If one assumes (reasonably, IMHO) that the probability of SIE is monotonic in E_t, then “an elevated growth rate” trivially increases it. It doesn’t increase it super-exponentially, no… it’s merely an exponential increase in the probability of SIE. But exponentials get big suddenly, so I’m not sure why you’re objecting to this.
Under Eth and Davidson’s model – by far the most common and reasonable approach to modelling the SIE – a necessary condition for an SIE is that the growth rate of is itself growing. So “the probability of SIE is monotonic in ” is not true, or rather it’s only weakly monotonic.
What is your definition of an SIE? I’m fairly confident it involves an acceleration that is different from exponential growth in effective compute. Because exponential growth in effective compute has been true for the past decade, but nobody would classify the past decade as an SIE.
That’s the crux, no?
If one assumes (reasonably, IMHO) that the probability of SIE is monotonic in E_t, then “an elevated growth rate” trivially increases it. It doesn’t increase it super-exponentially, no… it’s merely an exponential increase in the probability of SIE. But exponentials get big suddenly, so I’m not sure why you’re objecting to this.
Under Eth and Davidson’s model – by far the most common and reasonable approach to modelling the SIE – a necessary condition for an SIE is that the growth rate of
What is your definition of an SIE? I’m fairly confident it involves an acceleration that is different from exponential growth in effective compute. Because exponential growth in effective compute has been true for the past decade, but nobody would classify the past decade as an SIE.