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Comment by adwn | Hacker News Reader

> In fact, I think we're approaching the "runaway" part of an exponential curve.

Tangential nitpick: There's no "runaway" part of an exponential curve. At every point along the x-axis (typically time), the curve looks exactly the same. This property is often abused by writers who want to make you believe that now is the time when everything changes – although in fairness, they often deceive themselves.

If you don't believe me, look at plots [1] and [2]. In both cases it looks like the past was flat and the "knee" of the curve is right in front of you, promising an exciting future!

[1] https://www.wolframalpha.com/input/?i=plot+exp%28x%29+x+%3D+...

[2] https://www.wolframalpha.com/input/?i=plot+exp%28x%29+x+%3D+...

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You're fighting the good fight. I've recently seen the term "exponential" used in the press to mean all sort of things, but mostly as equivalent to "really fast". This kind of thing may be inevitable, but it's a pity that such sharp and descriptive terminology is decaying into just another term for "growing quickly".

I've seen this abuse of the term "exponential" a lot in the press as well (i.e. meaning "really fast"). This is unfortunate in these pandemic times; a new infection does indeed spread through a susceptible population exponentiaally (at least while the susceptible population is much larger than the infectious population).

By degrading the language, journalists deprive themselves of the ability to talk clearly about the spread of the pandemic. I think this abuse of "exponential" is supposed to make the writer look erudite, even though they haven't a clue what the word means.

There are journalists who understand the meaning of "exponential."

Relative to an absolute viewpoint and habitat, there is a runaway though. Beings are not relativistic.

Update: I guess this is a tangent on a tangent, pun intended.

> Relative to an absolute viewpoint [...]

Any yet this "absolute" viewpoint is never really absolute, but always relative to the authors current position in time – as if by coincidence.

EDIT: To clarify, when an author uses an exponential curve to make the "runaway" argument, they almost never justify why the current absolute value of the curve should have special significance over the absolute values at other points in time. For example, in forgotmypw17's original post, there's no explanation why the current status of free software is at a special threshold – or what "exponential curve" they're even talking about.

If your cellar is filling up with water exponentially, the last half could fill up in the last timeperiod.

In a limited world, exponential changes are sometimes catastrophic.

The “relativeness” comes from time, not from us. Judging the curve today, the past looks flat and the future looks steep. In 5 years the same will be true: today will seem flat and the future will seem steep — that’s the point of OP showing both of those ranges. It is this relative perspective that precisely creates the illusion of a runaway point, an “absolute” perspective gives you the fractal understanding that the graph is the same at every dimension.

Perhaps this use of “fractal” is technically incorrect, which could spawn another, smaller, yet similar discussion in response...

Most exponential curves are only exponential until they hit a limit and become an S-curve. These sort of have a runaway point. But in this article full of hyperbole and falsehoods, steelmanning its bad arguments might not be appropriate.

Many things aren't actually exponential. Adoption of something new may look exponential at the start, but then becomes an S curve. The middle of the S is the point of maximum slope and does represent a transition.

Sure, but it’s a transition to slowing down, not going faster.

Definitely agree if we're just talking about the curve itself, but the "runaway" part comes from the context of what it's measuring. If we're talking exponential deaths - I don't care if the "curve" looks the same on day 5 as day 20. It's certainly starting to runaway if now instead of 32 deaths a day there are 1 million a day (2^x)

Sorry, I am not a statistician, nor a mathematician, and I appreciate your clarification.

What I meant was that the part of the adoption curve which has been nearly horizontal for a long time is curving upwards and is about to hit a near-vertical. May or may not be actually "exponential".

If you know of a good way to express this which will not annoy field experts, please let me know.

That's because you scale the y axis along with it. If you were to define the y axis as added value from 0(no added value) to 10(very high added value), then this is only going to start getting interesting around x=0. Before that the change is still exponential but the value not significant according to our (arbitrarily) defined value scale.

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