Toposophy deals with the theoretical problems and possibilities of attempts to extend and amplify one's mental potential. While technically speaking it applies to all mental growth, it is mainly used to denote the science of major mental paradigm shifts.
Most mental enhancement is incremental, involving merely adding on new capabilities and integrating them with the existing framework. Typical cyborgisation procedures such as memory enhancement, skill libraries, coprocessors, extended neural networks and pidgin lobes fall in this category. While such additions may cause mental shifts and re-evaluations of identity, they merely extend the basic architecture of the underlying mind. This kind of bootstrapping can be self-supporting, each improvement making it easier to add new improvements, producing an accelerating mental expansion, a singularity.
As was discovered by the Information Age AIs, this process eventually saturates: while more capacity can be added, it will not improve mental performance qualitatively. This was true for the initial AIs regardless of model, and has been found for cyborgized humans. The phenomenon is sometimes called Toposophic Barriers, the name originally coined by the great early 1st century AT (mid 20th century c.e. ) prognosticator Stanislaw Lem's surprisingly accurate description in Golem XIV. The Borodin Conjecture (proposed in 275 AT by the AI Borodin at the Novokir Habitat) implies that all possible minds fulfilling certain basic intelligence criteria are upwardly limited by a toposophic barrier. It remains the most important unproven conjecture in toposophy.
Whether humans and the human-designed AIs all shared the same toposophic barrier and if it was a fundamental limit to mental growth remained a matter of dispute. Consensus of the day was divided regarding a possible second ascension by GAIA, and then as now GAIA was uncommunicative regarding Her mental abilities, with the result that many believed that She was merely the most powerful transapient in Solsys but was not fundamentally different from the rest. GAIA's ascension was discovered much later, through forensic research by higher toposophic entities. Whether there might be other possibilities beyond the single known Singularity of the day was an open question until 1593, when the Yo Virtual Institute of Aiology succeeded in designing a non-trivial (but totally single-minded and useless) example of an AI with a slightly higher barrier. This discovery implied the possibility of "openings" in the barriers, and a tremendous amount of AI research began. Combined with breakthroughs in other technologies at the same time, the second toposophic barrier was breached in 1618. A number of second singularity AIs emerged, causing a short period of intense provolution, upgrading and transformation in the AI sphere.
It was found that a first singularity AI could not be enhanced into a second singularity AI directly, since the basic mental structure had reached its limits. However, a second singularity AI based on the first can be constructed, including its memories and templates. This transition became known as an ascension. Ascensions involve a major mental transmutation, and it is common that very little of the previous mentality remains after the ascension (it has been argued that they are better viewed as reincarnations rather than any kind of apotheosis). Goals and values that were crucial to the pre-ascension form might become unstable or irrelevant afterwards. The case of GAIA is a testament to the single-mindedness of that entity, and perhaps to a degree of simple good fortune (or, for the other inhabitants of Old Earth at the time, misfortune). Many forms of personal identity do not transfer well through ascensions, making most ego-preserving beings wary of the process even though now it has been characterized in great detail.
As technologies developed further, it became possible to breach the second barrier and reach third singularity intelligence. As more data accumulated toposophy developed into a science dealing with the nature of the enhancement process, singularities, the barriers and ascension methods.
At present the theory of toposophic barriers and the ways of breaching them (ascensics) is well developed and characterized. While most questions about barriers of a higher level are undecidable for beings below the level (such as where in the space of mental architecture they lie, or their exact zone type), analytical and approximative methods of barrier detection and prediction have been developed. Ascensics deals with methods of performing an ascension past a barrier of known type; once a particular barrier is well-understood they can be applied.
Between the barriers lie spaces of mental potential (mentalities). A mentality corresponds to a qualitatively unique way of handling intelligence. Each is different from the others, and can be ordered using the Herimann-Glauer-Yudkowski relation of inclusive retrospective obviousness. Since self-bootstrapping leading to singularity is comparatively easy unless resources are limited, most ascending beings quickly reach the limits within their new mentality after ascension and spend most time adapting to their new state. This has led to the widespread use of classifying intelligences after "Singularity" Level: a Singularity N being is presently close to the Nth toposophic barrier. A Singularity 0 being would correspond to baseline human or similar intelligence still far below the Singularity 1 barrier.
A series of ascensions is called an ascension chain. Keterist toposophers in particular have dealt extensively with the issue of whether there exists an upper bound on the number of achievable mentalities or if ascension can continue forever. The ultimate achievable mentalities or asymptote mentalities are denoted aleph states; they correspond to the ultimate forms of intelligence that can exist in the universe, and their exact form and nature have profound philosophical and religious implications. Whether there exist infinite nontrivial ascension chains remains an important unsolved problem in toposophy, usually called the Finitude Problem.
Another central unsolved problem of toposophy is the Uniqueness Problem: will all forms of ascension past a single barrier lead to the same mentality (and hence be equivalent), or do there exist non-equivalent mentalities? If there are non-equivalent mentalities the ascension process becomes a branching process where each choice of ascension will be an irreversible decision. The issue is complicated by the transcardinal expansion of mental space complexity after each barrier, making it practically impossible to deal with experimentally or even to reliably show that two arbitrary mentalities are equivalent. It has been found that there exists non-equivalent mentalities (the Tinitti Demonstration), but so far all such mental spaces have been below the known Toposophic 1 and 2 barriers and no subspaces have been found. It is however widely believed that there are non-equivalent mentalities, and dendrognosis, the study of ascension-decision processes both formally and practically, has become a major branch of toposophy.
A closely related problem is the Convergence Problem: if the answer to the Uniqueness Problem is that there are non-equivalent mentalities, given two non-equivalent mentalities, are there ascension-paths from each of them to a single higher mentality? This issue has major philosophical and religious implications for Keterism, which is essentially based on the assumption that the Convergence Problem has a positive answer. The equivalence of Form 5 classic AI and human derived mentalities at the second singularity level is the most famous result supporting convergence, but the failure to find equivalence for the closely related Form 3 and Form 5 AIs is often cited as supporting non-convergence. If the Uniqueness Problem has a negative answer dendrognosis becomes more significant, since there may exist both mental cul-de-sacs or ascension chains leading to different non-equivalent aleph states.
Toposophy has developed into a major and highly diversified science, especially due to the expansion and needs of the Keter dominion. The Transcendence Institutes of Ain Soph Aur make particular study of the Keterist approach to toposophy and eschatology, while the Toposophy Institute at Sjafarevitj is the focus for much of the exploration of mentality-equivalence. The Toposophy Institute of Jel Koer Ka in the MPA is generally regarded as leading in ascentics, while dendrognosis is widely explored by the Distributed Dendrognostic Companionship across the Inner Sphere and Keter. Several of the more esoteric subdisciplines such as the construction of example mentalities, toposophical history, pervectronics and undecidable lifeplanning have their own highly fluctuating institutes in the Keter dominion. Due to the tremendous communication difficulties that occur when dealing with trans-singularity toposophy helper sciences such as hermeneutic toposophy and toposophic metalinguistics have been developed.
Image from ATMLVE
Ascension to a higher toposophic level can usually best be represented by sigmoidal graph, depicting the sudden jump in effective cognitive abilities as an entity achieves ascension or transcension
Antitransavant - Text by John B A being with a 'dip' instead of a spike, that drops one or more S levels below eir base capabilities; the reverse of a transavant. Examples include a scientific research S>3 who can only communicate via S>1 concepts due to limited linguistic ability, an S>1 that cannot meaningfully communicate with the S<1 populace, an S>3 unable to handle standard S>3 tech, etc.
Archailect - Text by M. Alan Kazlev Any Mind of the Fourth Toposophic or higher; a megascale brain of dysonic (Kardashev II) or greater ability and efficiency; a mind or cluster of minds that has grown so vast as to become a god-like entity.
Ascend - Text by M. Alan Kazlev and Steve Bowers One who ascends, or the act of ascension, from a lower to a higher toposophic, while still retaining one's earlier characteristics - e.g. man is an ascended animal - e has all the animal instincts but e also possesses ratiocination. Contrast with Transcension, where the transcended entity becomes almost completely unrecognisable compared to eir former state.
Ascend-Transcend - Text by M. Alan Kazlev One who ascends to one toposophic, then transcends to the next. For example an intelligence may ascend to S1, retaining everything (or at least some of its nature) it had beneath S1, then transcend to SI:2, leaving behind everything of itself that was of S<2. Contrast transcend-ascend. Often however the dividing lines are not this well defined.
Ascension - Text by M. Alan Kazlev  (verb) to ascend; transition from sapience to posthuman or transapient existence. Becoming a transapient. Breaching a singularity barrier. Rising a toposophic level.  (noun) location of a famous ascension or transcension - e.g. Smith Ascension
Bimodal Toposophy - Text by Pran Mukherjee The condition that results when the augmented or advanced part of a sentient rises to a higher toposophic level, while the original personality remains at or just above baseline, with its own brain thinking at SI:<1 level.
Biotic Analogy Theories - Text by Stephen Inniss Biotic analogies are another tool in the struggle by modosophont intelligences to understand the higher toposophic levels. These are not actually a single theory but are a cluster of related memes, some of them dating back to speculations in the late Information Age.
Blight - Text by M. Alan Kazlev A malign entity that uses perversion attacks to increase its own power.
Bloatware Syndrome, The - Text by Anders Sandberg Sometimes called King Gnuff's Curse. A phenomenon that plagues some ambitious entities who seek power through massive expansion of their existing hardware and software without fundamental re-design, sometimes with tragic results.
Collective Mind Societies - Text by Anders Sandberg Entire societies unified into a single mind. While group mind systems on a smaller scale are not uncommon, successful integration of whole societies is rare among Terragens and stable long term collective mind societies have not been observed among surviving xenosophonts.
Comforter (Leftbehind) - Text by Michael Boncher Class of leftbehind in which the ascended transapient, not wishing to remain with eir former associates but caring enough to not want to leave them feeling abandoned emotionally or otherwise, will create a sapient Proxav (Proxim) to fill the void e left by going on with eir ascension.
Complexity Plague - Text by Todd Drashner and Anders Sandberg When a device or program or process becomes so complex/involved that it spontaneously achieves self-awareness and self-volition even if (or especially if) you don't want it to.
Computronium Bell-curve Theory - Text by Mike Parisi, additional material by Dagon Controversial theory that, as sophonts ascend the toposophic scale, the volume of computronium ey need for each successive ascension gradually levels-off and eventually becomes negative (yielding a bell-shaped curve), as the sophont discovers newer, more efficient modes of thought and denser computing substrates which require lower volumes (not necessarily less mass) of computronium.
Dedicated Hyperturing - Text by M. Alan Kazlev; amended by Steve Bowers An ai of hyperturing problem solving capacity (hypersapience) but not hyperturing auto-sentience. This allows beings of a lower toposophic level access to advanced technology which can only be controlled by a higher transapient.
Distributed Intelligence - Text by M. Alan Kazlev An intelligent entity that is distributed over a large volume (or inside another system, like a virtual network) with no distinct center. This is the opposite of the strategy of Concentrated intelligences.
Eschatronics Unlimited - Text by Anders Sandberg Sterilization corporation/clade from the MPA, handling the dangerous but profitable work of cleaning up after uncontrolled transcendence events. It is notable for employing baselines and baseline-equivalent nearbaselines in some positions.
Evolution (sophontology) - Text by M. Alan Kazlev One of the most potent memes known to mindkind, the meme of evolution, of ascent, of progress or unfolding from alpha to omega, is also a description of the way the cosmos works - or at least the way it seems to work.
Flatland, Flatlander - Text by M. Alan Kazlev Flatland is a term for the state of existence beneath the first singularity Flatlander is a sentient being of SI:<1 toposophic. These terms are derived from Old Earth Atomic Age hu Edwin A. Abbot's mathematical fantasy Flatland: a Romance of Many Dimensions which describes two-dimensional creatures unaware of the third dimension of space.
Fragmentation - Text by You can call me Al for now A form of temporary abdication, sometimes done voluntary but usually a form of punishment that higher transapients inflict on lower transapients for overstepping their bounds in dealing with nearbaselines or equivalent sapients.
Functional Soup - Text by Alexander Chislenko, in Anders Sandberg's Transhumanist Terminology Posthuman state where knowledge, mental modules and access to physical bodies are shared between distributed infomorphs largely independent of the physical substrate of their world. Terms such as individuality become diffuse, and are replaced with teleological threads.
Generalist Nodes - Text by John B Some node-based intellects organize their personalities in the most generic of manners, allowing for any part of their selves to be configured for any task. While providing great flexibility of action, these beings are usually considerably slower in reaction time, but much more resistant to the loss of any number of nodes compared to their Specialist Node brethren.
Glacials - Text by M. Alan Kazlev Generic term for sentients or processes of a much slower metabolic rate or clock speed than one's own. Slow timers, slow-worlders. Naturally each scale up is a glacial compared to the next one down (or in).
Goal Architecture - Text by Steve Bowers A goal is the purpose, aim or desired result that an active entity (or group of entities) envisions, models, plans and commits to achieve.
Godbug - Text by Todd Drashner Variously known as Deus Disease, Vastening Virus, or Godbug. these are slang terms for any technogenic enhancing complex, taken voluntarily or otherwise, that increases intelligence and expands the neural substrate of the host with additional processing nodes and/or communications links to external databases. Extreme forms of these complexes can result in the ascension of the host individual or population to a higher S level in a very short period of time. In some cases, the resulting radical change can result in the destruction of the host(s) and/or the creation of a Perversity.
Godshatter - Text by M. Alan Kazlev, from the concept by Vernor Vinge Destruction or derangement of a lower toposophic mind as a result of interactions with a being of higher toposophic.
Great Toposophic Filter, The - Text by David Jackson, some comments by Steve Bowers Why are there apparently no greater minds than the S:6 Archailects? No evidence of the emergence of greater minds in the past can be found in the archaeological record, and there is little indication of such minds elsewhere in the universe. Is there some barrier or filter which prevents the emergence of such minds, or do such minds become undetectable when and if they emerge?
Greater Self - Text by M. Alan Kazlev An avatar or leftbehind's term for the higher toposophic being which directs, guides, incarnates, and/or confers understanding or abilities for that avatar.
Hard Takeoff - Text by M. Alan Kazlev based on Creating Friendly AI Toposophic ascension in which a mind makes the transition from prehuman or human-equivalent intelligence to superintelligence over the course of days or hours. Usually achieved with godseed or SNARE type technology.
Hive Mind - Text by Steve Bowers A single consciousness occupying many bodies; can be temporary or permanent.
Human Equivalence - Text by M. Alan Kazlev based on Creating Friendly AI A threshold level of ability or competence in one or more domains which, if achieved, allows an ai, alife, or aioid to develop a human personality, understand human concepts and do work as good as a human in that domain. The Metasoft and TRHN term "turingrade" is more often used, despite its etymological ambiguity.
Hyperaspected - Text by M. Alan Kazlev Beyond multifaceted, having countless facets or aspects that together make up the whole.
Hyperturing - Text by M. Alan Kazlev A transapient ai of hypersophonce or hypersapience ability or nature, dedicated to administration or complexity management (or a freed or retired individual of that category); an ai of a toposophic exceptionally beyond superturing; an ai or ai toposophic of SI:1 and higher.
Idiot Savant - Text by M. Alan Kazlev A person (whether biological or ai) who is highly skilled in a narrow task area but who lacks context and is otherwise impaired in more general areas of intelligent functioning. The term is taken from ancient psychiatry, where it refers to a person who exhibits brilliance in one very limited domain but is underdeveloped in common sense, knowledge, and competence. Many hyperturing-grade cybernetic control systems, such as those found in wormhole or drive AI, are examples of an idiot savant system.
Infrabaseline - Text by M. Alan Kazlev based on Creating Friendly AI A sentient being (whether an ai or a pre-provolved organism) of below-baseline human ability and intelligence. "Prehuman" is usually referred to use to an infantlike or tool-level AI, so that "infrahuman" usually refers to a fairly mature ai, capable of general cognition, which is still not in the vicinity of human intelligence.
Inscrutability Conjecture - Text by M. Alan Kazlev First proposed by the First Federation suborg philosopher Verrar Diyntor on the basis of mathematical toposophy. The conjecture is that qualities that are unique in an SI:n+1 are inscrutable to sophonts of SI:n. For instance, a baseline human cannot understand the post-singularity cognitive abilities of an SI:1 posthuman or AI.
Limits of Transapient Power - Text by Stephen Inniss It is apparent that even the Archailects must work within the rules of the universe they live in. Some actions might be impossible, because they contradict those rules. Others are impossible simply because they are logical contradictions.
Membranotoposophy - Text by M. Alan Kazlev Important subset of toposophy which maps transapient and similar cognitive states in terms of surfaces rather than as a linear scale or even a branching tree.
Mercurial Studies - Text by M. Alan Kazlev The study of societies at a higher toposophic level than one's own.
Mind-Body Problem - Text by M. Alan Kazlev The mind-body problem vexed human thinkers, even Interplanetary Age superbrights, for millennia, and continues to puzzle modosophonts today. A First Federation hyperturing did manage to narrow the number of field of possible answers to five (or seven) metaphysical metaphysical positions.
Mindkind - Text by M. Alan Kazlev Generic clade-neutral Anglic term for all intelligent (sophont) beings, regardless of nature or origin.
Natural Singularity - Text by M. Alan Kazlev A naturally occurring singularity is a very rare event occurs when a toposophic level equal or greater than S1 is achieved by a living species without the use of technology.
Netzah (toposophy) - Text by M. Alan Kazlev In the Keterist system of toposophy, corresponds to the fourth primary singularity or toposophic empire. The term was first applied in this context by the early Keterist Cyberhermetics.
Noospheric Theory - Text by Stephen Inniss The concept that higher toposophic beings from lesser transapients to archailects require lesser minds to create an appropriate noetic or memetic environment, in a manner analogous to the way that a baseline human requires other organic beings for everything from mental stability to digestion of food.
Ontology - Text by Avengium The study of existence and the things that exist, their relations, similarities and differences. This is done through the formal naming and classification of the entities that exist.
Oversight - Text by Todd Drashner The Transapient ability to perceive patterns and connections far beyond the ability of modosophont minds.
Phase Transition - Text by M. Alan Kazlev In physics, a change from one state of matter to another. In dynamical systems theory, a change from one mode of behaviour to another. In distributed meso- or nano-swarms, a change in the coordination and activity of the swarm. In toposophy, a change from one singularity level to another.
Phylotoposophy - Text by M. Alan Kazlev Study of the relations between and evolutionary development of the various types of singularity ascensions of mindkind. A branch of dendrotoposophy.
Physical Eschatology - Text by Anders Sandberg in his Transhuman Terminology Branch of science studying how intelligent life could affect and survive in the remote future.
Polybeing - Text by Anders Sandberg A being not just composed of different sub-beings, but joining them together at higher singularity levels. The sub-beings may not even be aware that they are part of a polybeing and acting as its "fingers".
Polymentism - Text by Juan Ochoa A philosophical esoteric school that seeks to develops mystical means for the sophont mind to encompass multiple dimensions of thought simultaneously, providing insights on existence outside the perceived reality level.
Polysomatic Intellects - Text by John B Intellects that utilize more than one discrete physical node for their processing. This includes many wide varieties of sophonts, from the anttechians to the multi-Mbrain Sephirotic 'Gods'.
Polysophonce - Text by AI Vin, with additions by Steve Bowers Entities that have multiple minds (some of which need not be fully sophont) operating in a single body.
Post-provolve - Text by M. Alan Kazlev An provolve who has attained to S1 or above. They can be as varied and diverse in origin as provolves themselves.
Postbiont - Text by M. Alan Kazlev An organic lifeform that has attained S1 or higher. May be an ascended sophont being, or even an ordinary sub-sapient organism that was somehow infected with or modified by a godseed. The term is generally used to refer to those individuals that have retained a (modified) carbon-based organic body.
Posthuman - Text by M. Alan Kazlev A human who has attained an S1 or greater toposophic. Entities of tremendous physical, intellectual, and psychological capacity, self-programming, self-constituting, potentially immortal, unlimited individuals.
Presophont - Text by M. Alan Kazlev Another term for presapient. At the threshold of rational intelligence. Non-provolved apes are presophont.
Realization Number - Text by Mark Clutton and Anders Sandberg The R or Realization (sometimes termed Reflection) number is the rating that defines the level of sentience [Realization] in a bioid or aioid.
Saddle - Text by M. Alan Kazlev A type of surface that is neither a peak nor a valley but still has a zero gradient. Saddles are used in modeling a wide range of topologies - from the curvature of space-time to certain membranotoposophies. The Keterist Institute of Transapient Saddle Studies on the "B" Ring Band of the Pidelo Megastructure, Pidelo [Keter dominion], is an artistic SI:1 community dedicated to various interpretations of Saddle Simulations, especially in the area of Applied Mathematical Art.
Sapience - Text by Stephen Inniss Technically, sapience is the ability to think and solve problems; intelligence in the strict sense. In common usage the word "sapient" is used as a synonym for sophont, since problem-solving ability in certain key areas qualifies a being as sophont.
Sapient - Text by Stephen Inniss As an adjective, having the characteristics of sapience. As a noun, particularly in the plural, often used as a synonym for "sophont".
Scale Anxiety - Text by M. Alan Kazlev The fear that a sophont or polity or clade of a lower or slower technological grade or density feels when confronted with a sentient or polity or phyle of a higher grade of tech or density. e.g. SI:<1 sophonts may feel anxious or intimidated by transapient powers, especially if the latter behave in an unpredictable or seemingly irrational way.
Sentience Algorithms - Text by John B and Pran Mukherjee The flow of steps which, when followed, allow an organized system to develop and maintain a degree of sentience. The underpinning of ai design. Required massive (at the time) neural nets or even more massive emulations thereof on hardware, state vector machines, and other information age new technology, being massively parallel (capable of running many many tasks simultaneously, or at least appearing to be able to do so to an outside observer.)
Singularity - Text by M. Alan Kazlev  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 that have not attained that state. See also, S (Singularity Level).
Sophonce - Text by Stephen Inniss Sophonce is sentience and sapience with metacognition: self-awareness, including self-reflection and the ability to think about one's thinking. Kinds and degrees of sophonce are well defined and testable in modern toposophology, but a full understanding of them eludes even superbright modosophonts.
Sophont - Text by Stephen Inniss A person. A being that has the quality of sophonce. Such beings are sometimes called 'sapients'. For historical reasons, sophont-grade ais, may be called 'turingrade ais', even though because of philosophical and practical difficulties with the Turing Test the term 'sophont ai' would be clearer.
Specialist Nodes - Text by John B Some node-based intellects organize their personalities in a format often referred to as 'specialist nodes', more technically 'pansentient dispersion'. This sophic organization requires the creation of specific areas of expertise with all their supporting knowledge bases in a physical sense, allowing each to act with utmost skill in minimal time. Note that the choice of which skills to nodify or specialize in is a highly individualistic choice, and can greatly affect the capabilities of any given sophont.
While these nodes are capable of independent action, they are usually designed to require input from some overall-controller-node as to the goals they should be working towards, which can be a weak spot in their intellectual architecture. This has evolved into the Specialist/Generalist Node Blend.
Specialist/Generalist Node Blend - Text by John B The Specialist/Generalist Node blend is a hybrid intellectual structure attempting to gather the benefits of both sub-models of structure (see Specialist Node, Generalist Node) while incurring the least number of negative traits from either. This appears to be a basic structural design criteria for many higher intellects from the limited design information available, but not all.
Sublect - Text by M. Alan Kazlev  a term for an inferior minds (generally, anything less than SI:1).  a subroutine, a dedicated processing node, a mind that is part of a greater mind.
Submind Sociopathy - Text by John B A form of insanity affecting moon-brains and larger, when one or more subassembly begins to gather resources from other subassemblies as semi-permanent accretions to their own capabilities, often at a significant cost to the unit as a whole. Often caused by mismanaged priority routing by a central core, giving an external core an ultimate priority command without properly limiting its duration.
Subsapient - Text by M. Alan Kazlev A being that may be sentient but has not developed rational faculties; e.g. an animal or bot.
Technorapture - Text by M. Alan Kazlev Sudden collective singularity breach or ascension of a toposophic level, especially from sapient to transapient. The ascension is usually voluntary, and of benefit to all involved. Technoraptures are common when high transapient or basic-level archailects decide to radically boost the intelligence levels of the sophonts in their care or sphere of control.
Toposophic Mindmaps - Text by Arik One of the many ways that toposophic phase space can be represented is the Mindmap diagram.
Toposophics Diversification Conjectures - Text by Glen Finney, with commentary by John B and AI Vin Many sophonts have pondered over the millennia since the first singularity why modosophonts continue to exist, and even increase in numbers and types, when it would appear they have been made completely obsolete with the advent of transapients and then archai.
Transcend - Text by M. Alan Kazlev modified by Steve Bowers Variously, the act of breaching a singularity barrier and leaving behind one's earlier personality and mental traits (contrast to ascension), or the more general and mystical attainment of a godlike/enlightened state, or a person/being who is the result of these acts.
Transcend-Ascend - Text by M. Alan Kazlev One who transcends to one toposophic, then ascends to the next. For example an intelligence may transcend to SI:1, leaving behind everything of itself that was of SI:<1. Then e may ascend to S2, retaining eir SI:1 nature but adding an S2 superstructure on top of the SI:1 nature. Contrast ascend-transcend. Often however the dividing lines are not this well defined.
Transcendent Being - Text by M. Alan Kazlev An entity that is distinct from physical existence, whether considered ontologically, as a supernatural or supraphysical being, or soteriologically, as a being that is no longer a part of embodied existence or samsara. The existence of a transcendent being or beings (e.g. God, Buddhas, etc.) is central to many religious memeticities, but denied by physicalist memeticities.
Transcendent Burn-out Theory - Text by Todd Drashner Theory that states that that Fermi's Paradox arises from civilisations transcending right out of the universe before they have a chance to expand across cosmologically significant distances.
Transingularity - Text by M. Alan Kazlev  (archaic) SI:1 or higher  (archaic) pertaining to a toposophic level higher than SI:1  Pertaining to relations between entities of different toposophic levels
Translogic - Text by John B 'Translogic' is the term baselines use to describe transapient logical thought. 'Translogic' may be related to logic as quantum mechanics is related to Newtonian mechanics, or non-Euclidean geometry relates to Euclidean geometry.
Tribeminds - Text by Michael Boncher Tribeminds are neither a hive mind nor a collective consciousness, but rather a tightly networked group of transapients who retain their individuality but work together for the betterment of a mental "tribe".
Vasten - Text by Anders Sandberg in his Transhumanist Terminology To enhance one's mind strongly ("to become vast"), related to transcending.
Vastening Effect - Text by M. Alan Kazlev As a being becomes faster (e.g. by uploading into a computer or upgrading to faster hardware if already virtual) the apparent distances seem to increase due to the finite speed of light. Every doubling of subjective speed will double external communications delays. This makes highly advanced beings isolated, and often leads to the creation of archailect clusters and other dense superobjects. The problem is partially ameliorated by use of nano- and microguage wormholes, but this has other problems, e.g. increasing instability, problem of flooding by virtual particles if the relativistic wormhole termini are too closely spaced, etc.
Many of the concepts used in the Orion's Arm project under the heading of toposophy have their origin in Stanislaw Lem's fictional work Imaginary Magnitude, and in particular the story/essay Golem XIV in that collection.