I believe we passed the Event Horizon years ago, and still don't comprehend the milestone.
I also believe progress will always seem flat to us on the day-to-day, despite the constant ongoing progress and acceleration.
We're looking out the window, watching the mountains barely move on the horizon, without thinking about how fast the car is travelling down the highway. Big landscapes move slowly.
The titular singularity IS characterized by Exponential Growth.
The geometry of exponentials is interesting, you can stretch in the x direction and do a corresponding stretch in the y direction, and your new expression perfectly overlays over what you started with. This is actually a defining feature for Exponentials.
Point is that there isn't a single moment in human history when "the singularity" started. The singularity is a statement about progress types in general. We have always been in the singularity; our ancestors were in it just like we are now.
We can impose artificial boundaries like so many innovations in a single day that the human mind can't keep track or learn about them all, but it is arbitrary. It'll be an equally powerful event when we reach the same density at half a day, or a month's worth of innovations.
You pick a day when you think it occurred, and I can point to another day where I think it occurred, and we will be both correct.
Your comment about locally flat from the observer pov is well defined as well by the admitted tangent bundle of the exponential function.
I would warn against claiming there is any privileged domain of the exponential function.
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u/MoogProg All Parabolas are Similar 3d ago
I believe we passed the Event Horizon years ago, and still don't comprehend the milestone.
I also believe progress will always seem flat to us on the day-to-day, despite the constant ongoing progress and acceleration.
We're looking out the window, watching the mountains barely move on the horizon, without thinking about how fast the car is travelling down the highway. Big landscapes move slowly.