Yes! I can't seem to find a copy of the article. But going on your description and the figures, it looks like an excellent example of treating hierarchy as something to measure rather than impute. (The silverchair.com link didn't work, unfortunately.)
Until I can find a copy, some of what you say is provocative. It seems to me that talking directly about the graph (or network, an alternative Potochnik mentions) is the more literal concept, where level and hierarchy are the more metaphorical ones. Even the concept of accretion (temporal layering) is, to me, more meaningful than level or hierarchy. So, the question remains *what* advantage do we gain from "zooming out" and thinking in terms of hierarchy and levels that we didn't already have in terms of [a]cyclic, temporal or structural, graphs? Is the advantage largely rhetorical and communicative, accounting for the variations in the way the audience and participants think? Or are there, eg experimental design, questions and measures we can take that are made more precise and testable in terms of level and hierarchy versus graphs? On 4/24/19 4:51 PM, Eric Smith wrote:
Here is a nice example, of that onus accepted and handled clearly. https://www.nature.com/articles/nature07749 Topic is the accretionary dependency structure in the large subunit of the ribosome. In particular, see Fig. 2, which my image-page on chrome is showing me at this URL (don’t know if these URLs produce equivalent output for different users): https://www.google.com/search?q=bokov+and+steinberg+ribosome&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjXjfm58unhAhXKzLwKHXG5B60Q_AUIDigB&biw=1371&bih=745#imgrc=uExkhZIl02WciM: The primitive data is a set of links between locations in folded RNA, which can be assigned a directionality that is very likely a dynamically meaningful one. The result is a graph with directed links. It is an empirical question whether the graph is cyclic or acyclic, with the answer being the latter. The primitive data structure is only the acyclic graph. However, a second question is whether the nodes in the graph admit a partial order, and if so, which sets of nodes constitute each distinct level within that order. That question too has an answer in terms of the maximal extent to which the equivalence class defining a level can be extended, without violating the dependency structure in the underlying DAG. Nodes in a level need not have been historically contemporaneous, but they reflect assembly conditions, as nodes at higher levels “plug into” nodes at lower levels, and thus require them to be in place. This seems extremely likely to reflect an actual historical accretionary sequence, in which equivalence of nodes within a level quantifies the ambiguity of how they may have related in time. Lots more has been done to extend this data to a detailed module decomposition, with or without the level post-processing. Through all of it, the level decomposition continues to be salient, as levels by the analysis of the DAG also correspond roughly to horizons for generations of peptide structure. See https://watermark.silverchair.com/msx086.pdf?token=AQECAHi208BE49Ooan9kkhW_Ercy7Dm3ZL_9Cf3qfKAc485ysgAAAjwwggI4BgkqhkiG9w0BBwagggIpMIICJQIBADCCAh4GCSqGSIb3DQEHATAeBglghkgBZQMEAS4wEQQMGr_TvxBlD6v5A3yIAgEQgIIB77pRGYntr9gP-GNtZajC6JIiEDLCsmZFdcSgAVoYO43dh_vul542Uzn2GyejvMgnqthKt7u3ZnQoenITwMrwvneJMWZ9n6-UlYuottaxIkpxp6lWIfiTIla83YKJqigjdIbWtQx_W2y2J2pJgAKOBdbvvTctto3COkdwh4C6VH5AARmbw0bRfaMH_gRW8IKRNw8m4Gw--SbRMDlkHqaXRY8WJlbkrN8uB-ygTiu4TL12LHhNiWlxCLH0LP3pLKPBMmBG0tKM5sMIuO2CDVltBItUIT6i91Z0q2x-l6u5yBWqPFlDfpYNok--att5kqPbtzT1H7IzZev-AsWYpq_ek2RdyHxrthXdn2rTzvhMjmUlb1JHoeJX6holXrs8j1PKzwg_pW-3wtR6cYZg3VBLM6V_cTnMlyNIMABBkyix8D9pBvq6Hj7zLWABE8Oq0nuVUH5vd0U8RVbqpF5SS1OKd2Y13BN_bq-4P7B3RKKYmoecn2SVqoYPHZBV7csmkq9duwoydMQFbcGsk8BYopz6zEti3BuZJxXa2J6YT1i1pXQNMvSTHXRKdsIntCJkSZsPRwS-q6GiM5r7BtTU9hOLZLq__67NMjBDpWUcOG7pglEYuqENH7xy4abOEoE5TusJg9aU6PE9Tj9ayBkHnIONBg and Fig.5 within it: https://www.google.com/search?q=bokov+and+steinberg+ribosome&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjXjfm58unhAhXKzLwKHXG5B60Q_AUIDigB&biw=1371&bih=745#imgrc=HRSn_FYi9cUYDM: It’s great when people take on small enough questions that they have time to speak in full sentences.
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