- Email: [email protected]
Assimilation and discovery
0732.llRX
83130”+“0”
c 1983 Prrgamon
ASSIMILATION of Philosophy,
Northern
Lrd
AND DISCOVERY
HAROLD Department
Prrar
I. BROWN
Illinois
University,
DeKalb,
IL 60115,
U.S.A
Abstract - My aim in this paper is to examine a rational discovery strategy that I call “assimilation”, the attempt to understand a new domain by systematically interpreting the items it contains in terms of an established conceptual structure. The claim that this approach can lead to important new discoveries is illustrated by considering Galileo’s attempt to develop a mathematical theory of the strength of materials and his discovery of mountains on the moon.
My aim in this paper is to examine one method by which scientific discoveries have been made. The very statement of this project is contrary to a long which maintains that there are no methods of philosophical tradition discovery, that discovery is a fundamentally nonrational process, and that there is nothing philosophically interesting about scientific discovery. This tradition has been under persistent attack for the past two decades, and as a result of this attack we have begun to develop a clearer and richer understanding of such notions as “rationality” and “method”*. In particular, it has become clear that we must not restrict our concept of a rational process to those cases in which we have a set of rules that guarantee a solution to a problem after a finite number of mechanical steps. Similarly, the idea of a method must not be wedded to that of an algorithm or mechanical procedure. For, while many problems can be solved by algorithms, and while it is surely desirable to develop algorithms wherever possible, there remains a wide variety of situations in which no algorithms currently exist, and perhaps some in which no algorithms are possible, but in which we do have methods for attempting to solve problems. These methods, which are generally referred to as heur&tics, provide maxims or guidelines for attacking a problem and in many instances these are guidelines which we know to have worked in the past for analogous problems. A person equipped with a set of relevant heuristics is in a position to attack a problem in an organized, coherent and rational manner, even though there is no prior guarantee that any of these approaches will lead to a satisfactory solution. This point has long been recognized, at least implicitly, by researchers and teachers in the sciences and mathematics. Consider, for example, the striking differences between the procedures of differential and integral calculus. In the former case there is a set of algorithms which permits the determination of the derivative of a function in a wholly mechanical fashion. Integral calculus is much more complex: there is no effective procedure for determining whether a *For a discussion of both the older tradition and the emergence in recent years of another alternative approach to the philosophy of science, see Brown [l]. I have considered the notion of rationality in some detail in [Z]. 89
90
H. I. BROWN
given function has an integral, and no algorithm for integrating those functions which are integrable. But this does not mean that there are no methods for integration nor that one can only proceed by making stabs in the dark. Rather, there is a variety of methods for integrating functions (e.g. change of variable or trigonometric substitution); they are methods which are known to work in specific cases, and students can be taught how to make use of these methods. These are heuristic methods in that there is no guarantee that they will work in a specific case; their use requires a degree of talent and skill, and some people will use them much more effectively than others. Still, they are methods which can be taught, and the person who has learned these methods is in a position to tackle integration problems in an organized and rational manner. Methods of scientific discovery are heuristic methods in just the sense described above, and I think that a major present concern of those interested in the analysis of scientific discovery must be to look back over the history of science and attempt to identify, formulate, and examine methods that creative scientists have made use of. In this. paper I will describe one such method, which I will refer to as assimilation, and illustrate its operation in two of Galileo’s research projects. I borrow the term “assimilation” and the underlying idea, although not the details of the analysis, from Piaget. According to Piaget, “no form of knowledge, not even perceptual knowledge, constitutes a simple copy of reality, because it always includes a process of assimilation to previous structures” [3, p. 41. The thrust of this claim is spelled out a bit further in the following passage: “Every relation between a living being and its environment has this particular characteristic: the former, instead of submitting passively to the latter, modifies it by imposing on it a certain structure of its own” [4, pp. 7-81. A part of Piaget’s thesis - the part that will concern us here - is that we deal with situations that we encounter by interpreting or understanding them in terms of “schemata” that we already have available before entering the particular situation at hand, and assimilation is the process of understanding items in our environment in terms of these schemata. When we encounter objects that resist Piaget calls the latter process this assimilation, we modify our schemata. H e emphasizes that, strictly speaking, assimilation “accommodation” [4, p. 81. and accommodation are two poles of a single process and can only be separated by abstraction [3, p. 1731, b u t we will be concerned only with assimilation in the present paper. In order to make use of this idea we must first clarify what we are to understand by a “schema”. Piaget includes a wide range of items, running from motor reflexes to the theories of mathematical physics, under this rubric, but it is not my intention in this paper either to attempt to expound Piaget in detail or to cover anywhere near this much ground. Rather I will limit myself to cases in which objects are dealt with by subsuming them under a system of concepts and thereby assimilating them to what I will call a “conceptual structure”, i.e. a set of systematically related concepts. For example, if I identify the object in front of me as a typewriter I am doing a great deal more than just attaching a
ASSIMILATION
AND DISCOVERY
91
label that will serve a purely indexical function, for if I tell you that the thing in front of me is a typewriter I am providing a great deal of information about this object that I would not give you if I had only reported that it is “item 27 on the 1980 inventory sheet”. To tell you that an object is a typewriter is to tell you, among other things, that it is a manufactured object, that it was produced by a society that has reached a fairly high level of technological development, and that it is used for writing. At the same time, this information will, should you be curious, inform you that certain questions can legitimately be asked about this object while others would be inappropriate. For example, it would now be appropriate to ask whether it is manual or electric, or what sort of ribbon and what size type it uses, but not what it ate for breakfast. All of this becomes possible because the concept of a typewriter is one member of a system of interrelated concepts, and to describe an object as a typewriter is to invoke this entire conceptual structure. Indeed, as Sellars [5] has maintained, concepts only function as members of conceptual systems, and it is only because concepts always occur in relation to other concepts that we convey information about an object when we subsume it under a concept. To subsume an object under a concept, then, is to assimilate that object to a particular conceptual structure, and a major advantage of such assimilation is that it now becomes possible to think productively about that object. If I describe an object only as “item number 27” I do, of course, make it possible to infer such things as that it is either item 27 or a green tiger, but that is not the sort of inference that will in any way enhance knowledge or guide the pursuit of further information. Similarly, if I encounter an object that I cannot identify, I can seek information about it by further manipulation, with all of the peril to life and limb that this entails, but one advantage of identifying an object in terms of a conceptual structure, even tentatively, is that this permits us to withdraw from the object itself and deal with the relevant conceptual structure alone. We will, to be sure, want to return to the object from time to time in order to test the results of our reasoning, especially in cases in which the original identification was only tentative or in which we are unsure of some of the connections in our conceptual net; but it is only after we have assimilated an object to a conceptual structure that this sort of rational, directed testing becomes possible. The significance of conceptual assimilation can often be seen most clearly in those cases in which a particular object is susceptible, at least at a particular time, to alternative identifications, i.e. in which it seems to be assimilable to more than one conceptual scheme. A dark spot in the distance may be identifiable as a shadow or as a hole, and each of these identifications will in turn lead to different expectations as to what will be found upon closer examination and to the raising of different questions; we do not, for example, seek the same sorts of causes for a shadow that we seek for a hole. Similarly, after further investigation convinces us that we are, say, dealing with a hole, we might then attempt to identify it further by assimilating it to a richer conceptual structure, e.g. by identifying it as a mine shaft or as a meteorite crater. Again, different expectations and different further questions become appropriate for each of these identifications. (For further discussion see ref [6].) Just how much infor-
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H. I. BROWN
mation a particular identification brings along with it depends on the scope and precision of the conceptual structure to which the object has been assimilated; to identify an object as a hole is to integrate it into a much poorer conceptual structure than to identify it as a mine shaft. Further, a conceptual structure that includes only qualitative connections provides a good deal less information than one that includes quantitative connections as well; recognizing an object as a typewriter gives some general limits as to its size and weight, identifying an object as an electron involves quite precise claims about its charge, mass, etc. As the above suggests, conceptual structures range from the relatively sparse and imprecise systems operative in much of our everyday experience, to the much richer and more detailed frameworks provided by explicit scientific theories. But in all of these cases, to identify an object in a cognitively productive manner is to assimilate it into a conceptual structure that provides a basis for thinking about and understanding that object. Now it might seem that assimilation provides a paradigm example of a conservative way of approaching new situations since it requires that we attempt to understand these situations in terms of already existing conceptual structures. Fundamental innovations, it might be suggested, would seem to be more likely in cases of accommodation; such discoveries as Copemican astronomy or relativity and quantum mechanics all involved basic changes in accepted conceptual structures, rather than the mere integration of new situations into an existing structure. But while it is true that many of the most dramatic discoveries required the alteration of established conceptual structures, it does not follow that assimilation can have no role in the discovery process. Indeed, we will find that important discoveries can be made as a result of a systematic assimilation of a new domain to an established conceptual structure. Before illustrating this thesis, however, it is necessary that we first consider conservative assimilations a bit further, for it is a major thesis of this paper that assimilation is a rational strategy, and we must therefore not leave the impression that assimilation occurs only in those cases in which we happen to notice that some object can be identified in a particular way. For while this often may occur, I want to argue that there are also cases in which one systematically undertakes to assimilate a situation to a particular conceptual structure, and that a great deal of scientific and technical training consists of learning how to carry out such assimilations. Consider first a civil engineer who must analyze a particular structure such as a factory building. He will first represent the structure by a diagram such as that of Fig. l(a) in which the lines represent the various structural members, and then add representations for the loads and the reaction components as in Fig. l(b). The resulting diagram will not look at all like the structure in question to a person unfamiliar with structural theory, but the engineer now has a version of the structure that is analyzable using the techniques of this theory. In effect, he has reconceived the structure in terms of the conceptual apparatus of structural theory. In doing so he has assimilated it to this theory, and until this reconceptualization has taken place it is not possible to apply the techniques of the theory to the structure. Now this is typical of the way in
ASSIMILATION
AND DISCOVERY
Fig.
93
I.
which a physical theory is applied to a set of physical objects. For the theory to become relevant it is first necessary that the objects to which it is being applied be reconceived in terms of the conceptual apparatus of the theory, and a large part of the education of the scientist or engineer consists in learning how to rethink the objects in a particular domain in terms of the concepts of a theory It is this process of assimilation in order to apply the theory to that domain*. that is at work when an astronomer redescribes the solar system as a set of massive points with forces acting on them, or when a physicist seeks the proper Hamiltonian operator for an atomic system - for the Hamiltonian is the appropriate redescription of a system which is to be dealt with via the conceptual machinery of quantum mechanics. The same process is at work when a logician translates an argument into logical symbolism in order to be able to test its validity by means of the techniques of symbolic logic. In all of these cases one can systematically and rationally pursue the end of assimilating and people are trained to carry out such objects to a conceptual structure, assimilations, even though in all of these cases there is no algorithm available which can guarantee that an appropriate assimilation will be found. The above discussion has been aimed at clarifying what I wish to understand and showing that assimilation can be pursued in an organizby “assimilation” ed and systematic way. I want now to argue that fundamental discoveries can be made as a result of assimilating some new domain to a previously well developed conceptual structure, and I will do so by examining two cases from Galileo’s work, one theoretical and one observational. The first case I will consider is Galileo’s attempt to develop a mathematical theory of the strength of materials on the Second Day of the Two New Sciences. The key to Galileo’s attempt is that he already understands the operations of levers and that he believes that he can redescribe beams as systems of levers. Once beams have been assimilated to levers, the well known principle of the operation of levers provides the basis for determining the previously unknown load carrying capacities of various kinds of beams. At the outset of the Second Day Salviati tells us, “In such speculations I take as a known principle one which is demonstrated in mechanics about the pro*This
point has been developed
in considerable
detail
by Polanyi
[7] and Kuhn [S].
H. I. BROWN
94
perties of the rod which we call the lever: that in using a lever, the force is to the resistance in the inverse ratio of the distances from the fulcrum to the force and to the resistance” [9, p. 1091. After offering a proof of this law Galileo first applies
it to the case of a cantilever
loaded
at the end (ignoring
the weight
of
the beam itself). Taking a beam of the sort shown in Fig. 2 as his example, Galileo maintains that “if it must break, it will break at the place B, where the niche in the wall serves as a support, BC being the arm of the lever on which the force
is applied.
. . .” [9, pp. 114-l
The
BA of the solid is the other
thickness
151. What
Galileo
has done is to redescribe
AB and BC with the common resisting force of the beam, R, is supplied uniformly along its thus provides a resisting moment equal to one-half R times AB, while the length of the beam BC provides the moment of counterbalancing
For a beam that
can
arm of this lever
the beam
as a pair
fulcrum
B. The
levers
of fixed
be sustained
dimensions is equal
and resistance,
therefore,
thickness AB and the moment arm arm for the load.
the maximum
load
to 1/2AB X R/BC.
Fig. 2. This is a contemporary version of the diagram: Galileo’s is considerably more artistic (cf. [9, p, 1151)
drawing
Modern theory holds that this result is mistaken, and that the the beam is proportional to the square of its thickness, but this is our present concerns. The modern theory is developed as a result tion of the beam to a very different mathematical theory, one not Galileo, but we cannot hold Galileo at fault developments, and we must not fall into the Galileo’s results were incorrect, his procedure tional*. Rather, we should note that, as Drake known attempt to formulate a mathematical [9, p. 115n], and that Galileo was able to
resistance of irrelevant to of assimilaavailable to
for failing to anticipate later trap of believing that because must have been somehow irrapoints out, “Galileo’s is the first theory of strength of materials” make the attempt because he
recognized the possibility of systematically treating beams as systems of levers, items whose properties were already understood. On this basis Galileo proceeds to tackle a wide variety of further problems, e.g. the effect of different support configurations, of different beam cross-sections, and the ability of a variety of beams
to carry
their
*See [2] for further
own weight.
discussion
of this point.
ASSIMILATION
95
AND DISCOVERY
It is not necessary to follow the details of Galileo’s analysis any further for our present purpose, which is solely to illustrate the way in which the systematic assimilation of a new domain to one that is already understood can serve as a technique for making new theoretical discoveries. I want now to consider Galileo’s discovery that the moon is mountainous in order to illustrate this same process at work in an observational case. The key point to recognize here is that while examining the moon through his telescope Galileo literally saw a number of changing patterns of light and dark areas that he initially described in relatively phenomenal terms, and that it was only when he was able to identify these patterns as the typical effects of sunlight in a mountainous region that he can be said to have d&covered mountains on the moon. Let us look at some of what Galileo has to say about his observations and their significance, beginning with his descriptions of light patterns. On the fourth or fifth day after new moon, when the moon is seen with brilliant horns, the boundary which divides the dark part from the light does not extend uniformly in an oval line as would happen on a perfectly spherical solid, but traces out an uneven, rough, and very wavy line _. Indeed, many luminous excrescences extend beyond the boundary into the darker portion, while on the other hand some dark patches invade the illuminated part. Moreover a great quantity of small blackish spots, entirely separated from the dark region, are scattered almost all over the area illuminated by the sun ,.. [T]he said small spots always agree in haying their blackened parts directed toward the sun, while on the side opposite the sun they are crowned with bright contours, like shining summits [lo, p. 321. [M]any bright points appear within the darkened portion of the moon, completely divided and separated from the illuminated part and at a considerable distance from it. After a time these gradually increase in size and brightness, and an hour or two later they become joined with the rest of the lighted part which has now increased in sire [lo, p. 331. There were also a great number of dark spots in both the horns .,. [T]he blackish portion of each spot is turned toward the source of the sun’s radiance, while a bright rim surrounds the spot on the side away from the sun in the direction of the shadowy region of the moon [lo, p. 341.
At this point Galileo has not yet discovered that the moon is mountainous, for while he has observed something that has never been seen before, it is possible that he is seeing a completely new phenomenon, one which has no earthly counterpart, a possibility which would have been highly approved by the conventional physical wisdom of his day. But Galileo does not draw this concluhe proceeds to assimilate sion. Rather, these observed phenomena to phenomena he is familiar with from terrestrial experience. Thus, in the first of the quoted passages, after noting that the bright areas he describes are “like shining summits”, Galileo continues: There is a similar sight on earth about sunrise, when we behold the valleys not yet flooded with light though the mountains surrounding them are already ablaze with glowing splendor on the side opposite the sun. And just as the shadows in the hollows on earth diminish in size as the sun rises higher, so these spots on the moon lose their blackness as the illuminated region grows larger and larger [lo, p. 321.
Similarly,
with respect to the bright areas in the dark portion
of the moon:
H.
96 And
on the
earth,
mountains becoming
the
go on spreading
illuminated?
of plains
and
rising
of the
by the sun’s
illuminated
not the light tion
before
I. BROWN
while
And
the larger
when
hills finally
sun,
rays while
are
the
not
the
plains
central
parts
the sun has finally
risen,
become
one?
[lo,
highest
remain
peaks
of the
in shadow?
of those does
Does
mountains
not
are
the illumina-
p. 331.
and finally: [Allmost
in the
center
perfectly
round
in shape
would tains
a region
of the
like Bohemia
arranged
exactly
moon
there
As to light if that
in a circle
is a cavity
and shade,
were
[lo,
larger
it offers
enclosed
than
all the
the same
on all sides
rest,
and
appearance
by very lofty
as
moun-
p. 361.
Galileo’s approach here is to attempt systematically to understand what he is seeing in terms of a conceptual structure that is already available to him, rather than suggesting that he had discovered a completely and proposing a new conceptual structure or a fundamental
new phenomenon alteration in an
existing conceptual structure to make sense of it. But the fact that he proceeded by assimilating a new observation to an existing conceptual structure in no way prevented him from having made a radically new discovery, a discovery which
played
cosmos celestial
a fundamental
role in undermining
the Aristotelian
view of the
by greatly reducing the plausibility of the view that objects in the and terrestrial realms must be understood on the basis of quite dif-
ferent conceptual structures. This discovery, sunspots and his discovery of four of the moons that both celestial and terrestrial phenomena
along with Galileo’s of Jupiter, all served must be assimilated
studies of to indicate to a single
conceptual structure. One upshot of this discussion, then, is that assimilation is not always a conservative approach, and anyone familiar with the history of reductionist and unificationist programs will recognize that the suggestion that phenomena which terms
appear to be of fundamentally different kinds can be understood of a single conceptual framework, may be a very radical proposal
in in-
deed. More importantly in the present context, assimilation provides one technique for attempting to understand phenomena in a new domain, i.e. by undertaking to redescribe items in that domain in terms of a conceptual structure developed in a different domain. Moreover, we know that this is an approach
that
has been
used successfully
in the past.
REFERENCES Brown
H.
University Brown Piaget
I.
Perception,
of Chicago
H. I. On J.
Biology
Press,
being
Adams
& Co.
and Commitment:
Chicago
(translated
of Intelligence
Paterson,
The New
Philosophy
of Science.
(1979)
American
rational.
and Knowledge
Chicago (1971). Piaget J, The Psychology field,
Theory
NJ (1963).
Philosophical by Walsh
(translated
Quarterly B.).
by Piercy
15, 241-248
University
(1978).
of Chicago
M. & Berlyne
D. E.,)
Press, Little-
ASSIMILATION 5. 6. 7. 8. 9. 10.
AND DISCOVERY
97
Sellars W. Empiricism and the philosophy of mind. In Science, Perception and Reality, pp. 127-196. Humanities Press (1963). Brown H. I. Problem changes in science and philosophy. Metaphilosophy 6, 185-187 (1975). Polanyi M. Personal Knowledge. University of Chicago Press, Chicago (1958). Kuhn T. S. The Structure qf.Scientz$c Revolutions, 2nd edn. University of Chicago Press, Chicago (1970). Galileo, Two New Sciences (translated by Drake S.). University of Wisconsin Press, Wisconsin (1974). Galileo, The Star-ry Messenger (translated by Drake S.) In Discoveries and Opinions qf Galileo. Doubleday & Co., New York (1957).
83130”+“0”
c 1983 Prrgamon
ASSIMILATION of Philosophy,
Northern
Lrd
AND DISCOVERY
HAROLD Department
Prrar
I. BROWN
Illinois
University,
DeKalb,
IL 60115,
U.S.A
Abstract - My aim in this paper is to examine a rational discovery strategy that I call “assimilation”, the attempt to understand a new domain by systematically interpreting the items it contains in terms of an established conceptual structure. The claim that this approach can lead to important new discoveries is illustrated by considering Galileo’s attempt to develop a mathematical theory of the strength of materials and his discovery of mountains on the moon.
My aim in this paper is to examine one method by which scientific discoveries have been made. The very statement of this project is contrary to a long which maintains that there are no methods of philosophical tradition discovery, that discovery is a fundamentally nonrational process, and that there is nothing philosophically interesting about scientific discovery. This tradition has been under persistent attack for the past two decades, and as a result of this attack we have begun to develop a clearer and richer understanding of such notions as “rationality” and “method”*. In particular, it has become clear that we must not restrict our concept of a rational process to those cases in which we have a set of rules that guarantee a solution to a problem after a finite number of mechanical steps. Similarly, the idea of a method must not be wedded to that of an algorithm or mechanical procedure. For, while many problems can be solved by algorithms, and while it is surely desirable to develop algorithms wherever possible, there remains a wide variety of situations in which no algorithms currently exist, and perhaps some in which no algorithms are possible, but in which we do have methods for attempting to solve problems. These methods, which are generally referred to as heur&tics, provide maxims or guidelines for attacking a problem and in many instances these are guidelines which we know to have worked in the past for analogous problems. A person equipped with a set of relevant heuristics is in a position to attack a problem in an organized, coherent and rational manner, even though there is no prior guarantee that any of these approaches will lead to a satisfactory solution. This point has long been recognized, at least implicitly, by researchers and teachers in the sciences and mathematics. Consider, for example, the striking differences between the procedures of differential and integral calculus. In the former case there is a set of algorithms which permits the determination of the derivative of a function in a wholly mechanical fashion. Integral calculus is much more complex: there is no effective procedure for determining whether a *For a discussion of both the older tradition and the emergence in recent years of another alternative approach to the philosophy of science, see Brown [l]. I have considered the notion of rationality in some detail in [Z]. 89
90
H. I. BROWN
given function has an integral, and no algorithm for integrating those functions which are integrable. But this does not mean that there are no methods for integration nor that one can only proceed by making stabs in the dark. Rather, there is a variety of methods for integrating functions (e.g. change of variable or trigonometric substitution); they are methods which are known to work in specific cases, and students can be taught how to make use of these methods. These are heuristic methods in that there is no guarantee that they will work in a specific case; their use requires a degree of talent and skill, and some people will use them much more effectively than others. Still, they are methods which can be taught, and the person who has learned these methods is in a position to tackle integration problems in an organized and rational manner. Methods of scientific discovery are heuristic methods in just the sense described above, and I think that a major present concern of those interested in the analysis of scientific discovery must be to look back over the history of science and attempt to identify, formulate, and examine methods that creative scientists have made use of. In this. paper I will describe one such method, which I will refer to as assimilation, and illustrate its operation in two of Galileo’s research projects. I borrow the term “assimilation” and the underlying idea, although not the details of the analysis, from Piaget. According to Piaget, “no form of knowledge, not even perceptual knowledge, constitutes a simple copy of reality, because it always includes a process of assimilation to previous structures” [3, p. 41. The thrust of this claim is spelled out a bit further in the following passage: “Every relation between a living being and its environment has this particular characteristic: the former, instead of submitting passively to the latter, modifies it by imposing on it a certain structure of its own” [4, pp. 7-81. A part of Piaget’s thesis - the part that will concern us here - is that we deal with situations that we encounter by interpreting or understanding them in terms of “schemata” that we already have available before entering the particular situation at hand, and assimilation is the process of understanding items in our environment in terms of these schemata. When we encounter objects that resist Piaget calls the latter process this assimilation, we modify our schemata. H e emphasizes that, strictly speaking, assimilation “accommodation” [4, p. 81. and accommodation are two poles of a single process and can only be separated by abstraction [3, p. 1731, b u t we will be concerned only with assimilation in the present paper. In order to make use of this idea we must first clarify what we are to understand by a “schema”. Piaget includes a wide range of items, running from motor reflexes to the theories of mathematical physics, under this rubric, but it is not my intention in this paper either to attempt to expound Piaget in detail or to cover anywhere near this much ground. Rather I will limit myself to cases in which objects are dealt with by subsuming them under a system of concepts and thereby assimilating them to what I will call a “conceptual structure”, i.e. a set of systematically related concepts. For example, if I identify the object in front of me as a typewriter I am doing a great deal more than just attaching a
ASSIMILATION
AND DISCOVERY
91
label that will serve a purely indexical function, for if I tell you that the thing in front of me is a typewriter I am providing a great deal of information about this object that I would not give you if I had only reported that it is “item 27 on the 1980 inventory sheet”. To tell you that an object is a typewriter is to tell you, among other things, that it is a manufactured object, that it was produced by a society that has reached a fairly high level of technological development, and that it is used for writing. At the same time, this information will, should you be curious, inform you that certain questions can legitimately be asked about this object while others would be inappropriate. For example, it would now be appropriate to ask whether it is manual or electric, or what sort of ribbon and what size type it uses, but not what it ate for breakfast. All of this becomes possible because the concept of a typewriter is one member of a system of interrelated concepts, and to describe an object as a typewriter is to invoke this entire conceptual structure. Indeed, as Sellars [5] has maintained, concepts only function as members of conceptual systems, and it is only because concepts always occur in relation to other concepts that we convey information about an object when we subsume it under a concept. To subsume an object under a concept, then, is to assimilate that object to a particular conceptual structure, and a major advantage of such assimilation is that it now becomes possible to think productively about that object. If I describe an object only as “item number 27” I do, of course, make it possible to infer such things as that it is either item 27 or a green tiger, but that is not the sort of inference that will in any way enhance knowledge or guide the pursuit of further information. Similarly, if I encounter an object that I cannot identify, I can seek information about it by further manipulation, with all of the peril to life and limb that this entails, but one advantage of identifying an object in terms of a conceptual structure, even tentatively, is that this permits us to withdraw from the object itself and deal with the relevant conceptual structure alone. We will, to be sure, want to return to the object from time to time in order to test the results of our reasoning, especially in cases in which the original identification was only tentative or in which we are unsure of some of the connections in our conceptual net; but it is only after we have assimilated an object to a conceptual structure that this sort of rational, directed testing becomes possible. The significance of conceptual assimilation can often be seen most clearly in those cases in which a particular object is susceptible, at least at a particular time, to alternative identifications, i.e. in which it seems to be assimilable to more than one conceptual scheme. A dark spot in the distance may be identifiable as a shadow or as a hole, and each of these identifications will in turn lead to different expectations as to what will be found upon closer examination and to the raising of different questions; we do not, for example, seek the same sorts of causes for a shadow that we seek for a hole. Similarly, after further investigation convinces us that we are, say, dealing with a hole, we might then attempt to identify it further by assimilating it to a richer conceptual structure, e.g. by identifying it as a mine shaft or as a meteorite crater. Again, different expectations and different further questions become appropriate for each of these identifications. (For further discussion see ref [6].) Just how much infor-
92
H. I. BROWN
mation a particular identification brings along with it depends on the scope and precision of the conceptual structure to which the object has been assimilated; to identify an object as a hole is to integrate it into a much poorer conceptual structure than to identify it as a mine shaft. Further, a conceptual structure that includes only qualitative connections provides a good deal less information than one that includes quantitative connections as well; recognizing an object as a typewriter gives some general limits as to its size and weight, identifying an object as an electron involves quite precise claims about its charge, mass, etc. As the above suggests, conceptual structures range from the relatively sparse and imprecise systems operative in much of our everyday experience, to the much richer and more detailed frameworks provided by explicit scientific theories. But in all of these cases, to identify an object in a cognitively productive manner is to assimilate it into a conceptual structure that provides a basis for thinking about and understanding that object. Now it might seem that assimilation provides a paradigm example of a conservative way of approaching new situations since it requires that we attempt to understand these situations in terms of already existing conceptual structures. Fundamental innovations, it might be suggested, would seem to be more likely in cases of accommodation; such discoveries as Copemican astronomy or relativity and quantum mechanics all involved basic changes in accepted conceptual structures, rather than the mere integration of new situations into an existing structure. But while it is true that many of the most dramatic discoveries required the alteration of established conceptual structures, it does not follow that assimilation can have no role in the discovery process. Indeed, we will find that important discoveries can be made as a result of a systematic assimilation of a new domain to an established conceptual structure. Before illustrating this thesis, however, it is necessary that we first consider conservative assimilations a bit further, for it is a major thesis of this paper that assimilation is a rational strategy, and we must therefore not leave the impression that assimilation occurs only in those cases in which we happen to notice that some object can be identified in a particular way. For while this often may occur, I want to argue that there are also cases in which one systematically undertakes to assimilate a situation to a particular conceptual structure, and that a great deal of scientific and technical training consists of learning how to carry out such assimilations. Consider first a civil engineer who must analyze a particular structure such as a factory building. He will first represent the structure by a diagram such as that of Fig. l(a) in which the lines represent the various structural members, and then add representations for the loads and the reaction components as in Fig. l(b). The resulting diagram will not look at all like the structure in question to a person unfamiliar with structural theory, but the engineer now has a version of the structure that is analyzable using the techniques of this theory. In effect, he has reconceived the structure in terms of the conceptual apparatus of structural theory. In doing so he has assimilated it to this theory, and until this reconceptualization has taken place it is not possible to apply the techniques of the theory to the structure. Now this is typical of the way in
ASSIMILATION
AND DISCOVERY
Fig.
93
I.
which a physical theory is applied to a set of physical objects. For the theory to become relevant it is first necessary that the objects to which it is being applied be reconceived in terms of the conceptual apparatus of the theory, and a large part of the education of the scientist or engineer consists in learning how to rethink the objects in a particular domain in terms of the concepts of a theory It is this process of assimilation in order to apply the theory to that domain*. that is at work when an astronomer redescribes the solar system as a set of massive points with forces acting on them, or when a physicist seeks the proper Hamiltonian operator for an atomic system - for the Hamiltonian is the appropriate redescription of a system which is to be dealt with via the conceptual machinery of quantum mechanics. The same process is at work when a logician translates an argument into logical symbolism in order to be able to test its validity by means of the techniques of symbolic logic. In all of these cases one can systematically and rationally pursue the end of assimilating and people are trained to carry out such objects to a conceptual structure, assimilations, even though in all of these cases there is no algorithm available which can guarantee that an appropriate assimilation will be found. The above discussion has been aimed at clarifying what I wish to understand and showing that assimilation can be pursued in an organizby “assimilation” ed and systematic way. I want now to argue that fundamental discoveries can be made as a result of assimilating some new domain to a previously well developed conceptual structure, and I will do so by examining two cases from Galileo’s work, one theoretical and one observational. The first case I will consider is Galileo’s attempt to develop a mathematical theory of the strength of materials on the Second Day of the Two New Sciences. The key to Galileo’s attempt is that he already understands the operations of levers and that he believes that he can redescribe beams as systems of levers. Once beams have been assimilated to levers, the well known principle of the operation of levers provides the basis for determining the previously unknown load carrying capacities of various kinds of beams. At the outset of the Second Day Salviati tells us, “In such speculations I take as a known principle one which is demonstrated in mechanics about the pro*This
point has been developed
in considerable
detail
by Polanyi
[7] and Kuhn [S].
H. I. BROWN
94
perties of the rod which we call the lever: that in using a lever, the force is to the resistance in the inverse ratio of the distances from the fulcrum to the force and to the resistance” [9, p. 1091. After offering a proof of this law Galileo first applies
it to the case of a cantilever
loaded
at the end (ignoring
the weight
of
the beam itself). Taking a beam of the sort shown in Fig. 2 as his example, Galileo maintains that “if it must break, it will break at the place B, where the niche in the wall serves as a support, BC being the arm of the lever on which the force
is applied.
. . .” [9, pp. 114-l
The
BA of the solid is the other
thickness
151. What
Galileo
has done is to redescribe
AB and BC with the common resisting force of the beam, R, is supplied uniformly along its thus provides a resisting moment equal to one-half R times AB, while the length of the beam BC provides the moment of counterbalancing
For a beam that
can
arm of this lever
the beam
as a pair
fulcrum
B. The
levers
of fixed
be sustained
dimensions is equal
and resistance,
therefore,
thickness AB and the moment arm arm for the load.
the maximum
load
to 1/2AB X R/BC.
Fig. 2. This is a contemporary version of the diagram: Galileo’s is considerably more artistic (cf. [9, p, 1151)
drawing
Modern theory holds that this result is mistaken, and that the the beam is proportional to the square of its thickness, but this is our present concerns. The modern theory is developed as a result tion of the beam to a very different mathematical theory, one not Galileo, but we cannot hold Galileo at fault developments, and we must not fall into the Galileo’s results were incorrect, his procedure tional*. Rather, we should note that, as Drake known attempt to formulate a mathematical [9, p. 115n], and that Galileo was able to
resistance of irrelevant to of assimilaavailable to
for failing to anticipate later trap of believing that because must have been somehow irrapoints out, “Galileo’s is the first theory of strength of materials” make the attempt because he
recognized the possibility of systematically treating beams as systems of levers, items whose properties were already understood. On this basis Galileo proceeds to tackle a wide variety of further problems, e.g. the effect of different support configurations, of different beam cross-sections, and the ability of a variety of beams
to carry
their
*See [2] for further
own weight.
discussion
of this point.
ASSIMILATION
95
AND DISCOVERY
It is not necessary to follow the details of Galileo’s analysis any further for our present purpose, which is solely to illustrate the way in which the systematic assimilation of a new domain to one that is already understood can serve as a technique for making new theoretical discoveries. I want now to consider Galileo’s discovery that the moon is mountainous in order to illustrate this same process at work in an observational case. The key point to recognize here is that while examining the moon through his telescope Galileo literally saw a number of changing patterns of light and dark areas that he initially described in relatively phenomenal terms, and that it was only when he was able to identify these patterns as the typical effects of sunlight in a mountainous region that he can be said to have d&covered mountains on the moon. Let us look at some of what Galileo has to say about his observations and their significance, beginning with his descriptions of light patterns. On the fourth or fifth day after new moon, when the moon is seen with brilliant horns, the boundary which divides the dark part from the light does not extend uniformly in an oval line as would happen on a perfectly spherical solid, but traces out an uneven, rough, and very wavy line _. Indeed, many luminous excrescences extend beyond the boundary into the darker portion, while on the other hand some dark patches invade the illuminated part. Moreover a great quantity of small blackish spots, entirely separated from the dark region, are scattered almost all over the area illuminated by the sun ,.. [T]he said small spots always agree in haying their blackened parts directed toward the sun, while on the side opposite the sun they are crowned with bright contours, like shining summits [lo, p. 321. [M]any bright points appear within the darkened portion of the moon, completely divided and separated from the illuminated part and at a considerable distance from it. After a time these gradually increase in size and brightness, and an hour or two later they become joined with the rest of the lighted part which has now increased in sire [lo, p. 331. There were also a great number of dark spots in both the horns .,. [T]he blackish portion of each spot is turned toward the source of the sun’s radiance, while a bright rim surrounds the spot on the side away from the sun in the direction of the shadowy region of the moon [lo, p. 341.
At this point Galileo has not yet discovered that the moon is mountainous, for while he has observed something that has never been seen before, it is possible that he is seeing a completely new phenomenon, one which has no earthly counterpart, a possibility which would have been highly approved by the conventional physical wisdom of his day. But Galileo does not draw this concluhe proceeds to assimilate sion. Rather, these observed phenomena to phenomena he is familiar with from terrestrial experience. Thus, in the first of the quoted passages, after noting that the bright areas he describes are “like shining summits”, Galileo continues: There is a similar sight on earth about sunrise, when we behold the valleys not yet flooded with light though the mountains surrounding them are already ablaze with glowing splendor on the side opposite the sun. And just as the shadows in the hollows on earth diminish in size as the sun rises higher, so these spots on the moon lose their blackness as the illuminated region grows larger and larger [lo, p. 321.
Similarly,
with respect to the bright areas in the dark portion
of the moon:
H.
96 And
on the
earth,
mountains becoming
the
go on spreading
illuminated?
of plains
and
rising
of the
by the sun’s
illuminated
not the light tion
before
I. BROWN
while
And
the larger
when
hills finally
sun,
rays while
are
the
not
the
plains
central
parts
the sun has finally
risen,
become
one?
[lo,
highest
remain
peaks
of the
in shadow?
of those does
Does
mountains
not
are
the illumina-
p. 331.
and finally: [Allmost
in the
center
perfectly
round
in shape
would tains
a region
of the
like Bohemia
arranged
exactly
moon
there
As to light if that
in a circle
is a cavity
and shade,
were
[lo,
larger
it offers
enclosed
than
all the
the same
on all sides
rest,
and
appearance
by very lofty
as
moun-
p. 361.
Galileo’s approach here is to attempt systematically to understand what he is seeing in terms of a conceptual structure that is already available to him, rather than suggesting that he had discovered a completely and proposing a new conceptual structure or a fundamental
new phenomenon alteration in an
existing conceptual structure to make sense of it. But the fact that he proceeded by assimilating a new observation to an existing conceptual structure in no way prevented him from having made a radically new discovery, a discovery which
played
cosmos celestial
a fundamental
role in undermining
the Aristotelian
view of the
by greatly reducing the plausibility of the view that objects in the and terrestrial realms must be understood on the basis of quite dif-
ferent conceptual structures. This discovery, sunspots and his discovery of four of the moons that both celestial and terrestrial phenomena
along with Galileo’s of Jupiter, all served must be assimilated
studies of to indicate to a single
conceptual structure. One upshot of this discussion, then, is that assimilation is not always a conservative approach, and anyone familiar with the history of reductionist and unificationist programs will recognize that the suggestion that phenomena which terms
appear to be of fundamentally different kinds can be understood of a single conceptual framework, may be a very radical proposal
in in-
deed. More importantly in the present context, assimilation provides one technique for attempting to understand phenomena in a new domain, i.e. by undertaking to redescribe items in that domain in terms of a conceptual structure developed in a different domain. Moreover, we know that this is an approach
that
has been
used successfully
in the past.
REFERENCES Brown
H.
University Brown Piaget
I.
Perception,
of Chicago
H. I. On J.
Biology
Press,
being
Adams
& Co.
and Commitment:
Chicago
(translated
of Intelligence
Paterson,
The New
Philosophy
of Science.
(1979)
American
rational.
and Knowledge
Chicago (1971). Piaget J, The Psychology field,
Theory
NJ (1963).
Philosophical by Walsh
(translated
Quarterly B.).
by Piercy
15, 241-248
University
(1978).
of Chicago
M. & Berlyne
D. E.,)
Press, Little-
ASSIMILATION 5. 6. 7. 8. 9. 10.
AND DISCOVERY
97
Sellars W. Empiricism and the philosophy of mind. In Science, Perception and Reality, pp. 127-196. Humanities Press (1963). Brown H. I. Problem changes in science and philosophy. Metaphilosophy 6, 185-187 (1975). Polanyi M. Personal Knowledge. University of Chicago Press, Chicago (1958). Kuhn T. S. The Structure qf.Scientz$c Revolutions, 2nd edn. University of Chicago Press, Chicago (1970). Galileo, Two New Sciences (translated by Drake S.). University of Wisconsin Press, Wisconsin (1974). Galileo, The Star-ry Messenger (translated by Drake S.) In Discoveries and Opinions qf Galileo. Doubleday & Co., New York (1957).