Interesting text, but flawed in many ways. A couple of the more important flaws: - Exponentials often look linear in short x axis observations. Science at t-50

Interesting text, but flawed in many ways. A couple of the more important flaws: - Exponentials often look linear in short x axis observations. Science at t-50 and t-100 may be too short an observation period. Looking at the past 3000 years the exponential characteristic is quite obvious. - Measuring scientific progress as defined in the paper is obviously simplistic. You don't have a limited set of equal valued discoveries to be found randomly. You have a limited set of increasingly valuable[a] discoveries, with dependencies, to be found. The value rate of discoveries is ignored in the text, but is relevant. Say, observing the periodicity of star movement was important, but the gravitic theory built on that to produce even more valuable information. One allows you to count time, the other is fundamental in travelling to the moon. One can be discovered by an uneducated farmer, the other requires calculus knowledge. [a] The definition of value is itself difficult. Impact value, as in practical application value, is a metric. Foundational value, as in which doors are now open for research is another. The utility function is probably a mix of both. I'd wager more recent discoveries are better than older ones in both counts (antibiotics vs immune system programming for example). Do not get fooled by the relative impact (you get a division by zero error in the first scientific discovery ever made)