Shell sort [edited to provoke]

[Distinguishable entities operating identically by simple rules can form structures high in specified complexity. That is, the crabs in the video differ in size, but not in the “program” they execute. Want more specified complexity? Just add crabs.]

Not to mistaken for the Shellsort algorithm devised by Donald Shell (1924-2015).

14 thoughts on “Shell sort [edited to provoke]

  1. Is it the purpose of any one of the crabs, or even of the collective, to form a sorted sequence of shells? Not that I can see. It seems that each crab acts “greedily” to get a better shell. A bigger crab will stop a smaller crab from getting ahead of it in line. A smaller crab cannot stop a bigger crab from getting ahead of it. I haven’t searched yet for publications on this behavior, but will suggest that the apparent cooperation results from competition. [ETA: Qualify this by the observation that crabs that differ substantially in size are not in competition for the same shells.] Please don’t argue the point without bothering to check out the relevant science.

    If the collective of crabs has a purpose, then it is to reallocate a scarce resource, not to sort seashells in order of size.

  2. Distinguishable entities operating identically by simple rules can form structures high in specified complexity.

    We’ll take your word for it. 🙂

  3. BBC nature documentaries are an important part of my sleep anti-hygiene. (Today — this afternoon — I actually failed in my first attempt to make coffee.) If you watch them closely, you’ll see that the filmmakers know much more science than comes through in the narratives. The video clip above shows a crab, having outgrown its shell, literally sizing up a shell that is far too large for it, and moving on. Then it shows a crab waiting at a shell that is somewhat too large for it, and a second crab waiting for its shell, and a third crab waiting for the second crab’s shell, etc. I’m guessing that the rules are to wait close to an empty shell that is a bit too big for you, and to wait close to an occupied shell that is about the right size for you, provided that the occupant is waiting. It would have been nice to see the line reassemble, after the occupant-to-be of the empty shell arrived.

    I should be reading instead of writing. But I don’t have much of a brain today.

  4. OP: Distinguishable entities operating identically by simple rules can form structures high in specified complexity.

    Mung: We’ll take your word for it. 🙂

    That’s no fun. When I say provoke, I mean provoke. Of course, I would not have highlighted the claim unless I had thought about how an ID proponent would go about calculating the specified complexity of the sequence of seashells. I am not thinking terribly well today, so I may well have made a mistake. Want to find out?

    As it happens, I reviewed, back in 2003, a conference submission that made much of the failure to obtain a sort by genetic programming. The chairman of the conference, Garry Greenwood, evidently noticed the review. He never mentioned the paper to me — that would have been inappropriate — but he did bring up the topic of ID in a conversation at the conference. That conversation led to our chapter, “Intelligent Design and Evolutionary Computation,” in the edited volume Design by Evolution. (Yes, I know that you know about the chapter. It derives ultimately from my response to a claim that evolution cannot produce a sorting algorithm. Now you know why the video is particularly interesting to me.)

  5. By the way, I am not saying that what we see in the video is execution of a sorting algorithm. There is not an input of shells to sort. But there does emerge a sequence in which the shells are sorted according to size. “Sorted by size” is a correct description of shells in the sequence.

  6. dazz: God smuggled all the specified complexity in the shells

    Astute remark. So we’re looking a sequence of objects that are all high in specified complexity. And the specified complexity of the sorted-by-size sequence of objects can be high (ignoring fine features of the objects), given enough crabs.

  7. A good search term to use in Google Scholar is “hermit crab” shell fight OR exchange. The first problem I note is that “hermit crab” is not a single species. I won’t make the convenient assumption that shell fights/exchanges are similar in different species. I searched bbc.com for an identification of the species in the video, but found nothing.

    Moving to Wikipedia, I find in “Shells and Shell Competition” that I’ve got the right idea, and references to some perhaps-helpful sources:

    As hermit crabs grow, they require larger shells. Since suitable intact gastropod shells are sometimes a limited resource, vigorous competition often occurs among hermit crabs for shells. The availability of empty shells at any given place depends on the relative abundance of gastropods and hermit crabs, matched for size. An equally important issue is the population of organisms that prey upon gastropods and leave the shells intact.[8] Hermit crabs kept together may fight or kill a competitor to gain access to the shell they favour. However, if the crabs vary significantly in size, the occurrence of fights over empty shells will decrease or remain nonexistent.[9] Hermit crabs with too-small shells cannot grow as fast as those with well-fitting shells, and are more likely to be eaten if they cannot retract completely into the shell.[10]

    As the hermit crab grows in size, it must find a larger shell and abandon the previous one. This habit of living in a second-hand shell gives rise to the popular name “hermit crab”, by analogy to a hermit who lives alone.[11] Several hermit crab species, both terrestrial and marine, have been observed forming a vacancy chain to exchange shells.[12] When an individual crab finds a new empty shell it will leave its own shell and inspect the vacant shell for size. If the shell is found to be too large, the crab goes back to its own shell and then waits by the vacant shell for anything up to 8 hours. As new crabs arrive they also inspect the shell and, if it is too big, wait with the others, forming a group of up to 20 individuals, holding onto each other in a line from the largest to the smallest crab. As soon as a crab arrives that is the right size for the vacant shell and claims it, leaving its old shell vacant, then all the crabs in the queue swiftly exchange shells in sequence, each one moving up to the next size.[13] Hermit crabs often “gang up” on one of their species with what they perceive to be a better shell, and pry its shell away from it before competing for it until one takes it over.[14]

    My claim about the specified complexity of the sequence of shells doesn’t depend on the relevant science. (And that’s actually an indictment of specified complexity.)

  8. Tom English: So we’re looking a sequence of objects that are all high in specified complexity. And the specified complexity of the sorted-by-size sequence of objects can be high (ignoring fine features of the objects), given enough crabs.

    … except that by the post-2005 Dembski definition of specified complexity it’s not SC unless it cannot be achieved by natural evolutionary forces such as natural selection. And we don’t know whether that is true. At least, we don’t have any convincing argument that it is true. Therefore we don’t know that it really is Specified Complexity.

    By the way, the general shapes of mollusc shells are describable by a modest number of parameters in a model, due to the late and great David Raup in 1961:

    Java applet

    The paper

  9. Joe Felsenstein: the post-2005 Dembski definition of specified complexity it’s not SC unless it cannot be achieved by natural evolutionary forces such as natural selection.

    The natural processes are indeed natural evolutionary processes in the examples that matter most to him (and to us). But I never took the theory to be so restricted in “Specification: The Pattern that Signifies Intelligence” (2005). (I’ve returned to parts of the paper over and over, but haven’t read the whole of it since 2007.) Now that Ewert, Dembski, and Marks have restricted specification to algorithmic specification, and have applied the algorithmic specified complexity measure to non-biological objects (never to biological structures, as I recall), the issue is academic. I will mention, though, that Dembski’s “search for a search” regress would not have worked if “search” were restricted to biological evolutionary processes.

    Joe Felsenstein: By the way, the general shapes of mollusc shells are describable by a modest number of parameters in a model, due to the late and great David Raup in 1961

    That is why an ID proponent can target a small subset of the space of possible shells, and give a concise description of it. (Thanks for reminding me of the details.) The descriptive complexity of the target is low. If we do not provide a probabilistic evolutionary model in which the target event occurs with non-low probability, the ID proponent will claim that the probabilistic complexity of the event (inversely related to the probability) is high. Taking the difference of high probabilistic complexity and low descriptive complexity, the ID proponent assigns high specified complexity to the event.

    By the way, Ewert, Dembski, and Marks have abandoned the universal probability bound. They do not give threshold levels of algorithmic specified complexity at which we must infer design.

  10. P.S. — I do not know how to measure algorithmic specified complexity for any event but a singleton, which is to say, an individual object. I wrote at least one of the authors, asking whether they had a generalization to larger events, and got no response. In the case of mollusc shells, they might discretize the parameter space of Raup’s model, and target a single shell. Who would ever say that a particular shell was anything but a very low probability outcome of evolution?

  11. Mung: We’ll take your word for it.

    No, even better if those words invoke the supernatural to explain the mundane, were written roughly 2 millenia ago by anonymous authors, and in several places got manually copied and translated multiple times. THEN we’ll take their word for it.

    How are you not melting from irony overload?

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