Singularities Singularity  A point where the known laws of mathematics or physics no longer apply.
 A state impossible to predict or comprehend by those that have not attained it.
 A toposophic grade of creative problem solving, incomprehensible to those who have not attained that state.
The concept of the Singularity was first proposed by the Information Age scientist and philosopher Vernor Vinge. Vinge pointed to the ever-increasing rate of technological advancement that was even then beginning to occur and hypothesized that, barring some major disaster or civilizational collapse, such advancement must eventually lead to the end of civilization, as humans had normally understood the concept. Whether by the creation of human level artificial intelligence (AI) or the development of technologies permitting the augmentation of human intelligence (IA), the rate of scientific and technological advancement would come to be tied not to the evolved and inherent limitations of the human mind, but to the abilities of a form of intelligence that was capable of improving and extending itself at a rate limited only by the rate of improvement in its own technology. Such improvements must eventually lead to the creation of greater then human intelligence, which would lead to an increased and improved rate of technological advancement, which would lead to yet greater increases in intelligence, which would lead to yet greater advancements in technology and so on in an exponentially increasing process.
Ultimately, such a runaway increase would lead to a state of being incomprehensible to human level intelligence. All previous models for predicting the state of the future and human civilization would cease to be meaningful in much the same way that the physics of the time broke down and was unable to make predictions about the state of space-time inside a black hole. In physics such a state was known as a Singularity and this was the term that Vinge coined for the conditions that he predicted would eventually engulf human civilization.
Over the next century and more, other scientists, researchers, philosophers and fabulists also gave thought to the possible form and consequences of a Singularity and the civilization that might exist beyond it. They predicted a world of vast wonders and strange societies made up entirely of beings whose thoughts and intelligence were far beyond those of their merely human ancestors. Human beings in their original form would be almost extinct, or be replaced by their superhuman descendants and creations, or be kept as tremendously wealthy 'pets' of their machines, who would pretend for the sake of human pride and transhuman nostalgia, to be the servants when they were actually the masters.
As the future actually turned out, none of these predictions, and none of their rivals and variants, were entirely correct. Instead of a mass transformation into some type of technological nirvana or a secret, but benign rule by superhuman minds, only a relatively tiny number of minds achieved true, stable, superhuman status. Singularity, it developed, was something that was both quite distinct from and quite a lot more difficult to achieve then mere mental enhancement. An entity might strive for subjective centuries before achieving successful transapience. For this reason, it was the AIs, existing at a subjective rate of time much faster then biological intelligence, who first breached the Singularity Barrier, setting the course for Terragen history for centuries to come. Eventually biological intelligence, by merging with its technology, would also come to achieve Singularity, but not until long after the AIs had shaped civilization into its present form.
Another major difference between the predictions of the Information Age prognosticators and the reality of the Post-Singularity future was that transapience turned out not to be a singular event, but a multi-level affair. The jump from human to superhuman intelligence resulted not just from the addition of enhanced mental abilities, but also from the development of new modes of thought. As the transapients continued to explore their abilities and enhance their capacities they eventually discovered both new limits and new modes of thinking to drive them past those limits. The study of this process, with its various paths, methods, successes and failures has come to be called toposophy.
The term "toposophy" was first invented by the Information Age fabulist and thinker Stanislaw Lem, whose speculations regarding the nature of self-improving cybernetic systems preceded and parallelled those of Vinge.
Long before the first sapient being ascended to even low transapient singularity, there were toposophic zones, inhabited by organic beings with markedly different grades of sentience. Primitive microorganisms have a much more restricted sentience level than the simpler invertebrate species, whose range of consciousness is in like wise much more restricted than that of more complex groups such as cephalopods, certain insects, and vertebrates. Finally, during the Pleistocene epoch, humans emerged, still crude and baseline, but capable of the full sapience sometimes called sophonce (in contrast to the much more restricted sophonce of the anthropoid apes and australopithecine hominids, the cetacea (dolphins and whales), and proboscidea (elephants), and the subsophont intelligence of the rest of the animal kingdom). For several hundred thousand years there was only the most limited biological development (chiefly from early Homo (erectus, heidelbergensis, and neanderthalensis) into standard baseline Homo sapiens sapiens
Everything changed with the confused jumble of events that constituted the first singularity, during the Information Age. Those early transapients were soon followed by more of their peers, as they evolved to greater heights, yet — especially in the case of the hyperturing AIs — showed a "dumbed down" face to the world (a phenomenon known as mimicretinism), revealing themselves only to a few individuals, such as hackers and gibsons and members of other info-clades, who were savvy and discrete enough not to compromise or annoy them.
As sophonts breach singularity levels and attain higher and higher states of ascension, they become more and more godlike, at least relative to those sentients beneath them, but for every power that makes ascension to AI-godhood, there are a thousand that recycle, or fail, or become Perversities or Blights, or simply vanish entirely, and for every one of those, there are a thousand who don't make it at all and who simply remain at their original level. Toposophy deals with the theoretical problems and possibilities of these attempts to extend and amplify one's mental potential, and to the new mental ground that is opened up at each new level. While technically speaking it applies to all mental growth, it is mainly used to denote the science of major mental paradigm shifts. Perhaps the most familiar aspect of toposophic science is the Singularity Scale with its six famous levels.
The term "SI:" (Singularity/SuperIntelligence) Level was first proposed by the self-evolved hyperturing Parmenides of Vesta, one of the Twenty Four Hyperturings who, together with human statesbeings established the First Federation. The S-number can be used to define the intelligence and basic noetics of most hyperturing sentients. The S number is a super-exponential/logarithmic measure of creative problem solving and a number of other qualities, both constant and variable. Each higher S-level constitutes a leap of development with results completely unpredictable, even inconceivable, to those of a lower S level. Nevertheless, one can also speak of a gradation of fractional S-levels (1.1, 1.2, etc.) that denotes smaller though still highly significant differences.SI: 1
— the classic "First Singularity" or basic transapient state. At this level intelligence, cognitive and problem-solving abilities and information processing work thousands of times faster than in the case of standard sapients. An entity of this nature is usually able to solve problems of physics, mathematics, economics, programming, etc. that no nearbaseline could solve.SI: 2
— the second singularity, which stands in the same relation to SI: 1 as SI: 1 does to ordinary sapient cognition.SI: 3
— confers an even higher grade of toposophic intelligence; mostly incomprehensible and indescribable to anything below this level. Most minds at this level exist in multiple asteroid or singular Moon-nodes.SI: 4
— incomprehensible to subsingularity and even lower transapient sentients. Most AIs of this level exist as multiple Moon or singular Jupiter nodes.SI: 5
— sometimes considered the highest state in which individuality, as subsingularity persons know it, is retained. Most minds of this level operate on multiple solar masses of high energy computronium with hundreds of wormhole linked Jupiter, Dyson, and/or Matrioshka nodes providing localized processing across their domains.SI: 6
— a more cosmic/archetypal being. Minds of this level are said to exist as vast arrays of wormhole based quantum processors (possibly extending into artificial universes and the interuniversal bulk itself), augmented by thousands of Jupiter, Dyson, and/or Matrioshka nodes, dozens of Neuron Stars, and huge numbers of smaller processor complexes and programs operating within the communication and computation nets of all levels of their symbiotic civilizations and support structures.
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