[jmathes]

> Continued advancement doesn't mean that it is accelerating, and even if this does represent an unexpected achievement that doesn't mean that future development will maintain that pace.

Advancement faster than predictions does mean accelerating advancement, coupled with the (true) fact that people's predictions tend to assume a constant rate of advancement [citation needed]. Actually, all you'd need to show accelerating advancement is a trend of conservative predictions and the fact that these predictions assume a non-decreasing rate of advancement; if we're predicting accelerating advancement and still underestimating its rate, advancement must still be accelerating.

It even seems like this latter case is where we're at, since people who assume an accelerating rate of advancement see to assume that the rate is (loosely) quadratic. However, given that the rate of advancement tends to be based on the current level of advancement (a fair approximation, since so many advancements themselves help with research and development), we should expect it to be exponential. That's what exponential means.

However, the reality seems like it might be even faster than exponential. This is what the singularitarians think. When you plot humanity's advancements using whatever definition you like, look at the length of time between them to approximate rate, and then try to fit this rate to a regression, it tends to fit regressions with vertical asymptotes.