>>1844776
my particular autism when it is directed at numbers has been thinking through ways to replace Peano's successor relation with some other relation (Set of relations actually) that more richly describes the natural numbers. So breaking the naturals into classes based on the lowest prime factor and then:
calculating the relative density of the resulting classes in the naturals via the euler totient. This supplies all of the naturals, but lacks the resources to determine the position and hence the order.
Attempting to supply order via the geometric postion of each number inherent in it's prime factors when one of the powers of one (in this case the lowest) of the facors is allowed to be variable. So each member of the series generated by 2^n*3 (6, 12, 24, 48 …) has a fixed geometric position relative to 2^n; in this case at the midpoint between 2^n and 2^(n+1).
But clearly each and every prime factorization can be treated this way no matter how many prime factors are involved (proof would be via mathematical induction) so order can be given to the naturals via this route (it is really using doubling, tripling, quintupling and so on with the primes to generate the naturals instead of succession). The restant issue is that order is not basic, but is relative to the position of the base prime in the factorization (so 15, 45, 135…have their position fixed against 5^n numbers).
No maths background, just made this shit up thinking about Godel and Goldbach and as such may be nonsense and noise. Autism takes one to some strange ass places.