[r-t] Blue Line Difficulty

[Don Morrison]

​On Tue, Aug 29, 2017 at 8:25 AM, Mark Davies <mark at snowtiger.net> wrote:
> What Graham is trying to achieve should probably be described as "a
> measure of blue line difficulty with the assumption that the method
> and its work is not familiar".

That's still not well defined. I ring with a fellow who learned Cornwall
before Cambridge or Yorkshire; in fact, while he's rung several peals of
different surprise major methods, he's still never rung one of a
Cambridge-above method. What he reports finding more or less difficult is
noticeably different than many others do, even when not related to anything
he's already rung. We all have contexts, and they make a huge difference.

It is telling that at lower stages, after a certain point in our ringing
careers we typically don't learn individual methods any more, we learn
larger collections of them in parallel. How does that fit into a metric of
difficulty?

I think what you have to aim at is "a metric of how difficult a method is
as measured by exactly this metric." As you note, not necessarily a
worthless thing, but I think we need to keep our eyes open about what it
really measures.

> How many bits do we need to represent it? This must have an analogue
> in the number of brain cells required to remember it.

It all depends upon how you chunk it. Which is going to vary by individual
taste and inclination, and by the individual's past experiences.

That said, I work with lots of folks who have spent their whole careers
worry about things like list learning--I'll ask around and see if anyone
has any useful insights. I suspect they do.

And no, I don't think what we can remember and number of brain cells has
quite the relationship you are implying. It works differently than that.
It's still way, way, way, horribly overly naïve, but if you insist on a
simplistic, reductionist approach it might be better to think in terms of
the number of possible connections. While there are many wonderful things
to be said about Von Neumann machines, "being a faithful model of human
cognition" is not one of them.

> In addition to this, it is I think necessary to give weight to factors
which ringers find subjectively difficult:
>
> 1. Frequent changes of direction
> 2. Wrong hunting
> 3. Non-PB leadheads

Why not symmetries, as well? I don't think they just fall out by worrying
about the entropy: I'm pretty sure glide symmetry contributes just as much
redundancy as the usual palindromic symmetry, but I'm guessing most ringers
find the latter considerably more helpful to learning a method (because
it's what they're used to--I'm pretty sure that's the main reason Non-PB
leadheads raise the difficulty). And symmetries don't necessary just make
things easier: I think some classes of error in ringing are probably driven
by "this bit is a lot like that bit, and I got confused between
them"--symmetries sometimes give us more opportunities to make these sorts
of errors.

How does lead length fit into the metric? How should Bastow, Little Bob,
Plain Bob, Crayford Little Bob, Gainsborough Little Bob, Wellington Little
Bob, Kent Treble Bob, Oxford Treble Bob, Albion Treble Bob and Rivendell
Treble Bob rank against one another? And stage? Is Kent Max harder than
Kent Minor--in some ways it's easier, isn't it? Same can be said for
Cambridge or Stedman.

And even those properties that contribute to difficulty depend upon their
contexts. I think the big, double dodges in Buckfastleigh constitute
"Frequent changes of direction" but they are not what, I think, most
ringers find difficult in remembering the method. The difficulty is the
nasty little bits in the middles of the rows between the sets of big dodges
(and long Stedman turns on the ends). Those, too, have frequent changes of
direction, but at about the same rate, or perhaps even a little slower,
than those in the big dodges. Hmm, speaking of "chunking," that's exactly
what that description was doing, where "nasty little bits" refers to
"really hard to chunk".



-- 
Don Morrison <dfm at ringing.org>
"Cognition is at least as complex as the weather."
  -- Ken Forbus, keynote address to the 2015 ACT-R Workshop
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