Hi, Tommaso, thanks for the detailed and insightful comments!
1. The mess left on the ground by Menelaus for achieving his objective was indeed enormous, but in this example of goal achievement it is not immediately clear to me, as an observer in charge of 'creating' agents, where entropy reduction took place.
The entropy reduction of the bacterium is instantiated by the fact that no matter how nucleotides are arranged in the initial state, they become tidily arranged for DNA replication in the final state. The entropy reduction of Menelaus is larger. He manages to achieve DNA recombination not only irrespective of the initial spatial arrangement of molecules in Helen's womb, but also, irrespective of the initial location of Helen herself (Troy). Both he and the bacterium are able to circumvent obstacles, but his require an even more complex strategy. We are the observers of them both, and we evaluate the complexity of their strategies (I do not mean to say that complex strategies are always virtuous). Anyway, the need of all these explanations probably demonstrates that the example was far from optimal, I just meant to say that evolution makes goal-seeking agents increasingly complex.
2. You write: "In this essay, the distinction between micro and macro-states is not emphasized, because the phenomena we deal with are not always divisible into separate scales." But immediately after this sentence you write: "The notion of goal-oriented behavior that is used here always brings about an entropy reduction." Being used to definitions of entropy that are fundamentally based on the distinction between micro- and macro- (levels, variables), I find these sentences as potentially contradictory.
Sorry, I should have clarified that I am speaking of Shannon entropy (negative sum of pi log pi), which does not require a distinction between microscopic and macroscopic. I like to think of Shannon entropy as the mean number of binary questions (and answers) required to specify the state of the system. In the football example, the initial state is described by a probability distribution that is fairly uniform throughout the stadium, and the final state has a peak at the goal. This description does not require us to think at a more microscopic level, for example, of the atoms composing the football players, or the grass of the stadium, etc.
3. I am afraid I found this passage (and its follow up) a bit obscure: "Once observers are in play, even if they might have never intended it, it turns out that the computation they perform is liable to iteration." Are you suggesting that the observers at level k decide to partition level (k-1) smartly enough as to let agents emerge within level (k-1), and that these (k-1)-agents produce the order used as fuel by the observers at level (k), which are in turn seen as agents by the observers at level (k+1)?
Not really, it is not the process of arrogating agency that I meant to iterate at different levels, but rather, the agents created by one single observer (let us think of him/her as outside of the world that he/she observes). Nested agency is an effective and economic description of the world at different levels, because the same concept is applied repeatedly. The agent "prokaryote bacterium" is an effective representation to describe the biochemical processes that take place when one such bug is around (metabolism, replication, displacements, etc). It is also effective because there are many such bugs, so the same concept can be applied repeatedly at the same level. And finally, it is also effective because prokaryotes keep replicating, and the offspring become the fuel for higher-level bugs. The observer can then envision the "eukaryote bacterium" as the association of two prokaryote cells, one inside the other. In turn, the definition of the agent "eukaryote" is not only a compact description for what this bug does in its environment (metabolism, replication, etc.), but it is also a good fuel to construct multi-cellular organisms, and so forth. A smart detection of agents, hence, is not only useful to describe what happens at one single level, but also to construct a whole edifice of levels. Observers tend to search for descriptions of the world that are compact and efficient at the grand scale. Of course, my comments in the essay were way too short to make this idea explicit.
4. "Here, noise is defined as the degrees of freedom that are irrelevant to predicting those features of the environment that affect the observer's fitness." This passage resonates with Rovelli's meaningful information (correlation between internal and external variables), as you may have already noticed. Another contact point with Rovelli: "Only if the initial location has proven to be arbitrary, and the traffic conditions variable, can goal-directed behavior be arrogated." A similar idea is pointed out also by him in his closing discussion on the modality of science.
I was very fond of Rovelli's essay, so all such connections make me happy. His merit, however, was to nail all this down in just a simple formula.
5. As you pointed out, I agree that also our essays are aligned on some aspects (e.g.: "We need an economic description, so we assign agency" is also a central point in my essay, where the economic description is referred to the 'goal').
Yes, indeed, I was happy to see we had many points in common.
Thanks again!
Inés.
