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= Singularity
A process with a fixed output rate, such as as a [[machine]] which produces one [[bee]] per second, leads to arithmetic growth - the total output from it increases linearly with time. However, if the growth rate is proportional to the current total, i.e. it grows by a fixed *percentage* at regular intervals - like simplified population growth without resource constraints - the total grows exponentially with time. Systems where the proportional rate of growth also grows as the total does can instead display hyperbolic growth: modelled mathematically, the the total grows arbitrarily large in finite time, and is then undefined at a "singularity". The idea of the technological singularity is that (some) technological progress leads to further, faster technological progress, and so the general state of economic development and technology increases arbitrarily fast and the world advances faster than unaugmented humans can update to it.
Empirically, this was [[https://docs.google.com/spreadsheets/d/1xEkh4jhUup0qlG6EzBct6igvLPeRH4avpM5nZQ-dgek/edit?gid=478995971#gid=478995971|cancelled]] around 1960, when growth fell off-trend. According to some, this is because hyperbolic growth of population stopped around this time; sufficiently advanced AI is capable of substituting for population, and could thus restore the trend.
= Depictions in fiction
* [[https://www.antipope.org/charlie/blog-static/fiction/accelerando/accelerando.html|Accelerando]] is centred around this, although its singularity hits a degenerate state where it does not expand beyond the inner solar system due to light-speed latencies and some humans continue to exist.
== Accelerando
[[https://www.antipope.org/charlie/blog-static/fiction/accelerando/accelerando.html|Accelerando]] is centred around this, although its singularity hits a degenerate state where it does not expand beyond the inner solar system due to light-speed latencies and its own coordination failures and some humans continue to exist.
> "Individuality is an unnecessary barrier to information transfer," says the ghost, morphing into its original form, a translucent reflection of her own body. "It reduces the efficiency of a capitalist economy."
> Take a human being and bolt on extensions that let them take full advantage of Economics 2.0, and you essentially break their narrative chain of consciousness, replacing it with a journal file of bid/request transactions between various agents; it's incredibly efficient and flexible, but it isn't a conscious human being in any recognizable sense of the word.
> From outside the Accelerated civilization, it isn't really possible to know what's going on inside. The problem is bandwidth: While it's possible to send data in and get data out, the sheer amount of computation going on in the virtual spaces of the Acceleration dwarfs any external observer. Inside that swarm, minds a trillion or more times as complex as humanity think thoughts as far beyond human imagination as a microprocessor is beyond a nematode worm. A million random human civilizations flourish in worldscapes tucked in the corner of this world-mind. Death is abolished, life is triumphant. A thousand ideologies flower, human nature adapted where necessary to make this possible. Ecologies of thought are forming in a Cambrian explosion of ideas: For the solar system is finally rising to consciousness, and mind is no longer restricted to the mere kilotons of gray fatty meat harbored in fragile human skulls.