Comment by 6gvONxR4sf7o | Hacker News Reader

Comment by 6gvONxR4sf7o | Hacker News Reader

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If you plot anything exponential from t=T-60 years to t=T, it'll look just as dramatic now as ever. Try it. Plot Imagine you have some function like population or number of transistors per dollar or something that's exponential. You can model it as y(t) = a * b^(t+c). To look at how it feels when you look backwards, make it relative to what life is like today (aka divide by the "normal" value y(t) to get a function of how it seems looking backwards y(t)/y(T) = b^(t-T).

Let's make a variable for `years from now:` dt = t-T. If we look at the last 60 years, this is just plotting b^dt from dt=-60 to dt=0. It doesn't matter when you look at it from. The last sixty years of exponential growth always looks the same. It's just b^dt from dt=-60 to dt=0, which (being the exact same function) looks equally dramatic from any point.

tl;dr let's make it concrete and plot 1.1^t from 1960 to 2020, and then plot 1.1^t 1060 to 1120. They look exactly the same, even though each just spans a human life time:

https://www.wolframalpha.com/input/?i=plot+1.1%5Et+from+t%3D...

https://www.wolframalpha.com/input/?i=plot+1.1%5Et+from+t%3D...

I understand how exponential functions work. The graph looks the same relatively when you normalize the axes obviously. From the human perspective, the absolute delta over those 60 years is what matters. If society improved 0.001 "civilization points" it will feel very different to an individual than if it improved by by 1000 points.

A prehistoric hunter-gather saw basically zero technological change within their lifetime.

> From the human perspective, the absolute delta over those 60 years is what matters.

This is what we disagree on. From the human perspective, it's the relative delta that matters, because we look at yesterday's change relative to life today.

But that isn't how humans notice exponential change...

We reside in a "level" of order of magnitude in time and space. Things that happen outside of that level, too big or too small, and we simply can't comprehend them. When something crosses from an order of magnitude below our level, to an order of magnitude above our level, that's when we can perceive it.

A block accelerating exponentially from 1e-10 m/s to the speed of light will look completely stationary until it reaches a level of order of magnitude that we can perceive, probably about 1e-5 m/s.

If I tell you I will give you an exponentially increasing amount of money by 1% every day, it matters a lot to you if I start you at 1e-200 dollars because you'll be dead before you earn a single cent. If you lived to 150, you’d be the richest person on the planet. The absolute amount matters because we are physical beings anchored to a particular order of magnitude that we care about.

You're neglecting the fact that human development is not exponential. Population, for instance increased in its growth rate over the past 1000 years, with a sudden step up due to the industrial revolution. It didn't look the same 1000 years ago as it does today. The growth rate was less than 10% of what it is now. If population was exponential, the growth rate would be constant.

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