[jjaredsimpson]

So I think the elbow analogy has value when you note that there are two ways of describing in an elbow in the exponential function when considering finite human lifetime.

Given two points in time t,u they have progress exp t and exp u and relative rates of progress exp u / exp t = exp (u-t). So of course the relative rate of progress between 2 points in time is fixed and so we can scale our y-axis to make any 2 points have the characteristic "elbow" of an exponential.

But if we consider absolute difference between 2 points on the scale of a human lifetime over different periods of time we can see that absolute difference doesn't have the same property as relative rate of progress.

exp u - exp (t-u+u) = exp u - exp u (exp(t-u)) = exp u (1- exp (t-u))

Which I guess I'll interpret as saying that the absolute difference of progress between 2 points in time is proportional to an exponential. So for most of history that exponential was very close to zero and humans did not experience must change in a lifetime. Now however we live in a time where the exponential can be said to be nearing an "elbow."

So while over time relative rates of progress between 2 points do not vary, absolute progress between 2 points certainly does vary can be described as an elbow when measured against a human lifetime.

[marcosdumay]

Ok, the lifetime of a person is a preferential zoomlevel for the time axis. But a zoomlevel for the productivity axis is still missing, so that everybody for the last 500 years did experience an elbow just before the time they were living.

And if our growth had been exactly exponential+, everybody for the last 500 years would have experience an elbow with the exact same shape. Just the magnitude would change, and so fast that everybody would dismiss the previous generation claims, just like you are doing now.

+ Now, it hasn't been exactly exponential. The exponent is accelerating since we got precise enough measurements, and funny thing is that this fact just extends that "no sudden change of behavior" further back, while still not creating any privileged zoomlevel for the productivity axis, and not letting any new generation have any claim that their time is different.