Introduction
Mayer et al. [1] relate the following anecdote:
"A turning point in Freeman Dyson's life occurred during a meeting in the SPring of 1953 when Enrico Fermi criticized the complexity of Dyson's model by quoting Johnny von Neumann [1] `With four parameters I can fit an elephant, and with five I can make him wiggle his trunk'", Mayer et al. [2].
They then go on to provide the first successful implementation of von
Neumann's claim, based on trunk-ated Fourier series. Reproducibility is key
to good science, so this page provides a Javascript implementation of the
full five-parameter elephant, including trunk-wiggling. Mayer et al.
require some censure for the lack of detail of their trunk-wiggling algorithm.
The approach taken here was to form a second elephant by reflection of the distal
portion of the proboscis of the primary pachyderm, parallel to the
x-axis. The wiggling was then implemented by linear interpolation
between the primary and secondary elephants, using a sinusoidally varying
mixing coefficient. While it has not been possible to reproduce their results
quantitatively, with complete accuracy, a qualitative reproduction of the main
result proved entirely feasible.
Conclusions
Von Neumann was right; you can fit an elephant with four (complex) parameters, and with a fifth, you can make his trunk wiggle.
References:
| [1] | Jügen Mayer, Khaled Khairy and Jonathon Howard, Drawing an elephant with four complex parameters, American Journal of Physics, volume 78, pages 648-9 (2010). (doi:10.1119/1.3254017) |
| [2] | Freeman Dyson, A meeting with Enrico Fermi, Nature (London), 427(6972), 297 (2004). |
Research Team: Gavin Cawley
