| ▲ | ajkjk 6 hours 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. |
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| ▲ | postexitus 5 hours ago | parent | next [-] |
| 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. |
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| ▲ | ajkjk 4 hours ago | parent | next [-] | | 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. | |
| ▲ | brianshaler 5 hours ago | parent | prev | next [-] | | 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. | | |
| ▲ | alwa 3 hours ago | parent | next [-] | | 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. | |
| ▲ | postexitus 5 hours ago | parent | prev [-] | | 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" | | |
| ▲ | 3 hours ago | parent | next [-] | | [deleted] | |
| ▲ | brianshaler 4 hours ago | parent | prev [-] | | > 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. |
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| ▲ | amelius 5 hours ago | parent | prev [-] | | The function log(x) also has derivative that goes closer and closer to 0. However lim x->inf log(x) is still inf. | | |
| ▲ | lkey 4 hours ago | parent [-] | | 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 and not unbounded logarithmic curves when referring to on our very finite world. |
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| ▲ | silveraxe93 5 hours ago | parent | prev | next [-] |
| 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. |
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| ▲ | emp17344 4 hours ago | parent [-] | | Well, that’s only because it exhibits all the signs of a bubble. It’s not exactly a grand conspiracy. |
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| ▲ | kordlessagain 5 hours ago | parent | prev | next [-] |
| You could use that logic to dismiss any analysis of any trajectory ever. Perfectly excusable post that says absolutely nothing about anything. |
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| ▲ | dragonwriter 5 hours ago | parent | prev | next [-] |
| > 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. |
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| ▲ | LPisGood 5 hours ago | parent [-] | | The adoption rate is the rate of adoption over time. | | |
| ▲ | wtallis 5 hours ago | parent | next [-] | | 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. | | | |
| ▲ | 2 hours ago | parent | prev | next [-] | | [deleted] | |
| ▲ | pclmulqdq 5 hours ago | parent | prev [-] | | Normally, the adoption rate of something is the percentage ratio of adopters to non-adopters. |
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| ▲ | tarsinge 5 hours ago | parent | prev | next [-] |
| 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. |
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| ▲ | ajkjk 5 hours ago | parent [-] | | 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) | | |
| ▲ | lucianbr 2 hours ago | parent | next [-] | | Person who draws comparison from current situation to derivatives points out that derivatives rules don't apply to current situation. Awesome stuff. | | |
| ▲ | ajkjk 31 minutes ago | parent [-] | | I don't understand your point. It seemed like the person I was replying to didn't understand how both claims could be simultaneously true so I was elaborating. |
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| ▲ | Neywiny 4 hours ago | parent | prev | next [-] | | 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 4 hours ago | parent | next [-] | | 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 3 hours ago | parent [-] | | 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. |
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| ▲ | alwa 3 hours ago | parent | prev [-] | | Not to be all “do you know who X is,” but I did have to chuckle a little when I saw who it is that you’re teaching differentiation to here… |
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| ▲ | alwa 3 hours ago | parent | prev | next [-] | | As seems to have sort of happened between March and April of this year, at least from the Ramp chart in TFA. I wonder what that was about. | |
| ▲ | umanwizard 4 hours ago | parent | prev [-] | | Derivatives in actual calculus don’t have to be continuous either. Consider the function defined by f(x) = x^2 sin(1/x) for x != 0; f(0) = 0. 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. |
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| ▲ | didgeoridoo 4 hours ago | parent | prev | next [-] |
| Yeah, what a jerk. |
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| ▲ | crote 5 hours ago | parent | prev | next [-] |
| 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? |
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| ▲ | prmph 35 minutes ago | parent [-] | | 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. |
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| ▲ | benatkin 4 hours ago | parent | prev | next [-] |
| 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. |
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| ▲ | scotty79 5 hours ago | parent | prev [-] |
| 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. |
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| ▲ | ajkjk 5 hours ago | parent [-] | | Hm that's true. Both seem plausible in English. I didn't look closely enough to figure out which they meant. |
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