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.ASEC(Scientific Discovery as Heuristic Search)

<<Write all this up nicely, or eliminate this Appendix completely. >

Just as AM treats research in mathematics as a heuristic search process, one may
try to apply this same view to the emulation of any
hard empirical science which can be simulated inside the machine.

View AM as providing a suggestive model for how to emulate a researcher.
This model is merely a modified heuristic search paradigm.

In other words, now consider what constraints/suggestions are made simply by
deciding that we want a system which will do scientific theory formation.
This will isolate them from those that were really specific to mathematics.
While the following material may all be included, its order may be changed.

.B APART

a) Scientific discovery as heuristic search: evolution of the model
	Each node in the space corresponds to a concept
		Concepts can be static (Sets) or Active (Composition)
		A relnship. (e.g., a theorem) is itself a concept
		An argument (e.g., a proof) is also considered a concept
	The "legal" moves (ways to expand the tree of nodes, to grow new ones)
		are too numerous to be seriously considered.
        The real operators are themselves heuristic rules of thumb
	So the "space" itself weeds out all nodes except those proposed for some
		good heuristic reason.
	As simple numerical calculations show, this space is still enormous.
	Using the big-switch idea, we can restrict our attention to 1 domain
		(e.g., math) and only use ITS nodes and heur. operators.
	Even so, space is still too big
	Refine the big-switch idea: 
		When worrying about nodes N1...,Nk, only consider heuristic
			operators known to be rele. to those concepts.
	Even so, the space is still too big
	We recurse: we use heuristics to reduce our search. These new meta-heuristics
		(strategies) guide our attention (which nodes to look at next,
		which operators are most promising to apply to each selected node).
	If these are good enuf, then we are through (else consider meta-meta-heurs.)

b) The model finally produced
	Recapping, we state explicitly how we decide what to do next at any moment.
	Indicate the data structures, the flavors of heuristics, control flow, etc.
			Note that "apply heur. operator F and add corresponding
			new node N" is considered primitive for the moment.

c) Evidence in favor of (empirical validation of) that simple model
	i) A prediction: Character of interdisciplinary research
	   For a novice in some field to do new research, he must learn the rele.
		already-known concepts, and (probably) must learn the rele. heurs.
		(e.g.: bubble-chamber physics exeriments, molec. genetics)
	   On the other hand, if he has expertise in another field, he brings with
		him many new heurs. to apply (hopefully a couple carry over and were
		never applied before in this new field), plus he brings with him the
		knowledge of a new net of concepts, from which he may draw analogies
	   Because of this, interdisciplinary research can be very productive 
		especially if you're the first such link (e.g.: Suppes)

	ii) Turn the model upside-down: Analyzing a given discovery
	   When we hear a new discovery, we try to perceive a path backwards from
		it, connecting to concepts we already know. The easier this is,
		the less mystified we are by the discovery. 
		Consequence: Discoveries in alien field seem magical and v. hard
		Consequence: Let-down after seeing how a magic trick is performed
		Consequence: Let-down after seeing how an AI program really works.
	   Reasons why going backwards is probably easier than going forwards
		Easier since you have a given starting point (the given discovery)
			The alternative is to find the "right" set of known concepts
			which will eventually lead to some interesting new concept.
		Easier since the target space is huge (move back from a particular
			interesting concept to any more elementary ones, vs.
			move forward from elementary ones to any interesting concept.
			Since nature is unkind, and very few avenues lead to 
			interesting new discoveries, valuable new concepts.
			On the other hand, in working backwards with our heurs,
			we worry about branching also, and must be able to quickly
			tell if we are really simplifying the situation!
			(i.e., Even if the model is right, we must herein worry
			 about the branching factor when going in reverse)
		Easier if you are shown the discovery step by step
			Since then you will know the necessary intermediate concepts
			Since then each step will seem "easy" and obvious
		Consequence: Reading journal article, feel "I could have done that"
		Consequence: Work 3 years, make discovery, kick yourself for not
			having seen it earlier, since it was so obvious.
		Consequence: given a math or physics problem, you're more impressed 
			with the solution if you spend (waste?) a few hours trying 
			to solve it, than if you just read thru the soln. at once.
	iii) "Failure" is due to missing some "right" heurs/concepts, or the wisdom
		(i.e., strategies, meta-heuristics, etc.) to use them effectively.
		Consequence: Teaching by example forces students to induce the 
			(meta-)heuristics themselves, often imperfectly.
			E.g.: many GP's failed the antibiotic drug prescription test
		Consequence: One probably can -- and should -- teach the strategies directly
			<is this verified anywhere? counter-indicated? Polya? >
	iv) Momentous occasion in science is typically due to discovery of a brand
		new heuristic, or else due to creation of a new concept unconnected
		to the existing concepts by some plausible operator.
		Occasionally, all one finds is a daring interdisciplinary analogy.
		Occasionally, just the first to follow a perfectly plaus. path.
		Examples: 
		  Non-Euclidean geometries ("Counter-intuitive systems may
			still be consistent and interesting")
		  Relativity ("Counter-intu. sys. may even have physical
			reality; simultaneity may be a local superstition)
		  Conway's Surreal Numbers (no contacts, not
			easy to see how/why their defn. was ever considered int.)
		  Schroedengier's wave equation (plucked out of thin air)
		  Methods of complex analysis (orig. based only on analogies)
		  Mendelev's periodic chart (first one to write down the
			recently-discovered data about atomic wts. systematically)
		  < ... more examples ? ... >
	v) Presence of Zeitgeist in Science: often, a discovery is made simultaneously
		Because many researchers simult. hear some fresh concepts, and apply
		the same bag of tricks. 
		Example: calculus (Newton, Leibnitz), ...
			
d) Questioning that model
	i) Misleading character of polished results
		It would seem, from reading texts and journals, that science itself
		is more a flowing, smooth development, than a backtracking search.
		This is illusory, as we scientists know. (we fend off this attack!)
	ii) Omissions:
		Serendipidy, incubation, unconscious, wealth of analogic materials
			(mass of introspections from great scientists are mystical)
		Error: accidental good fortune (Franklin using string, not wire;
			Lederberg picking one of the few bacteria that really do
			reproduce sexually; Galois forced to cram a lifetime of
			creativity into one pre-duel burst of writing).
		Inability to explain why "long-shot" investigations were undertaken.
			(eg: superconductivity discovered as a Master's project)
		Zeitgeist: popular trends/fads in science at the time;
		Cultural and political themes popular at the time.
			In CS: Heirarchy: Prussian army, bureaucracy
				Cooperating modular experts
				Tremendous dependence on existing hardware
				(also true of numerical analysis)
			Social taboos against experimenting with human subjects
		Difficulty of generating new operators and unconnected nodes
			Defense: this really IS rare, so again the model is OK
			Rebut: But it DOES happen every now and then!! How?!
		Focus of attention
			People inherently are biassed in favor of recently-considered
			nodes; they can't flit back and forth from one leaf to another.
			This can be simulated in a heuristic search (by artificially
			weighting the concepts and heuristics based on recency of
			use), but it is	not an inherent part of the model. It is part of
			human research policy probably only because of STM limitations.
	iii) Getting down to earth: limitations of the model
		What kinds of creative activities is this a bad model for?
			Brainstorming (intentional lack of plausibility)
			Problem-solving (very specific goal)
			Situations where there are very few heuristics (prop. calc)
			Situations where the major difficulty is applying a heuristic
				once it's chosen (e.g., soft fields like sociology)
			Absurdly robust or delicate chains of discoveries
				A delicate chain is really like problem solving
				(there exists only 1 interesting concept in this
				part of the space)
				A very robust section of space needn't worry about
				using heuristics (if every move produces something
				very interesting)
		Exactly what situations does it honestly capture?
			Essentially undirected research in a very hard science,
			with only secondary kinds of discoveries anticipated.
			Many heuristic operators exist for any given node,
			and a few meta-heuristics exist for the domain.
			Where the percentage of int. nodes "out there" is low
			  (under 10%) but not negligible (exists only one!)

		Pragmatic limitations
			Most seriously, it treats "add new node N" as primitive.
			In real life, people spend much time "adding a node".
			They have to answer many questions about it, play with it,
			and try to relate it to other known concepts. In this way,
			the worth of the node is estimated, and new empirical data
			is gathered which may trigger some heurs. to suggest the
			next drection to take, the next concept/relnship to explore.

e) Fixing up the model
	i) The most serious pragmatic limitation is this business about how much
		work must be spent to fill in any new concept. Fix this up by
		assuming that each concept has facets, not all of which need be 
		filled in at its conception. Then some heuristics (meta-heurs) can
		be concerned with tasks at the level of filling in a facet
		(deciding which facet of which concept to work on next). The basic
		control structure can in fact be oriented around filling in facets.
		If desired, the creation of new nodes can be a side effect!
		Give diagrams illustrating all this.
		Note: this is the way that the AM program actually was designed.

.E


Also include:

Assumptions about Nature:

.BN

λλ Nature is fair, uniform, regular.

λλ Coincidences have meaning. Belief in statistics.

λλ Rules of plausible reasoning [a la Polya] are assumed.

λλ Interestingness is partially the result of economy and regularity of form.


λλ Universal relations between superficiality, interestingness, intuitiveness,
unexpectedness, completeness of an analogy, safety.

λλ Universal trade-off between generality and power.

.E

.SCIENC: ASECNUM ;