: new keyword: probation

[Marc LeBrun]

 > Well, there are some, like A007656 (atomic numbers of elements) 
which not so contingent as others.
 > Contingent on the laws of physics, maybe ....

Good point.  And, for all we know, which isotopes are the most stable 
in our locale in space and time may very well be determined by 
parameters of some kind whose values are contingent on random details 
in the history of the universe.

Since we currently have no theory anywhere near capable of computing 
A007656(n) for any given n from first principles (it's not even 
monotonic--dig that crazy tellurium!), nor any theory yet which can 
absolutely rule out some degree of contingency, and because the 
values were thus necessarily only determined by careful observation, 
this sequence really *ought* to be regarded as contingent--at least 
until clearly proven otherwise by the advent of some suitably grand 
theory that can derive it.

Moreover, the various comments (eg the reference to A058317) make it 
unclear whether the criteria for this sequence really was "most 
stable" (whatever than means, considering elements such as copper 
with more than one stable isotope) or if it was "most abundant" 
(whatever the scope of that might be: the Earth's crust, the whole 
planet, the entire universe?  Today, or billions of years ago,  since 
decay can change the mix? etc).  That such considerations matter 
clearly demonstrates the definition's contingency.

 > At the other extreme are sequences like A000053 (New York Broadway 
line subway stops).

Agreed, but ultimately that's only a distinction in the degree of 
contingency, and is due to the fact that New York subways are 
relatively much more localized phenomena than chemical elements.

However 2+2=4 is, in contrast, assuredly non-contingent, and this is 
what distinguishes mathematical facts from other sorts of facts.

If we are to make only a binary distinction in classifying a 
sequence's contingency, it would seem this should be the criterion.