David Peat

On Incompleteness 29Mathematics: The Ultimate Certainty?And so we turn to mathematics for a final certainty and begin with oneof the simplest and purest operations—the act of counting. Of allthings, common sense tells us that counting should be totally certainand free from all ambiguity and confusion.Let us take a telling example. In his novel 1984, George Orwellportrayed a world in which the state controls the lives and minds of itscitizens. When one of these citizens, Winston Smith, mounts a smallpersonal rebellion he is arrested and sent to Room 101 for brainwashing.In a world in which all antisocial behavior has been eliminatedthe only remaining offense is that of “thought-crime.” The notion ofpunishment does not arise in 1984. For to punish would be to admit aflaw in the system, in that a citizen was capable of thinking and actingin ways other than those determined by the state. Instead, WinstonSmith must be reeducated, and, as with a mathematical theorem, hemust realize the inevitability of the state’s goodness and rightness. In aworld where reality is determined by Big Brother, Smith must graspthe simple fact that 2 + 2 = 5. That is not to say he should acquiesce orsimply agree to this absurd proposition. Rather, because the statewishes to welcome Smith back into its bosom, he must actually “know”and “see” that 2 + 2 = 5. When his tormentor holds up two fingers onone hand and two on the other, for a moment at least Winston is bothable to know and to see that they add up to five.Orwell chose this corruption of the pure act of counting as a wayof demonstrating the horror of a mind that had been totally controlledto the point where logic is denied and defied. Of all certainties countingseems to head the list. No matter what we may wish, no matterwhat society as a whole chooses to believe, counting and arithmeticremain objective certainties. We may believe that a ceremony canchange the weather, we may be certain of the winner of the next race,we may be convinced that certain mental practices will change thecrime rate in a city, but no matter how hard we try, we cannot “believe”that two plus two will ever equal five.If we should ever encounter beings on other planets, beings whoselives are utterly alien to our own, of one thing we all agree: that they