by Ron E. Hassner, University of California, Berkeley
Figure 1. A specimen of Heliconius erato. The Lorenz butterfly may be a member of this species.
Here is the most complete record yet compiled of the travels of the Lorenz butterfly.
The most famous butterfly in science made its first reported appearance in 1972, in a paper on chaos theory presented by Edward Lorenz to the American Association for the Advancement of Science.1 In the paper, Lorenz presented a cornerstone argument of chaos theory: very small differences in initial conditions can lead to large effects in complex systems. He entitled the paper with an appropriate example, calling it, “Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?”
Lorenz’s butterfly has since appeared in every conceivable reference to chaos theory. Yet despite its meteoric rise to fame, chaos theorists soon lost track of the butterfly’s whereabouts.
Reported Sightings
In 1987, James Gleick rediscovered Lorenz’s butterfly and announced triumphantly that “a butterfly stirring the air today in Peking can transform storm systems next month in New York.”2 Gleick could not explain when or why the butterfly had moved to Peking, of all places, why it should suddenly shift its attention from tornadoes in Texas to storm systems in New York, or where it had been in the intervening fifteen years. But in 1992, five years after Gleick’s discovery, the butterfly returned to Brazil—specifically to Rio de Janeiro—where it was spotted by Denny Gulick.3
Figure 2. Global movements of Lorenz’s butterfly.
At this point, the sightings grew more frequent. In 1993, the blockbuster movie Jurassic Park located the insect in Beijing. Two years after that, several scientists reported, in this journal, seeing the subject in Lausanne, Switzerland.4 In 1996, Don Edward Beck and Christopher Cowan found it frolicking in France, and immediately pronounced that “a butterfly flaps its wings in Paris… [which] results in a hurricane in Miamii.”5 The year after that, the butterfly returned to its previous haunt in China. However, as David Campbell and Gottfried Mayer-Kress were to document, it had focused its attention on the weather in San Francisco.6 Peter Smith confirmed the butterfly’s Chinese location in 1998, by which time its flapping was affecting the climate of South England.7 John B. Arden spotted the butterfly in Venezuela that same year.8
Despite its now advanced age, Lorenz’s butterfly continues to be tracked by chaos theorists. In the year 2000, it was spotted in both the Amazon rain forest and Harrisburg, Virginia.9 By 2001, it had moved to California. From there, it flew to Japan, where Grove, Ladas & Grove located it 2004.10 That same year it appeared once more in Brazil and then returned to China in 2006.11
Figure 3. The mathematical pattern known as the Lorenz attractor.
Discussion
The longevity and traveling speed of the famed butterfly have occasioned some dispute about its identity. The butterfly is possibly of the species Heliconius erato (also known as the “Red Postman”), famed for its extraordinary longevity (see Figure 3). Common in South America, it has an impressive tornado-inducing wingspan of 2.25 inches.12
Curiously, the pattern of the butterfly’s movements, as plotted on a world map, replicates a pattern that is characteristic of certain systems that exhibit so-called “chaotic” behavior. The tracings in Figure 1 compare easily with those in Figure 3, which shows a mathematical pattern known as the Lorenz attractor. This pattern was named after Edward Lorenz, the very man whose theory had first called attention to this novel branch of lepidoptery. More curiously still, the butterfly shape of the Lorenz attractor resembles none other than the Heliconius erato (compare Figure 3 with Figure 2). The significance or meaning of any of this has yet to be determined.
References
1. The Essence of Chaos, Edward Lorenz, University of Washington Press, 1993, pp. 14–5 and 181–4.
2. Chaos: Making a New Science, James Gleick, Viking, 1987, p. 8.
3. Encounters with Chaos, Denny Gulick, McGraw Hill, 1992, p. 92.
4. “Experimental Evidence of the Butterfly Effect,” D. Inaudi1, X. Colonna de Lega, A. Di Tullio, C. Forno, P. Jacquot, M. Lehmann, Max Monti, and S. Vurpillot, Annals of Improbable Research, vol. 1, no. 6, November–December 1995.
5. Spiral Dynamics: Mastering Values, Leadership and Change, Don Edward Beck and Christopher Cowan, Blackwell, 1996, pp. 156–7.
6. “Chaos and Politics: Application of Nonlinear Dynamics to Social-Political Issues,” David K. Campbell and Gottfried Mayer-Kres, The Impact of Chaos on Science and Society (Celso Grebogi and James A. York, eds.), 1997, p. 41.
7. Explaining Chaos, Peter Smith, Cambridge University Press, 1998, p. 1.
8. Science, Theology and Consciousness: The Search for Unity, John Boghosian Arden, Praeger, 1998, p. 23.
9. Complexity: Life at the Edge of Chaos, Roger Lewin, University of Chicago Press, 2000, p. 11; Conscious Acts and the Politics of Social Change, Robin L. Teske and Mary Ann Tetreault, University of South Carolina Press, 2000, p. 116.
10. Macroshift: Navigating the Transformation to a Sustainable World, Ervin Laszlo, Arthur Charles Clarke and Kay Mikel, Berrett-Koehler, 2001, p. 10; Periodicities in Nonlinear Difference Equations, E. A. Grove, Chapman & Hall, 2004, p. 38.
11. The Heart of Mathematics: An Invitation to Effective Thinking, Edward B. Burger and Michael Starbird, Springer, 2004, p. xxi; Science and Grace: God’s Reign in the Natural Sciences, Tim Morris and Don Petcher, Crossway Books, 2006, p. 332, note 23.
12. “Longevity Studies in a Tropical Conservatory: Are You Getting Your Money’s Worth?”, John R. Watts, Butterfly Pavilion of Westminster, CO, p. 8, table 2; “Schmetterlinge und Brustwarzen,” L. Arazi, Annals of the German Society for Entomology, vol. 8, no. 2, 1994; “Lifespan of Butterflies,” J. A. Scott, Journal of Research on the Lepidoptera, vol. 12, 1973.
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Figure 1. A specimen of Heliconius erato. The Lorenz butterfly may be a member of this species.
Here is the most complete record yet compiled of the travels of the Lorenz butterfly.
The most famous butterfly in science made its first reported appearance in 1972, in a paper on chaos theory presented by Edward Lorenz to the American Association for the Advancement of Science.1 In the paper, Lorenz presented a cornerstone argument of chaos theory: very small differences in initial conditions can lead to large effects in complex systems. He entitled the paper with an appropriate example, calling it, “Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?”
Lorenz’s butterfly has since appeared in every conceivable reference to chaos theory. Yet despite its meteoric rise to fame, chaos theorists soon lost track of the butterfly’s whereabouts.
Reported Sightings
In 1987, James Gleick rediscovered Lorenz’s butterfly and announced triumphantly that “a butterfly stirring the air today in Peking can transform storm systems next month in New York.”2 Gleick could not explain when or why the butterfly had moved to Peking, of all places, why it should suddenly shift its attention from tornadoes in Texas to storm systems in New York, or where it had been in the intervening fifteen years. But in 1992, five years after Gleick’s discovery, the butterfly returned to Brazil—specifically to Rio de Janeiro—where it was spotted by Denny Gulick.3
Figure 2. Global movements of Lorenz’s butterfly.
At this point, the sightings grew more frequent. In 1993, the blockbuster movie Jurassic Park located the insect in Beijing. Two years after that, several scientists reported, in this journal, seeing the subject in Lausanne, Switzerland.4 In 1996, Don Edward Beck and Christopher Cowan found it frolicking in France, and immediately pronounced that “a butterfly flaps its wings in Paris… [which] results in a hurricane in Miamii.”5 The year after that, the butterfly returned to its previous haunt in China. However, as David Campbell and Gottfried Mayer-Kress were to document, it had focused its attention on the weather in San Francisco.6 Peter Smith confirmed the butterfly’s Chinese location in 1998, by which time its flapping was affecting the climate of South England.7 John B. Arden spotted the butterfly in Venezuela that same year.8
Despite its now advanced age, Lorenz’s butterfly continues to be tracked by chaos theorists. In the year 2000, it was spotted in both the Amazon rain forest and Harrisburg, Virginia.9 By 2001, it had moved to California. From there, it flew to Japan, where Grove, Ladas & Grove located it 2004.10 That same year it appeared once more in Brazil and then returned to China in 2006.11
Figure 3. The mathematical pattern known as the Lorenz attractor.
Discussion
The longevity and traveling speed of the famed butterfly have occasioned some dispute about its identity. The butterfly is possibly of the species Heliconius erato (also known as the “Red Postman”), famed for its extraordinary longevity (see Figure 3). Common in South America, it has an impressive tornado-inducing wingspan of 2.25 inches.12
Curiously, the pattern of the butterfly’s movements, as plotted on a world map, replicates a pattern that is characteristic of certain systems that exhibit so-called “chaotic” behavior. The tracings in Figure 1 compare easily with those in Figure 3, which shows a mathematical pattern known as the Lorenz attractor. This pattern was named after Edward Lorenz, the very man whose theory had first called attention to this novel branch of lepidoptery. More curiously still, the butterfly shape of the Lorenz attractor resembles none other than the Heliconius erato (compare Figure 3 with Figure 2). The significance or meaning of any of this has yet to be determined.
References
1. The Essence of Chaos, Edward Lorenz, University of Washington Press, 1993, pp. 14–5 and 181–4.
2. Chaos: Making a New Science, James Gleick, Viking, 1987, p. 8.
3. Encounters with Chaos, Denny Gulick, McGraw Hill, 1992, p. 92.
4. “Experimental Evidence of the Butterfly Effect,” D. Inaudi1, X. Colonna de Lega, A. Di Tullio, C. Forno, P. Jacquot, M. Lehmann, Max Monti, and S. Vurpillot, Annals of Improbable Research, vol. 1, no. 6, November–December 1995.
5. Spiral Dynamics: Mastering Values, Leadership and Change, Don Edward Beck and Christopher Cowan, Blackwell, 1996, pp. 156–7.
6. “Chaos and Politics: Application of Nonlinear Dynamics to Social-Political Issues,” David K. Campbell and Gottfried Mayer-Kres, The Impact of Chaos on Science and Society (Celso Grebogi and James A. York, eds.), 1997, p. 41.
7. Explaining Chaos, Peter Smith, Cambridge University Press, 1998, p. 1.
8. Science, Theology and Consciousness: The Search for Unity, John Boghosian Arden, Praeger, 1998, p. 23.
9. Complexity: Life at the Edge of Chaos, Roger Lewin, University of Chicago Press, 2000, p. 11; Conscious Acts and the Politics of Social Change, Robin L. Teske and Mary Ann Tetreault, University of South Carolina Press, 2000, p. 116.
10. Macroshift: Navigating the Transformation to a Sustainable World, Ervin Laszlo, Arthur Charles Clarke and Kay Mikel, Berrett-Koehler, 2001, p. 10; Periodicities in Nonlinear Difference Equations, E. A. Grove, Chapman & Hall, 2004, p. 38.
11. The Heart of Mathematics: An Invitation to Effective Thinking, Edward B. Burger and Michael Starbird, Springer, 2004, p. xxi; Science and Grace: God’s Reign in the Natural Sciences, Tim Morris and Don Petcher, Crossway Books, 2006, p. 332, note 23.
12. “Longevity Studies in a Tropical Conservatory: Are You Getting Your Money’s Worth?”, John R. Watts, Butterfly Pavilion of Westminster, CO, p. 8, table 2; “Schmetterlinge und Brustwarzen,” L. Arazi, Annals of the German Society for Entomology, vol. 8, no. 2, 1994; “Lifespan of Butterflies,” J. A. Scott, Journal of Research on the Lepidoptera, vol. 12, 1973.
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