I have kept all of Herman's post, and put in my commentary. - I hope that I am not bothering many readers of sci.stat.edu by expanding in this direction. "Consciousness" is something that interests me enough that I don't want to drop the dialog yet, or shut out other possible contributors.
On 29 Apr 2004 09:48:08 -0500, [EMAIL PROTECTED] (Herman Rubin) wrote: > In article <[EMAIL PROTECTED]>, > Richard Ulrich <[EMAIL PROTECTED]> wrote: > > - warning - Another digression (being bright, and being conscious). > > This is very definitely the wrong word; see below. > > >On 27 Apr 2004 11:12:04 -0500, [EMAIL PROTECTED] (Herman > >Rubin) wrote: > > >> In article <[EMAIL PROTECTED]>, > >> Art Kendall <[EMAIL PROTECTED]> wrote: > >> >part 2 > >> >One thing that is being done very frequently today is to have children > >> >teach each other some of the time. Recall Seneca's "docens discimus", > >> >"in teaching, we learn". Trying to find different ways to communicate > >> >the same concept to people broadens and deepens our understanding. > > >> >In addition, my recall of my grammar school education is based on my > >> >perception at the time when my mind was much less developed. HR > > >> This may be the case for adults, but not necessarily for > >> children. When my son was 6, he understood, and could do, > >> algebra and logic, but he could not explain anything. > > >> One has to learn a lot to explain something which is, to > >> him, completely obvious, to someone who does not see it. RU > > >Oh! Now we introduce 'consciousness'. HR > > I said nothing about "consciousness". Sorry - Donald did not see the connection, either, in his post. I jumped ahead, I guess, figuring mathematicians might already share my language and conclusions about this. The phrase, "completely obvious", seemed to encode my own early experiences of the unconscious solution of easy math problems. On consideration of these negative reactions, I remember that I have now read numerous philosophical discussions of consciousness and intelligence. The terminology is a bit abstracted from the commonplace; or perhaps it is more exact to say, there are some widely shared conclusions about consciousness that are not yet commonplace. For instance: Expert performances are mostly not 'conscious' but employ well-learned unconscious routines under slight guidance. (The caterpillar walked just fine until he tried to figure out how.) I've been encouraged to think the ideas are spreading. Last year, there was a major league ballplayer whose problems with overthrowing first were blamed on being overly-conscious -- that was in the sports pages. HR> > Ramanujan, who produces hundreds of results in analytic > number theory and related parts of analysis, in fact only > published little of the ideas behind them. Most of the > proofs were published by others; I believe they are still > going through the "lost notebook", sent by his widow to > Hardy on his death, and relatively recently found. As to > how he got the results, he attributed them to a particular > Hindu goddess. - or, in the vocabulary, "unconscious processes." That is what is going on, when you know the result, and then have to figure out afterwards how you got there. HR > > The human mind is quite capable of dealing with concepts > which are, as far as we can tell, purely abstract, and even > of communicating them by describing their formal properties. > As to how one uses them, or decides which ones to use, this > is much harder to explain. Mathematicians do know that conscious thinking can be non-verbal. Much of it is spatial (spacial?), but I do not identify that with "purely abstract". In addition to the problem of figuring "how you got there", mathematicians sometimes need to figure "how to put it into words" or other symbols. RU > > >I have previously assumed that consciousness was a good thing > >for science and math, and underlies future learning. So, I would > >have expect that your well-advanced son could learn by teaching. HR > > He was fully conscious about what he knew. It is quite possible I don't see that you have any reason to assume that he was "fully conscious" in my terminology; if he is good at it, that would arrive some time *after* he could solve the easy ones. > that he might have been able to present the material as he > learned it, although I doubt that most can present the courses - and, as you have indicated again and again, most students do not *learn* much in their courses. I know that I improved some of my math understanding by teaching others. Now, maybe this is a bad approach for some subtle reason, but you have said nothing to show that the approach is bad, have you? > they took, but this would not help someone to solve a problem > in algebra as he did. RU > > >I thought that the arguments for 'natural ease' were confined to > >production in certain of the arts, as performed by very young > >people. Yes, adults want to get back to naturalness and > >unconsciousness, but we do that most fruitfully after training -- > >which (I think) is characterized by being conscious. > > >I am curious, do folks here assume the same, or otherwise? HR > > Most of those reading this newsgroup are familiar with the > Neyman-Pearson Lemma. I have yet to see a textbook provide > other than a formal proof, and low-level ones just a statement. > It is not difficult to present enough to make it "intuitively > obvious" to someone who can understand high-school level > discrete probability. -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
