I mean we'd do more than twice as well with one question than with two, and more than twice as well with three than with two. Usually, diminishing returns leads us to learn less from each additional question, but not here. How do I express that?
That's actually a claim of superexponential growth, but how you said it sounds ok. I'm actually not sure that you can get superexponential growth in a meaningful sense. If you have n bits of data you can't do better than having all n bits be completely independent. So if one is measuring information content in a Shannon sense one can't do better than exponential.
Edit: If this is what you want to say I'd say something like "As the number of questions asked goes up the information level increases exponentially" or use "superexponentially" if you mean that.
My best guess for each individual achievement gets better each other achievement I learn about, as they are not independent.
So if one is measuring information content in a Shannon sense one can't do better than exponential.
I was trying to get at the legitimacy of summarizing the aggregate of somewhat correlated achievements as a "level of civilization". Describing a civilization as having a a "low/medium/high/etc. level of civilization" in relation to others depends on either its technological advances being correlated similarly or ...
Here's the new thread for posting quotes, with the usual rules: