a singularity is a period of time during which the world's second derivative experiences an inflection point, making it effectively impossible to predict the future using cached heuristics learned from the past

if the rate of change of the rate of change is changing, ur in one
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RT @sama
Don't think there have ever been more simultaneous technological revolutions going on than right now.
https://twitter.com/sama/status/1465429134130040839

this is rather informal ofc, but if we wanted to quantify this a bit more...

obv we can't ever measure the actual "rate of change of the world", insofar as such a thing even has meaning, but we CAN arbitrarily select several of its assorted subsystems and sample them

for the sake of this thread lets define "subsystem" as "some abstraction of phenomenon which can be sampled & quantified using a common methodology"

for ex, a country's economy, which is sampled using taxation/quarterly reports and quantified as the GDP (in prob wrong here)

or, the climate, which is sampled using weather stations/satellites and quantified as various differential equations modeling the movement of air/water/heat

or a computer network, which can be sampled by intercepting traffic at nodes and quantified as information flow networks

many different subsystems of the world with many more ways of quantifying them, and no objectively correct way of doing so

we can, however, construct a useful metric by choosing properly representative systems to sample & quantifying them in ways which allow us to measure deltas

since sampling, by definition, produces a discrete timeseries of values, we can measure the differences btwn subsequent samples to identify the distribution of delta sizes over time, which then allows us to identify outlier deltas, indicating that the system is changing unusually

by measuring change in this distribution over time, we can determine the rate of change of the rate of change, which allows us to identify said time periods

ofc, arriving at a result is much simpler than arriving at a meaningful result; it's non-obvious which systems to sample

identifying the salient high-impact slices of the world requires us to do some domain modeling and systems ecology analysis; what systems exist, how do they affect each other, which ones cause changes in others, and which ones have an outsize impact on the rest of the world?

also important to mention is that singularities aren't necessarily global nor time-displaced; it's entirely possible for several to be occurring simultaneously in various subsets of the world

consider the simultaneous distinct revolutions occurring in fintech & synthetic biology

one might also define "the singularity" in a higher-level way, by examining the historical rate of singularity occurrence across some class of system and quantifying the rate of change thereof in the same way as previously described

a singularity is made of smaller singularities