Visualizing the Unseen: The role of analogy in physics

Meeting chaired by Phil Cooke

Ciara Muldoon

Department of Psychology, University of Bath

8 July 2005

Summary

Physicists often use analogy when trying to understand, or to explain, a physical process. The speaker will discuss the advantages and dangers, as revealed by her research.

Introduction

Research by cognitive scientists over the past 20 years has resulted in several detailed accounts of the cognitive processes involved in analogical reasoning. For example, it has been shown (by e.g. Dunbar, 1995, 1999, 2001; Gooding,1990, 2003; Gentner, 1983; Hesse, 1966; Harré, 1988; Holyoak & Thagard, 1995; Klahr, 2000; Nersessian, 1988, 2002, 2003;) that in scientific thinking some scientists use analogy to construct a framework within which to explore, discover, extend, and explain a new topic by mapping concepts from a source domain (an area which is well understood) to a target domain (an area which is not well understood).

In physics, drawing an analogy usually means identifying structural relations between two things. These relations can be superficial (where the analogies break down if taken beyond surface similarity), or deep (where analogies hold for a whole system of proportions), or they can be both.

For example, the flow of heat is analogous to the flow of electric charge (a) on a surface level as both systems can be visualized as fluids flowing within channels, and (b) on a deeper level, as the mathematical equations governing both systems are analogous. (Notice the symmetry between the equations):

Flow of heat : dH/dt = - K(T2 – T1)

is said to be analogous to the:

Flow of electric charge: dQ/dt = - G(V2 – V1)

H the quantity of heat is analogous to Q,
the electric charge.
K thermal conductance of the rod is analogous to G, conductance of the wire.
T temperature is analogous to V, voltage.

This analogy was put forward by Lord Kelvin in 1842, used by his contemporary JC Maxwell in his groundbreaking work on electromagnetism, and is still in use by science educators to this day.

The drawbacks of analogy

As Hesse (1966) explained, models have positive analogies (e.g. the earth orbiting the sun: the electron orbiting the nucleus), negative analogies (the size of the sun: the size of the nucleus), and neutral analogies (where the relation is not known). The drawbacks in employing analogy in cognition and communication have been outlined by many historians, philosophers, psychologists, and sociologists of science over the past 40 years. (e.g. Hesse, 1966; Larkin & McDermott, 1980; Gentner, 1983; Gentner & Gentner, 1983; Nersessian 1995; Holyoak and Thagard, 1996; Taber, 2001) As Holyoak and Thagard (1995: 204) caution: ‘Without guidance from a teacher, analogy is often a trap for the unwary novice, rather than a stepping stone to expertise.’

Primary research questions:

The forms of analogy used in different contexts

Although previous research established the importance of analogy as a means of providing and promoting understanding both in scientific discovery and in the communication of science, further investigations are needed to uncover the forms of analogy used by physicists in different contexts. For example, are certain forms of analogy more appropriate in an informal setting than a formal setting? What factors influence physicists’ use of analogy when communicating with experts and novices?

Method of investigation

To uncover the forms of analogy used by physicists in different contexts, I’ve analysed a sample of physics journals and popular science books; surveyed over 200 physicists of varying ages and research backgrounds, from across the UK and Ireland; interviewed a select sample; and made an historical case study of a retired physicist who is an enthusiast for analogy.

Findings

I’ve found that many physicists often use different forms of analogy to visualise and communicate things that are beyond their sense perceptions - from positron interaction to galaxy formation. Good analogies tend to be (a) useful heuristics (i.e. rules of thumb) in problem solving; (b) generative (i.e. suggesting new avenues to pursue); (c) easy to express (pictorially, verbally, symbolically), (d) work in different contexts (formal and informal settings; with experts, intermediates and novices).

Take, for example, Paul Coleman's humorous explanation of Positron Surface Interactions. [1] Imagine a ravine. On one side of the ravine is a forest of evenly spaced trees (analogous to a crystal lattice). Some of the trees have been up-rooted, leaving holes in the ground (analogous to vacancies or defects in the lattice). On the other side of the ravine, chickens are fired from a cannon (these are like positrons fired from a particle accelerator). The chickens get propelled across the ravine, smashing into the evenly spaced trees. Some stagger around on the ground, completely dazed (analogous to thermal positron diffusion). Some fall into holes in the ground (analogous to trapping by vacancies or defects beneath the surface). Some fall into the ravine (analogous to surface state trapping). Some, not so dazed, fly back across the ravine (analogous to positron re-emission).

 

1 Antichickens hovering outside the wood, waiting to whisk away hapless chickens of the opposite gender
2. Antichickens lurking in the Dark Wood with even more dastardly intent.
3 Branches in the ravine to catch falling chickens
4 Someone to operate the chicken cannon.
Over 90% of physicists surveyed said that the physics expertise of their target audience greatly influenced their use of analogy. As their audience’s expertise increases, some physicists use fewer analogies, others use more complex analogies. According to one respondent: ‘Inexact analogies are out of place for physics-expert audiences since they are equipped to understand the "proper" version. Rock solid analogies are still good, though.’[2] By ‘rock solid analogies’ he means mathematical analogies where a deep structural relationship exists between two systems being compared.

Although only 5% of respondents said that the nationality of their target audience greatly influenced their use of analogy, this minority group was very vocal in stressing the importance of ensuring that analogies translate across national and cultural boundaries (such as sport, money, geography and cooking). For example, one respondent warned: ‘Take care to avoid cultural reference; I have recently lectured in Poland.’[3] Another respondent remarked that: ‘analogies which rely on slang, gestures or particular social concepts may fall flat or even cause offence in other countries.’ [4] While another noted that: ‘Non-native English speakers often just have research paper English, which is different to the more colloquial phrases normally used in making an analogy.’[5]

Conclusions

Analogy is extremely useful in providing insight. This can be (a) pictorial insight, i.e. creating mental pictures of physical phenomena or of mathematical structures; or (b) physical insight, i.e. helping researchers get a ‘feel’ for how a system behaves by giving it a tacit, kinaesthetic component.

Many respondents also use analogy to market their research, i.e. to make their research accessible and memorable to peers, funding bodies and general public, thereby enlisting support. As the sociologist of science, Bruno Latour remarked: ‘You may have written a definitive paper…but this paper will not become definitive if others do not take it up and use it as a matter of fact later on. You need them to make your paper a decisive one.’ (6)

Thus, many physicists use a variety of analogies to bridge conceptual divides between, experts and novices, scientists from different disciplines, and even specialists within the physics community.

Ciara Muldoon

Notes

1. Prof. Paul Coleman’s inaugural lecture, ‘Probing Matter with Anti-Matter: a Career in Self-Annihilation.’ University of Bath, 1 May 2003.

2. Phys -127: a 24 year old, male, PhD student whose research interests include: ‘CP violation in B-mesons with the LHCb experiment. Interests in readout electronics, Monte-Carlo generators, SUSY and beyond SM physics, CP violating signatures and QCD.’

3. Phys - 216: 45 year old male, Lecturer.

4. Phys - 9: 32 year old male, Lecturer in Physics & Astronomy.

5. Phys - 27: 25 year old male, PhD student.

6 Latour, B. Science through Action: How to follow scientists & engineers through society (1987):104