5 ms·

Adoption = number of users Adoption rate = first derivative Flattening adoption rate = the second derivative is negative Starting to flatten = the third deri

by ajkjk 11mo ago

Adoption = number of users 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.

scotty79 11mo ago
Not really. In this context adoption might be number of users. But adoption rate is a fraction of users that adopted this to all users.
- ajkjk 11mo ago
  Hm that's true. Both seem plausible in English. I didn't look closely enough to figure out which they meant.
postexitus 11mo ago
Adoption rate is not derivative of Adoption. Rate of change is. Adoption rate is the percentage of uptake (there, same order with Adoption itself). It being flattening means first derivative is getting close to 0.
- amelius 11mo ago
  The function log(x) also has derivative that goes closer and closer to 0. However lim x->inf log(x) is still inf.
  - lkey 11mo ago
    Is it your assertion that an 'infinite' percentage! of the businesses will use AI on a long enough time scale? If you need everything to be math, at least have the courtesy to use the https://en.wikipedia.org/wiki/Logistic_function https://en.wikipedia.org/wiki/Logistic_function and not unbounded logarithmic curves when referring to on our very finite world.
- brianshaler 11mo ago
  It maps pretty cleanly to the well understood derivatives of a position vector. Position (user count), velocity (first derivative, change in user count over time), acceleration (second derivative, speeding up or flattening of the velocity), and jerk (third derivative, change in acceleration such as the shift between from acceleration to deceleration) It really is a beautiful title.
  - postexitus 11mo ago
    It is not velocity, it is not change. Have you read the graphs? What do you think 12% in Aug and Sep for 250+ Employee companies mean, that another 12% of companies adopted AI or is it a flat "12% of the companies have adopted in Aug, and it did not change in Sep"
    - brianshaler 11mo ago
      > Have you read the graphs? 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.
    - deleted 11mo ago
      [deleted]
  - alwa 11mo ago
    It is a beautiful title and a beautiful way to think about it—alas, I think gp is right: here, from the charts anyway, the writer seems to mean the count of firms reporting adoption (as a proportion of total survey respondents). 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.
- ajkjk 11mo ago
  I agree, I think I misunderstood their wording. In which case it's at least funny, but maybe subtract one from all my derivatives.. Which kills my point also. Dang.
silveraxe93 11mo ago
While there's an extreme amount of hype around AI, it seems there's an equal amount of demand for signs that it's a bubble or it's slowing down.
- emp17344 11mo ago
  Well, that’s only because it exhibits all the signs of a bubble. It’s not exactly a grand conspiracy.
crote 11mo ago
Looking at the graphs in the linked article, a more accurate title would probably be "AI adoption has stagnated" - which a lot of people are going to care about. 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?
- prmph 11mo ago
  When all the dust settles, I think it's probably going to be the biggest bubble ever. The unjustified hype is unbelievable. 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.
kordlessagain 11mo ago
You could use that logic to dismiss any analysis of any trajectory ever. Perfectly excusable post that says absolutely nothing about anything.
dragonwriter 11mo ago
> Adoption = number of users > 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.
- LPisGood 11mo ago
  The adoption rate is the rate of adoption over time.
  - wtallis 11mo ago
    One could try to make an argument that "adoption rate" should mean change in adoption over time, but the meaning as used in this article is unambiguously not that. It's just percentages, not time derivatives, as clearly shown by the vertical axis labels.
    - brianshaler 11mo ago
      There's another axis on the charts.
      - dragonwriter 11mo ago
        Yes, it charts the adoption rate (adopting firms/firms) against time. But it doesn't use the term "adoption rate" to mean the first derivative of "adoption" with respect to 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.
        brianshaler 11mo ago
        I assure you I don't have any wishes one way or another. 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.
tarsinge 11mo ago
I don’t understand, how can adoption rate change overnight if its derivative is negative? Trying to draw a parallel to get intuition, if adoption is distance, adoption rate speed, and the derivative of adoption rate is acceleration, then if I was pedal to the floor but then release the pedal and start braking, I’ll not lose the distance gained (adoption) but my acceleration will flatten then get negative and my speed (adoption rate) will ultimately get to 0 right? Seems pretty significant for an industry built on 2030 projections.
- ajkjk 11mo ago
  One announcement from a company or government can suddenly change the derivative discontinuously. 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)
  - Neywiny 11mo ago
    Not sure what kinda calculus you took at least here in the states it's very standard to learn about such functions in class, and yes there is a difference between discontinuous and the slope being really large (though finite) for a brief period of time
    - ajkjk 11mo ago
      You rarely study delta and step functions in an introductory calculus class. In this case the first derivative would be a step function, in the sense that over any finite interval it appears to be discontinuous. Since you can only sample a function in reality there's no distinguishing the discontinuous version from its smooth approximation. (I suppose a rudimentary version of this is taught in intro calc. It's been a long time so I don't really remember.)
      - Neywiny 11mo ago
        I'm sure it depends on who's teaching the class and what curriculum they follow, but we were doing piecewise linear functions well before differentiation so I think I do actually disagree as per your caveat. It's also possible that the courses triaged different material. As a calc for engineers not calc for math majors taker, my experience may have been heavier on deltas and steps.
didgeoridoo 11mo ago
Yeah, what a jerk.
- felipellrocha 11mo ago
  Hehehehehheeh
- voxleone 11mo ago
  You win today.
  - voxleone 11mo ago
    I can't believe i was down voted for this silly comment on a third derivative pun. Get a life, techie.
benatkin 11mo ago
I think it might be answering long-term questions about direct chat use of AIs. Of course as AI goes through its macroscopic changes the amount it gets used for each person will increase, however some will continue to avoid using AI directly, just like I don't fully use GPS navigation but I benefit from it whether I like it or not when others are transporting me or delivering things to me.

by ajkjk 11mo ago

scotty79 11mo ago

Not really. In this context adoption might be number of users. But adoption rate is a fraction of users that adopted this to all users.

ajkjk 11mo ago
Hm that's true. Both seem plausible in English. I didn't look closely enough to figure out which they meant.

postexitus 11mo ago

Adoption rate is not derivative of Adoption. Rate of change is. Adoption rate is the percentage of uptake (there, same order with Adoption itself). It being flattening means first derivative is getting close to 0.

amelius 11mo ago
The function log(x) also has derivative that goes closer and closer to 0. However lim x->inf log(x) is still inf.
- lkey 11mo ago
  Is it your assertion that an 'infinite' percentage! of the businesses will use AI on a long enough time scale? If you need everything to be math, at least have the courtesy to use the https://en.wikipedia.org/wiki/Logistic_function https://en.wikipedia.org/wiki/Logistic_function and not unbounded logarithmic curves when referring to on our very finite world.
brianshaler 11mo ago
It maps pretty cleanly to the well understood derivatives of a position vector. Position (user count), velocity (first derivative, change in user count over time), acceleration (second derivative, speeding up or flattening of the velocity), and jerk (third derivative, change in acceleration such as the shift between from acceleration to deceleration) It really is a beautiful title.
- postexitus 11mo ago
  It is not velocity, it is not change. Have you read the graphs? What do you think 12% in Aug and Sep for 250+ Employee companies mean, that another 12% of companies adopted AI or is it a flat "12% of the companies have adopted in Aug, and it did not change in Sep"
  - brianshaler 11mo ago
    > Have you read the graphs? 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.
  - deleted 11mo ago
    [deleted]
- alwa 11mo ago
  It is a beautiful title and a beautiful way to think about it—alas, I think gp is right: here, from the charts anyway, the writer seems to mean the count of firms reporting adoption (as a proportion of total survey respondents). 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.
ajkjk 11mo ago
I agree, I think I misunderstood their wording. In which case it's at least funny, but maybe subtract one from all my derivatives.. Which kills my point also. Dang.

silveraxe93 11mo ago

While there's an extreme amount of hype around AI, it seems there's an equal amount of demand for signs that it's a bubble or it's slowing down.

emp17344 11mo ago
Well, that’s only because it exhibits all the signs of a bubble. It’s not exactly a grand conspiracy.

crote 11mo ago

Looking at the graphs in the linked article, a more accurate title would probably be "AI adoption has stagnated" - which a lot of people are going to care about. 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?

prmph 11mo ago
When all the dust settles, I think it's probably going to be the biggest bubble ever. The unjustified hype is unbelievable. 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.

kordlessagain 11mo ago

You could use that logic to dismiss any analysis of any trajectory ever. Perfectly excusable post that says absolutely nothing about anything.

dragonwriter 11mo ago

> Adoption = number of users > 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.

LPisGood 11mo ago
The adoption rate is the rate of adoption over time.
- wtallis 11mo ago
  One could try to make an argument that "adoption rate" should mean change in adoption over time, but the meaning as used in this article is unambiguously not that. It's just percentages, not time derivatives, as clearly shown by the vertical axis labels.
  - brianshaler 11mo ago
    There's another axis on the charts.
    - dragonwriter 11mo ago
      Yes, it charts the adoption rate (adopting firms/firms) against time. But it doesn't use the term "adoption rate" to mean the first derivative of "adoption" with respect to 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.
      - brianshaler 11mo ago
        I assure you I don't have any wishes one way or another. 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.

tarsinge 11mo ago

I don’t understand, how can adoption rate change overnight if its derivative is negative? Trying to draw a parallel to get intuition, if adoption is distance, adoption rate speed, and the derivative of adoption rate is acceleration, then if I was pedal to the floor but then release the pedal and start braking, I’ll not lose the distance gained (adoption) but my acceleration will flatten then get negative and my speed (adoption rate) will ultimately get to 0 right? Seems pretty significant for an industry built on 2030 projections.

ajkjk 11mo ago
One announcement from a company or government can suddenly change the derivative discontinuously. 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)
- Neywiny 11mo ago
  Not sure what kinda calculus you took at least here in the states it's very standard to learn about such functions in class, and yes there is a difference between discontinuous and the slope being really large (though finite) for a brief period of time
  - ajkjk 11mo ago
    You rarely study delta and step functions in an introductory calculus class. In this case the first derivative would be a step function, in the sense that over any finite interval it appears to be discontinuous. Since you can only sample a function in reality there's no distinguishing the discontinuous version from its smooth approximation. (I suppose a rudimentary version of this is taught in intro calc. It's been a long time so I don't really remember.)
    - Neywiny 11mo ago
      I'm sure it depends on who's teaching the class and what curriculum they follow, but we were doing piecewise linear functions well before differentiation so I think I do actually disagree as per your caveat. It's also possible that the courses triaged different material. As a calc for engineers not calc for math majors taker, my experience may have been heavier on deltas and steps.

didgeoridoo 11mo ago

Yeah, what a jerk.

felipellrocha 11mo ago
Hehehehehheeh
voxleone 11mo ago
You win today.
- voxleone 11mo ago
  I can't believe i was down voted for this silly comment on a third derivative pun. Get a life, techie.

benatkin 11mo ago

I think it might be answering long-term questions about direct chat use of AIs. Of course as AI goes through its macroscopic changes the amount it gets used for each person will increase, however some will continue to avoid using AI directly, just like I don't fully use GPS navigation but I benefit from it whether I like it or not when others are transporting me or delivering things to me.