Chance in Life and the World
"... we know all atoms to perform all the time a completely
disorderly heat motion, which, so to speak, opposes itself to their
orderly behavior and does not allow the events that happen between a
small number of atoms to enrol themselves according to any recognizable
laws. Only in the co-operation of an enormously large number of atoms
do statistical laws begin to operate ... All the physical and chemical
laws that are known to play an important part in the life of organisms
are of this statistical kind; any other kind of lawfulness and
orderliness that one might think of is being perpetually disturbed and
made inoperative by the unceasing heat motion of the atoms" ....... Erwin Schrödinger, What Is Life?, 1944
Many people think of chance or randomness as that which disturbs order. For some, such disturbances might be desirable, for others not. Schrödinger suggests a different way to understand chance or randomness. They are not something which opposes order in Schrödinger's characterization. They are instead the ground from which order derives. Rather than thinking of order and chance or randomness as alternatives, Schrödinger encourages one to think of order as nothing more and nothing less than statistical regularities.
Serendip was conceived as evolving, as life itself does, with a significant dependence on chance or randomness. Perhaps though Serendip can also illustrate Schrödinger's concept of order as nothing more than statistical regularities. The applet below gives a sense of this.
Instructions: To run the applet click setup; step will advance the applet one timeframe and go will run it continuously. The Background-probability and Picture-probability sliders can be adjusted to vary the probability that any given pixel of either the background or picture will be purple. The picture drop-down menu allows one to chose either of two pictures.
Notice that with picture and background probabililties of 50%, you see only a noisy field in which no picture is visible. By increasing the picture probability you should be able to detect a pattern in the noisy field. When you can just begin to detect a regular pattern, try stepping one time interval at time and notice whether or not the pattern is visible in single time frames. Clearly, Serendip and Serendip's arrows are only statistical regularities and your visual system has evolved to detect statistical regularities.
Posted by Laura Cyckowski and Paul Grobstein 15 May 2008. Applet created using NetLogo , the availability of which is gratefully acknowledged.