280 to 400 is not doubling

I guess I was quoting the source in saying the pencil and paper estimate is in line with modern climate models

edit: from a cursory googling, looks like 450ppm is in line with 2C warning while 600pm is the higher end at 4C warning

note also temperature lags behind co2 (since heat is captured cumulatively over time) so even if we stabilized now at ~412ppm we will continue to see warming