From: Charles D Hixson (email@example.com)
Date: Sat Apr 15 2006 - 18:05:18 MDT
On Thursday 13 April 2006 05:14 am, Chris Capel wrote:
> On 4/12/06, Chris Capel <firstname.lastname@example.org> wrote:
> > On 4/12/06, Charles D Hixson <email@example.com> wrote:
> > > On Wednesday 12 April 2006 07:18 am, Chris Capel wrote:
> > > > Given the Flynn effect and the amount of time since the industrial
> > > > revolution, I think if humans do straddle the threshold, the
> > > > threshold would still be below the average IQ. Even in human beings,
> > > > the main component of intellectual accomplishment is dedication and
> > > > energy, leading to steady, long-term progress, not raw processing
> > > > power. Ask any bright person with ADD.
> > >
> > > To me it appears that there is something analogous to stack depth that
> > > renders some concepts unintelligible to many people, even though some
> > > others can understand them. This doesn't appear amenable to teaching
> > > or solvable through interest. I'll grant that for many concepts this
> > > doesn't apply, but for some it appears to.
> > >
> > > It's actually even worse (more extreme) than that...sometimes, e.g.
> > > when my allergies are acting up, I cannot understand thoughts that I
> > > had earlier...it's as if there is a step involved in processing that is
> > > a variable, and it must allow a certain depth of recursion or stack or
> > > something. Somedays I can't understand things that I couldn't on other
> > > days.
> > If what you say is true (and I have no opinion, though it sounds
> > plausible)
> Actually, I think I have an opinion. It seems like, on problems that
> are too complex for us to understand, we can actually make slow
> progress on them. But each additional piece of information required to
> understand the problem requires an exponential increase in the time
> required to understand it. Because information can be made to "shrink"
> so that we can fit more of it in our working memory. This is a major
> function of all learning, and it applies to specific problems. It just
> takes repeated exposure to the relevant ideas for them to become
> habitual, more easily brought to mind, and more easily worked with.
> So on an issue you're not very familiar with, you might see what
> Charles saw, that you can grasp it in its entirety when you're feeling
> especially insightful, but that you're not practiced enough with the
> concepts to bring them all to mind when you're feeling a bit slow. But
> with additional familiarization, you'll be able to bring those
> concepts to mind even at a diminished capacity.
> Alternatively, it could be that at some times one's capacity for any
> rational abstract thought is very diminished, but it turns out we
> don't really use that part of our minds as much as we think, so we
> only notice it when we try to think about complicated problems.
> Certainly, we use habitual neural pathways, and our unconscious mind,
> for a lot more than we often realize.
> Chris Capel
> "What is it like to be a bat? What is it like to bat a bee? What is it
> like to be a bee being batted? What is it like to be a batted bee?"
> -- The Mind's I (Hofstadter, Dennet)
What you describe is chunking, and chunking is definitely necessary. In fact
"proper chunking" is probably one of the hard problems. What I'm asserting,
however, is that chunking isn't sufficient. For problems at the edge of your
ability to solve, you may not be able to chunk them. If, somehow, you
acquire a pre-chunked description (e.g., you solve the problem on a good day)
then you may still be able to use the pre-computed chunking on other days,
but for problems of a certain inherent complexity, this isn't possible. This
doesn't mean that the problem isn't soluble. It means it's too
recursively(?) deep to hold in active memory, even when it's been chunked. I
can imagine that "external memory" (pencil and paper to pick a familiar
example) can provide this temporary external storage that allows one to work
on problems too complex to solve directly...but this has limitations in
speed, portability, etc. And in devising reproduceable and recognizable
symbols. Eventually, working beyond our capacity to understand, we arrive at
computers and things like the "proof" of the four color theorum. Proof is in
quotes here because NOBODY understands it. People understand parts of it,
and different people understand different parts, so we *may* have a complete
coverage. Perhaps humanity understands that proof, even though no single
The "Four color theorum proof" was the first example of a "thing" that we
believed we knew to be true, but nobody COULD understand exactly WHY we
believe it was true. The standards for a "mathematical proof" changed
tremendously with the publication of that proof, and it stands as a "first
example" of things that we can't understand because our "intelligence" (i.e.
stack depth, active memory size, what have you) is too weak. Each step of
the proof can be understood, but the thing as a whole cannot be.
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