[throwaway183839]

The argument isn't saying that arithmetic is random. It's saying that a lot of properties of number systems behave as if they are random.

A good example is finding arithmetic sequences of length K in the prime numbers (for example, the sequence 3, 5, 7 is an arithmetic sequence of length 3, as is 17, 23, 29). It can be shown that random sets that have a density similar to the primes (i.e. the chance that N is in the set is proportional to 1 / log(N)) have arbitrarily long arithmetic sequences - as, in fact, do the prime numbers.

[guard-of-terra]

"a lot of properties of number systems behave as if they are random"

Choosing a weird base (and yes, base ten is weird) certainly contributes to this effect.

[Jacqued]

This looks like an interesting perspective. Do you have any pointers to discussions of topics that become more intuitive/clearer when thought about in other bases ?

[guard-of-terra]

The whole topic of "why does this random (in base 10) number suddently behaves strange" doesn't exist in e.g. base 2.