Glen - I find this discussion very provocative in the best way as well. When I was working on the problem of helping researchers visualize the Gene Ontology, we were trying to do several things at once, though I'm not sure we were that clear on that as we did it. We were a small heterogenous team and we were trying to find hidden and subtle structure within a complex "aggregate" structure.
I think Ontologies like the GO provide a good study in what we are discussing here. Something like the GO is a mashup of *all* the extant knowledge of Genes and their gene products (Proteins and RNA) across all species (which includes all Kingdoms, or more accurately Domains) and with it comes potential errors and biases that might have been introduced by the researchers from many fields. In some ways, superposing the knowledge from highly disparate disciplines both increases the scope/parallax and "muddies" things. In some ways, modern ontologies seem like the best of things, worst of things for understanding this phenomenon. In your response to Eric's contribution, you acknowledge "accretion" (temporal layering) as a possibly more meaningful abstraction than mere "hierarchy". You have weighed in before on ideas like this, that "hierarchical structure may be an illusion" (my paraphrase) and I'm at least half-sympathetic with the point. The heritage of Classical Ontology, Aristotle's "Categories", and the general idea of "Abstraction" all seem to reflect or support (or both) our tendency toward hierarchical structuring with a bias toward *strict hierarchies*. It seems that at the very basis of most physical science, we have the ideal of "strict causality", possibly inherited from formal logic? We think in terms of A causes B which in turn causes C & D, etc. with a cascading "light cone" of consequences of every action. Maybe less obvious is the awareness of the construction of "golden threads" where in hindsight, we recognize the number of fortuitous precondiitons that were met to arrive at some observed event. "if my parents had not met at a picnic in 1943, they would not have courted, married, concieved and birthed me", "if my mother had not had a stoic, man-of-the-earth father, she would not have been captured by my father's dream of 'moving west' and I might have been born and raised in deep Appalachia instead of the wide open West, or perhaps not been born at all". "If my Paternal Grandfather had not written letters to my Grandmother while in Europe during WWI, she might have met and married another man...", etc. In either case, our Western conception of causality admits no more than a DAG (to deny causal loops) and privileges strict branching narratives. Similarly, Linnean Taxonomies as well as Cladistics are inherently strict hierarchies, the former based primarily on observational distinctions (birds with seed-cracking beaks vs birds with (insect catching vs carrion eating) beaks, etc.) or inferred evolutionary (multi?)bifurcations. By debunking or deflating or de-emphasizing (strict?) hierarchies, what types of structure remain for us to recognize? Is this problem anything more than model (over?) fitting? By starting with a generalized graph or network, we leave room to recognize other interesting structures (than strict hierarchies), does introducing ideas like temporal aggregation or other weak sisters to "causality" bring back (at least) *directed acyclic* graphs as candidate models? Are POsets (partially ordered sets) uniquely valuable? I'm both rusty and under-informed in this depth of analysis of knowledge structures. I'm hoping (you and?) others here have more up to date knowledge or understanding. - Steve On 4/25/19 8:53 AM, glen∈ℂ wrote: > 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. > ============================================================ > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com > archives back to 2003: http://friam.471366.n2.nabble.com/ > FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove > ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives back to 2003: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove
