Good post; in particular good job distinguishing between the natural abstraction hypothesis and my specific mathematical operationalization of it.
The outer appearance vs inner structure thing doesn’t quite work the way it initially seems, for two reasons. First, long-range correlations between the “insides” of systems can propagate through time. Second, we can have concepts for things we haven’t directly observed or can’t directly observe.
To illustrate both of these simultaneously, consider the consensus DNA sequence of some common species of tree. It’s a feature “internal” to the trees; it’s mostly not outwardly-visible. And biologists were aware that the sequence existed, and had a concept for it, well before they were able to figure out the full sequence. So how does this fit with natural abstractions as “information relevant far away”? Well, because there’s many trees of that species which all have the roughly-the-same DNA sequence, and those trees are macroscopically far apart in the world. (And even at a smaller scale, there’s many copies of the DNA sequence within different cells of a single tree, and those can also be considered “far apart”. And going even narrower, if there were a single strand of DNA, its sequence might still be a natural abstraction insofar as it persists over a long time.)
Causally speaking, how is information about DNA sequence able to propagate from the “insides” of one tree to the “insides” of another, even when it mostly isn’t “outwardly” visible? Well, in graphical terms, it propagated through time—through a chain of ancestor-trees, which ultimately connects all the current trees with roughly-the-same sequence.
Good post; in particular good job distinguishing between the natural abstraction hypothesis and my specific mathematical operationalization of it.
The outer appearance vs inner structure thing doesn’t quite work the way it initially seems, for two reasons. First, long-range correlations between the “insides” of systems can propagate through time. Second, we can have concepts for things we haven’t directly observed or can’t directly observe.
To illustrate both of these simultaneously, consider the consensus DNA sequence of some common species of tree. It’s a feature “internal” to the trees; it’s mostly not outwardly-visible. And biologists were aware that the sequence existed, and had a concept for it, well before they were able to figure out the full sequence. So how does this fit with natural abstractions as “information relevant far away”? Well, because there’s many trees of that species which all have the roughly-the-same DNA sequence, and those trees are macroscopically far apart in the world. (And even at a smaller scale, there’s many copies of the DNA sequence within different cells of a single tree, and those can also be considered “far apart”. And going even narrower, if there were a single strand of DNA, its sequence might still be a natural abstraction insofar as it persists over a long time.)
Causally speaking, how is information about DNA sequence able to propagate from the “insides” of one tree to the “insides” of another, even when it mostly isn’t “outwardly” visible? Well, in graphical terms, it propagated through time—through a chain of ancestor-trees, which ultimately connects all the current trees with roughly-the-same sequence.