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∂16-AUG-76  1339	FTP:DON COHEN(C410DC01) at CMUA	I've been reading your thesis again...
From: DON COHEN(C410DC01) at CMUA
Date: 16 Aug 1976 1638 EDT
Subject: I've been reading your thesis again...
To:   DBL at SAIL
- - - -
I finally got around to looking at the next version of you thesis.
(It almost fell of the end of the stack for a while.)  Besides all
of the usual typos (that you've probably found by now) here are
the new bunch of responses:
1. It is still not quite clear to me what checking is all about.
After reading the heuristics the activity still does not seem like
a unified one.  Related to this confusion: why do you ever add something
to a facet without making sure that it is ok?  Also related to this,
it is not at all clear to me what happens when errors find their way
into the data base.  How do tey propogate? What is the worst consequence
that they can have? (Could the system be really screwed up by them?)
2.footnote 3, p.15 (rational research) - I don't see this at all.
3.p.22, conj.1 - you mean always, not never.
4. p.129 (7.1.3) "...although much worse than a real mathematician
   would have done..." - that judgement seems unfounded.  Besides, I
   don't really think that math research at all resembles AM's activity.
   I think that research is largely (blind, in comparison to AM's heur.
   guided) search.  It would be hard to imagine how anyone could ever
   know such a small set of concepts with such a large set of heuristics
5. p.128 - example of a real loser:  This idea seems (to me) fairly 
   close to the IF(pred,thenvalue,elsevalue) function which would have
   been a real winner.
6.p.227 , footnote 11: how about this explanation - think of the 
structure as a tree, consider a path from the root to a leaf, where
the operations are descend (current exp. becomes first member of
old exp.) and next.  Then AMEM means that along every such path
(to every leaf) one sees at least one x.
7.heur. 132(p.234) seems to conflict with your previous use of dom/rng-
  this rule would prevent mult. from having the entry 
   odd#,odd#->odd#, since 2*2=4   - perhaps you mean that every example
   which fits a domain entry must fit the corresponding range entry.
8. heur.238 - makes me think I don't understand ordered structs. Doesn't
 every ordered struct have to satisfy this heuristic?

P.S. I am just wondering, how are the #divisors of max.divisable nums
distributed?  Not surprisingly, all max.divisable numbers seem to be
in this set.  In particular, I wonder about the asymptotic density of
both sets. Any answers?  (what heuristics make me wonder about that?)

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