Mathematics and Applied Mathematics
September 08, 2020
Thomson lamp, supertask, actual infininty
The discussions on Thomson’s lamp analyzed in the precedent chapter can be formalized (at least up to a certain point) by introducing a simple symbolic notation that allows to define the lamp and its functioning in abstract terms. The symbolic definition can then be used to develop formulas that represent the functioning laws of the lamp. Being independent of the number of times the lamp is turned on/off, these laws represent the universal attributes and the universal behaviour of a Thomson’s lamp. As we will see, some of those laws are not compatible with the assumption that a Thomson’s lamp can be switched infinitely many times during a finite interval of time. This conclusion proves that, as its author defended, Thomson supertask is inconsistent.