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Yes, exponentials are infinitely differentiable. We took Calculus 101. The author's point about kink is about opportunity. When does a technology cross a perfo
by CalChris 5y ago
Yes, exponentials are infinitely differentiable. We took Calculus 101.
The author's point about kink is about opportunity. When does a technology cross a performance boundary and then the Principle of Competitive Exclusion comes into effect. That point is kinda kinky, maybe not in performance but in demand.
- whatshisface 5y ago>Yes, exponentials are infinitely differentiable. We took Calculus 101. The OP was not pointing out that exponentials are C^infinity, they were pointing out that d/dt e^t = e^t no matter how many times you differentiate, meaning that the curve is "kinking upwards" at all orders in the same way.
- azeemazhar3 5y agoYes. Roughly speaking that is my point. It's obviously a smooth, continuous function - anyone with a smattering of High School mathematics would understand that. But we can experience a shift - either the presentation of opportunity or fundamental reflection in some metric we can measure. Take one example: in 2008, the largest firms in the world (by market cap) were oil companies, car firms, telcos, conglomerates and banks. By 2016, it was mostly tech companies (and even more so today).