Computers and Thought Lecture: The Ubiquity of Discovery

1. INTRODUCTION

Much of the behavior which .we regard as "intelligent" in valves some sort of dis~overy process.2 This is obvious for some of the .the most creative and intellectually difficult human activities (identifying an unknown chemical compo(md, composing a new sonnet, deriving a new cosmological model, conjecturing a new theorf'ffi, solving the NY Times crossword puzzle, ... ). We'll see that it's no less true for our everyday activities (cutting cheese, finding our way about . Boston, solving the Pittsburgh Press crossword pmzle, ... ).

1.1. Modei-Building_in Science

We in the field of Artificial Intelligence (AI) want to understand how. its's possible to do such things, to understand the mechanisms of intelligence. To go about it scientifically, we must first propose some hypotheses; use the· results of experiments to modify and develop them into a theory, and then embody that theory in · several concrete, testable models. This is the paradigm of Science; it has great power, ~s we all know. · . .

In very "hard" sciences, objective data are available a bout isolated and relatively simple phenomena. This enables the construction of .small yet quite rigorous, predictive models, using the .language of mathematics (e.g., Max well's equations for electromagnetism). But in the so-called "soft" ·fields, the phenomena cannot be measured precisely, or are not so reproducible, or (as in the case of human intellig:ence) cannot be easily isolated for stw;ly. The resulting mociels. are usually only descriptive, and ·may often be presented in everyday prose (e.g., psychological theories of personality).

2 Much of the rest of "intelligence" involves algorithmic solving of well-structured problems. That topic will not be emphasized in this paper . We take the position that "algorithms known and used by experts" is just a proper subset of "knowledge ex·perts use to reduce search".

Scientific models ~erve two functions: (i) to unify large masses of empirical data; and (ii) to fnedict new effects, which subsequently' can be tested for by conducting experiments. The physici st's model (his set of equations) is better than the psychologist's .model (his prose clesct'iption) because he is able to draw on the power of established mathematics3 to make his model · quantitatively predictive.

What kind of model can we build for the phenomena of discovery and creativity? The more formal, mathematical models have the greatest potentia.! prt;>d ictive power, but humans seem just too complicated, sophisticated, and unpredictable for .their behavior to be captured by a few equations.4 Planets and atoms behave in much more regular a fashion than do people.

Is that the en:d, then? Are we forced to build purely descriptive models of cre<~ti v ity? Are we limited to sterile prose discussions about the mysteries of incubation and illumination (e.g., as in [Poincare' 1929) and [Polya 1954))? Can we draw only metaphorical pictures (e.g., as in the 'hooked atoms' image that Einstein reports by introspection [Hadama'rd .1945))? The answer, until quite recently, was . unfortunately "Yes".

1.2. Choosing an AJ?proach in Science

Each science is differentiated from the others not 'merely by the set of phenomena it claims as its object of.study, but also by the a.pproa.C/1 it takes (the SCienc~'s VieW of · those phenomena; its paradigm [Kuhn 1970), if you will).

So even though we've decided to study the phenomena of human intelligence (creativity, problem solving, etc.), we must still choose a view of Man. ·

3 The power to solve <\nalysis problems in closed form (e.g., to .solve a differential equation simply by repeatedly · manipulating it according to known transformations), or the · power to make approximations when necessary, or the power to somehow ... run ... the model (to "grind out ... solutions to his equations). ·

4 Attempts to for.malize ... soft... phenomena do go on continually, but the interpretation of the resultant rigorous mathematics is often a topic of heated debate (a current example is Catastrophe theory [Kolata 1977]).

If we view M <~n as 11 Gcsto!t actor whose internal thought processes can't be investigated, then we are called ... classical psychologists ... and we study his external beh;~vior . If we view Man <H a brain, as <1 piece of hardware .built out of neurons. then we're called "biologists" and we study neurophysiological responses (e.g., by implanting electrodes) If we view Man as a machine, then we're called "cyberneticists ... , and .we investigate mathematical properties of feedback networks of simple components. If we view Man as a collection of atomic p<~rticles, then we're called foolish 0: this is too fine a "granularity" with which to investigate intelligence.

Another view arose about twenty years ago, from tinee sr:'p<~rate sources: engineering (Broadbent), psycholinguistics (Chomsky), and computer science (Newell and Simon). Man can be viewed as a symbolic information processor. If we adopt that view of Man,6 ;mel are interested iu the mechanisms of human memory, then we're c;~lled "cognitive psychologists.... If we adopt that view and .are interested ·in the mechanisms of human thinking, then we're "inform;~tion processing psychologists". Finally, if we view Man as information processor only to learn more about problem solving and creativity, then we!re working in the .field of "Artificial Intelligence ....

1.3. The Foundation for Artifi~ial Int~!l~nce

Suppose we view Man as in.fornntion processor [Newell <mel Simon 1976). How c;~n we conStruct some mociels of intelligence which are predictive rather than just descriptive? We might build operational models, which can exMbit whatever behavior ounheory called for. To do this, we need to use a general purpose symbol manipulator, an automatic way to carry out each bit of information processing.

5 · Unlike the Brownian motion of atoms in a perfect gas, the fundamental information processes of intelligence are not [.llnd(lffi.

6 No one view is "right" or "wrong ... ; each is adopted because from it we can ·build ·a model, which it1 turn has some practical c.onsequences and uses. When I'm ill, I want to go to a doctor who practices medicine based on Man as an animal, not Man as an ec.onomic agent. II is not productive to argue whether or not any specific view of Mctn is "correct", is "immoral", etc. AI the present limited state of our understanding, any one view is bound to be simplistic and .incomplete. On the other hand, · we never capriciously adopt a view with impunity. It is the whole mari who lives and react.s, even ·though we can only view him, first this way, then that.

A general purpose in formation processing system must provide (i) a w'ily to specify wh<~t processing gets done when, (ii~ a memory in which to store symbol structures, and (iii) an "engine" which can actually c'iluse such proce~sing to occur. The science of Artificf~l Intelligence ("AI") sprang intn being soon after the invention of one such computational engine: the genera.I purpose l'lectronic digital computer. In fact , A I 'is ~ometillles ca lll'd "M 'ilch ine Intelligence".

Computational models of some task can · be used directly to c<~rry out ('il simulation of) the ·modelled activity (composing sonnets, doing astrophys.ics research, clev ising new . w.ays to cut cheese, defining and invP.stlg<iting new conc.epts in mathematics, n'ilvigating this city, etc.). If our computer program does perform the desired task adequately, then we accept. it a.s veriflc'iltion that our theory 'ilcleC]uately exj>la.i.Jis one way in which intelligent performance at that t·ask might be 'aChieved.

We in A I have evolvl'd the following .paradigm:

1. Choose some human cogniti've aCtivity (like playing chess, proving theoren,s, understai1ding spoken English).
2. ii) Develop hypotheses and eventua.lly a theory about what kinds of information processing could be taking place to produce such 'ability. ·
3. iii) Incorporate that theory into a computer .program, which serves as the mode1.8 That computer program is m'ilde to carry out the original 'activity, ·and the researcher can observe how well it does.
4. iv) By experimenting w.ith his program, he attempts to find out whl're the apparent "intelligence" is really coming from.

Over the last twenty years, we've hypothesized and tested scores of models, for several different sophisticated tasks. There have been many successes, and many fa i.lures - and we've learned much from them. Some ·of these experiments will be described later (Section 3); for now, I just want to present a single, very central result.

7 Symbol processing is not · the same as mere data processing. A "llniversai· Turing machine", e.g., is just a dilta processor, because the marks on its tape aren't symbols, they don't represent anything but themselves. It was some years after its discovery that the .digital computer was perceived as il 11.eneral svmbol manipu·liltor.

8 AI deviate~ f.rom c:ognitiv; psychoiogy at thi~ . stage. Psychologists would run experiments on people, to see if · they re11lly do fit the theory. We in AI are mare concerned with whether the programs containing the hypothes ized mechanisms are c.apable of ~ sort of "inteliigent" behavior -- even if differs somewhat from humiln performance at that task.

It turns out that w~ can model a surprising variety of cognitive activities (problem solving, .invention, recognition) as a search or exploration, in which the performer is guided by a larg"' collection .of informa.l .rules of thumb, which we sh;jll call "heuristics". But what's really exciting is that not only can this sfngle theory (intelligence as heuristic rule guided search) Px plain the behavior of thf" brainstorming math resea rcher and the wandering 1\oston visitor, but when we go off and build up such models in detail, we find that they cap all contain more or less the same informal rules.

Before trying to justify this r~~sult, let's notice two rather surprising consequences of it: .

• (i) Every day, each of us is forced to - and do~s successfully _: carry out a great deal of "creative research" just to deal elfecti vely with our complicated world;
• (ii) There's a large component of non-formal, "plain common sense" knowledg·e that is necessary to do creative new work in the sciences or the arts.

Now that you see where r want to takeyou, let's see how to get therE'. I'll have to spell out this "heuristic rule based search" theory of intelligence, convince you that it makes sense and that it can ·account for the way in which people perform such di sparate tasks as solving the 8·-puzzle and performing scientific research . Also, I must demonstrate that there is a large core 'of heuristics which is common to a.ll such activities.

2. HEURISTIC RULE GUIDED SEARCH

2.1. The Theory

There Is a theory of intelligence lurking here, upon which some models - some computer programs- have been constructed . The theory goes something like this:

1. Human· cognitive tasks can be cast as searches, as explorations wandering toward ·s·ome goal which is well- or ·ill-defined.
2. We are guided in thes~ searche.s by a hu·ge collection of informal rules of thumb: heuristics.
3. We access potentially relevant heuristics in each situation, and either (a) select and then follow .a single relevant heuristic, or . (b) quickly · "sUtch together" some of the relevant ones, . and then follow the "combined" advice.

That's it.9 It sounds plausible; in f~ct, it sounds trivi.al. Yet the models which incorporate this theory are capable of simulating · sophisticated behavioi's at many tasks which one would suppose require intelligence: organic chemistry problem solving, organic· chemistry resea.rch, chess playing, discovery of new math concepts and conjectures.

?..1.1 Intelligence and Information

The theory contains two important implicit assumptions, which might be worth stating explicitly:

• > Man is viewed as a processor of symbolic information.
• > Man ex hi bits "intrlligence" by his . performance at various cognitive tasks.

Let's ta.ke a moment to try to justify these ·remarks, that intelligence ·has something to do with informa!ion processing.

Twenty-seven years ago; Alan Turing [ 1950) rejected as meaningless the question "Can machines · think?". He replaced it with a game, called the Imitation Game (now commonly referred to as the Turing Test). One version of that game woLtld go as follows : A human interrogator is placed in an isolated room. A teletype exists in the room, t~nd by using it he c;:~n communicate with a computer and with another human, both located in the next room. The interrogator asks them each some questions, and then must guess which is the huma.n and which is the machine. If we can program the. machine in such a way that it fools the interrogator .into making the wrong identification at least 501. of the time, then we shall say that the machine (t~s programmed) is "intelligent". Many of you are familiar with this game. Now let me introduce you to a slightly different 'on.e:

Thirteen years ago, Keith Gunderson [1964) rejected as meanirigless the question "Can rocks think.?". He replaced it with a ·game, an Imitation Game.. A human. interrogator is placed in an isolated room. A s.maU hole ex.ists near the bottom of the door, thrc;>ugh which the interrogator can shove most of his. foot. On the other side of the door are located a hurmlll and a rock . Sometimes the human .will stomp on the interrogator's foot, and sometimes the rock will be dropped on it. The interrogator must guess which one is the human. If we can shape a rock In such a way that it fools the interrogator at least .'50'7. of the time, then we shall say that the rock is "int":lligent".

9 No1ice the conspicuous absence of the ward "representation" anywhere in the theory .. To .design and construct a ·model for this theory would entail grappling with representational issues, much as any running ins I ance of an abstract algorithm must exist 'on some particular machine. But the validity and · power of the theory are independent of representation; just as the validity and complexity of an algorithm are independent of which machine it's implemented on.

Why does the dialogue-tE'st sound so much less silly, so much more indicative of intelligence, than the stomping­ to:>st? Because unrestricted ·di.alogue is open -ended; to do well at . it requires a m;~ssive wraith of knowiedge, experiences, cognitive abilitiE's, emotions, and common sense. Unrestricted foot stomping requires none of these .. In short, the first test permits genirine interrogation of infQrmation <~nd information processing capabilities, while the second test doesn't. If you agree that the first tl"st is genuine aild the second one bogus, it must be because intelligence has something to do with sophisticated processing of massive quar.rtities of information.

Thus it see.ms that. the informalion processing view of Man is an especially good one from which to study intelligence. Let's elaborate on it a bit more, and then go on and see what happens when one tries to build models based on it.

Let's take a look at some heuri~tic ·searches that people perform, and in the process hopefully ·convey their universality, their ubiquity, and their power. We'll then be in a position to examine some specific AI modeis (computer programs) th;~t they have built; this will be done in Section 3.

2.2.1 Everyday .Problem Solving

Suppose we decide to plan a I rip fi·om CMU to MIT. How can we find a good route to take? We will prob<tbly find a detailed road map ;md begin sea.rc~ing. We have some powerful rules of thumb which make our search very .short, usually. We look for some main highways that will take us most of the way, and then do · some ''fixing up" around the tor:mini (from CMU to the frrst highway, from the end of that ·stretch to the beginning of the next one, ... , to MIT).

This is the heuristic of planning in an abstraction space: we take the original detailed map (our ."search space") and simply ignore all but the biggest roads marked on it. Needless to say, this makes the map much simpler. We also assume that whenever two ))ig roads go nearby ea.ch other, they do in · fact connect; and that big roads which go near to citic'~ do in fact p<·ss through them. Next. we solve the problem in thi s very small space (callf:'d the "abstraction space"). Finally, we use that solution· a~ the skeleton of a real solution We may have a few more searches to perform (e.g .. how do we really g·?t from the Boston ex it to thf' MIT camtHls itself) - but notice that all these add itional searches will be small, locali7.ed fi x-ups to the >kelcton .~oh\tion . Using· thf:' heuristic method of pimwing has reduced our w<~rch dr<~maticillly.

This brief example h as hopefull y demonstrated how we ca n explain evcryc;lay proiJicm solving behavior in terms of the "heuristic rule sf'~rch" I henry of intelligmce. \'l'e've seen a typical problem, and explained how to mocll?l it, how one could imagine even a computer being <thlc to solve it: Ca.st it as a Cjllest fnr a solution in some hup;e ".~e ;nch spilce", with the searchr. r being heavily Cll ll str<t ined by knowleclg;e . embedded in general common -sense rules of tl1t11nb (heuristics). ln the next subsection, we'll show that the s<tme kind of analysis can explain episodes of brai nstorminr:; (in particular, the inventing some new kitchen gadget).

2.2.2 Everyday Invention

Suppose we're confronted with the following probi_em: wt;>'re fond of. eating clwese, but every time we. cut it with " knife, it crumbles if we try to cut it very thin. Vve could continue just cutting chresr the old wily, but let's assume we try to des ign an improved tool. We are now facing a search in an enormous space of possibilities. But we have many informal rules of thumb which may help us:

• I . Sometimes, there will be a good way (perhaps a recent invention) to do something !!L~Q g£_1J£!:Rl than what is strictly asked for.
• Consider whut variabl.es· affect the su.ccer.s/failure of the current (inadequate) technique. LooJ<, for motivation at \ht> £1!Jt:.~1nc cases of \he various known · relationships involvinr, those variables.
• 3 . Look carefully at what. is truly wanted; maybe the problem can be completely bypassed; · at least, perhaps it's over-specified.

One of them ( .. 2) says to look for motivation at the f:>:treme cases of various . known relatio11ships. There seems to be some relationship between the thickness of thr knife a.ncl the thinness of the slices we can cut. So we might consider as an extreme the thinnest knife pos.s ible, just a knife edgt:, and voila.', w·e'·ve invented the wire cheese cutter. Or we ntight look at the extreme C<tSe of the relation that says that most cheese can be CUt thinner if . it's softer. We ri1ay ask ourselves if we call" get the cheese very soft;. an extreme case of tl1at would be to get the chee.se directly u.ndcr the .knife-edge completely molten; and uoila.', we've invented the "hot­ knife"; probably General Electric will come out with (:llle soon .

Notice that the same heuristic leads to several solutions. This WilS but a tiny exan1ple of heuristic guid~nce in action. In reality, we possess many hundreds of heuristics. Incorporating them into a computer model which could then til·eless ly i!pply them seems like a very promising direction to follow. We'll follow it in Section 3. Ue;~r in mind, however, that inventions are rarely . rna de with little search. In the · cheest'-cutting case, there might be many ways of t~pplying e(lch heuristic, only a few of which are even remotely viable.

It's worth noting thilt .both of ·the other heuristics might be used, .too, for this situation. The first one could h(lve us look at recent inventions which "cut": a. laser for cheese-slicing? The third heuri stic might have us build il better mousetrap: go into business selling already sliced cheese; or try to devise a "cheese press" that takes the crumbs and sqlteezes .them together into slices.

Let's put our theory to a most severe test, by asking whether it can account for our everyday judgments e~bout wh;lt is ilnd isn't "intereMing". This would seem to be the realm of intuition, emotion .. tilste, and aesthetics -- the antithesis of logical empiricism.

If in filet thr.re is ·a large "hormonal componr.nt" to such · judgments, then it is not surprising if they lie outside the power of any theory founded on a view of Man which ignores that aspect of him. So even a partial success ill explaining "taste" in terms of heuristic rules would be a. major triumph. for the theory, showing it had some relevance to these phenomena .

Such -a partial explanation is e<~sy to find. · Texts on the arts abound with "ru.les" of composition. They analyze ~·orks in terms of symmetry, coincidence, recency, unconventionality, harmony. bal<lnce, utiiHy, associations, etc. A typical rule might say

) " (.I\' (I appanmt.ly "isparale pari.< or the work are .suddenly recogni7.etl as hc"ing very dooely rclatetl,· .

TH I·:N that increases the interest iugncss or hoth parts, and

or tho whole work as well.

This explains the eternal P.Opularity of .the "recurrent theme" in ail genres of literature a.nd cinema. It explains· .the impact of having a single melody recur frequently but with slight differences each time (the concept of "m.us.ical variations"). Dickens' success is due in no small measure to his mastery of this heuristic (i~e. ,

"coincidence"): the reader is alw;~ys astonished and plc<t s~;d when two scp<tr~tl? ch<tr<tctl?rs are ctiscoven:d to · be one <1nd the s.ame person. The ilbove · heuristic also expl<~ins why (asi~le from cost) the hot-knife might be bl?l'ter received than the laser -knife (the consumer <tlrcildy possesses hot combs, electric blankets, dectric knives,... so the . hot-knife would be ·instantly <tccommodated, with even a modicom of pleasure at the· new bit of "closure" that h<td occurred in his world).

2.~ . 3 Sdcntific Problem Soll'ing

Suppose we're designing a molecul<1r genetics experiment, which will ultimately result in a certain · biochemical end product. We must dPsign a very long chain of steps (perhaps reach.ing into the thousands)., each of the form "raise the tP,mperature to x", "add .the following nucleotide .. . ", etc.

The search for a successful solution (a path, a sequence of steps le<~ding to the final product) is made tmtch simpler when we're able to aJiply somE' heuristics. It's a common practicf:', for example, to igttore certain kinds of minor strvs, ;md to conccntratf:' on finding a relatively sma II sequence of important int..,rmedi<tte products. That is, we should Jlrst ftnd a solution in .a heavily restricted (hence small) spacP.. A fterwilrds, we can "fix. up" the connections between these ·steps (r.g.; in case one of them must occur <tt 12° and the next must occur at 2 [, 0 ) by adding mat~y minor steps. We don't begin to execute the ftt ·st step until this detailed sequence of stepg is fully specified . We solved the problem by applying a g·eneral heuristic: planning. The basic technique of planning can be expressed as follows:

• II' yon arn fac:nol wil.lo a "<:arr.h through a laq;c ~par.n of po~~i hie f:olnl.iorl', anol ~onw a~pnd~ of caclo "intnrrnroliate ~tate" along tloe way to a ~olo.rt.ion arc rrrorc ill1jJOrl.llnl. than ollo c: r,,
• TIJ'Io:N· l.ry lo ignorn ~orrw of tloc oktailcol a~pcr.l.~ of the· prohlrm, llonrnhy 'irnplifying it. Solvn !.he ~implcr prohlnm, arool lry In ex.l.c·oool tloat solnt.ion into a ~olul: ion of t.lon original loarol prohlcrn.

In the molecular genetics case, we chose to ignore su'Ch · f11ctors as the temperature at which a ·step must be carried out. The heuristic used is just the one we used in the previous subsection to find a route from CMU to MIT. There, w'e chose to ignore <~II minor roads on the map. This repetition is not arridental; it illustrates the commonality between everyday problem solving and scientific problem solving. The next section will show the similarity between everyd<~y invrntion and scientific invention. And that's what we ~et out to show!

?. . ~.4 Scientific Invention

Suppose we're confronted with the following problem.: we're fond of factoring numbers (e.g., 12~1x3), but often there are many little sets of factors that they crumble · into (e.g., 12 crumbles into the following four sets: {1,12}, { 1,2 ,6}, { 1,3,4}. { 1,2,2,3}). We may be content with this situation, or we may try to improve it in some way, or we may wish merely to find out more about factoring._

Tlrr latter two options both involve searches in ettormous sp<~ces (looking for a new kind of factor'ing; looking for new facts about factoring). Gut ·we have many rules of thumb to help us, including the three rules which were displayed in Section 2.2.2.

One of them (#2) says to look for rnotivation at the ex treme cases of Vilrious known relationships. The relation in this case is "Divisors--of". It m11ps a number into a set of numbers (e.g., Divisors-of(I2) { 1,?..3,1,6,12}). An extrrme Cilse would be when it mapped a number into an extreme kind of set- say a . s in p.; leton, doubleton, or emJ'!ty set. In other words, consider the· set of numbers with no divisors, with one divisor, and with two divisors. Voila', we've. invetHed prime numbers. Notice that we used the very same lteuristic (·2 in Section 2.2.2) that Jed .earlier to the invention of the wire cheese cutter and the hot·knif.e.

2.2A./ ]rrrlairra 'lrrtm·l'.<t

.i.rrgrr,.<.<'

Even allowing that the "heuristic rule guided search"­ theory co.uld account for the discovery of prime numbers, could it also explilin how a. reseilrcher might have noticed that they were valuable, interesting, worth naming, and worth remembering? ·

Let's look at how the following three heuristic rules cou lei lead to the conclusion that "Primes" is interesting,

soon after it h;~d first .been defined.

IF ~r·eciali:~.at.ion' of corwepL C have ju~t. hecn r.rcat.col, anol tloo' en rrcr.rt. t;~~k i~ t.o finol <\X ample~ of nao:lr of thnrn,

• TH I·:N one met hool i~ t.n look .o''"" lion known cxampk~ of C; 1 hey may he examples of ~orne of t.hc new ~pcciali7.oo:ol r.oncnpl.~ as wnll.

IF lrll nxarnplr~ of a conc:rrJt. C t.nrn out l.n he cxarnplc~ ·of lHJnlloo~r concept I) a~ well, anol C wa~ not. prcviou~l.y known t.n he a ~pec:iali1.alinn of D·,

TH I·:N conjcr.torre !.hat C i~ a ~pcr.illliurtion of D, ancl rai~n t.hn "irrt.erc~l ingnc~~" value of hot.lo concept.~:

I Jo' all cxarnpln~ of a concept lllrrr out. t.o he in t.hc ·lomain of a rarely-applicahl(' fJIIlclion f,

TI·IJ<:N il'~ worlh t:OIIIJ!U iing Hll llocir F-vHiuc~ (l.hni r irn~gcR under lhc funclion 1'), arul sluolying lh al collcclion of 1"- · va1 ur:~ a~ a ~cparal.c .conr.CJ)L

Suppose we've just defined thl' sl't of numbers which have no divisors, the set of numbers which have only or1e divisor, only two divisors, on ly three -divisors. The first of the three heilristics tells \IS a quick way to find PX<H11ples of tho.<e new special kinds of numbers: look at the known examples of numb.ers, say the integers from I to I 000, and dump each one into whichever new specia lized set(s) it belongs. If we do this, we get the following empirical results:

Numbers wit/· no divisors: (none found)

Nu.nibcrs with I divisor: I Numbers with 2 divisors: 2. 3, ~~. 7, II, 13, 17, 19, ...

Numbers with !Jdivisors: 1, 9, 25, '19, 12 1, .169, 289, ...

We can then apply the second heuristic to each set of numbers, to see if it's interesting. In this way, we'll notice that the last set, numbers with three divisors, are all perfect squares. Heuristic <~3 directs us to take their squ;:~re roots. Lo and behold they're pr.ecisely the third set of numbers (i.e., numbers with two divisors; i.e, primes). Heuristic ·2 · notices this, and drastically increases the interestingness vaJues .of both Nos-wit h-3divisors and Primes.

So we were ;tble to fit this kind of judgmental evaluation of "interestingness" into the same theory. Notice that thl" heuristics ;:~bove are ;:~ctu<~lly quite gener;:~l : they (or at least analogues of them) can be used to evaluate works of art and new mecha11ical gadgets, as well .as to evaluate new milthematic<~l dcfmitions. We SilW the an;:~logue of heuristic ·2 used before, in Section 2.2.2: I, 10 to help judge the interestingness of A Tale of Two Cities ;mel of a new kind of cheese cutter. Other ~nalogous heuristics, which favor ·various kinds of "closu re" are used in all sciences (e.g., consider the popular ity of "fh<~rm", even before the confirming discovery of the D­ mc~on [Richter 1977]). Parti <~l de-mystific<~tion of such phenomena as illumination, incubation, aesthetic taste, etc., is one valuable result of this kind of Alresearch. ·

3. MODELS

Let me now describe a few landmark computer programs that have been written, models Insect on th~ theory of intelligence <IS heuristic rule guided search.

10 In .the terminology of that section, the two "disparate parts" were "numbers-with-2-divisors" and "numbers­ with-3-divisors".

These progr~ms form but a thin· sliver of the work· that h as gone on under lhe label of "Artifici~l Intelligence". I don't want to distr<lct from thr thrmcs of this talk by cata loging the various efforts; ~ glimpse at the t<4ble of contents of this conference's proceedings· will give· you a picture of their scope. II

Probably one of the earliest AI programs written was the Lope Theorist ("LJ"", to it> friends) [Newell, Shaw, ;md Simon 1957]. It w~s n·pe;:~lrdly given symbolic logic t heorems from Principia Mat!.ema.tica, ~nd its t<~sk W<JS to find a. formal proof of e;:~ch theorem. t.:r had some g iven axioms "nd rules of infrrence. To search for a proof, in a completely ex haustive, systc.m~Jic manner, would be quite an undert<~kin[;! But L T hild il few· heuristics which constrained its se<~rch:

" .... <electi.!le principles tho.t eno.ble solut.i.otts to be fol .tnd after exami.ning only a relatively ti.tty subset of the set of possibilities. One such principle - - illu.ttrated by the methods in the Logic Theorist - ·· is to genei-c>t f' only elr.ments of t.he set tho.t o.re. o.lreo.dy fJI .I.o.ro.nt.eed -to pos.<ess o.t least some of the properties tho.t define o. solution. Another principle - - illustra.tcd by the matching process i.n L T - - is to nto.lce use of informo:ti.otl obtained sequent i.o.lly in t.he r.ourse of genero.ting possible -solu.t ion.< in order to guide the continuing sea.rch. A thi.r'd principle -­ i.lltt straterl by the use of si.milo.ri.ty tests in L T -­ is to abstract from the detail of tlze problem expressions and to worlr. in terms of the si.mpler

ab.<tra.cti.ons."

-[Newell and Simon 1972], p. 137.

After they leiirned the power of heuristics from L T, the s;:~me gt.·oup of researchers then worked on ~ progr~m ca lied G PS, for Genera.! Problem Solver. Its aim was to embed the above heuristics in a domain -independent form, one not tied to solving any p<~rti(lll<lr problem, the way that L T w~s. tied to propmition<!l calculus. It W<~s hoped that any problem could be represented in the GPS formalism, and hence solved by GPS. CPS contained ~few new heuristics:

I. Means ends analysis: Taking differences (between the· current state <~nd the desired go<~ I), locating oper<~ton relevant to reducing. those differences,

1 I AI includes such · disparate pursuits as machine perception (r.peech understanding, image parsing, ... ), natural language understanding, novel ways to represent knowledge, novel ways to control the attention of the computer, and ways to trans fer some of what's been learned into improved teaching methods for peopl.e.

• and applying those opl"rators. Note that this hettristic guides fruward search toward a goal
• Setting up subgoals, especially subgoals of the form "GPS wa.nts to apply operator X, so X's precond iticins must become satisfied (True)". This heuristic is equivalrnt tn the idea of jnoblem reductiMl, to divide and conquer strato>gies, etc.
• Work on the most difllcult of the subproblems first. Try to reduce the most import<~nt difference first.
• Planning in an ab-straction space: Systematically ignore some kind of details in the. original problem. This results in a much smaller search space, in which a solution can be more readily found. This solu-tion is then used as. a guide to finding a ~olution in th!' ori~inal, huge search space.

I .r.t's -s'ily a few morr. words 'ilbout that last heuristic, planning. :md how it was used when GPS was set to the ve ry same task which LT had atletTlptecl: propositional C"<Jlculus theorem proving. What GPS did WilS to take all the axioms, · rules of infNence, and the desired theorem, and then simjJly remove all the logical connectives from them. Thus the modus ponens rule of itiferr.nce wottld be transformed from "from 'P' and 'P imf·lics Q', conclude 'Q'" into this more abstract form: "from 'P' and 'PQ', conclude 'Q"'. This would sorn.etimes produce fall<icious proofs, or proofs with missing steps, etc., but by and large it was quite cost-effective, allowing the rapid solution of many ·otherwise intractable problems. After the planning process was ov!:'r, there would still have to be some "fixing up" of the detail~ between steps; this was also what we observed fo.r route pl<-1nning an.d for molecul;1r genetics · experiment planning. · ·

1\ decade or two of research h~. s shown that, yes, a large array of problems can be cast in terms that GPS can deal with (states, operators, difference tables), but no, G PS' general heuristics JUSt aren't powerful enough to solve problems as dillicult as . can be tackled by humans.

The next giant step along the line of development -we're following was taken by Ed Feigenbaum and joshua Lederberg [Lederberg 1964]. soon to be joined by Bruce [)uchanan [Buchanan et al 1969). They 12 recognized what was lacking: experttse. Humans had to train in specialized fields for quite a while before th·ey were able to solve any hard probiP.ms in thetil . This ph('nomcnon · might not just be a reflection of ·ltuman brain frailties, it might indicate a necessary requirement for . intelligent problem solving in a complex knowledge-rich domain.

12 At about the same time, Joel Moses independently arrived at the same conclusions. He developed an expert program for the task of symbplic integration [Moses 1967].

·

In 1965 they con.ceived a new computer program, and jn the process a who.le new ilpproach for AI: they were willing to commit their progra·m to working on a very specific kind of problem .,...- in their case, the enumeration of atom-bond graphs of organic molecules {based on analysis of mass spr.cti ·o_gr<~ph data and nuclea.r n1ass resonance dat<~)c They built their proRram, DENDRAL, around a body of heuristics - not Jtt;t a few, but a few tens of heuristic ri.lles. SomP- of them were as general as the rules that LT h·acl, but most of ·them were clom;~in­ speciftc informal rules of thumb which they extracted from chemists (including some of the top experts in the · lkld). These new heuristics WC're ta~k-clependent: they won't work equally well . for identifying imagf's as for identifying unknown compounds; they were specific to the field of tll<HS ~pectroscopy. ·Even more important than their specificity is their power.: they constrain the searching tremendously.13

The success of this t:esearch ({)nfirmed some of the co11clusions of Newell, Shaw, and Sirnon: the tradeoff bf'tween generality and power, the importance of hemistics for guidance. Feigenbaum, Lederberg, and P.uchanan were willing to tap some of the "power" .that humans need for .speciftc technical tasks.

WP now jump .to quite recent r.rscarch, by the author. The next step in lhe progression we're chronicling involved collecting hundreds of heuristics, used in some 7'cry diflicult task, on the frontiers of what -hum<~ns can perform. In this case, the task chosen was that of discovering interesting new concepts in elementary m;~them<ttics, that of scientific theory formation, of open­ ended research. This is scientific invention, iiS compared to Dendra!, which performs scientific problem solving.l4

13 The size of the . space lo be searched is greatly reduced, hence searching will lake much less. time. Thus, heuristics (which serve lo tonstrain) are equivalent· to power (more efficient searching). _

14 This is not the "inductive vs. dedudive" issue: both Dendra! and author's program, called AM, performed quite inductive tasks. The difference was that Dendral was given specific problems to solve (specific mass spectra to identify), whereas AM's activities were open-ended research, with no particular goal specified_

1\ M's heuristics guided it to m<~ke promiSing new definitions, explore those new coricepts, e~nd judge the interestingness of its discoveries. AM noticed connections betwee11 concepts, and was thus a theorem . f>rof>oser, but it had no thf?orem Jnoving abilities whatsoever . . A di.fferent set of heuristics would be required if AM were suppost>cl to prove a-ny of the conjectures it proposes. M <~king the necessary definitions to ·notice the fundament<~! theorem -of ;~rithmetic (·~umbers fe~ctor uniquely into .primes) is quite a bit different (more il1-d('.fined , more wphistic11tcd) than proving it .once you've conjecturl?d it.

3.3.1 Math Di ,scovery as Heuri .~tic Rule-Guided Search

The task which 1\ M performs is the discovery of new mathematics concepts t~nd rel<~t·ionships between them: The simple paradigm it follows for this task is the one specified by our theory (in Section 2.1):

1. The activity of open-ended math research is ·viewed as a search, an exploration in a space of pt~rtially -cleveloped concepts. The goe~l of this search is ill-defined; it is to maximize the interestingness va.lue of what's being worked on at the moment.
2. AM is guided in this process by a collection of a few hundred heuristic rules. They are relatively general rules of thumb which guide it to "define and study the most plausible thing ·next.
3. ln each situation, AM . ac:cesses potentially relevant heuristic rules, finds which of them .are truly relevant, and then follows them.

For example, AM possessed a rule of the form "Iff is an interesting relation, Then look at its inverse". This ru.le fired (was relevant and was actually followed) after 1\ M had studied "multiplication" for a while. The rhs (right hand side, THEN- part) of the rule directed AM to define Clnd study the rel<ltion "divisors-of" (e.g., cl i visors-of( 12) = {I ,2,3,4,6,12)). Another heuristic rule which later fired said "Iff is a relation from A into B, then it's worth examining" those members of A which map into extremal members of B". This is a speci<llized version of our old: friend, rule ·2 from Section 2.2.2. In this case, f was m<ltched to "divisors-of", A was "numbers", B was "sets of numbers", and an extremal member of B might be, e.g., a. very small set of numbers. Thus th.is heuristic rule caused AM to define the· set of numbers with no divisors, the set of numbers with only I divisor, with only 2 divisors, etc. One of these sets(the last one mentioned) turned out subsequently to be quite important; these numbers are of course the primes (as we s~w in Section 2.2.4). The above heuristic also dirl'cted AM to study numbers with very many divisors; such "highly-composite" numbers were also foLJ.nd to be interesting (by AM, by . the author, and by professional mathematicians). Heuristics like those in -Section 2.2.4.1 quickly led AM t.o ·boost the "interestingness" rating of the Primes concept.

3.3.2 Hepresentation of Mathematical l{nowledge

W h<~t exactly does it .mean for !\ M to "have the notion of" a · concept? It means · that AM represents that concept somehow, that there is a data structure of some kind which is meant to coiTPspond to, and contain information Clbout, that concept. While the entire issue of representation of knowledge hils been de-emphasized in this paper, it is helpful to glance Cit how one typical concept looked <lfter AM h<ld· defined and explored it:

N 1\1\H:: Prime Numhm·~, Prirnc", Numher~-wilh-2-Divisors m:FINl'l'lONS:

OH IC IN: Numhcr.-of-olivigors-nr{x) = 2 PRED.-C.I\LC:IIl.IJS:· Prirnr.(x) e (V.1.)(1.[x-> 1.=1 XOR 1.=x) l'l'f·:H 1\TI VE: (f.<>r x>ll: Vor i from 2 to x-1, ~(i[x)

I·:XAMF'l.I·:S: 2, J, !i, 7, 11, 1:!, 17

1\0liNDI\HY: 2,:!

1\0IJNDAHY-Ft\II.IIHI·:S: 0,1

Jo'i\l Llll\Jo:S: 12

GJ·:NKHI\LlZt\TIONS: Niunhcrs, Numl~en wit.h an even no. of clivi~ors, Numbers wilh a prime no. of clivisors SPIO:Cl 1\l.IZI\'I'IONS: Vri1nc Jl<tirs, Prime uniqucly-arlrlabll!s CONJ I~CS: Unique fact.oriiat.ion, !ioldhach's conject.ure 1\Nt\LOGIES: Max.imally-divi·ihlc nllrnhcr~ Arc convcr~c ext rcrnc~ of Divisors-.of

I NTI·.:IU:ST: Conjcc's tyiug Primes t.o Timr.s, t.o DivisorJ;-of, an<l t.o _olhr.r closdy rclalcrl opera bon~ WOHTH: ROO

The representation of a concP.pt is as a collection of facets, eilch of which ciln h<lve some Clssociated value. For ex<lmple, the value of the Worth f<lcet of the Primes concept is 800. An.other sample concept, "Sets", is presented earlier in these proceedings, in Section 2.1 of [Lrnat 1977).

3.3.3 Flow of Contr()l

AM is initially given a collection of 115 core con.cepts, with only a few facets (i.e., slots) filled in for each. AM repeatedly chooses some facet of some concept ·. and tries to fiJI in some entries for that particular slot. Thus ·a "job" for AM is simply to engage in a mini-research project, to commit a simple act of discovery. Its overall task - to discover interesting concepts and conjectures - is acco~plished as a composition of hundreds of these repeated attempts at little dlscoveries. To decide which sm<lll job to work on next, AM maintains an agenda of jobs, a global queue ordered by priority. A typical job is "Fill-in examples of Primes". The agenda may contain hundreds of such entries. AM repeatedly selects the top job from the agenda and tries to carry it out. This is the whole control structure! Of course, we mmt still expl<~jn how AM creates plausible new jobs to place on the agenda , how AM decides which job will be the best one to execute next, and how it carries out a job.

A heuristic rule is rcle1'ant to a job if ;mel only if executing th<~t rule bring~ AM closer to satisfying· that job. Potential relevance is determined a i'riori by where the rule is stored. A rule tack ed onto the Domain/range facet of the Compose· concept would be presumed potentially relevant to the job "Fill in the Domain of Sort-a-Insert". The left hand side (IF- part) of each potentially relevant rule is evaluated to determine whether the rule .is truly relevant.

Once a job is chosf.'n from the agenda, AM gathers together all the potentially relev~nt heuri~tic rulrs - the ones which might accomplish that job. . The truly relevant ones are executed (followed), and then AM picks a new job. While a rule is executing, three kinds of actions or effects can occur:

• (i) Facets of some concepts can get filled in (e.g., examples of primes may <Jctuillly be found and tacked onto the "Examples" facet of the "Primes" concept).
• (ii) New concepts .may be created (e.g., the concept "primes which are uniquely representab.le as the sum of two other primes" may be somehow be deemed worth studying). ·
• (Ui) New jobs may be added to the agenda (e.g., the current activity may suggest that the following ojob is worth considering: "Generalize the concept of prime numbers").

The concept of an agenda is certainly not new: schedulers have b.een arouhd for a long time. But one important feature of AM's agenda scheme is a new idea: attaching - and using....: a list of quasi-symbolic reasons to each job which explain why the job is worth considering, why it's plausible. It is the responsibility of the heuristicrules to include ·reasons for any. jobs they propose.

AM uses each job's list of reasons in three ways:

1. W.hen a jol~ already on the agenda is re-suggested, the supporting reasons are examined: If the job is being .proposed for a new reason,. then its priority (and hence its position on the agenda) will be raised; but if the job is being proposed for an already-recorded reason .. then It's priority rating won't change.
2. Once a. job has been selected, the quality of the
3. reasons is used to decide how much time and
4. space the job will be permitted to absorb, before AM quits and moves on to a new job. .
5. To explain to the human observer precise ly why the chosen (current) job is a plausible thing for AM to concentrate upon.

Each of. AM's 250 heuristic rules is attache~! to the most . genera l (or abstract) concept C for which it is deemed appropriate. The relevance of heuristic rules is assumed to be inherited by all C's specializations. For example, a heuristic niethod which is capnble of 'inverting any relation will be attached to the concept "Relation"; but . it · is certainty also capable of inverting any permutation. If there are no known met hod s spec ifJC to the l·atter JOb, then AM wilt follow the �ener;~liz. ation links upward from Permut;~tion to Tiiject ion to Function to Rel<~tion ... , seek ing methods for inv.ersion . Of course the more general concepts' methods tend to be weaker than those of the specific concepts.

In other words, the <!ggregate of the Generali7.ation/Speciali7.ation relationships among the . ccmccfJts induces a similar graph st ructure npo~ the set of heuristic rules. This "inheritability property perm1ts potentially i·elevant rules to be locatrd efficiently.

3.3.4 Behavior of this Rule Sy.s tem

AM began its investigations wilh scanty knowledge of a hundred elementary concepts of finite set theory. Most of the obvious set-theoretic concepts and rei at ionships · were quickly found (e.g., de Morgan's laws; singletons), but no sophisticated set theory w;~s ever done (e.g.,. diagonali7.ation). Rather, AM discovered natural numbers ;~nd went off exploring elementary number t heory. Arithmetic oper<~tions were soon .found (as <'Ina logs to set-theoretic oper at ions), and AM defined such concepts as prime pairs, Dioph<~ntine equ<~tions, the unique factorization of numbers ini'O primes, and Goldbach's conjecture. Many concepts which we know to be crucial . were never 15 uncovered, . however: remainder, gcd, greater-than, infinity, proof, etc.

15 AM did not run forever (despite what anybody at SUMEX ·tells you). An the discoveries mentioned were made in a run las ting one cpu hour (lnterlisp+100k, SUMEX PDP~ lO Kl). Two hundred jobs in toto were selected from the ;~genda ;~nd executed. On !he ;~verage, a job was gr;~nted 30 cpu seconds, but' actuany used only 18 seconds. For· ·a typic;~l job, ;~bout 35 rules were located as potenti'ally relevant, and about a dozen actually fired . AM began with 115 concepts and ended up With three times that many. Half of the synthesized concepts were technically t'ermed "losers" (both by the author and by AM).

Although /1. M fared well <~ccording to $everal different measmes of performance (see Sect ion 7.1 in [Lenat 1976)), it had some difTiculties. As· /1. M ran longer and longer, the concepts it defined were furthei· ;~nd further from the primitives it began wilh; while the general set­ theoret ic heurist ics were technically valid for. dealing with primes and arithmetic, they were simply too general, too weak to gu ide effectively. The key deficiency was the lack of adequate m·eta-rules [Davis 1977): heuristics which cause the creation and mod ification of new heuristics. We are attempting , to remedy this in EURISKO (see SecLion 3.1).

/1. M did demomtratc that scientific theory formation (the de fi lling and exploring of new concepts and relationships) could be mechani1.ed, cou ld be modelled as heuristic rule guided sc~rch, using a few hun<;lred heuristics for guidance. This is a $ig;nificant verification of the theory of intelligence presented in Section 2. 1.

3.4. Other Heuristic Rule Guided Exr:>crt PrQgr.?ms ---------·------------- --------· .. ----- ----~

There are several programs like AM in ex istence,. knowledge based rxpert programs which perform under the guida iKe of a large collect ion of heuristic rules.

• > The MYCIN program [A iki ns 1977] [Shortliffe 1974] contains a couple hund red JUdgmental rules which were extracted from physicians, and it uses them to make diagnoses of various blood <llld meningitis infections.
• > TEIRESlAS [Davis 1977] uses "meta-level" knowledge rules to aid a hum~n expert in transferring his knowledge to a program. Its initial task has been to assist physicians in addii1g nPw rules to MY~IN .
• > MOLGEN [Martin et .~1 1977] attacks the molecular genetics experiment-planning problem discussed earlier (in Section 2.2.3).
• > META-DENDRA L (Buchanan and Mitch ell 1977] is a theory formation program whi.ch looks over mass spectra and their correct iden.tificalions, and then abstracts that data into new fragmentation rules, new . pieces of mass spe-ctroscopy thf"ory. These rul.es are . then usable by the Dendra! program, as if they had been extracted from a humw ·expert.
• > The PECOS program (Barstow 1977] co1itains rules about computer progrilmming, and is a key component in an automatic programming system.
• > UT-ITP (Bledsoe and Tyson 1975] is a natural deduction system, · guided by a collection of judgmental rules useful whE'Il constructing formal proofs.
• > The PROSPECTOR program [Duda et al 1977] perfm:ms geological aJialysis of aerial photographs, aiding a human expert in the evaluation of the mineral potential .of exploration sites. Tts rules . were gleaned from geologists, much as MVCIN's .were from physicians.
• > The M -Method program (Zaripov 1975] for improvising variations on a given melody is based around a body of musi-cology rules.
• > PUFF is a medical expert program, much like · MYCIN in design, whose · field of expertise is pulmonary disorders. "Everything PUFF knows about pulmonary · function diagnosis js 'conta1ned in (currently) 55 rules of the IF ... THEN... form." [Feigenbaum 1977]
• > The · EURISKO program [Lenat et al 1977] is perhaps the most ambitious effort yet along this Une, attempting ·to discover .new heuristic rules ·in the · domains it investigates. It ·is "ambitious" because even professional scie11tists are very . ·poor at formulatin~ ~ or even · recognizing - new heuristics. I EUR ISK O's method for discovering and developing .heuristics is simply to not (fistinguish . between concepts ·and h~ristics; i.e., each heuristic is . represented internally a.s a full-fledged concept. So, e.g., any heuristic which can advise when it;s time to generalize or forget any · concept, can a.Iso · automatically tell when it's time to generalize or fprget any heuristic. Any method for creating a new·concept out of old ones can be used to create new heuristics out of old ones. Evaluating the new h'euristics is done just like evaluating any new concepts: by observing them in a.ction, by gathering empiriCal data about them.

16 Often, discovering a single powerful heuristic can trigger .a scientific revoluti.on [Kuhn 1970] (e .g~ , Einstein's discovery of the ·heuristic "counterintuitive mathematiCal systems might have physical reality" led to a relatiJely important new paradigm in physics not too long ago. "Counterintuitive. mathematical systems may be consistent ·. and interesting" led to ·a parallel revolution in geometry fifty years,earlier. · .

4. CONCLUSIONS

4.1. The Main Points to · Remember

• > We view M;m as a processor of symbolic information. Keeping in mind that this is but one narrow 'View, we find it a useful vantage point from which to study the phenomenon of human intelligence . .
• > Most cognitive tasks can be .cast · as explorations ·' through more or less enormous 17 · search spaces .. "Intelligence" is' the ability to zero · in effectively on a . solution, despite the apparent size of the search space:
• > We theorize that humans posse~s hundreds (perhaps : thousands) of informal rules of thumb (heuristics) which they use to guide them in these searches. These rules are the prime repository for domain-specific knowledge (Le., for expertise). The ·source of intelligence is thus having .(and being able to acquire) such rules, and being able to access them effectivelY'-
• >> We now have seen the relationship between knowledge, search, and reiterate them: Search Knowledge reduces search. is Intelligent. . intelligence.. To · is ubiquitous. Using knowledge
• » The theory of Intelligence as heuristic rule guided search contains all the power of "production systems": additivity of many piec;es of "local" knowle(ige, and ease of introdu.cing neW pieces of knowledge. .
• » Unlike so-called "pure" production systems (Len at and Harris 1977], we · demand that · each of our rules · be a meaningful chunk of domain~specific knowledge. That is, it must have some significance to a human expert. Thus each model of the theory will be self­ explaining: it need only inform the human observor of which rules are executed. This coarse granularity of rules gives the theory the full power of general "heuristic search": a rule can express any arbitrarily complex heuristic.
• > Sever·al' example scenarios have been presented, to show .that this theory . can account for everyday

17 The less structu~ed the domain, the larger the search space. One extreme of thls · is. an algorithm, · which is a highly . "compiled" search. ·

• problem · solving and invention , and also for scientific problem solving and invention . . Moreover, the very sanle heuristics a.re useful in all four types of situations. l8 We also saw how heuristic rules could judge ~'Interestingness'.' ·· of newly synthesized Inventions (both real-world and abstract).
• > Three kinds of models, pased on this theory, were examined: LT/GPS, Dendra!, and AM. The efforts are separated in time by. periods of ten years (1957, 1967, 1977) and factors of ten In the number of heuristics they utilized (3, 30, 300). A II three s~rve to · support the above theory.
• > We saw In particular how AM is a.ble to use its heuristics to guide atten.tion (add and modify jobs on Its age1ida), to synthesize new concepts, · to explore them (fill in their facets), and to evaluate them (judge Interestingness) . .This demonstrated that the general heur.istic rules . are · not merel.Y a descriptive · commentary, they are . an operat ional part ·of the theory. We mentioned several similar progr~ms, to show that AM · and its predecessors are not merely lucky a.cc·idents.

4.2. The Futurfi! of AI

The ultimate good of 'Science is ·the enhancement of Man. Medicine views him as an animal, and is able to provide biological enhancement: better health, longevity. Engineering views him as a dynamic actor, a.nd is able to provide physical enhancement: faster ·transportation, mechanical sensory augmentation (e.g., . radio). Computer Science - and especially AI - view Man as an information processor, and provide mental enhancement: aids to reasoning. . bookkeeping, composing, discovering theorems, understanding of his own intelligence, and perhaps - in the dist.ant future ..,.. even finding one's· way a.round Boston. · ·

ACKNOWLEDGEMENT

The .,author wishes to acknowledge a few of the many individuals who have inspired him with their ideas, ideas which in no few cases have filtered down into this talk: Bruce . Buchanan, Edward Feigenbaum, Greg Harris · Donald Knuth, Merle Lena.t, John McDermott, . ' '

18 There ar·e of course, some more specialized . heuristics, which ~re only useful, .say, in scientific problem solving, or even only in organic chemistry problem solving, or just in·. cleating with ketones, etc.

A lien Newell, Raj Reddy, Earl . Sacerdoti, Herber-t Simon, and Patrick Winston.