2035. Probably earlier. » Article » that's Magazines Shanghai, Beijing, Guangzhou, ShenzhenNick Land / text
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"2035. Probably earlier."
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by nickland @ Friday, 13 May 2011 07:54
City Beat
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There's fast, and then there's ... something more
Eliezer Yudkowski now categorizes his article 'Staring into Singularity' as 'obsolete'. Yet it
remains among the most brilliant philosophical essays ever written. Rarely, if ever, has so
much of value been said about the absolutely unthinkable (or, more specifically, the
absolutely unthinkable for us).
For instance, Yudkowsky scarcely pauses at the phenomenon of exponential growth,
despite the fact that this already overtaxes all comfortable intuition and ensures
revolutionary changes of such magnitude that speculation falters. He is adamant that
exponentiation (even Kurzweil's 'double exponentiation') only reaches the starting point of
computational acceleration, and that propulsion into Singularity is not exponential, but
hyperbolic.
Each time the speed of thought doubles, time-schedules halve. When technology, including
the design of intelligences, succumbs to such dynamics, it becomes recursive. The rate of
self-improvement collapses with smoothly increasing rapidity towards instantaneity: a true,
mathematically exact, or punctual Singularity. What lies beyond is not merely difficult to
imagine, it is absolutely inconceivable. Attempting to picture or describe it is a ridiculous
futility. Science fiction dies.
"A group of human-equivalent computers spends 2 years to double computer speeds. Then
they spend another 2 subjective years, or 1 year in human terms, to double it again. Then
they spend another 2 subjective years, or six months, to double it again. After four years
total, the computing power goes to infinity.
"That is the 'Transcended' version of the doubling sequence. Let's call the 'Transcend' of a
sequence {a0, a1, a2...} the function where the interval between an and an+1 is inversely
proportional to an. So a Transcended doubling function starts with 1, in which case it takes
1 time-unit to go to 2. Then it takes 1/2 time-units to go to 4. Then it takes 1/4 time-units
to go to 8. This function, if it were continuous, would be the hyperbolic function y = 2/(2 x). When x = 2, then (2 - x) = 0 and y = infinity. The behavior at that point is known
mathematically as a singularity."
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