The physicist's toolkit
Martin H. Krieger
University of Southern California.
Los Angeles, California 90089-0042
(Received 27 August 1986; accepted for publication 23 January 1987)
A physicist's "toolkit" might include mathematical, diagrammatic, and modeling tools, including such models as a crystalline solid, a harmonic oscillator, or an inverse square law of interaction. The notion of a toolkit provides a meeting ground for scientists, philosophers, and teachers for appreciating what scientists do. For doing science may be thought of as a craft, skillfully employing a kit of tools.
We may think of scientific work as a craft with an associated toolkit, practiced in guild. The number and kind of tools and practices can be seen as small, teachable, and specifiable. (See Table I for such a kit.) Taking physics "toolishly," physics has nature under its command if it has an effective toolkit and craft of practice.1 Physicists carefully choose and formulate their problems so they can work on them using their kit of tools. As we shall see, they persist in picking out the linear or at least linearizable situations (including the seemingly nonlinear ones). And they invent good ground states to hide the nonlinearities. Physicists explain their capacity to encompass nature by giving an account of the hierarchies of forces (and the monotonicity of a temperature scale) and of the stability of matter. Then their linear perturbative approach should "work," since at each level in the hierarchy one has a stable base from which to work.
Toolishness provides us with a powerful way of understanding and describing what scientists do. We may describe just what is in the physicist's toolkit and the skills and judgment needed for effective practice. We account for how a scientific theory is effective, in that it provides the right tools for doing the work and justifies that work as the appropriate work to be done. Now, in general, a craft may selectively borrow and adapt tools from other crafts. And so, for example, physics and mathematics, or physics and engineering, borrow from each other. So toolishness may suggest why mathematics works in physics.
The notion of a toolkit is attractive because it gets around the conventional separation of theory, hypothesis, and idea - versus experiment, testing, and instruments. All of these might be taken as tools. The traditional questions about scientific truth, knowledge, or belief do not disappear, but they now allow for a rather more concrete approach.
In Sec. II, I describe how physicists conceive of themselves as having a toolkit, and what tools are. Next I shall exhibit a kit's general structure, aiming for comprehensiveness rather than detail. (The reader interested in the contents of a physicist's kit can skip to Sec. III immediately.) The kit I describe is suited for the paper-and-pencil conceptualizing, explanatory, and problem - solving work of a physicist. The toolkit is contemporary, a particle physics and field theoretic one, congenial with modern views of condensed matter. It is drawn from texts, exams, and handbooks. Finally, in Sec. IV I elaborate on some of the consequences of taking physics toolishly.
II. PHYSICISTS AND TOOLS
Physicists like to think of themselves as possessing a set of tools, and contemporary writing about science has taken that claim seriously. Fermi was notorious for approaching problems in a simple fashion, using a small number of models -
Table I The physicist's toolkit.
1. Mathematical tools
space-time vacuum, hydrogen atom, crystal, continuous elastic medium, fluid, gas
particles and excitations, oscillators, fields and waves; linear operators including
differential equations and groups; correlations; properties including energy,
momentum, and translation operators
objects with objects and with media (potentials, particle exchange, force field,
scattering), Interaction Lagrangian, response functions
good vacuum or ground state, equilibrium, conservative potentials; analogy
and heuristic, homology of equations and solutions; n log n vs n 2
qualitative methods (e.g., Migdal): become friendly with nitty-gritty material like Coulomb wave functions; look for big contributions, the physics lies in the poles; use a classical picture, supplemented by quantum rules; things fall off, but asymptotics are important; know about potential wells, oscillators, one- particle transitions, polarizable media,...
( such as electromagnetism ) and adapting them as needed. Back of the envelope calculations and order of magnitude estimates are part of the legends of physics. Pais begins his recent study of Einstein with a one_sentence scientific biography: "Better than anyone before him, he knew how to invent invariance principles and make use of statistical fluctuations." Landau's course of theoretical physics, "the theoretical minimum," is well known. Less well known is the talismanic or emblematic list of his "Ten Commandments," his most useful formulas and models, engraved in stone, given to him by his students on his 50th birthday. Feynman's diagrammatic methods were tools for expressing the physics and for doing the calculational work. Peierls gives a list of the standard models in physics which include: hypothetical, phenomenological, approximate, simplified, instructive, analogical, and Gedanken models. Kenneth Wilson has described a new set of tools based on computation and computer science.2
Physicists also readily offer coaching advice about choosing a problem to work on, the right level of difficulty to start out with, or where to search for new laws. For example, Dyson following Bragg: "Don't try to revive past glories. Don't do things just because they are fashionable. Don't be afraid of the scorn of theoreticians."3 As means of guidance and caution Peierls describes surprises in theoretical physics, surprises in that initial intuitions and approaches proved incorrect.4 A. B. Migdal has written an advanced text in quantum mechanics that aims to expose the student to how-to-do-it qualitatively, like a real pro. Comprehensive and explicitly a toolkit, I summarize some of its guidance in Table I [items 3b(2)] under "Commonplaces.''5
A physicist's toolkit might be divided
into three parts: mathematical, picturing or diagrammatic, and descriptive
or rhetorical. As can be seen from Table I, the kit includes models of
media such as a crystal, models of objects such as a particle, and models
of interactions such as a collision. And the practice includes strategies
and commonplaces, such as looking for equilibrium states. Using a toolkit
requires technical skill for adept manipulation of mathematical and diagrammatic
expressions. It also requires judgment, for assessing and deciding which
tool or model is appropriate to a situation, or when a strategy is likely
to be effective.
A. Tools in general
Tools are things we use for doing our work. Tools feel objective and are literally shareable, while skills are personal and imitated. A toolkit of seemingly abstracted or objective tools comes along with a practice of tool-using - how to work and how the work is organized, and a sense of what it is the craftsperson is doing. Carpenter's toolkits surely have hammers and chisels, but carpenters use nails and work with wood, they know how to swing a hammer, they work during regular hours along with other crafts, and they are in the business of constructing something. The toolkit's contents and practices depend on the historical time, where the work is being performed, the kinds of material being worked on ( wood, metal, atoms, condensed matter), and what is being constructed. There are standard tools, as well as personal and jerry-built devices. The term "toolkit" suggests a small number of versatile tools meant to work together.
Tools can be notional, as in Kuhn's description of exemplary or standard problems and paradigmatic practice. Ravetz explicitly develops the tool model in great detail, describing tools as multifunctional, robust, designed, standardized, and so forth.6 In a recent history of contemporary particle physics, field theorists are described as having an interest in exploiting their tools and expertise, and the coming of a suitable problem as allowing them to go to work. Earlier they were "mechanics without tools" for calculating low-energy quantum chromodynamics, where particle properties were well known already.7 And Hacking treats particles as probes, means of intervening in the world that cause well-defined and measurable effects. He says "Long-lived theoretical entities, which don't end up being manipulated, commonly turn out to have been wonderful mistakes."8
Another, more literal and materialist, version of "instrumentalism" is becoming important. Scientists encourage national commitments to the material devices vital to their work, such as telescopes and synchrotrons. They present their research as device driven, rather than people or idea driven. Greater emphasis is being placed on the importance of craft and of instruments, and their limits and capacities in scientific investigation. Particular features of instrumentation, and the interpretation of what those instruments produce (data), are being shown to play a subtle role in the making of science. And anthropologists, using the framework of cultural and material anthropology, show how tools such as accelerators and detectors organize the culture and production of science. 9
We might discern two traditions for describing tools, the objective and the situational.
In the objective tradition a tool is an object, such as a hammer or microscope, possessing certain capacities. A trained person picks up a tool and uses it to do something. Such a tool may be made by a toolmaker and when it is done it is then available for use. In modern times, making and use are for the most part separated, although it is well known that effective craftspersons will modify a tool for particular uses or to suit their own idiosyncracies. A tool here is for the most part passive, objective, and modular.10
Skills are capabilities for using tools, and those skills come to be automatic and unnoticed. But different users of what we take as the same tool have different skill and practices. Crystallographers and elementary particle physicists use group theory, but in different ways. Still it is taken as the same tool. One becomes more skillful in using tools through practice, say doing many integrals, and more versatile, say solving a harmonic oscillator as an F = ma differential equation, as an Euler-Lagrange problem, or in action-angle variables.
In the situational tradition tools are defined in terms of the work to be done. They are ways of getting ahold of the world and manipulating it, taming its many degrees of freedom and getting a handle onto it. We discover tools as such, as abstract objective things, when they do not work.11 We notice the hammer when its head flies off. We have to pay attention to an asymptotic expansion when it blows up. In this tradition a world is as handled, tools exist in practice, practice is learned and commanded in specific environments and for specific tasks.
The two traditions are complementary, and each tradition inherits a complementary problem. The objective tradition must give an account of how tools are used and are versatile, an account of play. The situational tradition must account for how tools come to be seen as objective, separable and disengaged from their original contexts, and as universal, available to all. Still, both traditions agree that a tool is something that can be seen as objective and shareable, that it is affected by how it is used, that the world we discover and make is intimately related to the tools we use. Tools are versatile and depend on their users .12
Masters of a craft employ tools in more inventive and subtle fashions and produce finer than usual objects.13 Their products are masterpieces, but not so distinctive or difficult they cannot be produced by others once they see how.
Those of us who were fortunate enough to watch Enrico Fermi at work marveled at the speed and ease with which he could produce a solution to almost any problem in physics brought to his attention. When he had heard enough to know what the problem was, he proceeded to the blackboard and let the solution flow out of his chalk. He kept in trim by doing a lot of problems, either for the courses he taught, the talks he gave, or the papers he wrote. Most frequently, he worked out his own solutions to problems he heard about, in seminars, or in discussions with those who came to talk physics with him. Fermi's solutions were almost simpler and easier to understand than the ones obtained by the person who raised the question in the first place. 14
Fermi's style and methods were appreciated, learned, and then taught to several generations of physicists. His lecture notes became texts, his approach repeated by his students to their own.
A toolkit and a craft are successful if there is important work they can do.15 A guild succeeds because its craftspersons find both work to do and a market for their products. It is within a context of tools and craft that a practice is orderly, clear, natural, and simple. And it is in terms of tools and craft that a personal style is realized.
III. THE TOOLKIT
A fairly straightforward version of a physicist's toolkit would include specific model systems such as crystalline solids or a heat engine, specific objects such as Newtonian particles or Maxwellian fields, and specific modes of attack such as linearization, potential theory, phase space formulations, and least-action principles. There is, for example, as Peierls describes them, a small number of frequently used gaseous or atomic models, or kinds of interparticle interactions. 16
Here I shall describe the toolkit somewhat more schematically (See Table I). I suggest that the physicist's toolkit and skill consists of a trivium: ( 1) mathematics, (2) picturing or diagrammatic, and (3) description or rhetoric corresponding roughly to number and structure, picture and pattern, and language and argument. Tools (3a) including the model worlds or media [3a ( 1 )] we employ in doing physics, the model objects [3a (2)] that populate each medium, the model interactions [3a (3)] among the objects themselves and with the medium, and the strategies [3b (1)] for formulating and working on a problem.
I want to describe briefly the mathematical and diagrammatic parts of the toolkit, and then discuss the descriptive or rhetorical part in some detail.
Mathematics is perhaps most apparent as a skill and set of tools. I hazard a synoptic description of the scope of such skill: A physicist has to be able to count and make approximations (Table I, item la), and hence in the toolkit there are tools of combinatorics, statistics, and asymptotics. One has to master patterns ( 1b), and hence there is geometry and the calculus of variations, symmetry principles and conservation laws, and rules of propagation for waves and boundary influences. And there is a mastery of the principles of linearity and limits and stability (1c): in the calculus, in optimization procedures, and in linear representations.
Assuming that physics itself might explain why the mathematics is useful, one might begin to justify the mathematics as follows. Physically, counting and approximation (la) are usually about fluctuations and perturbations and their smallness, which is true for many of the situations physicists concern themselves with. Patterns (lb) are about the small number of good classifications in nature, again as physicists concern themselves with it. And linearity and limits (lc) are about the fact that there is a hierarchy of well-separated forces, measured in terms of their strengths, and that there are stable objects which may be linearly (or almost so) perturbed. Built into this subset of mathematics are the deepest principles of the world as physicists understand it. And so mathematics naturally seems to apply to physics.
A second set of tools are picturing or diagrammatic tools (Table I, item 2), figures that represent the world, and from which we may "write down" and "read of" the physics. These figures might be seen as either geometric and spatial (2a), or algebraic and symbolically patterned (2b) . Vector diagrams, Feynman graphs, and boundary condition pictures are of the first sort, while covarient expressions and canonical forms of equations are of the second. Of course, diagrams have to be interpreted correctly. A symmetric Lagrangian can have an asymmetric ground state (as in freezing); parallelism on a sphere is not the same as on a plane.
Again assume that physics itself might explain the diagrammatics. We might say that diagrammatic (2) expresses the fact that physics literally accounts for nexuses and flows, and so there can be conservation laws. Vectors and the like, and covariant expressions, are tools for expressing the flows and conservation laws more or less automatically. And physics is also a story of symmetries and systematic categories, such as groups, for organizing phenomena. The various patterned symbolisms are set up to do this work.
The third skill (Table I, item 3) is a mastery of the descriptive or rhetorical tools of the craft, or modeling, what might be called "the art of addressing nature," as Rabi puts it.l7 The tools here are the models invoked when we encounter a situation, models that make nature something we can talk about. They include models of media [3a(1)] objects [3a(2)], and interactions [3a(3)]. There are also more explicit strategic skills [3b(1)] such as searching for conserved quantities, and using commonplaces [3b(2)] such as those Migdal suggests.
What is distinctive about this mode of description or rhetoric is that the various media, objects, and interactions are nicely separable, and they may be combined in seemingly arbitrary ways - x medium with y object with z interaction mechanism. Nature for a physicist comes in almost isolable yet combinable parts. States of matter are separated by sharp phase transitions; particles have well-defined properties; and there is a hierarchy of fundamental interactions.
A. Physical tools and skills
When physicists approach a situation as physicists they immediately take it as a physical world or a medium. The media [Table I, item 3a(1)] include: the space-time vacuum; an atom or a solar system; an orderly crystalline solid; continuous elastic media (including liquid drops and drum surfaces); and fluids and gases.
The media are often treated as sequences tending to greater symmetry and higher temperature (for example, solid/liquid/gas or atom/nucleus/quark). As the temperature rises each medium "melts" into one of the next ones and so unfreezes some degrees of freedom. There are "phase transitions" between them. In each of these media there is fluctuation, and generally those fluctuations increase with temperature. High fluctuation or susceptibility (at phase transition) alternate with the smooth and highly damped stable states.18 This heuristic picture of media is inspired by current models of the early universe and of elementary particles, as well as those of condensed matter.19
While settling on the medium the physicist immediately identifies the things in that medium, using models such as particles. Calling these things objects, what seems crucial about objects [3a(2)] is that each object is individual yet addable - typically, linear and superpositionable - even if it, itself, is made up of much more complicated stuff. Objects are demographic. The total effect of a group of objects is a matter of adding up their individual marginal effects. Often there are conservation rules, so that it does not matter how you do the adding up. If it proves impossible to do such demographic addition, one then looks for normal modes, eigenstates, and quasiparticles that do allow for such addition.
Objects may be things or motivating entities. (We will get to the latter shortly). As things there seem to be particles, oscillators, and fields and waves. Conspicuous in their absence are actual structures, such as levers and beams. Their substantiality and extension delegate them to the realm of engineering, where effects of scale and nonlinearity are taken into account.
A medium can be an object in another medium, so a gas of electrons can fill a crystal. And there are modes of transformation among the objects. A particle can come to be seen as a wave; or a wave becomes an oscillator. A crystal taken as an N-body symmetric field is seen as being a space populated by particles such as phonons. Because those transformations are not only at a single scale, but between scales, an atomic hypothesis tells us "look more closely."
While my description of the toolkit is schematic, in actual usage tools are taken quite specifically. A crystalline solid is likely to be cubic, an atom will be the hydrogen atom, a gas will be ideal or van der Waals, a field will be Maxwell's electromagnetic one, and an interaction may be inverse square.
Media and objects interact, eventually perhaps changing from how they started out. Interaction [Table I, item 3a(3)] requires actors, means, and resolution. Objects may interact with each other in a medium ( two electrons in a vacuum), an object may interact with a medium in which it is embedded (an electron in a crystal); or an object may interact with a medium taken as an object (an electron bouncing off a crystal, both in a vacuum). Interactions may be expressed as forces and influences ( in contact, propagated through a medium, or at a distance), as exchanges of information, as energies, or as probing feelers and responses in polarizable medium. Eventually interaction may be seen to have expended itself. The now-interacted and perhaps changed objects and medium may once more go along independently - until the next episode of interaction. This is expressed by the scattering matrix, by the existence of constants of motion as in action-angle variables, and by stable quasiparticles representing a "sum" of most interactions.
Motivating entities are means for interaction, conveying the media and objects toward each other, and eventually freeing them from each other. Differential equations "move" objects around, or push them forward in time. Group theory shows how they might be combined. Correlation or transfer functions relate what happens in one part of a medium to another. Conserved properties, such as energy or angular momentum lead to translation operators [exp(-iHt), exp(-ipx), exp(-iJ )] that take a world into a similar world at a different time, place, or orientation. Motivating entities, expressed as linear operations, are combined and added to get nature going, just as objects are in general combined to make up nature. But unlike objects as things, the space these objects occupy is explicitly mathematical or formal.
Populating a medium with interacting objects brings all the tools to bear to a situation. However, a physical explanation requires using those tools effectively. One needs a mode of addressing nature.20
There are a number of such strategies of address [Table I, item 3b(1) ]. The most crucial is to find a good ground state or vacuum, such as a crystal lattice or quasiparticles in that lattice, the physical space-time vacuum, Cooper pairs in a Bardeen-Cooper-Schrieffer ( BCS) ground state, a singlet S state hydrogen atom, or an ideal gas. A study of the ground state's perturbations or excitations is fruitful in finding out about its structure. It may be possible to find conservative potentials, such as electrical or thermodynamic ones, which characterize how it changes quasistatically. If you have to invent new particles, such as a neutrino, or new quantities, such as entropy, to get good conservation laws, it may well be worth it.
Two other strategies should be mentioned. The first is that of analogy and heuristic. If you can get away with treating a black body as an ideal gas, or light as a particle, or nuclear forces as potential forces, do it. Also, recall that the same equations have the same solutions, and that there are physical analogies behind this.21
A second strategy concerns what might be called the restricted plenitude of nature.22 When you address nature, do not be surprised if a "good" stable world is not always the best of all possible worlds, but rather the one that simply is quite popular or orderly. Statistically, equilibria have many macroscopically equivalent microscopic states, combinatorically, some structures are more stable and self-reinforcing than most others. Gases, markets in economics, and the macroscopic inverse square law, are examples of this cunning of nature or of the invisible hand.23
We might summarize the strategies as follows: Get ahold of something that will mostly stay put and that will allow for simple yet productive investigations. Use all you know about one situation to investigate another that seems to be like it. And assume that the world is tractable, one way or another, to your understanding.
In creating this schematic toolkit I have slighted some crucial tools. Diagrams are often of pieces of apparatus, rather than vectors or algebra. Thermodynamics conceived of in terms of heat engines, electricity in terms of resistors and capacitors, and optics conceived of as mirrors, lenses, and light rays, may be fit into this kit, but they do not quite belong. In part, this kit concentrates on the microscopic world. And in part this toolkit, and the set of skills and strategies for employing it, are concerned with paper-and-pencil problem-solving activities.
When the problems are derived more directly from experiment and empirical investigation, we might imagine additions to the kit. There would be both tools of inquiry and of recognition.24 For inquiry, there are logical tools, such as electronics or filters, for picking out events; amplifiers for making them more prominent; and stimulators or probes, to search for and bring out the cases of interest. For recognition there are tools and skills of simulation or empathy, in order to figure out how, say, an electron might act in an apparatus; tools to manage dissimulation, for dealing with how chance and fakery produce events; and tools for emulation, to set up situations so that they are the same, so as to provide for reproducibility and stable outputs (namely, good data). In a good toolkit the problem solving and the experimental tools are intimately connected, so that, as Hacking suggests, a particle had better be a probe, and filters and amplifiers had better be interaction mechanisms.
IV. TAKING PHYSICS TOOLISHLY
These tools and skills give us a version of nature that is additive, smooth, and dumb or deanimated. Nature is a "sum" of its parts; the parts interact smoothly as in the calculus, and discontinuities may be shown to disappear, say in a higher dimension; and the tools are objective and independent of context, they have no memory or will of their own, only we craftspersons do.25 The modularity of the toolkit is a mirror of pictures of modern society composed of individuals.
Physics, taken as a craft possessing a toolkit, is true because the toolkit works and leads to interesting work. It focuses on reproducible and explainable phenomena, within a historical tradition that gives to the craftsperson an idea of what it means to work and to be interesting. When the toolkit does not work or becomes of limited interest, new tools and practices need to be invented, new probes, filters, and models created. The new tools may be seen as adaptations of the old, even if they are used rather differently from them. For example, modern electroweak theory is taken as just another step in the tradition of Maxwell's equations for electromagnetism.
A description of a toolkit begins to be adequate if it fairly encompasses standard texts, exams, and handbooks. The reaction of practitioners of the craft and members of the guild to such a description is also important. It should strike a chord of recognition. The description should seem familiar and right, to be an "of course." Now the pervasive belief in a toolkit and the admiration for masters in using it, means that if a toolkit is offered and it seems roughly adequate, it is likely to strike the appropriate chord. It occasions debate about its specific details and its articulation, and it is just in that debate that the adequacy of the proposed toolkit is judged.
The proposed toolkit and set of skills can be made more comprehensive. How does such a kit actually vary in different institutions and nations and eras, and how have tools entered and left the kit? ( A nice problem would be to study the fate of the harmonic oscillator in the last several hundred years. ) Does it help to look at the division of labor - instrument making crafts and performing or user crafts - in the doing of physics?26 What is the role of style and fashion in tool use?27 Are there corresponding toolkits for chemistry, biology, or geology?
How does coaching take place? And how is training not only substantive but behavioral? How do masters pick their disciples?28 What are the examples and counterexamples that are brought up when a point needs to be made? How is error and surprise treated?29
One of the interesting developments in physics in the last few decades has been the large research team and the bureaucracy it becomes, the concomitant rise of the use of standardized detectors, and the growth of symbolic manipulation programs. What was once crafted is now manufactured. How does the work of science change in the age of mechanical reproduction?30
Scientific work is a skillful craft. A physicist's toolkit begins to describe just what it is that scientists do, how they do it, and how that is related to the structure of nature as they discover it.
I began this paper at the National Humanities
Center and at the Van Leer Jerusalem Foundation. More recent work was supported
by the Exxon Education Foundation through a Science, Technology, and Society
Research Fellowship at the Massachusetts Institute of Technology, and by
the Russell Sage Foundation.
1Tools, of course, are not restricted to carpentry or physics. Tools in computer science include "software tools" that are used to build and organize large programs, and recursion and data structures ( say as embodied in LISP); literary studies nowadays use classical rhetoric and so-called "deconstructionist" strategies; and lawyers and physicians will speak of professional skills and tools. But not all fields lay claim to their tools as tools. Much of political theory and the humanities see themselves as in opposition to tools or methods. [See S. Wolin, Am. Poll Sci. Rev. 63, 1062 (1969).] So it is interesting that physics sees itself as having a toolkit.
2 E. M. Purcell, Am. J. Phys. 51, 11 (1983); P. B. James and J. S. Rigden, Am. J. Phys. 50, 1069 (1982); G. Holton, The Scientific Imagination (Cambridge U. P., Cambridge, 1973); A.Pais, "Subtle is the Lord..." The Science and Life of Albert Einstein ( Oxford U. P., New York, 1982 ); A. Livanova, Landau: A Great Physicist and Teacher ( Pergamon, Elmsford, NY, 1980); R. Peierls, Contemp. Phys. 21, 3 ( 1980); University of Chicago Graduate Problems in Physics With Solutions, edited by J. A. Cronin, D. F. Greenberg, and V. L. Telegdi (Addison-Wesley, Reading, MA, 1967).
3 F. Dyson, Phys. Today 23, 23(September 1970); R. P. Feynman, The Character of Physical Law (MIT Press, Cambridge, MA, 1965 ).
4 R. Peierls, Surprises in Theoretical Physics (Princeton U.P., Princeton, NJ, 1979).
5 Migdal's methods reflect a situation in which computers are comparatively unavailable. Wilson has argued for a theoretical science based on computation, with a different set of tools or models. A. B. Migdal, Qualitative Methods in Quantum Theory (Benjamin, Reading, MA. 1977): K. Wilson, CERN Courier 23, 172 (June 1983).
6 T. S. Kuhn, The Structure of Scientific Revolutions (Univ. of Chicago Press, Chicago, 1970); J. Ravetz, Scientific Knowledge and Its Social Problems (Clarendon, Oxford. 1971); M. Heidegger, Being and Time
(Harper and Row, New York, 1962). See also, on skills, M. Polanyi, Personal Knowledge (Univ. of Chicago Press, Chicago, 1958). Heidegger employs tool-using as a central image in his work; Wittgenstein uses craft practice in the initial parts of the Philosophical Investigations (Macmillan, New York, 1968). "Tools" and "craft" are the metaphors of a philosophy concerned with function versus essence, with practice versus ideas, with technology versus nature.
7 A. Pickering, Constructing Quarks (Univ. of Chicago Press Chicago, 1984); see also, J. T. Cushing, Synthese 50, 5 (1982).
8 I. Hacking, Representing and Intervening (Cambridge U. P., Cambridge, 1983), p.. 275.
9 M. Harwit, Cosmic Discovery (Basic, New York, 1982); D. D. Price, Nat. Hist. 93, 49 (January 1984); B. Latour and S. Woolgar, Laboratory Life ( Sage, Beverly Hills, 1979); H. Garfinkel, M. Lynch, and E. Livingston, Philos. Social Sci. 11, 137 (1981); P. Galison, Rev. Mod. Phys. 55, 477 (1983); S. Traweek, in Les Savoirs dans les Pratiques Quotidiennes, edited by C. Belisle and B. Schiele (Editions du Centre National de la Recherche Scientifique, Paris, 1984).
10 Kuhn, Ref. 6; Ravetz, Ref 6; A. H. Dupree and H. W. Dupree, "Performer Crafts and Instrument Maker Crafts: The Persistence of Craft Traditions in Industrial Transformation." Mimeo, 7 May 1979.
11 Heidegger, Ref. 6; A. R. Luria, Cognitive Development: Its Cultural and Social Foundation (Harvard U. P., Cambridge, MA, 1976).
12 See Ref. 6, and for example, M. Harris, Culture, People, and Nature ( Harper and Row, New York, 1980).
13 See, e.g., R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures in Physics (Addison-Wesley, Reading, MA 1964). On Feynman's practice, see F. Dyson, Disturbing the Universe (Harper and Row, New York, 1979).
14 Physics Vade Mecum, edited by H. L. Anderson (American Institute of Physics, New York' 1981).
15 G. Kubler, The Shape of Time ( Yale U. P., New Haven, CT, 1962).
16 Peierls Ref. 2.
17 I.I. Rabi, Columbia Today, 6, (Winter 1977).
18 Strictly speaking, this is an account of second-order phase transitions.
19 Henry Adams tells a similar story in "The Rule of Phase Applied to History (1909)" in A Henry Adams Reader, edited by E. Stevenson(Anchor, Garden City, 1958).
20 I should note that I have paralleled my description of the toolkit to descriptions of rhetoric, the classical art of address, For in addressing nature we are as well producing persuasive demonstrations for ourselves and others. Media corresponds to genres, objects to tropes, interaction to plot, strategies to modes of address, and qualitative methods to commonplaces.
21 Feynman, Ref. 3. And just because two systems have the same equations does not mean they are the same - the approximations used in getting those equations may be different.
22 A. Lovejoy, The Great Chain of Being ( Harvard U. P.. Cambridge, MA, 1936).
23 H. Simon, The Sciences of the Artificial (MIT Press. Cambridge, MA, 1969); S. Kirkpatrick, C. D. Gellatt, Ir., and M. P. Vecchi, Science 220, 671 (1983).
24 See Hacking, Ref. 8, on representing and intervening, and Cushing, Ref 7 for an alternative vision in S-matrix theory.
25 The rational economic man in neoclassical microeconomics is similarly smooth, adaptable, and objective. A. Marshall in his Principles of Economics ( Macmillan, London, 1890, 1920) states this in terms of a "Principle of Continuity." See also, M. H. Krieger; J. Poll. Anal. Management 5, 779 (1986). Another example of making the world suit the physicist is the recent interest in "chaos," a way of studying aspects of formerly intractable "nonlinear" phenomena in a form physicists can handle conventionally.
26 Dupree, Ref 10.
27 M. H. Krieger, Fundam. Sci. 2, 425 (1981).
28 S. Traweek has described this process for the field of elementary particle physics in both the US and Japan. See her forthcoming, Particle Physics Culture (Harvard University Press).
29 Peierls, Ref. 4; C. Bosk, Forgive and Remember (Univ. of Chicago Press, Chicago, 1979).
30 W. Benjamin, Illuminations (Schocken, New York, 1969).
Reprinted with permissionfrom the American Journal of Physics 55 (11), November 1987 pp. 1033 - 1038
Section B2, The Physicist's
Toolkit from: Connecting Research in Physics Education with
An I.C.P.E. Book © International Commission on Physics Education 1997,1998
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