take some agent as the fundamental starting point but instead take a mechanistic physical system as the starting point, and look for a definition of knowledge accumulation in terms of physical patterns.

In this post I explore directly looking within the territory for a physical map that resembles the territory.

Example: Shipping container

In the shipping container example from the previous post, if we found within some region of interest a physical map with markings that clearly corresponded to the arrangement of items in the shipping container, then we could say, yes, knowledge exists within this region. If we revisited this region over several time steps and observed the markings on the map coming into closer and closer correspondence to the configuration of the overall shipping container then we could say that knowledge is accumulating there.

Example: Sailing ship

Suppose we examined a sailing ship from a few hundred years ago and asked whether knowledge was accumulating on that sailing ship. If we found physical sheets of paper with drawings of nearby coastlines then we could say, yes, there is a process happening on this ship that is resulting in the accumulation of knowledge.

Resemblance

But what exactly does it mean for one thing to resemble another? The original lesswrong 1.0 had the following header at the top of each page, pointing at a certain concept of map/territory resemblance:

Suppose we converted both the "map" and "territory" image to grayscale and then looked at a 2D histogram of pixel intensities with pixels from the "map" on the X axis and pixels from the "territory" on the Y axis.

We would find that the "map" and "territory" pixel intensities are predictive of one another, in the sense that knowing the "map" pixel intensity gives us some information about the corresponding "territo...

The accumulation of knowledge