Borek said:
I am known to be occasionally wrong
I am known to be more than occasionally wrong especially when I come here at night and post in a hurry as now - and I know Borek has this all at his fingertips.
But firstly I think all the OP meant by 'sigmoid' was just 'S-shaped' like some other curves he has met that have that description.
Where he has met them I don't know. But he could have met them in positively co-operative binding curves, e.g. of oxygen to haemoglobin or other ligands to certain proteins. These have often been called 'sigmoid' although actually sigmoidicity is not the same as co-operativity but strongly co-operative curves are sigmoid. But watch out! - what that means is that the curve of amount bound
as a function of oxygen (or whatever
ligand) concentration is sigmoid. But what the OP means is that the amount of protons, let's say, bound to the base is sigmoid as a
function of the log of the concentration of protons in solution! A simple non-cooperative binding or titration curve is sigmoid in that sense - and symmetrical.
Then, at the risk of lateness of the hour errors, aren't the people who are denying it's symmetrical and sigmoid doing it too exactly? Shouldn't we say to students 'if you're getting quadratic or cubic equations you're doing it wrong'? At least for 99% of the problems they come here with? (always the same ones). (One of the ways) they get stuck is when they get equations that look too complicated for them, do not seem like anything they remember from class, because they don't realize what terms they can and should consider negligible. Just once or twice here did I see a necessity for those complete equations, and that was with a good student who wanted to understand in depth, completely abnormal, and even then the corrections were numerically of pretty academic significance.
