No. 82: Jul-Aug 1992
Back in the 1960s, kids used to watch the TV series Lost in Space. Starring on this show was a robot which, when asked a stupid or answerless question replied, "It does not compute!" More seriously, we now ask, "Does Nature compute?"
Science believes very deeply that mathematics reflects the real world, that we live in an ordered universe where everything can be reduced to mathematical expressions. The progress of science, particularly physics, seems to bear out this symbiotic relationship between mathematics and the physical world.
However, P. Davies points out that that there are uncomputable numbers and operations. In fact, there are infinitudes of them. All the world's computers could chug away forever and not come up with answers in these cases. So far, Nature has been kind, or we have been lucky, because we have been able to nicely mirror Nature with "doable" math. Davies wonders if it has been entirely a matter of luck:
"Einstein said that God is subtle but not malicious, and we must hope that the laws of physics will turn out to be computable after all. If so, that fact alone would provoke all sorts of interesting scientific and philosophical questions. Just why is the world structured in such a way that we can describe its basic principles using 'do-able' mathematics? How was this mathematical ability evolved in humans?"
Are our minds and, therefore, our computers so structured that we can understand (compute) only a limited portion of Nature? Have other entities evolved in ways such that what we know of Nature is uncomputable to them?
(Davies, Paul; "Is Nature Mathematical?" New Scientist, p. 25, March 21, 1992.)