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
this usage of singularity has now significantly diverged from the mathematical/physical definition, so perhaps we need a qualifier?
it's not just economic or technological, and sort of system can experience one of these phenomenon.
systemic singularity perhaps?
this is all still pretty informal, if you wanted to you could probably do something clever with vector spaces representing the state of systems & network flow models to identify the causal relationships btwn them, mb represent these state deltas as matrices and do some linalg
but I don't feel like doing this nor do I know exactly how so let it just suffice to say that this is probably possible and left as an exercise to the sufficiently motivated and insane reader
now can we please all stop talking about The Big Bad Scary AI Singularity?
oh and credit is due to @robinhanson for getting me to think about this idea in a much more useful way than any I'd heard previously
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