00100	Notes on "A Study of Children's Thinking" by Margaret Donaldson,
00200	Tavistock Publications, London 1963
00300	
00400	Popper in "The Poverty of Historicism" London 1957 distinguishes
00500	between 'prophetic' and 'technological' predictions.
00600	
00700	Alice Heim, "The Appraisal of Intelligence" 1954
00800	p. 18.  It is regarded as obvious that the child who experimentally
00900	fits the manikin together and then readjusts wrong fits is less
01000	intelligent than the child who figures it out without looking and
01100	then does it right the first time.  This is not right, because one
01200	style of work may be better in one circumstance than another, and,
01300	in particular, postponement of the physical trial until the matter
01400	is fully worked out may represent only a neurotic fear of being
01500	seen to make a mistake.
01600	
01700	A simple elimination problem is given to 11 year olds.  All the 
01800	children seem to understand the problem, but they make the following
01900	kinds of errors:
02000	
02100		1. Forgetting part of the problem like one of the schools.
02200	(Perhaps they skipped when reading the problem).
02300	
02400		2. Forgetting an intermediate result.
02500	
02600		3. Losing track of the state of reasoning and guessing.
02700	
02800	Queries:  Did they see the problem on paper?
02900	
03000		Did they use paper?  I did.
03100	
03200		Would a stronger motivation to solve the problem have
03300	invoked more checking?  How confident were they of their wrong
03400	answers.  I bet I could have gotten better results by motivating
03500	them more strongly.
03600	
03700		All this seems irrelevant to AI, because our problem would
03800	have been to write a program that would uunderstand the problem.
03900	
04000		If we take this problem too seriously, we would conclude that
04100	all human minds use the same adequate algorithms; the only problem is
04200	that the low level hardware has bugs, and the motivation is often
04300	inadequate to sustain the effort.
04400	
04500		Any person intellectual enough to work seriously on the more
04600	sophisticated elimination problems used as puzzles would have a clear
04700	picture of his state of solution of the problem and could solve it
04800	drunk or stoned if motivated.
04900	
05000		Suppose we divide human intelligence into possession of
05100	algorithms and having good hardware.  A test for possession of
05200	algorithms should result in the same score drunk or sober.  Therefore,
05300	unlimited time, pencil and paper should be allowed.  Adequate motivation
05400	should be assured by paying for each problem successfully solved.
05500	
05600		Now we consider the group  Y  experiments.
05700	
05800		1. Some of these younger children attempted to introduce
05900	extraneous information from general experience like asking what
06000	districts the boys lived in.  In a real life problem, the full set
06100	of relevant information is not given in advance; hence the behavior
06200	is rational.  The older children were more sophisticated about set
06300	problems and understood that in such a problem, all relevant information
06400	is presented by the questioner.
06500	
06600		2. The fact that old people introduce supplementary information
06700	might be explained similarly.  They too are farther from the set
06800	problem than the twelve-year-olds, even assuming that their educations
06900	included an equal amount of it.  Failure to understand that one is
07000	dealing with a set problem might be regarded as a kind of social
07100	unawareness rather than as a lack of intellect.
07200	
07300		3. Phil's conclusion that there should be more than four
07400	questions would make more sense if he were complaining that there are
07500	only four assertions to determine the schools of the five boys.  This
07600	is a legitimate worry; the fifth assertion is that the boys go to
07700	different schools.
07800	
07900		4. The assumption of one-to-oneness is  an  assumption  about
08000	the  kind  of  problems teachers give; it would not be made in a real
08100	life situation.  In a real  life  situation,  one  would  not  expect
08200	information about to what schools particular boys go to be deducible,
08300	it would either be explicitly given or obtainable only by asking 
08400	questions.
08500	
08600		5. Problem B1 would be more correctly stated if it asked,
08700	for "a piece of information that would solve the problem" and 
08800	explicitly precluded asking for information that trivially solves
08900	the problem such as the age of one of the children.
09000	
09100	How could we make one of the authors of the book make one of the
09200	errors by introducing a confusion between real life problems and
09300	set problems.