11 ms·
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 fin
by throwaway183839 11y ago
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.
- deleted 11y ago[deleted]
- guard-of-terra 11y ago"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 11y agoThis 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 11y agoThe whole topic of "why does this random (in base 10) number suddently behaves strange" doesn't exist in e.g. base 2.