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. >> 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. >Oh! Now we introduce 'consciousness'. I said nothing about "consciousness". 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. 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. >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. He was fully conscious about what he knew. It is quite possible that he might have been able to present the material as he learned it, although I doubt that most can present the courses they took, but this would not help someone to solve a problem in algebra as he did. >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? 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. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University [EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
