Let J be a random variable ranging over software jobs and distributed as in nature. Now let c(j,k) be the penalty for having to work around a lack of knowledge k while holding job j.
You seem to be saying that for certain values of k (e.g., k = “basic probability theory”), E[c(J,k)] is large enough that not having k qualifies a “deficit.” But the empirical evidence suggests that there’s a sizable set of respectable jobs X for which these deficits don’t matter. That is, for those exact same values of k, E[c(J,k) | J in X] is so small that the market effectively doesn’t care enough to withhold those jobs from people lacking k.
All of this is to say that when you say “software developers,” I think you’re imagining a set of people which is a lot narrower than the set the market actually maps to that job title. Today, “software development” admits a lot of jobs that don’t have a large dependence mathematics or computer science. The guys hammering out HTML and CSS all day long probably aren’t suffering for their probability-theory deficits. And yet most people do consider them software developers.
You seem to be saying that for certain values of k (e.g., k = “basic probability theory”), E[c(J,k)] is large enough that not having k qualifies a “deficit.” But the empirical evidence suggests that there’s a sizable set of respectable jobs X for which these deficits don’t matter. That is, for those exact same values of k, E[c(J,k) | J in X] is so small that the market effectively doesn’t care enough to withhold those jobs from people lacking k.
All of this is to say that when you say “software developers,” I think you’re imagining a set of people which is a lot narrower than the set the market actually maps to that job title. Today, “software development” admits a lot of jobs that don’t have a large dependence mathematics or computer science. The guys hammering out HTML and CSS all day long probably aren’t suffering for their probability-theory deficits. And yet most people do consider them software developers.