In which case it's at least funny, but maybe subtract one from all my derivatives.. Which kills my point also. Dang.
It really is a beautiful title.
Which paints a grimmer picture—I was surprised that they report a marked decline in adoption amongst firms of 250+ employees. That rate-as-first-derivative apparently turned negative months ago!
Then again, it’s awfully scant on context: does the absolute number of firms tell us much about how (or how productively) they’re using this tech? Maybe that’s for their deluxe investors.
Yes. The title specifically is beautiful. The charts aren't nearly as interesting, though probably a bit more than a meta discussion on whether certain time intervals align with one interpretation of the author's intent or another.
However lim x->inf log(x) is still inf.
If you need everything to be math, at least have the courtesy to use the https://en.wikipedia.org/wiki/Logistic_function and not unbounded logarithmic curves when referring to on our very finite world.
> Adoption rate = first derivative
If you mean with respect to time, wrong. The denonimator in adoption rate that makes it a “rate” is the number of existing businesses, not time. It is adoption scaled to the universe of businesses, not the rate of change of adoption over time.
When it talks about the adoption rate flattening it is talking about the first derivative of the adoption rate (as defined in the previous paragraph, not as you wish it was defined) with respect to time tending toward 0 (and, consequently, the second derivative being negative.) Not the third derivative with respect to time being negative.
What tickled me into making the comment above had nothing to do with whether adoption rate was used by the author (or is used generally) to mean market penetration or the rate of adoption. It was because a visual aid that is labeled ambiguously enough to support the exact opposite perspective was used as a basis for clearing up any ambiguity.
The purpose of a time series chart is necessarily time-derivative, as the slope or shape of the line is generally the focus (is a value trending upward, downward, varying seasonally, etc). It's fair to include or omit a label on the dependent axis. If omitted, it's also fair to label the chart as the dependent variable and also to let the "... over time" be implicit.
However, when the dependent axis is not explicitly labeled and "over time" is left implicit, it's absolutely hilarious to me to point to it and say it clearly shows that the chart's title is or is not time-derivative.
I know comment sections are generally for heated debates trying to prove right and wrong, but sometimes it's nice to be able to muse for a moment on funny things like this.
Perfectly excusable post that says absolutely nothing about anything.
Corporate AI adoption looks to be hitting a plateau, and adoption in large companies is even shrinking. The only market still showing growth is companies with fewer than 5 employees - and even there it's only linear growth.
Considering our economy is pumping billions into the AI industry, that's pretty bad news. If the industry isn't rapidly growing, why are they building all those data centers? Are they just setting money on fire in a desperate attempt to keep their share price from plummeting?
For some reason I can't even get Claude Code (Running GLM 4.6) to do the simplest of tasks today without feeling like I want to tear my hair out, whereas it used to be pretty good before.
They are all struggling mightily with the economics, and I suspect after each big announcement of a new improved model x.y.z where they demo shiny so called advancement, all the major AI companies heavily throttle their models in use to save a buck.
At this point I'm seriously considering biting the bullet and avoiding all use of AI for coding, except for research and exploring codebases.
First it was Bitcoin, and now this, careening from one hyper-bubble to a worse one.
Derivatives irl do not follow the rules of calculus that you learn in class because they don't have to be continuous. (you could quibble that if you zoom in enough it can be regarded as continuous.. But you don't gain anything from doing that, it really does behave discontinuous)
The derivative at 0 exists and is 0, because lim h-> 0 (h^2 sin(1/h))/h = lim h-> 0 (h sin(1/h)), which equals 0 because the sin function is bounded.
When x !=0, the derivative is given by the product and chain rules as 2x sin(1/x) - cos(1/x), which obviously approaches no limit as x-> 0, and so the derivative exists but is discontinuous.
(I suppose a rudimentary version of this is taught in intro calc. It's been a long time so I don't really remember.)
Awesome stuff.
Adoption rate = first derivative
Flattening adoption rate = the second derivative is negative
Starting to flatten = the third derivative is negative
I don't think anyone cares what the third derivative of something is when the first derivative could easily change by a macroscopic amount overnight.