Orwell was not speaking about mathematics in the quote above from his book1984. Rather, he was commenting on how totalitarian governments attempt to define, and impose, their own notion of reality on the public. Speaking mathematically, it is as clear as the back of your hand that 2 + 2 = 1 and 1 + 2 = 0. That is, if you belong to a three fingered species. We have grown so used to the ten fingers on our hands, that we forget that there is nothing special about base 10. Since the invention of thenumber 0 by Indian mathematicians of the fifth century, this means that all of our numbers are composed of the digits 0 through 9. To three fingered species this means that their number system uses the digits 0 through 2 so that 3 wraps around to 0 and 4 to 1. Thus 2 + 2 = 1 and 1 + 2 = 0 in base 3. Orwell’s above statement is thus valid for all bases 5 and larger unless, of course as he alludes, the totalitarian regime in power says otherwise.

1. 1.

   The numerator equalsp(p − 1)!.

Authors and Affiliations

1. (Home address), Beverly, MA, USA

   Randolph Nelson

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