Comment by kjhughes | Hacker News Reader

Comment by kjhughes | Hacker News Reader

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You're right about hierarchy in the world, but there's a deeper truth that you're missing that relates to hierarchical structures being more amenable to description:

  The fact then that many complex systems have a nearly decomposable,
  hierarchic structure is a major facilitating factor enabling us to
  understand, describe, and even "see" such systems and their parts.
  Or perhaps the proposition should be put the other way around.  If
  there are important systems in the world that are complex without
  being hierarchic, they may to a considerable extent escape our
  observation and understanding.  Analysis of their behavior would
  involve such detailed knowledge and calculation of the interactions
  of their elementary parts that it would beyond our capacities of
  memory or computation.

  - Herbert A. Simon, "The Sciences of the Artificial", 2nd edition, page 218

Also, hierarchy in the physical world is not just due to one object being able to only be in one location at a time (or only one object being in a one location). It also arises due to the improved evolvability of hierarchic systems. Again, see Herb Simon's "The Sciences of the Artificial" for a delightful treatment of hierarchic systems and our cognitive relationship with them.

Nit: The pigeonhole principle is exactly the opposite of "only one object being in one location at a time".

It says that if you have m pigeons and n holes, and m > n pigeons, at least one hole is going to have two pigeons in it.

You're right. I've removed the erroneous reference so that it doesn't detract from the rest of the post. Thank you.

It's not the same pigeon that's twice in the same hole though, so it's not "exactly the opposite" -- just orthogonal.

I guess my POV is that hierarchic systems are inherently limiting to us, for data that isn't truly hierarchical (as is usually true for data).

Using graphically-linked data, one could write a process that would generate a hierarchical structure that minimizes crosslinks, and that hierarchy would presumably remain stable right up until the point that a certain relationship is changed, at which point the entire generated hierarchy might be reshuffled. But if we manually assert such a hierarchy, then we have incentive to ignore relationship changes, or try to force them to work within the same hierarchical structure that doesn't serve it anymore. It inhibits our ability to process and understand.

We have more and more ability to visualize true graphical structures and I think it's underutilized in general.

Thanks for the recommendation; I will check it out.

The observation that hierarchical things are easier to describe is interesting. Maybe it has something to do with the adjointness of syntax and semantics [1], and that posets induced by hierarchical structures just naturally share more structure with our hierarchically-structured languages, so they are easier to glue together with Galois connections.

[1] https://en.wikipedia.org/wiki/Galois_connection#Syntax_and_s...

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