On Thu, Mar 20, 2014 at 4:26 PM, Robert Hansen <email@example.com> wrote:
> That is what is happening here. I am talking about mental processes that > neither of you have experience with.
Sounds like something out of 'Varieties of Religious Experience' (William James).
Humans are perennially claiming access to a higher knowledge based on intuition or whatever. I respect intuition but the other shoe is testing, evidence, empiricism. Track record is part of it. If you predict things and they happen, that helps establish your track record.
Case in point: I've been written up in the local paper, The Oregonian, twice, as a local futurist. In the 2nd article, I was going on and on about hypertext, and this was pre web. I predicted "hypertext kiosks" that would tell you about health insurance options in hospital lobbies. Some years later, my friend David Lansky said "Kirby, I want to show you something". Yes, twas a spanking new hypertext kiosk wit health plan information, in the lobby of St. Vincent's hospital, where both of us worked.
I have compiled several pages of notes these last few days days that I > still need to sort though, but the gist is that Piaget's last cognitive > stage, the formal stage, was not the actual last stage. There is a higher > stage and that stage is where new theories and the elements of those > theories are born. The formal stage that is documented is actually the > ability to understand formal theories and apply that understanding to > problems. That activity though does not engage an even higher level of > thinking that is required to distill new theory. Essentially, Piaget's > theory is lacking an explanation for Piaget's theory. > > So now comes the evidentiary piece where you have some replicable way to measure these later stages.
Just saying you have mental feelings that others can't or won't, is not in itself evidence of much beyond telling us you're a navel gazer, which I recognized early on.
In Joe's case for example, I was noting at least a year ago that there was > something "off" in his take on mathematics. But I couldn't put my finger on > it. It was a "mental feeling".
You get a lot of mileage out of these "feelings" of yours....
> Over time the clues kept coming in and I am the type that can't let > unsolved riddles go. I put out my theories regarding the illusion of > pedagogical effectiveness in mathematical illustrations and visual > examples. Joe's response? "Says you!".
Like, I think it's effective to show visually why any square number is the sum of two triangular numbers. I'm not sure I can do it here -- in plaintext mode maybe, but there's a picture here:
> Well, yeah, it's my theory, so yes, I said it, but that isn't the response > I get from most people when I describe it. And this has continued and the > vitriol has increased.
Yes, because when people disagree with you or cast aspersions on your theories, your response is to invent a theory to explain their mental defects.
Joe can't understand you because of a kind of blindness you impute. Which is exactly how mystics stereotypically talk. "If you could only see what I see, you would know I was right, but alas, your third eye is still closed."
This attitude / belief / bias of yours gets old after awhile, rubs people the wrong way. But some may find your self-confidence delightful.
> But there is a silver lining to this cloud. I finally, a month or so ago, > solved the riddle. I realized that Joe cannot understand art (another word > for this higher cognitive stage).
Poor old Joe. He'll never reach that higher level Piaget also missed.
> He can read books and apply some of that to problems, but he doesn't > understand how it all is made. And when I say art, it isn't the art of > problem solving. The art I am talking about draws on those facilities but > it goes much deeper than that. When you solve problems at this stage you > change the course of the subject itself. >
Right, you're the genius artist through whom truth simply flows, a conduit to a deeper knowledge.
Whereas I'm adopting a sarcastic tone, you'll say "now you understand, at last you're on topic". The topic seems to be: what makes BH a genius and how might we modify our education system to help people realize their inner Bob?
> > But one doesn't have to change the course of the subject to gain the > advantages of this higher stage of thinking. This higher stage of thinking > affects your experience with mathematics whether you discover the next > paradigm shift or not. And understanding this higher stage of thinking is > crucial to understanding all of the lower stages of thinking. It gives you > that necessary insight to understand the development of mathematical > ability in a student. >
Yep, if only you could bottle and sell it.
> > I accept that in this case I can never convince Joe that this is not a > trick nor that I am just making this up.
Making what up again? What I think Joe sees is drivel. It's not like something fantastic where he's going "how on earth did you come up with such a brilliant thought?" but more like "do you have any idea how much more there is to promulgating truly useful theories?"
At least that's my reading of Joe's tone. He's free to correct me of course.
> And I aways realized that school math stops short of this higher stage, > probably because it is rare, but only now realized the significance of > that. I thought maybe they should add another course devoted to this art > but we know how that would turn out.
Yeah, they'd try to teach it to all kinds of below-average people, thinking it might "close the gap".
But we can't all be born geniuses can we?
> One of the reasons for such poor ideas in math education in the lower > stages is that few people even make it to those stages. The rarity of this > higher stage would only compound this further. I hope my work in AI, when > published, will break through that somehow. As Lou has shown, people have a > better go at it when the theory is complete and the ontology nice and neat. > But no theory will ever solve the politics of education. > > Bob Hansen
Was that AI stuff going to include that "Python without the objects" language you were speaking of?