What does this equation mean?

The named argument belongs to Philippe Aghion, Benjamin F. Jones, and Charles I. Jones, whose 2017 National Bureau of Economic Research paper works out formally what happens when artificial intelligence automates tasks inside the idea-production function itself, rather than only inside the production of ordinary goods. Their result, worked through with an idea-production function in which a fraction of research tasks can be automated, is that in the case without automation their model collapses to exactly the semi-endogenous relation from Section 3 above — the growth rate of ideas proportional to the growth rate of the human research population, discounted by diminishing returns — matching what they describe as the original point of Jones’s 1995 model [ 6 ] . Automation changes the equation by adding a second term: $g_A = \frac{g_C + g_S}{1-\phi}$. where $g_S$ is the growth rate of human research labor, exactly as before, and $g_C$ is a new term generated by the continuous automation of research tasks — one that can be strictly positive even when $g_S$ is zero, because a fixed number of human researchers can still be automated onto an exponentially shrinking share of remaining, not-yet-automated tasks, concentrating human attention ever more narrowly on the residual problems machines cannot yet touch while machines handle a growing share of the rest [ 6 ] . In plain terms: if enough of what a researcher actually does — running the experiment, searching the literature, proposing the next candidate molecule, checking the math — can be handed to a machine, population no longer has to be the thing that’s growing for the idea-production function to keep growing too. Aghion, Jones, and Jones are explicit that this is one channel among several they model, and that full automation of the idea-production function is a mathematical limiting case — one route, among the several “singularity” scenarios their paper works through formally, to an unbounded growth rate, which they treat as a theoretical possibility to be checked against evidence rather than a forecast [ 6 ] .